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Substructure strengthening in nickel alloys Clegg, Maurice Alexander 1969

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SUBSTRUCTURE STRENGTHENING IN NICKEL ALLOYS by MAURICE ALEXANDER CLEGG B.A. (Hons), Cambridge U n i v e r s i t y , 195^ M.A., Cambridge U n i v e r s i t y , 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY In the Department of Metallurgy We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA I i July, 1969 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agre e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n of t h i s - t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department o f M e t a l l u r g y The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date J u l y 25, 1969 i ABSTRACT Pure N i c k e l , 8C$ Ni-2C# Cr, 98% Ni-2# Th0 2 and 7&% Ni-2C# Cr-2% ThOg have been studied to compare the mechanisms of dispersion streng-thening i n the l a t t e r two materials. A l l four materials were subjected to a wide range of thermo-mechanical treatments i n c l u d i n g cold r o l l i n g r e -ductions up to 90$ and annealing treatments which i n the case of the materials containing ThC^ were at temperatures up to 0,97Tm (l^fOC^C). In each condition the materials were examined by an x-ray l i n e p r o f i l e technique to determine the d i s t r i b u t i o n of non-uniform l a t t i c e s t r a i n , the coherent c r y s t a l l i t e domain s i z e and the twin and stacking f a u l t p r o b a b i l i t i e s . The x-ray data were also interpreted i n terms of d i s l o c a -t i o n configurations. Supporting transmission electron microscopy v/as c a r r i e d out on each material. T e n s i l e t e s t s were done at room temperature and at an elevated temperature on a l l materials to determine the strength properties and i n i t i a l work hardening rate. It was concluded that the room temperature strength and the high temperature strength of a l l materials were determined by the presence of a f i n e domain or c e l l s i z e and that the high temperature strength was al s o determined by the degree of polygonization of the f i n e substructure boundaries. In the case of the dispersion strengthened a l l o y s the sub-structure boundaries were s t a b i l i z e d by the presence of ThC^* It was observed that the Ni-Cr-ThtX, material developed a d i f -ferent l a t t i c e s t r a i n d i s t r i b u t i o n during cold r o l l i n g than d i d the Ni-ThC^o This was characterized by a very small domain s i z e and a high l e v e l of i i l a t t i c e s t r a i n averaged over short distances. I t i s proposed that t h i s s t r a i n d i s t r i b u t i o n favours r e c r y s t a l l i z a t i o n and grain growth and leads to the i n f e r i o r s t r u c t u r a l s t a b i l i t y i n cold r o l l e d Ni-Cr - T h 0 2 at elevated temperatures compared to Ni-ThO-i i i i ACKNOWLEDGEMENTS The author wishes to express h i s sincere gratitude to h i s Research Supervisor, Dr. J.A. Lund, f o r h i s advice and assistance at a l l stages of the work. Helpful discussions with other f a c u l t y members and fellow graduate students, p a r t i c u l a r l y the Candidate's Ph.D. Committee members, Drs. N.R. Risebrough and D. Tromans, are also g r a t e f u l l y acknowledged. S p e c i a l thanks are expressed f o r the generous assistance given by many members of the departmental t e c h n i c a l s t a f f , p a r t i c u l a r l y by Messrs. N. Walker, P. Musil and A. L a c i s . The author i s pleased to acknowledge g r a t e f u l l y that he was ass i s t e d f i n a n c i a l l y by the Aluminum Company of Canada through the award of the Alcan Fellowship f o r the two years 1967-69* TABLE OF CONTENTS Page No« 1. INTRODUCTION 1 1.1 Dispersion Strengthening 1 1.2 Measurement of S t r a i n Energy and Substructure 3 1.3 Scope of the Present Investigation 7 2. EXPERIMENTAL PROCEDURES 9 2.1 Supply of Materials 9 2.2 Thermo-raechanical Treatments 12 2.3 X-Ray D i f f r a c t i o n 12 2.3.1 Specimen Preparation 12 2.3.2 X-Ray D i f f r a c t i o n Procedure Ik 2,k E l e c t r o n Microscopy 18 2.^ .1 Specimen Preparation 18 2.^ .2 Electron Microscopy Procedure 19 2.5 T e n s i l e Testing 19 2.5.1 Specimen Preparation 19 2.5.2 T e n s i l e Testing Procedure 20 2.6 Computer Analysis 21 3. EXPERIMENTAL RESULTS -25 3.1 X-Ray D i f f r a c t i o n 25 3.2 Electron Microscopy 32 3.2.1 N i c k e l 32 3.2.2 Nickel-Chromium 3^  3.2.3 Nickel-ThO, 3^  Table of Contents (Continued) Page No. 3 . 2 . 4 Nickel-Chroraium-Th0 2 35 3 . 3 O p t i c a l Microscopy 36 3.4 Te n s i l e Tests 36 4. DISCUSSION 4l 4 .1 S i g n i f i c a n c e and R e l i a b i l i t y of the X-Ray Line P r o f i l e Analyses 4l 4.2 C a l c u l a t i o n of D i s l o c a t i o n Densities and Configurations from X-Ray Data 48 4 .3 C o r r e l a t i o n of X-Ray Data and Electron Microscopy 56 4.4 L a t t i c e Residual Macro S t r a i n 62 4 .5 T e n s i l e Strength 64 4.5*1 Room Temperature Properties 6k 4 . 5 . 1 . 1 Nickel 6k 4 . 5 . 1 . 2 Nickel-Chromium 66 4 . 5 . 1 . 3 Nickel-Th0 2 69 4.5.1.4 Nickel-Chromium-Th0 2 ?4 4 .5 .2 High Temperature Properties 77 4 . 5 . 2 . 1 Nickel 81 4 . 5 . 2 . 2 Nickel-Chromium 83 4 . 5 . 2 . 3 Nickel-Th0 2 84 4.5.2.4 Nickel-Chromium-Th0 2 85 4.6 The E f f e c t of Texture on Te n s i l e Properties 88 5 . SUMMARY 91 6 . CONCLUSIONS 95 7 . SUGGESTIONS FOR FUTURE WORK 97 Table of Contents (Continued) Vi Page_No, APPENDIX 1 A Review of the Th e o r e t i c a l Basis of the Measurement of Non-Uniform L a t t i c e S t r a i n and C r y s t a l l i t e S i z e i n Metals by the X-Ray Line Broadening Technique 1 5 6 APPENDIX 2 A Computer Programme to Determine Non-Uniform L a t t i c e S t r a i n and C r y s t a l l i t e Domain Size by the Analysis of X-Ray Line Broadening 1 9 8 APPENDIX 3 Specimen Computer Output From the Programme of Appendix 2 2 0 8 BIBLIOGRAPHY 2 2 7 v i i LIST OF TABLES Number Page Ho. 1(a) Suppliers ' Chemical Analyses 11 1(b) Chemical Analyses of Tensile Specimens 12 II Summary of Material Conditions 13 H I Domain Sizes and Lattice Strain Distributions 29 IV Summary of Anci l lary X-Ray Diff rac t ion Data 33 V Summary o f Room Temperature Tensile Test Data 38 VI Summary of High Temperature Tensile Test Data 39 VII Domain Sizes Corrected for Twins and Stacking Faults 53 VIII Dislocation Densities and Configurations 55 IX Lattice Residual Macro Strain 62 X Computer Programme Statements 205-207 XI Computer Output. Original X-Ray Intensities for (200) Reflection from Annealed Nickel Powder Standard 208 XII Computer Output. F inal Corrected X-Ray Intensities for (200) Reflection from Annealed Nickel Powder Standard 209 XIII Computer Output. Sin 6 values for (200) Reflection from Annealed Nickel Powder Standard 210 XIV Computer Output. Peak Parameters for (200) Reflection from Annealed Nickel Powder Standard 210 XV Computer Output. Original X-Ray Intensities for (400) Reflection from Annealed Nickel Powder Standard 211 XVI Computer Output. F inal Corrected X-Ray Intensities for (400) Reflection from Annealed Nickel Powder Standard 212 XVII Computer Output. Sin © Values for (kOO) Reflection from Annealed Nickel Powder Standard 213 L i s t of Tables (Continued) v i i i Number xvni XIX XX XXI XXII XXIII XXIV XXV XXVI XXVII XXVIII XXIX Page No. Computer Output. Peak Parameters f o r (hOO) R e f l e c t i o n from Annealed Nickel Powder Standard 213 Computer Output. O r i g i n a l X-Ray I n t e n s i t i e s f o r (200) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 2lh Computer Output. F i n a l Corrected X-Ray Intensity Values f o r (200) R e f l e c t i o n from Ni-ThO_ Cold Rolled 75% 215 Computer Output. S i n 6 Values f o r (200) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 216 Computer Output. Peak Parameters f o r (200) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 216 Computer Output. O r i g i n a l X-Ray I n t e n s i t i e s f o r (400) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 21? Computer Output. F i n a l Corrected X-Ray I n t e n s i t i e s f o r (kOO) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 217 Computer Output. S i n 6 Values f o r (kOO) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75$ 218 Computer Output. Peak Parameters f o r (kOO) R e f l e c t i o n from Ni-Th0 2 Cold Rolled 75% 218 Computer Output. Fourier C o e f f i c i e n t s f o r Ni-ThO_ Cold Rolled 75% 219 Computer Output. V a r i a t i o n of L a t t i c e S t r a i n and Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-Th0 2 Cold Rolled 75% 220 Computer Output. Domain Size i n Ni-Th0_ Cold Rolled 75% 221 i x LIST OF FIGURES Number Page No. 1 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r N i c k e l i n Various Thermo-mechanical Conditions 99 2 V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Nickel i n Various Thermo-mechanical Conditions 100 3 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r Ni-Cr i n Various Thermo-mechanical Conditions 2.01 k V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-Cr i n Various Thermo-mechanical Conditions 102 5 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r Ni-ThOg i n Various Thermo-mechanical Conditions 103 6 V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-ThO_ i n Various Thermo-mechanical Conditions 1C4 7 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r Ni-Cr-TM^ i n Various Thermo-mechanical Conditions 105 8 V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-Cr-TWX, i n Various Thermo-mechanical Conditions 106 9 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance i n the As Received Condition f o r Various Compositions 107 10 V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance i n the As Received Condition f o r Various Compositions 108 11 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance i n the Cold Rolled 50$ Condition f o r Various Compositions 109 12 V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance i n the Cold Rolled 5°# Condition f o r Various Compositions 110 13 V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance i n the Cold Rolled 50# and Annealed Condition f o r Various Compositions 111 Ik V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance i n the Cold Rolled 50# and Annealed Condition f o r Various Compositions Lis t of Figures (Continued) x Number Page NoB 1 5 Variation of Lattice Strain with Lattice Distance i n the Cold Rolled 7 5 % Condition for Various Compositions 1 1 3 1 6 Variation of Domain Size Coefficient with Lattice Distance i n the Cold Rolled 7 5 $ Condition for Various Compositions l l * f 1 7 Variation of Lattice Strain with Lattice Distance i n the Cold Rolled 7 5 $ and Annealed Condition for Various Compositions 1 1 5 1 8 Variation of Domain Size Coefficient with Lattice Distance i n the Cold Rolled 7 5 $ and Annealed Condition for Various Compositions 1 1 6 1 9 Variation of Lattice Strain and Domain Size Coefficient with Lattice Distance i n the Cold Rolled 9 0 $ and Annealed Condition for Ni-ThC>2 1 1 7 2 0 Transmission Electron Micrograph of Nickel i n the As Received Condition 1 1 8 ' 2 1 Transmission Electron Micrograph of Nickel i n the As Received Condition 1 1 9 2 2 Transmission Electron Micrograph of Nickel i n the As Received Condition 1 2 0 2 3 Transmission Electron Micrograph of Nickel i n the Cold Rolled 5 0 $ Condition 1 2 1 2k Transmission Electron Micrograph of Nickel i n the Cold Rolled 5 0 $ Condition 1 2 2 2 5 Transmission Electron Micrograph of Nickel i n the Cold Rolled 5 0 $ and Annealed Condition 1 2 3 2 6 Transmission Electron Micrograph of Nickel i n the Cold Rolled 5 0 $ and Annealed Condition 1 2 ^ 2 7 Transmission Electron Micrograph of Nickel i n the Cold Rolled 5 0 $ and Annealed Condition 1 2 5 2 8 Transmission Electron Micrograph of Nickel i n the Cold Rolled 7 5 $ Condition 1 2 6 2 9 Transmission Electron Micrograph of Nickel i n the Cold Rolled 7 5 $ Condition 1 2 7 L i s t of Figures (Continued) x i Number Page No. 3 0 Transmission Electron Micrograph of Ni c k e l i n the Cold Rolled 1% and Annealed Condition 128 31 Transmission Electron Micrograph of N i c k e l i n the Cold Rolled 73% and Annealed Condition 129 32 Transmission Electron Micrograph of Ni-Cr i n the As Received Condition 130 33 Transmission Electron Micrograph of Ni-Cr i n the As Received Condition 131 34(a) Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 5C$ Condition 132 34(b) Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 50% Condition 133 35 Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 5&% Condition 134 3 6 Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 5Q& and Annealed Condition 135 37 Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 50% and Annealed Condition 136 38 Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 50% and Annealed Condition 137 39 Transmission Electron Micrograph of Ni-Cr i n the Cold Rolled 50% and Annealed Condition 138 40 Transmission Electron Micrograph of Ni-TM^ i n the As Received Condition 139 41 Transmission Electron Micrograph of Ni-ThO ? i n the Cold Rolled 5C# Condition 140 42 Transmission Electron Micrograph of Ni-ThO_ i n the Cold Rolled 50% and Annealed Condition l 4 l 43 Transmission Electron Micrograph of Ni-ThO_ i n the Cold Rolled 75% Condition 142 44 Transmission E l e c t r o n Micrograph of Ni-ThO- i n the Cold Rolled 75% Condition 143 45 Transmission Electron Micrograph of Ni-ThO ? i n the Cold Rolled 75% and Annealed Condition 144 Lis t of Figures (Continued) x i i Page No. 1*8 Transmission Electron Micrograph of Ni-ThC>2 i n the Cold Rolled 90$ and Annealed Condition 1 ^ 5 k7 Transmission Electron Micrograph of Ni-Th0_ i n the Cold Rolled 90$ and Annealed Condition d l * f 6 Transmission Electron Micrograph of Ni-ThOp i n the Cold Rolled 90$ and Annealed Condition Ik? ^ 9 Transmission Electron Micrograph of Ni-Cr-Th0 2 i n the As Received Condition 1 ^ 8 5 0 Transmission Electron Micrograph of Ni-Cr-ThO_ i n the As Received Condition 1 ^ 9 5 1 Transmission Electron Micrograph of Ni-Cr-ThO_ i n the Cold Rolled 5 0 $ Condition 1 5 0 5 2 Transmission Electron Micrograph of Ni-Cr-ThO_ i n the Cold Rolled 5 0 $ and Annealed Condition 1 5 1 5 3 Transmission Electron Micrograph of Ni-Cr-ThO_ i n the Cold Rolled 7 5 $ Condition 1 5 2 5 ^ Transmission Electron Micrograph of Ni-Cr-ThO_ i n the Cold Rolled 7 5 $ and Annealed Condition 1 5 3 5 5 Transmission Electron Micrograph of Ni-Cr-ThO_ i n the Cold Rolled 7 5 $ and Annealed Condition 1 5 ^ 5 6 Optical Micrograph of Nickel i n the As Received Condition. Grain Size Standard 1 5 5 5 7 Optical Micrograph of Ni-Cr i n the As Received Condition. Grain Size Standard 1 5 5 5 8 Computer Graphs showing Sequence of Corrections for (200) Reflection from Annealed Nickel Powder Standard 2 2 2 5 9 Computer Graphs showing Sequence of Corrections for (400) Reflection from Annealed Nickel Powder Standard 2 2 3 6 0 Computer Graphs showing Sequence of Corrections for ( 2 0 0 ) Reflection from Ni-Th0 2 Cold Rolled 7 5 $ 22k 6 1 Computer Graphs showing Sequence of Corrections for (ifCO) Reflection from Ni-Th0 2 Cold Rolled 7 5 $ 2 2 5 L i s t of Figures (Continued) x i i i Number Page No» 6 2 Computer Graph showing V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r Ni-Th02 Cold Rolled 7 5 # 2 2 6 6 3 Computer Graph showing V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-ThO ? Cold Rolled 7 5 # 2 2 6 lo INTRODUCTION 1.1. Dispersion Strengthening The i n t r o d u c t i o n of a commercially a v a i l a b l e dispersion streng-thened n i c k e l a l l o y ^ i n 1962 provided industry with an e x c i t i n g new material with an i n t e r e s t i n g p o t e n t i a l i n the f i e l d of high temperature turbine engines, and at the same time stimulated research on d i s p e r s i o n strengthening i n the N i - T f c ^ system. E a r l i e r research on other systems had re s u l t e d i n several strengthening models. The high strength of dispersion strengthened a l l o y s has been s u c c e s s f u l l y correlated with the well-known Orowan r e l a t i o n -(2) ship given by K e l l y and Nicholson . This r e l a t e s the increase i n y i e l d s t r e s s due to the presence of the dispersoid to the i n t e r - p a r t i c l e spacing and a r i s e s from the o r i g i n a l p r e d i c t i o n of Orowan^^ based on the s t r e s s to bow a d i s l o c a t i o n between two obstacles. The model assumes that the i n t e r -p a r t i c l e spacing of the d i s p e r s o i d i s small so that l i t t l e d i s l o c a t i o n motion can occur before the d i s l o c a t i o n encounters a p a r t i c l e , and no work hardening of the matrix due to d i s l o c a t i o n i n t e r a c t i o n s i s predicted. The f i n a l form of Orowan's equation, using N a b a r r o ' s ^ 1 ^ expression f o r the l i n e tension of a d i s l o c a t i o n , i s given by K e l l y and Nicholson as, 1 where G shear modulus of the matrix b Burgers vector r mean p a r t i c l e radius d average spacing of p a r t i c l e s s i n i t i a l y i e l d s t r e s s of matrix 1/2 (1 + 1 ) 1-0 Poisson's r a t i o . 2 (4) The consideration by Mott and Nabarro of the effect on dislocation move-ment of strain f i e l d s around particles predicted a greater increase i n strength than did the Orowan model since particles not i n the dislocation glide plane could exert an influence through their associated strain f i e l d s . (5) An alternative model proposed by Ansell and Lenel predicts that the i n i t i a l y ie ld stress of a dispersion strengthened material i s deter-mined by the shear strength of the dispersoid par t ic les . Since a pile-up of straight dislocations at a particle would result i n a stress greater than that necessary to expand the leading dislocation between two part ic les , i t i s assumed that pile-ups take the form of dislocation loops around the d i s -persoid part ic les . These loops result i n an increment of y ie ld stress and an applied stress on the part ic les , which i s limited by their fracture strength. Ansell and Lenel suggested that the bowing and bypassing of particles by dislocations would not produce detectable plastic strain and that the y ie ld point occurred only when the particles were sheared. Kelly (2) and Nicholson raised objections to this suggestion and also reported no experimental evidence of part icle fracture at the y i e l d stress. Investigating C u - A l ^ ^ and Cu-SiO^ alloys prepared by high' speed hot extrusion of powder compacts, Preston and G r a n t ^ found that the strength could not be related simply i n this type of material to the degree of dispersion and they postulated that i t was related to retained strain energy. The strain energy was developed during the extrusion process because the high strain rate and the presence of the dispersoid impeded (7) normal recovery. White and Carhahan concluded s imilar ly that the optimum strength of Ni-ThO^ at ambient temperature was largely a function of stored energy imparted by extrusion followed by various strain-anneal cycles. 3 The importance of dislocation sub-structure has been pointed out by von Heiraendahl and Thomas ^ and by Wilcox and C l a u e r ^ . These authors associated the strength of Ni-ThO,, with the existence of a highly stable dislocation substructure that was not removed at elevated tempera-tures. This stable substructure was regarded as indicating a high stored energy. An attempt by von Heimendahl and Thomas to relate the strength of Ni-ThO^ to the grain size using the Hall^ 1 0 ^-Petch^ 1 " 1 "^ relationship was unsuccessful. Although most of the earl ier work was based on simple pure metal-dispersoid systems, the introduction of a commercially available d i s -(12) persion strengthened nickel-chromium alloy i n I966 permitted the. study of the combined strengthening effects of a dispersoid and a so l id solution. The addition of chromium to the new Ni-Gr-ThO^ al loy provided a very desirable increase i n the oxidation resistance, thus permitting the high temperature strength to be u t i l i z e d i n more industr ial applications. A l -though the low temperature strength was enhanced by the chromium i n s o l i d solution, the high temperature strength was somewhat lower than that of the parent Ni-ThC>2 a l l o y ( l ) . 1.2 Measurement of Strain Energy and Substructure The measurement of stored energy i n dispersion strengthened (13) copper has been reported recently by Chin and Grant . The procedure used was to measure by a calorimetric method the energy released during high temperature annealing. Only at temperatures /high above the normal recrystal l izat ion temperature of pure copper was the energy release observed. A calculation of the in ter fac ia l free energies for surfaces, k grain boundaries, stacking faults and twins has been made i n N i , Ni-ThO^ and Inconel 600 by Murr, Smith and G i l m o r e ^ 1 ^ . This was accomplished by the observation of interface intersection morphologies. The evaluation of non-uniform la t t i ce strain and small c ry s ta l -l i t e domain size i n metals from the measurement of x-ray di f f rac t ion l i n e broadening i s re la t ively straightforward when these two effects occur separately, and treatments can be found i n the standard t e x t s»(l6)^ When the two effects occur together, as i s usually the case with metals, (17) the evaluation i s more complex. Grierson and Bonis used an x-ray l ine broadening technique to measure the matrix elastic s train i n Ni-ThO^. An (l8) excellent account of the overall subject has been given by Warren and based on this.and other works, the theoretical basis of the x-ray l i n e broadening technique has been reviewed i n Appendix 1. The starting point i s to consider an elementary crystal di f f rac t ing x-rays i n accordance with Bragg's Law and then to decide from fundamental considerations how this coherent x-ray intensity w i l l be affected i f at the same time the crystal i s subjected to an arbitrary strain displacement and i s also limited to a re la t ively few unit c e l l s i n one direction so as to relax one of the three Laul conditions. Under these restrict ions of non-uniform l a t t i c e s t rain and small c r y s t a l l i t e domain size an expression i s derived giving the experimentally-measured diffracted x-ray power per unit length of di f f rac t ion l ine at a given Bragg angle. In Appendix 1 this expression i s equation (12), q'(26) = K(6) | - ^ N(t) {cos2nJ1tcos2uhX(t) - s ^ T t ^ t s ^ n h X t t ) 3 (12) In this expression i s a function of the angle (26), h i s the order of the ref lect ion (hOO), X(t) i s a function of the la t t i ce s train and -4—^  i s a function of the 1 5 domain size for integer values of the harmonic number ( t ) . To obtain X(t) and ^-7T^ experimentally they are combined i n the following def ini t ions , 1 A(t) = cos2nhX(t) 1 B(t) = - sin2rthX(t) 1 Also k(6) i s eliminated by an angular correction and the (2©) variable i s redefined i n terms of the distance x on the (26) axis of the experimentally recorded x-ray di f f rac t ion p r o f i l e . In addition, the harmonic number (t) i s shown to be related to true distance (L) measured i n the crystal i n the direction perpendicular to the di f f rac t ing planes. Thus the theoretical x-ray intensity of equation (12) can be expressed i n the form of equation (27) i n Appendix 1, q(x) = 2 L A ( L ) c o s 2 7 l L + B(L)sin2uL | x l (27) — CO The important thing about equation (27) i s that i t has the form of a Fourier series for a function q(x) from which the coefficients A(L) can be obtained from the transform integration. Thus from the experimentally measured x-ray prof i le of q(x) versus x, values of A(L) for chosen values of (L) can be obtained. By d e f i n i t i o n , A(L) = E & L cos2TihX(L) 1 Also i n the or iginal derivation X(L), or X(t) as i t was i n i t i a l l y , was a function of the l a t t i c e strain and -n—^ was a function of the crystal 1 domain s i z e . Hence la t t i ce s train and domain size can be obtained from the experimentally measured x-ray prof i le q(x). Since cos2TihX(L) depends on h , the effect of s train on q(x) i s also dependent on the order of the 6 ref lect ion (h0O), whereas the effect of domain size i s related to and i s independent of order. In Appendix 1, i s defined as the Domain 1 D Size Coefficient A ( L ) and COS2TIJIX(L) i s defined as the order dependent Strain Coefficient A ( L t h Q ) . The f i n a l working expression i s equation (32), l n A(L,h Q ) = l n A D ( L ) - 2TC 2 & 2 L 2 h 2 ^ j a 2 i n which £ i s the la t t i ce strain i n distance L , "a" i s the f . c . c . l a t t i c e parameter and the other terms have been defined above. From this expres-sion, using two orders of an (hOO) reflect ion and graphical methods des-cribed i n Appendix 1, values of the la t t i ce s train i n a distance L i n the £hOcT] direction and the c r y s t a l l i t e coherent domain size can be obtained. The form of the la t t i ce strain data i s a graph of the root mean square strain 2 1/2 versus :L showing the distr ibution of non-uniform strain as a function of distance i n the c rys ta l . The domain size comes from a graph of A ^ ( L ) versus L and gives the c r y s t a l l i t e size i n Angstroms i n the direction [hOO] from which the coherent x-ray diffracted intensity i s being received. The boundary of a domain could be a grain boundary, sub-grain boundary, stacking fault or twin boundary across which the misorien-tation of the two adjacent la t t ices i s such that the Bragg law cannot be sat isf ied by them both for a common incident x-ray intensity . A large part of Appendix 1 i s devoted to the problem of obtain-ing an experimental x-ray ref lect ion prof i le which i s broadened by strain and domain size effects only but i s free from the broadening which arises from the x-ray optics of the apparatus used. This i s generally known as (19) "Stokes correction" which involves the unfolding of the observed con-volution of intensit ies using a standard prof i le obtained from a s t r a i n -7 free annealed sample of re la t ively coarse grain s i z e . Other important considerations covered i n Appendix 1 which w i l l not be reviewed at this time include the choice of or igin of the x-ray ref lect ions , terminal errors i n the Fourier series resulting i n what i s usually described as the "hook e f f e c t " ^ ^ ^ ^ ^ ^ ^ limitations on t or L to avoid errors ar is ing from osci l lat ions i n the components of (22) the Fourier coefficients at large harmonic values , and the contribution to the domain size coefficient from stacking faults and twin boundaries. 1.3 Scope of the Present Investigation The work to date on dispersion strengthening offers no s a t i s -factory explanation of the high strength at elevated temperatures. The dislocation-particle interaction model i s not tenable at temperatures where cross-s l ip and climb processes proceed readily , and the precise role of stored energy has not been established i n a model for high temperature strength. Although the presence of a dislocation substructure has been correlated with room temperature strength, there i s a lack of published data relat ing high temperature strength and microstructure. Furthermore, much of the work has been done solely on dispersion strengthened materials without the knowledge of how the parent matrix would respond to similar thermo-mechanical treatments. In view of the above si tuation, i t appeared desirable to investigate a family of alloys comprising both single component and s o l i d solution parent matrices, with and without dispersion strengthening. Size and volume fraction of dispersoid were not chosen as variables since part ic le-dislocat ion interactions and room temperature strength were not considered to be of primary importance. The effect of retained l a t t i c e 8 strain and substructure domain size on tensile strength were chosen for study, and to this end the selected materials were subjected to a wide range of thermomechanical treatments. 9 2. EXPERIMENTAL PROCEDURES 2.1. S u p p l y o f M a t e r i a l s The f o l l o w i n g were t h e b a s i c s t a r t i n g m a t e r i a l s f o r t h e i n v e s -t i g a t i o n , ( a ) N i ( b ) 80# N i - 2C# C r ( c ) 9%% N i - Z'/o Th02 ( d ) 78?. N i - ZQ>% C r - 2% Th02 M a t e r i a l s ( a ) a n d ( b ) were p r e p a r e d i n t h e F o u n d r y S e c t i o n o f t h e M i n e s B r a n c h , D e p a r t m e n t o f M i n e s a n d T e c h n i c a l S u r v e y s , O t t a w a , b y vacuum i n d u c t i o n m e l t i n g a n d c a s t i n g u s i n g t h e f o l l o w i n g raw m a t e r i a l s , ( i ) I n t e r n a t i o n a l N i c k e l Company, N i c k e l 270, h o t f i n i s h e d r o d , 0.250 i n . d i a m e t e r , ( i i ) K o c h - L i g h t L a b o r a t o r i e s L t d . , E n g l a n d , c h r o m i u m f l a k e , t y p e 8l82, g r a d e kll. B e f o r e d e s p a t c h t o O t t a w a , m a t e r i a l ( i ) was c h e m i c a l l y p o l i s h e d t o remove s u r f a c e o x i d e b y i m m e r s i o n , f o r a p p r o x i m a t e l y one m i n u t e i n t h e f o l l o w i n g s o l u t i o n a t 85°C, 50# CS^COOH 30;' HNO3 1C# i<y/o HgSO^ A s r e c e i v e d f r o m t h e M i n e s B r a n c h , m a t e r i a l s ( a ) a n d ( b ) w e r e i n t h e f o r m o f h o t r o l l e d b i l l e t s w e i g h i n g a p p r o x i m a t e l y 5 l b . e a c h a n d m e a s u r i n g a p p r o x i m a t e l y 10 i n . x 2 i n . x 0.75 i n . M a t e r i a l s ( c ) and ( d ) were o b t a i n e d f r o m E . I . d u P o n t de Nemours a n d Company as t h e f o l l o w i n g 10 corresponding commercial products, (c) TDNi, sheet, 36 i n . x 2k i n . x 0.0^0 i n . (d) TD NiC, sheet, 2k i n . x 11.75 i n . x 0.0^0 i n . and, 2k i n . x 12 i n . x Q.OkO i n . The suppliers ' analyses of these materials are given i n Table 1(a). Materials (a) and (b) were analyzed after they had been processed to s t r ip for test specimens. The results are contained i n Table K b ) . A series of r o l l i n g and annealing tests was carried out on materials (a) and (b) to arrive at a procedure resulting i n sheet approxi-mately 0.0*1-0 i n . thick with an equiaxed annealed grain size not greater than 50u. The selected technique was to hot r o l l the nickel b i l l e t from 0.750 i n . to 0.160 i n . at 1000°C, cold r o l l 75$ reduction from 0.160 i n . to O.O f^O i n . , anneal at 500°C for 6 min.; and to hot r o l l the Ni-Cr b i l l e t from 0.750 i n . to O.Oto i n . at 1100°C, cold r o l l 25$ reduction from O.OHO i n . to 0.030 i n . , : anneal at 850°C for 1 hr. The hot r o l l i n g was done from a Dynatrol electric furnace with an a i r atmosphere and the hot and cold r o l l i n g were done i n a two-high Stanat r o l l i n g m i l l with k i n . diameter r o l l s . Material (a) was processed by the above procedure and the grain size was confirmed to be approximately 50p, by examination at a magnification of 220X following standard metallographic preparation and etching i n a solution of 50$ CH^COOH + 30$ HNO^ + 10$ H^PO^ + 10$ HpSO^ at 50°C. Material (b) was processed as described above and the grain size confirmed to be approximately 50\i after etching i n a solution of 33$ HC1 + 17$ HpO., (30$) + 50$ HpO at room temperature. Grain size micrographs of materials (a) and (b) are shown in Figures 56 and 57 respectively. 11 For the prupose of the remainder of the study, these four materials, (a) Ni (b) 80$ Ni - 20$ Cr (c) 98$ Ni - 2$ T h 0 2 (d) 78$ Ni - 20$ Cr - 2$ T h 0 2 processed as described above, were deemed to be i n the As Received condi-t i o n . Element ($) Nickel 270 Cr Flake 8182 h TD Ni TDNiC C 0.01 O.OOHO 0o0247 Mn <0.001 Fe < 0.001 0.01 S < 0 .001 0.0016 0.0052 S i < 0.001 Cu < 0 .001 0.0010 Ni Bal . Cr < 0 . 0 0 1 99o99 0.01 19,58 T i < 0 .001 < 0 . 0 0 1 Mg < 0 .001 Co . < 0.001 0„01 N 0.006 T h 0 2 2.6 1.9 Table 1(a). Suppliers' Chemical Analyses 12 Material Chemical Analyses (ppm) 0 C S Ni S t r i p 17 25 8CT/o Ni-2C$ Cr S t r i p 525 27 61 Table 1(b). Chemical Analyses of Tensile Specimens 2o2. Thermo-mechanical Treatments The four basic materials were subjected to a series of cold r o l l i n g reductions of increasing severity and to various annealing cycles. In the case of the ThO^-containing materials, two annealing temperatures were used, but i n the case of the other two materials, annealing was always according to the cycle which had been established previously to produce a grain size of 50u, since a grain size greater than t h i s would not have been acceptable for the subsequent x-ray d i f f r a c t i o n analysis. Annealing was done under, an atmosphere of cylinder hydrogen. The various thermo-mechanical treatments were intended to pro-duce a wide range of s t r u c t u r a l conditions embracing different d i s l o c a t i o n densities and d i s t r i b u t i o n s , and different l a t t i c e strains and c r y s t a l , domain s i z e s . Table I I summarizes the material-conditions. 2.3. X-Ray D i f f r a c t i o n 2.3.1. Specimen Preparation The required specimen size for x-ray d i f f r a c t i o n tests was from 2-2.5 cm. wide by 3-3.5 cm. long. Suitable specimens were sheared from s t r i p i n each of the conditions of Table I I , the longer dimension being 13 Material Thermo-mechanical Condition 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Ni Ni Ni Ni Ni 80% Ni-20% Cr 80% ni-20% Cr 80% Ni-20$ Cr 98% Ni-98% Ni-Ni-Ni-98% Ni-98% Ni-98% Ni-98% 98% •2% ThO, •2% ThO^ •2% ThO* •2% ThO^ •2% ThOt •2% ThO* •2% ThO^ 78% Ni-20% Cr-2% ThO„ 78% Ni-20% Cr-2% ThO^ 78% Ni-20% Cr-2% ThO* 78% Ni-20% Cr-2% ThO^ 78% Ni-20% Cr-2% ThO* As received Cold rol led 50$, 0.040 i n . to 0.020 i n . Cold rol led 50$, Ann. 500°C 6 rainD Cold rol led 75%, 0.040 i n . to 00 10 i n . Cold rol led 75%, Ann. 500°C 6 min. As received Cold rol led 50%, 0.030 i n . to 0.015 i n . Cold rol led 50%, Ann. 850°C 1 hr . 0.040 i n . to 0.020 in„ Ann. 1200°C 10 hr . As received Cold rol led 50%, Cold rol led 50%, Cold rol led 75%, 0.040 i n , to 0.010 i n . Cold rol led 75%, Ann. 1400°C 20 hr . 0.040 i n . to 0.004 i n . Ann. 1400°C 20 hr . Cold rol led Cold rol led 90% As received Cold rol led 50$, Cold rol led 50$, Cold rol led 75%, Cold rol led 75$, 0.040 i n . to 0.020 i n . Ann. 1200°C 10 hr . 0.040 i n . to 0.010 i n . Ann. 1400°C 20 hr. Table I I . Summary of Material Conditions i n the direction of prior r o l l i n g . Both surfaces were l i g h t l y polished by hand on three zeros and four zeros emery paper with kerosene lubricant , followed by 5n and l\i diamond paste, only as much as was necessary to remove any surface blemishes and contamination. This was followed by chemical polishing i n the case of the chromium free materials and by electropolishing i n the case of the chromium containing materials so as to remove 0.001 i n . of material from each surface. The chemical polishing was carried out as described previously i n Section 2.1. and two immersions of half a minute were s u f f i c i e n t . The electropolishing was carried out at room temperature i n the following solution: 40$ H^PO^ 14 35% E2sok 25% H 20 A potential of 6 volts and a current density of 0.3 araps/cra. were used with magnetic s t i r r i n g . Times of about 16 mins. were required to remove 0.001 i n . from each surface. For convenience of future reference, the electro-polishing solution was designated Solution A. To ensure that the l ighter gauge specimens were f l a t , they were then bonded to a half section of a standard microscope glass s l ide using a domestic adhesive. The need to polish chemically and to electropolish was estab-lished i n a separate series of experiments. A sample of %<3% Ni-209e> Cr was mechanically polished and examined i n the x-ray diffractometer using the procedure to be described i n the next section. It was then re-examined following successive removals of 0.00025 i n . of material from each surface by electropolishing. In each case, the (200) ref lect ion was recorded using CuKtx- radiation and the c r i t e r i a of improvement were the peak to background ratio and the resolution of the KoCl/KcX2 doublet. It was found that after the removal of 0.001 i n . of material from each surface, no further improvement i n the chosen parameters could be made. 2.3.2. X-Ray Diffract ion Procedure A review of the theoretical basis of the x-ray analysis has been given i n Appendix 1. What was required experimentally was a set of x-ray intensity measurements taken at known angular increments across the (200) and (400) reflections for each material condition of Table I I . The apparatus used was a combination of the Phi l ips x-ray Generator PW 1011/02 with a ver t i ca l Goniometer PW 1049/10 and the Step 1 5 Scanning Device PW IO63 / O O with the Step Scanning Control Combination PW 1357/00. The Pulse Height Analyzer was the PW 1355/10 which fed the Counter Assembly PW 1352/10 and the Timer Counter PW 1353/10. The numerical output i n the form of the number of pulses counted and/or the duration of counting was printed by the Printer Combination PW 135^ /00 on the High Speed D i g i t a l Printer PW 4202/00. The goniometer divergence s l i t and scatter s l i t were each set to 2° and the receiving s l i t to 0.2 mm. These values were recom-mended by the manufacturer for the specimen size and angular range of this investigation. A copper target was used with an applied voltage of 30 KV and a nickel f i l t e r was inserted between the x-ray tube and the specimen to remove the CuKyB wavelength and the shorter wavelength components of the background. No f i l t e r was used at the counter. Tube currents from 14 -30 m.a. were used, depending on the grain size of the specimen, to keep the counting rate within prescribed l imits discussed below. An i n i t i a l attenua-t ion of 8X was applied to the signal coming from the proportional counter as recommended by the manufacturer and this was followed by a threshold pulse height analysis to remove the longer wavelength components of the back-ground. A step-scan procedure was used i n which the goniometer was advanced automatically in steps of either 0.01° (2©) or 0.05° (20) from the selected starting angle on the low © side of the reflect ion peak. At each step, a measurement was made of the time i n seconds taken to count a constant number of 20,000 x-ray pulses. Steps of 0.01° were used for the sharper peaks from annealed samples where a range of about 6 ° (2©) was scanned resulting i n a set of 600 readings, and steps of 0.05° were used for the broader peaks from cold rolled samples where a range of about 20° (2©) was scanned resul t -ing i n a set of '+00 readings. The choice of a constant count of 20,000 was the result of the 16 following consideration of the ove r a l l accuracy of the procedure. The manufacturer's data on the accuracy of the Timer indicate that when operating on a preset count, the error i s -0.01 sec. - 0.01$ of the reading, whereas on preset time, the maximum error i s - 0.0001 sec. - 0.01% of the adjusted time. Coupled to these errors was the probable error of the number of x-ray pulses counted, a r i s i n g from the s t a t i s t i c a l nature of the a r r i v a l of x-ray quanta. In a t o t a l of N random counts, the Probable Error 67 having a 50% pro b a b i l i t y i s given by 0.6745/N, or -^p. . To increase the V N p r o b a b i l i t y to 96%, the error must be increased to 3x Probable Error of 3 x . (Since Probable Error = 0.6745 x Standard Deviation, 3x VN Probable Error = 2.024 x Standard Deviation, giving a 96$ pro b a b i l i t y as 2x Standard Deviation gives a 95.^ +5% p r o b a b i l i t y ) . Hence a t o t a l of 20,000 •2- Cjjy counts has a 96% proba b i l i t y of being within an error 100/2 To hold the error i n the Timer and the s t a t i s t i c a l error i n the Counter to the same approximate magnitude of about 1%, i t was decided to use the preset count technique for a fixed count of 20,000 and to adjust the x-ray tube current so that the (200) r e f l e c t i o n from a sp e c i f i c material had an int e n s i t y not greater than 20,000 counts/sec. Thus, the minimum time counted was 1 sec. with a Timer error of 1.01%, a l l longer times having a smaller error, and a l l counts were to 20,000 with, a 96% p r o b a b i l i t y of an error within 104%. Having located the (200) r e f l e c t i o n peak and adjusted the x-ray tube current according to the above c r i t e r i o n , a long range continuous scan was made through the (200) and (400) re f l e c t i o n s to define the lower and upper angular l i m i t s to be used for the step scan. For t h i s continuous scan, a goniometer movement of O.25°(20)/mino was used, coupled with a s t r i p 17" chart speed of 600 ram./hr., a time constant of 4 sec. was used for the ratemeter and the recorder f u l l scale deflection was set at a low value not greater than 1,000 counts/sec. For each (200) and (400) re f lec t ion , a range of 20° - 30° (26) was scanned continuously, depending on the sharp-ness of the peak. With this arrangement, the lower and upper angles, 29^ and 2 0 2 , between which the x-ray intensity was above background, could be determined accurately. The times to count 20,000 pulses at each step of the step scan were printed automatically on a paper s t r i p . Thus, the output from the x-ray tests consisted of sets of approximately 400-600 numbers representing the inverse of x-ray intensity at either 0.01° or 0.05° (26) steps across the (200) and (400) reflections for each material condition of Table II. Since background counts were sometimes as low as 20 counts/sec. a total time of eight days was sometimes required to complete the (200) and (400) step scans on one material. In a l l , the programme required the equivalent of about four months continuous operation of the x-ray dif f rac t ion equip-ment. As discussed i n Appendix 1, a set of data as described above was required from a sample having no x-ray l ine broadening due to la t t i ce s train or small domain s ize , as a standard against which the instrumental l ine broadening could be unfolded from the convolution of measured x-ray l ine intensity . This standard did not have to be of the same material as those under investigation, but had to have a reasonably strong x-ray reflect ion at approximately the same angle as those used i n the main study. For this purpose, a 1 micron nickel powder was annealed i n hydrogen at 760°C for 1: hr . The data from this standard gave rise to the Fourier coefficients defined i n Appendix 1 as G(L). 18 2.4. Electron Microscopy 2.4.1. Specimen. Preparation Several specimens from each material of Table I I were prepared as t h i n f o i l s suitable for transmission electron microscopy. I n i t i a l l y , 0.125 i n . diameter discs were spark machined from the s t r i p material immersed i n kerosene using 100V and approximately 0.4 amps. The cutting time was about 2 min. depending on the thickness. The thicker discs were then reduced to 0.010 i n . by l i g h t hand polishing on four zeros emery paper with kerosene. Subsequent reduction of the discs was achieved by an electro-polishing technique with the disc as the anode suspended between two ho r i z o n t a l l y opposed jets of e l e c t r o l y t e . The electrolyte was that recom-mended by von Heimendahl and Thomas which i s designated as Solution A i n Section 2.3.1. The arrangement was such that the disc and j e t s were below the surface of the e l e c t r o l y t e . The jets consisted of two horizontal s t a i n -l e s s s t e e l standard hypodermic needles of size 20 gauge with t h e i r ends approximately 0.5 i n . apart. The j e t s were fed with electrolyte through an e l e c t r i c pump which was controlled by a Variac transformer to maintain a l i g h t impingement of the electrolyte against the two surfaces of the speci-men disc. The stainless s t e e l jets were used as cathodes and a c e l l voltage of 6V was maintained with a t o t a l current 0.4 amps which was equivalent to 2.5 amps/cm. as recommended by von Heimendahl and Thomas. A polishing time of about 5 mins. v/as used with frequent inspections towards the end to obtain a s l i g h t l y concave t h i n f o i l not yet penetrated. F i n a l electro-polishing was carried out i n the same apparatus but with the f o i l held at the side of and p a r a l l e l to the two j e t s . In t h i s position, the f o i l received overall polishing and the moment of penetration was determined by 1 0 -close observation with a 10X magnifying lens. The penetrated f o i l was washed i n water and dried i n alcohol. Although other techniques were t r i e d , including a single ver t i ca l jet with the specimen above the surface of the electrolyte, and other' electrolytes, the procedure described above was found to be the most successful and was used for the majority of the materials. 2*4.2. Electron Microscopy Procedure The electron microscope used was the Hitachi HU-11A. Thin f o i l specimens of 0.125 i n . diameter prepared as described above were suitable for immediate insertion into the microscope specimen holder. This avoided the p o s s i b i l i t y of damage arising from cutting and handling the f o i l i n the f i n a l stages. A voltage of 100 KV was used and use v/as made of a t i l t i n g specimen stage to confirm the contrast effects at dislocations and other structural features. Several photographs at magnifications up to 50»000 X were taken of transmission f o i l s from each of the materials i n Table I I . 2.5* Tensile Testing 2.5«1« Specimen Preparation The tensile blanks were i n s t r i p form measuring 4 i n . long x 1 i n . wide and i n thicknesses ranging from 0.004 i n . to 0.040 i n . , as dictated by the various r o l l i n g schedules of Table I I . The specimens were sheared from these blanks by a pneumatically operated punch and die producing a para l le l section 1.25 i n . long x 0.253 i n 0 wide joined by 0.5 i n . r a d i i to the 1.0 i n . ends. A 0.25 i n . diameter hole was punched i n the centre at each end to f a c i l i t a t e the attachment of pin and clevis grips for the high temperature tests. The sheared edges were polished l i g h t l y by 20 hand with fine emery paper. 2.5.2. Tensile Testing Procedure Tensile tests were carried out at room temperature and at an elevated temperature for each material. The room temperature tests were done on an Instron machine and the high temperature tests on a Tinius Olsen machine equipped with a platinum wound muffle furnace with an a i r atmos-phere. For the ThO^-containing materials, i . e . , Nos. 9-20 i n Table I I , the high temperature tests were at 1200°C; for the 80% Ni-20% Cr materials, i . e . , Nos. 6-8, the high temperature tests were at 850 C and for the Ni materials, i . e . , Nos. 1-5, they were at 500°C. The temperatures chosen f o r the high temperature tests were those at which i t was thought the materials _2 would s t i l l have y i e l d strengths s i g n i f i c a n t l y greater than 1. Kg. mm. and at which annealing treatments "on other specimens had been followed by x-ray d i f f r a c t i o n and electron microscope studies. Thus supporting i n f o r -mation would be available on the condition of the materials at the time of beginning the high temperature t e n s i l e t e s t s . For a l l t e n s i l e tests the machine cross-head speed was 0.02 i n . / min. giving a s t r a i n rate of 0.0l6/min., and the recorder chart speed was 2 in./min. From the recorder charts, the following values were calculated for each material condition from both room temperature and high temperature t e s t s , (a) 0.2% Proof Stress (b) 1.0% Proof Stress (c) Ultimate Tensile Strength (d) % Elongation on 1.25 i n . gauge length (e) Work Hardening Rate from 0.2-1% s t r a i n 21 2.6. Computer Analysis A detailed description of the computer programme i s given i n Appendices 2 and 3. An i n i t i a l treatment of the numerical data from the x-ray d i f -f r a c t i o n analysis was necessary to remove the contributions to i n t e n s i t y from The1., r e f l e c t i o n s i n the case of the ThO^ containing materials. For the Ni and Ni-Cr (200) re f l e c t i o n s occurring at approximately 2© = 52°, the overlapping ThO,, re f l e c t i o n s were, ( i ) Th0 2 (220) at 2© = 45.78° ( i i ) Th0 2 (311) at 2© = 54.26° ( i i i ) Th0 2 (222) at 2© = 56.93° For the Ni and Ni-Cr (400) r e f l e c t i o n s occurring at approximately 26 = 121° barely discernable overlapping high order ThO., re f l e c t i o n s were, ( i ) Th0 2 (620) at 26 = 120.90° ( i i ) Th0 2 (533) at 26 = 128.82° ( i i i ) Th0 2 (622) at 26 = 131.70° The contributions to i n t e n s i t y from the overlapping Th0 2 r e f l e c t i o n s were removed by smoothing out the trace on the diffractometer chart recording i n the appropriate regions. The interpolated Ni and Ni-Cr i n t e n s i t y values so obtained were then inserted as appropriate reciprocals i n place of the corresponding time values i n the set of times for 20,000 counts obtained previously from the diffractometer printer output. The sets of corrected times for 20,000 counts, one set for the (200) r e f l e c t i o n and one for the (400) r e f l e c t i o n for each of the material conditions i n Table I I , together with two sets for the annealed ni c k e l powder standard, amounted to 40 sets comprising a t o t a l of approxi-22 mately 20,000 f ive figure numbers. These were transferred to coding sheets and punched onto computer data cards. The computer programme then carried out the following operations, which have been discussed i n detai l i n Appendices 1 and 2, for each material condition. (a) Corrected for the angular dependence'of x-ray intensity, inc lud-ing that of the atomic scattering factor. (b) Converted the data into corresponding intensity values at equal intervals of s in 6 . (c) Subtracted the background intensity . (23) (d) Applied the Hachinger correction to remove the intensity contribution from the K©<2 component of the KoC doublet. (e) Calculated the centroid of the ref lect ion and rescaled the intensity data to the centroid as origin on the s in © axis. (f) Carried out the integrations of equations 30(a) to 30(d) of Appendix 1 and the complex divisions of equations 28(a) and 28(b) to obtain the Fourier coefficients for each x-ray ref lec t ion . (g) Used these coefficients to calculate the root mean square la t t i ce s train as a function of la t t i ce distance for each 2 1/2 material condition, i . e . , ( £ ) versus L, and the domain size coefficient A^(L) versus L, as described i n Appendix 1. 2 1/2 D (h) Plotted ( £ ) versus L and A (L) versus L as graphical outputs. ( i ) Calculated the coherent crystal domain sizes from the la t ter graphs according to two c r i t e r i a given i n Appendix 2. 23 On selected materials, plotted a sequence of graphs of x-ray-to (e) above. Printed out i n numerical form the following results i n addition to the graphs of (h) and (j) above, ( i ) Material type, Thermo-mechanical condition, Reflection ( i i ) Starting angle of step scan ( i i i ) Angular increment (iv) Number of data points (v) Atomic Scattering factors at each end of the reflect ion (vi) Original intensity values (times) ( v i i ) Corrected intensity values ( v i i i ) Corresponding values of s in © : ( i x ) Sin © increment (x) Number of sin © data points (xi) A r t i f i c i a l la t t i ce parameter, a^' defined i n Appendix 1 (x i i ) Reflection origin 2©q based on the peak centroid ( x i i i ) Lattice parameter based on the peak centroid (xiv) Reflection origin 2©q based on the peak maximum (xv) Lattice parameter based on the peak maximum (xvi) Peak asymmetry between centroid and and maximum (xvii) A table of the following Fourier coefficients , as defined i n Appendix 1, versus la t t i ce distance L from 0 to 500°; GR(L), GI(L), PR(L), P I(D, FR(L), FI(L) , A(L), LNA(L) 2 1/2 ( x v i i i ) A table of root mean square strain values ( € ) ' and domain size coefficients A^(L) versus la t t i ce distance 2k o L from 0 to 500A (xix) Coherent c r y s t a l domain sizes D according to the two c r i t e r i a given i n Appendix 2. t 25 3. EXPERIMENTAL RESULTS 3.1. X-Ray D i f f r a c t i o n The x-ray d i f f r a c t i o n results obtained from the procedure of Section 2.3.2. were i n the form of sets of numbers representing the inverse of i n t e n s i t y for each material condition. These were then the source material for the computer analysis of Section 2.6. A t y p i c a l set of output data from the computer for one p a r t i c u l a r material, TD Ni Cold Rolled 75/^ , i s given i n Appendix 3o I t i s preceeded by the data for the annealed n i c k e l powder standard which was used i n each case to unfold the convolution of i n t e n s i t i e s according to S t o k e s ^ ^ correction as described i n Appendix 1. The tabulated data i n Appendix 3 show the o r i g i n a l i n t e n s i t y . values, which i n fact are r e a l l y times inversely proportional to i n t e n s i t y , i n Tables XIX and XXIII and the f i n a l corrected i n t e n s i t y values, i n Tables XX and XXIV but the intermediate steps of correction to the data for angular dependence, background, doublet wavelength, etc., as described b r i e f l y i n Section 2.6. and i n more d e t a i l i n Appendix 2, are not shown. However, as discussed previously, on selected materials the computer' was programmed to show graphically that these corrections were being applied and t h i s was done i n the case of TD N i C o l d Rolled 75#. Thus, Appendix 3 includes sets of graphs for the (200) and (koo) r e f l e c t i o n s from.the annealed n i c k e l powder and for the (200) and (kOO) r e f l e c t i o n s from the TD N i Cold Rolled 75%* Each set comprises four graphs showing the x-ray i n t e n s i t y at the following stages, (a) As recorded, Figures 58(a), 59(a), 60(a) and 6l(a). • (b) Corrected for the angular dependence of the Lorentz-P o l a r i z a t i o n Factor and the Structure Factor, Figures 26 58(b), 59(b), 60(b) and 6l(b). (c) Corrected for (b) above and for a non-uniform background i n t e n s i t y , Figures 58(c), 59(c), 60(c) and 6l(c). (d) The f i n a l corrected i n t e n s i t y values having been corrected as for (c) above and for the doublet wavelength by the (23) Rachinger correction, Figures 58(d), 59(d), 60(d) and 61(d). It i s clear from the graphs of Appendix 3 that the K 2 doublet i s resolved more at the higher angles of the (400) r e f l e c t i o n as would be expected, and that the doublet i s not resolved i n the cold worked material. The graphs demonstrate that the computer programme correctly carried out the necessary preliminary corrections to the data. The tabulated data i n Appendix 3 also include i n Tables XXII and XXVI the peak positions 2©q calculated from both peak centroid and peak maximum, f.c.c. l a t t i c e parameter "a" calculated from these and peak asymmetries. From the corrected i n t e n s i t y values the Fourier co e f f i c i e n t s were obtained for each order of x-ray r e f l e c t i o n and these follow i n Appendix '3, Table XXVII. These co e f f i c i e n t s were then used to calculate the 2 1/2 D table of percent s t r a i n , ( € ) x 100, and domain size c o e f f i c i e n t , A ( L ) , versus l a t t i c e distance ( L ) , included as Table XXVIII. These values give r i s e to the f i n a l two graphs of Appendix 3 showing percent s t r a i n and domain size coe f f i c i e n t versus l a t t i c e distance ( L ) , Figures 62 and 63 respectively. The f i n a l section of the tabulated output i s shown as Table XXIX i n Appendix 3 and gives the domain size calculated from the l a t t e r graph according to the two c r i t e r i a given i n Appendix 2. 27 One set of data as shown i n Appendix 3 was obtained for each of the material conditions of Table I I , Section 2.2. It can be seen from Figures 62 and 63 of Appendix 3 showing percent s train and domain size coefficient versus l a t t i c e strain that at large values of (L) the functions cease to decrease and begin increasing. This region arises from i n s t a b i l i t i e s i n the Fourier series at large values of harmonic number (t) as discussed i n Appendix 1 with reference to (22) Mitchell . Consequently, i t i s necessary to disregard the r i s i n g regions of the graphs at large values of (L). With this l imitat ion i n mind, the computer data were replotted i n Figures 1-8 to show the effect of various thermc—mechanical treatments on the la t t i ce strain and domain size for each material composition. Using the same data the graphs were re-grouped into Figures 9-19 to enable a comparison to be made between different material compositions i n the same thermo-mechanical condition. As described i n Appendix 2 and as referred to b r i e f l y above with regard to Appendix part of the computer output was an estimation (24) of the domain size by two c r i t e r i a . The f i r s t c r i te r ion , due to Wagner , u t i l i z e d the area under the curve of domain size coefficient versus distance (L). In the present study, this cr i ter ion was applied within the computer programme before the degree of error at large values of (L) due to osci l la t ions i n the components of the Fourier series had been assessed. Thus domain sizes estimated by this f i r s t cr i ter ion w i l l be too (21) large. The second c r i t e r i o n , an adaptation of that due to Wagner , attempted to avoid the error due to the negative curvature or "hook effect" i n the graph of domain size coefficient versus distance (L) at low values of (L) and took the negative reciprocal slope at a point on the curve where 28 L = 0.2 x D ( l ) , D(l) being the domain size calculated by the f i r s t c r i -t e rion. Again t h i s second c r i t e r i o n was applied within the computer pro-gramme which did not permit a judgment to be made as to whether or not 0.2 x D(l) was the correct distance to be ignored to avoid the "hook-ef f e c t " before taking the negative reciprocal slope of the curve to give (25) the domain size as shown by Bertaut . Thus values of Domain Size (2) from the second c r i t e r i o n may also be i n error. From the corrected graphs of Figures 2, 4, 6 and 8 , best estimates of the domain size D were made and these are given i n Table I I I . Also included i n Table I I I are values of the root mean square s t r a i n expressed as percent s t r a i n for l a t t i c e distances 0 0 0 of 50A, 100A and 150A. These s t r a i n values were taken from Figures 1 , 3 » 5, and 7 and are included i n Table I I I for comparison with the estimated domain size i n the various thermo-mechanical material conditions. (The o o strains quoted for 50A are the peak values occurring near to 50A). As described i n Appendix 2 and shown i n Tables XXII and XXVT of Appendix 3 the computer output included the calculated r e f l e c t i o n o r i g i n s , 2©q, based on the peak centroids and on the peak maxima, the f.c.c. l a t t i c e parameters calculated from these 2© values and the peak asymmetries between centroid and maximum. These data were used to determine the twin f a u l t p r o b a b i l i t y , stacking f a u l t probability and l a t t i c e macro s t r a i n . The significance of twins and stacking f a u l t s as contributions to the domain size coe f f i c i e n t i s discussed i n the l a t t e r part of Appendix 1 . To evaluate peak s h i f t s some absolute standard must be used. In the case of the ni c k e l materials the annealed n i c k e l powder was used as the stand-ard. This produced the (200) r e f l e c t i o n at 2© = 5 1 . 8 ^ 9 ° based on the peak centroid using CuKoC 1 radiation, which compares very closely with the. 29 Material Condition Domain Size D o A % Str a i n at Distance (L) 0 0 0 50A 100A 150A 1. N i , As Received >1,000 O.38 0.10 0.07 2. N i , Cold Rolled 50% 360 0.37 0.17 0,14 3. N i , Cold Rolled 50% and Annealed >1,000 0.36 0.11 0.08 k. N i , Cold Rolled 75% 400 0.44 0.26 0.16 5. N i , Cold Rolled 75% and Annealed >1,000 0.05 0 0 6. Ni-Cr, As Received >1,000 0.10 0.02 0 7. Ni-Cr, Cold Rolled 50% 160 OAS 0.19 0.12 8. Ni-Cr, Cold Rolled 50% and Annealed >1,000 0.11 0 0 9. N-Th02, As Received 380 0.07 0.07 0.06 10. N-Th02, Cold Rolled 50% 700 0.14 0.12 0.11 11. Ni-ThO , Cold Rolled 50% and Annealed 350 0 0 0 12. Ni-Th0 2, Cold Rolled 75% 460 0.14 0.12 0.11 13. Ni-ThO , Cold Rolled 75% and Annealed >1,000 0 0 0 15. Ni-ThO , Cold Rolled 90% and Annealed >1,000 0 0 0 16. Ni-Cr-Th0 2, As Received 500-1,000 0 0 0 17. Ni-Cr-Th0 2, Cold Rolled 30% 270 0.21 0.19 0.14 18. Ni-Cr-Th0 2, Cold Rolled 50% and Annealed 500-1,000 0.09 0.07 0.05 19. Ni-Cr-Th0 2, Cold Rolled 75% 180 0.32 0.23 0.09 20. Ni-Cr-Th0 2, Cold Rolled 75% and Annealed 1,000 0.23 0.07 0.04 Table I I I . Domain Sizes and Lat t i c e Strain Distributions 3 0 ( 2 6 ) A.S.T.M. value of 26 = 5 1 . 84? . This result also served to demonstrate that the x-ray apparatus was correctly aligned. For the 8 0 $ Ni-20^ Cr alloys no powder standard was available and the la t t i ce parameter data of (27) Bechtoldt and Vacher was taken as the standard. This yields 2© = 5 1 . 4 9 8 ° for the ( 2 0 0 ) ref lect ion and 1 2 0 . 6 5 4 ° for the (400) ref lec t ion . . Usually the stacking fault probability «< i s determined from the change i n the separation between the (200) and ( i l l ) peak maxima since this cr i ter ion compensates p a r t i a l l y for errors ar is ing from overall d i s -tortion of the l a t t i c e . Equation (37) of Appendix 1 i s that used by (1P) Warren for this purpose. Similarly the twin fault probability can be determined from the change i n the separation of the (200) and ( i l l ) peak centroids since this partly eliminates errors arising from asymmetry due to instrument effects . Equation (42) of Appendix 1 i s that used by (21) Wagner for this purpose. In the present study the cold rol led materials exhibited a strong preferred orientation with the (220) plane i n the plane of r o l l i n g and with the standard diffractometer geometry the ( i l l ) r e f l e c -tions were too weak to measure. Thus equations (37) and (42) of Appendix 1 could not be used to measure oC and p . Alternatively, the following equations from Appendix 1 were used, IT CG PM 0^% , „ o ( 3 4 ) ( 3 5 ) ( A S ^ 1 ) (200) = ( 2 e \z00) ~ ( 2 6 5(200) = - l ^ * * 6 o (? 8> CG PM ( A s y m ) ( f t 0 0 ) = ( 2 6 ° ) ( Z f 0 0 ) - ( 2 6 ° ) ^ = + 14 .6/3 tan 6 ° ( 3 9 ) 31 Since equations (3*0 and (35) are of opposite sign they provide a means of deciding whether or not the peak s h i f t i s due to stacking f a u l t s or l a t t i c e macro s t r a i n , as stacking f a u l t s would move the (200) and (400) ref l e c t i o n s further apart whereas l a t t i c e macro s t r a i n would displace them i n the same di r e c t i o n , to higher angles for a compressive s t r a i n and to lower angles for a t e n s i l e s t r a i n . S i m i l a r l y , equations (38) and (39) being of opposite sign provide a check as to v/hether the observed peak asymmetries are due to twinning or to some instrument or doublet wavelength effect. The l a t t i c e residual macro s t r a i n was calculated from the d i s -placement of the peak centroids since the determination of planar spacing from Bragg's Law requires the o r i g i n to be that of the t o t a l integrated i n t e n s i t y . In the case of the materials containing TM^, i t was thought that observed asymmetries may have been due i n part to errors i n the estima-t i o n of the ni c k e l peak background i n the presence of overlapping ThO^ re f l e c t i o n s . Also, on the low angle side of the (200) r e f l e c t i o n s , the estimation of the background may have been i n error due to overlapping of the n i c k e l ( i l l ) r e f l e c t i o n . Since the Ni-ThO., materials displayed the • largest peak asymmetries and yet were found to be r e l a t i v e l y free from twins as observed by electron microscopy, the observed asymmetries may well have been erroneous. Consequently, i t seemed j u s t i f i a b l e to estimate l a t t i c e macro s t r a i n from the standpoint of the displacement of the peak maxima rather than the peak centroid. As broadening due to micro s t r a i n , domain size and stacking fa u l t s i s symmetrical, i n the absence of twinning and using monochromatic radiation, the peak centroid and maximum would coincide. This a n c i l l a r y x-ray data r e l a t i n g to peak positions and 32 asymmetries and the estimates of twin f a u l t p r o b a b i l i t y , stacking f a u l t . probability and l a t t i c e macro-strain are summarized i n Table IV. 3.2. Electron Microscopy Figures 20-53 show the structures of each material condition as observed by t h i n f o i l transmission electron microscopy. These are arranged according to material composition and thermc-mechanical condition i n the order f i r s t established i n Table I I of Section 2.2. 3.2.1. Nickel I t i s apparent from Figure 20 that the selected annealing cycle based on o p t i c a l metallography with the objective of producing a fine r e -c r y s t a l l i z e d grain s i z e , did not produce complete r e c r y s t a l l i z a t i o n . Although Figure 22 shows that r e c r y s t a l l i z e d grains are present i n the As Received condition, there i s evidence of retained d i s l o c a t i o n tangles within the grains. Figures 23 and 2k of the Cold Rolled 50% condition show a high density of dislocations. In addition to the dark bands a c e l l structure i s apparent. Figures 25-27 represent the Cold Rolled 50% and Annealed condi-t i o n . There i s evidence of r e c r y s t a l l i z e d grains containing random d i s -locations. This i s s i m i l a r to the As Received structure which was prepared by the same annealing cycle. Figures 28 and 29 indicate a high disl o c a t i o n density with well developed c e l l s a f t e r a cold r o l l i n g reduction of 75^ . On subsequent annealing the r e c r y s t a l l i z e d grains of Figure 30 were formed, with no evidence of dislocations within the grains despite the i n t e r s e c t i n g 7. '8. 10. H. 12. 13. 15. 16. 17. 18. 19. 20. Material Condition 0. Annealed Nickel Powder Standard 1. N i , As Received 2. N i , Cold Rolled 50% 3. N i , Cold Rolled 505° and Annealed 4. N i , Cold Rolled 75% 5. N i , Cold Rolled 75% and Annealed 6. Ni-Cr, As Received Ni-Cr, Cold Rolled 50% Ni-Cr, Cold Rolled 50^. and Annealed 9. Ni-Th0.2~v As Received '.- V'-- -Ni-Th6"2:, Cold Rolled 50% Ni-Th0 ?, Cold Rolled 50% and Annealed Ni-Th02, Cold Rolled 75$ Ni-Th0 2 , Cold Rolled 75% and Annealed Ni-Th02, Cold Rolled 90% and Annealed Ni-Cr-Th02,As Received Ni-Cr-Th0o, Cold Rolled 50% 2 Ni-Cr-ThO , Cold Rolled 50?i and Annealed Ni-Cr-Th0_, Cold Rolled 75% 2 Ni-Cr-ThO , Cold Rolled 75% and Annealed Reflection • H C3 O O U - P O O Ci CD 0 —^' (200) 51.85 (400) 121.87 (200) 51.79 (400) 121.56 (200) 51.80 (400) 121.62 (200) 51.79 (400) 121.70 (200) 51.79 (400) 121.82 (200) 51.84 (400) 121.93 (200) 51.42 (400) 120.31 (200) 51.44 (400) 120.35 (200) 51.42 (400) 120.28 (200) 52.21 (400) 121.86 * s O^OM o O O CD CM ^—' o -P CU « ^ S O O E <D P J C M CO ^ — -< I e y—\ 0 • u . <M %~ >> • H ro - P a CS OJ • H ro •rl ro O w • s rH >» X ro rH •rl U O O O •P O O . O 0 . X - P fn CD +> 10 . CD H CD H ni a> Pw CM X OJ . CM . •° § 0 ca 0 d ^ S < 0 S S o u a <IH < U SH S to 0 erf '—^  0 - O <: ro s E O O E O O - p «1 - P - p fr 0 CD <D «H H H S CD CM <D CM •rl U • H • 3 O fcO«H O w O w Xi O CO ^ O CO S ro u fr <H £<! H o rH ^ 0 -p - p "it! O 0 >> ro s Ri B ro • cci +> i-a 0 1-} O 0) O <D U +> - H v u ^0. ^ OH S «H EH CO rH 5^. <H (200) (400) (200) (400) (200) (400) (200) (400) (200) (400) (200) (400) (200) (400) (200) (400) (200) (4oo) (200) (400) 52.24 121.90 51.84 121.82 52.16 121.81 51.79 121.79 51.73 121.64 51.54 120.55 51.55 120.55 51.61 120.55 51.30 120.40 51.32 120.57 51.87 121.93 51.86 121.91 51.84 121.94 51.83 121.94 51.82 121.90 51.86 121.94 51.44 120.35 51.54 120.70 51.45 120.36 51.79 121.85 51.90 121.95 51.80 121.85 51.85 121.85 51.80 121.85 51.75 121.70 51.50 120.55 51.60 120.60 51.50 120.60 51.40 120.55 51.40 120.45 -0.02 -0.06 -0.07 -0.35 -0.04 -0.32 -0.04 -0.24 -0.03 -0.08 -0.02 -0.01 -0.02 -0.04 -0.10 -0.35 -0.03 -0.08 +0.42 +0.01 +0.34 -0.05 +0.04 -0.03 +0.31 -0.04 -0 .01 -0.06 -0.02 -0.06 +o.o4 0 -0.05 -0.05 +0.11 -0.05 -0.10 -0.15 -0.08 +0.12 0 0 -0.06 -0.31 -0.05 -0.25 -0.06 -0.17 -O.O6 --0.05 -0.01 +0.06 -0.08 -0.34 -0.06 -0.30 -0.08 -0.37 +0.36 -0.01 +0.39 +0.03 -0.01 -0.05 +0.31 -0.06 -0.06 -0.08 -0.12 -0.23 +0.04 -0.10 +0.05 -0.10 +0.11 -0.10 -0.20 -0.25 - 0 . l 8 -0.08 0 0 -0.01 -0.02 -0.03 +0.01 -0.04 +0.01 -0.05 -0.03 -0.01 +0.01 -0.06 -0.30 +0.04 +0.05 -0.05 -0.29 -0.08 -0.08 +0.03 +0.02 -0.07 -O.O8 0.003 0 0.010 0 0.006 0 0.006 0 0.004 0 0.003 0 0.003 0 0.014 0 0.004 0 0 0 0 0 0 0 0 0 0.003 0 0.008 0.001 0.010 0.001 0.013 0 0.003 0.001 0.016 0 0 0.007 0.013 0 0.021 0 0 0.003 0.018 0 0 0 +0.108 +0.151 +0.090 +0.122 +0.108 +0.083 +0.108 +0.024 +0.018 -0.029 +0.145 +0.170 +0.109 +0.150 +0.145 +0.185 -0.642 +0.005 -0.695 -0.015 +0.018 +0.024 0 0 +0.018 +0.010 +0.054 -0.005 +0.072 -0.005 +0.090 +0.015 +O0oi8 -0.005 +0.109 +0.150 -0.072 -0.025 +0.091 +0.145 +0.144 +0.039 -0.054 -0.010 +0.126 +0.039 -0.02 0 0.005 -0.553 +0.036 -0.08 0 0 +0.029 +0.039 -0.07 0.001 0.018 +0.108 +0.126 -0.08 0 0 +0.039 +0.039 -0.12 0.003 0.031 +0.221 +0.216 -0.23 0 0 +0.108 +0.111 0 0 0 -0.072 0 -0.10 0 0 +0.050 +0.050 +0.10 0.007 0 -0.090 -0.181 -0.05 0 0 +0.050 +0.025 0 0 0 -0.199 0 -0.05 0 0 +0.050 +0.025 -0.10 0.014 0.026 +0.363 +0.181 -0.10 0 0 +0.125 +0.050 -0.10 0.011 0.026 +0.327 +0.181 -0.20 0.005 0 +0.040 +0.100 Table IV. Summary of A n c i l l a r y X-Ray D i f f r a c t i o n Data VKI 3* extinction contours. Figure 31 shows annealing twins i n the same condition. The grain boundaries i n the annealed nick e l contained evidence of contamination by a grain boundary phase. This i s apparent from a com-parison of the n i c k e l boundaries i n Figures 22, 26, 27, 30 and 31 with the much cleaner boundaries i n nickel-chromium i n Figures 32, 36 and 37, although t h i s appearance i s partly due to different d i s l o c a t i o n configurations..The possible consequences of t h i s on t e n s i l e d u c t i l i t y are discussed i n Section "2 h. 3.2.2. Nickel-Chromium Figure 32 i s t y p i c a l of the As Received Ni-Cr a l l o y , showing equiaxed r e c r y s t a l l i z e d grains. Hoiifever, a low density of dislocations could be found within the grains as shown i n Figure 33. Following a cold reduction of 50%, Figures 3^(a) and (b) show adjoining f i e l d s of view with a high disl o c a t i o n density intersecting twins and an extremely fine c e l l formation. Figure 35 of the same condition indicates elongated grains and the same fine sub-structure. On subsequent annealing, an equiaxed r e c r y s t a l l i z e d grain structure was formed, with no dislocations v i s i b l e at the extinction con-tours as shown i n Figures 36 and 37, and a low dislocation density within the grains as seen in'Figures 3° and 39. 3.2.3. Nickel-ThO Figure '+0 of the As Received condition shows a high disl o c a t i o n density and evidence of a small c e l l size between dislocations. After 35 cold r o l l i n g 50% the c e l l size as seen i n Figure 'tl appears to be larger. This i s also true a f t e r cold r o l l i n g 75% as shown i n Figures 43 and 44. In the Cold Rolled 50% and Annealed condition, the general d i s l o c a t i o n density i s lower but a fine c e l l structure has been developed as evident i n Figure 42. Annealing following a cold reduction of 75% or 90% produced a very large substructure of c e l l s containing a very low density of d i s l o c a -tions. This i s shown i n Figures 45, 46, and 47. Figure 47 also i l l u s t r a t e s the rather low contrast between two adjacent grains. This was common to a l l the Ni-ThO^ materials where no t y p i c a l r e c r y s t a l l i z e d grains were found i n the annealed condition. The boundary i n Figure 47 appears to be a region of high dislocation density. Figure 48 of the Cold Rolled 90% and Annealed condition shows an agglomeration of ThO., p a r t i c l e s ; a narrow annealing twin i s also present and the dislocation density i s low. 3.2.4. Nickel-Chromium-Th0o Figure 49 of the As Received condition contains r a d i a l extinction contours running towards a penetration i n the f o i l , but there i s no evidence of a high disl o c a t i o n density. Examples of stacking fa u l t contrast can be seen. Figure 50 of the same condition shows stacking f a u l t boundaries and twins but no high disl o c a t i o n density. From these two figures, the c r y s t a l -l i t e domain size appears to be very large. Figure 51 of the material, cold r o l l e d 50% and Figure 53 as cold r o l l e d 75% both show a high dislocation density and a very small c e l l s i z e . These structures are s i m i l a r to that of the cold r o l l e d pure Ni-Cr. On annealing after 50% and 75% cold r o l l i n g a structure of large c e l l size with a low dislocation density and annealing twins was 36 developed, as shown i n Figures 52, 5^ and 55• °n annealing following 75$ cold r o l l i n g , r e c r y s t a l l i z e d grains more t y p i c a l of the pure Ni-Cr than of the other materials containing ^ hO^ were formed, as indicated i n Figure 5^. 3.3 . Optical Microscopy As discussed i n Section 2 on experimental procedures, a series of r o l l i n g and annealing cycles was investigated to produce a r e c r y s t a l l i z e d grain size not greater than 50u for the As Received condition of materials (a) and (b) i . e . , pure Ni and pure Ni-Cr. The selection of suitable fabricating cycles was based on the results of o p t i c a l metallography, the procedures of which were described e a r l i e r . Figure 56 shows the As Received grain size of the Ni s t r i p and Figure 57 that of the Ni-Cr s t r i p . Both figures indicate that the selected cycles have produced r e c r y s t a l l i z e d grains not greater than 50p,. A comparison between Figures 56 and 57 supports the previous evidence of electron microscopy that the grain boundaries i n the Ni show evidence of contamination whereas those of the Ni-Cr do not. The observa-t i o n of annealing twins i n Ni-Cr i n Figure 57 and not i n Ni i n Figure 56 i s also i n agreement vri.th the results of electron microscopy reported i n Section 3 .2 . 3.4. Tensile Tests The t e n s i l e test results are summarized i n Tables V and VI. The consistent low d u c t i l i t y i n the room temperature tests on Ni compared . to Ni-Cr was associated with a weakness due to grain boundary contamination. Evidence to support t h i s was found i n the electron microscopy results where 37 many ni c k e l t h i n f o i l s were penetrated prematurely along grain boundaries. Also electron micrographs Figures 22, 26, 27, 30 and 31 of annealed n i c k e l show less sharply defined grain boundaries than do Figures 32, 36 and 37 of annealed nickel-chromium. The same i s true of o p t i c a l micrographs Figures 56 and 57. I t was thought that sulphur contamination may have arisen during heat treatment. Consequently, broken t e n s i l e test specimens of Ni and Ni-Cr i n the cold r o l l e d 50$ and annealed condition were submitted for chemical analysis for oxygen, carbon and sulphur. The a n a l y t i c a l results are given i n Table 1(b).' The lower l e v e l of sulphur i n the Ni compared to the Ni-Cr does not help to explain the corresponding lower d u c t i l i t y , but does demonstrate that i f grain boundary sulphur was the cause of the low d u c t i l i t i e s then Ni-Cr i s not sensitive to the same contamination. Olsen, Larkin and S c h m i t t ^ ^ have reported that high purity n i c k e l containing as l i t t l e as 9 ppm sulphur can be embrittled by annealing i n the range 450-600°C after cold workings The Work Hardening Slopes i n Tables V and VI are only approxi-mate figures. They were obtained by subtracting the 0.2$ Proof Stress from the 1$ Proof Stress and dividing the result by 0.8$. They serve as a means of comparing the slopes of the various curves i n t h i s region. In general, the elevated temperature of testing f o r each material was that used for annealing so that information on the structure of the material heat treated at the t e n s i l e test temperature would be known. The exception was i n the case of the Ni-ThO,, and Ni-Cr-ThO^ materials cold r o l l e d 75$ and 90$ and annealed at ltf00°C but t e n s i l e tested at 1200°C, i . e . , Nos. 13, 15 and 20 of Table VI. Material Condition Test Temp. (°C) Proof Stress (KR. mmT2) 0.2% 1.0% U.T.S_.2 (Kg..'mm. ) % Elong. on 1.25 i n gauge Work Hardening., Slope. (Kg. mm."" / unit s t r a i n ) 1. N i , As Received R.T. 9 . 9 1 13.11 1 3 . 8 6 1.6 400 2. N i , Cold Rolled 5 0 % R.T. 6 5 . 3 9 7 1 . 9 9 7 1 * 9 9 1.4 826 3 . N i , Cold Rolled 5 0 % and Annealed R.T. 9 . 3 5 11.32 1 1 . 3 2 1.1 2 4 6 4. N i , Cold Rolled 7 5 % .R.T. 7 3 . 1 9 7 5 . 9 3 7 5 . 9 3 1.4 3 4 2 5 . N i , Cold Rolled 7 5 % and Annealed R.T. 1 1 . 5 3 1 4 . 6 9 1 5 . 6 1 1 . 7 395 6. Ni-Cr, As Received R.T. 2 0 . 6 7 2 4 . 1 2 6 2 . 8 5 5 9 . 7 431 7 . Ni-Cr, Cold Rolled 5 0 % R.T1. 9 5 . 4 8 109*33 109.33 2.0 1730 8S Ni-Cr, Cold Rolled 5 0 % and Annealed R.T. 2 9 . 3 9 3 2 . 3 4 4 6 . 8 369 9 . Ni-Th0 2, As Received R.T. 3 8 . 7 4 4 1 . 8 3 49 . 2 1 10.4 387 10. Ni-ThO , Cold Rolled 50% d R.T. 57o90 6 0 . 5 3 60.53 2.5 3 3 4 11. Ni-Th0 2, Cold Rolled 5 0 % . and Annealed R.T. 3 3 . 8 9 3 8 . 3 2 47.53 6 . 8 554 12. Ni-Th0_, Cold Rolled 7 5 % - R.T. 6 0 . 7 5 6 2 . 7 1 6 2 . 7 1 0.6 2 4 6 1 3 . Ni - T h 0 2 , Cold Rolled 7 5 % and Annealed R.T. 3 5 . 8 6 3 8 . 9 5 4 7 . 6 7 6.2 387 14. Ni-ThO , Cold Rolled 9 0 % d R.T. 7 3 . 3 3 73 . 4 7 73 . 4 7 0 . 4 18 1 5 . Ni-ThO , Cold Rolled 90% and Annealed R.T. 4 5 . 2 8 5 1 . 5 ^ 5 4 . 2 1 1.7 781 1 6 . Ni-Cr - T h 0 2 , As Received R.T. 6 6 . 7 9 74.81 9 8 . 2 9 1 7 . 6 1003 1 7 . Ni-Cr-ThO , Cold Rolled d 5 0 % R.T. 8 2 . 9 6 1 2 9 . 0 8 1 3 0 . 7 7 2.6 5765 1 8 . Ni-Cr-ThO , Cold Rolled 5 0 % and Annealed R.T. 6 8 . 2 0 79 . 8 7 9 8 . 7 8 22.0 1 4 6 2 1 9 . Ni-Cr-ThO , Cold Rolled d 7 5 % R.T. 132.53 146.24 1 4 6 . 2 4 1.6 1715 20. Ni-Cr-ThO , Cold Rolled 7 5 % and Annealed R.T. 87.53 9 0 . 3 4 1 0 2 . 0 9 8.0 352 Table V. Summary of Room Temperature T e n s i l e Test Data Material Condition Test Tempo ( ° c ) Proof Stress (Kg. nun. ) 0.2% 1.0% U . T . S . 2 (Kg.; mm. ) % Elong. on 1.25 i n gauge Work Hardening., Slope.(Kg. mm." / unit strain) 1. N i , As Received 500 3o22 6.65 10.83 16.7 430 2. N i , Cold Rolled 50% 500 4.25 5.75 10.32 32.9 187 3. N i , Cold Rolled 50% and Annealed 500 6.12 7.44 9.60 6.3 165 4. N i , Cold Rolled 75% 500 3.87 5.34 10.76 30.2 180 5. N i , Cold Rolled 75% and Annealed 500 6.55 7.84 10.69 7.4 161 6. N i - C r , As Received 850 9.00 9.82 11.71 23.4 103 7. N i - C r , Cold Rolled 50% 850 8.62 9.65 9.96 27.3 129 8. N i - C r , Cold Rolled 50% and Annealed 850 9.07 9.81 10.71 29.0 92 9. Ni-Th0 2, As Received 1200 7.30 8.26 8.26 6.2 120 10. Ni-Th0 o, Cold Rolled 50% 2 1200 5.63 8.07 8.46 4.9 305 11. Ni-ThO , Cold Rolled 50% and Annealed 1200 6.22 8.65 9.10 4.0 303 12. Ni-ThO , Cold Rolled 75% 1200 4.64 7.14 7.96 5.2 312 13. Ni-ThO , Cold Rolled 75% and Annealed 1200 5.91 7.80 8.09 2.6 238 15. Ni-ThO , Cold Rolled 90% and Annealed 1200 7.71 9.00 9.00 o.« 161 16. Ni-Cr -Th0 2 , *s Received 1200 6.28 7.70 7.70 1.5 177 17. Ni-Cr-ThO , Cold Rolled ^ 50% 1200 2.14 3.30 4.08 5.6 145 18. Ni-Cr-ThO , Cold Rolled 50% and Annealed 1200 2.92 . 3.43 3.60 5.3 64 19. Ni-Cr-ThO , Cold Rolled 75% 1200 . 2.90 3.21 3.34 8.6 38 20. Ni-Cr-ThO , Cold Rolled 75% and Annealed 1200 2.93 3.25 3.29 7.2 39 Table VI . Summary of High Temperature Tensile Test Data For n i c k e l , with a melting point of 1455°^ , the t e n s i l e test temperature of 1200°C was equal to 0.8^ 2 Tm and l400 OC was equal to O.968 Tm. For 80$ Ni-20# Cr, with a melting point of l450°C, 1200°C was equal to O.855 'fm and l400°C was equal to O.969 Tm. 4. DISCUSSION 4.1. S i g n i f i c a n c e and R e l i a b i l i t y of the X-Ray Line P r o f i l e Analyses Interp r e t a t i o n of the Figures showing l a t t i c e s t r a i n d i s t r i b u t i o n s i n the present work i s straightforward. The s t r a i n s are average values f o r a l l distances of a chosen L measured i n the t C^ OOj di r e c t i o n . Since x-rays of the i n t e n s i t y used have an e f f e c t i v e penetration of about 25]i i n Ni, t h i s i s the distance within which an average of a l l s t r a i n s i n length L i s calculated. Furthermore the s t r a i n i s measured as 2 1/2 (£ ) j / to account for both p o s i t i v e and negative s t r a i n s , and the r e s u l t i s also an average with respect to the area of specimen i r r a d i a t e d under 2 the x-ray beam which i n the present v/ork was about 2 cm. It would be expected that the average s t r a i n over a short distance would be greater than that averaged over a long distance, thus the s t r a i n d i s t r i b u t i o n should decrease continuously with in c r e a s i n g L. In a l l cases t h i s was not so for very small values of L. In t h i s range where L approaches zero the analysis i s u n r e l i a b l e and the s t r a i n graphs cannot; be interpreted. I t could be assumed that from the maximum s t r a i n values o shown at L - 50A the true average s t r a i n continues to increase i n a c o n t i -nuous manner as L decreases to zero 0 The upper l i m i t of L to which the s t r a i n d i s t r i b u t i o n s can be interpreted cannot exceed the domain s i z e . This must be so since the misorientation across the domain boundary i s such that Bragg's law i s not s a t i s f i e d and thus no d i f f r a c t e d i n t e n s i t y can be received from c r y s t a l distances greater than the domain s i z e . With t h i s l i m i t a t i o n i n mind, i t i s apparent from the s t r a i n d i s t r i b u t i o n s that the dispersion strengthened h2 m a t e r i a l s t e n d t o d e v e l o p l a t t i c e s t r a i n s o v e r l a r g e l a t t i c e d i s t a n c e s when c o l d r o l l e d . I t i s e v e n more a p p a r e n t , as s e e n i n F i g u r e 11, t h a t when c o l d r o l l e d , t h e ThC\_,-free m a t e r i a l s d e v e l o p v e r y l a r g e s t r a i n s i n a o v e r y s h o r t l a t t i c e d i s t a n c e ^ e . g . , 0,k% i n 50A, w h e r e a s t h e d i s p e r s i o n s t r e n g t h e n e d m a t e r i a l s do n o t . To i n t e r p r e t t h e d o m a i n s i z e g r a p h s due n o t e must be t a k e n o f t h e known e r r o r s i n t h e p r o c e d u r e and how t h e s e w i l l a f f e c t t h e d i s t r i -b u t i o n o f A ^ ( L ) v e r s u s ( L ) . F i r s t l y i t must be r e a l i z e d t h a t t h e r e i s a n u p p e r l i m i t t o t h e d o m a i n s i z e above w h i c h t h e c r y s t a l c a n no l o n g e r be r e g a r d e d a s i m p e r f e c t due t o s m a l l c r y s t a l s i z e i n a c h o s e n d i r e c t i o n , a n d f o r w h i c h no x - r a y l i n e b r o a d e n i n g o c c u r s . T h i s u p p e r l i m i t d e p e n d s o n t h e r e s o l u t i o n o f t h e d i f f r a c t i o n a p p a r a t u s i n t h e a b i l i t y t o m e a s u r e t h e d i f -f e r e n c e i n l i n e p r o f i l e b e t w e e n two s i m i l a r r e f l e c t i o n s . U s i n g S c h e r r e r ' s f o r m u l a C u l l i t y ^ ^ ^ c a l c u l a t e s t h a t w i t h n o r m a l e q u i p m e n t i f no l i n e b r o a -o d e n i n g c a n be d e t e c t e d t h e c r y s t a l l i t e d o m a i n s i z e i s g r e a t e r t h a n 1.000A. B r o a d e n i n g i n t h i s c a s e w o u l d be t h a t m e a s u r e d a t h a l f p e a k i n t e n s i t y . I n t h e more d e t a i l e d a n a l y s i s o f t h e p r e s e n t s t u d y a s p e c i m e n h a v i n g no b r o a d e n i n g due t o p a r t i c l e s i z e w o u l d n o t p r o d u c e d e c r e a s i n g v a l u e s o f d o m a i n s i z e c o e f f i c i e n t A ^ ( L ) f o r i n c r e a s i n g v a l u e s o f ( L ) . T h u s i n the d o m a i n s i z e g r a p h s o f S e c t i o n 3*1 a d i s t r i b u t i o n o f A ^ ( L ) v e r s u s ( L ) a s a r i s i n g f u n c t i o n g r e a t e r t h a n u n i t y i s t a k e n t o i n d i c a t e a d o m a i n s i z e g r e a t e r o t h a n 1,000A. o F o r d o m a i n s i z e s l e s s t h a n 1,000A t h e t h e o r e t i c a l a n a l y s i s o f A p p e n d i x 1 p r e d i c t s t h a t t h e d i s t r i b u t i o n o f A ^ ( L ) v e r s u s ( L ) s h o u l d t a k e t h e f o r m o f a f u n c t i o n d e c r e a s i n g f r o m u n i t y a t L = 0 a n d a l w a y s . h a v i n g p o s i t i v e c u r v a t u r e . H o w e v e r , as d i s c u s s e d i n . A p p e n d i x 1, i f t h e t r u e b a c k g r o u n d o f t h e x - r a y r e f l e c t i o n s h a s n o t b e e n m e a s u r e d a c c u r a t e l y 43 t h i s gives r i s e to a well known error commonly c a l l e d the "hook e f f e c t " which results i n convex or negative curvature i n the plot of A^(L) versus (L) near to L = 0. This region has to be ignored when taking the negative reciprocal slope of the curve to obtain the domain s i z e . In the present study d i f f i c u l t y was experienced i n measuring the true background for the ref l e c t i o n s from the dispersion strengthened materials due to the presence of ThO^ re f l e c t i o n s overlapping the t a i l s on both sides of the Ni (200) and.(400) r e f l e c t i o n s , and a considerable "hook e f f e c t " was anticipated. That t h i s proved to be the case i s evident i n Figure 6. However from the cause of the "hook e f f e c t " i t would be expected that the negative curvature would persist to L = 0 whereas Figure 6 shows a return to positive curvature for very low values of L. The v a l i d i t y of the results for very low values of L was questioned for the s t r a i n d i s t r i b u t i o n since a decreasing s t r a i n for a decreasing L was unacceptable, and the same question arises for the D 2 1/2 function A (L) versus (L). This i s so since both s t r a i n ( £ ) and- domain size c o e f f i c i e n t A^(L) come from equation (32) of Appendix 1, the former from the slope of a straight l i n e and the l a t t e r from the intercept of the same l i n e with the y-axis. Thus the region of positive curvature i n A^(L) versus (L) near to L = 0 cannot be u t i l i z e d to determine the domain s i z e . The values of domain size i n 'Table I I I were best estimates taken from the slope of A D(L) versus (L) i n the region of positive curvature at a value of L greater than that to which the negative curvature of the "hook e f f e c t " extends. A further j u s t i f i c a t i o n for t h i s approach comes from a consideration of the domain sizes involved. Again re f e r r i n g to Figure 6, o i f the i n i t i a l part of the curve for L = 0-50A were used very small domain sizes would be indicated, p a r t i c u l a r l y i n the cold r o l l e d condition where the tangent at L = 0 would intercept the x-axis at a domain size of o approximately 100A. To check the c r e d i b i l i t y of such a result we can use Scherrer's formula as given by C u l l i t y ^ ^ , B = °'9% t cos© where B i s the increase i n l i n e breadth at half peak height,, measured i n radians, t i s the c r y s t a l l i t e domain s i z e , ]\ i s the x-ray wavelength, © i s the Bragg angle. The increase i n breadth B i s related to the measured breadth B and the m unbroadened breadth of the annealed powder standard peak B g i n the form of an error curve giving, 2 2 2 IT = B - B m s Scherrer's formula i s only applicable to broadening by small domain size when l a t t i c e s t r a i n broadening i s not present. Thus i t i s not generally applicable to the present study but i s being used here as an approximate o test of the v a l i d i t y of the Fourier method. Inserting a value of t = 100A i n Scherrer's formula and using the width at hal f peak height obtained experimentally for the (200) r e f l e c t i o n from the annealed n i c k e l powder standard as the value of B gives B = 0.92°. Since Scherrer's formula s to m makes no allowance for s t r a i n broadening the above result indicates that i n the presence of non-uniform l a t t i c e s t r a i n , which was c e r t a i n l y the case o for Ni-ThO^ cold r o l l e d 50?J and 75r/°, a domain size of 100A would result i n a (200) r e f l e c t i o n with a h a l f peak breadth greater than 0.92°. In fact the ha l f peak breadth's of these two refle c t i o n s were 0.31° and 0.32° 45 respectively which supports the decision not to take the i n i t i a l slope near to L = 0 i n the graph of A^(L) versus (L) to obtain the domain s i z e . Scherrer's formula can be used to check the accuracy of certain s p e c i f i c values of domain size obtained by the Fourier method. Due to the l i m i t a t i o n s of Scherrer's formula the closest agreement should be 2 1/2 found where the x-ray analysis has indicated the l a t t i c e s t r a i n ( £ ) to be zero. A case of p a r t i c u l a r interest i s that of Ni-ThO,, cold r o l l e d 50$ and annealed since Figures 5 and 6 and Table III show that although the o l a t t i c e s t r a i n was zero the domain size was 350A. This i s different from the Ni-ThO., cold r o l l e d 75$ and 90$ and annealed since these both showed o zero l a t t i c e s t r a i n with domain sizes >1,000A. Applying Scherrer ' s formula to the (200) hal f peak breadth of Ni-Th0 2 cold r o l l e d 50$ and annealed o gave a value of domain size t = 360A, which i s a remarkably close agreement o with the value of 350A obtained from Figure 6. 2 1/2 Another case where l a t t i c e s t r a i n ( £ ) has been i n d i -cated to be zero, and where therefore Scherrer's formula should agree with the Fourier method i s that of Ni-Th0 2 cold r o l l e d 90% and annealed. Figures p ,/p ° 5 and 6 and Table III show (£ ) ' = 0 and D > 1,000A, thus the x-ray re f l e c t i o n s should show no increase i n broadening over that of the annealed powder standard. The breadth of the powder standard (200) r e f l e c t i o n at half peak height was 0.250°. The (200) r e f l e c t i o n from the•Ni-ThO cold r o l l e d 90% and annealed was at f i r s t sight an e n t i r e l y different peak being an order of magnitude greater i n in t e n s i t y due to the much fi n e r grain s i z e , but i t s breadth at half peak height measured 0.248°. Thus Scherrer's formula o would indicate a domain size greater than 1,000A i n t h i s material, i n agree-ment with the Fourier method. 46 Returning to the case of Ni-ThO^ cold r o l l e d 75$ which was used i n i t i a l l y with Scherrer's formula to test whether the observed o l i n e broadening was commensurate with a domain size of 100A, data from t h i s material have been included as a t y p i c a l set comprising Appendix 3. Thus we have available curves of the (200) r e f l e c t i o n s for the annealed powder and for Ni-ThO^ cold r o l l e d 75$ as f i n a l l y corrected for angular factors, background and doublet broadening, see Figures 5'3 and 60 of Appendix 3* Using the breadths of the monochromatic (200) r e f l e c t i o n s at half peak o height Scherrer's formula gave domain size = 4?4A for Ni-TWX, cold r o l l e d o 75$. This i s i n good agreement with the value of 460A estimated from• Figure 6. However i t must be noted that i n t h i s case l a t t i c e s t r a i n was. 2 1/2 also present, e.g.', (£ ) 0 = 0.14$ i n Table I I I , and therefore i t would ' 50A be expected that Scherrer's formula would indicate a lower value of domain size than that obtained by the Fourier method. As th i s was hot the case o the Fourier estimate of 4 6 0 A may be too low, but the domain size i s cer-o t a i n l y not 100A as would have been the result i f the i n i t i a l region of Figure 6 had been used. One further result of the Fourier analysis of domain size seemed i n need of a confirmation by Scherrer's formula. This was the case of pure Ni-Cr cold r o l l e d 50$. The x-ray method, Figure '+, indicated a domain size of 160A, the smallest of the entire s e r i e s , but t h i s was wel l supported by electron microscopy i n Figures 34 and 35. Due to the indicated presence of l a t t i c e s t r a i n , see Figure 3» t h i s case was not i d e a l l y suited to the application of Scherrer's formula. However, t h i s method indicated o o the domain size to be 220A which i s quite close to the value of 160A quoted above. As i n the previous case, the disagreement i s i n the wrong d i r e c t i o n since the presence of l a t t i c e s t r a i n should make Scherrer's formula predict a lower value of domain size than that from the Fourier method. One must o conclude that the estimate of 160A from Figure k may be too low. In certain cases the thermo-mechanical treatments would be expected to produce s i m i l a r s t r a i n d i s t r i b u t i o n s and domain sizes and the fact that t h i s was so confirms the re p r o d u c i b i l i t y of the analysis. In the case of the pure Ni, the As Received material and the As Cold Rolled 50?o and Annealed material had ess e n t i a l l y i d e n t i c a l microstructures (see Figures 20 and The close s i m i l a r i t y of the s t r a i n d i s t r i b u t i o n s i n these two conditions can be seen i n Figure 1 , and both have domain sizes > • ,P 1,000A. This s t r a i n pattern was not retained after cold r o l l i n g 75$ and annealing since complete r e c r y s t a l l i z a t i o n took place. A s i m i l a r comparison can be made betv/een the Ni-Cr As Received and As Cold Rolled 50$ and Annealed, since the As Received condi-t i o ^ constituted cold r o l l i n g followed, by annealing with the same cycle. In Figures 3 and k the s t r a i n and domain size graphs for these two material conditions are seen to be i n very close agreement. One further case where two material conditions could he expected to produce s i m i l a r s t r a i n d i s t r i b u t i o n s i s that of Ni-ThO^ cold r o l l e d 50$ and cold r o l l e d 75'$. Remembering that the As Received condition i n t h i s case i s as supplied commercially, i t i s to be expected that the material has been processed by a high deformation rate technique such as high speed extrusion to produce a structure that i s raetallurgically stable to withstand fabrication and high temperature service. Figure 5 indicates that cold r o l l i n g 50$ and 75$ from the As Received condition has increased the l a t t i c e s t r a i n within the c r y s t a l l i t e domains, but that both 50$ and if8 75% reductions have produced remarkably s i m i l a r s t r a i n d i s t r i b u t i o n s , possibly at a saturation l e v e l f o r t h i s material. V.2. C a l c u l a t i o n of D i s l o c a t i o n Densities and Configurations from  X-Ray Data (29) Williamson and Smallman have derived expressions g i v i n g the d i s l o c a t i o n density calculated from the domain s i z e as, e = 2n (Jf3) D - • • where £ i s the d i s l o c a t i o n density, n i s the number of d i s l o c a t i o n s i n each face of the c r y s t a l l i t e domain, D i s the domain s i z e . They a l s o give the d i s l o c a t i o n density c a l c u l a t e d from the s t r a i n broa-dening of the x-ray l i n e as, £ _ 6TES A$ 2 ub 2F ln(£- ) o where E i s Young's modulus, A i s a factor depending on the shape of the s t r a i n d i s -t r i b u t i o n , § i s the breadth of the s t r a i n d i s t r i b u t i o n , r / r i s the r a t i o of radius of the volume of c r y s t a l con-o t a i n i n g the d i s l o c a t i o n to the d i s l o c a t i o n core radius, which a r i s e s from the usual expression f o r d i s l o c a t i o n e n e r g y , b i s the Burgers vector of the d i s l o c a t i o n , F i s the d i s l o c a t i o n i n t e r a c t i o n f a c t o r . 49 The f a c t o r A and § can be eliminated i n favour of the mean square 2 s t r a i n of the l a t t i c e £ since Williamson and Smallman show that Thus the d i s l o c a t i o n density calculated from the l a t t i c e mean s t r a i n can be expressed as, 2 ^ — 6TIE £ Tib 2? l n ( r / r o ) Williamson and Smallman .assigned as t y p i c a l values, £ = 2 .6 , In ( r / r Q ) = 4 . ' In the present i n v e s t i g a t i o n we may take, b = 1/2 a [110J where aT= 3»523oA, the l a t t i c e parameter f o r f . c . c . Ni O .% b = 2 .5 A , F 2 . , -16 To u t i l i z e equations (43) and (44) we assign values of un i t y to n and F, thereby assuming that there i s only one d i s l o c a t i o n per domain boundary i n expression (43) and that no d i s l o c a t i o n i n t e r a c t i o n occurs i n expression (44). Williamson and Smallman used the subscripts p and s when these assumptions have been made, thus, e P = h ^) 50 £ = 2 e 2 x 10 1 6 (46) B I f i t i s found that = £ s then the assumption that n and F equal u n i t y i s correct and the d i s l o c a t i o n configuration i n the material i s random. I f (*g > ^ then a pile-up configuration i s i n d i c a t e d . Both F and n are greater than unity and F = n. S u b s t i t u t i n g equations (45) and (46), i n t o equations (4j5) and (44) r e s p e c t i v e l y , and assuming that both the p a r t i c l e s i z e model and s t r a i n model should give the same d i s l o c a t i o n density (J . we can solve f o r n as follows. n<?P = ? = es = is F n • » n e p e s V 2 = ( — ) (47) Defined o r i g i n a l l y as the number of d i s l o c a t i o n s i n each face of the domain, n i n the pile-up model i s the average number of d i s l o c a t i o n s i n a pile-up. Having obtained n, we obtain the true d i s l o c a t i o n den-s i t y from the above expression, ^ = n • P I f Q > o then a polygonized substructure i s indicated, p s The energy of each d i s l o c a t i o n i s reduced i n the polygonized array, Which i s tantamount to F having a value l e s s than unity. Since a ^ s • • 5 1 The value of (J under conditions of polygonization can be obtained from the following expression of Williamson and Smallman, 1 0 ? 5 _ 1 / I n ] <«) The above expressions enable quantitative data on dis-location densities and configurations to be obtained from x-ray dif f r a c -tion results. This approach has been applied recently to the Ag-MgO dis-(31) persion strengthened system by Klein and Huggins . Before use can be made of equation (43) the domain size D must be corrected for the contribution to line broadening of stacking fault and twin boundaries. This has been discussed i n detail i n Appendix 1. If we define, D = domain size as determined from x-ray data, F D = domain size due to twins and stacking faults, D = true substructure domain size excluding fault boundaries, then these are related as reciprocals as follows: 1_ _ 1 1_ x ~ D + F D D Appendix 1 gives = + P ) $ where ol = Stacking Fault probability, i3 = Twin Fault probability, £L = f.c.c. l a t t i c e parameter, and this expression applies specifically to the case of (200) and (400) 52 r e f l e c t i o n s i n an f . c . c . unit c e l l with f a u l t s i n the planes. Values of o{ and p were calculated f o r each material condition as des-cribed i n Section 3.1. and are given i n Table IV. As discussed i n that s e c t i o n the s h i f t s of the peak maxima f o r (200) and (400) r e f l e c t i o n s must be i n opposite d i r e c t i o n s to prove p o s i t i v e l y the presence of stacking f a u l t s , otherwise l a t t i c e macro s t r a i n may be the cause of the s h i f t , not-withstanding the more complex case of both e f f e c t s being present. Con-sequently, corrections to D f o r stacking f a u l t s were made only i n cases of p o s i t i v e i d e n t i f i c a t i o n , which were Nos. 2, 3, and 5 i n Table IV. I t i s F X not possible that D be smaller than D f o r i f i t were so then the x-ray F X F technique would measure the smaller domain s i z e D and give D = D . In t h i s case the r e l a t i o n s h i p , would give D = oo , which simply means that the substructure domain s i z e i s greater than the f a u l t domain s i z e . For materials, 2, 3» and 5 of Table IV the l a r g e r value of oi. f o r the (200) peak s h i f t was too large F X i n each case to meet the above c r i t e r i o n that D > D , p o s s i b l y due to a r e s i d u a l macro t e n s i l e s t r a i n i n the £200] d i r e c t i o n . I t was decided to use the lower values of ©<. from the (400) peak s h i f t s . The same c r i t e r i o n of p o s i t i v e i d e n t i f i c a t i o n was applied to the values of twin f a u l t p r o b a b i l i t y ft given i n Table IV. Based on equations (38) and (39) of Appendix 1 the asymmetries of the (200) and (400) r e f l e c t i o n s must be of opposite sign to prove p o s i t i v e l y the presence of twinning. Only i n one case, No. 20, Ni-Cr-Th0 2 cold r o l l e d 75% and annealed, was t h i s p o s i t i v e i d e n t i f i c a t i o n of twinning found. This r e s u l t 5 3 finds support i n Figure 55 which showed a high density of twins. Although this leaves l i t t l e doubt that some value can be assigned to J5 , unfortu-nately the values derived for Table IV are too large. The smaller of the F ° X ° two, p = 0.005, gives D = 705A, but we also have D > 1,000A, and F X this would give D smaller than D which i s not acceptable. Direct measurement on Figure 55 shows that the twin fault spacing i s approxi-F ° mately 1.0 - 2.0 cm. at 80,000X magnification, giving D = 1,250 - 2,500A, F ° or as an average, D = 1875A. This value was used i n place of jS to X correct D for material No. 20. It i s equivalent to p = 0.002. The X corrections to D to give D i n the presence of stacking faults and twins for materials 2, 3, 5? and 20 are given i n Table VII. Material No. °l p D X o (A) D 0 (A) 2 0,001 0 360 425 3 0.001 0 1,000 1,740 5 0.001 0 1,000 1,740 20 0 0.002 1,000 2,150 Table VII. Domain Sizes Corrected for Twins and Stacking Faults Using the corrected domain sizes of Table VII and other-wise the measured domain sizes from Table III equation (45) was used to calculate ^ assuming n = 1. The mean square strain values were ob-P 2 1/2 tained by squaring the values of ( £ ) Q i n Table III and these were 50A used with equation (46) to calculate ^ assuming F = 1. The d i s -location configuration was determined according to the following c r i t e r i a : 54 £ = ^ f o r Random, o y & f o r Pile-ups, ^ • p S - v f o r Polygonization 0 In the case of Pile-ups the average number of d i s l o c a t i o n s per p i l e - u p , n, was determined from equation ( 4 7 ) . These r e s u l t s appear i n Table VTIIo Williamson and Smallman point out that i n annealed metals with low r e s i d u a l s t r a i n s the estimation of p i s f a r more uncertain s than that of • This i s because the l i n e broadening due to s t r a i n • P i s then small compared to the other p r o f i l e aberrations removed i n the unfolding of the convolution of i n t e n s i t i e s . In c e r t a i n cases, zero values of p were obtained because of these errors and these were r e -placed by a value f o r an annealed metal based on a random array, i . e . , f o r F = 1 i n the s t r a i n model. Judging from values from several sources g tabulated by Williamson and Smallman the f i g u r e of 1 x 10 f o r ^ i n the f u l l y annealed condition seemed appropriate and t h i s has been ins e r t e d i n parenthesis i n Table VIII. Under conditions of pile-up, i . e . , when ^ s > ^ p * * r u e d i s l o c a t i o n density i s given by ^ = n or ^ = f 6 / F » these values of ^ have been included i n Table VIII. Under conditions of polygonization ^ > ^ s ^• n* e r a c* :'- o n f a c t o r F < 1. D i s l o c a t i o n density i s given by ^ = ^ S //p and i t can be seen that the logarithmic factors i n equation ( 4 8 ) are equivalent to ~. In-spection of equation ( 4 8 ) shows that F decreases as ^ increases and as D increases. Hence a minimum value to F would a r i s e from maximum values 12 -3 of ^ and D. Taking these maxima to be (> = 10 cm.cm. and Material Condition D(A) u .3 (cm.cm, ) uh1? 50A XlOO e s —3 (cm.cm. ) n (cm.cm. ) Configuration 1. Ni, As Received 1,000 3 x 1 0 1 0 0.38 2.9 x 1 0 n 3.1 9.3 x IO 1 0 Pile-up 2. Ni, CR 50$ 425 1.7 x IO 1 1 0.37 2.7 x 1 0 n 1.3 2.2 x IO 1 1 Pile-up/Random 3. Ni, CR 50% + Ann. 1,740 1 x IO 1 0 0.36 2.6 x IO 1 1 5.1 5.1 x IO 1 0 Pile-up 4. Ni, CR 75$ 400 1.9 x IO 1 1 0.44 3.9 x IO 1 1 1.4 11 2.7 x 1 0 x x Pile-up/Random 5. Ni, CR 75$ + Ann. 1,740 1 x IO 1 0 0.05 5 x IO 9 Polyg./Random 6. Ni-Cr, As Received 1,000 3 x l 0 1 0 0.10 2 x IO 1 0 Polyg./Random .7. Ni-Cr, CR 50$ 160 12 1.2 X 10 X 0.46 4.2 x IO1 1 Polyg. 80 Ni-Cr, CR 50$ + Ann, 1,000 3 x IO 1 0 0.11 2.4 x IO 1 0 Polyg./Random 9. Ni-Th02, As Received 380 2.1 x IO 1 1 0.07 9.8 x IO9 Polyg. 10. Ni-Th02, CR 50$ 700 6.1 x IO 1 0 0.14 3.9 x IO 1 0 Polyg./Random 11, Ni-Th02, CR 50$ + Ann, 350 2.5 x IO 1 1 0 (io y) Highly Polyg. 12. Ni-Th02, CR 75$ 460 1.4 x IO 1 1 0.14 3.9 x IO 1 0 Polyg./Random 13. Ni-ThO?,CR 75$ + Ann, 1,000 3 x IO 1 0 0 (10 s) Highly Polyg. 15. Ni-Th02,CR 90$ + Ann. 1,000 3 x IO 1 0 0 (10°) Highly Polyg. '•: 16. Ni-Cr-Th02, As Rec'd. 500-1,000 3 x IO1 0 - 1 . 2 x 10 J" L 0 (IO8) Highly Polyg. 17. N*~Cr-ThOp, CR 50$ . 370 4.1 x l.O11 .0.21 8.8 x IO 1 0 - t i •» Polyg./Random * i f * ,* * 18. Nd-Cr-ThO , GR 50$' *• Ann. H -»500-1,000 T 3 x l Q ' • > ' i n --1.2 x 10 i J - 0.09 1.6 x 1 0 A W - - • r Polyg./Random 19. Ni-Cr-Th02l CR 75$ 1, 180 9.3 x IO 1 1 0.32 2.1 x IO 1 1 Polyg./Random 20. Ni-Cr-Th0 2, CR 75$ + Ann, 1 12,150 6.5 X IO 9 0.23 1.1 x IO 1 1 4.0 2.6 x IO 1 0 Pile-up Table VIII. Dislocation Densities and Configurations 56 D = 2 x 10 cm. gives F - 0.2 f o r a minimum value. Therefore under condi-t i o n s of polygonization the maximum value that £ could take would be approximately 5 P • This l i m i t a t i o n would suggest that the values f o r 0 i n the polygonized configurations i n Table VIII are too low. However, the values of ^ ^ are thought to be more r e l i a b l e . The values of £ ^ and £ g f o r the polygonized configurations cannot be analyzed by equation (48) to give values of ^ , presumably because of errors i n £ g . I f a value of £ =• >^ i s i n s e r t e d i n t o the logarithmic expression f o r |j i n equation (48) i t i s found that independent of the value of D the expression f o r F takes the form, ln(x) F = ln(x/2) which w i l l be greater than unity. A value of F greater than unity i n d i c a t e s a pile-up configuration whereas F must be l e s s than unity i n the case of polygonization. Hence i t can be concluded from equation (48) that i n poly-gonized configurations the d i s l o c a t i o n density ^ w i l l be not only greater than £ s but also greater than ^ ^. Thus i n Table VIII the d i s l o c a t i o n d e n s i t i e s under conditions of polygonization can be assumed to be greater than the values given f o r ^ ^. Although the corresponding values of £ g are thought to be low they nevertheless can be taken to serve i n the general r e l a t i o n s h i p ^ ^ ^ g to i n d i c a t e a polygonized configuration. 4.3» C o r r e l a t i o n of X-Ray Data and Electron Microscopy The x-ray r e s u l t s f o r the cold r o l l e d n i c k e l are compatible with the e l e c t r o n micrographs showing a high d i s l o c a t i o n density and a small domain s i z e . The f u l l y r e c r y s t a l l i z e d material as cold r o l l e d 75% and annealed, Figures 30 and 31, has the lowest d i s l o c a t i o n density. The large 57 value f o r n i n Table VIII f o r Ni As Received and f o r Ni CR 50% + Ann. i s thought to be a r e s u l t of the p a r t i a l r e c r y s t a l l i z a t i o n as evidenced i n the electron micrographs. In the cold worked state the domain s i z e i s small and during the ea r l y stages of r e c r y s t a l l i z a t i o n these boundaries must migrate to form the l a r g e r domains as indic a t e d by Nos. 2 and 3 of Table VIII. In the condition of materials 1 and 3 the d i s l o c a t i o n density has been reduced below that of the cold worked st a t e , (No. 2), by t h i s i n i t i a l r e c r y s t a l l i z a t i o n process, and the domains have grown, but the number of d i s l o c a t i o n s i n each domain boundary i s now greater. This number i s n which i s 3-5 i n the cases mentioned. This would i n d i c a t e a high energy mobile boundary. Conversely the fac t that there are fewer d i s l o c a -tions per pile-up a f t e r cold working, Nos. 2 and k, i s at f i r s t misleading but t h i s i s because the domain s i z e has been reduced, thereby reducing the number of d i s l o c a t i o n s per unit area of domain surface. This e f f e c t of cold r o l l i n g producing a more random d i s l o c a -t i o n d i s t r i b u t i o n due to reduction i n the domain s i z e , i s c a r r i e d a step further i n the case of the s o l i d s o l u t i o n a l l o y Ni-Cr. In t h i s case (No. 7) the domain s i z e i s so f i n e that the d i s l o c a t i o n configuration has gone beyond random to polygonized with F < 1. Nevertheless the l a t t i c e s t r a i n energy and consequently (J are the highest values i n Table VIII. E l e c t r o n micrographs indi c a t e d a high d i s l o c a t i o n density and a small domain s i z e i n the cold worked s t a t e , see Figures 3^ and 35« On annealing the domain s i z e grew and the d i s l o c a t i o n density was reduced, taking on an almost random array. The dispersion strengthened Ni-ThO^ materials have e n t i r e l y d i f f e r e n t d i s l o c a t i o n configurations. From Table VIII i t i s apparent that 58 polygonized substructures predominate i n these materials. It has been suggested by Klein and H u g g i n s ^ ^ and by Brimhall and Huggins^ 2 ^ that the dispersoid particles act as sources of dislocations leading to the activation of many s l i p systems during deformation. It must be remembered that i n the present study the As Received condition for Ni-ThO^ and Ni-Cr-ThO., was that as supplied commercially and i t i s known that the materials had received considerable amounts of prior deformation and heat treatment. Brimhall and Huggins suggest that the par t ic les , besides acting as dislocation sources also act as barriers to long range dislocation motion which prevents c e l l formation during i n i t i a l deformation. In the case of the commercial dispersion strengthened materials this i n i t i a l stage has been exceeded i n the As Received condition and a polygonized structure i s i n d i -cated i n Table VIII. The result of further cold r o l l i n g i s to increase the dislocation density and to reduce the degree of polygonization as shown i n Nos. 10 and 12 of Table VIII . However electron micrographs Figures 41, 43, and kk indicate a well developed c e l l structure to be present i n the o o cold rol led condition. This i s supported by domain sizes of 700A and 460A i n Table VIII . Klein and Huggins working with Ag-MgO found evidence that a substructure was developed as a direct result of plastic deformation without the need for further annealing. Some support for this comes from the present work i n which Ni-ThOg CR 75% (No. 12) showed a greater degree of polygonization than did Ni-ThO^ CR 50% (No. 10). However there i s no doubt that a highly polygonized substructure developed when the cold rol led Ni-ThO^ materials were subsequently annealed. This i s shown i n Figures 45, 46, and 47. Brimhall and Huggins reported that the c e l l structure formed i n dispersion hardened alloys i s characterized by less misorientation across 59 the boundaries than i s the case i n s imilarly deformed pure materials. The present electron micrographs lend support to this view since typical re -crystal l ized grains were never observed i n the Ni-ThOg materials, instead the typical boundary was that shown i n Figure 47. Brimhall and Huggins suggested that this low misorientation i s the result of the operation of many different s l i p systems with no congregation of large numbers of d i s -locations of predominantly one sign. They concluded that i t i s this loca l concentration of dislocations of one sign which results i n s l i p bands and deformation textures i n pure materials. The s t a b i l i t y of the polygonized substructure i n Ni-ThC^ i s thought to arise partly due to the pinning action of ThCX, particles i n the domain boundaries and partly due to the absence of a high degree of la t t i ce s train i n localized regions ( s l ip bands) since the la t ter would promote boundary migration and recrysta l l izat ion . The formation of the substructure i n the f i r s t place arises partly during deformation because the operation of multiple s l i p systems prevents the formation of high energy boundaries, but more so during annealing since the c e l l boundaries cannot migrate freely to carry out the process of recrystal l izat ion and a polygonized substructure i s formed as an alternative. The substructure should withstand both defor-mation and annealing treatments. The Ni-Cr-ThCXj material, according to Table VIII, possessed the desired polygonized structure i n the As Received condition. This indication was supported by Figures 49 and 50. However i n a l l other condi-tions the polygonized structure could neither be preserved nor developed. Table VIII indicates a dislocation configuration between polygonized and 60 random f o r the cold, r o l l e d 50$ and 75$ conditions (Nos. 17 and 19) and f o r the cold r o l l e d 50$ and annealed material (No. 18). Material No. 20, CR 75$ + Ann. showed the complete l o s s of the o r i g i n a l polygonized structure r e s u l t i n g i n a pile-up configuration. In Table VIII there i s a s i m i l a r i t y between t h i s material and pure n i c k e l materials Nos. 1 and 3 which i t has been suggested were i n the p a r t l y r e c r y s t a l l i z e d condition, the domains o having grown to 1,000-2,000A and the boundaries being of r e l a t i v e l y high energy containing 3-5 d i s l o c a t i o n s . Figure 54 supports t h i s view showing a structure much more l i k e those of r e c r y s t a l l i z e d pure Ni and Ni-Cr than l i k e the other materials containing ThO,,. The behaviour of the Ni^Cr-Th0 2 under deformation was s i m i l a r to that of the pure Ni-Cr rather than the Ni-Th0 2; very high l o c a l i z e d l a t t i c e s t r a i n s were developed and a very small cold r o l l e d domain s i z e . In Table VIII compare Nos. 17 and 19 with No. 7., and compare Figures 51 and 53 with Figures 34 and 35» Although the presence of ThO^ p a r t i c l e s should promote the formation of a polygonized substructure, the presence of l o c a l i z e d regions of high l a t t i c e s t r a i n , found i n cold r o l l e d Ni-Cr-Th0 2 but not i n cold r o l l e d Ni-ThOg, would favour r e c r y s t a l l i z a -t i o n to a high angle grain boundary configuration. As seen i n Table VIII, a f t e r 50$ c o l d r o l l i n g the l o c a l i z e d l a t t i c e s t r a i n i n Ni-Cr-Th0 2 was 0.21$ which was not as great as the values found i n the cold r o l l e d Ni and Ni-Cr, 0.3-0.4$, which r e c r y s t a l l i z e d on annealing. However a f t e r 75$ reduction the Ni-Cr-Th0 2 showed a l o c a l i z e d l a t t i c e s t r a i n of 0.32$ and upon annealing i t p a r t i a l l y r e c r y s t a l l i z e d . In view of the much higher annealing tempera-ture used f o r the Ni-Cr=Th0 2 (1200°C and 1400°C) compared to the pure Ni-Cr (850°C) the former material has demonstrated considerable s t r u c t u r a l s t a b i l i t y , but not equal to that of the Ni-Th0 2, due i t i s thought to the d i f f e r e n t l a t t i c e s t r a i n d i s t r i b u t i o n . 61 The absence of localized regions of high la t t i ce strain i n Ni-ThC^ has been attributed to the operation of multiple s l i p systems during deformation. The failure of this argument to apply completely to the Ni-Cr-ThC^ system possibly l i e s i n the influence of Cr on the stacking fault energy of N i . Since Cr i s known to reduce the stacking fault energy (62) of Ni cross-s l ip w i l l be more d i f f i c u l t i n Ni-Cr than i n Ni resulting i n a greater tendency to form localized dislocation bands i n the former material. This view i s supported by Table VIII which shows that after 50$ cold r o l l i n g the localized la t t i ce strain i n Ni was 0.37$ whereas i n Ni-Cr i t was 0.46$. This resistance to cross-s l ip i n Ni-Cr w i l l negate i n part the advantages of the multiple s l i p generated by the dispersoid i n Ni-Cr-ThO. thus permitting localized strains to develop, e . g . , 0.21$ after 50$ cold r o l l i n g and 0.32$ after 75$ cold r o l l i n g for Nos. 17 and 19 i n Table VIII . This argument finds support i n the electron micrographs of Ni-Cr and N i - C r - T M ^ showing the presence of twins and stacking faults , see Figures 34, 35, 49, 50, 52, and 55. The anci l lary x-ray data of Table IV confirmed the presence of twins i n Ni-Cr-ThOg cold rol led 75$ and annealed but the presence of stacking faults was not confirmed. It i s suggested that this lack of agreement between the electron microscopy and the anci l lary x-ray data may arise from the choice of origin (26q) as a standard for an annealed 80$ N i - 20$ Cr al loy free of stacking faul ts . The value coming from the (27) data of Bechtoldt and Vacher was used but i f this or the diffractometer that was used contains even a very small error the x-ray peak shif ts from which the stacking fault parameters t>C were calculated w i l l contain very large errors. Since the twin fault parameter (3 comes from the peak asymmetry i t would not be affected at a l l by an error i n the value of (28Q) 62 of the standard, thus the x-ray data could be correct f or £ and i n e r r o r f o r o< . The evidence of the electron microscopy showing the presence of twins and stacking f a u l t s i n the Ni-Cr and Ni-Cr-ThC^ materials i s favoured over the contradictory values f o r ©< i n Table IV. 4.4. L a t t i c e Residual Macro S t r a i n The a n c i l l a r y data i n Table IV include values of l a t t i c e macro s t r a i n . As discussed i n Section 3.1 the l a t t i c e s t r a i n should be measured from the s h i f t of the peak centroid but i n the present work the centroid p o s i t i o n s were i n more doubt than the maxima posit i o n s because of unc e r t a i n t i e s a r i s i n g from overlapping peaks. Before accepting the macro s t r a i n values of Table IV the following c r i t e r i a were applied. F i r s t l y , the displacements of the (200) and (400) r e f l e c t i o n s must be of the same s i g n . Secondly, i n the absence of severe asymmetry due to twinning the d i s p l a c e -ments of the centroid and peak maximum should agree i n s i g n . T h i r d l y , since the d i f f e r e n t i a l of Bragg's Law i n d i c a t e s that f = - cot 0. $6, the d i s -placements of the higher angle (400) r e f l e c t i o n s should be used f o r greater accuracy. Applying these c r i t e r i a the values of Table IX were selected from Table IV. Table IX. L a t t i c e Residual Macro S t r a i n Material Residual Macro S t r a i n (%) 1. N i , As Received + 0.01 4 . N i , CR 7 5 % + 0.02 6 . Ni-Cr, As Received + 0 . 1 5 8 . Ni-Cr, CR 50% + Ann. + 0.12 10o Ni-Th0?, CR 5 0 % - 0.01 11. Ni-ThO^, CR 5 0 % + Ann. + 0.02 13. Ni-ThO^, CR 7 5 % + Ann. + 0.04 1 5 . Ni-ThO^, CR 9 0 % + Ann. + 0.11 19. Ni-Cr-ThO-, CR 7 5 % + 0 . 0 5 20. Ni-Cr-Th0|, CR 7 5 % + Ann. + 0.0** 63 As discussed i n connection with the estimation of stacking fault probability from peak s h i f t , i n the case of the Ni-Cr materials peak shif ts may be i n error due to the choice of origin as a standard for zero peak s h i f t . Consequently the values i n Table IX for Ni-Cr materials may also be i n error. The values given for Ni-ThC^ have a consistency which suggests that i n the annealed condition the material shows a residual l a t -t ice macro strain which increases with the amount of cold r o l l i n g prior to annealing. This i s a tensile strain i n the Q 2 0 0 J direction perpendicular to the surface of the sheet. (34) Greenough has reviewed the work on the determination of macro strain from x-ray l ine shif t and reported i n the case of mild steel 2 with a yield stress of 17 tons/ in . that after removal of the tensile stress 2 of 2 6 tons/ in . a residual la t t i ce expansion (positive strain) of 0 . 0 7 $ was observed i n the direction perpendicular to the applied tensile stress, and similarly a residual la t t i ce contraction of 0.06% was observed i n the direction perpendicular to an applied compressive stress of 3 2 tons / in . when the stress was removed. The magnitudes and directions of these macro strains are i n agreement with those observed i n N i - T W ^ except that the la t ter strains were recorded after annealing. Greenough states that although residual la t t i ce s train arises from some form of locked up stress due to non-uniform yielding of local regions i n the crystal , calculations show that the intergranular surface forces usually cited would not be large enough to account for more than one sixth of the observed la t t i ce parameter changes. Other factors contributing to non-uniform yielding are suggested as regions of high dislocation density, grain boundaries and crystal orien-tation effects . If this i s so then i t i s possible that dispersion strengthened 64 materials may behave d i f f e r e n t l y from pure metals with regard to r e s i d u a l l a t t i c e macro strain,, 4.5. T e n s i l e Strength 4.5.1. Room Temperature Properties 4.5.1.1. Nickel From Table V we see that the average room temperature 0.2$ Y.S. of the n i c k e l As Received and i n the two annealed conditions was 10.3 —2 —2 Kg.mm. and the average 1$ Y.S. was 13.0 Kg.mra. . The same grade of n i c k e l as that used i n the present work but supplied i n the form of s t r i p would have a t y p i c a l 0.2% Y.S. according to s p e c i f i c a t i o n ^ " ^ of 9.1 Kg.mm."2 i n the annealed condition. The 10^ higher y i e l d s t r e s s observed i n the present work may be the r e s u l t of trace impurities encountered i n the manufacture, since a s l i g h t l y l e s s pure grade of n i c k e l from the same su p p l i e r has a s p e c i f i e d ^ " ^ minimum 0.2$ Y.S. of 10.5 Kg.mm.""2 and a t y p i c a l value of _2 10.5-21 Kg.mm. i n the annealed condition. A l t e r n a t i v e l y the annealed Ni i n the present programme may possess a strengthening increment due to retained substructure following the rather low annealing temperature of 500°C (0.45 Tm.). Parker and H a z l e t t ^ ^ have studied substructure strength-ening i n pure n i c k e l and to develop various amounts of substructure they used an annealing treatment of 1 hr. at 800°C following p r i o r s t r a i n i n g i n tension of 1, 2, 3, and 6%, They defined an "index of density of sub-boundaries" determined by x-ray examination and showed that the index increased with the amount of s t r a i n p r i o r to annealing at 800°C and that the room temperature 0.25$ Y.S. increased proportionately a l s o . The increase —2 following only 2% p r i o r s t r a i n was approximately 5.000 p . s . i . (3.5. Kg.mm. ) which was regarded as very large since the ad d i t i o n of 1$ T i , a notably 65 potent alloying element i n nickel , raised the 0.25% Y.S. by 4,000 p . s . i . (2.8 Kg.mm. ). Parker and Hazlett assumed that as the substructure boundaries were formed by plastic flow and heating i t was reasonable to assume that they were dislocation boundaries. They referred to. Gottrel l who showed theoretically that such a dislocation wall was a barrier to moving dislocations. Although the amounts of deformation used i n the present work, 50% and 75%, were larger than the 1-6% used by Parker and Hazlett, the d i s -location configurations of Table VIII lend support to the view that the nickel annealed after cold r o l l i n g 75% may be strengthened by substructure. Microscopically i t appeared to be more recrystall ized than the As Received nickel or that annealed after 50% cold r o l l i n g , compare Figures 30 and 31 with Figures 20-22 and 25-27. However Table VIII indicates that the nickel annealed after 75% reduction (No. 5) had a more polygonized dislocation con-figuration than did the other annealed nickel materials, and this same material although f u l l y recrystal l ized, had the highest strength (0.2% Y . S . , 1% Y.S. and U.T .S . ) of the three annealed conditions. It i s f e l t that this benefit from polygonization with regard to room temperature strength i s important only when the materials i n question have the same approximate domain s ize , which was the case for the three annealed nickel samples. It does not negate the much greater strength of the cold rol led nickel which, whilst not having a polygonized substructure, did have a fine domain or c e l l size and a very high Y.S. These two materials, Nos. 2 and 4, showed a decreasing domain size with an increasing amount of cold r o l l i n g and an increasing 0.2% and 1% Y.S. with decreasing domain size , see Tables V and VIII. This correlation between domain size and room temperature strength 66 i s good throughout a l l four material compositions, taken both separately and together, and the o v e r a l l c o r r e l a t i o n w i l l be made subsequently* In -2 -2 general i t i s f e l t that the average values of 10 Kg.mm, and 13 Kg.mm. obtained i n t h i s study f o r the room temperature 0.2$ and 1$ Y.S. of annealed pure n i c k e l are r e l i a b l e standards against which to compare the strengths of the other materials. The observed room temperature t e n s i l e d u c t i l i t i e s f o r annealed n i c k e l were extremely low, i . e . , 1-2$ elongation to fra c t u r e , and were no greater than those of the he a v i l y cold r o l l e d materials. Evidence was given i n Sections 3.2 and 3*3 to show the presence of a grain boundary phase i n the annealed n i c k e l samples and reference was made to the work of Olsen, Larkin and Schmitt who showed that as l i t t l e as 0.0009$ sulphur by weight could cause grain boundary embrittlement i f cold work was followed by heat t r e a t i n g i n the range 450-600°C. Annealing of the n i c k e l i n the present work was c a r r i e d out at 500°C to obtain a very f i n e g rain s i z e f o r x-ray analysis and Table 1(b) of Section 2.1 shows that 0.0025$S was present. ( S u r p r i s i n g l y the suppliers of the same grade of n i c k e l i n s t r i p form i n d i c a t e that annealing can be c a r r i e d out i n the range 450-550°C depending on the degree of p r i o r cold work and quote 45$ as the t y p i c a l t e n s i l e (35) elongation f o r annealed s t r i p ). 4.5.1.2. Nickel-Chromium The r e s u l t s of Table V show that f o r the two annealed samples the Ni-Cr has the following average properties, 0.2$ Y.S. = 25 Kg.mm."2 1$ Y.S. = 28 Kgomra." 2 U.T.S. = 68 Kg.mm."2 6 7 Elongation to fracture = 53$ on 1.25 i n . The above referenced work of Parker and Hazlett also reports the e f f e c t of a l l o y i n g elements on the flow s t r e s s of n i c k e l but does not cover the effect, of chromium s p e c i f i c a l l y . They studied additions of up to 1% T i , 10% Fe, 10% Cu and 20% Co separately i n n i c k e l and found that the order of incre a s i n g effectiveness i n r a i s i n g the flow s t r e s s was Co, Cu, Fe, T i . Bearing i n mind the r e l a t i o n s h i p of Cr to the elements tested with regard to the periodic c l a s s i f i c a t i o n , atomic r a d i i and electrode p o t e n t i a l , i t i s reasonable to conclude that additions of Cr would strengthen Ni more so than does Fe but l e s s so than does T i . Extrapolation of Parker's r e s u l t s f o r Fe in d i c a t e s that an addition of 20% would r a i s e the 0,2% Y.S. of N i at room temperature by approximately 8.5 Kg.mm. . The r e s u l t s f o r T i can-not be extrapolated r e l i a b l y since they go only to 1% but the strengthening e f f e c t was very much greater than that of Fe. In the previous section the average 0.2$ Y.S. f o r annealed -2 -2 N i was 10 Kg.mm. and f o r annealed Ni-Cr the average was 25 Kg.mm. . The Ni and Ni-Cr materials were prepared from the same n i c k e l stock using 99.99% chromium flake and w i l l be of comparable p u r i t i e s . I t i s not thought that substructure e f f e c t s could be contributing to the increase i n strength over that of n i c k e l since Table VIII shows s i m i l a r domain s i z e s and d i s -l o c a t i o n configurations i n the two cases and i t i s concluded that the observed 15 Kg.mm. i s the true increase i n the room temperature 0»2% Y.S. of Ni due to the s o l i d s o l u t i o n a l l o y i n g of 20$ Cr. It i s f e l t that t h i s increment i s i n good agreement with the r e s u l t s of Parker and H a z l e t t . In contrast to the Ni samples the Ni-Cr materials showed excellent room temperature t e n s i l e d u c t i l i t i e s . I f t h i s i s due to the 68 apparent absence of a grain boundary sulphide, i t may arise from the use of a higher annealing temperature (850°C) which was outside the c r i t i c a l range o cited by Olsen et a l . (450-600C), but more probably i t arises from a lack of susceptibil i ty of the 80% Ni-20% Cr alloy to this phenomenon. The high tensile d u c t i l i t y of the Ni-Cr material i s also an expected result of the increased work hardening rate of the s o l i d solution a l loy . In the tensile test a high work hardening rate prevents the onset of necking and results i n overall larger elongations. The approximate work hardening slopes i n Table V show generally greater values for Ni-Cr than for Ni i n the same condition. The origin of this increase can be found by con-sidering the effect of cross-sl ip on work hardening. Common to most models of work hardening i n f . c . c . crystals i s the reduction i n work hardening rate (39) when barriers to dislocation motion can be by-passed. Seeger proposed that this occurs by c ross -s l ip . In the case of chromium additions to nickel (62) i t has been shown that the stacking fault energy would be reduced . Thus the p o s s i b i l i t y of cross-sl ip would be reduced and the work hardening rate increased. Seeger also proposed an alternative model i n which the strain f i e l d s around solute atoms render cross-sl ip more d i f f i c u l t and thereby increase the work-hardening rate. In the present work only one cold rol led condition was studied i n the Ni-Cr composition, i . e . , No. 7« This material had a very high 1% -2 ° Y.S. of 109 Kg.mm. (Table V) and a very small domain size of 160A (Table VIII) . These values are i n keeping with the results for Ni and show a relationship between a high room temperature strength and a small domain o s ize . The annealed samples, Nos. 6 and 8, with domain sizes > 1,000A and —2 (37) an average 1% Y.S. of 28 Kg.mm."" also f i t the pattern. Parker and Hazlett 69 have stated that substructure strengthening occurs i n a d d i t i o n to s o l i d s o l u t i o n strengthening and the two e f f e c t s are a d d i t i v e . In the case of annealed Ni and Ni-Cr, Nos. 1, 3, 5. 6, and 8, there was l i t t l e or no sub-structure present and the r e s u l t s neither prove nor disprove the above argument. In the case of the cold r o l l e d materials, Nos. 2, 4, and 7% the o o Ni-Cr had a much f i n e r domain s i z e (160A) than d i d the n i c k e l (400-425A) and had a higher 1% Y.S., 109 Kg.mm. compared to an average of 74.7 -2 Kg.mm. f o r N i . Thus v/ithout further r e s u l t s to show a c o r r e l a t i o n i t i s not possible to say whether or not the high room temperature strength of c o l d . r o l l e d Ni-Cr i s a function of small domain s i z e only or whether s o l i d s o l u t i o n strengthening i s also present. From the models proposed f o r s o l i d (4) (30) (40) so l u t i o n strengthening * ' , i t would be expected that the s o l u t i o n increment would be present i n a d d i t i o n to the strengthening of a fi n e sub-st r u c t u r e . 4.5.1.3. Nickel-Th0 2 In the present study the Ni and Ni-Th0 2 materials were of comparable p u r i t y and i t should be possible to obtain from the r e s u l t s an i n d i c a t i o n of the strengthening increment due to the presence of the t h o r i a . —2 Taking from Table V the average value of 13 Kg.mm. f o r 1% Y.S. f o r —2 annealed n i c k e l and 43 Kg.mm. f o r annealed Ni-Th0 2 we have a value of —2 (8) 30 Kg.mm."" f o r the strengthening increment, von Heimendahl and Thomas working with the same commercially a v a i l a b l e Ni-2$ Th0 2 a l l o y determined experimentally the mean planar i n t e r p a r t i c l e spacing and the mean p a r t i c l e radius to enable them to ca l c u l a t e the increase i n c r i t i c a l resolved shear st r e s s using the Orowan r e l a t i o n s h i p given i n Section 1. Their r e s u l t s were as follows: 70 o Mean planar i n t e r p a r t i c l e spacing = 2,800A o Average p a r t i c l e diameter = 393A They assumed a value of 7 x 103 Kg.mm."2 f o r the shear modulus of the -7 "2 matrix, 2.5 x 10 mm. f o r the Burgers vector, 0.7 Kg.mm. f o r the i n i t i a l y i e l d s t r e s s of the matrix and a value f o r Poisson's r a t i o such that the constant 0 had the value 1.25. Using Orowan's r e l a t i o n s h i p these values predict an increase i n the c r i t i c a l resolved shear st r e s s of 9»3 Kg.mm. . By considering only the increase i n y i e l d s t r e s s rather than the t o t a l s t r e s s we avoid the disagreement over the value of the i n i t i a l y i e l d s t r e s s of the matrix which was higher i n the present work than the f i g u r e used by von Heimendahl and Thomas. They then doubled the c r i t i c a l resolved shear s t r e s s to obtain the appropriate t e n s i l e s t r e s s , g i v i n g an increment i n the y i e l d s t r e s s of 18.6 Kg.mm. due to the Orowan mechanism. In t h e i r work they observed an increment of y i e l d s t r e s s i n the N i - T h ^ about 50% greater than t h i s , although t h i s was reported i n terms of the t o t a l observed y i e l d s t r e s s being about 50% greater than predicted. They associated t h i s beha-vio u r with an a d d i t i o n a l strengthening con t r i b u t i o n due to gra i n boundaries, twin boundaries and e f f e c t s associated with preferred o r i e n t a t i o n . The increment i n 0.1% Y.S. observed by von Heimendahl and Thomas i n annealed —2 —2 Ni-Th02 was approximately 28 Kg.mm. compared to the value of 30 Kg.mm." i n the present work based on the 1% Y.S. The c o r r e l a t i o n between y i e l d s t r e s s and domain s i z e i s not as good f o r the Ni-ThOg r e s u l t s as i t i s f o r the pure materials. Cold r o l l i n g d i d not appear to cause a decrease i n the domain s i z e of Ni-ThC^ as i t d i d i n the pure N i materials Nos. 2 and 4, yet the cold r o l l e d materials Nos. 10 and 12 had the highest room temperature y i e l d strengths of the 71 Ni-ThCv, s e r i e s . Presumably work hardening i n the Ni-ThC^, materials during col d r o l l i n g has proceeded p a r t l y by a d i s l o c a t i o n m u l t i p l i c a t i o n process r e s u l t i n g i n the observed higher y i e l d s t r e s s without ne c e s s a r i l y the smallest domain s i z e s . I t i s thought that the secondary s l i p model proposed (ifl) by Ashby could account f o r the observed behaviour. In t h i s model Ashby f i r s t proposes that d i s l o c a t i o n loops are formed around p a r t i c l e s by the bowing of d i s l o c a t i o n s between p a r t i c l e s as i n the Orowan model. The r e s u l t i n g large stresses i n and around the p a r t i c l e s are r e l i e v e d by p l a s t i c r e l a x a t i o n i n the matrix. This r e s u l t s i n the nucleation of secondary g l i d e loops and prismatic loops which i n general i n t e r s e c t the primary s l i p plane f i l l i n g the volume between p a r t i c l e s with secondary d i s l o c a t i o n s . These secondary d i s l o c a t i o n s act as a forest impeding the movement of primary g l i d e d i s l o c a t i o n s . Thus i n Ashby's model we have the concept of a d i s l o c a -t i o n forest i n t e r s e c t i n g a g l i d e plane but not c o n s t i t u t i n g an i n t e r s e c t i n g domain boundary, since the g l i d e d i s l o c a t i o n i s presumed to i n t e r s e c t the f o r e s t and continue on i n the same g l i d e plane, which would not be the case i f i t i n t e r s e c t e d a d i s l o c a t i o n substructure boundary. The model of William-(29) son and Smallman used i n Section 4.2. presupposes that a l l d i s l o c a t i o n s are i n substructure boundaries. The model permits the d i s l o c a t i o n con-f i g u r a t i o n to vary from piled-up to polygonized but nevertheless assumes the array to constitute a substructure boundary. From the present work i t i s f e l t that the model of Williamson and Smallman i s an o v e r s i m p l i f i c a t i o n since the r e s u l t s obtained on Ni-ThOg showed a pronounced work hardening without a corresponding reduction i n domain s i z e . The model of Ashby could account f o r the observed r e s u l t s . In the x-ray analysis the l a t t i c e s t r a i n and the domain s i z e are both measured i n the [100] d i r e c t i o n . Thus i n terms of d i s l o c a t i o n configurations i t i s the component of the Burgers 72 vector i n the ClOO] d i r e c t i o n that constitutes the s t r a i n measured i n the x-ray a n a l y s i s . Presumably i n the model of Williamson and Smallman these d i s l o c a t i o n s l i e i n walls that are generally p a r a l l e l to the £100^] d i r e c t i o n since those i n the (100) planes would constitute domain boundaries and l i m i t s of e x t i n c t i o n , but the x-ray analysis does not require t h i s to be so. I t seems more probable that a coherently d i f f r a c t i n g domain can contain within i t s e l f s t r a i n due to d i s l o c a t i o n s having Burgers vectors l a r g e l y i n the £100^) d i r e c t i o n . In the case of the domain s i z e measured by the x-ray a n a l y s i s , we obtain simply the extent of coherent c r y s t a l measured i n the CKWjf d i r e c t i o n . Having corrected f o r twins and stacking f a u l t s the remaining concept of a domain boundary i s that of a normal high angle grain boundary or more c e r t a i n l y , i n view of the small domain s i z e s obtained, a substructure low angle boundary. For grain boundaries with misorientations of 20-25° i n t e r p r e t a t i o n i n terms of i n d i v i d u a l d i s l o c a t i o n s i s not possib l e , but f o r low angle boundaries of < 5° misorientation many (33) models based on elementary edge d i s l o c a t i o n s have been proposed . Thus the d i s l o c a t i o n configuration c o n t r i b u t i n g to the domain s i z e as measured i n the x-ray a n a l y s i s i s simply a planar array i n t e r s e c t i n g the ClOO] d i r e c t i o n with a misorientation of about 1° or greater. From the above remarks i t does not seem that the s i m p l i f i c a t i o n s of Williamson and Smallman are n e c e s s a r i l y binding on the data obtained from the x-ray a n a l y s i s . The domain s i z e - y i e l d s t r e s s r e l a t i o n s h i p s of the cold r o l l e d Ni-ThO^ materials, although not consistent with the other Ni-TWX, materials are i n fa c t e n t i r e l y consistent with the cold worked pure Ni materials. I f we compare Nos. 2, 4, 10 and 12 on Tables V and VIII we f i n d the order of increasing domain s i z e to be also that of decreasing 1% Y.S., namely Nos. 73 4, 2, 12, 10, without regard to the presence of ThO^ at a l l * In the sequence 2, 4, 10, 12 i t i s apparent that f or each composition the 75$ cold reduction has produced a f i n e r domain s i z e than d i d the 50$ reduction, but the cold r o l l e d pure Ni materials had f i n e r domain s i z e s and higher y i e l d strengths than the cold r o l l e d Ni-ThOg materials. This l a s t observation suggests that the co n t r i b u t i o n of ThO^ p a r t i c l e s t o the strength of Ni-TM^ materials i n the present work i s not by way of the Orowan mechanism at a l i o The substructure i n the As Received, cold r o l l e d , and cold rolled-and-annealed Ni-ThO^ was i n most cases f i n e compared to the mean planar i n t e r p a r t i c l e spacing. Under these circum-stances i t i s probably not j u s t i f i e d to invoke Orowan strengthening. Thus the strengthening e f f e c t of t h o r i a p a r t i c l e s i n these materials i s i n t e r -preted i n terms of the e f f e c t of the p a r t i c l e s on the operation of multiple s l i p systems during deformation, the i n h i b i t i o n of dynamic recovery, and the re t a r d a t i o n of s t a t i c recovery and r e c r y s t a l l i z a t i o n . The case of o annealed Ni with a domain s i z e > 1,000A and annealed N i - T t ^ also with a o domain s i z e > 1,000A (Nos. 13 and 15 but not Nos. 9 and 11) required further comment. With s i m i l a r domain s i z e s the N i - T i ^ materials are -2 approximately 30 Kg.mm. higher i n the 1% Y.S. than the Ni materials. The true domain s i z e s are not known but i t i s possible that i n these cases they o exceed the ThO^ mean planar i n t e r p a r t i c l e spacing of 2,800A. I f t h i s i s so then a strengthening increment by an Orowan mechanism would be pla u s i b l e i n the case of these annealed Ni-ThOg materials. However as pointed out e a r l i e r t h i s increment would be approximately 19 Kg.mm. compared to the _2 observed d i f f e r e n c e of 30 Kg.mm. and therefore some incremental sub-structure strengthening i s indicated i n the annealed Ni-Th0_ even when the 74 domain size i s s i m i l a r to that of the annealed Ni. It i s reasonable to add substructure strengthening to Orowan strengthening when D >> d because of boundary continuity, but not v i c a versa when D << d. Higher work hardening rates have been reported for materials (42) containing dispersions . This i s thought to arise from the operatxon of multiple s l i p systems due to the presence of the dispersoid. However t h i s observation relates to the i n i t i a l cold working of dispersion streng-thened materials and i t i s to be expected that with increasing amounts of cold work the work hardening rate would decrease. The dispersion streng-thened materials used i n the present study were supplied commercially and i t i s known that they have received considerable amounts of p r i o r cold work. Consequently as would be expected, the work hardening rates for Ni-ThCX, i n Table V are not unusually high. 4.5.1.4. Nickel-Chromium-Th02 The room temperature strength of the annealed Ni-Cr-ThC^ material was higher than would have been predicted by simple addition of the increments due to s o l i d solution and dispersion strengthening discussed i n the proceeding sections. The domain sizes of the cold r o l l e d materials were r e l a t i v e l y small compared to the dispersoid i n t e r p a r t i c l e spacing and the i n c l u s i o n of an Orowan strengthening increment does not seem to be j u s t i f i e d . In the case of the annealed Ni-Cr-ThO^ materials with the re-c r y s t a l l i z e d grain structures Orowan strengthening i s probably operative. However the present Ni-Cr matrix may be deemed to have a 1% Y.S. of approxi-mately 28 Kg.mm0"" i n the annealed condition according to Section 4.5.1.2. whereas the annealed Ni-Cr-ThO« alloys had an average annealed 1% Y.S. of 75 82 Kg.mm. according to Table V. Even i f we add the strengthening increment observed i n Ni-ThCX, over Ni due to the presence of the disper-s o i d , namely 30 Kg.mm. , we have a predicted 1% Y.S. f o r annealed =2 =2 Ni-Cr-ThO^ of only 58 Kg.mm. , s t i l l 24 Kg.mm. lower than that observed. The discrepancy cannot be resolved by considerations of domain s i z e since the annealed Ni-Cr - T h 0 2 materials had generally l a r g e r domain s i z e s than the annealed Ni-ThO^, see Table VIII. I t appears from these r e s u l t s that i n the Ni-Cr-TM^ materials the chromium i n s o l u t i o n and the T h 0 2 have combined s y n e r g e t i c a l l y t o produce room temperature strengths greater than would be predicted by the e f f e c t s of Cr and T h 0 2 separately i n n i c k e l . This observation has not previously been explained. From the present work i t i s suggested that even at room temperature c r o s s - s l i p i n N i - T h 0 2 r e s u l t s i n a smaller strengthening increment by the Orowan mechanism than would be pre-d i c t e d by the r e l a t i o n s h i p given i n Section 1 , but that i n the Ni-Cr -ThO, , the reduced tendency to c r o s s - s l i p permits the Orowan strengthening to be more e f f e c t i v e , approaching the t h e o r e t i c a l increment predicted by the equation. This argument i s only p l a u s i b l e i f the t h e o r e t i c a l Orowan con-t r i b u t i o n i s considerably l a r g e r than that c a l c u l a t e d by von Heimendahl and Thomas f o r a s i m i l a r N i - T h 0 2 material. This would be the case i f a lar g e r estimate were taken f o r the l i n e tension of a curved d i s l o c a t i o n (45) (46) as has been done i n some instances ' . That c r o s s - s l i p occurs i n dispersion strengthened materials i s supported by the observation by Ashby (47) and Smith of prismatic d i s l o c a t i o n loops around the di s p e r s o i d p a r t i c l e s a f t e r deformation. Additional strengthening i n Ni-Cr - T h 0 2 over that of Ni - T h 0 2 i n the present study may have been derived from the frequency of stacking f a u l t s and twins which was observed i n the former material by electron microscopy, see Section 3 o 2 . 4 . 76 Although the above suggestion of the influence of cross-s l i p on Orowan strengthening could not apply to the case of cold r o l l e d materials with domain s i z e s much smaller than the dispersoid i n t e r p a r t i c l e spacing, t h i s i s consistent with the present r e s u l t s which show that i n the Cold Rolled 50% condition the Ni-Cr and Ni-Cr - T h 0 2 materials had s i m i l a r strengths and domain s i z e s . Only i n the annealed condition with a large domain s i z e d i d the Ni-Cr - T h 0 2 material d i s p l a y a strength much greater than would be predicted from the constituent Ni-Cr and Ni - T h 0 2 materials. A review of the strengths of the Ni-Cr - T h 0 2 s e r i e s i n Table V with the corresponding domain s i z e s of Table VIII shows that f o r t h i s composition there i s a good c o r r e l a t i o n between domain s i z e and room temperature y i e l d s t r e s s . This a r i s e s from the observation that cold r o l l i n g t h i s a l l o y composition produced the f i n e s t domain s i z e s and the highest strengths. As observed i n a l l previous cases, cold r o l l i n g 75% produced a f i n e r domain s i z e and greater strength (0,2% YA., 1% Y.S. and U.T.S.) than did cold r o l l i n g 50%, This marked reduction i n domain s i z e due to cold r o l l i n g was not observed i n the N i - T h 0 2 s e r i e s . In t h i s respect the Ni-Cr - T h 0 2 s e r i e s behaved more l i k e the T h 0 2-free Ni and Ni-Cr materials as was pointed out i n Section 4.3. c o r r e l a t i n g d i s l o c a t i o n configurations with microstructures. A reasonably good c o r r e l a t i o n can be found between the room temperature 1% Y.S. values and the domain s i z e f o r both Ni-Cr and -2 Ni-Cr - T h 0 2 , p a r t i c u l a r l y i n the cold worked condition. 109 Kg.mm. f o r o the 1% Y.S. of Ni-Cr cold r o l l e d 50% with a domain s i z e of 160A compares _o favourably with the value of 129 Kg.mm. f o r Ni-Cr-ThO. cold r o l l e d 50$ 77 o with a domain size of 270A; see Nos. 7 and 17 i n Tables V and VII I . This again indicates that the primary factor determining the high y i e l d stress at room temperature i s the fine substructure rather than the presence of the ThCX,. There may be an Orowan strengthening increment due to the ThO^ o per se i n the annealed materials where the domain size i s > 1,000A, but th i s i s not the case i n the cold worked conditions where the substructure i s very f i n e . Table V shows that the work hardening slopes for Ni-Cr-TM^ at room temperature were the highest of a l l compositions. The role of Cr and of ThO., i n increasing the rate of work hardening i n Ni has been d i s -cussed i n Sections 4.5.1.2. and 4,5.1.3. respectively. The combination of Cr and ThO^ i n Ni appears to result i n a higher work hardening rate than was observed i n either Ni-Cr or N i - T t ^ . The effect of work hardening on tens i l e d u c t i l i t y due to the reduction of necking was discussed i n Section 4.5.1.2. with respect to Ni-Cr. The same influence was apparent i n the Ni-Cr-ThO., series which showed room temperature t e n s i l e elongations (Table V) closer to those of the Ni-Cr series than to the Ni-TWX, series. 4.5.2. High Temperature Properties Several general aspects of the elevated temperature tests can be reviewed before discussing the results with ind i v i d u a l compositions. The temperatures of testing were those used for annealing each material composition with the exception of those materials annealed at l400°C and tested at 1200°C. As fractions of the melting point on the absolute scale, Tm, the ten s i l e testing temperatures were as follows: Ni 500°C 0.45 Tm Ni-Cr 850°C O.65 Tm 78 Ni-Th0 2 1200°C O.85 Tm Ni-Cr-Th0 2 1200°C O.85 Tm (33) In general, solution hardening models invoke some form of concentration of solute atoms i n the neighbourhood of dislocations, and this constitutes a barrier to dislocation movement. The models predict that the logarithm of the localized concentration of solute atoms w i l l be inversely proportional to the absolute temperature. Thus at high temperatures due to dispersion of the solute concentrations solution har-dening becomes less effect ive . Furthermore from expressions given by (33) Hirth and Lothe , i t i s apparent that thermal activation can assist dislocations i n breaking away from the loca l solute concentrations, leading to a decrease i n solution strengthening at elevated temperatures. Therefore as the tensile testing temperature was raised from room temperature (0.17Tra) to O.85 Tm i n the present work, i t was to be expected that the so l id solution strengthening increment due to Cr i n Ni would become re la t ively inneffective. A similar rationalization can be made with respect to the effect of temperature on the increased work hardening rate attributed to the presence of Cr i n N i . It was argued ear l ier that this increased work hardening rate occurred because of the reduction i n stacking fault energy and the resulting reduction i n cross-s l ip due to the increased separation between dissociated par t ia l dislocations. Hirth and Lothe speculate that the temperature dependence of cross-s l ip i s associated with the temperature dependence of the Peierls stress or with the temperature-dependent re-association of extended par t ia l dislocations. In either case, the temperature 79 dependence i s such that at elevated temperatures the ease of cross-sl ip i s increased and the presence of Cr i n Ni w i l l become less effective i n increasing the work hardening rate. Thus at elevated temperatures, one can expect work hardening rates i n general to be low due to the ease of bypassing dislocation barriers , with l i t t l e difference to be expected between the Ni and the Ni-Cr a l loys . (37) Parker and Hazlett i n the work discussed ear l ier also reported stress-strain curves for nickel alloys at 700°C (0.5oTm). Their results showed that the order of the alloying elements with respect to increasing yield ;s t ress and work hardening rate at room temperature was preserved at 700°C but the increases were very much less . Thus at 700°C up to 10$ Co i n Ni produced negligible change i n strength or work hardening, up to 5$ Cu i n Ni produced a negligible change i n y i e l d stress but a small increase i n work hardening rate, and 10$ Fe i n Ni produced an increase of approximately 3,000 ps i i n the 0.25$ Y .S . and an increase i n the work hardening rate. This increase i n y ie ld strength i s approximately one half of the strengthening increment reported for 10$ Fe i n Ni at room temperature by the same authors. Based on the comparison made ear l ier between Fe and Cr as al loying elements i n Ni i t might be expected that i n the 850°C tensile tests of the present work, some of the strengthening increment due to the presence of 20$ Cr i n Ni at 20°C w i l l s t i l l be a v a i l -able. However, i n tests at 1200°C (0.85 Tm) on Ni-Cr-Th02 no s o l i d solu-t ion hardening i s to be expected. Of general application to a l l materials i n the series i s the nature of the high temperature tensile test . Both deformation and 80 recovery processes are operating together and the precise s t r a i n rate and temperature used influence greatly the mechanism of the t e s t . In the present work a l l specimens were strained at 0.016 min.~ i and the t e s t temperatures ranged from 0.45 - O.85 Tm. Under these conditions i t may be expected that some dynamic recovery w i l l take place due to the ease of c r o s s - s l i p and climb processes, and that the a p p l i c a t i o n of high applied stresses at these temperatures may r e s u l t i n the migration of grain boundaries and substructure boundaries. However the dynamic recovery i n the high temperature t e n s i l e t e s t i s not equivalent to that which would occur i n an anneal at the same temperature i n the absence of an applied s t r e s s . This subject has been reviewed recently by Jonas, S e l l a r s and (43) Mc.G. Tegart . In a s t a t i c anneal following p r i o r cold work recovery processes lead to the development of a polygonized substructure i n which the d i s l o c a t i o n s have climbed i n t o boundaries permitting a configuration of lower energy. This has been discussed i n connection with annealing p r i o r to room temperature t e n s i l e t e s t s , see Section 4.5.1.1. Under the dynamic conditions of deformation and heat treatment i n the high tempera-ture t e n s i l e t e s t the formation of a polygonized d i s l o c a t i o n substructure i s apparently discouraged by the m o b i l i t y of the boundaries under the a c t i o n of the applied s t r e s s . At a temperature of O.85 Tm i t i s to be expected that p a r t i c u l a t e b a r r i e r s w i l l not e f f e c t i v e l y block d i s l o c a t i o n motion, due to the ease of both c r o s s - s l i p and climb. Therefore the d i s p e r s o i d - d i s -l o c a t i o n i n t e r a c t i o n involved i n the Orowan model f o r room temperature strength would provide l i t t l e increase i n the y i e l d s t r e s s at the elevated temperature. To be e f f e c t i v e at high temperatures, the d i s l o c a t i o n b a r r i e r s 81 must be planar or continuous i n nature and must also be stable under the applied conditions of temperature and s t r e s s . C o t t r e l l has shown t h e o r e t i c a l l y that a substructure d i s l o c a t i o n wall i s a b a r r i e r to moving d i s l o c a t i o n s and i t w i l l be shown i n the subsequent discussion that the present work i n d i c a t e s that at high temperatures the major b a r r i e r to d i s -l o c a t i o n movement i s such a planar boundary of a f i n e polygonized sub-structure. I t appears that although t h i s requirement presupposes a f i n e domain s i z e , t h i s i n i t s e l f does not produce maximum high temperature strength since at elevated temperatures i t i s also the degree of polygoni-zation of the substructure boundaries that i s important. Thus i t i s necessary to d i s t i n g u i s h between a small c e l l s i z e and a small substructure s i z e although both are analyzed simply as the domain s i z e i n the x-ray a n a l y s i s . H.5.2.1. Nic k e l It can be seen from Table VI that annealing a f t e r cold r o l l i n g r e s u l t s i n an increase i n the O.V? Tm strength of n i c k e l over that of the p r i o r cold worked state. This improvement i s also true f o r the other three compositions but the increase i s not as great. In the case of n i c k e l annealed a f t e r cold r o l l i n g 75% the increase i n the high temperature 1% Y.S. was 2.5 Kg.mm. or 48%. Reference to Table VIII shows that t h i s p a r t i c u l a r anneal changed the d i s l o c a t i o n configuration from pile-ups to polygonization. By comparison between Tables VI and VIII i t appears that there i s an o v e r a l l a s s o c i a t i o n between a high value of 1% Y.S. at elevated temperature and a high degree of polygonization. The s h i f t from pile-ups to random constitutes a move to a higher degree of polygonization and the elimination of d i s l o c a t i o n pile-ups may produce a greater increase i n high 82 temperature strength than does the further development from a random to a polygonized s t r u c t u r e . I f t h i s i s so a greater improvement would be expected when annealing n i c k e l , due to the d i s l o c a t i o n pile-ups i n the c o l d worked state (see Table V I I I ) . The above c o r r e l a t i o n between the change i n the d i s l o c a t i o n configuration and the change i n the 1% Y.S. i s not shown by data f o r n i c k e l annealed a f t e r 50% cold r o l l i n g . I t i s thought that t h i s discrepancy may r e s u l t from the p a r t i a l l y r e c r y s t a l l i z e d state of material No. 3 which appeared to have d i s l o c a t i o n pile-ups and l a t t i c e s t r a i n according to the x-ray data but a r e c r y s t a l l i z e d grain structure i n the electron micrograph of Figure 22. Hence the x-ray r e s u l t s may not be t r u l y representative of the material as a whole. The generally low absolute strengths of pure n i c k e l at 0.45 —2 Tm are to be expected. As cold worked the average 1% Y.S. was 5*5 Kg.mm. and a f t e r annealing 7.6 Kg.mm. . Although t h i s increase a f t e r annealing i s thought to be associated with polygonization, the generally low strength i n d i c a t e s that the substructure boundaries are not strong b a r r i e r s to d i s -l o c a t i o n movement under the conditions of the high temperature t e n s i l e t e s t . This i s presumably because the boundaries are r e l a t i v e l y mobile under the applied s t r e s s and temperature. The influence of possible grain boundary sulphides on the t e n s i l e elongation of the pure n i c k e l was apparent i n the high temperature o t e s t s i n a manner which was consistent with the predictions of Olsen et a l . A s seen i n Table VI i t was the two cold r o l l e d n i c k e l materials which showed high elongations i n the t e n s i l e t e s t s at 500°C. Cold r o l l i n g apparently disrupted the c o n t i n u i t y of p r i o r grain-boundary 8 3 sulphides, whereas annealing allowed the sulphur to become reassociated with grain boundaries. Apparently the duration of the t e n s i l e tests at 500°C i n the present study was unsufficient to serve as a c r i t i c a l annealing treatment for cold r o l l e d specimens. Also the dynamic conditions of the test would not favour segregation to grain boundaries. 4.5.2.2. Nickel-Chromium The average 1% Y.S. of annealed Ni-Cr at 850°C (0.65 Tm) was 9.8 Kg.mm. . This was considerably higher than that of annealed ni c k e l tested at only 500°C (0.45 Tm). From the room temperature t e n s i l e data i t was concluded that the presence of 20% Cr i n solution i n ni c k e l _2 raised the 1% Y.S. by 15 Kg.mm. . Allowing for the difference i n testing temperature above for Ni and Ni-Cr i t appears that a s i g n i f i c a n t part of the 15 Kg.mm."2 strengthening increment i s s t i l l present at 850°C (0.65 Tm). As discussed e a r l i e r i t i s to be expected that the increase i n the work hardening rate due to the presence of Cr i n Ni would also be temperature dependent. As far as one can judge from the approximate work hardening slopes of Table VI the Ni-Cr alloys did not work harden more rapidly than the pure n i c k e l i n the te n s i l e test at elevated temperature, again allowing for different temperatures. From t h i s observation i t appears that the influence of Cr on the work hardening rate of Ni i s more temperature dependent than i s the solution strengthening due to the same element. The smallest increase i n high temperature 1% Y.S. observed as a result of annealing a cold r o l l e d material occurred i n the case of the pure Ni-Cr, see Nos. 7 and 8 of Table VI. This behaviour i s supported by the data of Table VIII which shows that the degree of polygonization was 84 very similar before and after annealing. The fact that the cold rolled Ni-Cr i s indicated as having a polygonized dislocation configuration i n o Table VIII i s a direct result of the very fine domain size of 160A. A s l i g h t l y larger domain size would result i n a lower value for £ and the prediction of a configuration closer to random. This would render the x-ray data more consistent. It can be shown from equation (43) that a o domain size of greater than 2k0h would result i n a value of £ for cold rol led Ni-Cr of less than 5.25 x 1 0 l x „ thus indicating from the ratio of £ p / ^ s that the material was less polygonized than the cold rolled and annealed material. The p o s s i b i l i t y that the domain size as cold rol led o was greater than 240A i s very real since i n Section 4.1. Scherrer's formula o indicated a domain size of 220A and i n the presence of l ine broadening due to la t t i ce strain Scherrer's formula should indicate a smaller value than the true domain s ize . 4.5.2.3. Nickel-Th0 2 From Table VI i t can be seen that the average 1% Y.S. of Ni-Th0 2 at 1200°C (O.85 Tm) i s 8.1 Kg.mm." 2 . In view of the high homologous temperature and the presence of only 2% of thoria dispersoid this result i s quite remarkable though typical of oxide dispersion strengthened al loys . Within the Ni-ThCX, series the results show consistently that annealing after cold r o l l i n g increases the 1% Y.S. i n tensile tests at elevated temperature. This confirms the observation made for pure nickel that the development of a polygonized substructure during static annealing enhances the high temperature strength of the material. In the case of the dispersion strengthened materials, the dispersoid particles are thought to 85 exert a pinning e f f e c t on the boundaries due to considerations of i n t e r -f a c i a l energies and thereby to provide the s t a b i l i t y of substructure which was observed i n the present study and which has been reported by other (8) workers . The substructure boundaries are e f f e c t i v e b a r r i e r s to d i s l o c a -t i o n motion and r e s u l t i n the remarkable high temperature strength. The Ni-ThC^ s e r i e s does not show a c o r r e l a t i o n between domain s i z e (Table VIII) and y i e l d s t r e s s (Table VI). The tendency of t h i s material not to form exceedingly f i n e domains during c o l d r o l l i n g has received comment i n Section 4.5. and i n Section 4.5.1.3. However a b e t t e r c o r r e l a -t i o n with y i e l d s t r e s s i s observed i f account i s taken of the degree of polygonization of the substructure boundaries, which supports the proposal made e a r l i e r i n t h i s s e c t i o n . Table VI shows that the work hardening slopes of Ni-ThCX, at 0.85 Tm were i f anything greater than those of Ni-Cr-Th0 2. This i s thought to a r i s e from the presence i n Ni-ThO., of the stable substructure boundaries invoked above to explain t e n s i l e strength. Evidence that a s i m i l a r sub-structure was not present i n the Ni-Cr-Th0 2, other than i n the As Received material, w i l l be discussed i n the following s e c t i o n . The higher y i e l d s t r e s s and work hardening slope of Ni-Th02 as compared to Ni-Cr-ThO., are consistent with the higher degree of polygonization predicted from x-ray r e s u l t s f o r the former material. 4„5°2.4. Nickel-Chromium-Th0 2 In the As Received condition the Ni-Cr-Th0 2 possessed a high temperature strength comparable to that of the Ni-Th02. Table VI shows that the 1% Y.S. at 1200°C (O085 Tm) was 7.7 Kg.mm0" compared to 86 the average value of 8.1 Kg.mm. fo r Ni-ThO,,. In support of t h i s obser-vation Table VIII shows that the x-ray data ind i c a t e d a highly polygonized d i s l o c a t i o n configuration i n the As Received Ni-Cr-ThCX, which i s i n accord with the e a r l i e r remarks that the polygonized substructure i s the streng-thening f a c t o r . However there was a marked di f f e r e n c e between Ni-Cr-ThO^, As Received and the other conditions f o r t h i s same composition as shown i n Table VI. Only i n the As Received condition did the Ni-Cr-Th0 2 show a high temperature strength approaching that of Ni-Th0 2. In a l l other condi-t i o n s the 136 Y.S. of the Ni-Cr-Th0 2 at 1200°C (O.85 Tm) was l e s s than h a l f of the o r i g i n a l As Received value, i . e . , the average f o r Ni-Cr-Th0 2 materials other than No. 16 As Received was 3.3 Kg.mm. fo r the 1% Y.S. whereas the As Received value was 7.7 Kg.mm. . As discussed i n Section 4.3. and as indi c a t e d i n Table VIII the highly polygonized substructure of the As Received Ni-Cr-Th0 2 could not be reproduced by subsequent r o l l i n g and anneal-i n g treatments. These r e s u l t s give further very strong support to the sub-structure strengthening model f o r high temperature strength. The transmission e l e c t r o n microscopy confirms the absence of a s t a b i l i z e d substructure i n the annealed Ni-Cr-Th0 2. Figures 52 - 55 show r e c r y s t a l l i z e d grains with a high density of annealing twins. These micro-structures are very d i f f e r e n t from those of the annealed Ni-Th0 2 where no t y p i c a l r e c r y s t a l l i z e d grains were found. As discussed i n Section 4.3., the r e c r y s t a l l i z a t i o n of the cold r o l l e d Ni-Cr-Th0 2 was associated with the presence of high l o c a l i z e d l a t t i c e s t r a i n s which i t i s thought were a r e s u l t of the influence of chromium on c r o s s - s l i p . -2 It must be recognized that the 196 Y.S. of 3.3 Kg.mm. f o r Ni-Cr-ThO- at 1200°C (O.85 Tm) i s much higher than could be expected from 87 pure Ni-Cr at the same temperature and therefore indicates a residual strengthening effect direct ly or indirec t ly due to the presence of ThCv,. At the temperature i n question i t i s l i k e l y that this i s due to a sub-structure boundary effect although not the optimum configuration. In Section 4.2. i t was noted that Figure 55 of Ni-Cr-ThC»2 cold rol led 75% and o annealed shows the twin boundary spacing to be approximately 1,250-2,500A. These boundaries w i l l contribute to substructure strengthening and w i l l account i n part for the high temperature strength of N i - C r - T h 0 2 . (44) In a recent paper Raymond and Neumann reported tests of thermal s t a b i l i t y on two Ni-Cr-Th0 2 alloys of similar composition to that used i n the present study. They reported that upon exposure to annealing treatments at temperatures from 982°C (l800°F) up to 13l6°C ( 2400°F) one material retained i t s stable microstructure whereas the grain size of the other increased. They concluded that this behaviour was associated with a o larger thoria part icle size (820A) i n the material which recrystall ized o than i n the thermally stable material (550A). The Ni-Cr-Th0 2 material used i n the present study was the same commercial product as that found by Raymond and Neumann to be thermally stable. However i n the work of Raymond and Neumann the heat treatments were carried out without prior cold working whereas i n the present study i t i s thought that the particular strain d i s -tr ibution of the cold rol led N i - C r - T h 0 2 , having a high localized s t ra in , promoted recrystal l izat ion on subsequent annealing. As was to be expected at 1200°C (O.85 Tm) solution streng-thening by chromium was not significant compared to substructure streng-thening. The As Received Ni-Th0 2 had a 1% Y.So at 1200°C of 8.5 Kg.mm."2 whereas that of the As Received Ni-Cr-ThO_ was 7.7 Kg.mm. . Also as 88 expected at the higher temperatures the presence of chromium d i d not increase the work hardening r a t e . Table VI shows that the work hardening slopes of the annealed Ni-Cr-ThC^ materials at 1200°C were the lowest ob-tained on annealed materials. The fact that the annealed Ni-Cr-ThC^ showed a much lower work hardening slope at 1200°C than the Ni-ThO^ supports the view that the l a t t e r material contained stable substructure boundaries whereas the former d i d not. ^•6. The E f f e c t of Texture on Tens i l e Properties In the present i n v e s t i g a t i o n a study was not made of the texture and preferred o r i e n t a t i o n developed i n the four materials by the various r o l l i n g and annealing cycles, nor of the e f f e c t such a texture might have on the t e n s i l e properties. In a l l cases, cold r o l l i n g and t e n s i l e t e s t i n g were c a r r i e d out i n the d i r e c t i o n i n d i c a t e d by the s u p p l i e r as being the o r i g i n a l r o l l i n g d i r e c t i o n of the As Received materials. However the precise manufacturing process i s not known and i t seems most l i k e l y that i n the case of the wider s t r i p materials, e.g., Ni-ThC^ 3 f t . x 2 f t . x 0.0k i n . , considerable amounts of cross r o l l i n g w i l l have been used. Some of the possible e f f e c t s of texture on t e n s i l e properties w i l l be reviewed. ( 6 3 ) Mee and S i n c l a i r have reported the preferred o r i e n t a t i o n development a r i s i n g from the cold r o l l i n g and annealing of Ni-ThO., sheet. Their work covered the determination of numerous pole figures with supporting electron microscopy and hardness measurements but unfortunately did not include t e n s i l e t e s t s . They reported that the as extruded and cold forged material contained, amongst other textures, a considerable proportion of ( n o ] < 001> , but that cold reductions of up to 91$ retained and 89 strengthened t h i s texture component. Only a f t e r reductions greater than 91% did they report development of the normal f . c . c . r o l l i n g texture of ^135^ <^ 112^  . Annealing appears to have produced mixed textures, a l l of which contained some cube component |t 100} <^ 001^  and evidence of twinning but not a predominance of the cube texture as would have been the case presumably i n pure n i c k e l . Mee and S i n c l a i r a l s o postulate that i n Ni-Th02 the [ 110 ] <001> component could develop by a twinning-and-slip mechanism from the jfll2^ ^111^ component, which i n the f i r s t place could be developed by a high rate of c r o s s - s l i p during deformation. In general, the above work i s i n agreement with the present study i n which i t was observed that the As Received materials had a preferred o r i e n t a t i o n with the (110) planes i n the plane of r o l l i n g . As discussed i n Appendix 1, f o r t h i s reason the (222) r e f l e c t i o n was too weak as observed i n the normal diffractometer arrangement and i t was necessary to use (200) and (400) r e f l e c t i o n s to obtain reasonable i n t e n s i t i e s from two orders. The (MtO) r e f l e c t i o n , although the strongest second order r e f l e c t i o n , could not be used since i t occurs at too high an angle to be recorded. Doble and Quigg^°^ have studied the e f f e c t of deformation mode on the t e n s i l e anisotropy of Ni-Th02 bar, but d i d not include the determination of texture pole f i g u r e s . They c a r r i e d out cold working by swaging and by r o l l i n g . They found that the elevated temperature strength at 2000°F (1093°C) was not affe c t e d by p r i o r annealing at 2500°F (1371°C), even though i n the case of the cold r o l l e d material a " r e c r y s t a l l i z e d " structure was obtained. However the increase i n room temperature strength due to cold working was removed by p r i o r annealing. 9 0 Doble and Quigg reported a marked tensile anisotropy i n the As Received Ni-ThC^ bar stock. They concluded that the degree of anisotropy increased as the bar diameter decreased, i . e . , i t increased with the amount of accumulated deformation. Furthermore they showed that i t could be reversed somewhat by upsetting or side pressing operations. The tensile anisotropy was not apparent at room temperature and the results of Doble and Quigg showed the transverse and longitudinal tensile strengths to begin to diverge only above 5 5 0 ° F ( 2 8 8 ° C ) or roughly 0 . 3 3 Tm. The magnitude of the anisotropy became greatest at 1 0 0 0 ° F ( 5 3 8 ° C ) and above where the longitudinal strength exceeded the transverse by a factor of f i v e . From the above brief review of the work of Mee and S i n c l a i r and of Doble and Quigg, there i s l i t t l e doubt that the cold rol led Ni-ThCXj material tested i n the present investigation would probably have shown tensile anisotropy. However the same material also showed a certain s t a b i l i t y of texture during annealing and since i n the present work a l l r o l l i n g and tensile testing were carried out i n the same direct ion, i t i s thought that the present tensile results may be compared with each other without errors due to differences i n preferred orientation. In the case of the Ni-Cr-ThC^ material however, removal of preferred orientation may have contributed to a lower high temperature strength. 91 5. SUMMARY 5.1. The a p p l i c a b i l i t y of the f u l l x-ray l i n e p r o f i l e analysis of Warren to determine the l a t t i c e s t r a i n d i s t r i b u t i o n and c r y s t a l -l i t e domain size i n N i , Ni-Cr, Ni-ThO., and Ni-CrrTM^ has been demon-strated, including the determination of twin and stacking fault p r o b a b i l i t i e s . The results obtained were s e l f consistent, were i n agreement with a more elementary x-ray analysis i n certain l i m i t i n g cases where the simpler approach could, be applied, and were confirmed by transmission electron microscopy on a l l materials. 5.2. Many refinements were introduced to the analysis to correct for overlapping r e f l e c t i o n s , non-uniform x-ray background i n t e n s i t y , x-ray doublet effects and the angular dependence of atomic scattering and Lorentz-Polarization. A computer programme was written to carry out these corrections, to do the Fourier integrations of the p r o f i l e analysis and to calculate the d i s t r i b u t i o n of l a t t i c e s t r a i n and the c r y s t a l l i t e domain s i z e . 5.3« X-ray results indicated a much higher l o c a l i z e d l a t t i c e 2 1/2 s t r a i n i n the cold r o l l e d ThO p-free materials ( ( £ ) Q = 0.4%) 2 1/2 5 0 A compared to the Ni-ThO ( ( £ ) 0 = 0.14%). When cold r o l l e d 75%, 50A N i - C r - T l ^ behaved more l i k e the former materials and developed high 2 1/2 l o c a l i z e d l a t t i c e strains ( ( £ ) 0 = 0.32%. This high l a t t i c e 50A s t r a i n over a short distance i s interpreted i n terms of bands of concentrated s l i p , not found i n Ni-ThO., because of the operation of multiple s l i p systems. I t i s thought that these regions of high s t r a i n act as driving forces i n the process of r e c r y s t a l l i z a t i o n and I 92 promote grain growth i n the pure materials, Recrystallization was also observed on annealing the Ni-Cr-ThO^ after cold r o l l i n g 75$ but the cold rol led Ni-ThO^ did not recrysta l l ize 0 5.4» This difference i n strain distr ibution i n Ni-Cr-ThC^ compared to Ni-ThtX, i s thought to arise from the influence of Cr on the stacking fault energy of N i . The stacking fault energy i s reduced, the ease of cross-s l ip i s reduced and the tendency to form local concentrations of s l i p i s increased. This characteristic of the Ni-Cr-ThCX) to r e -crysta l l ize on annealing following severe cold working i s a serious l imitat ion on the material since i t does not allow the development of a fine polygonized substructure following a fabrication procedure. 5.5. Transmission electron microscopy confirmed the x-ray results , showing the small c e l l size and high dislocation densities i n the cold rol led materials and supported the conclusion that the c e l l size i n cold rol led Ni-ThO^ was not as fine as i n the other cold rol led materials, including the Ni-Cr-ThO.,. This resistance to the formation of extremely fine domains on cold r o l l i n g and the a b i l i t y to d i s t r i -bute la t t i ce s train at a re lat ively uniform level throughout these larger domains i s thought to be a result of the operation of multiple s l i p systems i n Ni-ThC^. This behaviour i s related to 5«3o above and i s believed to be a major factor determining the structural s t a b i l i t y of cold rol led Ni-ThCXj on subsequent annealing or service at elevated temperatures. 5.6. The x-ray data were also interpreted i n terms of dislocation (29) configurations following the method of Williamson and Smallman . 9 3 and i t was shown that the dispersion strengthened materials had a more highly polygonized substructure. 5 . 7 . Some evidence was found of the development of a residual l a t t i c e macro strain i n annealed Ni-ThC^ with increasing amounts of prior cold r o l l i n g . This observation i s consistent with the proposal that residual la t t i ce macro strain arises from the heterogeneity of the material. 5 . 8 . Room temperature tensile tests showed a good correlation bet-ween high strength and a fine domain s ize . In annealed Ni-ThC^ and o Ni-Cr-ThCL, with domain sizes > 1,000A there was some evidence of additional strengthening due to an Orowan mechanism with a greater contribution i n the case of the Ni-Cr-ThO.,. It i s thought that Orowan strengthening, when applicable, i s more effective i n the Ni-Cr al loy due to the d i f f i c u l t y of c ross -s l ip . In the case of cold worked materials with domain sizes less than the interpart icle spacing, sub-structure strengthening predominated and Orowan strengthening was not applicable. The sol id solution contribution to room temperature strength of 20% Cr i n nickel was ident i f ied as an increase of 1 5 Kg.mm. i n the 1% Y . S . , and a higher work hardening rate was observed i n the sol id solution a l l o y . 5 « 9 . High temperature tensile tests at temperatures up to 0 . 8 5 Tm i n the case of the materials containing Th0 2 showed a good correlation between high strength and a fine polygonized substructure. It appeared that the degree of polygonization of the substructure boundaries as well as the domain size determined the optimum p r o p e r t i e s . This substructure strengthening was very much greater i n the case of the Ni-ThCXj due i t i s thought, to the pinning of the boundaries by the ThCX, p a r t i c l e s . Optimum high temperature proper-t i e s were not obtained i n the cold r o l l e d and annealed Ni-Cr-ThOp^ since a f i n e polygonized substructure could not be developed i n these materials. At 850°C (0.65 Tm) s o l i d s o l u t i o n strengthening by chromium was s t i l l evident but at 1200°C (0.85 Tm) t h i s was no longer the case. 95 6. CONCLUSIONS The following general conclusions were drawn regarding the nickel alloys tested. 6.1. The room temperature strength was related primarily to a small dislocation c e l l s ize 0 In the case of annealed dispersion strengthened alloys with a domain size greater than the interpart ic le spacing additional strengthening was associated with the Orowan mechanism, and i n the case of the Ni-Cr alloys s o l i d solution strengthening by chromium was also evident. 6.2. The high temperature strength was related to the presence of a fine polygonized substructure which i n the Ni-ThOg material was s tabil ized by the dispersoid part ic les . Orowan strengthening and solution strengthening were not significant at elevated temperatures. 6.3. The la t t i ce strain distr ibution i n cold rol led Ni-Th0 2 showed re la t ive ly low strains over large distances whereas the ThOp-free materials showed high localized la t t i ce strains when cold r o l l e d . This difference i s thought to arise from the operation of multiple s l i p systems i n the dispersion strengthened al loys . N i - C r - T M ^ also developed high localized la t t i ce strains on cold r o l l i n g , due i t i s thought to the influence of chromium on c r o s s - s l i p . The cold rol led materials bearing a high localized la t t i ce strain recrysta l -l i z e d on annealing and did not develop the fine polygonized sub-structure required for high temperature strength. 96 6.4. The a l l o y system chosen can be analyzed by a r e f i n e d x-ray l i n e p r o f i l e technique to determine l a t t i c e s t r a i n and domain s i z e . This was evident from the s e l f consistent r e s u l t s and the supporting e l e c t r o n microscopy. 97 7. SUGGESTIONS FOR FUTURE WORK Suggestions 1-3 are made i n r e l a t i o n to the conclusions drawn from the present work whereas suggestions k and 5 are f o r other studies i n r e l a t e d f i e l d s on the same materials. 7.1. A study by transmission electron microscopy and x-ray d i f -f r a c t i o n should be made on the materials a f t e r high temperature t e n s i l e t e s t i n g . The objectives would be to e s t a b l i s h that a poly-gonized substructure i s not formed during the high temperature t e n s i l e t e s t i n g of cold r o l l e d materials, and to e s t a b l i s h from the d i s l o c a t i o n configurations why the materials given a p r i o r anneal . are stronger at elevated temperatures. 7.2. The Ni-Cr-ThOp^ material should be subjected to a range of cold r o l l i n g reductions from 0 - 75% i n small increments and examined at each stage by x-ray d i f f r a c t i o n and transmission e l e c t r o n microscopy i n both the cold r o l l e d and annealed conditions. The objective would be to e s t a b l i s h a threshold l e v e l of l a t t i c e s t r a i n f o r the r e c r y s t a l l i z a t i o n of t h i s material upon subsequent annealing. 7.3. An attempt should be made to t r y to compare the degree of c r o s s - s l i p i n Ni-Cr-ThOp with that i n Ni-ThOp during room tempera-ture deformation. The deformation should be i n small increments as i n 6.2. and at each stage the two materials should be examined by transmission electron microscopy f o r the presence of d i s l o c a t i o n loops as evidence of c r o s s - s l i p around ThOp p a r t i c l e s . This study 98 would help to c l a r i f y the influence of chromium on the d i s t r i b u t i o n of l a t t i c e s t r a i n i n Ni-Cr-ThC^. In p r a c t i c e much of the work proposed i n 6.2 and 6.3 could be done at one time. 7.4. A study should be made to determine the changes i n texture and preferred o r i e n t a t i o n i n a l l four materials due to various r o l l i n g and annealing c y c l e s , and to assess to what extent t e n s i l e properties are dependent upon texture. 7.5. The l a t t i c e s t r a i n should be determined, i n various thermo-mechanical conditions, i n the ThCX, p a r t i c l e s i n both Ni-ThC^ and. Ni-Cr-ThCv^o This could be done using the s i n g l e r e f l e c t i o n technique of Rothman and C o h e n o n the ThCX, (111) l i n e , and the r e s u l t s could be checked by a simple l i n e breadth method since the broadening due to small p a r t i c l e s i z e could be c a l c u l a t e d indepen-dently from the p a r t i c l e s i z e observed by electron microscopy. The d i f f e r e n t s t r a i n d i s t r i b u t i o n s i n the n i c k e l and Ni-Cr l a t t i c e s observed i n the present work may r e s u l t i n d i f f e r e n t s t r a i n s i n the ThO. p a r t i c l e s i n the Ni-ThC" compared to the Ni-Cr-ThO_. 99 Figure 1. -Variation of Lattice Strain with Lattice Distance for Nickel i n various Thermomechanical Conditions. 100 200 300 400 500 LATTICE DISTANCE ( L), ANGSTROMS F i g u r e 2. V a r i a t i o n o f Domain S i z e C o e f f i c i e n t . w i t h L a t t i c e D i s t a n c e f o r N i c k e l i n v a r i o u s T h e r m o m e c h a n i c a l C o n d i t i o n s . 101 Figure 3. V a r i a t i o n of Lattice Strain with. Lattice Distance for Ni-Cr in various Thermomechanical Conditions. 102 0,2 100 200 300 400 500 LATTICE DISTANCE ( L), A N G S T R O M S Figure 4. V a r i a t i o n of Domain S i z e C o e f f i c i e n t w i t h L a t t i c e Distance f o r Ni-Cr i n v a r i o u s Thermomechanical Conditions. 103 0.48 0.40 0.32 CR 50%+ANN, % STRAIN =0 < at t— 0.24 < 0.16 cs CR 7 5 % +ANN, % STRAIN =0 CR 90%+ANN, % STRAIN "0 0.08 R 5 0 % R 7 5 % 100 200 300 400 LATTICE DISTANCE ( L) .ANGSTROMS 500 Figure 5 . V a r i a t i o n of L a t t i c e S t r a i n w i t h L a t t i c e Distance f o r Ni-ThO i n v a r i ous Thermomechanical Conditions. 104 1.6 1.4 1 .2 1.0 < u a. ui o u UJ N < o 0.8 0 .6 0.4 0.2 - -CR 9 0 % + A N N . D M O O O A - CR 75 % +ANN,D?»I000A CR 5 0 % , D s 7 0 0 A CR 7 5 % , D s 4 6 0 A X A S R E C , D s 3 8 0 A CR 5 0 % + D S 3 5 0 A 100 200 300 400 LATTICE DISTANCE ( L), A N G S T R O M S 500 Figure 6. V a r i a t i o n of Domain Size C o e f f i c i e n t with L a t t i c e Distance f o r Ni-Th02 i n various Thermomechanical Conditions. 105 Figure 7. V a r i a t i o n of L a t t i c e S t r a i n with L a t t i c e Distance f o r Ni-Cr-ThC-2 i n various Thermomechanical Conditions. 106 1.6 t-1 .4 1 .2 3 LO < z UJ u LU o u UJ M to O o 0.8 0.6 0.4 0.2 CR 7 5 % + A N N , D ; H 0 0 0 A C R 5 0 % + A N N , D e 5 0 0 - l 0 0 0 A AS R E C , Dss500- I000A CR 7 5 % , D ^ 1 8 0 A \ p R 5 0 % , D » 2 7 0 A 100 200 300 400 LATTICE DISTANCE ( L), A N G S T R O M S 500 Figure 8. Variation of Domain Siza. Coefficient with Lattice Distance for Ni-Cr-ThC>2 i n various thermomechanical Conditions. 107 100 200 300 400 500 LATTICE DISTANCE ( L), A N G S T R O M S Figure 9 . Variation of Lattice Strain with Lattice Distance i n the As Received Condition for various Compositions. 108 100 200 300 400 500 LATTICE DISTANCE ( L), A N G S T R O M S Figure 10. Variation of Domain Size Coefficient with Lattice Distance i n the As Received Condition for various Compositions. 109 100 200 300 400 500 LATTICE DISTANCE ( L), A N G S T R O M S Figure 11. Variation of L a t t i c e Strain with L a t t i c e Distance i n the Cold Rolled 50% Condition for various Compositions. n o 1.6 1.4 1 .2 100 200 300 400 500 LATTICE DISTANCE ( L), ANGSTROMS Figure 12. Variation of Domain Size Coefficient with Lattice Distance i n the Cold Rolled 50% Condition for various Compositions. I l l 100 200 300 400 500 LATTICE DISTANCE ( L), A N G S T R O M S Figure 13. Variation of Lattice Strain with Lattice Distance i n the Cold Rolled 50% and Annealed Condition for various Compositions. 112 0 I _] L. 1 L 100 200 300 400 500 LATTICE DISTANCE ( L), ANGSTROMS Figure 14. Variation of Domain Size Coefficient with Lattice Distance i n the Cold Rolled 50% and Annealed Condition for various Compositions. 1 1 3 0.48 100 200 300 400 500 LATTICE DISTANCE ( L), ANGSTROMS Figure 15. Variation of Lattice Strain with Lattice Distance i n the Cold Rolled 75% Condition for various Compositions. Ilk 1.6 j-1.4 -1.2 -100 200 300 400 500 LATTICE DISTANCE ( L), ANGSTROMS Figure 16. Variation of Domain Size Coefficient with Lattice Distance in the Cold Rolled 75% Condition for various Compositions. 115 0.48 L_ 0.40 0.32 < 0.24 < 0.16 -0.08 0 I Ni -Th0 2 , % SU Ni -Cr -Th0 2 i i 100 200 300 400 LATTICE DISTANCE ( L), A N G S T R O M S 500 Figure 17. Variation of L a t t i c e Strain with L a t t i c e Distance i n the Cold Rolled 75% and Annealed Condition for various Compositions. 1.6 1.4 _ 1.2 _ 3 1 0 < z LU u o u LU M CO Z < o a 0.8 -0.6 0.4 e 1 1 6 Ni.DHOOOA Ni-Cr-Th0 2 , D H 0 0 0 A Ni-ThO,,,D^IOOOA 0,2 i 100 200 300 400 LATTICE DISTANCE ( L), ANGSTROMS 500 Figure 18. Variation of Domain Size Coefficient with Lattice Distance i n the Cold Rolled 75% and Annealed Condition for various Compositions. 1.6 117 1.4 1 .2 5 10 < z 5 0 8 IA. U -LM o tu M m Z < o 0.6 0.4 0.2 •Ni-ThO,,D>IOOOA Ni-Th0 2 , % STRAIN = 0 X _L 100 200 300 400 LATTICE DISTANCE ( L), ANGSTROMS 500 Figure 19. Variation of La t t i c e Strain and Domain Size Coefficient with La t t i c e Distance i n the Cold Rolled 90% and Annealed Condition for Ni-Th0 o. 1 1 8 119 Figure 21. Transmission electron micrograph of Nickel i n the As Received Condition. Figure 22. Transmission electron micrograph of Nickel i n the As Received Condition. 121 Figure 23. Transmission electron micrograph of-Nickel i n the Cold Rolled 50% Condition. 122 Figure 24. Transmission electron micrograph of Nickel i n the Cold Rolled 50% Condition. 123 Figure 25. Transmission electron micrograph of-Nickel i n the Cold Rolled 50% and Annealed Condition. Figure 26. Transmission electron micrograph of Nickel i n the Cold Rolled 50% and Annealed Condition. Figure 27. Transmission electron micrograph of Nickel i n the Cold Rolled 50% and Annealed Condition. Figure 28. Transmission electron micrograph of Nickel i n the Cold Rolled 75% Condition. Figure 29. Transmission electron micrograph of Nickel i n the Cold Rolled 75% Condition. Figure 30. Transmission electron micrograph of Nickel i n the Cold Rolled 75% and Annealed Condition. Figure 31. Transmission electron micrograph of Nickel i n the Cold Rolled 75% and Annealed Condition. Figure 32. Transmission Electron micrograph of Ni-Cr i n the As Received Condition. Figure 33. Transmission electron micrograph of Ni-Cr i n the As Received Condition. 132 Figure 34(a) Transmission electron micrograph of Ni-Cr-in the Cold Rolled 50% Condition. Figure 34(b). Transmission electron micrograph of Ni-Cr i n the Cold Rolled 50% Condition. 134 Figure 35. Transmission electron micrograph of Ni-Cr i n the Cold Rolled 50% Condition. 135 Figure 37. Transmission electron micrograph of Ni-Cr i n the Cold Rolled 50% and Annealed Condition. Figure 38. Transmission electron micrograph of Ni-Cr i n the Cold Rolled 50% and Annealed Condition. 138 Figure 39. Transmission electron micrograph of Ni-Cr.in the Cold Rolled 50% and Annealed Condition. 139 IhO Figure 41. Transmission electron micrograph of Ni-ThO„ i n the Cold Rolled 50% Condition. Figure 43. Transmission electron micrograph of Ni-ThO_ i n the Cold Rolled 75% Condition. 143 -Figure 45. Transmission electron micrograph of Ni-Th0 2 i n the Cold Rolled 75% and Annealed Condition. F i g u r e 46. Transmission e l e c t r o n micrograph of Ni-ThC^ i n the Cold R o l l e d 90% and Annealed Con d i t i o n . Figure 47. Transmission electron micrograph of Ni-ThC>2 i n the Cold Rolled 90% and Annealed Condition. Figure 48. Transmission electron micrograph of Ni-ThO^ i n the Cold Rolled 90% and Annealed Condition. Figure 49. Transmission electron micrograph of Ni-Cr-ThC-2 i n the As Received Condition. 149 Figure 50. Transmission electron micrograph of Ni-Cr-ThO i n the As Received Condition. 150 151 Figure 53. Transmission electron micrograph of Ni-Cr-ThO,, i n the cold Rolled 75% Condition. Figure 54. Transmission electron micrograph of Ni-Cr-ThC^ i n the Cold Rolled 75% and Annealed Condition. 154 Figure 55. Transmission electron micrograph of Ni-Cr-ThO^ i n the Cold Rolled 75% and Annealed Condition. Figure 56. Optical micrograph of Nickel i n the As Received Condition. Grain Size Standard. Figure 57. Optical micrograph of Ni-Cr i n the As Received Condition. Grain Size Standard. 156 APPENDIX 1 A Review of the Theoretical Basis of the Measurement of  Non-Uniform Lattice Strain and Crystal l i te Size i n Metals by  the X-Ray Line Broadening Technique The amplitude of a diffracted x-ray beam may be expressed i n complex exponential f o r m ^ 0 ^ as, A = A F exp(i0 ) ( l) o m m where A q i s a constant depending on the amplitude of the incident wave, and on the phase difference between the incident and diffracted wave at the o r i g i n , F i s the Structure Factor for the crystal unit c e l l , and 0^  i s the phase difference between the diffracted wave from the origin and the diffrac-ted wave from some point m. 0 The structure factor F i s the ratio of the amplitude of the wave scattered by a l l the atoms of a unit c e l l to the amplitude of the wave scattered by one e l e c t r o n ^ ^ . In terms of c e l l structure, F = 2 . fh exp | 2Tti(hUn + kVn + lWn)"\ where fn i s the atomic scattering factor, (hkl) i s the particular plane of ref lec t ion , and Un, Vn, V/n are the fractional co-ordinates of the atoms i n the unit c e l l . By d e f i n i t i o n , the constant A q embraces the factors included i n the equation of J . J . Thomson for the intensity of an x-ray beam scattered (l6) by a single electron. This i s given by , T T e** . 2 . r m c 157 where I q = i n t e n s i t y of the incident beam, C = v e l o c i t y of electromagnetic r a d i a t i o n , e = electron charge, m = ele c t r o n mass, r = distance from the electron at which I i s measured and oi. = the angle between the scattered beam and the d i r e c t i o n of acc e l e r a t i o n of the elec t r o n . In the case of an unpolarized incident beam, the e l e c t r i c vector E may be resolved i n t o two perpendicular components E and E i n the yz plane perpendicular to the y z incident beam. Since the d i r e c t i o n of E i s randpm i n the yz plane then on average E^ = 2 2 2 p and therefore E^ = E^ = 1/2 E . Since I q i s proportional to E % IQ can be resolved i n t o two components I = 1 = 1/2 I . The component I° e oy oz o oy accelerates an electron at the o r i g i n i n the y - d i r e c t i o n and the component I i n the z - d i r e c t i o n . From Thomson's equation, the i n t e n s i t y scattered i n the d i r e c t i o n (26) by the two incident components I and I w i l l be ^ oy oz 4 4 I e T T e . 2 TC _ _ e o Jy = Xoy 2 2 4 6 1 1 1 2 ~ oy 2 2 4 = „ 2 2 4 r m c r m c 2r m c ^ O rr k 1 = 1 o 6 o 4 s i n ( 5 - 29) = I e z oz 2 2 4 2 . r ra c r m c 4 2 2 I e cos 29 oz ~Tz^ c o s 2 6 = „°2 2 4 2r m c 158 The total intensity scattered i n the direction (26) i s given by 1 = 1 + 1 y z T o / 1 + cos 26 % i = - 2 2 T : ( 2 } r m c 2 1 cos 2^ The factor ( - — ^ —• 0 i s called the Polarization Factor and through this expression the constant A q of equation (l) i s dependent on the Bragg angle (29). If the diffracted amplitude i s defined i n terms of the scattering per unit electron, A q can be omitted and the amplitude can be expressed i n electron units as A = F | L exp(i#n) (2) ( l 8 ) Following the review of Warren based on the earl ier work of Stokes and W i l s o n ^ 9 ^ ' and of Warren and Averbach^"^, le t r be _m defined as a la t t i ce vector i n real space giving the position of a unit c e l l from the o r i g i n . If a^, a.^ and a^ are the unit vectors of the crystal axes, and m^, and m^ are corresponding integers, then, r^ = m ^ + m ^ + m ^ If the unit c e l l has undergone some arbitrary strain displacement given by, im — m a. + Y a_ + Z a , 1 m _2 mJ5 this can be included i n r such that, m ' 159 Let S and S be unit vectors i n real space representing the o "~" incident and diffracted x-ray beams respectively, and let r f f l represent the location of a unit c e l l at point B with respect to the origin at 0. The path difference between x-rays scattered from a unit c e l l at the origin and from the unit c e l l at B may be derived as follows, Path Difference =• Bx - Oy Since S q and 3 are unit vectors, S . r o m projection of rffl on s = Bx and, S . r — m = projection of r on S ° m — = Oy .*. Path difference = S . r - S . r o m — m = - (S-S ) .r — o m .*. Phase difference, 0 , = m 2K (S-S ) . r X - _ £ _m Hence from equation (2), A = F exp(i0m) m 1 6 0 A = F IE exp f-2ui m u (S-S ) — o To obtain the i n t e n s i t y , I, A i s m u l t i p l i e d by i t s complex conjugate A*, (S-S ) _ — _ £ -. A* = F A expl 2n± —-— 0 r 'J This i s the same function as a, inverted through the o r i g i n , and the two vectors r and r ' define the extent of the c r y s t a l i n opposite d i r e c t i o n s m m from the o r i g i n . S i m i l a r l y f o r the structure f a c t o r , | F j 2 = F.F* Thus, o r , r^fncos2n(hUn + kVn + lWn)] + r£fnsin2rc(hUn + kVn L-n J L n _ + lWn/p (S-S ) — o I = | F ) 2 2. §, expferci — — . ( r • - r ) ] ' ' m m ' 1 - A m m J A m m | F | 2 \ m 2 m^ m ^ my **P L > i - = • ( V " f m ) ] ( 3 ) (S-S ) — o The d i f f r a c t i o n vector, , can be expressed i n terms of (48) the r e c i p r o c a l space . 161 I n t h e c a s e o f c o h e r e n t s c a t t e r i n g r e s u l t i n g i n c h a n g e o f p h a s e b u t no c h a n g e o f w a v e l e n g t h , S = S o — W i t h t h e a n g l e o f i n c i d e n c e e q u a l t o t h e a n g l e o f d i f f r a c t i o n , a n d S^ = S , (S-S ) t h e r e s u l t a n t o r d i f f r a c t i o n v e c t o r — __o i s p e r p e n d i c u l a r t o t h e p l a n e s ( h k l ) . B y d e f i n i t i o n , g, t h e r e c i p r o c a l l a t t i c e v e c t o r i s a l s o p e r p e n d i -1 c u l a r t o t h e p l a n e s ( h k l ) , a n d i s o f m a g n i t u d e F o r d i f f r a c t i o n t o o c c u r i n c o m p l i a n c e w i t h B r a g g ' s L a w , A = 2d s i n 6,it i s n e c e s s a r y t h a t ^—~fo^ i s e q u a l t o g. L e t t h e v e c t o r * 2 — be r e p r e s e n t e d b y A O , o f l e n g t h p r o p o r t i o n a l t o -r I— A a n d r e a c h i n g t h e o r i g i n a t 0, a t a n a n g l e © t o t h e p l a n e s ( h k l ) . C o n -2 s t r u c t t h e c i r c l e o n OAB a s d i a m e t e r , o f l e n g t h p r o p o r t i o n a l t o ^ . Draw AC t o r e p r e s e n t t h e d i r e c t i o n a n d m a g n i t u d e o f t h e d i f f r a c t e d beam v e c t o r S — r — . S i n c e S = S , C l i e s o n t h e c i r c l e . A _£ — (s-s ) — o 162 oc = (s-s ) ~" — 2 s i n © = —-—/ -r A ' A (S-S ) — o 2 s i n © To s a t i s f y Bragg's Law, A = 2d s i n 9 , 2 s i n 9 _ 1 A " d(hkl) To s a t i s f y Bragg's Law, (S-S ) Izz 1 A d(hkl) I f the reciprocal l a t t i c e vector g (hkl) i s drawn perpendicular to the planes (hkl) and equal to '^'^^) o n * n e same scale as AO = ^ , i t w i l l also be represented by the l i n e OC and w i l l terminate at C on the c i r c l e . Thus, * ( h k l ) = dThfer -(s-s ) — o s o The sphere constructed with —r~ as radius, i s the sphere of r e f l e c t i o n , and a l l reciprocal l a t t i c e points l y i n g on the sphere w i l l give r i s e to coherent x-ray d i f f r a c t i o n i n accordance with Bragg's Law0 I f b^, b^ and b^ are the unit vectors of the axes of the reciprocal l a t t i c e , and j ^ , j , , 3^ a r e the corresponding continuous variables, then the d i f f r a c t i o n vector can be expressed i n reciprocal space as, (S-S ) o By d e f i n i t i o n , 163 and s i m i l a r l y the complex conjugate, r * = 'a., + m 'a_ + m ,'a, + 6m' m 1 1 2 2 3 3, "— For r e a l and reciprocal unit vectors i n any unit c e l l , a. .b. = 1 i f i = j _ i - J . R.'.b. = 0 i f i / j (where i and j are numerical suffices not related to the previous equations). Therefore, equation (3)» i n terms of the continuous variables ( j ^ jp j^ )» becomes, I ( - 1 l j 2 j 3 ) = 'F'" m 1m^ 3m 1 ,m ?»f 3 , e^f^iij ^ C m ^ - n L j) + ^ ( n ^ ' - i t ^ ) + j 5(m 3'-ra 3) + - ~ . ( Sra' -<£m)J j (4) l ( j ^ j p j 3 ) i s an interference function giving the in t e n s i t y i n electron units of the x-rays d i f f r a c t e d from one unit c e l l as a function of the d i f -fr a c t i o n vector —~ o which i s defined i n reciprocal space by the three A, continuous variables j ^ jp j j . To obtain an expression for the t o t a l power di f f r a c t e d from' a sample of several crystals at a part i c u l a r angle 28 l e t M be the number of crystals i n the sample and l e t dK be the number of crystals whose d i f f r a c -t i o n vectors are s u f f i c i e n t l y close to the point ( j ^ jp j 3 ) i n reciprocal space to produce a di f f r a c t e d i n t e n s i t y . I f the angular tolerance of the primary beam for d i f f r a c t i o n to occur i s d©C , then dM i s the number of crystals whose d i f f r a c t i o n vectors make angles from (90-9) to 90 - (© + do< ) with the primary beam0 (s-s ) — o Since the diffraction vector — - — i s equal to g, then the crystals at point ( j ^ j 2 ij) a r e o n t n e locus of a ci r c l e of radius g j s i n ( 9 0 - © ) , and the total number of crystals diffracting i s contained i n an annulus of width gdcc. The area of this annulus i s 2T i:£sin (90-©). £dot M2n£sin( 9 0 - © ) .£cW dM = * 5 4 T C £ 2 M c °. dM = 2" c o s e » d o C I f the diffracted beam i s received at a distance R from the crystal, then an element of area of the receiver i s defined as (RdfJ)(RdY), where d|J and dy are small angular variations i n the direction of the S diffracted beam vector, i n two mutually perpendicular directions, as illustrated above. The total diffracted power i s given by the product of the intensity per crystal and the number of crystals favourably oriented, 1 6 5 m u l t i p l i e d by the element of area of the receiver and integrated with respect to the three v a r i a b l e s , doC , d& and dV . Let the t o t a l d i f -fracted power be designated q. q = JjJ K ^ j g j j ) § cos G doCR 2d0 dV From the figure above i t can be seen that the angular change doc S o doc produces a small v e c t o r i a l change -jr perpendicular to — „ L i k e -dp A dY wise dp and d y produce small v e c t o r i a l changes of -j^ and -y perpen-S d i c u l a r to - y and perpendicular to each other. These three small v e c t o r i a l changes r e s u l t i n a movement of the terminal point of the d i f f r a c t i o n vector (S-S ) — at (j.. j _ j , ) . This movement defines a change of volume dV i n A 1 2 3 f o S r e c i p r o c a l space. The angle between —j  and - y i s 26, and by d e f i n i t i o n ~ and ^  are mutually perpendicular, therefore the element of volume dV at the terminal point ( j 1 j 2 i s g i v e n °y t n e s c a l a r t r i p l e product, ... doc , dP dr > D V = T ' ( T X T } dV = d * d f d Y s i n 26 A S u b s t i t u t i n g f o r (doc d£ dT ) i n the expression f o r q, ,2 A ? = j K ^ d ^ j ) f cos 6 R; q = MR2A5 f ^A^V . s i n 6 s i n 2© -2- - dV dV The element of volume dV can be represented by the s c a l a r t r i p l e product of three elementary r e c i p r o c a l l a t t i c e vectors, dV = d j ^ . C d j g b g x d j 5 b ^ ) dV = d j r fdj2 x dj^N a, \ a 2 a^ 166 dV = d j 1 d j 2 d j 3 where v i s the volume of the lattice unit c e l l , given by the scalar t r i p l e product of the unit vectors of the three axes, v = a^o(a., x a^) q = MR 2A 3 s in (5) Since any reflection in a cubic crystal may become (hOO) by a suitable choice of orthorhombic axes i t i s simpler to consider only an (hOO) reflection. Thus the diffraction vector, (S-S ) - o (S-S ) — o Since 2 sin G . i s a necessary condition for diffraction, 2 sin 6 . , — r ~ = J i b i 2 sin 0 Dif ferentiating, cos 6 A b, d(2G) Hence equation (5) can be expressed as, q = MR' -X3 ^vAbl JihW f ^ l d ( 2 e ) d ^ 3 MR 2 A 2  q = ^vAbT (6) The power diffracted at a specific angle 26 i s related to the 167 total diffracted power through the integral , q = J q(26) d(29) Thus omission of the integration with respect to d(26) i n equation (6) gives the expression for q(29). q(26) = T—^ane Jj l (hhb^H ( 7 ) The d i f f r a c t e d power q(26) i s r e c e i v e d i n the l o c u s of a c i r c l e of circumference 2TtRsin 29„ 0 0 « Hence the diffracted power measured experimentally per unit length of diffract ion l ine i s given by, q'(26) Therefore from equation (7), q(26) 2rcRsin26 MR2A2 i , ( 2 e ) = W b - ^ ^ R s i ^ o J J K3 1 3 2 3 3)dJ 2 d3 3 q'(26) = MR A 2 l6Tcvbj .sin 9 «, I(3 13 23 3)dj 2d3 3 (8) 1 6 8 Substituting from equation CO for i C ^ j p J ^ ) gives, q'(20) = MRA 2 l67tvb^sin 6 |F| 2 ^ 2 2 2 ^ . ^ r f / \ 1 1 m^mpm^n^'m^'my exp [2Tci<j^(m^'-m^) (S-S ) — o + j 2 ( m 2 ' - m 2 ) + j ^ d n y - m ^ ) + . ( S m ' - Sm)^j dj\d Let MRA21F|2 16-nrvb^sin 9 = k(e) q'(26) = k(6) f 5 ^ 2 , 2 , 1 , expfcrnljAm '-m.) + j (ra « -mJ JJ m^ra^^m^ m2' m,' L- ^ " i ± ± "d d d ( S - S Q ) + ^ ( m y - m - j ) + • (<Sm'-<gm) j] dj^dj^ (9) To include a l l diffracted intensity from the (hOO) ref lec t ion , integrations with respect to d j 2 and dj^ must be carried out from - 1/2 to + 1/2 along the b 2 and b^ axes i n reciprocal space. For example, u „ 1 expJ2Tiio 2(m 2 l-m 2)JdJ 2 = exp[jii(m 2 ,-m 2)] -exp- jjii(ra2'-m2)J 2ni(m 2 '-m 2) Using the relationship, iax -iax \ e -e \ s m ax = — ^7 , \ + —• 2 . expJ2TCiJ 2(m 2'-m 2)]dj, sini:(m2l-m2) n(m2'-m2) Hence the integrals with respect to d j 2 and dj^ are zero for any values of m 2 , m 2 ' and m^, m^ 1 , since (ra2' - m2) and (m^1 - m )^ w i l l have integral values, except for the case where m2 = m 2 ' and m^ = m^ 1 , when both have 169 indeterminate values. Thus i t i s necessary that m^ = n^' and m^ = m^ 1 , and this condition implies that for each value of m^ and m^ the crystal may be regarded as columns of unit ce l l s perpendicular to the (hPQ) planes i n the direction of the a^ axis . For = and m^ = m^', the two integrals i n equation (9) become, exp £o] dj = 1 1 " 2 Hence equation (9) becomes, ( S - S ) q'(2e) = k(6)22!25:, expf2Tii|j. (m-'-m^ + — P . ( o V - £ m ))] (10) ^ n^ n^ myn^ ' ^ 1 - ^ 1 1 1 ^ — — JJ Let the number of c e l l s i n the coherently diff rac t ing domain be N, where N = N-jN^N^ and N^, and are the average numbers of c e l l s i n the directions a^, a 2 , and a , respectively. The double summation 5 2 nura, results i n the summation of the diffracted intensit ies from a l l the columns of unit ce l ls i n the domain. Thus, lilm~ = N_ N_ d. 5 £ 5 _ N m 2 m 3 = The double summation m^ ra^' can be simplified by defining t = (m^'-m^), th and defining N(t) as the number of unit ce l ls with a (t) nearest neigh-bour i n the same column of unit c e l l s , i . e . , when t = 0, N(t) = N^, the average number of ce l l s per column, whereas when t = N , N(t) = 0. m l m l ' S \ N ( t ) ^ 2 . m^ m^' Equation (10) can be further simplified by expressing the 1 7 0 diff rac t ion vector as (S-S ) — o as was done before, and then assigning to this the maximum value of hb^  for the (ho©) reflection* Also by expressing <S_m i n terms of i t s components, Sm = X t + Y a + Z a , , — m 1 m Z m_2 and considering only the strain displacement perpendicular to the (hOO) planes, (<5mf -<5m) = a.(X • - X ) — _1 m m (s-s ) T" • — ( 8 m' - Sm) = hb. . a, (X • - X ) — — 1 x m m h(X • - X ) m m Since by defini t ion t = (m,' - m,), let the displacement (X • - X ) = X(t ) , . x x m m (s-s ) ZJ: . <4a' -«s>. wcct) Hence equation (10) becomes, q '(2e) = k(9) | - ^ N(t)exp[27ti(j 1t + hX(t))] ( l l ) Using Euler 's relationship, equation ( l l ) may be expanded as follows, ^ expJ27xi(j^t +hX(t))] = 25 xP ( 2 n iJi t ) e xP ( 2 L T I H X ( T ) )3 = 2 {( COS2TC j ' 1 t+isin2Tt j^t) ( cos2TihX (t) + isin2TthX(t))] = 2-{COS2TI j^t.cos2TthX(t)+icos2Tt3^toSin2TthX(t) + isin2Ttj^t.cos2TthX(t) - sin2uj^tsin2TihX(ty] 171 Since X(t) i s the displacement (X ' - X ), m m • (X-t) = - X ( t ) and since cos (-x) = cos x, and s in (-x) = - s i n x, 2 icos27i;J 1 t ,sin2TchX(t) = 0 a n d ^ isin2Tcj^ t.cos2TthX ( t ) = 0 2 exp[2Tti(j 1 t+hX(t)j = 2j^ o s 2 T t J 1 t o C o s 2 7 t h X ( t ) - s i n 2 n J 1 t . s i n 2 T c h X ( t ) ] q'(20) = k(6) | ~ ^ N(t) [ 0 0 8 2 7 1 0 ^ .cos2TchX ( t ) - 6in2TtJ 1 t . s i n 2 i T h X ( t ) } ( 1 2 ) Let p& cos2TthX ( t ) = A(t ) , 1 a n d " j ! ( t ) s i n 2 T c h X ( t ) = B(t) , 1 and express equation ( 1 2 ) as a Fourier series q ((26) = k(9)N ^ |A(t)cos27ij t + B ( t ) s i n 2 7 t j t ] (13) t = - o o 1 1 Both A(t) and B(t) are constants independent of 2 0 , c o s 2 i c j ^ t and s i n 2 T c j ^ t are dependent upon 20 through the continuous variable j ^ , and t i s the harmonic number. To express equation (13) as a Fourier series, i t i s assumed that the function q ' ( 2 0 ) i s periodic. Therefore the argument 2 n j ^ t must take values of - tn from the peak maximum as zero, i . e . , j ^ , a -function of 0 , takes values of - 1 / 2 . (48) From the condition for dif f rac t ion , 172 (S-S ) 2sin6 ** -°-"F" = "T = J i b i 2sin9 3-, J l " A b x J l 2a^sin6 Since A = 2d s i n 9 o 2a_^sin6Q .*. A = — for the (hOO) r e f l e c t i o n , h where 29 q i s the angle at which the r e f l e c t i o n occurs and i s the o r i g i n chosen for the 29 axis i n the plot of q* (2©) versus 26, 2a^sin6 o h = Therefore for a p a r t i c u l a r r e f l e c t i o n (hOO), equation (13) becomes, q ,(26) = k(e)N ^|A(t)cos2Trt(J 1-h) + B(t)sin2ut( ^ - h ) ] (Ik) t = - 0 O and the variable (j^-h) takes values from - 1/2 to + 1/2. Consequently, i n 2a 1 practice the function — (sin6-sin9 ) must take values from - 1/2 to + 1/2. T I f 26^ and 26., are defined as the lower and upper l i m i t s beyond which the (hOO) r e f l e c t i o n i s es s e n t i a l l y zero, t h i s i s then the range within which (j^-h) must have the values of - 1/2. Thus, ( 3 i. h) = _ ( s i ^ - sin9 Q) = - | and, (j-.-h) = — r ~ (sin9 - sin6 ) = + -" L j\ d O d 2a^ or, (sin9_, - sin6^) = 1 173 Values are assigned to 29^ and 29,, by experimental observation of the selected (hOO) reflection. These chosen values then serve to define an a r t i f i c i a l l a t t i c e parameter a^1 through the relationship, 2a 1' —j— (sin©2 - sin6 1) = 1 From previous considerations i t follows that distance L i n the crystal i n the QhOO] direction may be expressed i n terms of the unit c e l l parameter and the harmonic number i n the relationship, L = t However, when 29^ and 29^ have been chosen experimentally the new a r t i f i c i a l l a t t i c e parameter a^' thereby defined must be used i n conjunction with the harmonic number t to express crystal distance in the £h003 direction i n the relationship, L = t a1« The importance of this correction becomes greater the smaller i s the range of 26^ to 2©2 chosen for the observed reflection. For example, i f a Ni(200) reflection i s observed at 26 q = 52° using CuKot radiation of wave-length 1.54 A0, then, hA f l = 2sin9 Q (2)(1.5*0 = (2)(0,4384) = 3.51 A ° . Suppose that the intensity is judged to be greater than background through-out a 6° range from 49° to 55° (29). 17k © • V = 2(sin27.5-sin24.5) 1.5k 2(0.4617-0.414?) = 16.4 A°. = 4.7 which indicates the significance of t h i s correction i n calculations of cr y s t a l distance L. 20 should be analyzed i n terms of an abscissa having equal increments i n ( j ^ - h ) , i . e . , equal increments i n ( s i n 6 - s i n 8 Q ) , i f a numerical i n t e -gration i s to be carried out. With an automatically advanced goniometer, increments i n 26 corresponding to equal increments i n s i n 6 are not possible, and equal increments i n 26 must be used i n i t i a l l y . However, from values of q'(26) versus 26, values of q'(sin ©) versus s i n 6 can be obtained at equal increments of 6 s i n 6 by interpolation. The magnitude of the error i n t r o -duced i f t h i s procedure i s not followed becomes greater with increasing values of 6. where "a" i s defined as the width of the base of the (hOO) r e f l e c t i o n on the s i n 6 axis, and x takes values from — to — on the s i n 6 scale for the range within which the di f f r a c t e d i n t e n s i t y i s greater than background. Thus equation (lk) takes the form, t=-eo (15) 175 Before q'Csin 8) can be analyzed i n terms of the s i n © variable x, a correction must be applied for the angular dependence of k(6). Since p p r.2. k(6) = MR TV. |F I , t h i s amounts to dividing q'Csin ©) by — , where l 6 T r v b l S i n 2 e s i n 6 f i s the atomic scattering factor which i s dependent on scattering angle (2©). In addition a correction must be made for the Po l a r i z a t i o n Factor, 1 22© ( r-p—— ) , which i s part of the constant A q of equation ( l ) . A ^ was eliminated for s i m p l i c i t y by considering the d i f f r a c t e d amplitude i n terms of electron units, but since i n the f i n a l analysis i t i s absolute i n t e n s i t y i n ergs/cm. /sec. that i s measured, A must be assumed to be part of k(©) 2 2 and q'Csin ©) must be divided by f (l-t-cos 2©). The non-angular dependent 2 2sin'"© components of k(©) are not important as they affect only the height of the ChOC) r e f l e c t i o n and not the shape of the curve. In the analysis that f o l -lows constants of proportionality between the i n t e n s i t i e s of various x-ray refle c t i o n s do not affect the f i n a l r e s u l t . The angular dependence of the atomic scattering factor i s (52) apparent i n the expression used by Thomas ' , co „ i „/ x s i n kr , f = | UCr) — — — . dr where k = o JfKsin© U(r) = r a d i a l charge density of the atom, r = distance from the nucleus. / Also, U(r) = W2|V|2 , where Cj7 = the wave function of the electron,, For the l i g h t e r elements Hartree ~ ~* was able to calculate U(r) and thus obtain f, but for the heavier elements with atomic numbers greater than 25 176 the expression for the radial charge density U(r) was too complex. As an (52) alternative, Thomas assumed that for the heavier elements there i s an effective electr ic f i e l d depending on the distance from the nucleus and determined by the charge of the nucleus. This f i e l d potential i s used i n place of U(r) i n what i s termed Thomas' Method of calculating f . Thomas calculated f for Caesium and showed that i t could be plotted as a smooth function of f versus S i n ^ ^ . Bragg and West^**^pointed out that with Thomas' curve for Caesium, atomic scattering factors could be calculated for other elements simply by making a change of scale on both axes such that, f(n) = f(55) x ~ , 55 at a point on the S i n ^ 6 scale given by, ( s l " &\ _ J L _ Z _ ( £_ >V3 ( s in 6. ~ K 55 ' » A 55 where Atomic Number of Caesium = 55 and Atomic Number of chosen element = n . (55) This procedure was used by James and Brindley to calculate their table s in @ of atomic scattering factors giving values of f versus — ^ — for a wide range of elements. This table i s the primary reference which has been reproduced i n several more recent publicat ions^ x "^ ' 1 (56)^ Within the range of a few degrees covering any one x-ray ref lec t ion , the atomic s in 0 scattering factor f ( s i n 6) versus — ^ — i s approximately l i n e a r . Thus, values of f ( s i n 6) can be obtained by l inear interpolation between sin 9^ s in 6^ f ( s i n 9^) at — and f ( s i n 6^) at — ^ — . Hence the x-ray reflect ion q ' ( s i n 9) can be corrected for a l l angular dependent factors other than x 2 2 the argument 2n:t — by dividing by f (sine)(l+cos 26) . Since x i n a -2sin 9 equation (15) i s i n units of s in 9, the angular corrected function can be 177 designated q(x), and i f the constants are omitted as they are not relevant to the later analysis, the corrected function becomes, q(x) = ]A(t)cos2rtt - + B(t)sin2nt - \ ( l 6 ) , — '— a a - 1 t = - o O In practice, the observed x-ray prof i le i s not described com-pletely by equation (l6) but contains i n addition a certain degree of instrumental broadening which i s due to the x-ray optics and imperfections of the apparatus used. Part of this broadening, talcing the form of an asymmetry towards higher angles, arises because of the dual wavelengths of the Kot^ /KoCp doublet i f Kc< radiation i s being used. The Kot^  wavelength can be removed at the source using a crystal nonochromator, or alternatively i t s contribution to the observed x-ray l ine prof i le can be removed by a step-(23) wise procedure known as the Rachinger correction . The procedure makes the reasonable assumptions that the ratio of intensit ies of Ko{ to Krx^  i s known and that the wavelength separation between Ko<^  and Kot^  i s known. The true instrumental broadening can be determined by measuring the x-ray l ine prof i le for the same chosen (hOO) reflect ion from a sample of f u l l y annealed material, of a coarse grain structure and assumed to be strain free. If the 26 axis i s scaled i n units of x, this f u l l y annealed reference profi le can be defined as the function g(x). The prof i le of q(x) given by equation (l6) i s the theoretical profi le due to c rys ta l l i te size and non-uniform strain , which ignores instrumental broadening. The profi le actually observed and measured, due to c rys ta l l i te imperfections and instrumental broadening, w i l l be called p(x). Hence g(x) and p(x) can be measured experimentally but q(x) must be determined to interpret equation (l6) . The ( 1 9 ) procedure to be followed i s that described by Stokes The observed function p(x) has the form known as the Convolution, and i s sometimes termed 178 the " f o l d " of q(x) and g(x). They are related by t h e equation, -foO p(x) = j q(y)g(x-y)dy (17) -co Since the width of the base of the r e f l e c t i o n has been defined as "a", and since x = 0 at 26^, the o r i g i n of the r e f l e c t i o n , then the l i m i t s of i n t e -+ a gration can be changed to - ^  , as the functions are not periodic and are + a equal to zero outside the l i m i t s of - — • Hence, p(x) = 1 q(y)g(x-y)dy (l8) 1 The three functions can be expressed as the sums of Fourier series i n the same form as that used for the theoretical function of equation (16), A(t)cos2Ttt . a a + 0° - i q(x) = JA(t)cos2Ttt - + B(t)sin2nt - ] - oo +oO_ g(x) = ^|G(t)co82Tct I + D(t)sin2nt | ] - c O and s i m i l a r l y for p(x). Using complex coef f i c i e n t s F(t) = A(t) + i B(t),. and s i m i l a r l y G(t) and P ( t ) , q(x) = y F(t)exp(-2nit -) (19a) -oo + 9 0 g(x) = > G(t)exp(-2Ttit -) (19b) f a ^ • C O +00 X p(x) = V P(t)exp(-2Ttit -) (19c) ^— 3. 179 Substitute equations (19a), (19b), and (19c) into equation ( l 8 ) , and assume i n i t i a l l y that the integer t i s not the same i n both q(x) and g(x). n + f +00 +00 a 2 t=—oo So p(x) = Rearranging, p(x) = ^ F ( t ) G ( t ' ) F(t)exp(-2nit J) ^ G(t' )exp(-2KLt' (x-y) ^ ( 2 Q ) t ' = - o o * + 2 a 2 exp ij-27ii I (t-t * )] exp(-2irit11)dy (21) Now exp[-2ixi ^ ( t - t ' ) j d y = 0 f o r t / t 1 , a " 2 but = a, for t = t*. Thus the only terms remaining i n equation (21) are for t = t 1 , and the series becomes, p(x) = a 2 F(t)G(t)exp(-2iTit -) t a Equating p(x) i n equation (19) to equation (22) gives, P(t) = aF(t)G(t) As p(x) and g(x) are measurable functions, P(t) and G(t) the complex coefficients can be obtained from the transform relationships, (22) (23) P(t) = ± a a 2 p(x)exp(27iit —)dx a (24a) G(t) = i a g(x)exp(2nit —)dx (24b) 180 where t takes positive values. Using equations (23) and (24) F(t) can be obtained by complex d i v i s i o n . As defined for equations (19a), (19b), and ( 1 9 c ) , and also for equation ( l 6 ) , F(t) = A(t) + i B ( t ) . Thus the Fourier c o e f f i c i e n t s of the theoretical function q(x), equation (16), can be determined experimentally from the measured functions p(x) and g(x). To carry out the integrations of equations (24a) and (24b) sum-mations are made from — to —^ by d i v i d i n g the range "a", on the x-axis into intervals of S x at each of which the value of the function p(x) or g(x) i s measured. Thus.the range —^ to acquires a numerical value depending on the i n t e r v a l Sx, and "a" i s the t o t a l number of readings on the x-axis. For these summations to be true representations of equations (24a) and (24b), P(t) and G(t) must f a l l approximately to zero for values of t not larger than the range to — S i n c e g(x) for the f u l l y annealed standard i s a sharper r e f l e c t i o n than p(x), the components of G(t) w i l l decrease to zero less rapidly than w i l l the components of P ( t ) . Thus the number of sub-divisions i n t o which the x-axes of functions p(x) and g(x) are divided must be equal to or greater than twice the value of t for which the lowest frequency component G(t) becomes zero. In practice p(x) and g(x) are obtained from two separate experi-ments, and g(x) w i l l be a much sharper r e f l e c t i o n than p(x). In evaluating P(t) and G(t) the same range of integration, or i n practice summation, + a must be used for both functions, i . e . , the range of - ^ i s determined by the width of the broader function p(x) on the s i n 8 axis, although the i n t e r v a l <S x i s determined by g(x) as discussed above. I t i s more con-venient to use a smaller range "a" and a smaller sub-division $ x' to 181 evaluate the sharper function g(x) with s u f f i c i e n t accuracy than i s necessary for p(x). In t h i s case to evaluate equation (23), 1 P(t) F(t) = — , numerically equal values of t i n P(t) and i n G(t) cannot be used. Instead, coef f i c i e n t s of equal arguments must be used, i . e . , i f X \ X ^ 2nt — refers to the function p(x), and 2ut' —7 refers to g(x'), then these a a must be equal. a a' ' and equation (23) must be evaluated as, ~ a Wt7! (21) As demonstrated by Wagner , i t i s more convenient to express equations (24a) and (24b) i n terms of l a t t i c e distance L rather than harmonic number t , using the relationship, L = t °1 where a^' i s the a r t i f i c i a l l a t t i c e parameter. Since a^* i s related to the range of s i n 6 through the expression, 2a,' (sin 9^ - s i n 6 j = 1 2 1 i t w i l l have different values for the functions g(x) and p(x). However, appropriate values of t can be chosen to give common values of L for P(L) and G(L). Since the base of the r e f l e c t i o n on the s i n 6 axis has been defined as "a", .% a = (sin 9p - s i n 6^ ) 1 8 2 1 2 a l ' a Substituting this relationship into the arguments of equations (24a) and (24b) gives, x 2 a l ' 2Ttit — = 2 i t i t x — T — a A = '2TtiL ~ x A Equations (24a) and (24b) can then be written i n terms of l a t t i c e distance L, as follows, PCD = i a 2 p(x)exp(2TtiL — x)dx ( 2 5 a ) a A G(L) = i a 2 g(x)exp(2TtiL ^ x)dx ( 2 5 b ) a o - -With this form, equation (23) can then be evaluated direct ly as, F(L) = *M ( 2 6 ) even though the functions p(x) and g(x) w i l l have different intervals and ranges of x on the sin 6 axis. The constant factor ~ can be omitted, since l i k e the non-angular dependent constants of k ( 0 ) i n equation ( 1 5 ) t i t does not affect the analysis. S imilar ly , the theoretical function q(x), equation ( 1 6 ) , can be expressed i n terms of la t t i ce distance L i n place of harmonic number t , as follows, 183 q(x) = ^ [A(L)cos2TtL |x + B(L ) s i n 2 u L | x ] (27) As F(L), P ( L ) f and G(L) are complex quantitites the d i v i s i o n of equation (26) can be carried out from the following relationships, where s u f f i x r designates r e a l and s u f f i x i imaginary parts, F(rL) = P(rL)G(rL)-rP(iL)G(iL) G 2(rL)+G 2(iL) (28a) F ( i L ) = P(iL)G(rL)-P(rL)G(iL) G 2(rL)+G 2(iL) (28b) To obtain P ( r L ) , and P ( i L ) , etc., equations (25a) and (25b) must be expanded using Euler's relationship, P ( D a 2 2 2 p(x)(COS2ITL — x + i s i n 2 n L -r x)dx A A (29a) G(L) = i a r + 2 a 2 2 2 g(x) (cos2TtL — x + isin2-n:L — x)dx A A (29b) Equating r e a l and imaginary parts respectively gives, r 2 P(rL) = i a p(x)cos2nL — x dx A a U " 2 (30a) P(iL) = i a 1 + 2 p(x ) s i n 2 u L r x dx A (30b) 184 a r+ 2 G(rL) = ± a a 2 a r+2 g(x)cos2nli | x dx (30c) G(iL) = 4 a a 2 g(x)sin2nL ^ x dx (30d) The evaluation of equations (30a), (30b), (30c), and (30d) by summation of the experimental functions p(x) and g(x) permits the evaluation of equations (28a) and (28b). By d e f i n i t i o n , F(L) = A(L) ± iB(L) F(rL) = A(L) and F(iL) = B(L) Thus values can be obtained for the coeff i c i e n t s A(L) and B(L) of equation (27)c These co e f f i c i e n t s were defined to have physical significance when c simplifying theoretical equation (12). For the summation of equations (30a), (30b), (30c) and (30d) an o r i g i n must be chosen for x, i . e . , for s i n 6^, Whilst other c r i t e r i a (21) have been used, Wagner has shown that i f the centroid of the x-ray r e f l e c t i o n i s chosen as the o r i g i n the imaginary coef f i c i e n t s w i l l be small and the r e a l c o e f f i c i e n t s w i l l have only small o s c i l l a t i o n s . This i s apparent i f equation (25a) i s expanded as a power series using Maclaurin's theorem. aP(L) = J* p(x)exp(27iiL -^ x)dx = J p(x)d x + 2niL A J xp(x)dx - 2TC 2L 2 x p(x)dx + ... 185 I f the o r i g i n of x i s the centroid of p(x) then, :)dx = 0 Jxp(x) and the second term of the series i s zero, thus eliminating the f i r s t imaginary part of P(L). With the origins so chosen for the experimental functions p(x) and g(x), the sine c o e f f i c i e n t s B(L) of the derived function q(x) w i l l be small but from a knowledge of the cosine co e f f i c i e n t s A(L) both the c r y s t a l l i t e s ize and the extent of non-uniform short range e l a s t i c strains can be determined. To simplify equation (12), A(t) was defined as, A(t) = cos2nhX(t) 1 and the same i s true for A(L) i f N(t) and X(t) are chosen such that ' a l ' rcj^ i s related to the number of unit c e l l s i n the [h00]| dir e c t i o n and i s 1 N(t) independent of the order of the r e f l e c t i o n . Let - r t — be designated the 1 D Domain Size Coefficient A (L). Cos2irhX(t) i s related to the non-uniform l a t t i c e s t r a i n through X(t) the coeffic i e n t of the s t r a i n vector i n the a^ dire c t i o n and i s dependent upon the order of the r e f l e c t i o n (hOO). In the general case the order i s given by, 1/2 h = (hd + \t + l 2 ) o Let cos2nhX(t) be designated the Strain Coefficient A (L, h Q ) , the s u f f i x h Q i n d i c a t i n g ordjr dependence. A(L, h Q) = A D(L) A S(L, h Q) (3D 186 Since by d e f i n i t i o n , N(t) = when t = 0, and, X(t) s 0 when t = 0 both AD(L) and A S (L , h ) = 1 when t =0 A(L, h ) = 1 when t = 0 o Consequently, the experimentally determined values of A(L, hQ) must be normalized to unity for t = 0, i . e . , for L = 0, before further interpreta-tion of the coefficients can be carried out. If £ i s the strain i n a distance L measured i n the a^ direction, £ L = fiLjX(t) Therefore i n a cubic l a t t i c e , X(t) = a where "a" i s the unit c e l l l a t t i ce parameter. hX(t) = for an (hOO) ref lec t ion, a c Since A (L, hQ) = cos27thX(t) S /. A (L,h ) = cos2Tth£L/a o For small values of ^ ^ ^ , the cosine may be expressed as a series using Maclaurin's theorem, which, ignoring terms of the fourth power and higher, gives, A (L,h ) = cos2nh = 1 — - — ' r\ o J i 2 2a Taking logarithms of equation (31) and substituting the above expression for A (L,h Q ) gives, 187 lnA(L,h ) = lnA D(L) + l n ( l - ^ ) o d a Since for small values of x, x = l n ( l + x) , lnA(L,h ) = lnA D(L) - 2*2 6 ^A 2 ( 3 2 ) o d a Equation (32) i s the f i n a l expression from which values .of non-uniform e l a s t i c s t r a i n and domain size can be obtained using the values of the r e a l coefficients A(L,h Q) from the complex coefficients F(L) obtained by experi-ment. To u t i l i z e equation (32) variations i n h are required. A more 2 2 2 1/2 general study would show that variations i n the order h Q = ( h +k + 1 ) are required, but i f t h i s i s achieved by.using r e f l e c t i o n s from non-parallel planes, then the c r y s t a l should be e l a s t i c a l l y i s o t r o p i c . I f two orders of the (hOO) r e f l e c t i o n can be used then the strains i n question are i n the \^ hOoJ d i r e c t i o n and e l a s t i c isotropy i s not required. In cold r o l l e d . n i c k e l the (220) r e f l e c t i o n i s the strongest but the (¥+0) r e f l e c t i o n can-not be recorded on the standard diffractometer using CuKct radiation. The ( i l l ) and (222) ref l e c t i o n s are too weak due to preferred orientation and only the (200) and (400) r e f l e c t i o n s are of suitable i n t e n s i t y for analysis, 2 giving values of k and 16 for h . A series of values of A(L,h Q) i s obtained by experiment for a range of values of L and for two orders of h, and the values of A(L,h Q) are normalized to unity for L = 0 as discussed e a r l i e r . The upper l i m i t on the range of L i s determined by the s t a b i l i t y of the components i n equations (25a) and (25b), 188 P(L) = i I p(x)exp(2TtiL | x)dx (25a) G(L) = i a 2 g(x)exp(2niL j x)dx (25b) a 2 Since F(L) i s obtained from equation ( 2 6 ) , F(L) = | g ^ (26) i t follows that e r r a t i c fluctuations i n F(L) are l i k e l y to occur due to fluctuations i n P(L) and G(L) at large values of L when P(L) and G(L) are both approaching zero. This i n s t a b i l i t y i n unfolding the convolution has (22) been studied extensively by Mi t c h e l l " . He points out that large errors occur i n F(L), and subsequently i n A(L,h Q), when P(L) and G(L) approach t h e i r standard deviations. He has demonstrated that t h i s can be avoided by eliminating c o e f f i c i e n t s for which the modulus |G(L)I of the d i v i s o r i s less than an assigned l i m i t . In a more general treatment he applies the condition that F(L) i s to be taken as zero when the square root of i t s r e l a t i v e variance i s greater than 0.3. Errors w i l l also occur i n A(L,h Q) i f the o r i g i n of p(x) has not been chosen so as to make the sine c o e f f i c i e n t s B(L,h Q) equal to zero. The best choice of o r i g i n i s the centroid but with an asymmetric function the sine coefficients B(L,h Q) may s t i l l acquire s i g n i f i c a n t values. In t h i s case since B(L,h Q) would be zero i f the o r i g i n were correctly chosen, and since domain size and s t r a i n effects produce a symmetrical l i n e broadening with B(L,h Q) equal to zero, i t i s better to d e f i n e ^ 2 ^ , 189 1/2 A(L) = L~F2(rL) * F 2(iL)J rather than, A(L) = F(rL) Since the cosine coe f f i c i e n t s A(L) = F(rL) have been normalized by dividing by A(o), the sine coe f f i c i e n t s F(iL) must also be divided by A(o) before computing A(L) = £ F 2 ( r L ) + F 2 ( i L ) ] 1 / / 2 . 2 2 From the series of values of A(L,h ) for h = k and h = 16, a ° set of straight l i n e s can be drawn with values of lnA(L,h ) as ordinates 0 2 and the two values of h as abscissae, each chosen value of L r e s u l t i n g i n 2 one l i n e of lnA(L,h Q) versus h . This i s the graph required to interpret equation (32). The slopes of these l i n e s give values of ^ , from 2 a which values of the mean square s t r a i n £ are obtained for a range of 2 values of L. £ i s the s t r a i n normal to the r e f l e c t i n g planes (hOO), averaged over the length L, squared, and averaged over the region from 2 1/2 which the r e f l e c t i o n comes. The graph of ( & ) versus L shows the d i s t r i b u t i o n of non-uniform s t r a i n as a function of distance i n the c r y s t a l , and the effect of various thermo-mechanical treatments can be compared. 2 The intercepts of the straight l i n e s of lnA(L,h Q) versus h 2 D with the h =0 axis give the values of InA ( L ) , as indicated by equation (32), for each value of L. From InA (L), values of A (L) are calculated, normalized to A D(L) = 1 and plotted against L, as a series of curves for the various material conditions. B e r t a u t ^ 2 ^ has shown that i n a plot of A^(L) versus L, the f i r s t derivative at L = 0, i . e . , the i n i t i a l slope, equals the,negative reciprocal of the average domain s i z e , and that the second derivative, or 190 curvature, i s d i r e c t l y proportional to the f r a c t i o n of columns of length L present i n the c r y s t a l . Since the d i s t r i b u t i o n of columns of a given length can never be negative, the curvature of the graph of A^(L) versus L cannot be negative. Contrary to theory, i t i s sometimes found that the experimental values of A^(L) versus L produce a convex curve of negative curvature i n the region approaching L = 0. This has been described as the "hook e f f e c t " (18),(20),(2l)^ This error arises because of inaccuracies i n the measure-ment of the true background l e v e l of the function p(x) which result i n low values for the measured area under the x-ray peak. The experimentally determined values of A(L) were normalized to unity for L = 0, i . e . , A(o) = 1, and A(o), the f i r s t Fourier c o e f f i c i e n t , i s the t o t a l area under the peak. A low value of A(o) affects the values of A(L) and A^(L), p a r t i c u l a r l y for regions near to L = 0, and results i n the negative curva-ture sometimes found i n the plot of A^(L) versus L i n that region. An approximate correction for t h i s i s to ignore the region of negative curva-ture, and to extrapolate the adjacent region of the curve to intercept the A^(L) axis at some value greater than unity for L = 0. This new value of A^(o) i s then taken as unity, and the other values of A^(L) versus L are (21) normalized to i t . Wagner suggests that the region of the curve to be ignored because of the hook effect should extend from L = 0 to a distance equal to 0.1 D, i . e . , K $ of the domain s i z e . The magnitude of the error i n A(o) depends largely on the extent to which the function p(x) i s (l8) broadened by Strain Effects as against Domain Size Effects . Broadening due to non-uniform s t r a i n follows a Gaussian d i s t r i b u t i o n which decreases to zero at f i n i t e points on tho s i n 9 axis, whereas broadening due to small domain size follows a Catchy d i s t r i b u t i o n which has long t a i l s of s i g n i f i -cant intensity p e r s i s t i n g to very large values of s i n G. Thus i t i s the 191 l a t t e r effect which makes the accurate measurement of background l e v e l d i f f i c u l t , and results i n low values of A(o) and negative curvature i n the plot of fP(L) versus L near to L = 0 o (25) The conclusion of Bertaut can also be rationalized from the d e f i n i t i o n , A°(L) = ^ 1 N l " t i -N I 'ta- ' 1. - N. I s ! A°(L) = 1 - § where D i s the average column length i n the j>00] d i r e c t i o n , or the Domain Size. Therefore i n a plot of A^(L) versus L the negative reciprocal slope gives D. The above r a t i o n a l i z a t i o n i s true only for small values of t and therefore the i n i t i a l slope near to L = 0 should be taken. Since the axis of A^(L) has been normalized to unity for L = 0 the negative reciprocal slope of A^(L) versus L near to L = 0 i s also the intercept on the L axis of the tangent to the curve at L = 0, giving the Domain Size D d i r e c t l y for each therm o-mechanical material condition. The significance of Twins and Stacking Faults i n the measure-ments of l a t t i c e s t r a i n and domain size from x-ray l i n e broadening l i e s i n the fact that they both constitute domain boundaries and thus contribute to symmetrical l i n e broadening through the Domain Size Coefficient. I t has been shown that the average Domain Size i s given by the negative reciprocal 192 slope of A (L) vs. L near to L = 0, i . e . , dA D(L) dL 1 D L=0 However, i f twins and stacking f a u l t s are present the domain size r e l a t i o n -ship should be expressed as, dA°(L) dL L=0 D D F where P i s the domain size that i s required and D i s the contribution due (l8) (2l) to both twins and stacking f a u l t s . Expressions have been derived ' for ^c? for various unit c e l l s and various r e f l e c t i o n s . For the case of D (200) and (400) r e f l e c t i o n s i n an f.c.c. unit c e l l the expression i s , 1_ (1.5'* ) D F where OL i s the Stacking Fault probability, p i s the Twin Fault p r o b a b i l i t y , and "a" i s the f.c.c. l a t t i c e parameter. Thus, dAD(L) dL 1 (1.5 CA. + P ) (33) _tL=0 From the Fourier analysis dA D(L) dL p must be obtained independently. L=0 i s obtained and to find D &L and .(57) To t h i s end, the work of Paterson ' i s usually taken as the primary reference. He uses the Miller-Bravais indices and regards the f . c . C i l a t t i c e as being hexagonal with (00,l) close packed planes. In the f.c.c. structure a single ( i n t r i n s i c ) stacking fault on a ( i l l ) plane arises from a shear of 1/6 j_121j. Paterson shows that t h i s produces a change of phase i n the scattered x-rays, given by, 193 > = £ | ( - H + K ) i n Miller-Bravais indices for the hexagonal system, which converted to M i l l e r indices for the f.c.c. l a t t i c e i s equivalent to, 0 = | (h - 2k + 1) . 3 Thus 0 can have values of - , where n takes integer values. A more convenient way of expressing t h i s result i s to say that i n the presence of stacking f a u l t s on the ( i l l ) plane, (but not or. other •( 111^ planes), the r e f l e c t i o n 1 ( h k l ) w i l l be unchanged i f | h + k + 1 | = 3n. I f |h + k + 1 | = 3n + 1 the r e f l e c t i o n (hkl) w i l l be broadened and displaced towards a higher (2©) angle, and i f j h + k + l j = 3n - 1 the r e f l e c t i o n (hkl) w i l l be bro adened and displaced towards a lower (26) angle. In a p o l y c r y s t a l l i n e material the condition | h + k + 1 J = 3n i s never met since f a u l t s w i l l occur on several sets of non-parallel / 111^ planes. Thus although a fault on ( i l l ) leaves the ( i l l ) r e f l e c t i o n un-changed, fau l t s on a l l other {^1H^ planes w i l l affect the ( i l l ) r e f l e c t i o n . In the f.c.c. l a t t i c e the twin fault i s equivalent to a series of stacking f a u l t s on every ( i l l ) plane, whereas a series of atacking faults on every alternate ( i l l ) plane would result i n a perfect h.c.p. l a t t i c e . A l -though i t i s unlikely that an f.c.c. twin could be formed by a shear of 1/6 L_12l] on every ( i l l ) plane, i t i s possible that the twin could grow i n i t i a l l y from a double ( e x t r i n s i c ) stacking f a u l t . In view of the growth model, i t i s more convenient to regard the twin as being related to the parent l a t t i c e by a rotation of l8o° about a < 111^> axis. Applying Paterson's analysis to the twin case leads to the conclusion that twin f a u l t s produce an asymmetric 194 l i n o broadening and a very small displacement of the peak maximum int e n s i t y , whereas deformation stacking fa u l t s produce a symmetrical broadening and a larger peak s h i f t . (l8) Based on Paterson's work, Warren has developed expressions giving the stacking fa u l t p r o b a b i l i t y i n terms of displacement of the peak maximum. For (200), (400) and (111) r e f l e c t i o n s i n an f.c.c. l a t t i c e h i s expressions are, PM r~ IS (20°) ( l f O o ) = + ^ 5 oC tan e Q (35) TC PM /— A ( 2 0 O ) ( 1 1 1 ) = + 2 2 3 t a n % ( 3 6 ) TC To compensate p a r t i a l l y for any o v e r a l l d i s t o r t i o n of the l a t t i c e due to macro stresses, Warren combines two of the above expressions of opposite sign to obtain an expression for the change i n the separation between (200) and ( i l l ) peak maxima due to stacking f a u l t s , A PM PM ( 2 6 ° 'C20O) - <2e°W) - 45 -i>3 TC t a n 6(200) + 2 t a n G ( l l l ) j ( 3 7 ) Also r e f e r r i n g to Paterson, Wagner^ 2^ uses the Fourier coef-f i c i e n t s , for which the o r i g i n must be the peak maximum, to calculate the twin f a u l t p r o b a b i l i t y $ . He uses the expression, 1— P> = -j/3 tan ti , , - i . i l -i • i_ ±. sine c o e f f i c i e n t . where }i xs tne phase angle gxven by, tan yi = c o s i n e c o e f f i c i e n t ^ should be independent of harmonic number t or l a t t i c e distance L. (l8) Warren obtains j& from the excess i n t e n s i t y above true background at a point between the overlapping ( i l l ) and (200) t a i l s , since twin fa u l t s produce opposite asymmetries i n these two peaks. 195 More recently Cohen and Wagner developed an expression for /3 using only the faulted peak without reference to the annealed s t a r t i n g material. The peak asymmetry, i . e . , the displacement of the peak maximum from the centroid, i s used. For (200), (400) and ( i l l ) r e f l e c t i o n s i n an f.c.c. l a t t i c e t h e i r expressions are, CG PM ( A S ^ ' ) ( 2 0 0 ) = ( 2 G O ) ( 2 0 0 ) " ( 2 e O ) ( 2 0 0 ) = - lk'6 P t a n 6 o ( 3 8 ) CG PM Us^\k00) = ( 2 e ° W ) - ( 2 e O ) ( 4 0 0 ) = + l k ' 6 P t a n G o ( 3 9 ) CG PM ( A s y m . ) ( m ) = ( 2 0 ° ) ( n i ) - ( 2 0 ° ) ( m ) = + 11 p tan 0 q (4O) As was done i n the case of c< , two expressions of opposite sign can be com-bined to eliminate partl y any instrument or doublet asymmetric broadening that i s present. Thus, (Asym.)( l i ; ]j - ( Asym.) ( 2 0 0) = (lltan©^ ^ + 14.6 t a n © ^ ^ ) (4l) In a l l the above expressions f> should r e a l l y be replaced by (fJ+ 4.5 o O ' j for f.c.c. structures, where i s the twin f a u l t probability and oC*' i s the double (extrin s i c ) stacking f a u l t p r o b a b i l i t y. Since ( 2 9 ) ^ annealed = ( 2 6 ) ^ annealed, then assuming no residual macro s t r a i n s , ( 2 9 ) P M annealed = ( 2 9 ) P M faulted I I i n the case where f a u l t i n g i s due to £> and <x . , • C ? A l ^ PM v 'annealed = (2©) r u faulted. This argument permits a re-arrangement of the left-hand side of equation (4l) to y i e l d an expression describing the change i n the separation of (200) and ( i l l ) peak centroids due to twinning, since, 196 ( A s y m . ) ( l l l ) - ( A s y m . ) ( 2 0 0 ) = ^ 2 6 ) ^ , - ( 2 0 ) ^ Thus equation (4l) can have a s i m i l a r form to equation (37), as used by ,, (21) Wagner , CG CG A Q ^ W - ( 2 6 0 ) ( 1 1 1 ) J = P ( 1 1 t a n G ( l l l ) + l k ' 6 t a n 9 ( 2 0 0 ) ) ( Z f 2 ) However, equation (42) has the disadvantage that i t requires measurements on the annealed s t a r t i n g material, as does equation (37)* whereas equation (4l) does not. Thus, the use of equation (37), together with either equation (4l) or (42), would y i e l d both c< and p> which when inserted into equation (33) would give the required domain size D. In the case of cold r o l l e d n i c k e l a l l o y s , there i s a strong l-: preferred orientation with the (220) plane i n the plane of r o l l i n g . With the standard diffractometer geometry, the ( i l l ) r e f l e c t i o n s are very weako This l i m i t a t i o n prevents the use of equations (37)1 (4l) and (42) to deter-mine oC and 6 » As an alternative,equations (34) and (35) can be used to determine 1 and equations (38) and (39) to determine f> . Since equations (34) and (35) are of opposite sign, they provide a self-consistent check as to whether the observed peak s h i f t i s due to stacking fa u l t s or to residual l a t t i c e macro s t r a i n , since the l a t t e r cause would displace both (200) and (400) refl e c t i o n s i n the same dir e c t i o n . S i m i l a r l y , since equations (38) and (39) are of opposite sign, i t should be possible to determine whether the observed peak asymmetry i s due to twinning or to some instrument or doublet effect. Residual l a t t i c e macro strains i f present w i l l result i n x-ray 197 peak s h i f t which w i l l permit the calculation of l a t t i c e .0train i n the direct i o n perpendicular to the r e f l e c t i n g planes, using the relationship, (d - d ) % e = . 0 x 100 . d o Since l a t t i c e spacing d i s calculated from Brags 's Lav; using measurements of t o t a l integrated i n t e n s i t y , i t i a correct that the peak positions for o CO s t r a i n measurements should be (2© ) W v", the cantroids. In the absence of twinning, since broadening due to micro s t r a i n , domain size and stacking faults i s a l l symmetrical, (29°) = (26°) \ and either could be used. 198 APPENDIX 2 A Computer Programme to Determine Non-Uniform Lat t i c e S t r a i n  and C r y s t a l l i t e Domain Size by the Analysis of X-Ray Line Broadening This programme has been written i n Fortran IV for the IBM 360/70 computer. Reference was made to other computer programmes used i n t h i s f i e l d by De A n g e l i s ^ ^ \ Grierson and B o n i s ^ ^ \ and Wagner^ 2^. The primary objective was to carry out the summations of equations (30a),-(30d) of Appendix 1 to obtain the Fourier c o e f f i c i e n t s P ( r L ) , P ( i L ) , G(rL) and G(iL), and then to obtain the cosine c o e f f i c i e n t s A(L) of the theoretical x-ray function q(x) by complex d i v i s i o n as i n equation (28a) of Appendix 1. In addition, the following s i x preliminary steps were taken to prepare the experimental data of the x-ray functions g(x) and p(x) for !' both (200) and (400) r e f l e c t i o n s before commencing the above summations. ( i ) Correct for the angular dependence of the atomic scattering factor f. Calculate values of f^ at s i n 9^ and fp s i n ©p covering the range of each r e f l e c t i o n , obtain intermediate values of f (sin 0) by in t e r p o l a t i o n , divide each value of measured in t e n s i t y by the appropriate value of f"\sin 9). As the experimental data v/ere obtained as times for a fixed number of x-ray quanta counts, reciprocals were f i r s t taken to give i n t e n s i t i e s before correcting for f, ( i i ) Correct for the angular dependent components of A q i n equation ( l ) and k(0) of equation (15.) i n Appendix 1. This amounts to dividing a l l i n t e n s i t i e s by the corresponding value of (1 + c o s 2 29) P s i n "9 ( i i i ) Rescale the (29) axes to s i n 9, choose a fixed i n t e r v a l &sin9 199 and obtain new values of the i n t e n s i t y functions p(x) and This requires interpolation between the o r i g i n a l values of p(x) and g(x) versus (28). Subtract the background i n t e n s i t y . Set up a gradient from the background at s i n ©^ to that at s i n ©., and obtain the necessary intermediate values by interpolation. Subtract the appropriate value of t h i s sloping background from each value of i n t e n s i t y versus s i n 8. Apply the Rachinger correction to remove the i n t e n s i t y contribu-t i o n from the Kc*2 wavelength of the CuKoC doublet. From the d i f f e r e n t i a l of Bragg's Law obtain the s h i f t i n s i n 8 r e s u l t i n g from the difference i n wavelength Sk between CuKoCl and CuK oC 2. Assume I(Ko<.l) = 2I(Kcrt.2) and carry out a stepwise subtraction of the Kc<2 in t e n s i t y s t a r t i n g at s i n 0^. For ease of working, i t i s essential that i n Step ( i i i ) the i n t e r v a l S s i n © i s so chosen that an i n t e g r a l number of these i n t e r v a l s f i t s exactly into the s h i f t i n s i n © considered here due to the doublet. As the choice l i e s only i n step ( i i i ) and not i n step (v), step (v) must be considered before step ( i i i ) i s carried out. Calculate the centroid of each r e f l e c t i o n from the relationship, where x and CG are i n units of s i n 6. Subtract CG from a l l values of s i n © from s i n ©^ to s i n ©^ so as to obtain a new set of s i n © readings having both positive and negative values g(x) at in t e r v a l s of & sin© i n the range s i n ©.. to s i n 0_. 200 from the centroid as o r i g i n . The data so obtained for (200) and (400) r e f l e c t i o n s , giving corrected monochromatic i n t e n s i t i e s above background, versus positive and negative values of s i n 8 from the centroid as o r i g i n , are then integrated to obtain the Fourier c o e f f i c i e n t s i n accord with equations (30a) to (30d). To demonstrate that the above s i x corrections are being carried out cor r e c t l y the computer programme plots out a sequence of graphs of the i n t e n s i t y functions at several intermediate stages of correction i f required to do so for selected materials. Having obtained values of A(L) = F(rL) by complex d i v i s i o n as i n equation (28a) of Appendix 1 for a chosen range of L, for both (200) and C+00) r e f l e c t i o n s , the programme f i r s t normalizes a l l values of A(L) to unity for L = 0, takes logarithms and then plots lnA(L,h o) versus h for each value of L to interpret equation (32) of Appendix 1. From the slopes 2 1/2 of these l i n e s the programme calculates the moan l a t t i c e s t r a i n ( £. ) versus L and plots t h i s as a graph for each material condition. 2 2 From the intercepts of lnA(L,h Q) versus h with the h =0 axis values of lnA^(L) are obtained as indicated by equation (32) of Appendix 1, converted to A^(L), normalized to unity for L = 0, and plotted as a function of L for each material condition. The programme then c a l -culates the average domain size by two- c r i t e r i a ; f i r s t l y from twice the area under the curve and secondly from the negative reciprocal, slope of A^(L) versus L near to L = 0, but at a specified distance from L.= 0 equal to 0.2 x Domain Size ( l ) o 2 1/2 D In addition to the graphs of (£ ) versus L and A (L) versus 201 L for each material condition, and the sequence of graphs of i n t e n s i t y for selected materials, the programme also prints out the following numeri-c a l results for each material condition: ( i ) Material type, Thermo-mechanical Condition and Reflection Starting angle of scan Angular increment Number of data points Atomic Scattering factors at each end of the r e f l e c t i o n Original i n t e n s i t y values Corrected i n t e n s i t y values Corresponding values of s i n 0 Sin 0 increment Number of s i n 0 data points A r t i f i c i a l l a t t i c e parameter, defined i n Appendix 1 ( i i ) ( i i i ) ( i v) (v) (vi) ( v i i ) ( v i i i ) ( ix) (x) ( x i ) ( x i i ) ( x i i i ) (xiv) (xv) (xvi) ( x v i i ) ( x v i i i ) (xix) Reflection o r i g i n 20 q based on the peak centroid Lattice parameter based on the peak centroid Reflection o r i g i n 2©q based on the peak maximum Latt i c e parameter based on the peak maximum Peak asymmetry between centroid and maximum A table of the following Fourier c o e f f i c i e n t s , defined o i n Appendix 1, versus l a t t i c e distance L from 0 to 500A; GR(L), GI(L), PR(L), PI(L), FR(L), F I ( L ) , A(L), LNA(L). 2 1/2 A table of root mean square s t r a i n values, (£ ) , and domain size coefficients A^(L) versus l a t t i c e d i s t -o ance L from 0 to 500A. Coherent domain size D from the two c r i t e r i a given e a r l i e r . 202 The variable names i n the computer programme have the follow-ing meanings. o WAV Wavelength of radiation used, e.g., CuKotl, A. DWAV Difference i n wavelength between CuKoCl and CuKo<2. NGP Number of points on f i n a l graph, e.g., 100. o GINT Interval on x-axis of f i n a l graph, e.g., 5.GA. NDP Number of data points for each r e f l e c t i o n . ANG (20) angle for each data point. ANG(l) (20-^), the s t a r t i n g point of the scan. DAN Increments i n (20), e.g.,0.01°. k PX1 Data values as times i n seconds for 2 x 10 counts. PX3 Data values as i n t e n s i t i e s . SAN1 Values of s i n 0. F l Atomic scattering factor at s i n 6^. F2 Atomic scattering factor at s i n Q^, F ( l ) Intermediate values of atomic scattering factor. FF(X) Atomic scattering factor squared. PX1 Previous variables, also used for i n t e n s i t y values corrected for angular dependence. PPX1 The maximum value of PX1. IMAX The reading number which i s the maximum. BINT Interval i n s i n © between the maximum i n t e n s i t y and the previous reading. DANG The displacement i n s i n © due to the v/avelength difference between CuKcxl and CuKoc2. EINT An i n t e r v a l i n s i n © close to BINT but also exactly d i v i s i b l e i n to DANG. 203 SAN2" New values of s i n 6 at equal intervals of .EINT. NSDP The number of values of S/UI2. PX2 New values of in t e n s i t y for each value of SAN2. PX2 Previous variable, also used for i n t e n s i t i e s corrected for a sloping background, PX F i n a l i n t e n s i t y values after the Rachinger correction for the CuK o< 1/CuK oC 2 doublet, AREA Area under the r e f l e c t i o n peak, CG Centroid of the area on the s i n 6 axis, SAN Sin^ 6 values re-scaled to run positive and negative from CG, MAT A t i t l e for each material condition. • IH,IK,IL (hkl) KONT A control number to route the execution. 2 s i n 9 DVSC D i f f r a c t i o n vector, - -A A1P A r t i f i c i a l l a t t i c e parameter, a'^ = 2 ( s i n 9 — s i n 6 ) Al True l a t t i c e parameter based on peak centroid. AIM True l a t t i c e parameter based on peak maximum. TTZ Bragg angle (29 q) based on peak centroid. TT Bragg angle (29 q) based on peak maximum. H02 ( h 2 + k 2 + l 2 ) . ASYM Asymmetry, (TTZ-TT). DIST(L) Crystal distance L i n angstroms. ARG (L j- x) i n the arguments of the Fourier components. DEC The decimal part of ARG. PR Real Fourier coe f f i c i e n t s for each material. PI Imaginary Fourier coefficients for each material. GR1 Real Fourier coefficients for annealed powder standard (200) r e f l e c t i o n . 20k Imaginary coef f i c i e n t s as for GR1. Real Fourier coef f i c i e n t s for annealed powder standard (kOO) r e f l e c t i o n . Imaginary co e f f i c i e n t s as for GR2. Unfolded r e a l Fourier co e f f i c i e n t s for each material. Unfolded imaginary Fourier co e f f i c i e n t s for each materialo A = [C F R ) 2 + ( F I ) 2 ] 1 / 2 Natural logarithm of A. Negative slope of LNA versus H02. Intercept on LNA axis of LNA versus H02. Lattice s t r a i n 6 i n distance L. Percent l a t t i c e s t r a i n , £ x 100, i n distance L. Domain Size c o e f f i c i e n t . Twice the area of the graph of AD versus L. Domain Size ( l ) calculated from Y. A point on the L axis of AD versus L equivalent to 20$ of Domain Size ( l ) . Domain Size (2) calculated from the negative reciprocal slope of AD versus L at the point L = IL. Table X i s a reproduction of the computer programme statements. 205 F O R T R A N I V G C O M P I L E R MAIN 0 6 - 0 5 - 6 9 10:10:11 PAGE 0 0 0 1 OOO? 0 0 0 3 0 0 0 4 0 0 0 ? _ O 0 0 6 0 0 0 7 0 0 0 8 OCOO 0 0 1 0 0 0 1 I 0 0 1 7 O o f 3 0 0 1 * 0 0 1 5 0 0 1 6 0 0 1 7 0 0 1 B 0 0 1 9 0 0 2 0 0 0 2 1 0 0 ? ? 0 0 2 3 0 0 2 + 0 0 2 5 0 0 2 6 0 0 2 7 0 0 2 6 0 0 2 9 0 0 3 0 0 0 3 1 0 0 3 2 0 0 3 3 0 0 3 + 0 0 3 5 0 0 3 6 0 0 3 7 0 0 3 8 0 0 3 9 0 0 + 0 00+1 00+2 0 0 + 3 00++ 0 0 * 5 0 0 + 6 00+7 oo+a 0 0 + 9 0 0 5 0 0 0 5 1 C A N A L Y S I S flF X RAY L I N E BROADENING D I M E N S I O N « N G ( 9 0 0 l f P K K 9 0 0 1 ,SAN1 ( 9 0 0 ) , S A N 2 I 1 0 0 0 ) , P X 2 ( 1 0 0 0 ) , P X ( 1 0 0 0 11 . S A N l 1 0 0 0 ) »D!ST( 101 I ,PR( I C l ) , P I U 0 1 ) , G R I ( 1 0 1 I ,GI H 1 0 M . G R 2 I 1 0 1 ) , G 1 1 2 1 1 0 1 » , F « I 1 0 1 1 , F ||10 1 ) . L N A ( 1 0 1 I . H L N A I 1 0 1 I . F P S H 1 0 I> * P C S T ( 1 0 1 > , A D ( M 0 1 I . H A T I 1 5 ) , F ( 9 0 0 ) , F F ( 9 0 0 ) . A 1 1 C I I , P X 3 ( 9 0 0 ) R E A l L NA K F A n(i, t o o i M A v.nuAv R F A O(5. 101 )NGP»GIfcT.NG « A R * 3 . 1 + 1 5 9 3 / 1 8 0 . C A L L P L P 1 S 99 R F A n i S , 1 0 2 1 ( M A T ( J ) »l» I. 1 5 ) , I H , I K , I L WR| TF 1 6 , 1 0 3 H MAT( I ) . I M , 1 5 ) , l H « I K , I L RfAPIS,10*1 ANG( 1),DAN,NOP )F1,F?,KONT,(PXHIltI-1.NOPt MR IT£(6,105)ANGI I ) , O A N , N D P , F I , f 2 . K O N T , ( P K 1 I I 1 , I M . N O P ) GOTH*! _ 9 f l RE AnI 5,10 2 .E N0= + ? ) I M A T I l ) , I M , 1 5 ) , I H , l K , I L WRI T E I f t , I 0 3 M M A T U ) , ) M . 1 5 ) , I H , I K , I L RE A O ( 5 , 1 1 5 ) A N C I 1 ) , O A N , N D P , F 1 , F ? , K O N T , { P X I(I)» t » 1 t N D P I rf«ITF(6,l16)ANGt I ) , D A N , N O P , F 1 , F 2 , K U N T , ( P X 1 ( I ) , 1 * 1 , N O P ) +3 0011=2.NOP 1 A N G ( I ) = A N G ( 1 - 1 ) » D A N DD*+IM»NDP ++ P X 3 ( I 1 * 5 0 0 . / P X 1 I ) i 002lM,NDt» S A N 1 | I ) = S I N ( A N G ( I > * R A D / 2 . ) F ( I I*F1.|F?-F 1) / I S A N l ( N O P ) - S A N K 1 ) ) * I S A N l ( I ( - S A N K L) ) F F ( I 1 = F ( I J * F ( I I _2 »1.) = P1L3J I J M S A h l 1 I ) * * ? ) / ( ( ! . * I C O S J A N G t I > * R A O M 2 ) » F F ( I I I P P X 1 - P X H I ) "~ 1MAX=1 D 0 3 l = 2 , N O P I F I P X 11 I » . L E . P P X 1 I G 0 T Q 3 P P X I = P X I ( I ) I M A X M 3 ' C O M I N U E " ~ * B I N T = S A N 1 I 1 H A X ) - S A N 1 I 1 N A X - 1 ) O ANG*0WAV*SANU IMAX)/WAV R N U « * D A N G / 8 I N T * 1 . N U ^ R N U H RhUM*NUM EINT-OANG/RNUM " ~ S A N 2 ( 1 ) * S A N 1 < 1 ) 0 0 * 1 * 2 . 1 0 0 0 S A N ? ( I ) *S AN2 ( l - D + E I N T IF I S A N 2 ( I I . G T . S A N K N O P ) I G 0 T 0 5 _+ CONTINUE _ hFOPMOOO"' " - - - - -GDT06 5 N E D P M - 1 6 N M O n 7 I M , N E O P DOBJ-N.NOP l F ( S A N U J I - S A N 2 l t ) ) 6 , 9 , L 0 8 CFINTINUE 9 P X 2 ( I ) * P X 1 I J ) I 5 A 15B 15C 15D 156 16 17 1TA 178 18 19 20 21 22 2 3 30 31 32 33 FORTRAN IV G COMPI L E R PAGE 0 0 0 2 0 0 5 3 t o P X 2 ( I l = P X 1 I J - 1 I M P X 1 I J t - P X U J - l ) ) / ( S A N l I J ) - S A N l 1 J-1> >«I S A N ? ( I l - S A N 51 I 1 I J - 1 I I 52 0 0 5 + 11 N=J _ „ 53 0 0 5 5 7 CONTINUE 5+ 0 0 5 6 RN«NF0<> 55 0 0 5 7 G f t A D M P X ? ! N E O P ) - P X Z I i n / l » N - l .) 56 0 0 5 8 M 0 L 0 - P X 2 ! 1 ) 57 0 0 5 9 3+ D 0 1 2 1 M . N E 0 P 58 0 0 6 0 R I - I 5 9 0 0 6 1 P X 2 ( I ) = P X ? ( I ) - H D L D - G R A O » ( R I - l . ) 6 0 0 0 6 2 12 I F ( P X 2 ( I ) . L T . O . )PX2(I)«0. 6 1 0 0 6 3 0 0 1 3 L M . N U M 62 0 0 6 + P X ( L ) * P X 2 I L ) 6 3 0 0 6 5 D O l + I M . N E D P 6+ 0 0 6 6 IN*NUH*I+L 6 5 0 0 6 7 I N N M N - N U M 6 6 • 0 0 6 8 I f ( I N . G T . N E 0 P I G O T 0 1 3 6 7 - 0 0 6 9 P X ( I N I * P X 2 ( I N ) - 0 . 5 * P X 1 INN) 6 8 0 0 7 0 1 + | F ( P X ( I N ) . L T . O . I P X I I N 1-0. . 66 A 0 0 7 1 13 CONTINUE 6 9 0 0 7 2 AREA-O. 7 0 0 0 7 3 AM-O. 71 0 0 7 + O O 1 5 I M . N F 0 P 72 0 0 7 5 ARE A*AR EA + P X ( I 1 73 0 0 7 6 15 AH*AM+PXI I ) *S AN21 I ) 7+ 0 0 7 7 CG*AM/ARE A " 75 0 0 7 8 D V E C « C G * 2 . / W A V 76 0 0 7 9 0 0 1 6 1 * 1 , N E O P 77 0 0 8 0 16 S A N I I ) * S A N 2 ( I ) - C G 78 0 0 6 1 I F ( S A N l I )»SANINEOPI 1 2 7 , 2 8 , 2 9 79 0 0 8 2 27 A l P * M A V / ( * . * t - S * N U } H T9A 0 0 8 3 GOT030 79B 0 0 8 + 2 8 A l P * U A V / ( 2 . « ( S A N I N E 0 P > - S A N t 1 ) I I 79C 0 0 8 5 GOT030 79D 0 0 8 6 29 A 1 P * W A V / I + . * S A N ( N E 0 P ) ) 79E 0 0 8 7 3 0 H 0 2 M H * I H » I K « I K M L * I L 80 0 0 8 6 H O * S Q R T ( H 0 2 I 81 0 0 8 9 A l - H O / O V E C 62 0 0 9 0 H P I T E I 6 . 1 0 6 M P X I I ) , l - l . N E D P I 6 3 0 0 9 1 W R I T E < 6 , 1 0 7 M S A N U 1 . I - l . N E D P I 8+ 0 0 9 2 W R I T E ( 6 , 1 0 8 ) E I N T , N E O P . A I P 6 5 0 0 9 3 T T Z * 2 . * A R S I N I C G I / R A 0 8 6 0 0 9 + A l M * H 0 / 2 . / S A N l ( I M A X ) * H A V 66A 0 0 9 5 T T * 2.*ARS I N I S A N l U M A X ) ) / R A O 8 6 6 0 0 9 6 A S Y M M T Z - T T 66C 0 0 9 7 W R I T E ( 6 I 1 0 9 ) T T Z , A 1 , T T » A 1 M , A S Y H 87 0 0 9 8 0 0 1 7 L M . N G P 88 0 0 9 9 R L * L - 1 89 0 1 0 0 0 1 S r i L I - G I N T * R L 90 0 1 0 1 P R I L t - O . 91 0 1 0 ? P I I L )»0. 9 2 0 1 0 3 D 0 1 B I * 1 , N E D P 9 3 0 1 0 + A R G * D I S T ( L ) * 2 . * S A N I I I / W A V 9* 0 1 0 5 1ARG'ARG 9 5 Table X. Computer Programme Statements 206 I FORTRAN IV 6 COMPILER MAIN 0 6 - 0 5 - 6 9 l O U O U l PAGE 0003 0106 ARGU*IARG 96 1 010T OEC»(ARG-ARGUt 97 oioe P R ( l ) . P R ( L I * P K I U*C0SI6.283165»0EC> 98 0109 18 P I ( L I " P I I L I » P X I l l * S I N I 6 . 2 a 3 1 8 5 « D E C I 99 0110 PR IL)'PR (L)/AREA 100 0111 17 Pt I D . P I 1 L I / A R E A 101 0112 CALL SCALE 1 A N G , N D P , 1 0 .,XM I N , O K , 1 1 17C 0113 CALL AXIS (0.,0 . .19HTwn THETA IDEGREES1, -19 .10. .0. . XM1N,DX) 170 0114 CALL SCALE IPX3 ,NDP, 1 0 . , VM IN.OY, 1) 17E 0115 CALL AXIS 1 0 ..0., 9HINTENSITV,9 ,10. , 9 0 . , V H I N , D V 1 17F 0116 CALL LINE ( A N G . P X 3 , I N O P - l > ,11 17G 0117 CALL SYM1QL 11 .,9.,0.14.MATI1>.0 . .60 l 17H | o n a CALL SYMBOL 1 1 .,8. , 0 . 1 4 , 1 3 H ( A S RFCOROED) ,0. ,13) 171 ! 0111 CALL PLCT 1 1 2 . , 0 . , - 3 1 17J , 0120 CALL SCALE 1SAN1,NOP,10 . ,XH IN ,DX ,1 ) 22A 1 0121 CALL AXIS ( 0 . , 0 . , 1 0 H S I N E T H E T A , — 1 0 , 1 0 . , 0 . , X H I N , D X I 22B 1 0122 CALL SCALE I P X 1 . N O P , 1 0 . , Y M I N . U V , 1 ) 22C 0123 CALL AXIS ( 0 . , 0 . , 9 H I N T E N S I T V , 9 . 1 0 . , 9 0 . , V M I N , D Y ) 220 j 0124 CALL LINE 1 S A N 1 , P X 1 , I N D P - l i , 1 ) 22E -j 0125 CALL SYMBOL 1 1 . , 9 . . 0 . 1 4 , M A T ( 1 ) , 0 . , 6 0 ) 22F i 0126 CALL SYMBOL 11.,8. ,0.14,24H1CORRECTED FOR LP AND F l , 0 . , 2 4 ) 22G 1 0127 CALL PLOT 1 1 2 . , 0 . . - 3 1 22H ; 0128 CALL SCALE 1SAN2,NEOP,10 . ,XMIN ,DX ,1» 61A i 0129 CALL AXIS ( 0 . . 0 . . 1 0 H S I N E T H E T A , - 1 0 , 1 0 . , 0 . , X M I N , D X 1 61B ' 0130 CALL SCALE I P X 2 , N E D P , 1 0 . . V M I N . O Y , 1 1 61C 0131 CALL AXIS I 0 . , 0 . . 9 H I N T E N S I T Y , 9 , 1 0 . , 9 0 . , Y H I N . D V 1 610 1 0132 CALL L1NF I S A N 2 . P X 2 , I N E D P - 1 I , 1 ) 61E 0133 CALL SYMBOL U . , 9 . , 0 . 1 4 , M A T U I . 0 . , 6 0 ) 61F 0134 'CALL SYMBOL 11.,8. .0 .14,36HIC0RRECTE0 FOR L P , F AND BACKGROUND),0. 61G 1*361 61H 0135 CAL l PLCT l l 2 . , 0 . , - 3 > 611 0136 CALL AXIS I 0 . , 0 . , 1 0 H S 1 N E T H E TA . - 1 0 , 1 0 . , 0 . , X H I N . O X 1 69B 0137 /CALL SCALE I P X , N E D P , 1 0 . , V M I N , O Y , 1 ) 69C 0138 CALL AXIS I O . , 0 . . 9 H I N T E N S I T Y , 9 , 1 0 . . 9 0 . . Y H I N . O Y I 69D 0131 CALL LINE ( S A N 2 . P X , I N E D P - 1 1 , 1 1 69E 0140 ' CALL SYMBOL 1 1 . , 9 . . 0 . 1 4 , M A T 1 1 ) , 0 . , 6 0 1 69F 0141 CALL SYMBOL 1 1 . , 6 . , 0 . 1 4 , 3 7 H [ C O R R E C T E D FOR L P , F, BG AND DOUBLET I ,0 69G I . . 3 7 1 69H 0142 CALL PLOT 1 1 2 . . 0 . . - 3 ) 691 0143 IFIKONT.GT.1IGOT036 102 0144 D020LM.NGP 103 0145 G R I I L I ' P R I L ) 103A 0146 20 G I I I L I ' P I I L ) 103C 0147 G0T099 104 0148 36 1F(K0NT.GT.2)G0T019 105 0149 D037L*1,NGP 106A 0150 GR21L)-PRIL> 106B 0151 37 G I 2 I L I - P I I L ) 106C 0132 G0T098 1060 0153 19 I F | K O N T . G T . 3 ) G 0 T 0 4 l 107 0154 D021L-1.NGP 108 0135 F R I L I ' I P R I L I > G R 1 I L > « P I I L | 4 G I I < L I I / I G R 1 I L I * G R 1 I L I « G 1 1 I L I * G I I I I I I 109A 0156 F I ( L I - I P ! I L > » G R 1 1 L > - P R ( L ) * G [ 1 ( L I > / I G R 1 ( L I * G R I I L I » G 1 1 1 L ) * G I 1 ( L I I 1098 0157 A I L P - S O R T I F B I L I ' F R I D . F I ( L I ' F I I L I 1 110A 0158 21 INA IL I -ALOGIA IL I ) H O B FORTRAN IV G COMPILER NAIN 0 6 - 0 5 - 6 9 10110131 PAGE 0004 0154 UR ITE I6 .1 I0 ) 111 0160 D022L'1 .NGP 112 0161 22 • R 1 T E 1 6 • 1 1 1 I D I S T I L I , G R 1 I I I , G l l l l l , P R I I I . P I I L I . F R I L I . F I ( L I . A l l l . l W k 113 111) 113A 0162 H1-H02 115 0163 A1H0-A1 116 0164 D02 3L -1 .NGP 119 0165 23 H L N A I L ) ' L N A ( L ) 120 0166 G0T098 121 0167 41 D038L-1.NGP 114A 0168 F P I L ) . | P R I L I > G R 2 I L I » P I I L I « G I 2 I L I I / I G R 2 I L ) P G R 2 I L | . G I 2 I L ) » G I 2 ( L I I 114B 0169 F l ( L I * I P I I L > « G R 2 t L > - P R I L I « G I 2 I L I I / ( G R 2 I L > * G R 2 t L ) » G 1 2 ( L I * G I 2 I L I > 114C 0170 A l l ) - S Q R T ( F R I L ) * F R I L 1 + F U L I * F I I L I 1 1140 0171 38 LNAIL ) .ALOGIA(L ) ) 114E 0172 HRITE(6,110I 114F 0173 0039L -1 ,NGP 1I4G 0174 39 W P [ T F I 6 , 1 1 1 ) 0 ! S T ( L I , G R 2 ( L ) , G I 2 ( L I , P R ( L ) , P 1 I L I , E R ( L I , F I ( L I , A ( L I , L N A 114H 1IL) 1141 0175 24 Y « o . 122 0176 0025L -1 .NGP 123 0177 R L - L - 1 124 0178 H2.H02 126 0179 S L C N . I L N A t L I - H L N A ( L ) 1 / I H I - H 2 I 127 0180 C . I L N A I L I « H 1 - H L N A ( L I * H 2 I / I H 1 - H 2 I 128 0181 I F I S L O N . L E . O . I E P S I I L I = 0 . 129 0182 ! F ( S L O N . G T . 0 . I E P S I I L I « S Q R T I S L O N I * A l H O / S O R T I 2 . 1 / 3 . 1 4 1 5 9 3 / D I S T I L I 130 0183 P C S T ( l ) « E P S I ( L ) * 1 0 0 . 131 0184 I F ISLON.LE .O .1AD(L ) -EXP|HLNA(L ) ) 132 0185 I F ISLON.GT .0 . )AO I l l=EXP IC I 133 0186 . . 25 Y . Y * A D I L » * 2 . 134 0187 D 0 N 1 « G ! N T * ( Y - 1 . 1 135 - 0188 !L*00M1»0 .2/G!NT*2. 136 0189 D O M 2 « 5 . » G I N T / ( A 0 I I L l - A O l 1 1 * 5 1 1 137 0190 URITEI6 ,112I 138 0191 D026L- I .NGP 139 0192 26 HRITE (6 ,113I01ST1L I ,PCST (L I .AD1L I 140 0193 WRITE(6.114ID0M1,00H2 141 0194 CALL SCALEIPCST,NGP,10. ,YM!N ,DV ,1) 141A 0195 CALL AX IS I0 . .0 . .14HPERCENT S T R A I N , 1 4 , 1 0 . , 9 0 . , Y H I N » D V 1 141B 0196 CALL AX IS I0 . .0 . .20HDISTANCE 1 A N G S T R O M S ) . - 2 0 . 1 0 . . 0 . , 0 . . 5 0 . 1 141C 0197 D040LM.NGP 141C1 0198 40 O I S T U I - D I S T I L I / 5 0 . 141C2 0199 CALL L I N E ( D I S T , P C S T , I N G P - 1 I , 1 I 141D 0200 CALL S Y M 8 n L ( l . * 9 . , 0 . 1 4 , M A T ( l l , 0 . , 6 0 l 141E 0201 CALL PLOT 1 1 2 . , 0 . , - 3 ) 141F 0202 CALL SCALEIA0,NGP*L0. ,YM1N,0Y ,1 ) 141G 0203 CA1L AXISIO. ,0 . ,23HOOHAIN S U E COEFF IC IENT ,23 ,10 . , 9 0 . , Y K I N . D V 1 141H 0204 CALL A X I S ( 0 . . O . , 2 0 H 0 I S T A N C E 1 A N G S T R O M S ) . - 2 0 , 1 0 . , 0 . . 0 . , 5 0 . 1 1411 0205 CALL L INE(01ST ,AD, INGP-1 ) ,1> 141J 0206 CALL SYMBOL 1 1 . , 9 . . 0 . 1 4 , M A T ( 1 1 , 0 . , 6 0 1 141J1 0207 CALL P L O T ( 1 3 . , 0 . , - 3 1 141K 0208 G0I098 141L 0209 42 CALL PLOTNO 141H 0210 STOP 0211 100 F0RHATI2F10.6) 142 Table X Continued . 20? FORTRAN IV C C O M P I L E R MAIN 06-05-6") 1 0 : 1 0 : 3 1 PACE 0 0 0 5 0 2 1 2 101 FORMAT ( K , F h . l , K I 1 4 3 0 2 1 3 102 F O W M A T 1 1 5 A 4 . 3 I 2 ) 1 4 * 0 2 1 4 1 0 3 F 0 P M A T ( 1 H 1 , 1 0 X , 1 5 A 4 , 1 3 H R E F L E C T I O N ( , 3 I ? , 2 H ) ) 145A 0 2 1 5 1 0 4 F O R M A T ! F 8 . 3 r F 6 . 3 . 1 4 , 2 F 6 . 2 , 1 2 / 1 1 OF 8 . 3 ) ) 146 0 2 1 6 1 0 5 "FORMAT r//l6x,16H SCAN B E G I N S AT . F R . 3 . 1 9 H D F G R F F S TWO ~THETA> 10X.2 147 H H ANGULAR INCREMENT - . F 6 . 3 . 9 H O E G R F E 5 / 1 0 X , 2 5 H NUMBER OF DATA PO 148 11NTS * . I 4 / 1 0 X . 4 5 H ATOMIC S C A T T E R I N G FACTOR AT TWO THETA ( I t - , F 6 149 1 . 2 / 1 0 X . 4 5 H ATOMIC S C A T T E R I N G FACTOR AT TWO THETA ( 2 1 * , F 6 . 2 / t O X t l 149A 11H CONTROL = * I 2 / / / / 1 0 X , 2 6 H O R I G I N A L I N T E N S I T Y V A L U E S Z / t 1 X . 1 6 F 8 . 3 ) 149B 11 _ 149C 0 2 1 7 106 F O R M A T ! 1 H 1 / / / 1 0 X , 3 3 H F I N A L CORRECTED I N T E N S I T Y V A L U E S / / I 1 X , f l E 1 6 . 7 ) ' 1 5 0 A I I 1 5 0 B 0 2 1 B 107 F O R M A T ! 1 H 1 / / / 1 0 X . 3 5 H CORRESPONDING VALUES OF S I N E THETA//1 1X, 1 6 F 8 . 151A 1511 1 5 1 B 0 2 1 9 1 0 8 - F O f t M A T I 1 H 1 / / / 1 0 X . 2 3 H S I N E THFTA I N T E R V A L » , FB . 5 / 1 0 X . 3 6 M NUMBER OF 1 5 2 A 1 S I N E THETA DATA PQ |_N T S__^_ » I 4/ 1 0 X . 3 2 H A R T I F I C I A L L A T T I C E PARAMETER 1S2B 1 « . F 9 . 5 . 1 1 H ANGSTROMS) - 152C 0 2 2 0 1 0 9 FORMAT I / 1 0 X , 3 8 H TWO THE TA ZERO (CENTRE OF G R A V I T Y ! « , F 8 . 3 , 9 H DEG 1 5 5 I R F E S / 1 0 X . 4 1 H L A T T I C E PARAMETER (CE N T R E OP G R A V I T Y ) ^ . F 9 . 5 . 1 1 H AN 1 5 6 A 1GSTROMS//10X.33H TWO THF T A ZFRO ( P E A K MAXIMUM) = , F B . 3 , 9 M DEGREES 1 5 6 B 1 / 1 0 X . 3 6 H L A T T I C E PARAMETER ( P E A K MAXIMUM) = , F 9 . 5 . 1 I H ANGSTROMS// 156C l l C X . l f l H PEAK ASYMMETRY *_»_F7.J,9H_ D E G R E E S ) 1S6D 0 2 2 1 110 F 0 R H A T t l H l / / / B X , 6 H 6lS~T t L I »7X,6H GRIL i » 7X,6H G I I L 1 , 7 X , 6 H P R I L ) , 7 X , 1 5 7 A 16H P M L U 7 X . 6 H F R ( L ) , 7 X , 6 H F I I L ) . 7 X , 5 H A ! L ) , 8 X , 7 H L N A ( L ) / 6 X . I 2 H (A 1 5 7 B . I N G S T R O M S m 157C 0 2 2 2 M l F 0 R M A T | F 1 5 . l , F 1 5 . 4 . 7 F I 3 . 4 J 159 0 2 2 3 1 1 2 F O R M A T ! 1 H 1 / / / 1 0 X , 1 3 H D I S T A N C E ( L ) . 1 0 X , 1 5 H PERCENT S T R A I N * 1 0 * • 2 4 H 0 160A 1 0 H A I N S I Z E C O E F F I C I E N T / I P X . 12H (ANGSTROMS!/) : 1 6 0 6 0 2 2 4 1 1 3 F 0 R M A T I F 1 9 . 1 . F 2 5 . 4 . F 2 9 . 4 ! 162 0 2 2 5 1 1 4 F 0 R M A T ( 1 H 1 / / / 1 0 X , 1 9 H DOMAIN S I Z E I I ) « , F B . 2 , 1 1 H ANGSTROMS//10X,1 163A 19H DOMAIN S I Z E ( 2 ) = . F 8 . 2 . 1 1 H ANGSTROMS) 163B 0 2 2 6 1 1 5 F 0 R H A T ( F 8 . 3 , F 6 . 3 , I 4 , 2 F 6 . 2 . I 2 / ( L 0 F 8 . 3 I ) 166A 0 2 2 7 116 F 0 R M A T ( / / 1 0 X , 1 6 H SCAN B E G I N S AT . F 8 . 3 . 1 9 H DEGREES TWO T H E T A / 1 0 X . 2 167 I 1 H ANGULAR INCREMENT - t F 6 . 3 , 9 H O E G R E E S / I P X , 2 5 H NUMBER OF OA TA PQ 16B 1 I N T S - , I 4 / 1 0 X , 4 5 H ATOMIC S C A T T E R I N G FACTOR AT TWO THETA I I I - . F 6 169 1 . 2 / 1 0 X . 4 5 M ATOMIC S C A T T E R I N G FACTOR AT TWO THETA l ? l = , F 6 . 2 / 1 0 X , 1 170 11H CONTROL - . 1 2 / / / / 1 0 X . 2 6 H O R I G I N A L I N T E N S I T Y V A l U E 5 / / 1 1 X , 1 6 F B . 3 ) 171A 1) 172 0 2 2 8 END 1 6 5 Table X Continued. APPENDIX 3 208 Specimen Computer Output from the  Programme of Appendix 2 NI POwOFR ANNEALED P E F 1 E C T I 0 N 1 2 0 0 ) SCAN B E G I N S A l 4 9 . 0 0 0 O E G R F E S T WD THFTA ANGULAR INCRFHENT = ' 0 . 3 1 0 DECREES _U_Mft_R OF OATA P O I N T S - 6 0 1 ATCMIC "SCATTERING FACTOR IT TWO THF T A ( I I = 1 8 . 2 8 ATOMIC S C A T T E R I N G FACTOR AT TWO THFTA ( ? ) = 17.21 CONTROL - 1 ORT&TNAL™ I N T E N S I T Y V A L U E S " * ~ 1 1 7 . 7 8 0 1 1 6 . 0 8 0 1 1 7 . 8 9 0 1 1 7 . 9 0 0 1 1 6 . 9 5 0 1 1 6 . 0 9 0 1 1 5 . 7 0 0 1 1 5 . 0 8 0 1 1 7 . 3 7 0 1 1 6 . 2 7 0 1 1 6 . 9 2 0 1 1 8 . 3 1 0 1 1 6 . 6 9 0 1 1 7 . 2 3 0 1 1 7 . 7 1 0 1 1 6 . 6 8 0 1 1 7 . 4 9 0 1 1 5 . 7 ) 0 1 1 6 . 9 0 0 1 1 6 . 8 8 0 1 1 6 . 7 0 0 1 1 7 . 6 5 0 1 1 5 . 9 2 0 1 1 T . 3 0 0 1 1 7 . 7 1 0 1 1 6 . 2 0 0 W T . T 7 0 1 1 5 . 8 5 0 1 1 6 . 4 7 0 1 1 5 . 6 7 0 1 1 5 . 6 9 0 1 1 6 . 4 7 0 1 1 7 . 0 5 0 1 1 5 . 9 5 0 1 1 6 . 4 6 0 U B . 3 5 0 1 1 B . 2 6 0 1 1 6 . 1 4 0 1 1 6 . 0 5 0 1 1 5 . 1 2 0 1 1 6 . 9 3 0 1 1 7 . 2 2 0 1 1 6 . 6 5 0 1 1 9 . 1 6 0 1 1 7 . 6 3 0 1 1 6 . 9 8 0 1 1 6 . 1 9 0 1 1 6 . 6 1 0 1 1 6 . 5 7 0 1 1 6 . 5 1 0 1 1 5 . 2 0 0 1 1 7 . 2 3 0 1 1 6 . 8 4 0 1_17.860 1 1 7 . 9 1 0 1 1 5 . 8 2 0 1 1 6 . t O O 1 1 5 . 7 8 0 1 1 6 . 5 4 0 1 1 5 . 6 9 0 1 1 6 . 0 7 0 1 1 6 . 9 9 0 1 1 5 . 9 3 0 1 1 6 . 8 0 0 1 1 7 . 9 8 0 1 1 7 . 0 9 0 1 1 6 . 7 9 0 1 1 5 . 8 7 0 1 1 7 . 4 7 0 1 1 7 ^ 6 9 0 1 1 6 . 5 4 0 1 15".B40 1 1 6 . 6 4 0 i l ' 7 . 7 7 0 1 1 4 . 9 3 0 1 1 5 . 8 6 0 1 1 6 . 4 0 0 1 1 4 . 7 7 0 1 1 9 . 7 6 0 1 1 5 . 6 5 0 1 1 6 . 8 4 0 1 1 7 . 9 6 0 1 1 7 . 3 2 0 1 1 7 . 4 5 0 1 1 6 . 2 4 0 1 1 8 . 5 8 0 1 1 7 . 4 7 0 1 1 7 . 4 2 0 1 1 5 . 6 8 0 1 1 6 . 7 3 0 1 1 5 . 2 5 0 1 1 5 . S I O 1 1 6 . 6 5 0 1 1 5 . 2 6 0 1 1 4 . 6 1 0 1 1 4 . 1 7 0 1 1 6 . 0 0 0 1 1 6 . 5 2 0 1 1 4 . 6 4 0 1 1 4 . 5 4 0 1 1 4 . 7 3 0 1 1 5 . B 3 0 1 1 4 . 1 7 0 1 1 4 . 4 6 0 1 1 3 . 7 4 0 1 1 3 . 5 2 0 1 1 3 . 7 6 0 1 1 3 . 1 6 0 1 1 4 . 0 0 0 1 1 4 . 0 0 0 1 1 2 . 8 6 0 1 1 2 . 5 8 0 1 1 1 . 6 6 0 1 1 2 . 3 7 0 1 1 2 . 5 4 0 1 1 3 . 7 9 0 1 1 3 . 3 1 0 1 1 2 . 0 2 0 1 1 2 . 9 4 0 1 1 2 . 9 9 0 1 1 1 . 9 7 0 1 1 3 . 5 7 0 1 1 1 . 9 9 0 1 1 3 . 1 4 0 1 1 2 . 5 3 0 1 1 3 . 4 6 0 1 1 3 . 7 6 0 1 1 2 . 5 9 0 1 1 2 . 6 7 0 1 1 2 . 5 2 0 1 1 2 . 7 6 0 1 1 2 . 6 1 0 1 1 1 . 6 4 0 1 1 2 . 1 7 0 1 1 2 . 1 7 0 1 1 3 . 4 9 0 1 1 1 . 3 9 0 1 1 3 . 0 5 0 1 1 2 . 8 5 0 1 1 2 . 0 1 0 1 1 2 . 4 0 0 1 1 3 . 2 9 0 1 1 1 . 6 2 0 1 1 2 . 6 1 0 1 1 2 . 7 2 0 1 1 3 . 5 1 0 U 1 . 6 6 0 1 1 1 . 9 1 0 1 1 1 . 7 4 0 1 1 2 . 0 8 0 1 1 1 . 1 8 0 1 1 1 . 8 1 0 1 1 2 . 5 1 0 1 1 0 . 6 7 Q 1 1 1 . 6 6 0 1 0 9 . 3 5 0 1 1 0 . 2 5 0 U 2 . 1 4 0 1 U . 9 0 0 1 1 1 . 7 1 0 1 1 0 . 5 3 0 1 1 1 . 5 4 0 1 1 1 . 6 2 0 U 1 . 9 4 0 ~ 1 1 0 . 5 0 0 1 1 1 . 8 5 0 1 1 0 . 2 3 0 1 1 0 . 8 0 0 1 1 1 . 6 7 0 1 1 0 . 4 2 0 1 I 1 . 1 B 0 1 1 1 . 0 7 0 1 1 0 . 7 8 0 1 1 0 . 5 3 0 1 0 9 . 6 8 0 1 0 6 . 2 3 0 1 C 9 . 9 0 0 1 C 8 . 7 4 0 1 0 9 . 4 1 0 1 0 9 . 2 6 0 1 0 9 . 1 6 0 1 C 8 . 8 0 0 1 0 B . 5 7 0 1 0 8 . 3 8 0 1 0 1 . 9 6 0 1 0 8 . 7 6 0 1 0 8 . 4 2 0 1 0 8 . 1 8 0 1 0 6 . 5 6 0 I C S . 2 2 0 1 0 6 . 0 1 0 1 0 7 . 5 9 0 1 0 8 . 5 9 0 1 0 7 . 5 7 0 1 0 7 . 6 9 0 1 0 7 . 6 0 0 1 0 6 . 5 3 0 I C S . 6 1 0 1 0 7 . 7 4 0 1 0 8 . 0 4 0 1 0 7 . 4 6 0 1 0 7 . 1 8 0 1 0 7 . 6 4 0 1 0 6 . 3 1 0 1 0 6 . 6 6 0 1 0 7 . 4 4 0 1 0 5 . 8 3 0 1 0 6 . 7 3 0 1 0 5 . 3 4 0 1 C 5 . 9 0 0 1 0 4 . 9 3 C 1 0 5 . 4 3 0 1 0 3 . 7 6 0 1 0 4 . 7 0 0 1 0 4 . 5 9 0 1 0 4 . 7 2 0 1 0 4 . 0 4 0 1 0 3 . 2 1 0 1 0 3 . 6 1 0 1 0 3 . 8 7 0 1 0 3 . 7 5 0 1 0 2 . 7 7 0 1 0 1 . 9 B 0 1 0 1 . 4 1 0 9 9 . 8 9 0 1 0 0 . 3 0 0 1 0 0 . 6 4 0 1 0 0 . 1 0 0 9 9 . 0 9 0 9 9 . 4 9 0 9 9 . 3 4 0 9 7 . 8 3 0 9 7 . 2 6 0 9 7 . 5 3 0 9 7 . 4 4 0 9 5 . 5 5 0 9 5 . 4 9 0 9 5 . 0 3 0 9 3 . 1 0 0 9 2 . 8 8 0 9 1 . 4 3 0 9 1 . 6 3 0 9 0 . 6 7 0 8 8 . 3 4 0 9 7 . 9 3 0 8 7 . 4 1 0 B 4 . B 3 0 8 4 . 7 B 0 _ 6 3 . 2 0 0 8 1 . 4 6 0 7 9 . 6 3 0 7 7 . 8 7 0 7 6 . 2 0 0 7 5 . 1 8 0 7 3 . 0 2 0 7 0 . 6 3 0 6 9 . 2 5 0 6 5 . 9 1 0 6 4 . 1 5 0 6 3 . 3 3 0 5 9 . 9 6 0 5 8 . 6 1 0 55.BOO 5 3 . 5 9 0 5 2 . 0 4 0 4 8 . 4 7 0 4 7 . 1 1 0 4 4 . 5 6 0 4 1 . 6 2 0 3 8 . 7 3 0 3 5 . 7 4 0 3 3 . 2 0 0 3 0 . 5 4 0 2 7 . 7 8 0 2 4 . 7 6 0 2 2 . 3 0 0 1 9 . 9 8 0 1 7 . 4 8 0 1 5 . 4 7 0 1 3 . 4 2 0 1 2 . 1 5 0 1 0 . 5 7 0 9 . 5 1 0 8 . 6 7 0 B . 0 3 0 7 . 5 6 0 7 . I B 0 7 . 0 5 0 7 . 0 0 0 7 . 3 4 0 7. 6 1 0 7.890 8 . 4 3 0 9 . 0 2 0 9 . 5 6 0 1 0 . 0 4 0 1 0 . 4 1 0 1 0 . 6 4 0 1 0 . 5 5 0 1 0 . 7 6 0 1 1 . 1 0 0 1 1 . 4 3 0 1 1 . 7 9 0 1 2 . 7 2 0 1 3 . 4 4 0 1 4 . 8 7 0 1 6 . 6 3 0 1 8 . 6 6 0 2 1 . 3 0 0 2 3 . 9 4 0 2 6 . 9 3 0 3 0 . 6 0 0 3 3 . 8 4 0 3 7 . 1 4 0 4 1 . 4 1 0 4 4 . 0 1 0 4 7 . 0 3 0 5 0 . 1 7 0 5 3 . 1 9 0 5 5 . 6 5 0 5 8 . 4 3 C 6 0 . 7 0 0 6 3 . 3 7 0 6 5 . 8 9 0 6 6 . 6 9 0 7 0 . 5 4 0 7 2 . 3 5 0 7 4 . 0 1 0 7 5 . 4 B 0 7 7 . 4 9 0 7 8 . 9 5 0 8 1 . 2 4 0 8 2 . 4 9 0 6 4 . 7 2 0 8 4 . 6 6 0 6 6 . 7 3 0 8 6 . 9 0 0 6 8 . 9 6 0 9 0 . 1 7 0 9 1 . 1 4 Q 9 2 . 2 6 0 _ 9 4 . 2 3 0 9 3 . 9 5 0 9 4 . J 5 0 9 5 . 5 1 0 9 5 . 6 2 0 9 7 . 3 6 0 9 8 . 0 7 0 9 6 . 5 1 0 9 9 . 2 1 0 9 9 . 6 7 0 1 0 0 . 5 2 0 1 0 0 . 7 3 0 1 0 0 . 1 3 0 1 0 1 . 1 1 0 1 0 3 . 7 3 0 1 0 2 . 5 9 0 102.0 TO' 1 0 3 ; 6 8 0 1 0 4 . 2 2 0 10~2.760 1 0 4 . 4 3 0 1 0 3 . 0 5 0 1 0 5 . 2 4 0 1 0 5 . 4 5 0 1 0 5 . 5 1 0 1 0 5 . 9 6 0 1 0 6 . 2 7 0 1 0 5 . 8 2 0 1 0 5 . 5 4 0 1 0 7 . 3 6 0 1 0 6 . 9 8 0 1 0 7 . 2 1 0 1 0 7 . 8 0 0 1 0 B . 9 2 0 1 0 6 . 9 7 0 1 0 7 . 4 3 0 1 0 9 . 6 2 0 1 0 8 . 8 8 0 1 0 9 . 4 7 0 1 0 9 . 5 4 0 1 0 7 . 3 3 0 1 0 9 . 3 7 0 1 0 9 , 0 9 0 1 0 9 . 5 6 0 1 1 0 . 3 6 0 1 1 0 . 4 0 0 1 1 0 . 1 9 0 1 0 9 . 8 7 0 1 0 9 . 3 1 0 1 1 0 . 1 6 0 1 1 0 . 6 2 0 1 1 1 . 3 3 0 1 1 0 . 3 7 0 1 1 2 . 0 8 0 1 1 2 . 4 8 0 109.BOO 1 1 0 . 9 7 0 1 1 1 . 4 9 0 1 1 0 . 5 0 0 1 1 2 . 4 5 0 1 1 1 . 5 9 0 1 1 2 . 0 3 0 1 1 1 . 9 7 0 1 1 0 . 7 9 0 1 1 0 . 8 9 0 1 1 1 . 9 3 0 1 1 1 . 3 9 0 1 1 0 . 8 6 0 1 1 1 . 5 8 0 1 1 2 . 5 5 0 1 1 1 . 1 5 0 1 1 2 . 1 1 0 1 1 1 . 6 4 0 1 1 2 . 7 9 0 1 1 0 . 9 1 0 1 1 2 . 6 1 0 1 1 3 . 0 2 0 1 1 3 . 0 6 0 1 1 2 . 5 0 0 1 1 0 . 7 5 0 1 ) 2 . 3 1 0 1 1 3 . 0 5 0 1 1 3 . 3 6 0 1 1 3 . 3 0 0 1 1 2 . 1 0 0 1 1 4 . 0 8 0 1 1 2 . 7 1 0 1 1 3 . 4 0 0 1 1 2 . 6 4 0 1 1 3 . 7 6 0 1 1 4 . 2 1 0 1 1 1 . 3 0 0 1 1 3 . 8 5 0 1 1 3 . 1 5 0 1 1 3 . 2 8 0 1 1 2 . 3 9 0 1 1 3 . 6 4 0 1 1 3 . 0 6 0 1 1 3 . 7 B 0 1 1 4 . 6 5 0 1 1 2 . 2 3 0 1 1 2 . 9 9 0 1 1 2 . 0 3 0 1 1 3 . 6 7 0 1 1 3 . 4 5 0 1 1 4 . 7 5 0 1 1 2 . 6 3 0 1 1 3 . 3 2 0 1 1 4 . 3 5 0 1 1 4 . 2 2 0 1 1 4 . 6 6 0 1 1 4 . 4 1 0 1 1 2 . 8 6 0 1 1 4 . 3 4 0 1 1 4 . 4 R 0 1 1 4 . 1 5 0 1 1 3 . 6 8 0 1 1 3 . 2 4 0 1 1 4 . 1 0 0 1 1 6 . 6 2 0 1 1 4 . 7 8 0 1 1 3 . 1 2 0 1 1 3 . 6 7 0 1 1 5 . 9 4 0 1 1 4 . 3 3 0 1 1 5 . 3 8 0 1 1 5 . 1 1 0 1 1 5 . 2 7 0 1 1 4 . 5 6 0 1 1 4 . 7 0 0 U 6 . 1 4 0 1 1 4 . 2 0 0 1 1 3 . 9 4 0 1 1 5 . 1 0 0 1 1 5 . 6 4 0 1 1 4 . 1 4 0 1 1 3 . 7 4 0 1 1 2 . 6 5 0 1 1 3 . 6 5 0 1 1 5 . 6 6 0 1 1 5 . 0 7 0 1 1 5 . 3 8 0 1 1 5 . 5 2 0 114.BOO 1 1 4 . 5 9 0 1 1 4 . 0 0 0 1 1 5 . 2 0 0 1 ) 5 . 1 6 0 1 1 5 . 0 1 0 1 1 5 . 0 1 0 1 1 2 . 7 4 0 1 1 6 . 2 9 0 1 1 6 . 2 8 0 1 1 4 . 3 6 0 1 ) 6 . 9 6 0 1 1 6 . 0 3 0 1 1 5 . 3 6 0 1 1 6 . 0 4 0 1 1 4 . 0 9 0 1 1 4 . 6 6 0 1 1 4 . 6 2 0 1 1 5 . 9 5 0 1 1 7 . 0 6 0 M 6 . 7 3 0 1 1 6 . 4 2 0 1 1 4 . 5 & 0 1 1 5 . 1 2 0 1 1 4 . 2 0 0 1 1 7 . 3 3 0 1 1 6 . 9 6 0 1 1 5 . 3 3 0 1 1 5 . 7 9 0 1 1 9 . 6 4 0 1 1 6 . 7 7 0 1 1 4 . 7 8 0 1 1 4 . 4 7 0 1 L 5 . U 0 1 1 6 . 1 3 0 1 1 6 . 0 7 0 1 1 5 . 5 7 0 1 1 6 . 5 0 0 1 1 5 . V 3 0 1 1 5 . 3 7 0 1 1 4 . 4 5 0 1 1 5 . 6 4 0 1 1 5 . 4 4 0 1 1 5 . 2 3 0 1 1 6 . 7 9 0 1 1 5 . 6 2 0 1 1 5 . 3 8 0 1 1 4 . 3 6 0 1 1 5 . 4 6 0 1 1 5 . 4 1 0 1 1 5 . 9 0 0 1 1 5 . 9 2 0 1 1 5 . 0 5 0 1 1 6 . 2 3 0 1 1 4 . 3 6 0 1 1 5 . 2 8 0 1 1 7 . 5 1 0 1 1 4 . 0 7 0 U 5 . 6 3 0 1 1 5 . 2 3 0 1 1 4 . 3 5 0 1 1 9 . 4 3 0 1 1 6 . 1 4 0 1 1 6 . 9 5 0 : 1 1 5 . 3 2 0 1 1 6 . 1 7 0 1 1 7 . 8 4 0 1 1 5 . 7 9 0 1 1 5 . 6 5 0 1 1 6 . 5 2 0 1 1 6 . 6 7 0 1 1 8 . 1 9 C 116 . 5 5 0 Tl6 . 0 6 0 1 1 5 . 7 1 0 1 1 5 . 6 8 0 1 1 6 . 6 0 0 1 1 5 . 5 7 0 1 1 6 . 5 0 0 1 1 6 . 2 1 0 U 5 . 4 7 0 1 1 6 . 0 6 0 1 1 7 . 4 1 0 1 1 5 . 9 7 0 1 1 5 . 8 1 0 1 1 6 . 1 4 0 1 1 5 . 7 8 0 1 1 6 . 1 J O 1 1 7 . 7 9 0 1 1 7 . 0 3 0 1 1 6 . 1 9 0 1 1 6 . 3 5 0 1 1 6 . 2 6 0 1 1 6 . 0 9 0 1 1 5 . 7 7 C 1 1 7 . 5 8 0 . 1 1 7 . 1 1 0 1 1 6 . 4 2 0 1 1 7 . 3 C 0 1 1 6 . 9 5 0 1 1 5 . 7 4 0 U S . 3 5 0 1 1 6 . 150 1 1 6 . 5 6 0 1 1 6 . 1 1 0 1 1 5 . 5 3 0 1 1 7 . 9 4 0 1 1 6 . 2 6 0 1 1 7 . 9 3 0 1 1 6 . 3 2 0 1 1 5 . 0 7 C 1 1 7 . 5 0 0 1 1 8 . 3 2 0 11>>.390 1 1 5 . 8 9 0 1 1 6 . 7 8 0 H 7 . 5 6 0 Table XI. Computer Output. O r i g i n a l X-Ray I n t e n s i t i e s f o r (200) R e f l e c t i o n from Annealed N i c k e l Powder Standard* 209 F I N A L CORRECTED I N T E N S I T Y V A L U E S - 0 . 0 0 . 7 1 4 2 5 2 5 E - 0 4 0 . 0 0 . 0 0 . 8 0 6 0 1 6 0 6 - 0 5 0 . 1 8 9 L 3 0 4 E - 0 4 0 . 2 4 3 8 5 9 U - 0 + 0 . 3 1 7 3 8 1 8 E - 04 0 . B 1 3 8 8 8 6 6 - 05 0 . 1 3 1 6 7 5 1 F - 04 0 . 9 4 1 9 1 2 0 6 - 05 0 . 0 0 . 3 4 2 4 0 9 5 6 - 0 5 0 . 4 3 0 9 4 9 9 6 - 0 5 - 0 . 0 0 . 0 ' 0 . 5 7 5 6 7 3 B E - OA 0 . 1091+CIE - 04 0 . 7 2 4 3 3 6 1 E - 05 0 . 0 0 . 0 0 . 0 0 . 0 0 . 8 2 3 9 8 + 0 6 - 06 0 . 0 0 . 3 0 4 6 0 2 1 6 - 05 0 . 1 1 6 4 1 8 2 E - 05 0 . 0 0 . 1 1 9 5 0 2 4 E - 0 4 0 . 9 2 8 4 2 8 2 E - 0 5 0 . 1 6 0 7 7 0 0 6 - 0 4 0 . 7 6 4 3 9 6 8 6 - 05 0 . 0 - 0 . 0 0 . 9 7 6 1 5 5 6 E - 05 - 0 . 0 - 0 . 0 0 . 0 0 . 7 1 0 4 7 5 4 6 - 0 5 0 . 7 2 7 0 8 8 6 F - 05 0 . 1 8 3 0 9 6 1 E - 0* - 0 . 0 0 . 0 0 . 0 C O 0 . 0 - 0 . 0 0 . 1 7 5 2 2 2 5 6 - 05 0 . 0 - 0 . 0 - 0 . 0 0 . 1 1 4 5 6 1 7 F - 04 C O 0 . 0 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0 . 2 2 8 1 4 4 9 E - 0 6 ' 0 . 5 8 0 1 7 0 3 E - 0 6 - C O - 0 . 0 - 0 . 0 0 . 0 - C O - 0 . 0 - C O - 0 . 0 - C O - 0 . 0 - 0 . 0 - C O o . o : 0 . 0 0 . 6 2 6 8 3 5 4 E - 0 5 - 0 . 0 - C O 0 . B 1 0 5 0 0 9 E - 05 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - c o 0 . 0 - 0 . 0 - o . o • 0 . 0 - 0 . 0 - 0 . 0 0 . 2 8 7 6 R S 5 E - 05 0 . 1 1 0 6 4 3 0 E - 04 - 0 . 0 - 0 . 0 - c o 0 . 5 6 8 3 8 4 7 E - 0 5 0 . 3 7 9 6 6 9 7 E - 0 5 - 0 . 0 C 2 4 3 3 B 3 7 E - 05 0 . 7 2 7 7 6 0 2 F - 05 0 . 1 1 9 5 5 3 4 E -~64~~ 0 . 1 7 4 4 7 7 8 E - 04 0 . 1A323R4E - 0 4 0 . 1 9 3 0 6 5 9 6 - 0 4 0 . 1 4 7 0 5 3 4 E - 0 4 0 . + 7 9 0 1 0 5 E - 05 . 0 . 1 8 3 8 7 9 2 6 - 0* 0 . 2 8 3 6 8 3 9 E - 04 0 . 3 6 5 8 5 6 2 6 - 04 0 . 3 6 0 9 3 8 4 F - 04 C 2 9 6 6 2 4 5 F - 0 4 0 . 2 2 2 9 8 9 9 E - 0 4 0 . 1 2 4 1 9 0 8 6 - 0 4 0 . 2 0 9 9 5 1 + 6 - 0+ 0 . 2 5 8 3 3 4 5 6 - 04 0 . 1 3 4 6 2 6 8 6 - 04 0 . 1 7 8 3 0 6 7 E - 04 0 . 1 9 8 4 6 8 3 E - 0+ 0 . 1 0 9 6 8 2 8 E - 0 4 0 . 2 8 7 1 0 1 1 E - 0 4 0 . 1 0 5 9 7 9 1 6 - 0 4 0 . 9 + 7 0 2 9 2 E - 05 0 . 0 0 . 0 0 . 9 1 4 2 0 8 1 6 - 05 C 9 5 8 1 3 6 7 F - 05 C 1 8 3 6 6 9 2 E - 0 4 0 . 1 0 7 2 9 5 9 E - 0 4 0 . 1 1056156 - 0 4 0 . 3 0 1 6 9 6 + 6 - 0+ 0 . 1 9 9 9 4 1 4 E - 04 0 . 1 8 4 H 6 2 E - 04 0 . 3 0 9 4 6 9 4 E - 05 0 . 2 4 6 P B 9 2 E - 04 C 1 0 1 3 5 4 7 E -0+ 0 . 1 2 0 4 5 9 3 E - 0 4 0 . 2 8 2 8 9 3 7 6 - 0 4 0 . 2 3 6 9 1 3 9 6 - 0+ C 6 4 1 7 7 5 1 E - 05 C 2 6 0 1 7 9 9 E - 04 0 . 1 2 1 0 ? « I 6 E - 04 0 . 1 1 8 3 7 1 7 E - 04 0 . 15221856 - 0 5 0 . M 3 0 7 3 3 E - 0 4 0 . 19127056 - 0 4 0 . 2 0 6 4 5 6 3 6 - 0+ 0 . 2 4 8 2 4 8 5 E - 04 C 2 2 1 6 9 7 8 E - 04 0 . 2 6 3 7 7 5 0 6 - 04 0 . 1 4 B 8 2 9 3 E - 04 ~ 0 . 2 1 6 1 5 0 4 6 - 0 4 0 . 2 3 5 1 8 4 1 E - 0 4 0 . 4 8 8 0 3 9 5 6 - 0 4 0 . + 3 9 2 6 0 6 6 - 0 + 0 . 2 7 6 5 2 B 9 6 - 04 0 . 1 7 2 4 7 5 4 6 - 04 0 . 2 5 2 B 7 6 6 E - 04 0 . 3 U 4 B 1 0 E - 04 0 . 2 7 5 4 5 9 8 F - 0 4 0 . 1810485E - 0 4 0 . 15648716 - 0 4 0 . 2 * 7 4 9 + 9 6 - 0+ 0 . 2 1 9 4 3 8 2 6 - 04 0 . 2 6 1 7 2 7 7 E - 04 0 . 3 3 6 0 3 9 5 6 - 04 C 2 1 6 9 7 5 3 F - 04 0 . 7 5 5 B 3 0 B E - 0 5 0 . 1 7 9 3 4 6 4 E - 0 4 C . 1 B 5 0 9 7 6 E -0+ 0 . 2 5 9 8 5 0 5 6 - 0+ 0 . 2 5 9 6 1 C 0 E - 04 0 . 2 9 2 9 4 3 6 E - 04 0 . 4 6 8 0 3 0 3 E - 04 0 . 6 2 1 1596E - 04 0 . 4 6 6 5 3 2 7 F - 0 4 0 . 5 4 1 2 5 5 1 E - 0 4 0 . 4 7 0 2 4 6 2 6 - 0 4 0 . 4 6 B 0 6 5 0 E - 0+ 0.++8+5+7E- 0+ 0 . 5 6 2 8 1 3 2 6 - 04 C 6 6 6 9 7 3 5 E - 04 0 . 6 2 9 6 8 0 6 6 - 04 C 5 4 1 0 0 4 0 F - 0 4 0 . 5 3 4 6 5 8 8 E - 0 4 0 . 5 8 6 2 1 3 1 E - 0 4 0 . 6 0 2 1 0 0 2 E - 0+ 0 . + 5 1 8 7 6 0 E - 04 0 . 4 2 7 B 5 6 1 E - 0+ C 5 3 6 7 7 U E - 04 0 . 5 6 5 4 7 2 9 E - 04 0 . 4 4 0 7 + 9 7 E - 0 4 C 5 9 0 7 4 9 0 E - 0 4 0 . 5 9 0 1 2 9 8 E - 0 * 0 . 5 + 2 1 3 5 2 E - 0+ 0 . 6 5 0 6 6 5 8 E - 04 0 . R 2 6 8 1 2 3 6 - 04 0 . 5 7 6 4 3 3 1 6 - 0* 0 . 4 8 0 1 8 4 2 E - 0+ 0 . 5 2 3 5 8 0 4 E - 0 4 0 . 5 6 t J 8 5 9 3 E - 0* 0 . 5 8 8 8 7 6 0 E - 0 * 0 . 7 5 7 2 7 5 6 6 - 0* j 0 . 7 0 6 8 8 7 + 6 - 04 C 5 7 5 9 2 0 4 E - 04 0 . 8 0 1 4 7 7 1 E - 0+ 0 . 6 9 0 7 6 0 8 E - 04 0 . B 0 9 7 3 9 0 E - 0 4 0 . 8 4 0 2 9 4 7 E - 0+ 0 . 8 6 3 9 5 2 6 6 - 0 * 0 . 7 7 5 2 8 5 2 E -0* i 0 . 1 0 5 3 8 + 7 E - 03 0 . 1 1 0 8 5 7 6 E - 03 0 . 1 0 2 9 1 8 7 6 - 03 0 . 9 9 B 4 7 2 2 E - 0+ 0 . 1 0 4 5 1 1 1 E - 0 3 0 . 1 0 9 5 8 0 3 E - 03 0 . 1 1 4 8 9 9 7 E - 03 0 . 1 1 5 2 * 9 * E -03 I 0 . 1 0 2 4 8 9 3 6 - 03 0 . 1 1 7 6 5 7 7 F - 03 0 . 1 2 7 8 6 6 !>E- 03 0 . 1 3 9 0 0 5 4 E - 03 0 . 1 5 6 5 6 0 2 6 - 0 3 0 . 1 7 4 1 5 8 4 6 - 03 C 1 5 2 5 8 7 7 E - 0 3 0 . 1 + 9 7 9 2 1 E - 03 1 0 . 1 6 7 5 9 S 9 6 - 03 C 1 7 8 7 0 7 9 E - 03 0 . 1 7 2 0 2 0 0 E - 03 C 1 8 1 4 0 4 4 E - 03 0 . 2 0 3 0 4 1 1 6 - 0 3 0 . 2 0 9 1 7 9 4 6 - 03 0 . 2 1 1 9 0 8 2 6 - 0 3 0 . 2 1 6 3 1 3 9 E - 0 3 ] 0 . 2 + 0 9 9 3 6 6 - 03 0 . 2 3 8 6 2 4 5 E - 03 0 . 2 4 7 0 6 5 7 E - 03 0 . 2 7 3 0 2 5 8 E - 03 0 . 2 9 4 2 5 3 2 E - 0 3 0 . 3 2 2 1 9 3 1 6 - 03 0 . 3 1 2 9 9 7 7 E - 0 3 0 . J 3 5 2 5 6 1 E - 0 3 1 0 . 3 8 9 4 7 5 1 E - 03 C 3 9 5 4 4 8 6 E - 03 0 . 4 0 3 7 5 6 5 E - 03 0 . 4 6 3 1 3 1 3 F - 0 3 0 . 4 6 6 3 4 6 0 E - 0 3 0 . 5 0 8 7 4 2 2 6 - 03 0 . 5 + 7 3 1 3 + E - 0 3 0 . 6 0 + 3 2 9 9 E - 03 0 . 6 5 6 2 2 5 5 6 - 03 C 6 9 8 9 8 9 0 E - 03 0 . 7 2 3 6 6 3 5 6 - 03 0 . 7 8 7 2 7 7 2 E - 03 0 . 8 8 3 4 7 6 6 E - 0 3 0 . 9 2 9 8 7 0 2 E - 03 0 . 1 0 + 3 2 I 8 E - 02 0 . U 2 T + 5 9 E - 02 j 0 . 1 1 6 7 1 8 3 6 - 02 0 . 1 3 0 0 7 4 0 E - 02 0 . 1 3 8 7 1 0 7 6 - 02 0 . 1 5 2 5 3 0 3 6 - 02 0 . 1 6 5 6 8 1 3 6 - 0 2 0 . 1 7 4 5 1 8 8 E - 02 0 . 1 9 7 1 0 2 5 E - 02 0 . 2 1 0 0 5 9 8 E - 02 0 . 2 3 0 5 3 2 5 6 - 02 0 . 2 5 7 5 9 6 9 E - 02 0 . 2 8 7 8 0 7 9 E - 02 0 . 3 2 6 9 6 8 1 E - 02 0 . 3 6 4 2 6 7 0 6 - 0 2 C + IQ0822E - 02 0 . + 6 9 7 8 8 5 6 - 0? 0 . 5 + 3 9 8 2 9 6 - 0 2 | 0 . 6 2 8 9 1 9 9 E - 02 0 . 7 2 1 9 5 9 4 E - 02 0 . 8 4 5 9 7 0 6 E - 02 0 . 9 8 8 9 1 5 9 6 - 02 0 . 1 1 5 8 2 2 8 6 - 0 1 0 . 1 3 2 + 2 7 1 6 - 01 0 . 1 5 2 6 + 5 1 6 - 01 0 . 1 7 3 9 3 5 9 F - 01 | 0 . 1 9 3 2 6 1 5 F - 01 0 . 2 1 0 7 0 5 1 6 - 01 0 . 2 2 5 3 8 2 1 6 - 01 0 . 2 3 8 0 1 2 1 6 - 01 0 . 2 4 4 7 8 9 2 6 - 0 1 0 . 2 + 3 0 3 5 8 6 - Qi 0 . 2 3 3 1 9 1+6- 01 0 . 2 1 8 7 3 3 5 E - 01 0 . 2 0 3 0 6 0 + E - 01 0 . 1 B 3 3 4 7 1 E - 01 0 . 1 5 8 9 1 8 3 E - 01 C 1 3 6 3 7 9 5 E - 01 0 . 1 1 4 8 0 6 4 6 - 0 1 0 . 9 5 3 6 7 3 9 E - 02 0 . 7 9 8 1 8 6 3 6 - 0 2 0 . 6 B 5 + T 2 0 E - 02 1 0 . 6 0 4 3 0 5 8 6 - 02 0 . 5 0 8 3 8 8 1 6 - 02 0 . 4 1 9 2 9 3 7 E - 02 0 . 3 7 5 5 4 1 7 E - 02 0 . 3 4 7 6 6 3 1 E - 0 2 0 . 3 0 7 5 6 + + E - 02 0 . 2 8 2 8 1 9 6 F - 02 0 . 2 3 6 9 * 3 4 6 - 0 2 ! 0 . 2 1 8 2 3 0 9 E - 02 C 1 9 7 6 8 3 7 E - 02 0 . 1 7 8 7 3 6 8 6 - 02 0 . 1 7 3 6 2 1 3 E - 02 0 . 1 5 8 0 9 4 6 6 - 0 2 0 . 1 2 9 9 7 2 + E - 02 0 . 1 0 9 1 5 3*6- 02 0 . 1 0 3 1 4 9 2 E - 02 0 . 9 6 3 0 5 5 3 6 - 03 C . 8 9 0 5 1 9 0 E - 03 0 . 7 3 7 4 5 3 1 6 - 03 0 . 6 7 3 1 2 5 5 6 - 03 0 . 5 7 4 9 3 9 2 E - 0 3 0 . 6 3 + 4 5 6 3 E - 03 0 . 5 5 9 7 5 5 4 6 - 0 3 0 . 5 2 8 6 7 5 5 E - 03 i 0 . + 8 + 5 7 9 0 E - 03 0 . 3 9 3 8 6 2 8 E - 03 0 . 4 2 5 6 3 9 1 E - 03 0 . 4 0 + 1 8 5 B F - 03 0 . 4 3 6 1 3 1 8 6 - 0 3 0 . 4 0 3 0 6 0 6 E - 03 0 . 3 8 2 9 9 3 + C - 0 3 0 . 3 + 9 0 9 0 0 E - 03 j 0 . 3 7 6 6 9 3 9 6 - 03 C . 3 3 5 5 8 0 2 E - 03 0 . 3 4 5 9 2 5 1 E - 03 0 . 2 5 1 0 8 7 8 6 - 03 0 . 2 8 2 3 5 0 7 6 - 0 3 0 . 2 4 7 6 2 8 9 6 - 03 0 . 2 6 2 + 6 3 2 6 - 0 3 0 . 2 5 6 2 2 5 5 E - 03 1 0 . 2 0 7 2 9 3 8 E - 03 0 . 1 9 2 9 8 8 1 E - 03 C 1 4 9 7 2 4 3 E - 03 0 . 1 2 1 4 9 B 2 E - 03 0 . 1 3 1 5 2 9 5 E - 0 3 0 . 1 4 5 1 3 7 8 E - 03 0 . 1 0 3 7 1 2 8 E - 0 3 0 . 1 I 7 2 + 8 9 E - 03 0 . 7 9 1 2 1 0 9 E - 04 0 . 1 0 6 9 7 3 1 E - 03 0 . 8 0 6 5 2 4 2 6 - 0+ 0 . 8 4 0 5 2 7 9 E - 04 0 . 6 2 4 2 6 9 0 F - 0 4 0 . 5 1 8 5 3 2 5 E - 04 0 . 6 9 7 7 7 0 2 6 - 0+ 0 . 8 5 1 6 0 6 6 E - 0* 0 . 9 + + 6 9 5 2 E - 0+ 0 . 6 4 6 4 3 9 1 E - 0+ 0 . 6 1 9 4 8 6 7 E - 0+ 0 . 6 B 5 5 2 3 3 E - 04 0 . 6 9 4 1 6 2 4 E - 0 4 0 . + 5 7 3 7 + 8 E - 0+ 0 . 8 U 0 6 7 3 E - 0+ 0 . 5 3 7 2 + 7 + E - 0+ 0 . 7 + 1 6 7 3 3 6 - 04 C 5 3 2 0 0 6 + E - 0+ 0 . 4 6 6 8 5 8 6 E - 0+ 0 . 4 9 6 1 5 9 8 6 - 04 0 . 3 4 6 7 3 I 4 E - 0 4 0 . 2 0 0 0 0 3 6 E - 0+ 0 . 1 8 0 6 3 0 6 6 - 0+ 0 . 3 9 2 0 7 5 7 E - o+ ; 0 . 2 2 3 5 8 0 9 6 - 0+ 0 . 9 0 + 5 2 3 8 E - 05 0 . 8 8 6 1 4 7 6 E - 05 0 . 1 2 5 6 6 2 2 6 - 04 . 0 . 0 0 . 2 5 1 9 2 2 8 E - 0 5 0 . 3 5 8 9 2 8 8 E - 05 0 . 0 1 0 . 0 0 . 0 0 . 0 0 . 7 0 8 9 1 2 6 E - 05 0 . 1030249E - 0 4 0 , 0 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 0 0 . 0 C O - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0 . 0 0 . 0 - 0 . 0 - C O - 0 . 0 - C O - 0 . 0 -o'.o - C O - 0 . 0 - C O - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 i - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -co - 0 . 0 - 0 . 0 j - 0 . 0 - 0 . 0 - 0 . 0 - C O - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - C O - 0 . 0 - 0 . 0 - 0 . 0 -0.0 -0.0 -0.0 -0.0 rO.O -0.0 -0.0 -o.o -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 -0.0 - 0 . 0 - 0 . 0 , - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -co - 0 . 0 - 0 . 0 -0.fi - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -co - 0 . 0 - 0 . 0 o^._Q_ - 0 . 0 - 0 . 0 - 0 . 0 -o.o - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -co - 0 . 0 -co - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o.o -co - 0 . 0 -co - 0 . 0 -co -co - 0 . 0 - 0 . 0 - 0 . 0 r0.o_ -o.o -co - 0 . 0 • - 0 . 0 - 0 . 0 -o.o • -o.o - 0 . 0 - 0 . 0 -co - 0 . 0 - 0 . 0 -co -o . 0 -co - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0 . 2 3 2 S 3 0 6 E - 0 9 Table X I I . Computer Output. F i n a l Corrected X-Ray I n t e n s i t i e s f o r (200) R e f l e c t i o n from Annealed N i c k e l Powder Standard. 210 | CHARESPONCING VALUES OF S I N E THETA I - 0 . 0 2 2 4 9 - 0 ; 0 2 2 4 2 - 0 . 0 2 2 3 4 - 0 . 0 2 2 2 6 - 0 . 0 2 2 1 8 - 0 . 0 2 2 1 1 - 0 . 0 2 2 0 3 - 0 . 0 2 1 9 5 - 0 . 0 2 1 8 7 - 0 . 0 2 180-0 . 0 2 1 72-0 . 0 2 1 6 4 - 0 . 0 2 1 5 6 - 0 . 0 2 1 4 9 - 0 . 0 2 1 4 1 - 0 . 0 2 1 33 i - 0 . 0 2 1 2 6 - C . 0 2 1 1 B - 0 . 0 2 1 1 0 - 0 . 0 2 1 0 2 - 0 . 0 2 0 9 5 - 6 . 0 2 0 8 7 - 6 . 0 2 0 7 9 - 0 . 0 2 0 7 1 - 0 . 0 2 0 6 4 - 0 . 0 2 0 * 6 - 0 . 0 2 0 4 8 - 0 . 0 2 0 4 0 - 0 . 0 2 0 3 3 - 0 . 0 2 0 2 5 - 0 . 0 2 0 1 7 - 0 . 0 2 0 0 9 - 0 . 0 2 0 0 2 - 0 . 0 1 9 9 4 - 0 . 0 1 9 8 6 - 0 . 0 1 9 7 B - 0 . 0 1 9 7 1 - 0 . 0 1 9 6 3 - 0 . 0 1 9 5 5 - 0 . 0 1 9 4 7 - 0 . 0 1 9 4 0 - 0 . 0 1 9 3 2 - 0 . 0 1 9 2 4 - 0 . 0 1 9 1 6 - 0 . 0 1 9 0 9 - 0 . 0 1 9 0 1 - 0 . 0 1 8 9 3 - 0 . 0 1 8 8 5 - 0 . 0 1 B 7 8 - C . 0 1 8 7 0 - 0 . 0 1 8 6 2 - 0 . 0 1 8 5 5 - 0 . 0 1 0 4 7 - 0 . 0 1 8 3 9 - 0 . 0 1 B 3 1 - 0 . 0 1 8 2 4 - 0 . 0 1 8 1 6 - 0 . 0 1 8 0 8 - 0 . 0 1 8 0 0 - 0 . 0 1 7 9 3 - 0 . 0 1 7 8 5 - 0 . 0 1 7 7 7 - 0 . 0 1 7 6 9 - 0 . 0 1 7 6 2 - 0 . 0 1 7 5 4 - 0 . 0 1 7 4 6 - 0 . 0 1 7 3 8 - 0 . 0 1 7 3 1 - 0 . 0 1 7 2 3 - 0 . 0 1 7 1 5 - 0 . 0 1 7 0 7 - 0 . 0 1 7 0 0 - 0 . 0 1 6 9 2 - 0 . 0 1 6 B 4 - 0 . 0 1 6 7 6 - 0 . 0 1 6 6 9 - 0 . 0 1 6 6 1 - 0 . 0 1 6 5 3 - 0 . 0 1 6 4 5 - 0 . 0 1 6 3 8 - 0 . 0 1 6 3 0 - 0 . 0 1 6 2 2 - 0 . 0 1 6 1 5 - 0 . 0 1 6 0 7 - 0 . 0 1 5 9 9 - 0 . 0 1 5 9 1 - 0 . 0 1 5 8 4 - 0 . 0 1 5 7 6 - 0 . 0 1 5 6 8 - 0 . 0 1 5 6 0 - 0 . 0 1 5 5 3 - 0 . 0 1 5 4 5 - 0 . 0 1 5 3 7 - 0 . 0 1 5 2 9 - 0 . 0 1 5 2 2 - 0 . 0 1 5 1 4 - . - Q . 0 1 5 0 6 . r Q . 0 1 4 9 8 - 0 . 0 1 4 9 1 - 0 . Q 1 4 B 3 - O t 0 1 4 7 5 - 0 . 0 1 4 6 T - 0 t Q | 4 6 Q - 0 . 0 1 4 5 2 - 0 . 0 1 4 4 4 - 0 . 0 1 4 3 6 - 0 . 0 1 4 2 9 - 0 . 0 1 4 2 1 - 0 . 0 1 4 1 3 - 0 . 0 1 4 0 5 - 0 . 0 1 3 9 8 - 0 . 0 1 3 9 0 - 0 . 0 1 3 8 2 - 0 . 0 1 3 7 4 - 0 . 0 1 3 6 7 - 0 . 0 1 3 5 9 - 0 . 0 1 3 5 1 - 0 . 6 1 3 4 4 - 0 . 0 1 3 3 6 - 0 . 0 1 3 2 8 - 0 . 0 1 3 2 0 - 0 . 0 1 3 1 3 - 0 . 0 1 3 0 5 - 0 . 0 1 2 9 7 - 0 . 0 1 2 8 9 - 0 . 0 1 2 8 2 - 0 . 0 1 2 7 4 - 0 . 0 1 2 6 6 l - 0 . 0 1 2 5 8 - 0 . 0 1 2 5 1 - 0 . 0 1 2 4 3 - 0 . 0 1 2 3 5 - 0 . 0 1 2 2 7 - 0 . 0 1 2 2 0 - 0 . 0 1 2 1 2 - 0 . 0 1 2 0 4 - 0 . 0 1 1 9 6 - 0 . 0 1 1 8 9 - 0 . 0 1 1 8 1 - 0 . 0 1 1 7 3 - 0 . 0 1 1 6 5 - 0 . 0 1 1 5 8 - 0 . 0 1 1 5 0 - 0 . 0 1 1 4 2 i - 0 . 0 1 1 3 4 - 0 . 0 1 1 2 7 - 0 . 0 1 1 1 9 - 0 . 0 1 1 1 1 - 0 . 0 U 0 3 - 0 . 0 1 0 9 6 - 0 . 0 1 0 8 8 - 0 . 0 1 0 8 0 - 0 . 0 1 0 7 3 - 0 . 0 1 0 6 5 - 0 . 0 1 0 5 7 - 0 . 0 1 0 4 9 - 0 . 0 1 0 4 2 - 0 . 0 1 0 3 4 - 0 . 0 1 0 2 6 - 0 . 0 1 0 1 8 I - 0 . 0 1 0 1 1 - 0 . 0 1 0 0 3 - 0 . 0 0 9 9 5 - 0 . 0 0 9 8 7 - 0 . 0 0 9 B 0 - 0 . 0 0 9 7 2 - 0 . 0 0 9 6 4 - 0 . 0 0 9 5 6 - 0 . 0 0 9 4 9 - 0 . 0 0 9 4 1 - 0 . 0 0 9 3 3 - 0 . 0 0 9 2 5 - 0 . 0 0 9 1 8 - 0 . 0 0 9 1 0 - 0 . 0 0 9 0 2 - 0 . 0 0 8 9 4 i - 0 . 0 0 B 8 7 - 0 . 0 0 8 7 9 - 0 . 0 0 8 7 1 - 0 . 0 0 8 6 3 - 0 . 0 0 8 5 6 - 0 . 0 0 8 4 8 - 0 . 0 0 8 4 0 - 0 . O O B 3 2 - 0 . O O B 2 5 - 0 . 0 0 8 1 7 - 0 . 0 0 8 0 9 - 0 . 0 0 8 0 2 - 0 . 0 0 7 9 4 - 0 . 0 0 7 B 6 - 0 . 0 0 7 7 8 - 0 . 0 0 7 7 1 - 0 . 0 0 7 6 3 - 0 . 0 0 7 5 5 - 0 . 0 0 7 4 7 - 0 . 0 0 7 4 0 - 0 . 0 0 7 3 2 - 0 . 0 0 7 2 4 - 0 . 0 0 7 1 6 - 0 . 0 0 7 0 9 - 0 . 0 0 7 0 1 - 0 . 0 0 6 9 3 - 0 . 0 0 6 8 5 - 0 . 0 0 6 7 8 - 0 . 0 0 6 7 0 - 0 . 0 0 6 6 2 - 0 . 0 0 6 5 4 - 0 . 0 0 6 4 - 0 . 0 0 6 3 9 - 0 . 0 0 6 3 1 - 0 . 0 0 6 2 3 - 0 . 0 0 6 1 6 - 0 . 0 0 6 0 8 - 0 . 0 0 6 0 0 - 0 . 0 0 5 9 2 - 0 . 0 0 5 8 5 - 0 . 0 0 5 7 7 - 0 . 0 0 5 6 9 - 0 . 0 0 5 6 2 - 0 . 0 0 5 5 4 - 0 . 0 0 5 4 6 - 0 . 0 0 5 3 8 - 0 . 0 0 5 3 1 - O . 0 0 5 2 3 j - 0 . 0 0 5 1 5 - 0 . 0 0 5 0 7 - 0 . 0 0 5 0 0 - 0 . 0 0 4 9 2 - 0 . 0 0 4 8 4 - 0 . 0 0 4 7 6 - 0 . 0 0 4 6 9 - 0 . 0 0 4 6 1 - 0 . 0 0 4 5 3 - 0 . 0 0 4 4 5 - 0 . 0 0 4 3 8 - 0 . 0 0 4 3 0 - 0 . 0 0 4 2 2 - 0 . 0 0 4 1 4 - 0 . 0 0 4 0 7 - 0 . 0 0 3 9 9 ! - 0 . 0 0 3 9 1 - 0 . 0 0 3 8 3 - 0 . 0 0 3 7 6 - 0 . 0 0 3 6 8 - 0 . 0 0 3 6 0 - 0 . 0 0 3 5 2 - 0 . 0 0 3 4 5 - 0 . 0 0 3 3 7 - 0 . 0 0 3 2 9 - 0 . 0 0 3 2 1 - 0 . 0 0 3 1 4 - 0 . 0 0 3 0 6 - 0 . 0 0 2 9 8 - 0 . 0 0 2 9 1 - 0 . 0 0 2 8 3 - 0 . 0 0 2 7 5 - 0 . 0 0 2 6 7 - 0 . 0 0 2 6 0 - 0 . 0 0 2 5 2 - 0 . 0 0 2 4 4 - 0 . 0 0 2 3 6 - 0 . 0 0 2 2 9 - 0 . 0 0 2 2 1 - 0 . 0 0 2 1 3 - 0 . 0 0 2 0 5 - 0 . 0 0 1 9 8 - 0 . 0 0 1 9 0 - 0 . 0 0 1 8 2 - 0 . 0 0 1 7 4 - 0 . 0 0 1 6 7 - 0 . 0 0 1 5 9 - 0 . 0 0 1 5 1 , - 0 . 0 0 1 4 3 - 0 . 0 0 1 3 6 - 0 . 0 0 1 2 8 - 0 . 0 0 1 2 0 - 0 . 0 0 1 1 2 - 0 . 0 0 1 0 5 - 0 . 0 0 0 9 7 - 0 . 0 0 0 8 9 - 0 . 0 0 0 8 1 - 0 . 0 0 0 7 4 - 0 . 0 0 0 6 6 - 0 . 0 0 0 5 8 - 0 . 0 0 0 5 0 - 0 . 0 0 0 4 3 - 0 . 0 0 0 3 5 - 0 . 0 0 0 2 T 1 - 0 . 0 0 0 2 0 - 0 . 0 0 0 1 2 - 0 . 0 0 0 0 4 0 . 0 0 0 0 4 O . O O Q l l 0 . 0 0 0 1 9 0 . 0 0 0 2 7 0 . 0 0 0 3 5 0 . 0 0 0 4 2 0 . 0 0 0 5 0 0 . 0 0 0 5 8 0 . 0 0 0 6 6 0 . 0 0 0 7 3 0 . 0 0 0 8 1 0.00OB9 0 . 0 0 0 9 7 0 . 0 0 1 0 4 0 . 0 0 1 1 2 0 . 0 0 1 2 C 0 . 0 0 1 2 8 0 . 0 0 1 3 5 0 . 0 0 1 4 3 0 . 0 0 1 5 1 0 . 0 0 1 5 9 0 . C 0 1 6 6 0 . 0 0 1 7 4 0 . 0 0 1 8 2 0 . 0 0 1 9 0 0 . 0 0 1 9 7 0 . 0 0 2 0 5 0 . 0 0 2 1 3 0 . 0 0 2 2 1 0 . 0 0 2 2 8 0 . 0 0 2 3 6 0 . 0 0 2 4 4 0 . 0 0 2 5 1 0 . 0 0 2 5 9 0 . 0 0 2 6 7 0 . 0 0 2 7 5 0.002B2. 0 . 0 0 2 9 0 0 . 0 0 2 9 8 0 . 0 0 3 0 6 0 * 0 0 3 1 3 0 . 0 0 3 2 1 0 . 0 0 3 2 9 0 . 0 0 3 3 7 0 . 0 0 3 4 4 0 . 0 0 3 5 2 0 . 0 0 3 6 0 0 . 0 0 3 6 8 0 . 0 0 3 7 5 0 . 0 0 3 0 3 0 . 0 0 3 9 1 0 . 0 0 3 9 9 0 . 0 0 4 0 6 0 . 0 0 4 1 4 0 . 0 0 4 2 2 0 . 0 0 4 3 0 0 . 0 0 4 3 7 0 . 0 0 4 4 5 0 . 0 0 4 5 3 0 . 0 0 4 6 1 0 . 0 0 4 6 8 0 . 0 0 4 7 6 0 . 0 0 4 8 4 0 . C 0 4 9 1 0 . 0 0 4 9 9 0 . 0 0 5 0 7 0 . 0 0 5 1 5 0 . 0 0 5 2 2 0 . 0 0 5 3 0 0 . 0 0 5 3 8 0 . 0 0 5 4 6 0 . 0 0 5 5 3 0 . 0 0 5 6 1 0 . 0 0 5 6 9 0 . 0 0 5 7 7 0 . 0 0 5 6 4 0 . 0 0 5 9 2 0 . 0 0 6 0 0 0 . 0 0 6 0 8 0 . 0 0 6 1 5 0 . 0 0 6 2 3 0 . 0 0 6 3 1 0 . 0 0 6 3 9 0 . 0 0 6 4 6 0 . 0 0 6 5 4 0 . 0 0 6 6 2 0 . 0 0 6 7 0 0 . 0 0 6 7 7 0 . 0 0 6 8 5 0 . 0 0 6 9 3 0 . 0 0 7 0 1 0 . 0 0 7 0 8 0 . 0 0 7 1 6 0 . 0 0 7 2 4 0 . 0 0 7 3 2 0 . 0 0 7 3 9 0 . 0 0 7 4 7 0 . 0 0 7 5 5 0 . 0 0 7 6 2 0 . 0 0 7 7 0 0 T Q Q 7 7 8 0 . 0 0 7 6 6 0 . 0 0 7 9 3 0 . 0 0 8 0 1 0 . 0 0 8 0 9 0 . 0 0 6 1 7 0 . 0 0 B 2 4 - 0 . 0 Q 8 3 2 0 . 0 0 6 4 0 0 . 0 0 8 4 8 0 . 0 0 8 5 5 0 . 0 0 8 6 3 O.O0871 0 . 0 0 8 7 9 0 . 0 0 8 8 6 0 . 0 0 8 9 4 0 . 0 0 9 0 2 0 . 0 0 9 1 0 0 . 0 0 9 1 7 0 . 0 0 9 2 5 0 . 0 0 9 3 3 0 . 0 0 9 4 1 0 . 0 0 9 4 8 0 . 0 0 9 5 6 0 . 0 0 9 6 4 0 . 0 0 9 7 2 0 . 0 0 9 7 9 0 . 0 0 9 R 7 0 . 0 0 9 9 5 0 . 0 1 0 0 3 0 . 0 1 0 1 0 0 . 0 1 0 1 8 0 . 0 1 0 2 6 0 . 0 1 0 3 3 0 . 0 1 0 4 1 0 . 0 1 0 4 9 0 . 0 1 0 5 7 0 . 0 1 0 6 4 0 . 0 1 0 7 2 0 . 0 1 0 8 0 . 0 . 0 1 0 6 8 0 . 0 1 0 9 5 0 . 0 1 1 0 3 0 . 0 1 1 1 1 0 . 0 1 1 1 9 0 . 0 1 1 2 6 0 . 0 1 1 3 4 0 . 0 1 1 4 2 0 . 0 1 1 5 0 0 . 0 1 1 5 7 0 . 0 1 1 6 5 0 . 0 1 1 7 3 0 . 0 1 1 6 1 0 . 0 1 1 8 6 0 . 0 1 1 9 6 0 . 0 1 2 0 4 0 . 0 1 2 1 2 0 . 0 1 2 1 9 0 . 0 1 2 2 7 0 . 0 1 2 3 5 0 . 0 1 2 4 3 0 . 0 1 2 5 0 0 . 0 1 2 5 8 0 . 0 1 2 6 6 0 . 0 1 2 7 4 0 . 0 1 2 8 1 0 . 0 1 2 8 9 0 . 0 1 2 9 7 0 . 0 1 3 0 4 0 . 0 1 3 1 2 0 . 0 1 3 2 0 0 . 0 1 3 2 8 0 . 0 1 3 3 5 0 . 0 1 3 4 3 0 . 0 1 3 5 1 0 . 0 1 3 5 9 0 . 0 1 3 6 6 0 . 0 1 3 7 4 0 . 0 1 3 8 2 0 . 0 1 3 9 0 0 . 0 1 3 9 7 0 . 0 1 4 0 5 0 . 0 1 4 1 3 0 . 0 1 4 2 1 0 . 0 1 4 2 8 0 . 0 1 4 3 6 0 . 0 1 4 4 4 0 . 0 1 4 5 2 0 . 0 1 4 5 9 0 . 0 1 4 6 7 0 . 0 1 4 7 5 0 . 0 1 4 8 3 0 . 0 1 4 9 0 0 . 0 1 4 9 8 0 . 0 1 5 0 6 0 . 0 1 5 1 4 0 . 0 1 5 2 1 0 . 0 1 5 2 9 0 . 0 1 5 3 7 0 . 0 1 5 4 4 0 . 0 1 5 5 2 0 . 0 1 5 6 0 0 . 0 1 5 6 9 0 . 0 1 5 7 5 O t 0 1 S 8 ? 0 . 0 1 5 9 1 0 . 0 1 5 9 9 0 . 0 1 6 0 6 0 . 0 1 6 1 4 0 . 0 1 6 2 2 0 . 0 1 6 3 0 0 . 0 1 6 3 7 0 . 0 1 6 4 9 0 . 0 1 6 9 3 0 . 0 1 6 6 1 0 . 0 1 6 6 8 0 . 0 1 6 7 6 0 . 0 1 6 8 4 0 . 0 1 6 9 2 0 . 0 1 6 9 9 0 . 0 1 7 0 7 ' 0 . 0 1 7 1 5 0 . 0 1 7 2 3 0 . 0 1 7 3 0 0 . 0 1 7 3 6 0 . 0 1 7 4 6 0 . 0 1 7 5 4 0 . 0 1 7 6 1 0 . 0 1 7 6 9 0 . 0 1 7 7 7 0 . 0 1 7 8 5 0 . 0 1 7 9 2 0 . 0 1 6 0 0 0 . 0 1 6 0 8 0 . 0 1 8 1 5 0 . 0 1 8 2 3 0 . 0 1 8 9 1 0 . 0 1 8 3 9 0 . 0 1 8 4 6 C . 0 1 8 5 4 0 . 0 1 8 6 2 0 . 0 1 0 7 0 0 . 0 1 0 7 7 0 . 0 1 8 8 5 0 . 0 1 8 9 3 0 . 0 1 9 0 1 0 . 0 1 9 0 8 0 . 0 1 9 1 6 0 . 0 1 9 2 4 0 . 0 1 9 3 2 0 . 0 1 9 3 9 0 . 0 1 9 4 7 0 . 0 1 9 5 5 0 . 0 1 9 6 3 0 . 0 1 9 7 0 0 . 0 1 9 7 8 O . 0 1 9 6 6 0 . 0 1 9 9 4 0 . 0 2 0 0 1 0 . 0 2 0 0 9 0 . 0 2 0 1 7 0 . 0 2 0 2 5 0 . 0 2 0 3 2 0 . 0 2 0 4 0 0 . 0 2 0 4 8 0 . 0 2 0 5 6 0 . 0 2 0 6 3 0 . 0 2 0 7 1 0 . 0 2 0 7 9 0 . 0 2 0 8 6 0 . 0 2 0 9 4 0 . 0 2 1 0 2 0 . 0 2 1 1 0 0 . 0 2 1 1 7 0 . 0 2 1 2 9 0 . 0 2 1 3 3 0 . 0 2 1 4 1 0 . 0 2 1 4 8 0 . 0 2 1 5 6 0 . 0 2 1 6 4 0 . 0 2 1 7 2 0 . 0 2 1 7 9 0 . 0 2 1 8 7 0 . 0 2 1 9 5 0 . 0 2 2 0 3 0 . 0 2 2 1 0 0 . 0 2 2 1 8 0 . 0 2 2 2 6 0 . 0 2 2 3 4 0 . 0 2 2 4 1 0 . 0 2 2 4 9 O f 0 2 2 9 7 0 . 0 2 2 6 5 0 . 0 2 2 7 2 0 . 0 2 2 6 0 0 , 0 2 2 8 8 0 . 0 2 2 9 6 0 . 0 2 3 0 3 0 . 0 2 3 1 1 0 . 0 2 3 1 9 0 t 0 ? 3 2 7 0 . 0 2 3 3 4 0 . 0 2 3 4 2 0 . C 2 3 5 0 0 . 0 2 3 9 7 0 . 0 2 3 6 9 0 . 0 2 3 7 3 0 . 0 2 3 8 1 0 . 0 2 3 8 8 0 . 0 2 3 9 6 0 . 0 2 4 0 4 0 . 0 2 4 1 2 0 . 0 2 4 1 9 0 . 0 2 4 2 7 0 . 0 2 4 3 5 0 . C 2 4 4 3 0 . 0 2 4 9 0 Table XIII, Computer Output. Sin 9 Values for (200) Reflection from Annealed Nickel Powder Standard. S I N E THETA INTERVAL - 0 . 0 0 0 0 8 NUMBER OF S I N E THETA OATA P O I N T S * 6 0 8 A R T I F I C I A L L A T T I C E PARAMETER • , 5 , 7 1 7 0 3 ANGSTROMS. . TWO THETA ZERO I CENTRE OF G R A V I T Y ) • 5 1 . 8 4 9 DECREES L A T T I C E PARAMETER ICFNTRE OF G R A V I T Y ) » 3 . 5 2 3 6 8 ANGSTROMS TWO THETA ZERO I PEAK MAXIMUM) • 5 1 . 6 6 8 DEGREFS .LATT I C E J»Ajl AMf_ER _ ( P E A K MAX|N1J_| J 3 . 5 2 2 4 6 A_6$T«0NS PEAK ASYMMETRY - - 0 . 0 1 9 DEGREES __. ' j Table XIV. Computer Output. Peak Parameters for (200) Reflection from Annealed Nickel Powder Standard. 211 NI POWDER ANNEALED R F F L E C TION 1 4 0 0 1 j SCAN B E G I N S AT 118.SOO DEGREES TWO THETA ANGULAR INCREMENT * 0.010 DEGREES NUMBER OF OATA POINTS ' 701 . . i ATOMIC S C A T T E R I N G FACTOR AT TWH THETA 111 - 11.83 j ! ATOMIC SCATTERING FACTOR AT TWO THETA 121 • U . 5 4 CONTROL • 2 1 O R I G I N A L I N T E N S I T Y VALUES ~ : '• I -= ] 125.230 124.110 1 2 3 . 5 8 0 1 2 3 . 1 7 0 1 2 5 . 0 4 0 1 2 4 . 7 0 0 124.490 1 2 5 . 4 1 0 1 2 5 . 2 1 0 1 2 4 . 5 5 0 1 2 4 . 3 6 0 123.930 124.030 124.550 123.640 129.940 j 124.130 124.810 1 2 4 . 9 4 0 1 2 4 . 9 1 0 1 2 5 . 4 3 0 124.730. 1 2 4 . 6 8 0 1 2 4 . 5 9 0 126.110 124.520 1 2 5 . 3 5 0 1 2 5 . 6 2 0 122.660 124.540 124.190 124.400 j 124.860 125.340 1 2 5 . 0 4 0 1 2 5 . R 9 0 1 2 4 . 1 4 0 1 2 4 . 6 5 0 1 2 3 . 6 2 0 1 2 4 . 3 5 0 1 2 4 . 8 9 0 1 2 4 . 5 5 0 123.920 125.820 1 2 4 . 6 0 0 124.490 124.260 123.640 » 124.110 123.950 1 2 4 . 5 7 0 1 2 6 . 1 7 0 1 2 4 . 9 3 0 1 2 5 . 4 1 0 1 2 3 . 2 5 0 1 2 4 . 9 2 0 1 2 5 . 8 4 0 125.010 1 2 4 . 4 4 0 1 2 4 . 3 8 0 125.470 123.590 124.150 124.380 ! I 129.430 1 2 3 . 8 4 0 125.200 1 2 4 . 4 5 0 1 2 4 . 9 2 0 I 2 3 . 4 B G 125.620 1 2 4 . 9 7 0 1 2 5 . 8 7 0 1 2 4 . 8 3 0 1 2 3 . 6 5 0 122.620 1 2 4 . 8 9 0 126.430 125.590 126.180 129.690 123.290 1 2 4 . 5 4 0 1 2 5 . 5 1 0 1 2 4 . 3 1 0 122.860 1 2 3 . 0 3 0 1 2 4 . 8 8 0 1 2 3 . 6 5 0 1 2 6 . 0 2 0 1 2 4 . 1 3 0 1 2 4 . 2 1 0 125.370 1 2 3 . 6 6 0 129.060 123.820 1 125.010 123.470 1 2 6 . 1 8 0 1 2 5 . 2 7 0 1 2 3 . 6 7 0 1 2 3 . 6 1 0 1 2 3 . 8 7 0 1 2 5 . 0 8 0 1 2 4 . 6 6 0 1 2 4 . 3 T 0 122.910 124.310 1 2 4 . 1 7 0 126.550 124.990 129.540 j • 124.230 124.200 1 2 4 . 9 8 0 1 2 4 . 9 2 0 1 2 3 . 6 6 0 1 2 5 . 7 3 0 1 2 3 . 4 3 0 1 2 5 . 3 8 0 124.010 1 2 5 . 3 5 0 1 2 4 . 0 3 0 1 2 4 . 2 8 0 1 2 3 . 2 8 0 121.810 123.500 124.110 | i 124.850 124.510 1 2 3 . 0 9 0 1 2 4 . 8 3 0 1 2 3 . 9 5 0 1 2 4 . 0 9 0 122.280 1 2 5 . 2 3 0 1 2 5 . 2 3 0 1 2 5 . 6 7 0 1 2 5 . 5 7 0 1 2 3 . 4 8 0 126.080 123.800 123.190 123.870 124.340 124.380 1 2 4 . 6 9 0 1 2 4 . 7 0 0 124.110 1 2 4 . 0 8 0 1 2 5 . 0 0 0 1 2 3 . 7 4 0 1 2 4 . 0 3 0 1 2 3 . 6 4 0 1 2 4 . 6 0 0 1 2 5 . 8 0 0 1 2 3 . 1 * 0 1 25.090 122.630 122.440 = 122.840 124.960 1 2 4 . 5 1 C 1 2 4 . 0 9 0 1 2 4 . 4 1 0 122.560 1 2 3 . 5 5 0 1 2 4 . 3 2 0 124.030"123.5 10 122.820 1 2 4 . 4 9 0 123.260 123.560 123.960 124.590 I 123.090 124.340 1 2 3 . 8 6 0 1 2 3 . 4 9 0 1 2 4 . 4 7 0 1 2 3 . 0 0 0 1 2 3 . 2 8 0 1 2 2 . 7 5 0 1 2 3 . 5 5 0 1 2 4 . 6 5 0 123.100 122.580 1 2 4 . 0 9 0 123.540 124.510 123.T60 1 122.270 122.860 1 2 4 . 0 3 0 1 2 4 . 3 3 0 1 2 4 . 0 9 0 122.770 1 2 3 . 2 5 0 122 .6B0.123.160 1 2 3 . 2 9 0 1 2 3 . 4 5 0 122.590 1 2 3 . 5 1 0 123,840 123.060 123.120 1 122.910 121.440 1 2 1 . 3 4 0 1 2 1 . 9 0 0 121.550 122.130 122.920 12 4 . 0 8 0 122.9B0 1 2 3 . 9 3 0 1 2 3 . 2 1 0 122.660 122.370 123.390 124.230 123.440 122.410 124.300 1 2 4 . 5 4 0 122.350 1 2 2 . 1 2 0 121.090 122.750 121.380 122.960 1 2 1 . 6 7 0 1 2 1 . 1 2 0 1 2 0 . 9 6 0 121.910 1 2 3 . 9 0 0 121.690 122.230 j • 121.610 121.550 1 2 0 . 3 7 0 121.630 1 2 1 . 4 0 0 121.5B0 122.B70 121.370 1 2 1 . 4 3 0 122.920 121.UP 121.520 122.840 1 1 9 . 0 4 0 119.600 120.910 , 120.740 122.410 1 2 0 . 3 6 0 1 1 9 . 1 5 0 1 2 7 . 6 8 0 121.740 121.460 12 C . 6 0 0 1 2 0 . 3 4 0 1 2 0 . 3 1 0 1 2 1 . 1 6 0 120.U20 1 1 9 . 6 9 0 1 1 9 . 8 1 0 120.430 119.170 I 120.340 120.010 1 2 1 . 2 4 0 1 2 0 . 3 7 0 1 2 0 . 9 7 0 1 2 1 . 1 7 0 1 2 0 . 6 6 0 1 1 8 . 3 4 0 1 1 7 . 7 1 0 1 1 6 . 4 0 0 1 1 7 . 6 6 0 1 1 9 . 3 9 0 1 1 7 . 1 4 0 1 1 9 . 8 6 0 117.980 116.520 . 116.370 116.570 1 1 6 . 9 7 0 1 1 7 . 4 0 0 1 1 7 . 4 6 0 1 1 6 . 8 4 0 1 1 5 . 4 3 0 1 1 7 . 2 1 0 1 1 6 . 4 0 0 1 1 6 . 6 7 0 U 6 . 2 4 0 1 1 6 . 6 3 0 115.220 114.670 1 1 5 . 0 6 0 114.290 113.930 110.470 112.630 112.720 112.910 1 1 1 . 5 9 0 110.040 110.710 1 0 8 . 6 0 0 1 0 9 . 4 0 0 1 0 9 . 1 2 0 1 0 7 . 9 5 0 1 0 6 . 4 7 0 1 0 5 . 9 7 0 105.730 104.790 ) 1 0 4 . 4 6 0 103.170 101.150 9 9 . 5 3 0 100.160 9 6 . 7 1 0 9 6 . 9 7 0 9 4 . 3 0 0 9 3 . 9 1 0 9 1 . 5 1 0 9 0 . 1 3 0 8 8 . 6 7 0 6 7 . 0 8 0 8 5 . 4 2 0 83.710 81.270 80.750 77.530 76.Q4Q _ 7 4 . 3 4 0 7 4 . 2 1 0 71.910 _ 7 2 . ISO 71 .460 7 1 . 9 20 72^. 120_ 7 2 . 1 3 0 73.9 70 7 4 . B 6 0 7 5 . 6 5 0 7 6 . 8 6 0 79.680 t 81.020 8 1 . 7 0 0 8 5 . 1 2 0 8 4 . 9 0 0 8 8 . 4 6 0 8 9 . 5 1 0 9 0 . 3 9 0 9 1 . 7 0 0 9 3.750 9 5 . 2 1 0 "95.4 30 96.560 9 6 . 9 1 0 9 8 . 1 6 0 9 8 . 1 9 0 98.860 98.580 1 0 0 . 5 0 0 9 9 . 9 5 0 9 9 . 6 0 0 101.140 1 0 0 . 5 9 0 1 0 0 . 7 5 0 1 0 1 . 5 8 0 9 9 . 3 0 0 9 9 . 3 0 0 9 9 . 0 3 0 9 9 . 3 9 0 9 8 . 4 1 0 9 7 . 9 2 0 9 7 . 3 2 0 97.760 ! 95.930 9 4 . 2 6 0 9 3 . 7 3 0 9 2 . 2 4 0 9 2 . 3 2 0 9 0 . 2 7 0 9 0 . 2 3 0 I B . 4 4 0 B9.010 8 8 . 1 7 0 8 7 . B 4 0 8 7 . 9 5 0 8 8 . 7 8 0 89.060 88.780 88.680 | 91.760 9 3 . 1 5 0 9 3 . 3 6 0 9 5 . 0 7 0 96.110 9 8 . 7 9 0 9 6 . 2 9 0 9 9 . 5 2 0 101.780 1 0 2 . 5 5 0 1 0 3 . 6 1 0 1 0 5 . 3 1 0 1 0 4 . 6 0 0 105.110 107.140 107.190 I 1 106.890 1 0 8 . 3 6 0 1 0 9 . 4 9 0 1 1 1 . 1 6 0 110.510 1 1 1 . 6 9 0 1 1 2 . 6 1 0 1 1 3 . 6 2 0 112.960 1 1 3 . 6 7 0 1 1 3 . 8 9 0 112.560 1 1 3 . 9 0 0 1 1 4 . 6 5 0 116.110 114.690 j 115.930 115.110 U 6 . 4 2 0 1 1 5 . 8 2 0 1 1 6 . 3 8 0 1 1 8 . 6 2 0 1 1 7 . 9 6 0 1 1 7 . 3 7 0 1 1 7 . 7 3 0 1 1 7 . 5 0 0 1 1 8 . 4 2 0 1 1 7 . 7 7 0 U 8 T 8 0 0 1 1 6 . 7 1 0 1 1 7 . 3 9 0 117.640 I 116.880 1 1 9 . 2 7 0 1 1 9 . 4 9 0 1 1 9 . 7 1 0 1 1 9 . 1 3 0 1 1 8 . 1 6 0 1 1 9 . 6 7 0 1 2 0 . 0 6 0 1 1 8 . 2 7 0 1 1 9 . 5 6 0 1 1 9 . 2 9 0 1 2 0 . 0 4 0 121.940 1 1 8 . 8 9 0 1 2 0 . 8 3 0 1 2 0 . 4 8 0 1 2 0 . 2 9 0 1 2 0 . 1 2 0 121.300 1 1 9 . 7 2 0 122.790 121.550 1 2 0 . 5 8 0 1 1 9 . 8 6 0 1 2 0 . 0 0 0 1 2 0 . 2 0 0 122.870 122.970 122.640 1 2 0 . 8 6 0 121.280 121.990 121.880 121.430 121.200 121.860 121.960 121.800 1 2 3 . 0 3 0 122.650 122.750 1 2 1 . 7 7 0 1 2 2 . 4 4 0 122.160 1 2 3 . 3 4 0 1 2 4 . 5 6 0 122.180 122.TOO \ 121.960 122.070 1 2 7 . 1 3 0 173.220 1 2 3 . 2 5 0 1 2 2 . f l 30 122.650 1 2 3 . 1 1 0 1 2 3 . 5 9 0 1 2 3 . 9 3 0 1 2 2 . 7 2 0 122.520 1 2 2 . 4 5 0 123.800 :122.690 1 2 3 . 2 4 0 I 122.600 122.720 121.260 122.830 1 2 4 . 8 1 0 1 2 3 . 2 3 0 122.010 1 2 0 . 6 9 0 1 2 0 . 6 2 0 1 2 4 . 4 1 0 1 2 3 . 1 3 0 1 2 4 . 4 5 0 122.380 1 2 3 . 5 0 0 124.110 1 2 4 . 4 6 0 ! 1 2 4 . 2 4 0 124.220 1 2 3 . 3 5 0 1 2 3 . 120 122.710 1 2 2 . 4 2 0 1 2 3 . 4 6 0 124.2 50_123.720_X2 3._440 1 2 2 . 6 6 0 122.970 122.710 1 2 3 . 2 4 0 1 2 3 . 9 4 0 1 2 3 . 0 6 0 | 1 2 3 . 0 9 0 1 2 3 . 5 0 0 122.490 12 4 . 2 8 0 ' 1 2 3 ^ 8 1 0 1 2 3 . 5 70~ 1 2 4 . 610 1 2 2 . 660 121.480 1 2 3. 5 30 "l 2 3 ^ 350 124 .220 122.140 1 2 3 . 4 1 0 1 2 4 . 5 2 0 1 2 3 . 7 8 0 122.830 122.950 1 2 3 . 9 6 0 1 2 3 . 4 9 0 1 2 4 . 5 1 0 1 2 3 . 7 2 0 1 2 4 . 0 6 0 122.330 1 2 4 . 7 7 0 123 . 0 0 0 1 2 3 . 2 9 0 122.820 1 2 3 . 9 6 0 1 7 4 . 7 4 0 1 2 3 . 6 1 0 123.000 1 2 3 . 6 2 0 1 2 3 . 5 1 0 1 2 3 . 8 3 0 1 2 3 . 2 9 0 1 2 4 . 5 5 0 1 2 4 . 2 7 0 125.010 1 2 3 . 2 5 0 1 2 4 . 2 2 0 1 2 2 . 3 2 0 1 2 3 . 4 7 0 123.220 1 2 3 . 9 4 0 121.960 1 2 3 . 8 6 0 1 2 5 i 2 0 0 j 122.350 1 2 4 . 7 5 0 1 2 3 . 7 6 0 1 2 4 . 3 0 0 121.260 1 2 4 . 3 0 0 1 2 4 . 3 6 0 1 2 3 . 0 7 0 1 2 1 . 1 0 0 1 2 4 . 5 3 0 1 2 3 . 0 9 0 1 2 4 . 4 7 0 122.910 1 2 5 . 2 9 0 1 2 4 . 4 5 0 124.040 1 1 2 4 . 0 4 0 1 2 4 . 5 9 0 123.54C 1 2 7 . 9 7 0 1 2 3 . 6 2 0 1 2 3 . 0 6 0 1 2 5 . 5 1 0 1 2 4 . 3 3 0 1 2 3 . 8 2 0 1 2 1 . 3 4 0 1 2 3 . 2 1 0 122.950 1 2 3 . 9 5 0 1 2 4 . 3 7 0 1 2 3 . 9 8 0 1 2 4 . 6 4 0 | _ 1 2 3 . 4 1 0 1 2 4 . 3 5 0 1 2 3 . 9 7 0 1 7 3 . 6 1 0 1 2 3 . 4 4 0 1 2 2 . 7 4 0 1 2 3 . 160 1 2 3 . 8 7 0 1 2 5 . 0 3 0 1 2 3 . 0 3 0 1 2 3 . 7 3 0 1 2 3 . 6 7 0 1 2 3 . 4 9 0 _122.610 124.110 123.100 ! 1 2 4 . 1 3 0 1 2 5 . 5 6 0 1 2 3 . 2 5 0 1 2 3 . 6 6 0 1 2 6 . 4 6 0 1 2 3 . 7 9 0 1 2 3 . C 3 0 1 2 3 , 9 6 0 1 2 3 . 3 2 0 1 2 4 . 0 7 0 122.330 1 2 3 . 9 4 0 123.5TO 1 2 4 . 3 8 0 1 2 4 . 1 9 0 1 2 4 . 7 9 0 1 2 3 . 9 1 0 1 2 4 . 8 5 0 1 2 3 . 9 4 0 1 2 4 . 5 0 0 1 2 1 . 1 5 0 1 2 2 . 9 3 0 1 2 2 . 3 6 0 1 7 2 . 7 1 0 121.860 1 2 3 . 7 5 0 1 2 4 . 4 7 0 1 2 4 . 6 6 0 1 2 3 . 9 9 0 1 2 4 . 3 4 0 1 7 3 . 0 3 0 123.100 1 2 3 . 6 8 0 1 2 3 . 3 8 0 122.*6D 1 7 2 . 7 7 0 1 2 4 . 4 8 0 1 2 4 . 4 1 0 1 2 3 . 5 8 0 1 7 3 . 8 6 0 1 2 3 . 6 4 0 1 2 3 . 4 6 0 1 2 2 . 4 5 0 1 2 3 . 8 0 0 1 2 3 . 7 4 0 1 2 3 . 6 9 0 122.150 1 2 5 . 9 8 0 1 7 3 . 5 7 0 1 2 2 . 4 9 0 1 2 5 . 7 0 0 1 2 4 . 3 9 0 1 2 4 . 4 7 0 123 . 0 0 0 1 2 4 . 7 9 0 1 2 3 . 6 2 0 1 2 2 . 7 4 0 1 2 4 . 1 6 0 1 2 3 . 3 B 0 1 2 4 . 2 2 0 1 2 4 . 9 4 0 Table XV. s Computer Output. Original X-Ray Intensit ies 'for (400) Reflection from Annealed Nickel Powder Standard. 212 F I N A L CORRECTED I N T E N S I T Y VALUFS - 0 . 0 , 0 . 1 4 4 9 5 0 4 E -03 0 . 2 I 7 9 9 5 3 F -03 0 . 1 8 2 7 0 1 2 6 - 0 3 0 . 6 1 7 5 5 3 3 F -04 0 . 5 4 0 1 7 2 8 E - 0 4 0 . 8 6 1 5 8 4 6 6 - 0 * 0 . 2 7 8 4 2 1 4 F -04 0.0 0 . 3 3 5 4 0 5 6 E -04 0 . 9 5 4 0 2 1 1 E - 0 * 0 . 1 2 B 7 3 9 1 F - 0 3 0. 1 6 7 9 0 9 9 F -03 0 . 1 4 4 5 4 4 2 E - 0 3 0 . 9 5 0 0 0 9 9 E - 0 4 0 . 1 8 1 3 4 1 4 6 -03 0.0 0 . 6 5 4 4 6 3 7 6 -04 0 . 5 9 5 8 9 5 8 E -04 0 . 2 9 5 7 8 0 2 E - 0 4 0 . 2 7 7 5 5 7 1 F -04 O.U 0 . 1 2 2 6 4 7 1 6 04 0 . 5 5 1 0 I 1 R F -04 0 . 6 3 4 1 1 6 7 E - 04 0.0 0.0 0 . 4 S 9 7 9 1 5 E - 04 0.0 0.0 0 . 3 1 4 3 6 5 6 6 - 0 3 0 . 7 3 2 0 8 5 0 F -04 ! 0 . 1 2 3 0 1 8 7 E -03 0 . 9 2 9 4 3 8 4 F -04 0 . 3 5 5 7 0 0 2 E -04 0.0 0.0 0.0 0 . 2 5 3 7 B 8 3 F - 0 4 0 . 8 3 1 5 3 7 3 F -04 0 . 1 1 7 8 7 6 5 E - 0 3 0 . 1 4 9 9 7 6 7 E -03 0 . 6 3 2 2 5 2 6 F -04 0 . 2 8 0 0 5 7 4 6 - 04 0 . B 0 7 Z 9 1 5 E -04 0 . 1 0 1 4 0 C 2 E - 0 3 0.0 0.5 1 9 6 4 2 9 E -04 0 . 6 5 5 7 5 8 8 E - 04 0 , 9 4 6 9 2 ] j F -04 0 , 1 6 6 0 2 7 1 F - 0 3 0 . 1 2 6 8 5 8 7 F - 0 3 0.t32789»SE -P3._ 0 . 4 1 3 1 B 2 7 E -05 0.0 0.0 0.0 0 . 4 4 2 4 2 6 4 E -04 0 . 9 4 0 4 9 4 5 E -04 0.0 - 0 . 0 0.6 0 . 1 5 4 3 3 4 0 6 04 0.0 0.0 0 . 1 0 5 6 9 7 5 F -03 0 . 5 5 4 5 B 5 1 E -04 0.0 - 0 . 0 0 . 5 6 6 7 7 6 0 E -04 0.0 0 . 3 0 7 7 4 9 7 E -05 0.0 0 . 9 7 1 5 4 3 2 E -04 0 . 7 4 4 6 2 4 1 E -04 0.0 0.0 - 0 . 0 C . 3 9 5 5 B 1 9 F - 0 4 0 . 1 6 6 4 3 2 7 E -03 0 . 2 5 2 7 0 6 7 E - 0 3 - 0 . 0 0.0 0.0 0.0 0.0 0 . 1 2 9 0 6 4 0 6 - 0 3 0 . 6 7 0 9 3 5 8 6 04 - 0 . 0 0 . 3 5 1 6 5 2 9 E -05 0 . 1 6 9 4 5 4 2 E - 0 3 0 . 2 0 5 5 3 4 9 6 - 0 3 0.4665677F. -04 0.0 0.0 0.0 0 . 3 4 3 0 4 3 2 E - 04 0.0 - 0 . 0 0 . 8 9 0 5 2 1 0 6 - 0 4 0.0 0.6494140F. - 0 4 0.0 0 . 8 4 9 2 R 8 0 E -04 0.0 0.0 0 . 8 1 5 6 5 5 5 E - 0 * 0 . 1 3 9 3 8 1 4 E - 0 3 0 . 1 1 6 7 3 B 5 F -03 0.0 0.0 0 . 1 2 8 6 0 6 0 6 -04 0 . 1 2 5 4 7 9 2 E - 0 3 0 . 1 S 5 6 7 7 1 F -03 0 .376 3026E -04 - 0 . 0 - 0 . 0 0.0 0.0 0 . 4 5 9 5 8 5 0 6 - 04 0 . 4 2 6 1 Z 5 6 E - 04 0.0 -0.0 0 . 1 0 3 2 8 4 3 6 - 0 3 - 0 . 0 0 . 4 1 6 7 4 9 8 6 -04 0.0 0 . 1 3 9 9 7 9 2 6 -04 - 0 . 0 - 0 . 0 0 . 2 5 1 8 1 5 5 E -04 0 . 1 7 7 7 2 0 4 E - 0 4 0 . 5 5 7 0 7 7 8 E -05 o. Km.* zee - O J 0 . 1 0 0 1 5 9 5 6 - 0 3 0 . 9 B 0 1 9 3 7 E - -05 - 0 . 0 0 . 3 6 4 1 0 4 2 F -04 0 . 8 1 9 5 2 6 9 F -04 0.0 0 . 6 5 7 6 7 5 4 E -04 0 . 5 3 0 1 9 0 4 E - 0 4 0 . 2 I 4 3 6 1 6 E - 0 3 0.0 0.0 - 0 . 0 - 0 . 0 0 . 5 7 2 8 4 3 7 E - 0 4 _ 0.0 - 0 . 0 0 . 1 3 7 8 9 8 4 6 - 0 3 0 . 6 5 9 6 4 1 2 E 0 4 0 . 3 4 4 0 7 9 5 E - 0 4 0.0 - 0 . 0 0.0 - 0 . 0 0 . 3 2 3 2 6 0 9 E -04 0.0 0.0 0 . 1 5 2 0 1 3 7 E - 04 0 . 4 5 5 3 7 1 8 6 -04 0 . 8 2 B 0 0 6 2 E -04 0.0 0.0 0 . 5 8 2 8 2 7 9 E -04 0.0 0 . 1 8 2 * 2 9 0 6 0 3 0 . 2 5 2 3 8 3 1 6 - 0 3 0 . 2 1 2 5 9 2 8 E -03 - 0 . 0 0.0 0.0 -0.0 0.1 1 9 5 2 4 4 6 - 0 3 0 . 1 1 0 9 2 3 7 E - 0 3 0 . 4 3 0 0 1 9 9 E - 04 0.0 0 . 5 3 0 8 8 8 1 E -04 0 . 1 2 3 3 3 3 1 6 - 03 0 . 1 2 1 3 8 7 0 E -03 0 . 3 3 3 5 6 6 3 E - 0 5 0 . I 0 7 1 3 3 5 F - 0 3 0 . 6 7 2 9 6 4 4 F 04 0 . 1 4 3 4 2 0 7 E - 0 4 0.0 0 . 8 9 6 4 6 8 4 E -04 0.0 0 . 3 8 2 7 0 7 7 E -04 0.O95B521E -04 0.0 C . 1 2 9 0 244E- 0 3 0 . 9 2 3 6 6 2 7 E - 04 0 . 1 4 B 6 9 6 0 E -03 0.1 1 1 4 1 9 6 E -05 -0.0 0 . 6 5 0 0 9 5 8 6 -C4 0 . 1 8 4 J 7 1 0 E -O J 0 . 8 9 8 1 1 3 1 6 - 0 4 0 . 1 1 0 7 0 7 9 E - 04 0 . 6 8 2 5 4 7 4 6 - 05 - 0 . 0 0 . 6 4 6 1 7 1 7 F -04 0 . 1 8 6 5 9 6 6 6 - 0 3 0 . 9 3 1 B 2 0 5 F -04 - 0 . 0 - 0 . 0 0 . 3 4 6 0 4 7 9 E - 04 0 . 1 6 3 4 4 6 5 6 - 0 3 0. 1 0 3 B 6 4 6 E -03 0 . 1 7 9 7 5 0 9 E -03 0 . 1 1 7 0 T 2 2 E - 0 3 0 . 9 0 9 4 6 7 9 E -04 0 . 5 3 7 4 5 1 7 E -04 0. 1 5 1 9 4 9 1 E - 0 3 0 . 7 4 9 3669E- 04 0 . 2 3 5 5 3 1 3 6 - 04 0 . 8 C 1 6 7 3 0 E -04 0 . 1 1 9 1 3 9 1 ? -03 0 . 4 9 1 i e 3 S E - 0 4 0 , 1 7 7 7 R 4 i l f -03 0 . 2 5 9 9 5 4 0 F -03 0 . 3 1 4 B 2 9 6 F - 0 3 0 . 3 1 9 9 4 7 7 6 - 0 3 0 . 2 B 6 9 5 2 I E - 0 3 0. 1S844C0E -03 0.0 0.0 0 . 4 5 6 6 7 7 4 E -04 0 . 3 6 4 2 3 7 6 E -04 0 . 9 9 J 0 0 I 2 6 - 04 0 . 1 2 5 I 9 0 1 F - 0 3 0. 1 0 4 6 6 7 6 E - 0 3 0 . 3 1 4 7 8 4 0 E -04 0.0 0 . 5 6 6 9 8 5 8 E - 04 0 . 1 4 5 5 4 7 7 E -03 - 0 . 0 0.0 0 . 2 1 2 2 6 9 3 6 - 0 3 0 . 2 3 0 1 8 5 0 E - 0 3 0 . 3 4 8 2 6 B 5 E -03 0. I S 2 9 0 1 2 E -03 0 . 2 7 2 6 Z 9 8 E - 0 3 0 . 8 9 6 9 9 6 R F -04 0 . 2 0 7 4 9 4 6 6 -Ui 0 . 3 6 8 4 2 3 1 6 - 0 3 C . 3 9 8 9 1 6 2 6 - 0 3 0 . 2 5 9 6 2 5 3 E - 03 0.0 C. 1 6 6 0 0 B 2 F -03 0 . 2 3 3 5 5 9 6 E - 0 3 0 . 2 7 1 2 2 4 4 6 -03 0 . J O B 7 J 0 6 E -0 3 0 . 3 8 H 0 2 3 6 - 0 3 0 . 2 8 3 7 7 1 2 E - 0 3 0 . 1 1 4 4 6 7 2 6 - 0 3 0 . 1 7 6 9 9 8 1 E -03 0 . 2 1 4 6 6 0 2 E -03 0 . 1 9 7 7 7 0 9 E - 0 3 0 . 2 4 6 3 0 346 -03 0. 1 B 6 6 9 4 5 E -03 0. 1 1 2 0 4 5 4 E - 0 3 0 . 2 8 8 6 2 5 5 E - 03 0 . 2 0 3 8 5 3 7 E - 0 3 0 . 2 3 9 1 6 Z 3 E -03 0 . 5 7 4 6 9 5 6 E -03 0 . 5 0 B 0 0 6 7 E - 03 0 . 3 8 4 3 3 7 4 E -03 0 . 3 J 9 J 7 2 5 E -03 0 . 1 5 1 0 0 3 9 E - 0 3 0 . 4 6 3 2 2 T 3 E - 03 0 . 5 2 5 5 0 5 0 E - 0 3 0 . 7 8 8 0 5 7 5 E -05 0 . I 0 A M 4 4 E -03 0 . 1 4 4 6 3 7 5 E - 0 3 0 . 2 8 0 2 2 B 4 E -03 0 . 3 7 U 1 3 B 1 E -03 0 . 4 7 0 2 0 6 I E - 0 3 0 . 3 6 1 1 9 6 0 6 - 03 0 . 4 6 2 0 5 9 6 E - 0 3 0 . 5 3 1 6 4 8 5 E -03 0 . 4 9 5 1 B 2 1 E -03 0 . 4 0 7 6 9 7 2 6 - 0 3 0 . 5 3 3 6 1 7 1 F -03 0 . 4 9 5 0 1 2 2 E -03 0 . 4 9 2 3 3 6 7 E - 0 3 0 . 3 6 0 2 5 2 1 E - 0 3 0 . 3 3 2 7 8 4 6 E - 0 3 0 . 3 9 8 9 3 B 1 E -03 0 . 3 4 6 1 5 0 0 E -03 0 . 2 6 7 6 5 6 5 6 - 0 3 „ 0 . 4 7 2 8 5 7 4 6 -03 0 . 6 2 6 8 6 4 4 E -03 0 . 7 2 1 3 4 7 5 E - 0 3 0 . 6 5 6 2 7 B 3 6 - 0 3 0 . 6 9 7 2 0 9 0 E - 0 3 0 . 6 2 3 5 1 7 7 F -03 0 . 5 9 3 6 2 T 6 E -03 0 . 4 1 7 4 6 2 8 E - 03 0 . 6 4 4 5 0 1 IE -03 0. 7 2 4 5 5 8 3 6 -U3 0 . 6 4 8 2 3 6 6 F - 0 3 0 . 6 5 2 7 3 7 4 E - 0 3 0 . 8 0 7 6 4 9 2 6 - 03 0 . 7 2 8 9 1 6 2 E -03 0 . 6 9 9 0 4 7 5 E -03 0 . B 6 5 2 2 0 8 E - 0 3 0 . 1 0 9 B T 4 2 E -02 O.BJT J94TE -03 0 . 9 ^ ^ 4 4 7 3 F - 0 3 0.'>99'>54tE- o-* 0 . 9 3 5 2 9 3 5 E - 0 3 0 . 9 0 9 7 5 0 6 E -03 0.1 163559E -02 0 . 1 1 6 2 7 6 4 6 - 02 0.1 1461 I5E -0? 0. 1 2 4 7 1 2 1 E -02 0.I 13543HE- 02 0 . 1 6 9 2 1 4 4 E - 07 0 . 1 4 9 8 4 4 B E - 02 0 . 1 4 5 8 2 7 2 E -02 0 . 1 5 2 2 8 4 7 E - 0 ? 0 . 1 5 3 8 6 1 1 E - 0 ? C. 1 7 6 1 7 4 * 6 -0? 0 . 1 9 f O G 3 J t -02 0.2 1 8 6 4 2 1 E - 02 0 . 2 1 6 1 7 1 8 F - 02 . 0 . 2 0 8 8 0 7 ^ E - 02 0 . 2 2 0 1 3 3 8 E -02 0 . 2 3 9 8 6 5 2 F -02 0 . 2 6 0 6 6 7 9 6 - 02 0 . 2 6 1 7 5 B C F -c? 0.2 7G7664E -02 0 . 2 8 3 4 6 6 0 E - 02 0 . 3 0 4 7 1 3 7 F - 02 0 . 3 3 1 B 1 4 0 F - 02 0 . 3 7 C 5 1 5 0 E -02 0 . 3 B 0 1 0 9 5 F -02 0 . 4 1 6 3 3 2 1 E - 02 0 . 4 5 4 5 4 3 9 F -02 0.475(19476 -02 0.5l6«il25E- 02 0 . 5 5 0 4 9 I 4 F - 0 ? 0 . 5 8 9 1 3 4 2 E - 02 0 . 6 1 5 5 9 8 3 E -02 0 . 6 4 9 2 3 6 9 E -02 0 . 7 0 C 2 9 7 7 E - 02 0.7458ft("3F -0? 0.807 J 7 5 U -02 0. B66R263'=-0 2 0 . 9 1 7 4 0 9 4 E - 0 7 0 . 9 9 9 6 7 9 8 F - 07 0 . 1 0 5 0 7 8 & F -01 0 . 1 1 0 4 4 9 6 E -01 0. 1 1767t\5E- 01 0.1 i s o i ^ T r -01 0. 1 U 9 8 2 6 F - C t 0 . 1 2 1 2 9 C 3 E - 01 C . U 8 7 2 5 4 E - 01 0 . 1 1 6 8 3 0 6 6 - 01 0 . 1 1 7 3 1 P 4 E -01 0 . 1 0 9 9 5 5 7 6 -Ot 0. 1 0 6 7 2 9 9 F - 01 0. 1035 2t'(.F -01 0.9US-70Qlb -02 0 . H B 2 5 3 8 0 6 - 07 0 . B 3 9 1 7 0 4 E - 02 0 . B 1 8 1 B 7 7 F - 02 0 . 7 0 9 1 U 2 E -02 0 . 7 2 0 3 0 2 C E -02 0 . 5 9 4 5 7 7 0 6 - 02 - 0 . 5 7 4 3 4 7 7 F -0? 0 . 5 5 3 J 3 3 9 E -02 G . S 1 6 9 7 K F - 0 2 0 . 4 6 7 3 9 9 5 F - 02 0 . 4 2 0 1 7 7 0 6 - 02 0 . 4 0 0 6 4 5 7 E -02 0. 36rSB873F -02 0 . 3 5 8 2 1 9 1 E - 02 0 . 3 3 7 0 1 1 2 F -.07 0. 3 2 6 4 0 3 7 E -02 C . 3 0 * 2 4 5 7 F - 0 ? 0 . 2 9 6 0 3 B 9 F - 02 0 . 2 6 3 6 8 0 7 F - 02 0 . 2 5 9 H 9 4 3 F -02 0 . 2 6 1 6 9 4 0 F -02 0 . 7 2 T T 2 0 1 E - 02 O . ^ l S C i O ^ F -0? 0. 1 9 5 9 9 3 J L -02 0. 177<S422C_ 02 0 . 1 R 9 ! 8 1 3 F - 07 0 . 1 8 3 6 5 8 I E - 02 0 . 1 7 6 9 5 8 T E -02 0. 1 5 2 B 2 1 8 F -02 0 . 1 4 T R 1 7 4 F - 0? O.t425<109f -02 0. I 4 1 & 5 0 1 E -02 n.l22ft«0t>F- 0 2 6.t?03t6R£- 0 2 0 . 1 3 7 2 6 7 8 E - 02 0 . 1 2 B S 2 5 4 F -02 0.1267.669F -02 0 . U 3 9 3 0 9 E - 02 0.102< i R?lE -02 0 . 1 9 l t . f l R 3 F -03 0 . 1 0 0 0 6 6 5 F - 02 0 . 1 0 0 3 5 B 2 F - 02 0 . 7 4 6 9 B 0 3 E - 0 3 0 . 1 9 7 7 9 8 7 F -03 0 . 8 0 5 2 2 1 5 E -03 0.796H5Q2E- 03 0. 74t>0043E -03 0. 7 241U9JC: -0 3 0 . 1 1 4 1 1 5 0 F - 02 0 . 9 0 4 5 4 0 1 F - 0 3 0 . 4 9 2 7 7 0 2 F - 0 3 o.57338C9E -03 0 . B 3 1 0 5 2 7 E -03 0 . 7 7 0 7 1 3 3 E - 03 < | . * 1 3 6 t t 5 E -03 0 . 6 S 4 4 6 W E -03 0 . 5 7 1 7 C 1 7 E - 0 3 C.83169536-03 0 . 6 1 0 2 9 I 3 F - 0 3 0 . 5 3 5 0 7 1 2 6 -03 0.450H9»>OF -03 0 . 5 7 1 T 5 8 3 F - 01 0 . H 4 l 7 7 h 4 C -0 3 0 . 1*1 7 8 8 9 5 E -03 0 . 6 6 5 4 2 S 3 E - 0 3 C . 5 7 4 l 4 7 f r E - 0* 0 . 5 3 3 9 6 5 2 F - 0? 0 . 5 5 9 2 H 2 0 F -03 O i i J O 952.5 F -03 _ . - 0 f i 4 J ? i l . 1 F - 03 0,.49018S If -01 C. i^4197«(- 0. 1545C 73F- 0 1 0.26?«;2ft7Fr 03 0 . 3 4 6 S 4 8 7 F - 0 3 0 . 3 5 5 1 6 B 0 F - 03 6.50704136- 0 3 0 . 5 0 0 9 5 7 9 6 - 03 0 . 3 4 4 4 8 5 7 6 -03 0 . 2 1 3 9 0 1 5 E - Q3 0 . 2 6 9 6 6 4 9 6 - 0 3 0 . 3 6 8 1 3 5 9 E - 0 3 0 . 3 5 2 0 5 6 6 6 - 03 0 . 3 2 3 6 3 3 0 E - 0 3 0 . 3 1 7 4 2 9 9 F - 03 0 . 3 5 7 9 1 0 1 6 - 03 0 . 9 1 5 2 2 2 3 E -04 0.0 0 . 5 6 7 3 6 9 7 E - 0 4 0 . 1 5 5 9 1 6 7 E - 0 3 0 . 1 8 6 9 9 7 9 6 - 0 3 0. 1 7 7 5 6 5 0 6 - 03 0 . 1 1 6 3 9 5 1 E - 0 3 0 . 1 2 2 8 3 3 5 6 - 03 0 . 2 6 I 7 5 1 0 E -03 0 . 3 5 5 6 3 3 2 6 - 03 0 . 3 0 8 0 8 1 0 E - 0 1 0 . 2 1 1 1 4 2 9 6 - 0 3 0 . 1 1 2 3 4 1 9 6 - 0 3 0 . T 2 B 7 5 5 3 F - 04 0,0 0.0 0 . 2 7 0 9 4 9 2 E -03 0 . 2 6 6 2 9 0 0 E - 0 3 0.0 0 . 6 0 8 1 8 6 2 6 - 0 4 0 . 3 1 2 8 6 5 5 E - 0 3 0 . 6 3 0 6 1 9 5 6 - 04 0.10793BOE- 03 0.0 0.0 0 . U 4 7 9 5 1 E - 0 3 0.0 0.0 0.0 QrO.. . _ 0.0 0.0 0.0 0.0 0 . 6 0 5 U 1 7 E - 0 4 0 . 1 5 7 1 4 6 9 E - 0 3 0 . 5 7 7 2 6 6 7 E - 04 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 . 6 5 9 9 8 3 2 E - 05 0.0 0.0 0.0 0.0 0.0 0.0 0.0 - 0 . 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 o.o 0.0 0.0 0.0 - 0 . 0 - 0 . 0 0.0 0.0 - 0 . 0 0.0 0.0 0.0 0.0 - 0 . 0 - 0 . 0 0.0 -0.0 - 0 . 0 -O.D - 0 . 0 0. I 3 1 B 8 5 5 E - 0 3 0 . 1 7 4 6 5 1 2 6 - 0 3 - 0 . 0 - 0 . 0 0.0 0.0 0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0.0 0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 , 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -O.D - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 , 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 -K).0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 -o.o -0 .0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 , 0 0 . 2 3 2 8 3 0 6 6 - 0 9 Table XVI. Computer Output. F i n a l Corrected X-Ray Intensities for (400) Reflection from Annealed Nickel Powder Standard. 213 CORRESPONDING VALUES OF S I N E THETA _ - - p . q i 4 6 5 7 p . 0 1 4 6 1 - 0 . 0 1 4 5 6 - 0 . 0 1 4 5 2 -1 .01398-. 0 1 3 3 1 .0 1 2 6 5 -.01198-. 0 1 1 3 1 -. 0 1 0 6 5 -.00998-1.00931-1.00865-1.00798-.00732-1.00665-0.01394-0.01327-0 . 0 1 2 6 1 -•0.01194-0 . 0 1 1 2 7 -0 . 0 1 0 6 1 -1.00598-.00532-1.00465-. 0 0 3 9 8 -1.00332-.002 6 5 -0 . 0 0 9 9 4 -0 . 0 0 9 2 7 -0 . 0 0 8 6 1 -0.0O794-0.00727-0 . 0 0 6 6 1 -0 . 0 1 3 9 0 -0 . 0 1 3 2 3 -0 . 0 1 2 5 6 -0 . 0 1 1 9 0 -0 . 0 1 1 2 3 -0.01056-0 . 0 0 5 9 4 -O. 0 0 5 2 7 -•0.00461-0 . 0 0 3 9 4 -0 . 0 0 3 2 7 -0 . 0 0 2 6 1 -0 . 0 0 9 9 0 0 . 0 0 9 2 3 0.00856-0 . 0 0 7 9 0 0.00723-0.00657-0 . 0 0 5 9 0 -0 . 0 0 5 2 3 -0 . 0 0 4 5 7 r 0 . 0 0 3 9 0 -0 . 0 0 3 2 1 -0 . 0 0 2 5 7 -0.01386-0.01319-0.01252-0.01166-0.01119-0.01052-0.00986-0.00919-0.00852-•0.00766-0.00719-•0.00652-0.00586-0.00519-0.00452-0.00386-0.00319-0.00252-.00196-. 0 0 1 3 2 -. 0 0 0 6 5 -.00C02 . 0 0 0 6 8 . 0 0 1 3 5 . 0 0 2 0 2 . 0 0 2 6 8 . 0 0 3 3 5 . 0 0 4 0 2 . 0 0 4 6 8 . 0 0 5 3 5 •0.00194-0 . 0 0 1 2 7 -•0.00061-0 . 0 0 0 0 6 0 . 0 0 0 7 3 0 . 0 0 1 3 9 0 . 0 0 2 0 6 0 . 0 0 2 7 3 0 . 0 0 3 3 9 0 . 0 C 4 0 6 0 . 0 0 4 7 3 0 . 0 0 5 39 0.0019C-0 . 0 0 1 2 3 -0 . 0 0 0 5 7-0 . 0 0 0 1 0 0 . 0 0 0 7 7 0 . 0 0 1 4 3 . 0 0 6 0 2 . 0 0 6 6 8 . 0 0 7 3 5 . 0 0 8 0 2 . 0 0 8 6 8 '.00935 0. 0 0 6 0 6 0 . 0 0 6 7 3 C . 0 0 7 3 9 0 . 0 0 8 0 6 0 . 0 0 8 7 3 0 . 0 0 9 39 (.01002 . 0 1 0 6 8 . 0 1 1 3 5 . 0 1 2 0 2 . 0 1 2 6 8 . 0 1 3 3 5 . 0 1 4 0 2 . 0 1 4 6 8 0 . 0 1 0 0 6 0 . 0 1 0 7 3 0 . 0 1 1 3 9 0 . 0 1 2 0 6 0 . 0 1 2 7 3 0 . 0 1 3 39 0 . 0 1 4 0 6 0 . 0 1 4 7 3 0 . 0 0 2 1 0 0 . 0 0 2 7 7 0 . 0 0 3 4 3 0 . 0 0 4 1 0 0 . 0 0 4 7 7 0 . 0 0 5 4 3 0 . 0 0 6 1 0 " 0 . 0 0 6 7 7 0 . 0 0 7 4 3 0 . 0 0 8 1 0 0 . 0 0 8 * 7 0.0094_3_ o . o i b i o 0 . 0 1 0 7 7 0 . 0 1 1 4 3 0 . 0 1 2 1 0 0 . 0 1 2 7 7 0 . 0 1 3 4 3 0 . 0 1 4 1 0 0 . 0 1 4 7 7 0.00186-0.00119-0.00052-0 . 0 0 0 1 4 0.O00B1 0 . 0 0 1 4 8 0 . 0 0 2 1 4 0 . 0 0 2 B 1 0 . 0 0 3 4 8 0 . 0 0 4 1 4 0 . 0 0 4 8 1 0 . 0 0 5 4 8 0 . 0 0 6 1 4 0 . 0 0 6 8 1 0 . 0 0 7 4 8 0 . 0 0 8 1 4 0 . 0 0 8 8 1 0 . 0 0 9 4 8 0 . 0 1 0 1 4 0 . 0 1 0 8 1 0 . 0 1 1 4 B 0 . 0 1 2 1 4 0 . 0 1 2 B 1 0^.01348 0.61414 0 . 0 1 4 8 1 0.01448-0.0 1381-0 .01115-0.01248-0 . 0 1 1 8 1 -0 . 0 1 1 1 5 -0.01048-0 . 0 0 9 8 1 -0 . 0 0 9 1 5 -0.00848-0.00782-0.00715-O.Q0648-0.00582-0.00515-0.00448-0.00382-0.00315-0.00246-0 . 0 0 1 8 2 -0.00115-0.00046-0 . 0 0 0 1 8 0 . 0 0 0 8 5 0 . 0 0 1 5 2 0 . 0 0 2 1 8 0 . 0 0 2 8 5 0 . 0 0 3 5 2 0 . 0 0 4 1 B 0 . 0 0 4 8 5 0 . 0 0 5 5 2 0 . 0 0 6 1 8 0 . 0 0 6 6 5 0 . 0 0 7 5 2 0 . 0 0 8 1 8 0 . 0 0 8 8 5 0 . 0 0 9 5 2 0 . 0 1 0 1 8 0 . 0 1 0 6 5 0 . 0 1 1 5 2 0 . 0 1 2 1 8 0 . 0 1 2 6 5 0 . 0 1 3 5 2 0 . 0 1 4 1 6 0 . 0 1 4 8 5 0.01444-0.01377-•0.01311-•0.01244-0.01177-0 . 0 1 1 1 1 -0.01044--0.0097 7-•0. 0 0 9 U -•0.00844-•0.00777-0 . 0 0 7 1 1 --0^00644-: 0 . 0 0 5 7 7 : •0.00511--0.00444-•0.00377-•0.00311-•0.00244-•0.00177-•0.00 I 11-•0.00044-0 . 0 0 0 2 3 0 . 0 0 0 8 9 0^00 156 0.002 23' 0 . 0 0 2 8 9 0 . 0 0 3 5 6 0 . 0 0 4 2 3 0 . 0 0 4 8 9 0 . 0 0 5 5 6 0 . 0 0 6 2 3 0 . 0 0 6 8 9 0 . 0 0 7 5 6 0 . 0 0 8 2 3 0 . 0 0 8 6 9 0 . 0 0 9 5 6 0 . 0 1 0 2 3 0 . 0 1 0 8 9 0 . 0 1 1 5 6 0 . 0 1 2 2 3 0 . 0 1 2 B 9 0 . 0 1 3 5 6 0 . 0 1 4 2 1 0 . 0 1 4 8 9 0 . 0 1 4 4 0 - 0 . 0 . 0 1 3 7 3 - o i • 0 . 0 1 3 0 6 - 0 . 0 . 0 1 2 4 0 - 0 . 0 . 0 1 1 7 3 - 0 . - 0 . 0 1 1 0 6 - 0 . Q.01C40-0. • 0 . 0 0 9 7 3 - 0 . 0 . 0 0 9 0 6 - 0 . 0 . 0 0 8 4 0 - 0 . • 0 . 0 0 7 7 3 - 0 . 0 . 0 C 7 0 7 - 0 . 0 . 0 0 6 4 0 - 0 . 0 1 4 3 6 -0 1 3 6 9 -0 1 3 0 2 -0 1 2 3 6 -0 1 1 6 9 -0 1 1 0 2 -01Q_36-00 969-0 0 9 0 2 -008 36-0 0 7 6 9 -0 0 7 0 2 -0 0 6 36-0 . 0 1 4 3 1 - 0 , 0 . 0 1 3 6 5 - 0 , 0 . 0 1 2 9 8 - 0 , •0.01231-0, G . 0 1 1 6 5 - 0 , 0.01-096-0, 0 . 0 1 0 3 1 r 0 , 0 . 0 0 9 6 5 - 0 , 0 . 0 0 8 9 6 - 0 , 0 . 0 C 8 3 1 - 0 . 0 . 0 0 7 6 5 - 0 . 0 . 0 0 6 9 6 - 0 . 0 . 0 0 6 3 2 - 0 . 0 . 0 0 5 7 3 - 0 , 0 . 0 0 5 0 7 - 0 . •0.00440-0. 0 . 0 0 3 7 3 - 0 , •0.001C7-0, •0.00240-0, 0 . 0 0 1 7 3 - 0 , 0 . 0 0 1 0 7 - 0 , 0 . 0 0 0 4 0 - 0 , 0 . 0 0 0 2 7 0', 0 . 0 0 0 9 3 0. 0 . 0 0 1 6 0 _0. "6.002 2 7 0, 0 . 0 0 2 9 3 0. 0 . 0 0 3 6 0 0, 0 . 0 0 4 2 7 0, 0. 0 0 4 9 3 ^ 0 . 0 . 0 0 5 6 0 _ 0 , 0 . 0 0 6 2 7 6. 0. 0 0 6 9 3 0. 0 . 0 0 7 6 0 0, 0 . 0 0 6 2 7 0. 0 . 0 0 8 9 3 0. 0 . 0 0 9 6 0 0. 0. 0 1 0 2 7 0. 0. 0 1 0 9 3 0, 0 . 0 1 1 6 0 0, 0 . 0 1 2 2 7 0. 0 . 0 1 2 9 3 0. 0 . 0 1 3 6 0 0. 0 . 0 1 4 2 7 0, 0 . 0 1 4 9 3 00569-,00502-.00436-00369-00102-.00216-,00169 : .00102-0 0 0 3 6 -,00031 0 0 0 9 8 0 0 1 6 4 002 31 0 0 2 9 8 0 0 1 6 4 004 31 0 0 4 9 6 0 0 5 6 4 0 0 6 3 1 0 0 6 9 6 0 0 7 6 4 0 0 8 3 1 0 0 6 9 6 0 0 9 6 4 0 1 0 3 1 0 1 0 9 8 0 1 1 6 4 0 1 2 3 1 0 1 2 9 8 0 1 3 6 4 0 1 4 3 1 •0.00565-0 0 . 0 0 4 9 8 - 0 0 . 0 0 4 3 2 - 0 •0.00365-0, •0.00296-0 •0.00232-0, 0 . 0 0 1 6 5 - 0 0.00O9R-O, 0 . 0 0 0 3 2 - 0 0 . 0 0 0 3 5 0, 0 . 0 0 1 0 2 0. 0. 0 0 1 6 6 0. 0 . 0 0 2 3 5 0, 0.00 302 0, 0 . 0 0 3 6 8 0 0.004 35 0. 0 . 0 0 5 0 2 0, 0 . 0 0 5 6 8 0, 0 . 0 0 6 3 5 * 0 , 0 . 0 0 7 0 2 0, 0. 0 0 7 6 8 0, 0 . 0 0 8 3 5 0, 0. 0 0 9 0 2 0, 0^0O9&8J>, 0 . 0 1 0 3 5 0, 0. 0 1 1 0 2 0. 0 . 0 1 1 6 8 0. 0 . 0 1 2 3 5 0, 0 . 0 1 3 0 2 0, 0. 0 1 3 6 8 0. 0.014 35 "0, 01427-01361-01294-0 1 2 2 7 -0 1 1 6 1 -0 1 0 9 4 -0 1 0 2 7 -0 0 9 6 1 -008 94-0 0 6 2 7-0 0 7 6 1 -006 94-0 0 6 2 7 -00*561-0 0 4 9 4 -0 0 4 2 7 -00 361-0 0 2 9 4 -0 0 2 2 7 -0 0 1 6 1 -0 0 0 9 4 -0 0 0 2 7 -0 0 0 3 9 0 0 1 0 6 0 0 1 7 3 0 0 2 3 9 0 0 3 0 6 0 0 3 7 3 0 0 4 3 9 0 0 5 0 6 0 0 5 7 3 006 39 0 0 7 0 6 0 0 7 7 3 008 39 0 0 9 0 6 0 0 9 7 3 0 1 0 3 9 0 1 1 0 6 0 1 1 7 3 0 1 2 3 9 0 1 3 0 6 0 1 1 7 3 014.39 •C.01423-0 . 0 1 3 5 6 -0.01290--0.01223-•0.0 1156-•0.01090--0.0102 3-•0.009'56-•0.00890--0.00823-•0.00757-•0.00690-O^Op&^i -•"6.00557-•0.00490-0 . 0 0 4 2 3 -0 . 0 0 3 5 7 -•6.00290-0 . 0 0 2 2 3 -0 . 0 0 " l 5 7 * 0 . C 0 0 9 0 -0 . 0 0 0 2 3 -0 . 0 0 0 4 3 0 . 0 0 1 1 0 0 . 0 0 1 7 7 0 . 0 0 2 4 3 0 . 0 0 3 1 0 0 . 0 0 3 7 7 0 . 0 0 4 4 3 0 . 0 0 5 1 0 0 . 0 0 5 7 7 0 . 0 0 6 4 3 " 0 . 0 0 7 1 0 0 . 0 0 7 7 7 0 . 0 0 8 4 3 0 . 0 0 9 1 0 °.0Q9_77_ 0 . 0 1 0 4 3 0 . 0 1 I 1 0 0 . 0 1 1 7 7 0 . 0 1 2 4 3 0 . 0 1 3 1 0 0.01 J7_7_ 6.01443 0.01419j; 0 . 0 1 3 5 2 -0 . 0 1 2 8 6 -0 . 0 1 2 1 9 -0 . 0 1 1 5 2 -0 . 0 1 0 8 6 -0 . 0 1 0 1 9 -0 . 0 0 9 5 2 -0 . 0 0 8 8 6 -0 . 0 0 8 1 9 -0.00 752-0 .0C686-O.OOMy-0.01415-0.01348-0.01281-0.01215-0.01148-0 . 0 1 0 6 1 -0.01015-0.00948-0 . 0 0 8 8 1 -0.00615-0.00748-0.00682-0 . 0 0 6 1 5 -0 . 0 1 4 1 1 - 0 . 0 1 4 0 6 - 0 . 0 1 4 0 2 0 . 0 1 3 4 4 -0 . 0 1 2 7 7 -0 . 0 1 2 1 1-0 . 0 1 1 4 4 -0 . 0 1 0 7 7 -0 . 0 1 0 1 1-0 . 0 1 3 4 0 0 . 0 1 2 7 3 - 0 0 . 0 1 2 0 6 - 0 0 . 0 1 1 4 0 0 . 0 1 0 7 3 0 . C I 0 0 6 0 1 3 1 6 . 0 1 2 6 9 . 0 1 2 0 2 . 0 1 1 3 6 . 0 1 0 6 9 . 0 1 0 0 2 0.00944-0.00B77-0 . 0 0 6 1 1 -0 . 0 0 7 4 4 -0.006 7 7-0 . 0 0 6 1 1 -0 . 0 0 9 4 0 - 0 , 0 . 0 0 8 7 3 - 0 . •0.00806-0, 0 . 0 0 7 4 0 - 0 , 0 . 0 0 6 7 3 - 0 . 0 . 0 0 6 0 7 - 0 , 0 0 9 3 6 0 0 8 6 9 0 0 8 0 2 0 0 7 36 0 0 6 6 9 0 0 6 0 2 •0.00552-0 . 0 0 4 8 6 -•0.00419-0 . 0 0 3 5 2 -•J. 00286-•0.00219-0.*OC152-W . 0 0 0 8 6 -•0.00019-u . 00048 0 . 0 0 1 1 4 0 . 0 0 1 6 1 0".0G248 0 . 0 0 3 1 4 0 . O 0 3 b l 0 . 0 0 4 4 8 0 . 0 0 5 1 4 0 . 0 0 5 8 1 6 .00648 0 . 0 0 7 1 4 0 . 0 0 7 B 1 0 . 0 0 8 4 8 0 . 0 0 9 1 4 0 . 0 0 9 6 1 -0.0054B--0.00482-0.00415-0.00348-0.00262-0.002^5-•0. 00 148-0.00082-•0.00015-0 . 0 0 0 5 2 0 . 0 0 1 1 8 0.0018_5 6.00252 0.0 0 3 1 8 0 . 0 0 3 6 5 0.00452 0 . 0 0 5 1 6 0 . 0 0 5 8 5 6.00652" 0.0 0 7 1 8 0 . 0 0 7 8 5 0 . 0 0 8 5 2 0 . 0 0 9 1 6 0 . 0 0 9 6 5 0.00544-0 . 0 0 4 7 7 -0 . 0 0 4 1 1 -0 . 0 0 3 4 4 -0 . 0 0 2 7 7 -•0.00211-0 . 0 0 5 4 0 - 0 , 0 . 0 0 4 7 3 - 0 . 0.00407-0.00340-0.00273-0.00207-0.00144-0.00077-0 . 0 0 0 1 1-0 . 0 0 0 5 6 0 . 0 0 1 2 3 0 . 0 0 I R 9 • 0 . 0 0 1 4 0 - 0 . • 0 . 0 0 0 7 3 - 0 . • 0 . 0 0 0 0 7 - 0 . 0 . 0 0 0 6 0 0. 0 . 0 0 1 2 7 0. 0 . 0 0 1 9 3 0. 0 0 5 36 0 0 4 6 9 0 0 4 0 2 0 0 3 3 6 0 0 2 6 9 0C2O2 0 0 1 3 6 0 0 0 6 9 0 0 0 0 2 0 0 0 6 4 001 31 0 0 1 9 8 0 . 0 0 2 5 6 0 . 0 0 3 2 3 0 . 0 0 3 8 9 0 . 0 0 4 5 6 0 . 0 0 5 ? 3 0 . 0 0 5 B 9 0 . 0 0 2 6 0 0 . 0 0 3 2 7 0 . 0 0 3 9 3 0 . 0 0 4 6 0 i 0.005 2 7 • 0 . 0 0 5 9 3 . 0 0 2 6 4 . 0 0 3 3 1 . 0 0 3 9 8 . 0 0 4 6 4 . 0 0 5 3 1 . 0 0 5 9 8 0 . 0 1 0 4 8 0 . 0 1 1 1 4 0 . 0 1 1 6 1 0 . 0 1 2 4 8 0 . 0 1 3 1 4 0 ^ 0 1 3 6 1 0 . 0 1 4 4 8 0 . 0 1 0 5 2 0.01116 0 . 0 1 1 6 5 0 . 0 1 2 5 ? 0 . 0 1 3 1 8 0.01185 " 0 V6T 452" 0 . 0 0 6 5 6 0 . 0 0 7 2 1 0 . 0 0 7 8 9 0 . 0 0 8 5 6 0 . 0 0 9 2 3 0 . 0 0 9 6 9 0 . 0 0 6 6 0 0, 0 . 0 0 7 2 7 0, 0 . 0 0 7 9 3 0, 0. 0 0 8 6 0 0. 0.C0927 0. P . 0 0 9 9 3 0. 0 0 6 6 4 0 0 7 3 1 0 0 7 9 8 0 0 8 6 4 0 0 9 3 1 0 0 9 9 8 0 . 0 1 0 5 6 0 . 0 1 1 2 1 0 . 0 1 1 8 9 0 . 0 1 2 5 6 0 . 0 1 3 2 3 0.0X3_B_q  0 . 0 1 4 5 6 0 . 0 1 0 6 0 0. 0. 0 1 1 2 7 0. 0 . 0 1 1 9 3 0. 0. 0 1 2 6 0 0. 0. 0 1 3 2 7 0, 0 . 0 1 3 9 1 0. 0 1 0 6 4 0 1 1 3 1 0 1 1 9 8 0 1264 0 1 3 3 1 0 1 3 9 8 0 . 0 1 4 6 0 0 . 0 1 4 6 4 Table XVII. Computer Output. Sin 0 Values for (400) Reflection from Annealed Nickel Powder Standard. SINE THETA INTERVAL - 0 . 0 0 0 0 4 NUMBER OF S I N E THETA DATA POINTS • 711 A R T I F I C I A L L A T T I C E PARAMETER « 2 5 . 7 8 9 7 5 _ ANGSTROMS TWO THETA ZERO (CENTRE OF G R A V I T Y ) • 1 2 L 8 6 6 DEGREES L A T T I C E PARAMETER (CENTRE OF G R A V I T Y ! « 3.52*98 ANGSTROMS TWO THETA ZERO (PEAK H A X I ^ U M l - 1 2 1 . 9 2 8 OEGREES L A T T I C E PARAMETER ( P E A K MAXIMUM) - 3 ^ 5 2 3 ? ? .ANGSTROMS PEAK ASYMMETRY - - 0 . 0 6 2 DEGREES Table XVIII. Computer Output. Peak Parameters for (400) Reflection from Annealed Nickel Powder Standard. 2lk YD NI S H U * COLD 'ROLIFD 75 PERCENTREFLECT ION~(~ 2 0 0 ) SCAN B E G I N S AT' 4 4 . 0 0 0 1 E G R E F S 1*0 THETA • ANGULAR INCREMENT - 0.050 DEGREFS i<y*BE !L -P F D * T A POINTS - 541 ATOMIC S C A T T E R I N G FACTOR AT TWO THETA ( 1 ) = ' 1 9 . 1 9 ATOMIC S C A T T E R I N G FACTOR AT TWO THFTA 121 = 15.20 CONTROL - 3 O R I G I N A L I N T E N S I T Y V ALUES 2 4 7 . 3 3 0 2 4 5 . 2 8 0 2 4 7 . 2 4 0 2 4 7 . 4 8 0 2 4 6 . 6 3 0 2 4 4 . 8 9 0 2 4 2 . 5 3 0 2 4 0 . 2 1 0 2 4 0 . 7 1 0 2 4 0 . 3 6 0 2 3 9 . 8 0 0 2 3 B . 4 7 0 2 3 8 . 0 9 0 2 4 0 . 4 2 0 2 4 2 . 2 4 0 2 3 9 . 4 9 0 2 4 1 . 4 2 0 2 3 9 . 8 3 0 2 3 9 . 4 8 0 2 4 2 . 5 8 0 2 3 9 . 9 ? 0 2 3 7 . 0 2 0 2 3 8 . 4 1 0 2 4 0 . 4 0 0 2 3 7 . 8 9 0 2 3 6 . 6 1 0 2 3 6 . 0 0 0 2 3 5 . 5 5 0 2 3 5 . 1 0 0 2 3 4 . 6 5 0 2 3 4 . 2 0 0 2 3 3 . 7 5 0 2 3 3 . 3 0 C 2 3 2 . 8 5 0 2 3 2 . 4 0 0 2 3 1 . 9 5 0 2 3 1 . 5 0 0 2 3 1 . 0 5 0 2 3 0 . 6 0 0 2 3 0 . 1 5 0 2 2 9 . 7 0 0 2 2 9 . 2 5 0 2 2 8 . 8 0 0 2 2 8 . 3 5 0 2 2 7 . 9 0 0 2 2 7 . 4 5 0 2 2 7 . 0 0 0 2 2 6 . 5 5 0 2 2 6 . 1 0 0 2 2 5 . 6 5 0 2 2 5 . 2 0 0 2 2 4 . 7 5 0 _ 2 24 .J 0 0 _ 2 2 3 ._H50_2 2 3 . 4 0 0 2 2 2 . 9 5 0 2 2 2 . 5 0 0 2 2 2 . 0 50_ 7 2 1 . 6 0 0 221 .150 2 2 0 . 7 0 0 2 2 0 . 2 5 0 2 1 9 . 8 0 0 2 1 9 . 3 5 0 2 1 B . 9 0 0 2 1 8 . 4 5 0 2 1 8 . 0 0 0 2 1 6 . 2 4 0 2 1 7 . 3 6 0 2 1 4 . 7 2 0 2T3.710 2 1 5 . 6 2 0 2 1 3 . 1 2 0 2 1 3 . 0 9 0 2 1 3 . 5 0 0 2 1 3 . 0 3 0 2 1 3 . 6 7 0 2 1 2 . 5 3 0 2 1 0 . 9 9 0 2 1 1 . 7 7 0 2 0 8 . 8 2 0 2 0 9 . 6 4 0 2 0 8 . 7 7 0 2 0 6 . 7 7 0 2 0 7 . 9 6 0 2 0 6 . 2 2 0 2 0 6 . 4 0 0 2 0 5 . 8 1 0 2 0 1 . 3 4 0 2 0 2 . 0 9 0 . 2 0 2 . 1 5 0 1 9 7 . 8 0 0 1 9 9 . 6 2 0 1 9 7 . 2 4 0 1 9 7 . 0 3 0 1 9 2 . 5 0 0 1 9 0 . 3 8 0 1 9 0 . 6 8 0 1 8 9 . 3 1 0 1 8 7 . 7 9 0 1 8 6 . 6 9 0 1 9 7 . 0 2 0 1 8 2 . 9 0 0 I B ? . 4 7 0 1 7 6 . 1 6 0 1 7 8 . 3 7 0 1 7 5 . 9 7 0 1 7 2 . 9 4 0 1 6 9 . 5 5 0 1 6 9 . 8 1 0 1 6 7 . 0 5 0 1 6 2 . 5 3 0 1 6 2 . 5 3 0 1 5 7 . 9 1 0 1 5 4 . 8 9 0 1 4 8 . 1 6 0 1 3 9 . 0 2 0 1 2 8 . 5 4 0 1 1 2 . 3 6 0 9 6 . 0 6 0 8 4 . 1 3 0 7 6 . 0 4 0 7 2 . 3 1 0 6 7 . 7 9 0 6 6 . 0 8 0 6 4 . 5 7 0 6 2 . 4 5 0 5 9 . 8 3 0 5 8 . 6 4 0 5 7 . 5 6 0 5 6 . 1 6 0 5 3 . 8 0 0 5 2 . 5 7 0 5 1 . 1 2 0 4 9 . 9 9 0 4 7 . 7 8 0 4 6 . 2 7 0 4 3 . 2 9 0 4 1 . 2 3 0 3 9 . 1 2 0 3 6 . 3 1 0 3 4 . 0 6 0 3 1 . 2 0 0 2 7 . 8 4 0 2 4 . 6 4 0 2 1 . 3 1 0 1 7 . 9 6 0 14.7 20 11.3 70 8.700 6.340 4.4 10 2.990 1.660 _ 1.060 0.643 0.468 0 . 4 3 * 0.4 72 0 . 5 4 3 0.687 1.010 l.bib 2.710 4.200 5 . 9 6 0 " 8.280 10.740~ 1 3 . 3 9 0 16.310 19;"720 2 2 . 7 9 0 2 5 . RB0 2 9 . 3 4 0 3 1 . 8 2 0 35.020 38.020 4 1 . 0 70 4 3 . 4 5 0 4 5 . 6 6 0 4 8 . 2 8 0 4 9 , 5 4 0 5 1 . 3 70 5 3 . 8 0 0 5 4 . 1 4 0 5 6 . 6 2 0 5 7 . 9 6 0 6 0 . 5 8 0 6 1 . 3 7 0 62.6 20 6 3.330 6 5 . 0 7 0 6 6 . 1 5 0 6 7 . 0 5 0 6 7 . 7 6 C 6 9 . 4 7 0 7 0 . 5 7 0 7 0 . 2 0 0 7 1 . 3 7 0 7 1 . 4 1 0 7 3 . 3 0 0 7 2 . 3 3 0 7 3 . 9 0 0 7 3 . 3 8 0 7 4 . 3 3 0 7 5 . 0 0 0 7 5 . 6 0 0 7 6 . 2 0 0 7 6 . 8 0 0 7 7 . 4 0 0 7 B . 0 0 0 7 8 . 6 0 0 7 9 . 2 C 0 7 9 . 8 0 0 8 0 . 4 0 0 8 1 . 0 0 0 B 1 . 6 0 0 8 2 . 2 0 0 B 2 . 8 0 0 8 3 . 4 0 0 8 4 . 0 0 0 8 4 . 6 0 0 8 5 . 4 7 0 8 5 . 7 5 0 8 6 . 6 1 0 8 7 . 4 6 0 8 6 . 7 4 0 6 8 . 4 6 0 6 8 . 4 2 0 8 9 . 2 0 0 9 0 . 2 50 69.2 50 9 0 . 2 7 0 90.4 10 9 l . 3 i 0 9 2 . 9 5 0 9 2 . 8 30 9 0 * 3 1 0 9 3 . 4 80 9 2 . 8 0 0 9 3 . 2 5 0 9 3 . 9 2 0 9 4 . 4 5 0 9 4 . 9 6 0 9 5 . 4 9 0 9 6 . 1 3 0 9 7 . 3 4 0 _ 9 7 . 7 1 0 9 7 . 9 9 0 9 9 . 1 5 0 9 9 . 5 0 0 1 0 1 . 6 6 0 98.2+0 9 9 . 6 7 0 _ 9 8 . 4 9 0 9 9 . 6 6 0 9 9 . 9 3 0 1 0 0 . 0 0 0 1 0 C . 6 0 C 1 0 1 . 2 0 0 IDl.'flOO 102 .400 "i 03V600 1 0 3 . 6 0 0 l"04.200 104 . 6 00 "l 05 . 4 0 0 1 06 . 00Q~ f 06 . 600 1 0 7 . 2 0 0 1 07 . 800 1 06 . 4 00 109.000 1 0 9 . 6 0 0 1 1 0 . 2 0 0 1 1 0 . 8 0 0 1 1 1 . 4 0 0 1 1 2 . 0 0 0 1 1 2 . 6 0 0 1 1 3 . 2 0 0 1 1 3 . 8 0 0 1 1 4 . 4 0 0 1 1 5 . 0 0 0 . 1 1 5 . 6 0 0 1 1 6 . 2 0 0 1 1 6 . 8 0 0 1 1 7 . 1 5 0 1 1 9 . + 20 1 1 9 . 0 1 0 121.+60 1 2 0 . 8 4 0 1 2 2 . 3 2 0 1 2 3 . 4 1 0 1 2 2 . 7 9 0 1 2 2 . 5 7 0 1 2 4 . 9 4 0 1 2 4 . 0 0 0 1 2 4 . 6 9 0 1 2 6 . 2 3 0 1 2 4 . 8 0 0 1 2 7 . 3 7 0 1 2 6 . 9 6 0 1 2 7 . 0 2 0 1 2 7 . 8 8 0 1 2 6 . 7 6 0 1 2 6 . 9 4 0 1 2 8 . 4 5 0 1 2 8 . 5 0 0 1 3 0 . 6 1 0 1 2 9 . 3 6 0 1 3 0 . 9 7 0 1 2 9 . 5 6 0 1 3 1 . 0 6 0 1 3 0 . 4 0 0 1 2 8 . 9 6 0 1 2 8 . 7 3 0 1 3 0 . 4 0 0 1 3 1 . 9 2 0 1 3 1 . 5 9 0 1 3 2 . 8 2 0 1 3 3 . 6 6 0 1 3 4 . 9 9 0 1 3 6 . 8 0 0 1 3 7 . 4 7 0 1 3 8 . 8 9 0 1 3 8 . 4 6 0 1 3 9 . 7 2 0 1 3 0 . 6 5 0 1 4 0 . 7 6 0 1 4 0 . 6 2 0 1 4 1 . 7 4 0 1 4 1 . 4 8 0 1 4 2 . 9 8 0 1 4 3 . 5 2 0 1 4 3 . 0 7 0 1 4 3 . 6 5 0 1 4 6 . 0 5 0 1 4 6 . 2 4 0 1 4 7 . 0 9 C 1 4 6 . 9 8 0 1 4 6 . 6 9 0 1 4 6 . 4 5 0 1 4 B . 4 3 0 1+8.970 1 5 0 . 9 B 0 1 5 1 . 1 4 0 1 5 2 . 2 6 0 1 5 3 . 9 4 0 1 5 3 . 9 8 0 1 5 2 . 2 7 0 1 5 3 . 5 2 0 1 5 6 . 2 8 0 1 5 6 . 4 9 0 1 5 9 . 1 8 0 1 5 7 . 6 5 0 1 5 8 . 0 1 0 1 5 8 . 4 5 0 1 5 8 . 9 1 0 1 6 1 . 3 5 0 161.590" 1 6 2 . 9 5 0 1 6 C . 6 0 0 1 6 3 . 4 3 0 1 6 3 . 4 4 0 1 6 4 . 7 5 0 1 6 4 . 6 9 0 1 6 6 . 6 9 0 1 6 6 . 7 9 0 1 6 8 . 2 6 0 1 6 6 . 8 2 0 1 6 7 . 3 7 0 1 7 1 . 7 2 0 1 7 0 . 0 5 0 1 7 0 . 6 2 0 1 7 2 . 3 8 0 1 7 1 . 1 4 0 1 7 2 . 0 7 0 1 7 5 . 0 4 0 1 7 7 . 5 4 0 1 7 4 . 5 3 0 1 7 7 . 6 4 0 1 7 7 . 7 9 0 1 7 7 . 5 5 0 1 7 8 . 9 3 0 1 7 8 . 4 6 0 1 8 2 . 2 2 0 1 8 1 . 1 6 0 1 8 0 . 6 7 0 1 8 5 . 0 8 0 1 8 3 . 3 9 0 1 8 2 . 2 1 0 1 8 3 . 3 9 0 1 8 3 . 8 5 0 1 8 6 . 2 8 0 1 8 6 . 7 8 0 1 6 8 . 0 9 0 1 8 8 . 1 6 0 1 8 7 . 1 0 0 1 8 9 . 5 6 0 1 8 9 . 5 0 0 1 9 1 . 6 9 0 1 9 3 . 1 4 0 1 9 4 . 5 8 0 t 9 4 . 6 6 0 1 9 3 . 9 8 0 1 9 7 . 1 6 0 1 9 7 . 0 0 0 1 9 4 . 7 6 0 1 9 6 . 9 8 0 1 9 7 . 1 0 0 2 0 0 . 6 3 0 1 9 9 . 2 6 0 2 0 2 . 9 9 0 2 0 3 . 5 4 0 1 9 9 . 2 4 0 203.4+0 20+.610 2 0 3 . 6 6 0 2 0 2 . 9 9 0 2 0 7 . 1 9 0 2 0 2 . 3 4 0 2 0 3 . 4 4 0 2 0 8 . 3 8 0 2 0 6 . 0 4 0 2 1 0 . 0 9 0 2 0 7 . 9 2 0 2 0 8 . 2 4 0 2 0 7 , 5 0 0 2 1 2 . 9 0 0 2 1 0 . 4 6 0 2 1 2 . 4 6 0 2 1 3 . 0 9 0 2 1 1 . 7 6 0 2 1 3 . 1 6 0 2 1 5 . 7 3 0 2 1 3 . 6 2 0 _ 2 1 5 . 5 3 0 2 1 6 . 3 2 0 2 1 5 . 3 6 0 2 1 9 . 4 4 0 2 1 4 . 8 8 0 2 2 1 . 6 3 0 2 1 7 . 7 9 0 2 2 0 . 6 6 0 2 1 9 . 110 2 2 0 . 0 3 0 2 1 9 . 5 7 0 2 1 6 . 1 2 0 2 1 6 . 2 9 0 2 1 9 . 6 0 0 21+'."030"'?l U 0 4 6 2 0 9 . 5 8 0 2 0 6 . 4 5 0 2 0 6 . 0 1 0 2 0 6 . 2 8 0 2 1 2 . 8 5 0 2 1 1 . 4 9 0 215~.440 2 1 5 . 2 7 0 2 1 4 . 0 9 0 217.BOO 2 1 6 . 8 2 0 2 1 8 . 9 2 0 2 1 7 . 7 0 0 2 1 8 . 5 5 0 2 2 0 . 9 8 C 2 2 0 . 5 0 0 2 2 5 . 1 8 0 2 2 5 . 8 0 C 2 2 6 . 3 1 0 2 2 7 . 6 9 0 2 2 9 . 1 6 0 2 3 2 . 0 9 0 2 3 1 . 2 8 0 2 3 2 . 4 7 0 2 3 5 . 2 4 0 2 3 6 . 9 5 0 2 3 7 . 2 1 0 2 3 7 . 7 5 0 2 3 8 . 3 4 0 2 3 6 . 7 5 0 2 3 8 . 9 0 0 2 3 8 . 1 1 0 2 3 8 . 6 5 0 2 3 9 . 7 2 0 2 3 7 . 5 1 0 2 4 2 . 3 8 0 2 4 0 . 6 0 0 ' 2 4 2 . 3 5 0 2 4 0 . J 7 0 2 4 3 . 5 4 0 2 4 3 . 8 8 0 2 4 1 . 1 5 0 2 4 5 . 5 5 0 2 4 7 . 3 5 0 2 4 4 . 3 0 0 2 4 2 . 8 2 0 2 4 1 . 4 5 0 2 4 4 . 6 9 0 2 4 7 . 2 1 0 2 4 9 . 1 5 0 2 4 5 . 1 1 0 2 4 5 . 8 0 0 2 4 7 . 6 2 0 2 + 5 . 4 0 0 2 4 8 . 5 1 0 2 4 4 . 7 5 0 2 4 8 . 0 8 0 2 4 8 . 0 0 0 2 4 4 . 5 7 0 2 4 9 . 4 0 0 2 4 6 . 8 7 0 2 + 8 . 9 7 0 2 4 7 . 5 6 0 2+7.600 2 4 8 . 3 2 0 2 4 9 . 9 3 0 2 4 9 . 7 8 0 251.010 2 4 9 . 9 5 0 2 5 2 . 6 B 0 2 5 0 . 4 9 0 2 5 3 . 8 8 0 2 5 3 . 1 0 0 2 4 6 . 7 2 0 2 5 3 . 6 9 0 2 5 2 . 2 9 0 2 5 3 . 9 7 0 2 5 4 . 8 4 0 2 5 2 . 4 1 0 2 5 3 . 4 8 0 2 5 4 . 9 5 0 2 5 5 . 8 5 C 2 5 2 . 1 6 0 2 5 5 . 2 6 0 2 5 7 . 8 6 0 256.R 30 254.5_30 2 5 7 . 1 5 0 2 5 5 . 6 8 0  Table XIX. Computer Output. O r i g i n a l X-Ray I n t e n s i t i e s f o r (200) R e f l e c t i o n from Ni-ThO n Cold R o l l e d 75%. 215 F I N A L CORRECT EO I N T E N S I T Y VALUFS - 0 . 0 0. 186A207F< -05 0 . 0 -0.0 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -O.D - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 1 - 0 . 0 - 0 . 0 --o.o -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -O.C -o.o - 0 . 0 -O.C - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 -o.o - 0 . 0 - 0 . 0 - O i O - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o,o -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 -o.o - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o.o • - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0.2 3 2 7 3 7 5 6 - 05 0 . 2 4 9 3 3 8 3 F -•05 0 . 7 1 1 4 3 7 3 E -05 0 . 1 0 8 1 5 4 5 E -•04 0 . 1 3 7 6 5 0 6 6 --04 0 . 8 B 4 3 3 7 4 E - 05 0 . 2 3 5 7 2 7 1 E - 0 * 0 . 2 4 7 5 4 5 0 E -04 0 . 4 2 2 6 4 1 2 E -•04 0 . 3 9 3 3 1 3 B F - 04 0 . 4 4 1 5 4 2 7 E - 0 4 0 . 4 7 7 0 6 8 8 F --04 0 . 6 4 2 9 0 4 8 E --04 0 . 7 2 8 I 2 7 6 E -•w 0 . 7 2 0 6 9 7 6 E -04 0 . 7 B 9 1 1 0 2 F - 0 4 C.99O36B0F-•04 0 . 9 R 6 0 3 4 0 E -•04 0 . 1 1 9 B 2 0 4 E - 0 3 0 . 1 2 9 6 9 3 2 F --03 0 . 1 6 7 4 4 9 9 E --03 0 . 2 1 6 5 4 5 9 F -•03 0 . 2 9 2 1 7 9 4 F - 0 3 0 . 4 0 1 7 6 3 8 E - 0 3 0 . 5 7 3 1 B 6 2 E - •03 0 . 7 7 1 5 9 6 3 6 -•03 0 . 9 4 5 1 8 6 2 E -0 3 0 . I 0 5 4 6 2 0 E -•02 0 . 1 0 6 4 6 9 5 E --02 0 . U 2 5 1 5 1 E - •02 0. 1 1 4 4 5 7 5 6 - 0 2 0 . 1 1 9 9 6 9 3 E - 0 2 O . I 2 4 7 8 0 0 E - 02 0 . 1 3 4 2 0 9 5 E -•02 0 . 1 4 0 1 2 B 4 E -02 0 . 1 4 3 4 1 0 0 6 --02 0 . 1 4 4 7 7 0 5 E -•07 0 . 1 5 0 4 0 4 0 E - 07 0. 1 6 1 1 7 2 B E -02 0 . 1 6 8 0 5 8 9 E - 0 2 0 . 1 7 4 4 H 0 5 6 -•02 0 . I 7 6 B 7 1 7 E -•02 0. 1 8 7 9 4 7 6 6 -02 0 . 1 9 7 3 9 2 3 6 --02 0 . 2 1 6 9 4 9 2 E --02 0 . 2 3 3 3 1 9 6 6 -•02 0 . 2 4 9 5 9 0 4 F -02 0 . 2 6 6 6 9 3 4 E - 0 2 O.291.3001E- 02 0 . 3 1 7 5 8 6 4 E - 02 0 . 3 5 7 5 6 2 5 E -02 0 . 4 1 1 6 5 2 0 6 - 0 2 0 . 4 7 7 9 3 9 1 E --02 0 . 5 6 4 8 1 8 B F - 02 0 . 6 B 1 7 1 6 9 F -02 0 . 8 4 4 7 3 5 7 E -02 0.1 1 0 7 5 8 0 E - 01 0 . 1 4 5 B 9 6 7 E - 01 0 . 1 9 8 0 3 9 4 E -01 0 . 2 7 8 0 0 0 4 6 --01 0 . 4 0 1 7 4 2 3 E --01 0 . 6 0 3 3 8 7 1 E - 01 0 . 9 6 8 1 3 3 B E -01 0 . 1 6 1 2 2 7 I F 00 0 . 2 6 0 2 4 5 9 E 00 0 . 3 4 3 4 1 8 1 E 00 0 . 3 4 7 6 3 1 8 E 00 0 . 2 7 7 5 B 3 B E 0 0 0 . 1 9 2 7 4 9 1 6 0 0 0 . 1 3 0 5 5 4 9 E 00 0 . 9 0 6 6 6 9 5 E -01 0 . 5 8 0 9 U 6 E -01 0 . 3 1 9 3 6 3 5 E -•01 0. 1 6 9 9 8 6 4 F - 01 0 . 1 2 7 1 5 7 3 E -01 0. 1 4 0 1 0 3 3 6 - 0 1 0 . 1 3 3 9 3 0 7 E --01 0. 1 0 6 5 1 0 6 E - 01 0 . 6 7 0 8 7 4 9 F -02 0 . 4 5 5 5 114F -02 0 . 3 9 5 2 0 6 0 F - 02 0 . 4 5 2 8 6 0 4 E - 02 0 . 4 5 7 4 8 0 5 E -02 0 . 4 0 1 2 5 3 3 F -•02 0 . 3 0 7 6 2 6 6 6 -•02 0 . 2 5 6 5 7 6 4 F - 02 0 . 2 3 6 9 3 8 9 E -02 0 . 2 4 4 7 8 6 0 E -02 0 . 2 3 7 1 1 2 1 6 -•02 0 . 2 2 3 4 6 6 8 F - 02 0. 1997578E--02 0. 1 8 2 3 2 7 0 6 -•02 0. 1 7 B 9 1 5 6 6 --02 0 . 1 7 R 6 2 6 9 E - 07 0 . 1 7 2 2 9 3 7 E -02 0. 1 6 7 6 8 2 0 6 -02 6. 1 5 B 4 9 6 S E - 02 0 . 1 5 0 3 5 1 1 6 -•07 0.1432081E--02 0 . 1 3 7 7 6 7 4 E - 02 0 . 1 3 7 1 5 0 3 6 -•02 0 . 1 3 5 1 9 7 0 6 - 02 0 . 1 1 5 2 2 2 8 6 - 0 ? 0 . 1 2 9 0 3 7 2 E -02 0 . 1 2 4 M 1 2 6 -•02 0 . 1 2 1 0 5 5 6 6 - 02 0 . L 2 1 9 1 4 4 E -02 0.1 1 T 7 7 2 8 6 - 02 0 . 1 1 4 8 6 0 4 6 --07 0 . 1 1 4 2 0 9 6 E - 02 0. 1 1 4 6 0 9 0 E - 0 2 0 . 1 1 4 0 6 3 7 F -02 0.1 116 3 B 7 E -•02 0 . 1 0 8 4 3 5 1 E - 02 0 . U O O 3 3 1 E -02 0 . 1 0 7 3 3 3 8 E - •02 0 . U 0 4 6 3 3 E --02 0 . 1 0 6 6 C 3 8 6 - •02 0..10588936 - 0 2 0 . 1 0 2 5 2 7 1 E - 0 ? 0 . 1 0 2 6 B 7 0 E - 02 0 . 1 0 1 2 9 6 6 E - 02 0 . 1 0 1 2 5 0 7 E -02 0 . 9 9 4 6 4 7 6 6 - 0 3 0 . 9 8 4 7 3 9 3 F --03 0 . 9 6 B 3 0 6 1 E - 03 0.<-6076'36E - 0 3 0 . 9 4 9 4 4 7 0 F - 0 3 0 . 9 4 1 5 7 3 4 F - 0 3 0 . 9 2 9 4 3 3 4 E - •03 0 . 9 1 9 3 7 1 6 6 -G3 0 . 9 0 7 7 5 5 7 E - •03 0 . B 9 8 4 4 4 6 F - -03 0 . 8 8 8 2 7 0 1 E -•03 0 . B 7 9 0 4 6 7 F -03 O.96BR301E - 0 3 0 . 8 5 3 0 1 3 5 E -•03 0 . 8 4 7 7 Q 5 3 F - 03 0 . 8 3 6 6 J 0 1 E --03 O.B233tS69E- 0 3 0 . 8 7 7 8 7 7 4 6 -•03 0 . B 2 4 B 1 1 2 E - 0 3 0 . 8 0 5 8 2 C 6 E -03 0.79983<>9E -03 0 . 7 8 I 2 2 3 2 F - 0 3 0 . 7 7 5 5 1 B I E - 03 0 . B 0 0 5 6 7 4 E ' -03 0 . 7 8 6 5 5 8 3 E - 0 3 0.7B7964B» :-•03 0 . 7 5 4 3 6 9 0 E - 03 0 . 7 7 4 4 2 6 7 F -03 0 . 7 7 2 0 9 4 4 F -03 0 . 7 9 1 6 7 3 5 E - 03 0 . 7 6 9 9 2 M F - 0 3 0 . 7 5 S 6 5 5 3 F --03 0 . 7 2 3 5 7 0 8 6 - 0 3 0 . 7 2 2 5 6 5 5 6 -•03 0 . 7 1 6 8 7 3 7 E - •03 0 . 7 2 2 1 0 9 B E -03 0 . 7 U 9 9 3 3 E - 0 3 O . 7 0 3 8 7 7 8 F - 0 3 0 . 6 8 5 6 2 0 6 E - 0 3 0 . 6 6 6 8 1 1 B E -03 0 . 6 6 4 3 8 6 9 E - 0 3 0.66900OOF-•03 0 . 6 5 4 1 4 4 2 E - •03 0 . 6 4 8 0 9 1 5 E -03 0.6O56628F - 0 3 0 . 6 6 6 4 9 8 2 E - 03 0 . 6 6 7 1 4 2 4 6 -•03 0 . 6 9 7 3 7 7 7 E -03 0 . 6 6 3 3 3 1 9 E - 0 3 0 . 6 4 9 6 2 2 2 E - •03 0 . 6 3 2 2 5 6 0 E - 03 0 . 6 4 4 7 5 4 9 6 -03 0 . 6 4 0 0 9 7 1 E -03 0 . 6 3 7 3 6 5 3 E - 03 0 . 6 1 9 7 9 6 8 E - 03 0 . 6 1 0 9 0 0 1 6 --03 0 . 6 0 1 1 3 4 5 E - 0 3 0 . 5 9 8 8 7 8 1 6 -•03 0 . 5 9 7 3 7 9 6 E - 0 3 0.5P640216--03 0 . 5 7 6 7 4 9 0 E -03 0 . 5 6 9 3 1 6 6 6 - 03 0 . 5 6 1 7 0 B 1 F - 03 _P»_5 560 2Q3E--03 0.549 3 0 3 4 6 - 0 3 0 . 5 4 2 7 5 5 0 6 -•03 0 . 5 3 5 3 1 9 6 E - 03 0.52B477B6--03 0 . 5 2 1 6 3 3 1 E -03 0 . 5 1 5 3 0 8 5 F - 03 0 . 5 0 8 7 6 3 1 E - 03 0 . 5 0 2 2 9 1 6 6 --03 0 . 4 9 5 6 2 8 9 6 - 0 3 0 . 4 8 9 1 4 2 5 E - •03 0 . 4 8 2 6 9 9 1 6 - 03 0 . 4 7 6 4 2 0 6 6 -03 0 . 4 7 0 1 2 1 4 E -0 3 0 . 4 6 3 S 7 0 8 E -•03 0 . 4 5 7 6 0 4 0 F - 03 0 . 4 5 1 4 0 3 2 E --03 0 . 4 4 5 2 5 3 0 E - 0 3 0 . 4 4 7 6 7 3 5 E - •03 0 . 4 1 6 3 7 9 0 E -•03 0 . 4 1 3 3 * 5 4 6 -03 0 . 3 9 Z 3 5 7 4 E - 0 3 0 . 3 9 5 * 7 0 5 = - 03 0 . 3 9 0 1 4 9 4 6 - 03 0 . 3 8 0 6 4 4 3 E -03 0 . 3 7 4 2 7 7 1 E - 0 3 0 . 3 B 5 7 6 5 7 F - -03 0 . 3 8 2 1 1 2 6 6 -•03 0 . 3 5 B 9 7 8 1 E - 0 3 0 . 3 5 6 4 8 7 6 E -03 0 . 3 5 7 0 1 2 3 F - 03 0 . 3 5 0 5 4 4 2 6 -•03 0 . 3 7 1 B 6 3 1 E -03 0 . 3 3 2 7 2 7 1 F - 0 3 0 . 3 4 3 3 7 9 6 E - •03 0 . 3 3 3 2 0 5 6 F -•03 0 . 3 4 1 7 3 3 0 6 -03 0 . 3 2 3 7 8 B 5 E -03 0 . 3 5 0 1 6 7 5 6 - 0 3 0 . 3 3 6 2 2 8 6 E - 0 3 0 . J 3 8 8 7 2 2 E --03 0 . 3 0 5 4 7 3 1 6 - 0 3 0 . 3 1 2 4 7 2 5 E - •03 0 . 3 0 6 8 f l 4 3 E - 0 3 0 . 3 2 3 6 7 4 6 F -03 O . 3 ? 2 I 2 « . 0 E -03 0 . 3 1 6 8 5 9 2 E - 03 0 . 3 2 3 9 3 3 1 E - 0 3 0 . 3 4 1 9 5 1 8 E --03 0 . 3 4 1 2 3 1 7 E - 0 3 0 . 3 I 3 6 6 3 9 E -•03 0 . 2 P 7 8 1 5 9 E -•03 0.7910404E--03 0 . 2 8 8 0 3 1 4 F - 0 3 0 . 2 8 9 2 8 3 7 E - 03 0.269 3 3 2 7 6 -•03 0 . 2 4 6 0 4 2 6 E -03 0 . 2 3 6 1 7 5 0 E - 0 3 0 . 2 2 B 3 5 4 8 F - 0 3 0 . 2 4 3 2 9 3 7 E -•03 0 . 7 3 6 0 2 S 8 F - 0 1 0 . 3 3 9 3 6 3 7 F -03 0 . 7 6 1 4 2 1 3 E - 0 3 0 . 2 2 1 3 6 9 7 6 - 03 0 . 1 6 I 5 3 4 9 E --0 3 0. 1 9 7 4 1 5 5 E - 03 0 . 2 0 8 6 T 1 0 F - •03 0 . 2 2 6 0 7 4 2 E - 03 0 . 2 0 7 9 9 7 7 E -03 0 . 2 C 3 2 5 4 0 E - 0 3 0 . 1 7 8 5 8 8 4 E - 03 0 . 1 6 7 2 6 7 5 E - 03 0 . 1 6 5 3 B B I E -C3 0 . 1 7 0 9 U 3 E - 0 3 0. 1 7 B 6 4 4 4 E - 0 3 0. 1 7 7 6 2 6 S E -•03 0. 1 5 8 7 9 8 4 F -03 0 . 1 5 5 1 6 6 7 6 -03 0 . 1 4 R 4 5 9 1 E -•03 0 . 1 3 4 4 0 8 7 F - 03 0. U 4 9 4 2 IE -03 0. 1 2 5 5 6 9 9 F - 0 3 0.1 1 3 5 7 3 5 E -0 3 0 . 1 1 1 6 6 A 6 E - 03 0 . 1 3 4 7 2 7 2 E -03 0. 1 3 2 2 6 2 4 E -03 0 . 1 0 4 9 Q 9 B F - 0 3 0 . R 4 3 R 0 0 7 E - 04 0 . 6 3 4 8 6 0 8 E --04 0 . 7 9 7 9 8 2 2 E -•C4 0 . 9 4 1 0 4 1 4 E - 04 0. 1 0 0 4 4 6 3 E - 03 0 . 8 7 7 1 2 5 7 F -04 0.6401933E--04 0 . 4 6 4 9 3 7 6 6 - 04 0 . 4 4 9 9 B 1 7 E — 04 , 0 . 6 0 1 0 J 2 7 E --04 0 . 7 2 5 2 9 4 1 F - 04 0 . 5 3 9 1 8 5 0 E - 04 ''""0.42106086-•OA " 0 . 7 5 9 6 1 B 5 F -04 0 . 2 9 6 1 2 0 9 E -04 0 . 2 0 9 7 4 0 5 F - C4 0 . 2 5 6 1 0 5 1 6 - 04 0. l 3 r t 0 2 5 6 F --04 0 . 3 0 8 7 7 4 3 E - 0 4 0 . 1 9 3 9 9 6 4 6 - 04 c.o 0 . 0 0.0 -6 .0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - n . o - 0 . 0 -0.0 - 0 . 0 -0.0 -0.0 - 0 . 0 - 0 . 0 -O.G - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o.o -0.0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -9,o -0.0 - 0 . 0 - 0 . 0 -o.o -0.0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o.o - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -o.o - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 0 . 2 3 2 8 3 0 6 E - 0 9 .. Table XX. Computer Output. F i n a l Corrected for (200) Reflection from Ni-Th0 2 LX-Ray Intensity values Cold Rolled 75%. 216 CORRESPONDING VALUES OF S I N E THETA - Q . 0 6 3 7 6 - 0 1 ( 0 6 3 4 1 - 0 . 0 6 3 0 5 - 0 . 0 6 2 6 9 - 0 . 0 6 2 3 3 - 0 . 0 6 1 9 7 - 0 . 0 6 1 6 1 - 0 . 0 6 1 2 5 - 0 . 0 6 0 8 9 - 0 . 0 6 0 5 ? - 0 . 0 6 0 1 6 - 0 . 0 5 9 8 0 - 0 . 0 5 < l + 4 - 0 . 0 5 9 0 8 - 0 . 0 5 8 7 2 - 0 . 0 5 8 3 6 - 0 . 0 5 7 9 9 - 0 . 0 5 7 6 3 - 0 . 0 5 7 2 ! 7 - 0 . 0 5 6 9 1 - 0 . 0 5 6 5 5 - 0 . 0 5 6 1 9 - 0 . 0 5 5 83 - 6.055 4 7 - 0 . 0 5 5 1 0 - 0 . 6 5 4 7 4 - 0 . 6 5 4 3 8 - 0 . 0 5 4 0 2 - 0 . 0 5 3 6 6 - 0 . 0 5 3 3 0 - 0 . 0 5 2 9 4 - 0 . 0 5 2 5 7 - 0 . 0 5 2 2 1 - 0 . 0 5 1 8 5 - 0 . 0 5 1 4 9 - 0 . 0 5 1 1 3 - 0 . 0 5 0 7 7 - 0 . 0 5 0 4 1 - 0 . 0 5 0 0 5 - 0 . 0 4 9 6 8 - 0 . 0 4 9 3 2 - 0 . 0 4 8 9 6 - 0 . 0 4 3 6 0 - 0 . 0 4 8 2 4 - 0 . 0 4 7 6 6 - 0 . 0 4 7 5 2 - 0 . 0 4 7 1 5 - 0 . 0 4 6 7 9 - 0 . 0 4 6 4 3 - 0 . 0 4 6 0 7 - 0 . 0 4 5 7 1 - 0 . 0 4 1 3 5 - 0 . 0 4 4 9 9 - 0 . 0 4 4 6 3 - 0 . 0 4 4 2 6 - C . 0 4 3 9 0 - 0 . 0 4 3 5 4 - 0 . 0 4 3 1 8 - 0 . 0 4 2 6 2 - 0 . 0 4 2 4 6 - 0 . 0 4 2 1 0 - 0 . 0 4 1 7 4 - 0 . 0 4 1 3 7 - 0 . 0 4 1 0 1 - 0 . 0 4 0 6 5 - 0 . 0 4 0 2 9 - 0 . 0 3 9 9 3 - 0 . 0 3 9 5 7 - 0 . 0 3 9 2 1 - 0 . 0 3 8 6 4 - 0 . 0 3 8 4 6 - 0 . 0 3 B I 2-0.0 3 7 7 6 - 0 . 0 3 7 4 0 - 0 . 0 3 7 0 4 - 0 . 0 3 6 6 0 - 0 . 0 3 6 3 2 - 0 . 0 3 5 9 5 - 0 . 0 3 5 5 9 - 0 . 0 3 5 2 3 - 0 . 0 3 4 8 7 - 0 . 0 3 4 5 1 - 0 . 0 3 4 1 5 - 0 . 0 3 3 7 9 - 0 . 0 3 3 4 2 - 0 . 0 3 3 0 6 - 0 . 0 3 2 7 0 - 0 . 0 3 2 3 4 - 0 . 0 3 1 9 8 - 0 . 0 3 1 6 2 - 0 . 0 3 1 2 6 - 0 . 0 3 U 9 0 - 0 . 0 3 0 5 3 - 0 . 0 3 0 I 7 - 0 . 0 2 9 8 1 - 0 . 0 2 9 4 5 - 0 . 0 2 9 0 9 - 0 . 0 2 8 7 3 - 0 . 0 2 6 ? 7 - 0 T 0 2 8 0 0 - 0 . 0 2 7 6 4 - 0 . 0 2 7 2 8 - 0 . 0 2 6 9 2 - 0 . 0 2 6 5 6 - 0 . 0 2 6 2 0 - 0 . 0 2 5 8 4 - 0 . 0 2 5 4 8 - 0 . 0 2 5 1 1 - 0 . 0 2 4 7 5 - 0 . 0 2 4 3 9 - 0 . 0 2 4 0 3 - 0 . 0 2 3 6 7 - 0 . 0 2 3 3 1 - 0 . 0 229 5 - 0 . 0 2 2 5 6 - 0 . 0 2 2 2 2 - 0 . 6 2 1 8 6 - 6 . 0 2 1 5 0-6.0 2 1 1 4 - 0 . 0 2 0 7 8 - 0 . 0 2 0 4 2 - 0 . 0 2 O O 6 - 0 . 0 1 9 6 9 - 0 . 0 1 9 3 3 - 6 . 0 1 8 9 7 - 0 . 0 1 6 6 1 - 0 . 0 1 8 2 5 - 0 . 0 1 7 8 9 - 0 . 0 1 7 5 3 - 0 . 0 1 7 1 7 - 0 . 0 1 6 6 0 - 0 . 0 1 6 4 4 - 0 . 0 1 6 0 8 - 0 . 0 1 5 7 2 - 0 . 0 1 5 3 6 - 0 . 0 1 5 0 0 - 0 . 0 1 4 6 4 - 0 . 0 1 4 ? 7 - 0 . 0 1 3 9 1 - 0 . 0 1 3 5 5 - 0 . 0 1 3 1 9 - 0 . D 1 2 8 3 - 0 . 0 1 2 4 7 - 0 . 0 1 2 1 1 - 0 . 0 1 1 7 5 - 0 . 0 1 1 3 6 - 0 . 0 1 1 0 2 - 0 . 0 1 0 6 6 - 0 . 0 1 0 3 0 - 0 . 0 0 9 9 4 - 0 . 0 0 9 5 8 - 0 . 0 0 9 2 2 - 0 . 0 0 8 8 5 - 0 . 0 0 8 4 9 - 0 . 0 0 8 1 3 - 0 . 0 0 7 7 7-0.00 7 4 1 - 0 . 0 0 7 0 5 - 0 . 0 0 6 6 9 - 0 . 0 0 6 3 3 - 0 . 0 0 5 9 6 - C . 0 0 5 6 0 - 0 . 0 0 5 2 4 - 0 . 0 0 4 8 8 - 0 . 0 0 4 5 2 - 0 . 0 0 4 1 6 - 0 . 0 0 3 8 0 - 0 . 0 0 3 4 3 - 0 . 0 0 3 0 7 - 0 . 0 0 2 7 1 - 0 . 0 0 2 3 5 - 0 . 0 0 1 9 9 - 0 . 0 0 1 6 3 - 0 . 0 0 1 2 7 - 0 . 0 0 0 9 1 - 0 . 0 0 O 5 + - 0 . 0 0 0 1 8 0 . 0 0 0 1 8 0 . 0 0 0 5 4 0 . 0 0 0 9 0 0 . 0 0 1 2 6 0 . 0 0 1 6 2 0 . 0 0 1 9 9 0 . 0 0 2 3 5 0 . 0 0 2 7 1 0 . 0 0 3 0 7 0 . 0 0 3 4 3 0 . 0 0 3 7 9 0 . 0 0 4 1 5 0 . 0 0 4 5 1 0 . 0 0 4 8 8 0 . 0 0 5 2 * 6.00560 0 . 0 0 5 9 6 0 . 0 0 6 3 2 0 . 0 0 6 6 8 0 . 0 0 7 0 4 0 . 0 0 7 4 0 0 . 0 0 7 7 7 0 . 0 0 8 1 3 0 . 0 0 8 4 9 0 . 0 0 8 8 5 0 . 0 0 9 2 1 0 . 0 0 9 5 7 0 . 0 0 9 9 3 0 . 0 1 0 3 0 0 . 0 1 0 6 6 0 . 0 1 1 0 2 0 . 0 1 1 3 8 0 . 0 1 1 7 4 0 . 0 1 2 1 0 0 . 0 1 2 4 6 0 . 0 1 2 8 2 0 . 0 1 3 1 9 0 . 0 1 3 5 5 0 . 0 1 3 9 1 0 . 0 1 4 2 7 0 . 0 1 4 6 3 0 . 0 1 4 9 9 0 . 0 1 5 3 5 0 . 0 1 5 7 2 0 . 0 1 6 0 8 0.016+4 0 . 0 1 6 8 0 0 . 0 1 7 1 6 0 . 0 1 7 5 2 0 . 0 1 7 8 8 0 . 0 1 8 2 4 0 . 0 1 8 6 1 0 . 0 1 8 9 7 0 . 0 1 9 3 3 0 . 0 1 9 6 9 0.020O5 0 . 0 2 0 4 1 0 . 0 2 0 7 7 0 . 0 2 1 1 4 0 . 0 2 1 5 0 0 . 0 2 1 6 6 0 . 0 2 2 2 2 0 . 0 2 2 5 6 0 . 0 2 2 9 4 0 . 0 2 3 3 0 0 . 0 2 3 6 6 0 . 0 2 4 0 3 C . 0 2 4 3 9 0 . 0 2 4 7 5 0 . 0 2 5 1 1 0 . 0 2 5 4 7 0 . 0 2 5 8 3 0 . 0 2 6 1 9 0 . 0 2 6 5 6 0 . 0 2 6 9 2 0 . 0 2 7 2 8 0 . 0 2 7 6 4 0 . 0 2 8 0 0 0 . 0 2 8 3 6 0 . 0 2 6 7 2 0 . 0 2 9 0 8 0 . 0 2 9 4 5 0 . 0 2 9 8 1 0 . 0 3 0 1 7 0 . 0 3 0 5 3 0 . 0 3 0 8 9 0 . 0 3 1 2 5 0 . 0 3 1 6 1 0 . 0 3 1 9 7 0 . 0 3 2 3 4 0 . 0 3 2 7 0 0 . 0 3 3 0 6 0.033+2 0 . 0 3 3 7 8 0 . 0 3 * 1 * 0.C3+50 0 . 0 3 4 8 7 0 . 0 3 5 2 3 0 . 0 3 5 5 9 0 . 0 3 5 9 5 0 . 0 3 6 3 1 0 . 0 3 6 6 7 0 . 0 3 7 0 3 0 . 0 3 7 3 9 0 . 0 3 7 7 6 0 . 0 3 6 1 2 0.038+8 0 . 0 3 8 8 4 0 . 0 3 9 2 0 0 . 0 3 9 5 6 0 . 0 3 9 9 2 . 0 . 0 4 C 2 9 0 . 0 4 0 6 5 0 . 0 4 1 0 1 0 . 0 4 1 3 7 0 . 0 4 1 7 3 0 . 0 * 2 0 9 0.042+5 0 . 0 4 2 8 1 . 0 . 0 + 3 1 8 0 . 0 4 3 5 4 0 . 0 4 3 9 0 0 . 0 4 4 2 6 0 . 0 4 4 6 2 0 . 0 4 4 9 8 0 . 0 4 5 3 4 0 . 0 4 5 7 1 0 . 0 4 6 0 7 0.0+6+3 0 . 0 4 6 7 9 0 . 0 4 7 1 5 0 . 0 4 7 5 1 0 . 0 4 7 B 7 0 . 0 4 8 2 3 0 . 0 4 8 6 0 0 7 0 4 8 9 6 0 . 0 4 9 3 2 6.0+968 0 . 0 5 0 0 4 0 . 0 5 0 4 0 0 . 0 5 0 7 6 0 . 0 5 1 1 3 0 . 0 5 1 4 9 0 . 0 5 1 8 5 0 . 0 5 2 2 1 0 . 0 5 2 5 7 0 . 0 5 2 9 3 0 . 0 5 3 2 9 0 . 0 5 3 6 5 0 . 0 5 4 0 2 0 . 0 5 4 3 6 0 . 0 5 4 7 * 0 . 0 5 5 1 0 0 . 0 5 5 4 6 0 . 0 5 5 6 2 0 . 0 5 6 1 8 0 . 0 5 6 5 4 0 . 0 5 6 9 1 0 . 0 5 7 2 7 0 . 0 5 7 6 3 0 . 0 5 7 9 9 0 . 0 5 0 3 5 0 . 0 5 8 7 1 0 . 0 5 9 0 7 0 . 0 5 9 4 4 0 . 0 5 9 8 0 0 . 0 6 0 1 6 0 . 0 6 0 5 2 0 . 0 6 0 8 6 0 . 0 6 1 2 4 0 . 0 6 1 6 0 0 . 0 6 1 9 6 0 . 0 6 2 3 3 0 . 0 6 2 6 9 0 . 0 6 3 0 5 0.063+1 0 . 0 6 3 7 7 0 . 0 6 4 1 3 0 . 0 6 4 4 9 0 . 0 6 4 8 6 0 . 0 6 5 2 2 0 . 0 6 5 5 8 0.0659+ 0 . 0 6 6 3 0 0 . 0 6 6 6 6 0 . 0 6 7 0 2 0 . 0 6 7 3 6 0 . 0 6 7 7 5 0 . 0 6 8 1 1 0.068+7 0 . 0 6 8 6 3 0 . 0 6 9 1 9 0 . 0 6 9 5 5 0 . 0 6 9 9 1 0 . 0 7 0 2 8 0 . 0 7 0 6 4 0 . 0 7 1 0 0 0 . 0 7 1 3 6 0 . 0 7 1 7 2 0 . 0 7 2 0 8 0.0724+ 0 . 0 7 2 8 0 0 . C 7 3 1 7 0 . 0 7 3 5 3 0 . 0 7 3 8 9 0 . 0 7 4 2 5 0.07+61 0.07+97 0 . 0 7 5 3 3 0 . 0 7 5 7 0 0 . 0 7 6 0 6 0 . 0 7 6 4 2 0 . 0 7 6 7 8 0 . 0 7 7 1 4 0 . 0 7 7 5 0 0 . 0 7 7 8 6 0 . 0 7 8 2 2 0 . 0 7 8 5 9 0 . 0 7 8 9 5 0 . 0 7 9 3 1 0 . 0 7 9 6 7 0 . 0 R 0 0 3 0 . 0 8 0 3 9 0 . 0 8 0 7 5 0 . 0 8 1 1 1 0 . 0 8 1 4 8 0 . 0 8 1 6 4 0 . 0 8 2 2 0 0 . 0 8 2 5 6 0 . 0 8 2 9 2 0 . 0 8 3 2 8 0 . 0 8 3 6 4 0.08+0f 0 . 0 8 4 3 7 0 . 0 8 4 7 3 0 . 0 8 5 0 9 0 . 0 8 5 4 5 0 . 0 8 5 8 1 0 . 0 8 6 1 7 0 . 0 8 6 5 3 0 . 0 8 6 9 0 0 . 0 0 7 2 6 0 . 0 0 7 6 2 0 . 0 8 7 9 8 0 . 0 6 8 3 4 0 . 0 8 8 7 0 0 . 0 8 9 0 6 0 . 0 8 9 4 3 0 . 0 8 9 7 9 0 . 0 9 0 1 5 0 . 0 9 0 5 1 0 . 0 9 0 8 7 0 . 0 9 1 2 3 0 . 0 9 1 5 9 0 . 0 9 1 9 5 0 . 0 9 2 3 2 0 . 0 9 2 6 3 0 . 0 9 3 0 + 0 . C 9 3 4 0 0 . 0 9 3 7 6 0 . 0 9 4 1 2 0 . 0 9 4 4 8 0 . 0 9 4 0 5 0 . 0 9 5 2 1 0 . 0 9 5 5 7 0 . 0 9 5 9 3 0 . 0 9 6 2 9 0 . 0 9 6 6 5 0 . 0 9 7 0 1 0 . 0 9 7 3 7 0 . 0 9 7 7 + 0 . 0 9 3 1 0 0 . 0 9 0 4 6 0 . 0 9 0 6 2 0 . 0 9 9 1 0 0.0995+ 0 . 0 9 9 9 0 0 . 1 0 0 2 7 0 . 1 0 0 6 3 0 . 1 0 0 9 9 0 . 1 0 1 3 5 0 . 1 0 1 7 1 0 . 1 0 2 0 7 0 . 1 0 2 4 3 0 . 1 0 2 7 9 0 . 1 0 3 1 6 0 . 1 0 3 5 2 0 . 1 0 3 0 3 0 . 1 0 4 2 4 0 . 1 0 4 6 0 0 . 1 0 4 9 6 0 . 1 0 5 3 2 0 . 1 0 5 6 8 0 * 1 0 6 0 5 0.106+1 0 . 1 0 6 7 7 0 . 1 0 7 1 3 0.107+9 0 . 1 0 7 8 5 0 . 1 0 6 2 1 0 . 1 0 8 5 8 0 . 1 0 8 9 * 0 . 1 0 9 3 0 0.10966- C . 1 1 0 0 2 0 . 1 1 0 3 8 0 . 1 1 0 7 4 0 . 1 1 1 1 0 0 . 1 1 1 4 7 0 . 1 1 1 6 3 0 . 1 1 2 1 9 0.1125.5 0. 1 1 2 9 1 0 . 1 1 3 2 7 0 . 1 1 3 6 3 0 . 1 1 4 0 0 0 . 1 1 4 3 6 0 . 1 1 4 7 2 0.1 1506 0 . 1 1 5 4 4 0 . 1 1 5 8 0 0 . 1 1 6 1 6 0 . 1 1 6 5 2 0 . 1 1 6 B 9 0 . 1 1 7 2 5 0 . 1 1 7 6 1 0 . 1 1 7 9 7 0 . 1 1 6 3 3 0 . 1 1 8 6 9 6.11905 0 . 1 1 9 4 2 0 . 1 1 9 7 8 0 . 1 2 0 1 4 0 . 1 2 0 5 0 0 . 1 2 0 8 6 0 . 1 2 1 2 ? 0 . 1 2 1 5 8 0 . 1 2 1 9 4 0 . 1 2 2 3 1 0 . 1 2 2 6 7 0 . 1 2 3 0 3 0 . 1 2 3 3 9 0 . 1 2 3 7 5 0 . 1 2 * 1 1 0 . 1 2 4 4 7 0 . 1 2 4 8 4 0.1252C 0 . 1 2 5 5 6 0 . 1 2 5 9 2 0 . 1 2 6 2 8 0 . 1 2 6 6 4 0.1270C 0 . 1 2 7 3 6 0 . 1 2 7 7 3 0 , 1 2 0 0 9 0 . 1 2 8 4 5 0 . 1 2 8 8 1 0 . 1 2 9 1 7 0 . 1 2 9 5 3 0 . 1 2 9 8 9 0 . 1 3 0 2 5 0 . 1 3 0 6 2 0 . 1 3 0 9 8 0 . 1 3 1 3 4 0 . 1 3 1 7 0 0 . 1 3 2 0 6 0.132+2 0 . 1 3 2 7 8 0 . 1 3 3 1 5 0 . 1 3 3 5 1 0 . 1 3 3 0 7 0.13+23 0.13+59 0.13+95 0 . 1 3 5 3 1 0 . 1 3 5 6 7 0.1360+ 0.136+0 0 . 1 3 6 7 6 0 . 1 3 7 1 2 0 . 1 3 7 * 8 0 . 1 3 7 8 * 0 . 1 3 8 2 0 0 . 1 3 0 5 7 0 . 1 3 8 9 3 0 . 1 3 9 2 9 0 . 1 3 9 6 5 0 . 1 * 0 0 1 0*1+037 0.1+073 0 . 1 4 1 0 9 0.1+1+6 0.1+182 0.1+218 Table XXI. Computer Output. S i n 9 Values f o r (200) R e f l e c t i o n from Ni-Th0 o Cold R o l l e d 75%. SINE THETA I N T E R V A L - 0 . 0 0 0 3 6 NUMBER OF S I N E THETA DATA POINTS - 5 7 1 A R T I F I C I A L L A T T I C E PARAMETER - 2 . 7 0 6 7 6 ANGSTROMS ; TWO THETA 7ER0 (CENTRE OF G R A V I T Y ) • 5 2 . 0 0 1 DEGREES L A T T I C E PARAMETER (CENTRE Of G R A V I T Y ) * 3.51+08 ANGSTROMS TWO THETA *ER0 I PEAK MAXIMUM! - 51.6+8 DEGREES L A T T I C E PARAMETER I P E A K MAXIMUM) - 3 . 5 2 3 7 5 ANGSTROMS PEAK ASYMMETRY •" 0 . 1 5 3 DEGREES Table XXII. Computer Output. Peak Parameters f o r (200) R e f l e c t i o n from Ni-Th0 2 Cold R o l l e d 75%. 217 TO NI S T R I P COLD ROLLED 75 PFKCFNT R E F L E C T I O N t 4 0 0 1 SCAN B E G I N S AT 1 1 4 . 0 0 0 DEGREES TWO THETA ANGULAR INCREMENT » 0.050 DEGREES JfUHftE*.OF. DATA P D I N T S • 4 2 1 ATCMIC S C A T T E R I N G FACTOR AT TWO THETA 111 = 1 2 . 0 3 ATOMIC S C A T T E R I N G FACTOR AT TWO THETA ( 2 ) *= 11.21 CONTROL = 4 O R I G I N A L I N T E N S I T Y V A L U E S 2 6 6 . 8 6 0 2 6 2 . 0 9 0 2 6 5 . 1 1 0 2 6 1 . 8 1 0 2 6 3 . 2 4 0 2 6 2 . 9 2 0 2 6 2 . 3 4 0 2 6 2 . 0 9 0 2 6 1 . 9 5 0 2 6 1 1 3 0 0 2 6 1 . 6 4 0 2 6 1 . 8 9 0 2 6 2 . 2 2 0 2 5 7 . 7 1 0 2 6 2 . 8 3 0 2 5 8 . 1 2 0 2 5 6 . 9 1 0 2 6 3 . 0 1 0 2 6 1 . 3 9 0 2 5 6 . 9 2 0 2 5 8 . 4 4 0 2 6 1 . 4 1 0 2 5 8 . 3 6 0 2 6 1 . 4 6 0 2 5 7 . * 2 0 2 5 9 . 8 8 0 2 5 9 . 2 1 0 2 5 7 . 3 8 0 2 5 7 . 9 7 0 2 5 4 . 0 9 0 2 5 4 . 1 5 0 2 5 0 . 7 8 0 2 5 1 . 9 4 0 2 5 2 . 7 3 0 2 5 6 . 6 4 0 2 5 2 . 3 3 0 2 5 4 . 3 3 0 2 5 1 . 9 1 0 2 5 0 . 3 6 0 2 5 0 . 5 0 0 2 5 1 . 1 3 0 2 5 3 . 9 9 0 2 5 1 . 0 7 0 2 5 6 . 1 2 0 2 5 1 . 3 0 0 2 4 6 . 4 0 0 2 5 0 . 4 1 0 2 5 0 . 8 3 0 2 4 9 . 9 8 0 2 4 7 T 6 5 0 2 4 6 . 6 2 0 2 4 6 . 0 7 0 2 4 7 . 2 3 0 2 4 7 . 4 8 0 2 4 8 . 7 8 0 _245_.5 30 245.8.20 2 4 6 . 0 7 0 2 4 3 . 2 7 0 2 4 3 . 0 9 0 2 4 6 . 2 7 0 2 4 4 . 6 6 0 2 4 4 . 9 8 0 2 4 6 . 3 4 0 2 4 0 . 7 5 0 2 4 2 . 8 7 0 2 4 2 . 9 1 0 2 4 0 . 9 9 0 2 4 3 . 5 3 0 2 4 4 . 4 1 0 2 4 2 . 9 9 0 2 3 6 . 8 6 0 " 2 4 1 . 3 9 0 2 4 2 . 7 0 0 23~7.500 2 4 0 . 1 7 0 2 4 1 . 3 0 0 2 3 5 . 5 4 0 2 3 8 . 5 5 0 2 3 6 . 9 9 0 2 3 8 . 1 5 0 2 3 5 . 0 8 0 2 3 5 . 3 6 0 2 3 4 . 4 6 0 2 3 2 . 1 9 0 2 3 5 . 0 9 0 2 3 1 . 9 7 0 2 3 3 . 7 3 0 2 3 6 . 0 6 0 2 2 9 . 9 6 0 2 3 1 . 8 0 0 2 3 0 . 2 9 0 2 2 7 . 8 2 0 2 2 7 . 1 8 0 2 2 5 . 8 2 0 2 2 6 . 7 5 0 2 2 9 . 0 4 0 2 2 4 . 0 7 0 2 2 3 . 7 0 0 2 2 4 . 8 1 0 2 1 9 . 4 7 0 2 1 5 . 7 9 0 2 2 2 . 2 0 0 2 1 6 . 5 5 0 2 1 6 . 0 7 0 2 1 6 . 1 5 0 2 1 4 . 1 9 0 2 1 3 . 3 8 0 2 0 8 . 7 9 0 2 1 0 . 0 6 0 2 0 9 . 1 1 0 2 0 4 . 8 6 0 2 0 1 . 8 0 0 2 0 1 . 1 7 0 1 9 9 . 4 6 0 1 9 7 . 8 9 0 1 9 6 . 2 4 0 1 9 2 . 3 7 0 1 8 9 . 8 6 0 1 8 7 . 2 9 0 1 8 3 . 9 0 0 1 8 2 . 8 7 0 1 7 7 . 8 7 0 1 7 3 . 0 8 0 1 6 8 . 7 8 0 1 6 6 . 2 5 0 1 6 3 . 6 4 0 1 5 6 . 4 0 0 1 5 0 . 0 5 0 1 4 5 . 0 3 0 1 4 1 . 0 0 0 1 3 6 . 3 4 0 1 2 7 . 0 3 0 1 2 3 . 0 2 0 1 1 6 . 6 1 0 1 1 1 . 2 6 0 1 0 4 . 7 6 0 9 7 . 0 6 0 9 0 . 4 6 0 8 4 . 5 6 0 7 8 . 2 6 0 7 2 . 2 3 0 6 5 . 4 7 0 5 9 . 8 5 0 5 3 . 0 1 0 4 6 . 5 9 0 4 1 . 6 1 0 36.3 30 3 0 . 9 2 0 2 6 . 2 4 0 2 2 . 9 0 0 19.8 30 1 7 . 1 8 0 15.4 30 14 . 0 0 0 1 3 . 2 5 0 1 2 . 9 2 0 1 2 . 7 2 0 1 3 . 1 3 0 1 3 . 6 0 0 1 4 . 1 0 0 1 4 . 9 1 0 1 5 . 2 1 0 15.bio" 1 6 . 3 1 0 16.R60~ 16.5 70 1 8 . 6 5 0 1 9 . 8 6 0 2 1 . 7 4 0 2 4 . 2 5 0 2 7 . 0 6 0 3 0 . 2 8 0 3 4 . 6 6 0 3 8 . 5 1 0 4 3 . 6 6 0 4 8 . 9 6 0 5 5 . 1 6 0 6 1 . 2 2 0 6 6 . 5 3 0 7 3 . 3 2 0 7 9 . 3 9 0 8 4 . 4 9 0 6 1 . 2 9 0 9 6 . 2 1 0 1 0 4 . 1 0 0 1 1 0 . 5 3 0 1 1 5 . 7 5 0 1 2 1 . 9 2 0 1 2 5 . 5 6 0 1 3 1 . 5 3 0 1 3 7 . 7 8 0 1 4 0 . 8 7 0 1 4 7 . 5 3 0 1 4 9 . 8 1 0 1 5 4 . 5 3 0 1 5 6 . 3 5 0 1 6 3 . 1 2 0 1 6 4 . 6 1 0 1 6 9 . 4 2 0 1 6 9 . 5 6 0 1 7 7 . 6 1 0 1 7 7 . 6 5 0 1 8 0 . 9 2 0 1 6 4 . 4 5 0 1 8 5 . 9 9 0 1 8 7 . 0 8 0 1 8 9 . 2 4 0 1 9 3 . 6 5 0 1 9 2 . 5 4 0 1 9 4 . 5 5 0 1 9 7 . 0 7 0 1 9 9 . 9 1 0 2 0 1 . 5 2 0 2 0 3 . 0 0 0 2 0 5 . 8 0 0 2 0 6 . 0 2 0 2 0 4 . 1 8 0 2 0 7 . 4 3 0 2 0 9 . 6 4 0 2 1 1 . 6 3 0 2 1 0 . 9 0 0 2 1 2 . 6 3 0 2 1 1 . 3 6 0 2 1 5 . 3 9 0 7 1 5 . 6 9 0 2 1 5 . 2 7 0 2 1 8 . 2 5 0 2 1 9 . 0 3 0 2 1 9 . 6 3 0 2 2 4 . 3 4 0 2 2 4 . 4 2 0 2 2 3 . 3 6 0 2 2 3 . 7 6 0 2 2 4 . 4 1 0 2 2 7 . 1 4 0 2 7 3 . 7 8 0 7 7 2 . 8 9 0 2 2 6 . 0 7 0 2 2 8 . 3 8 0 2 2 6 . 9 2 0 2 3 1 . 6 5 0 2 2 9 . 9 6 0 2 2 9 . 0 5 0 . 2 30.2 50 2 2 8 . 9 1 0 2 3 1 . 2 4 0 2 3 0 . 8 9 0 2 3 6 . 2 5 0 _ 2 3 1 . 9 4 0 _ 2 3 4 1 1 6 0 2 3 4 . 2 0 0 2 3 3 . 2 6 0 2 3 4 . 4 9 0 2 3 5 . 5 8 0 2 3 2 . 7 9 0 2 3 6 . 5 6 0 2 3 8 . 0 4 0 2 3 8 . 5 6 0 2 3 6 . 1 6 0 7 3 9 . 1 6 0 2 3 3 . 2 6 0 2 3 7 . 0 5 0 2 3 6 . 8 0 0 2 3 4 . 2 8 0 2 4 2 . 4 9 0 2 3 6 . 5 9 0 2 3 8 . 8 0 0 2 3 6 . 0 5 0 2 3 6 . 0 6 0 2 3 6 . 1 3 0 2 3 5 . 3 6 0 2 3 8 . 5 6 0 2 3 7 . 4 5 0 2 3 4 . 7 7 0 2 3 4 . 6 5 0 2 3 5 . 0 1 0 2 3 9 . 6 0 0 2 3 6 . 2 6 0 2 3 7 . 5 4 0 2 3 5 . 6 1 0 2 4 0 . 2 2 0 2 4 0 . 8 1 0 2 3 7 . 1 4 0 2 3 9 . 1 0 0 2 3 9 . 3 0 0 2 3 7 . 0 4 0 2 3 6 . 9 9 0 2 3 7 . e 4 0 2 3 5 . 5 6 0 2 4 0 . 1 6 0 2 3 7 . 9 0 0 2 3 6 . 5 3 0 2 3 6 . 9 0 0 2 3 6 . 8 8 0 2 3 8 . 4 8 0 2 4 2 . 1 1 0 2 3 4 . 6 8 0 2 3 8 . 2 9 0 2 3 7 . 4 2 0 2 3 5 . 3 0 0 2 3 6 . 4 8 0 2 3 5 . 1 0 0 2 3 6 . 5 8 0 2 3 7 . 7 2 0 2 3 6 . 0 0 0 2 3 4 . 3 6 0 2 3 1 . 9 3 0 2 3 7 . 3 3 0 2 3 4 . 0 4 0 2 3 3 . 7 9 0 2 3 2 . 2 7 0 2 3 3 . 3 5 0 2 3 1 . 3 6 0 2 3 4 . 0 8 0 2 3 0 . 8 7 0 2 3 1 . 0 2 0 2 3 0 . 9 7 0 2 2 8 . 2 6 0 2 2 7 . 0 1 0 2 2 5 . 5 9 0 2 2 8 . 5 0 0 2 2 5 . 0 1 0 2 2 4 . 3 9 0 2 2 4 . 7 9 0 2 2 6 . 0 4 0 2 2 3 . 3 8 0 2 2 4 . 1 2 0 2 2 5 . 2 9 0 2 2 5 . 0 0 0 2 2 0 . 9 1 0 2 2 5 . 0 2 0 2 2 2 . 3 3 0 2 2 4 . 8 8 0 2 2 3 . 5 3 0 2 2 3 . 6 1 0 2 1 9 . 9 5 0 2 2 1 . 0 0 0 2 2 1 . 0 2 0 2 1 9 . 6 5 0 2 1 7 . 8 6 0 2 1 8 . 9 6 0 2 1 9 . 9 7 0 2 2 0 . 9 9 0 770-^SO 2.17.630 2 1 9 . 6 7 0 7 2 0 . 8 9 0 2 1 7 . 3 3 0 2 2 2 . 3 4 0 2 1 9 . 0 5 0 2 2 0 . 8 7 0 2 2 1 . 1 0 0 2 2 1 . 0 1 0 2 2 1 . 9 6 0 2 2 3 . 6 4 0 2 2 2 . 6 3 0 2 7 4 . 5 6 0 2 2 3 . 8 7 0 2 2 6 . 6 0 0 2 2 5 . 6 0 0 2 2 4 . 8 5 0 2 2 4 . 9 5 0 2 2 7 . 1 3 0 2 2 8 . 3 3 0 2 2 8 . 9 7 0 2 2 6 . 6 4 0 2 2 6 . 8 6 0 2 2 9 . 1 6 0 2 3 1 . 2 6 0 2 2 7 . 0 6 0 2 3 1 . 4 6 0 2 3 2 . 2 4 0 2 3 2 . 9 1 0 2 3 0 . 9 0 0 2 3 4 . 0 0 0 2 3 0 . 4 7 0 2 3 4 . 9 2 0 2 3 6 . 8 1 0 2 3 4 . 7 6 0 2 3 3 . 6 2 0 2 3 4 . 5 8 0 2 3 6 . 1 9 0 2 3 6 . 8 7 0 2 3 6 . 5 1 0 2 3 4 . 4 3 0 2 3 7 . 6 3 0 2 3 6 . 2 2 0 2 3 7 . 1 9 0 2 3 9 . 0 2 0 2 3 8 , 0 3 0 2 4 0 . 8 9 0 2 3 6 . 6 2 0 2 3 6 . 7 9 0 2 3 9 . 1 7 0 2 3 9 . 9 6 0 2 4 0 . 0 * 0 2 4 1 . 9 3 0 2 4 2 . 1 2 0 2 3 9 . 6 7 0 2 3 9 . 9 1 0 2 3 9 . 3 3 0 2 4 2 . 2 1 0 2 4 4 . 6 2 0 2 4 1 . 6 0 0 2 4 2 . 7 9 0 2 4 5 . 0 4 0 2 4 4 . 9 0 0 2 4 3 . 8 3 0 2 4 3 . 2 0 0 2 4 2 . 5 0 0 2 * 3 . 1 6 0 2 * 5 . 0 4 0 2 * 5 . 3 2 0 2 * 1 . 5 7 0 2 4 3 . 3 9 0 2 4 3 , 3 5 0 2 * 1 . 4 5 0 2 4 2 . 9 8 0 2 4 3 . 9 6 0 7 4 5 . 0 * 0 Table XXIII. Computer Output,. Original X-Ray Intensities for (400) Reflection from Ni-Th0 o Cold Rolled 75%. F I N A L CORRECTFD I N T E N S I T Y VALUES -0.0 0 . 1 1 6 3 2 6 7 6 - 0 3 0 . 7 8 8 9 5 7 4 E -04 0 . 9 4 9 7 U 5 6 - 04 0 . 1 2 9 8 7 * 2 6 03 0 . 1 0 0 1 9 5 6 E - 0 3 0.106+5+6E -03 0 . U 9 1 + 3 9 E - 0 3 0 . 1 2 5 5 2 6 1 6 - 03 0 . 1 2 8 4 5 6 7 6 - 03 ^ 0 . 1 3 5 1 2 4 0 6 -03 0 . 1 4 5 3 4 1 1 E - 03 " 0 . 7 6 7 2 7 5 8 F 04 0 . 8 7 2 4 8 1 8 E -0+ 0 . 6 9 + 6 5 9 0 E -04 0 . 1 1 4 9 6 8 B E -03 0 . 1 4 7 3 2 1 5 6 - 0 3 0 . 6 0 1 6 7 3 6 E - 04 0 . 1 7 7 9 8 9 5 6 -03 0 . 1 9 9 8 6 9 7 E - 0 3 0 . 7 5 1 6 4 1 9 6 - C4 0 . 3 4 5 7 5 6 7 E -0 + 0 . 1 0 0 8 3 2 2 E -03 0 . 2 1 3 2 7 8 6 E -03 0.16453+06- 03 0 . 9 4 3 8 6 * 1 6 - 0* 0 . 1 2 6 0 5 4 R E -03 0 . 8 1 0 5 6 6 4 6 - 04 0 . 1 3 0 9 2 3 9 6 0 3 0 . 1 2 6 6 5 5 8 E - 0 3 0 . 5 7 2 3 2 * 1 6 0 4 0 . 1 3 5 1 8 7 + 6 -03 0.1993179F- 03 0 . 1 6 5 6 + 6 6 E - 03 0 . 1 5 7 8 3 7 9 6 -03 0 . 2 4 5 7 1 0 9 E - 0 3 Q . 2 9 4 B 3 1 1 E 0 3 0 . 3 6 9 6 4 2 6 E -03 0 . 3 5 7 9 9 9 0 E -03 0 . 3 0 7 3 0 9 7 E -03 0 . 2 3 0 0 1 9 6 E - 0 3 0 . 2 6 1 4 7 3 9 E - 0 3 0 . 2 8 8 6 5 4 6 6 -03 0 . 2 1 2 9 4 1 1 6 - 0 3 0 . 7 9 4 6 5 7 0 6 - 0 3 0 . 3 4 1 7 4 9 5 E -03 0 . 3 0 3 3 0 9 9 E 0 3 0 . 2 6 * 7 2 3 6 6 - 0 3 0 . 1 8 2 0 6 8 2 6 - 03 0 . 1 4 4 3 0 4 2 6 - OV 0 . 2 3 1 4 7 0 H F -03 0 . 7 4 2 9 3 1 9 E - 04 0 . 2 0 3 1 3 0 3 6 0 1 0 . 3 4 1 J 9 8 2 E - 0 3 0 . 3 7 6 2 5 3 + E 0 3 0 . 2 5 7 3 1 4 2 E -03 0 . 2 2 7 5 5 U E - 0 3 0 . 2 7 1 0 5 7 0 F - 0 3 6.35542416 -03 0 . 4 2 9 2 5 5 7 6 - 0 3 6.46620636- 0 3 0 . 4 0 9 0 0 4 0 E -03 0 . * 6 1 7 1 T 6 E - 0 3 0.3810T26E -03 0 . 2 6 Q C 9 9 5 E - 0 3 0 . 3 5 6 0 9 9 1 6 - 0 3 0 . 4 1 5 1 6 7 3 6 - 0 3 0 . 3 7 6 6 * 6 5 6 - 0 3 0.40T6T136-03 0.4+85999£ -03 0.3B6+875E--03 0 . 2 8 7 3 2 6 3 6 -03 0 . 3 6 1 8 3 1 4 6 - 0 3 0 . 3 2 6 7 0 2 + E - 03 0 . 3 3 0 6 6 6 5 6 - 0 3 0 . 4 7 2 5 5 8 0 E - 0 3 0.4887693E- 03 0 . 4 1 2 7 0 7 0 E - 0 3 0 . * 3 9 2 3 7 B E 0 3 0 . * 7 7 3 0 9 1 6 •oy 0 . 3 7 6 3 9 0 5 6 - 0 3 0 . 3 7 0 9 3 0 6 E - 0 3 0.4*327516 - 0 3 0.53323+6E- 0 3 0 . 5 9 7 8 9 5 1 E - 0 3 0.4787385E -03 0.3920+2BE- 0 3 0 . 5 * 5 7 3 8 7 E - 0 3 0.4996795E- 03 0.++07279E- 03 0.5371883E -03 0 . 6 1 3 8 4 8 2 6 - 0 3 0 . 5 7 7 * l * 9 E - 0 3 0 . 5 6 5 5 6 9 8 E -03 0 . * 9 8 * 4 * 1 E 0 3 0 . 5 6 3 9 7 7 8 E -03 0 . 6 1 3 2 1 9 3 6 - 0 3 0 . 6 7 8 1 3 7 2 E - 03 0 . 6 6 1 8 * 0 9 6 - 0 3 0.6592527E- 03 0 . 6 7 7 3 2 9 7 E - 03 0 . 6 8 2 1 5 5 8 E -03 0 . 5 T 9 0 7 3 6 E - 0 3 0 . 5 2 6 1 + 9 3 6 -03 0 . 7 3 5 7 2 2 9 E - 0 3 0.731+0++E- 03 O . T 2 1 0 7 1 6 E -03 0 . 7 6 7 8 9 9 + E - 0 3 0 . 7 8 7 5 6 9 2 E - 0 3 0.8257327E -03 0 . 8 5 3 4 B 8 5 E - 0 3 0 . 6 0 3 0 6 2 7 E -03 0 . 7 U 8 1 2 T E - 0 3 0.9+10628F- 0 3 0 . 1 0 0 1 9 2 9 E - 0 2 0.868+020E- 0 3 0 . 9 7 3 7 2 6 6 E - 0 3 0. 1 1 4 9 2 36 E -02 0 . 1 1 2 6 3 + 9 E - 02 0 . 9 T 6 8 2 3 5 E -03 0.11497556- 02 0 . 1 1 5 2 3 3 6 6 - 02 0 . 1 1 7 1 9 4 7 E -02 0 . l 2 B O a 0 6 E - 02 0 . 1 2 1 0 2 * 8 6 - 02 0 . 1 3 1 1 2 6 3 6 -02 0.1+19+356- 02 0 . 1 3 6 M 9 1 E - 0 2 0 . I 3 5 9 4 8 8 F - 02 0 . 1 5 4 4 9 3 7 E - 02 0 . 1 7 4 8 9 0 1 6 - 0 2 0 . 1 6 6 6 6 8 8 6 - 02 0 . 1 7 6 0 5 1 1 6 - 02 0 . 1 8 2 3 8 6 4 E -02 0 . 1 8 + + 9 0 6 E - 0 2 0 . 2 0 2 5 1 0 3 6 -02 0 . 2 1 3 1 6 2 8 E - 02 0 . 2 1 9 5 6 9 4 6 - 02 0 . 2 3 7 8 4 5 0 6 - 0 2 0 . 2 5 4 2 5 8 4 E - 02 0 . 2 5 1 9 3 9 6 6 - 02 0 . 2 7 0 3 2 8 3 E -02 0 . 3 0 2 2 0 6 3 6 - 0 2 0 . 3 2 6 2 2 2 3 E - 0 ? 0.3423759E- 02 0 . 3 5 8 6 8 8 1 E - 02 0 . 3 8 6 5 8 8 8 E -02 0 . 4 3 3 1 9 5 8 6 - 02 0 . 4 7 8 0 7 2 1 6 - 02 0.5105935£ -02 0.5+0+1676- 02 0 . 5 8 9 * 5 9 0 6 - -02 0 . 6 8 1 5 4 9 7 E - 02 0 . 7 1 6 5 2 6 8 E - 02 0 . 7 8 1 2 5 9 8 6 -02 0 . R 5 4 3 9 3 8 C - 02 0 . 9 4 2 0 4 2 5 6 - 02 0 . 1 0 5 + T T S E -01 0 . 1 1 7 4 0 9 T E - 0 1 0 . 1 2 9 5 1 6 4 6 - 0 1 0.1+3+705E- 01 0 . 1 6 0 4 2 0 T E - 01 0 . 1 7 8 9 3 0 7 E - 0 1 0 . 2 0 1 4 2 4 5 6 - 01 0 . 2 2 6 9 3 1 6 E - 01 0 . Z 6 3 6 1 6 7 E -01 0.30B120TE-OI 0.352T971E- 01 0.+078Q37E- 01 0 . 4 B 3 1 0 0 3 E - 01 0 . S 7 B 0 6 1 5 E -01 0 . 6 7 9 5 2 2 2 6 - 01 0.7647732E- 01 0 . 9 0 9 6 3 9 0 E -01 0 . 1 0 4 3 1 9 0 6 0 0 0 . 1 1 5 6 8 2 8 E 0 0 0.1264517E OO 0 . 1 3 1 9 6 6 9 F 00 0 . 1 3 3 6 9 0 S E 00 0 . 1 3 3 4 5 1 5 6 00 0 . 1 2 6 5 0 9 5 6 00 0 . 1 1 6 7 6 7 2 E 00 0 . 1 0 6 6 6 I TE 00 0 . 9 5 0 2 7 6 9 F - 0 1 0 . 8 3 6 9 4 2 2 E - 01 0 . 7 4 1 6 6 0 6 E - 01 0 . 6 4 5 2 5 4 3 E -01 0 . 5 4 2 0 7 3 2 6 - 01 0 . 4 8 7 2 4 2 9 F - 01 0 . + 7 9 * 5 3 8 6 -01 0 . 3 5 + 2 6 9 1 E - 0 1 0.32558++E- 01 0 . 2 9 0 0 2 8 5 E - 01 0 . 2 4 8 6 4 8 2 6 - 01 0 . 2 2 2 6 9 6 7 E -01 0 . 2 0 1 6 1 6 8 E - 01 0 . 1 6 9 1 3 6 2 E - 01 0 . 1 5 3 1 3 1 0 E -01 0 . 1 * 6 6 1 9 5 6 - 01 0 . 1 2 0 5 2 0 3 E - 0 1 0.7784825E- 02 0 . 9 9 9 3 0 9 1 6 - 02 0 . B 2 7 7 2 7 1 E -02 0 . 7 4 5 2 9 4 6 F - 02 0 . 6 9 6 2 6 4 6 E - 02 0 . 6 3 3 9 0 5 6 E -02 0 . 6 2 3 7 6 7 5 E - 02 0 . 6 3 * 0 * 1 1 6 - 0 2 0 . 5 0 6 3 1 9 2 E - 02 0 . 4 2 7 5 9 8 5 E - 02 0 . 4 4 8 3 4 B 7 E -02 0 . 5 7 9 1 2 5 + F - 02 0 . 3 8 3 3 8 0 8 6 - 02 0 . * 1 5 2 5 5 9 E -02 0 . 3 9 0 6 1 1 6 6 - 0 2 0 . 3 * 6 0 9 0 1 6 - 02 0 . 3 3 3 8 6 + 2 E - 02 0 . 2 8 7 2 0 7 0 6 - 02 0 . 1 4 3 7 1 7 2 E -02 0. 2 7 5 1 6 9 5 F - 02 0 . 2 8 7 5 7 5 6 F - 02 0 . 2 + 4 4 4 9 6 E -02 0 . 1 * 3 8 7 7 0 6 - 02 0 . 2 2 1 9 2 2 2 6 - 02 0 . 1 8 2 4 2 2 2 E - 02 0 . 1 7 R 4 9 9 8 E - 02 0. 1 6 0 6 1 9 2 6 -02 0. 1 6 1 9 6 5 3 6 - 02 0 . 1 6 + 6 + U E - 02 0 . 2 1 6 7 1 7 9 E -02 0 . 1 + 2 0 2 6 6 E - 02 0 . 1 2 8 8 7 0 7 F - 02 0.13738156- 02 0 . 1 6 3 6 + 5 7 E - 02 0. 1 3 0 1 5 4 9 E -02 0 . 1 3 9 * 5 6 3 6 - 02 0 . 1 2 6 M 0 6 E - 02 0 . 1 2 2 5 1 9 6 E -02 0.1 1 2 7 2 6 7 E - 0 2 0 . 1 0 3 7 2 6 2 6 - 0 2 0.65101756- 03 0 . 9 0 + 6 9 2 5 6 - 03 0 . 1 1 1 1 3 7 4 6 -02 0 . 9 7 5 2 3 * 0 6 - 0 3 0 . 7 2 4 0 4 8 6 E - 03 0 . 7 9 4 6 0 1 6 E -03 0 . 7 3 6 5 5 0 * 6 - 0 3 0 . 7 5 1 6 3 3 * E - 0 3 0 . 7 B 2 5 1 1 2 E - 0 3 0 . 7 + 3 7 0 1 1 E - 0 3 ~ 0 . 7 0 3 5 3 2 7 E -03 0 . 8 9 7 9 1 5 3 6 - OJ " b . 6 6 6 3 8 8 B E - 03 0 . 5 2 2 1 2 0 6 E -03 0 . 5 5 7 9 8 2 6 E - 0 3 0 . 5 7 1 7 I 3 1 E - 0 3 0.+319167E- 03 0 . 4 7 5 9 7 8 5 6 - 0 3 0 . 4 8 0 9 4 7 3 E - 0 3 0 . 4 4 1 5 7 C 5 E - 01 0 . 3 9 5 8 0 9 6 6 - 0 3 0 . + 0 6 6 9 4 4 E -C3 0 . 3 9 9 7 2 9 5 6 - 0 3 0 . 4 8 1 6 5 2 B E - 0 3 0.+ 3 7 3 2 7 7 E - 03 0 . 3 8 3 2 7 7 2 F - 0 3 0 . 3 3 7 4 9 4 5 E -03 0 . 3 1 5 2 9 6 7 E - 0 3 0 . 3 * 3 2 U 7 f - 0 3 0 . 3 4 2 5 7 5 6 E -03 0 . 3 * 9 0 8 8 3 6 - 0 3 0 . 3 6 7 9 6 5 1 6 - 0 3 0.3074792E- 03 0 . 2 1 5 1 1 0 0 E - 03 0 . 8 5 3 8 6 8 0 F -04 0 . 2 1 9 4 7 2 7 E - 0 3 0 . 1 9 0 * 5 I 6 E - 0 3 0 . 2 2 2 1 6 5 4 E -03 0 . 2 3 3 7 5 3 0 6 - 0 3 0 . 1 7 3 0 3 2 6 6 - 0 3 0.186833+6- 0 3 0 . 1 6 6 0 5 B B E - 0 3 0 . 6 8 1 2 5 7 8 6 -04 0 . 5 5 7 8 2 1 5 E - 04 0 . 1 2 5 5 0 7 5 E - 03 0 . 1 6 6 0 3 7 8 E -03 0 . 1 5 5 8 6 8 2 E - 0 3 0 . 2 1 6 4 1 7 1 6 - 0 3 0 . 1 2 9 6 7 1 9 6 - 0 3 0 . 1 7 1 2 2 3 7 E - 0 3 0 . 9 3 5 6 9 8 0 E -04 0 . 5 1 1 9 0 4 4 F - 04 0 . 1 0 2 9 6 9 1 F - 03 0 . 1 7 8 6 2 9 3 E -03 0 . 2 2 + 2 6 7 5 6 - 0 3 0. 1 8 4 3 0 5 9 E - 03 0.1662625E- 03 0 . 1 1 + 3 9 8 7 E - 03 0 . 6 5 6 7 9 6 3 E -04 " 6.18 764 70E-0*3~ 6 7 i 9 6 3 3 l * E - 0 3 0 . 2 2 3 0 5 9 5 E -03 0 . 1 0 9 7 2 2 2 E - 0 3 0 . 1 3 7 8 6 5 2 E - 0 3 0 . B 2 7 1 7 1 6 E - 04 0 . 1 0 8 6 0 3 2 F - 0 3 0.0 0.0 0 . 1 0 1 3 3 I 3 E - 01 0 . 5 9 4 8 9 4 1 E -0+ 0.0 0 . 5 9 8 9 7 9 1 6 - 0 4 0 . 4 1 9 6 9 6 8 6 - 04 0 . 7 7 9 9 5 0 B E - 04 0 . 1 0 4 9 6 2 1 6 -03 0 . 6 1 2 7 0 1 2 6 - 05 0 . 6 7 3 9 9 6 6 E - 04 0 . 1 5 0 7 8 1 6 E -03 0 . I 3 6 8 6 + 6 E - 0 3 0 . 6 3 8 2 9 5 0 E - 0* 0.0 0 . 6 5 9 7 8 3 8 E - 04 0 . 1 0 9 1 0 9 4 6 -03 0 . 6 7 4 0 0 2 5 6 - 04 0. I 0 5 9 0 3 5 E - 01 0 . 9 1 5 5 2 8 9 E -0+ 0. 1 5 6 5 S 6 1 E -0 3 0 . 9 8 0 4 5 7 6 F - 0* 0 . 6 5 1 1 3 4 2 E - 05 0 . 5 4 9 2 5 5 6 E - 04 0 . 1 5 1 2 0 8 6 6 -03 0 . 2 7 2 0 9 1 7 6 - 0 3 0 . 4 3 0 8 2 1 7 E - 04 0 . 1 J 5 6 8 6 3 E -03 0 . 1 6 9 2 1 9 0 6 - 0 3 0 . I B 7 1 5 3 9 E - 0 3 0 . 1 7 7 4 9 1 6 6 - 0 3 0 . 1 6 4 4 6 3 0 E - 03 0. 1 6 6 4 8 3 3 6 -03 0 . 2 B 0 3 2 7 2 6 - 03 0 . 2 5 0 2 7 5 9 E - 03 0 . 2 5 8 8 1 ) 5 6 -03 0 . 2 6 9 9 + 1 1 E - 0 3 0 . 4 3 7 7 1 6 * 6 - 0 3 0 . 3 I 5 8 3 0 8 E - 0 3 0 . 3 5 8 8 2 6 5 E - 0 3 * " 6.41391636 -03 0 . 4 0 1 8 9 9 0 E - 0 3 0 . 3 6 3 5 5 3 6 E - 0 3 0 . 4 5 4 1 9 3 9 E -03 0 . 3 5 6 0 4 5 6 6 - 03 0 . 3 3 5 8 5 6 1 E - 0 3 0 . 3 9 6 4 2 7 9 F - 0 3 0 . 4 1 8 4 1 2 5 F - 03 0 . 2 9 4 7 3 4 7 E -03 0 . 3 4 1 6 * 6 1 6 - 0 3 0 . 1 1 2 7 5 0 7 E - 03 0 . 2 6 9 7 3 2 6 E -03 0 . + 2 2 5 7 5 5 E - 0 3 0 . 4 2 1 4 6 6 3 F - 03 0 . 3 7 0 1 3 6 1 6 - 0 3 0 . 4 7 7 8 9 9 8 6 - 0 3 0 . 5 4 2 6 8 0 3 6 -03 0 . 4 5 9 3 5 O 6 E - 0 3 0 . 1 9 8 6 6 6 4 E - 0 3 0 . 44 302 8 3 6 -03 0 . 4 9 3 8 2 5 6 F - 0 3 0 . 4 9 7 4 4 5 0 6 - 03 0 . 4 3 8 0 2 5 2 F - 0 3 0 . 4 8 1 8 6 5 6 F - 01 0 . 3 0 3 7 2 6 4 E -03 0 . 4 4 6 1 9 1 3 F - 03 0 . 3 1 5 5 7 2 B E - 03 0 . 2 7 2 1 9 3 9 E -03 0 . 2 9 9 1 1 1 0 E - 0 3 0 . 2 6 9 6 8 6 36- 03 0 . 2 2 4 9 5 2 4 E - 03 0 . 1 6 3 9 9 6 6 E - 0 3 0 . 1 5 6 4 3 5 6 E -03 0 . 8 6 9 2 3 3 6 6 - 04 0 . 9 3 3 6 7 4 2 E - 0* 0 . 2 0 8 6 1 2 4 E -03 0 . 1 U 6 1 7 4 F - 0 1 0 . 9 1 0 9 2 3 1 E - 0* 1 0 . 6 7 0 9 1 7 8 E - 04 0 . 8 6 0 1 6 1 2 E - 04 0.1 3 0 8 0 9 1 6 -03 0.761 1944E- 04 0 . 1 2 1 8 7 9 9 E - 04 0 . 1 5 9 8 3 9 9 E -03 0 . 2 + 8 6 8 9 9 6 - 0+ 0.0 0.0 0.0 0 . 3 6 2 8 3 7 5 E -05 0.0 0.0 0.0 0.0 0.0 ! 0.0 n.o -0.0 - 0 . 0 - 0 . 0 0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 -0.0 . -0.0 -0.0 - 0 . 0 - 0 . 0 -0.0 -0.0 - 0 . 0 - 0 . 0 -0.0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 - 0 . 0 . _0.«A56& 1 J E-09 : ! Table XXIV. Computer Output. Final Corrected X-Ray Intensities for (400) Reflection from Ni-Th02 Cold Rolled 75%. 218 CORRESPONDING VALUES OF S I N E THETA l.034B5-0,,_03465-:0. 0 3 4 * 1 6 - 0 . 0 1 * 2 6 - 0 . 0 3 * 0 6 - 0 . 0 3 3 8 7 - 0 . 0 3 3 6 T-Q.O 33". 7 - 0 . 0 3 3 2 6 - 0 . 0 3 3 0 8 - 0 . 0 3 2 8 8 7 0 . 0 3 2 6 9 - 0 . 0 3 2 4 9 - 0 . 0 3 2 2 9 - 0 . 0 3 2 0 9 - 0 . 0 3 1 9 0 - 0 . 0 3 1 * 0 - 0 . 0 3 1 5 0 - 0 . 0 3 1 3 1 - 0 . 0 3 1 1 1 - 0 . 0 3 0 9 1 - 0 . 0 3 0 7 2 - 0 . 0 3 0 5 2 - 0 . 0 3 0 3 2 - 0 . 6 3 0 1 2 - 0 . 0 2 9 9 3 - 0 . 0 2 9 7 3 - 0 . 0 2 9 5 3 - 0 . 0 2 9 3 4 - 0 . 0 2 9 1 4 - 0 . 0 2 8 9 4 - 0 . 0 2 B 7 5 - 0 . 0 2 B 5 5 - 0 . 0 2 8 3 5 - 0 . 0 2 B 1 5 - 0 . 0 2 7 9 6 - 0 . 0 2 7 7 6 - 0 . 0 2 7 5 6 - 0 . 0 2 7 3 7 - 0 . 0 2 7 1 7 - 0 . 0 2 6 9 7 - 0 . 0 2 6 7 B - 0 . 0 2 6 5 8 - 0 . 0 2 6 3 8 - 0 . 0 2 6 1 8 - 0 . 0 2 5 9 9 - 0 . 0 2 5 7 9 - 0 . 0 2 5 5 9 - 0 . 0 2 5 4 0 - 0 . 0 2 5 2 0 - 0 . 0 2 5 0 0 - 0 . 0 2 4 B 1 - 0 . 0 2 4 6 1 - 0 . C 2 4 4 1 - C . 0 2 4 2 1 - 0 . 0 2 4 0 2 - 0 . 0 2 3 8 2 - 0 . 0 2 3 6 2 - 0 . 0 2 3 4 3 - 0 . 0 2 3 2 3 - 0 . 0 2 3 0 3 - 0 . 0 2 2 8 4 - 0 . 0 2 2 6 4 - 0 . 0 2 2 4 4 - 0 . 0 2 2 2 4 - 0 . 0 2 2 0 5 - 0 . 0 2 1 8 5 - 0 . 0 7 1 6 5 - 0 . 0 2 1 4 6 - 0 . 0 2 1 2 6 - 0 . 0 2 1 0 6 - 0 . 0 2 0 8 7 - 0 . 0 2 0 6 7 - 0 . 0 2 0 4 7 - 0 . 0 2 0 2 7 - 0 . 0 2 0 0 8 - 0 . 0 1 9 8 8 - 0 . 0 1 9 6 8 - 0 . 0 1 9 4 9 - 0 . 0 1 9 2 9 - 0 . 0 1 9 0 9 - 0 . 0 1 8 9 0 - 0 . 0 1 8 7 0 - O . O I B 5 0 - 0 . 0 1 8 3 0 - 0 . 0 1 8 1 1 - 0 . 0 1 7 9 1 - 0 . 0 1 7 7 1 - 0 . 0 1 7 5 2 - 0 . 0 1 7 3 2 - 0 . 0 1 7 1 2 - 0 . 0 1 6 9 3 - 0 . 0 1 6 7 3 - 0 . 0 1 6 5 3 - 0 . 0 1 6 3 3 - 0 . 0 1 6 1 4 - 0 . 0.1.594-0. 0 1 5 7 4 - 0 . 0 1 5 5 5 - 0 . 0 1 5 3 5 - 0 . 0 1 5 1 5 - 0 . 0 1 4 9 6 - 0 . 0 1 4 7 6 - 0 . 0 1 4 5 6 - 0 . 0 1 4 3 6 - 0 . 0 1 4 1 7 - 0 . 0 1 3 9 7 - 0 . 0 1 3 7 7-0. 01 3 5 8 - 0 . 0 1 3 3 8 - 0 . 0 1 3 1 8 - 0 . 0 1 2 9 9 - 0 . 0 1 2 7 9 - 0 . 0 1 2 5 9 - 0 . 0 1 2 3 9 - 0 . 0 1 2 2 0 - 0 . 0 1 2 0 0 - 0 . 0 1 1 8 0 - 0 . 0 1 1 6 1 - 0 . 0 1 1 4 1 - 6 . o i l 2 1 - 0 . 0 1 1 0 2 - 0 . 0 1 0 8 2 - 0 . 0 1 0 6 2 - 0 . 0 1 0 4 2 - 0 . 0 1 0 2 3 - 0 . 0 1 0 0 3 - 0 . 0 0 9 8 3 - 0 . 0 0 9 6 4 - 0 . 0 0 9 4 4 - 0 . 0 0 9 2 4 - 0 . 0 0 9 0 5 - 0 . 0 0 8 8 5 - 0 . 0 0 8 6 5 - 0 . 0 0 8 4 5 - 0 . 0 0 8 2 6 - 0 . 0 0 8 0 6 - 0 . 0 0 7 8 6 - 0 . 0 0 7 6 7 - 0 . 0 0 7 4 7 - 0 . 0 0 7 2 7 - 0 . 0 0 7 0 8 - 0 . 0 0 6 B 8 - 0 . 0 0 6 6 8 - 0 . 0 0 6 4 8 - 0 . 0 0 6 2 9 - 0 . 0 0 6 0 9 - 0 . 0 O 5 B 9 - 0 . 0 0 5 7 0 - 0 . 0 0 5 5 0 - 0 . 0 0 5 3 0 - 0 . 0 0 5 1 1 - 0 . 0 0 4 9 1 - 0 . 0 0 4 7 1 - 0 . 0 0 4 5 1 - 0 . 0 0 4 3 2 - 0 . 0 0 4 1 2 - 0 . 0 0 3 9 2 - 0 . 0 0 3 7 3 - 0 . 0 0 3 5 3 - 0 . 0 0 3 3 3 - 0 . 0 0 3 1 4 - 0 . 0 0 2 9 4 - 0 . 0 0 2 7 4 - 0 . 0 0 2 5 5 - 0 . 0 0 2 3 5 - 0 . 0 0 2 1 5 - 0 . 0 0 1 9 5 - 0 . 0 0 1 7 6 - 0 . 0 0 1 5 6 - 0 . 0 0 1 3 6 - 0 . 0 0 1 1 7 - 0 . 0 0 0 9 7 - 0 . 0 0 0 7 7 r O . 0 0 0 5 8 - 0 . 0 0 0 3 8 - 0 . 0 0 0 1 8 0 . 0 0 0 0 2 0 . 0 0 0 2 1 0 . 0 0 0 4 1 0 . 0 0 0 6 1 0 . 0 0 0 8 0 0 . 0 0 1 0 0 0 . 0 0 1 2 0 0 . 0 0 1 3 9 0 . 0 0 1 5 9 0 . 0 0 1 7 9 0 . 0 0 1 9 9 0 . 0 0 2 1 8 0 . 0 0 2 3 8 0 . 0 0 2 5 8 0,QQ277 0 . 0 0 2 9 7 0 . 0 0 3 1 7 0 . 0 0 3 3 6 0 . 0 0 3 5 6 0 . 0 0 3 7 6 0 . 0 0 3 9 6 0 . 0 0 4 1 5 0 . 0 0 4 3 5 0 . 0 0 4 5 5 0 . 0 0 4 7 4 0 . 0 0 4 9 4 0 . 0 0 5 1 4 0 . 0 0 5 3 3 0 . 0 0 5 5 3 0 . 0 0 5 7 3 0 . 0 0 5 9 3 0 . 0 0 6 1 2 0 . 0 0 6 3 2 0 . 0 0 6 5 2 0 . 0 0 6 7 1 0 . 0 0 6 9 1 0 . 0 0 7 1 1 0 . 0 0 7 3 0 0 . 0 0 7 5 0 0 . 0 0 7 7 0 0 . 0 0 7 9 0 0 . 0 0 8 0 9 0 . 0 0 6 2 9 0 . 0 0 6 4 9 0 . 0 0 8 6 8 0 . 0 0 8 8 6 0 . 0 0 9 0 8 0 . 0 0 9 2 7 0 . 0 0 9 4 7 0 . 0 0 9 6 7 0 . 0 0 9 8 7 0 . 0 1 0 0 6 0 . 0 1 0 2 6 0 . 0 1 0 4 6 0 . 0 1 0 6 5 0 . 0 1 0 8 5 0 . 0 1 1 0 5 0 . 0 1 1 2 4 0 . 0 1 1 4 4 0 . 0 1 1 6 4 0 . 0 1 1 6 4 0 . 0 1 2 0 3 0 . 0 1 2 2 3 0 . 0 1 2 4 3 0 . 0 1 2 6 2 0 . 0 1 2 8 2 0 . 0 1 3 0 2 0 . 0 1 3 2 1 0 . 0 1 3 4 1 0 . 0 1 3 6 1 0 . 0 1 3 8 1 0 . 0 1 4 0 0 0 . 0 1 4 2 0 0 . 0 1 4 4 0 0 . 0 1 4 5 9 0 . 0 1 4 7 9 0 , 0 1 4 9 9 0 . 0 1 5 1 8 0 . 0 1 5 3 8 0 . 0 1 5 5 8 0 . 0 1 5 7 8 0 . 0 1 5 9 7 0 . 0 1 6 1 7 0 . 0 1 6 3 7 0 . 0 1 6 5 6 0 . 0 1 6 7 6 0 . 0 1 6 9 6 0 . 0 1 7 1 5 0 . 0 1 7 3 5 0 . 0 1 7 5 5 0 . 0 1 7 7 5 0 . 0 1 7 9 4 0 . 0 1 8 1 4 0 . 0 1 8 3 4 0 . 0 1 8 5 3 0 . 0 1 8 7 3 0 . 0 1 8 9 3 0 . 0 1 9 1 2 0 . 0 1 9 3 2 0 . 0 1 9 5 2 0 . 0 1 9 7 2 0 , 0 1 9 9 1 0 . 0 2 0 1 1 0 . 0 2 0 3 1 0 . 0 2 0 5 0 0 . 0 2 0 7 0 0 . 0 2 0 9 0 0 . 0 2 1 0 9 0 . 0 2 1 2 9 0 . 0 2 1 4 9 0 . 0 2 1 6 9 0 . 0 2 1 8 8 0 . 0 2 2 0 8 0 . 0 2 2 2 8 0 . 0 7 7 4 7 0_. 0 2 2 6 7 0.022B.7._0.02306 0 . 0 2 3 2 6 0 . 0 2 3 4 6 0 . 0 2 3 6 6 0 . 0 2 3 8 5 0 . 0 2 4 0 5 0 . 0 2 4 2 5 0 . 0 2 4 4 4 0 . 0 2 4 6 4 0 . 0 2 4 8 4 0 . 0 2 5 0 3 0 . 0 2 5 2 3 0 . 0 2 5 4 3 0 . 0 2 5 6 2 0 . 0 2 5 8 2 0 . 0 2 6 0 2 0 . 0 2 6 2 2 0 . 0 2 6 4 1 6 . 0 2 6 6 1 0 . 0 2 6 8 1 0 . 0 2 7 0 0 0 . 0 2 7 2 0 0 . 0 2 7 4 0 0 . 0 2 7 5 9 0 . 0 2 7 7 9 0 . 0 2 7 9 9 0 . 0 2 8 1 9 0 . 0 2 8 3 8 0 . 0 2 8 5 8 0 . 0 2 8 7 6 0 . 0 2 8 9 7 0 . 0 2 9 1 7 0 . 0 2 9 3 7 0 . 0 2 9 5 6 0 . 0 2 9 7 6 0 . 0 2 9 9 6 0 . 0 3 0 1 6 0 . 0 3 0 3 5 0 . 0 3 0 5 5 0 . 0 3 0 7 5 0 . 0 3 0 9 4 0 . 0 3 1 1 4 0 . 0 3 1 3 4 0 . 0 3 1 5 3 0 . 0 3 1 7 3 0 . 0 3 1 9 3 0 . 0 3 2 1 3 0 . 0 3 2 3 2 . 0 . 0 3 2 5 2 0 . 0 3 2 7 ? 0 . 0 3 2 9 1 0 . 0 3 3 1 1 0 . 0 3 3 3 1 0 . 0 3 3 5 0 0 . 0 3 3 7 0 0 . 0 3 3 9 0 0 . 0 3 4 1 0 0 . 0 3 4 2 9 0 . 0 3 4 4 9 0 . 0 3 4 6 9 0 . 0 3 4 8 8 0 . 0 3 5 0 8 0 . 0 3 5 2 8 0 . 0 3 5 4 7 0 . 0 3 5 6 7 0 . 0 3 5 8 7 0 . 0 3 6 0 7 0 . 0 3 6 2 6 0 . 0 3 6 4 6 0 . 0 3 6 6 6 0 . 0 3 6 8 5 0 . 0 3 7 0 5 0 . 0 3 7 2 5 0 . 0 3 7 4 4 0 . 0 3 7 6 4 0 . 0 3 7 8 4 0 . 0 3 6 0 4 0 . 0 3 8 2 3 0 . 0 3 8 4 3 0 . 0 3 8 6 3 0 . 0 3 8 6 2 0 . 0 3 9 0 2 0 . 0 3 9 2 2 0 . 0 3 9 4 1 0 . 0 3 9 6 1 0 . 0 3 9 8 1 0 . 0 4 0 0 1 0 . 0 4 0 2 0 0 . 0 4 0 4 0 0 . 0 4 0 6 0 0 . 0 4 0 7 9 0 . 0 4 0 9 9 0 . 0 4 1 1 9 0.041 38. 0 . 0 4 1 5 8 0 . 0 4 1 7 8 0 . 0 4 1 9 8 0.Q4217_ 0.04237_ 0 . 0 4 2 5 7 0 . 0 4 2 7 6 0 . 0 4 2 9 6 0 . 0 4 3 1 6 0 . 0 4 3 3 5 0 . 0 4 3 5 5 0 . 0 4 3 7 5 0 . 0 4 3 9 5 0 . 0 4 4 1 4 0 . 0 4 4 3 4 0 . 0 4 4 5 4 6 . 0 4 4 7 3 0 . 0 4 4 9 3 0 . 0 4 5 1 3 0 . 0 4 5 3 2 0 . 0 4 5 5 2 " 6.04572 0 . 0 4 5 9 2 0 . 0 4 6 1 1 0 . 0 4 6 3 1 0 . 0 4 6 5 1 0 . 0 4 6 7 0 0 . 0 4 6 9 Q 0 . 0 4 7 1 0 0 . 0 4 7 2 9 0 . 0 4 7 4 9 0 . 0 4 7 6 9 0 . 0 4 7 8 9 0 . 0 4 8 0 6 0 . 0 4 8 2 8 0 . 0 4 8 4 8 0 . 0 4 8 6 7 0 . 0 4 8 8 7 0 . 0 4 9 0 7 0 . 0 4 9 2 6 0 . 0 4 9 4 6 0 . 0 4 9 6 6 0 . 0 4 9 8 6 Table XXV. Computer Output. Sin 0 Values for (400) Reflection from Ni-Th0 2 Cold Rolled 75%. S I N E THETA INTERVAL - 0 . 0 0 0 2 0 NUMBER DF S I N E THETA DATA POINTS - 4 3 3 A R T I F I C I A L L A T T I C E PARAMETER * 7 . 7 2 4 9 ? ANGS_TRC?~_5 ; TWO THETA ZERO I CENTRE CF G R A V I T Y ) - 1 2 1 . 8 3 4 DEGREES L A T T I C E PARAMETER (CENTRE OF G R A V I T Y ) - 3 . 5 2 5 5 3 ANGSTROMS TWO THETA ZERO ( P E A K MAXIMUM) - 1 2 1 . 8 4 8 DEGREES 1 ATT I C E PARAMETER ( P E A K MAXIMUM) • 3 . 5 2 5 2 9 ANGSTROMS  PEAK ASYMMETRY - - 0 . 0 1 4 DEGREES Table XXVI. Computer Output. from Ni-Th02 Cold Peak Parameters for (400) Reflection Rolled 75%. 219 D I S T I L 1 I ANGSTROMS I 0.0 5.0 10.0 15.0 2 0 . 0 2 5 . 0 30.0 35.0 4 0 . 0 4 5 . 0 5 0 . 0 ...55, 0 6 0 . 0 6 5 . 0 9 0 . 0 9 5 . 0 1 0 0 . 0 1 0 5 . 0 1 1 0 . 0 USO 1 2 0 . 0 1 2 5 . 0 1 3 0 . 0 1 3 5 . 0 1 4 0 . 0 1*9.0 1 5 0 . 0 1 5 5 . 0 1 6 0 . 0 1 6 5 . 0 170.0 1 7 5 . 0 1 8 0 . 0 1 8 5 . 0 1 9 0 . 0 1 9 5 . 0 2 0 0 . 0 2 0 5 . 0 2 1 0 . 0 2 1 5 . 0 2 2 0 . 0 2 2 5 . 0 2 30.0 _.235.0 2 4 0 . 0 2 4 5 . 0 2 5 0 . 0 2 5 5 . 0 2 6 0 . 0 7 7 0 . 0 2 7 5 . 0 7 8 0 . 0 2 8 5 . 0 2 9 0 . 0 ....295.0 3 0 0 . 0 3 0 5 . 0 3 1 0 . 0 3 1 5 . 0 3 2 0 . 0 3 2 5 . 0 3 3 0 . 0 3 3 5 . 0 3 4 0 . 0 3 4 5 . 0 3 5 0 . 0 3 5 5 . 1 . 0 0 0 0 0 . 9 9 8 3 0 . 9 9 3 3 0 . 9B58 0 . 9 7 6 4 0 . 9 6 5 8 0 . 9 5 4 0 0 . 9 4 1 4 0 . 9 2 7 8 0 . 9 1 3 5 0 . 8 9 8 9 0 . 8 8 4 1 0 . 8 6 9 1 0 . 8 5 4 0 0 . 8 3 8 5 0 . 8 2 2 6 0 . 8 0 6 4 0 . 7 9 0 2 0 . 7 7 4 5 0 . 7 5 9 4 0 . 7 4 4 7 0 . 7 3 0 2 0 . 7 1 5 6 C . 7 0 0 9 0 . 6 8 6 1 0 . 6 7 1 5 0 . 6 5 7 2 0 . 6 4 3 3 0 . 6 2 9 7 0 . 6 1 6 2 0 . 6 0 2 9 0 . 5 9 0 0 0 . 5 7 7 3 0 . 9 6 4 9 0 . 5 5 2 7 0.5405, 0 . 5 2 8 2 0 . 5 1 6 0 0 . 5 0 4 0 0.4924 0 . 4 8 1 2 0 . 4 7 0 3 0 . 4 5 9 7 0 . 4 4 9 1 0 . 4 3 8 7 0.4284 0 . 4 1 B 3 _0.>0H4 " 0 . 3 9 8 7 0 . 3 P 9 0 0 . 3 7 9 4 0 . 3 7 0 1 0 . 3 6 1 2 . 0.3577, 0 . 3 4 4 6 0 . 3 3 6 5 0 . 3 2 8 4 0 . 3 2 0 1 0 . 3 1 1 8 0..3Q35., 0 . 2 9 5 6 0 . 2 8 8 1 0 . 2 8 0 8 0 . 2 7 3 7 0 . 2 6 6 6 0.2598. . 0 . 2 5 3 2 0 . 2 4 6 9 0 . 2 4 1 0 0 . 2 3 5 2 0 . 2 7 9 4 0 . 2 2 3 6 0.0 0 . 0 0 0 3 0.0017 0 . 0 0 3 3 0 . 0 0 6 5 _ 0 ? _ 0 . 0 5 _ 0 . 0 1 4 9 0 . 0 1 9 4 0 . 0 2 4 0 0 . 0 2 8 6 0 . 0 3 3 2 0 . 0 3 7 6 0 . 0 4 1 5 0 . 0 4 4 7 0 . 0 4 7 5 0.C500 0 . 0 5 2 5 0 . 0 5 5 2 0.058*0' 0 . 0 6 0 7 0 . 0 6 3 0 0 . 0 6 4 8 0 . 0 6 6 2 0 . 0 6 7 7 0 . 0 6 9 3 0 . 0 7 1 2 0 . 0 7 3 3 0 . 0 7 5 3 0 . 0 7 7 3 0 . 0 7 9 2 0 . 0 3 1 0 0.0R28 0 . 0 8 4 5 0 . 0 8 5 9 0.C870 _ 0 i 0 B 7 B _ 0 . 0 8 8 6 0.0894 0.0904 0 . 0 9 1 4 0 . 0 9 2 3 0 . 0 9 3 1 0.09 36 0.09 39 0 . 0 9 4 2 0 . 0 9 4 5 0 . 0 9 4 9 0.0951 0 . 0 9 5 3 0 . 0 9 5 5 0 . 0 9 5 7 0 . 0 9 6 1 0.0964 _ 0 . 0 ? A 6 . 0 .0964 0 . 0 9 5 8 0 . 0 9 4 8 0 . 0 9 3 7 0 . 0 9 7 7 _ P . C 9 1 9 0 . 0 9 1 1 0 . 0 9 0 3 0 . 0 8 9 * 0 . 0 8 8 3 0 . 0 8 7 2 0 f 0 6 6 3 0.0854 0 . 0 8 4 6 0 . 0 8 3 8 0 . 0 8 2 7 0 . 0 B 1 6 1.0000 0 . 9 6 1 7 0 . 9 2 6 2 0 . 9 0 3 7 0 . 8 7 3 4 0 . 8 4 2 5 _ 0 . 8 0 8 6 0 . 7 7 6 0 0 . 7 4 ) 7 0 . 7 0 5 8 0 . 6 6 9 0 0 . 6 2 9 9 0 . 5 B 9 1 0 . 5 4 7 3 0 . 5 0 4 6 0 . 4 6 7 2 0 . 4 2 0 5 0. 379 3 0.3 394 0 . 3 0 0 5 0 . 7 6 2 8 0 . 2 2 5 7 0. 18 9 5 _ 0 . 1 5 4 6 _ 0 . 1 2 1 3 0 . 0 8 9 7 0 . 0 6 0 1 0 . 0 3 2 1 0 . 0 0 6 4 - 0 . 0 1 7 5 _ - 0 . 0 4 0 2 - 0 . 0 6 1 0 - 0 . 0 8 0 4 - 0 . 0 9 7 9 - 0 . 1 1 3 7 - 0 . 1 2 7 9 - 6.1401 - 0 . 1 5 0 9 - 0 . 1598 - 0 . 1675 - 0 . 1 7 4 1 - 0 . 1791 - 0 . 1 8 3 1 - 0 . 1 8 5 8 - 0 . 1 8 7 3 - 0 . 1 1 7 6 - 0 . 1866 - 0 . 1 8 4 7 - 0 . 1820 - 0 . 1 7 8 5 - 0 . 1 7 4 3 - 0 . 16*95 - 0 . 1 6 4 3 -,0 . . 1 5 f l 4 _ - 0 . 1 5 2 2 - 0 . 1 4 5 1 - 0 . 1 3 8 1 - 0 . 1 3 0 7 - 0 . 173 0 - 0 . 1 155 - 0 . 1 0 7 3 - 0 . 0 9 9 8 - 0 . 0 9 1 9 - 0 . 0 8 4 2 - 0 . 0 7 6 6 - 0 . 0 6 9 0 _ - 0 . 0 6 1 8 - 0 . 0 5 4 5 - 0 . 0 4 7 8 - 0 . 0 4 1 4 .0352 . 0 2 9 6 0.0 - 0 . 0 2 2 5 - 0 . 0 9 3 9 - 0 . 1 4 9 2 - 0 . 1 9 9 2 . - 0 . 2 8 0 5 - 0 . 3 1 5 8 - 0 . 3 4 8 3 - 0 . 3 7 9 2 - 0 . 4 0 8 5 - 0 . 4 3 4 7 - 0 . 4 5 8 6 -0.47(36 - 0 . 4 9 4 9 - 0 . 5 0 7 7 - 0 . 5 1 6 6 7-0.5226 - 0 . 5 2 6 3 - 0 . 5 2 7 8 - 0 . 5 2 7 0 - 0 . 5 2 4 0 - 0 . 5 1 9 1 - 0 . 5 1 2 0 - 0 . 5 0 2 5 - 0 . 4 9 1 2 - 0 . 4 7 8 1 - 0 . 4 6 3 8 - 0 . 4 4 8 8 - 0 . 4 3 2 4 _ - 6.4156 - 0 . 3 9 8 0 - 0 . 3 7 9 7 - 0 . 3 6 0 9 - 0 . 3 4 1 1 - 0 . 3 2 1 4 - 0 . 3 0 1 4 - 0 . 2 8 1 4 - 0 . 2 6 1 9 - 0 . 2 4 2 2 - 0 . 2 2 3 2 -0._7043 _ - 0 . 1 8 56 - 0 . 1 6 7 3 - 0 . 1 4 9 4 - 0 . 1 3 2 1 - 0 . ! 1 5 3 - 0 . 0 9 9 2 - 0 . 0 6 3 9 - 0 . 0 6 9 3 - 0 . 0 5 5 6 - 0 . 0 4 2 3 - 0 . 0 2 9 7 r P i 0 l 7 . 9 _ _ - 0 . 0 0 6 7 0 . C 0 3 5 0 . 0 1 3 5 0 . 0 2 2 0 0.0304 _0.OJW3 0~~0442 ~ 0 . 0 5 0 3 0 . 0 5 5 7 0 . 0 6 0 7 0 . 0 6 5 0 . 0.0687.. 0 . 0 7 1 9 0 . 0 7 4 3 0 . 0 7 6 5 0 . 0 7 7 5 . 0 7 8 4 . 0 7 8 5 1.0000 0 . 9 6 3 3 0 . 9 3 2 3 0.9161 0.8931 _ 0 . J 6 ? 6 _ 0 . 8 4 2 8 0.8171 0.7 892 0.75B9 0.7264 0.6903 0 . 6 5 1 2 0 . 6 0 9 6 0 . 5 6 6 6 0 . 5 2 2 5 0.4778 _ 0 .4 31 7 _ 0.3 85*1 0 . 3 3 B I 0 . 2 9 1 0 0 . 2 4 3 5 0 . 1 9 5 9 0.14B7 0 . 1 0 1 8 0 . 0 5 5 3 0 . 0 1 0 2 - 0 . 0 3 4 0 - 0 . 0 7 6 1 - 0 . 1 1 6 7 - 6.1564 - 0 . 1 9 4 3 - 0 . 2 3 0 7 - 0 . 2 6 4 3 - 0 . 2 9 5 6 -_0_,3248 T0.351P - 0 . 3 7 5 6 - 0 . 3 9 7 5 - 0 . 4 1 7 2 - 0 . 4 3 4 8 - 0 . 4 4 9 l _ - 0 . 4 6 1 4 - C . 4 7 1 1 - 0 . 4 7 8 0 - 0 . 4 8 2 4 - C . 4 8 3 6 - 0 . 4 B 2 7 - 0 . 4 7 9 4 - 0 . 4 7 4 1 - 0 . 4 6 6 6 - 0 . 4 5 6 7 - 0 . 4 4 5 2 Z 0 , * 3 0 7__ - 0 . 4 1 4 7 - 0 . 3 9 6 2 - 0 . 3 7 7 3 - 0 . 3 5 7 6 - 0 . 3 3 5 9 - 0 . M < 5 _ - 0 . 2 8 9 3 - 0 . 2 6 5 6 - 0 . 2 398 - 0 . 2 1 3 9 - 0 . 1 8 7 6 - 0 . 1 6 0 1 . - 0 . 1 3 2 9 - 0 . 1 0 5 3 - 0 . 0 7 8 6 - 0 . 0 5 3 7 - 0 . 0 2 8 1 . 0 0 5 0 - 0 . 0 - 0 . 0 2 2 8 - 0 . 0 9 5 7 - 0 . 1 5 4 4 - 0 . 2 1 0 0 - 0 . 2 5 9 2 - 0 . 3 0 7 2 - 0 . 3 5 2 4 - 0 . 3 9 5 8 - 0 . 4 3 8 8 - 0 . 4 8 1 2 - 0 . 5 2 1 0 - 0 . 5 5 8 7 - 0 . 5 9 2 3 - 0 . 6 2 2 4 - 0 . 6 4 8 9 - 0 . 6 7 1 7 - 0 . 6 9 1 5 - 0 . 7 0 8 4 - 0 . 7 2 2 0 - 0 . 7 3 2 3 - 0 . 7 3 9 2 - 0 . 7 4 3 5 - 0 . 7 4 4 9 _ - 0 . 7 4 2 7 - 0 . 7 3 7 4 - 0 . 7 2 8 6 - 0 . 7 1 7 1 - 0 . 7 0 3 4 - 0 . 6 8 6 8 - 6.6682 - 0 . 6 4 74 - 0 . 6 2 4 0 - 0 . 5 9 8 6 - 0 . 5 7 0 7 - 0 . 5 4 1 9 - 0 . 5 1 1 8 - 0 . 4 8 0 4 - 0 . 4 4 8 4 - 0 . 4 1 4 4 - 0 . 3 8 0 4 _ r P . 3 4 5 4 - 0 . 3 J 9 8 - 0 . 2 7 4 1 - 0 . 2 3 7 9 - 0 . 2 0 L 9 - 0 . 1 6 6 0 - 0 . 1 3 0 4 - 0 . 0 9 5 9 - 0 . 0 6 1 9 - 0 . 0 2 8 8 0 . 0 0 4 4 0 . 0 3 6 6 __0«.0A.7^_ 0 . 0 9 6 5 0 . 1 2 3 3 0 . 1 5 0 1 0 . 1 7 3 4 0.19 74 0 . 2 1 8 2 0 . 2 3 8 7 0 . 2 5 8 0 0 . 2 7 4 7 0 . 2 9 0 9 0 . 3 0 5 1 0 . 3 1 7 7 0 . 3 2 9 0 0 . 3 3 7 0 0 . 3 4 4 8 0 . 3 4 8 2 0 . 3 5 1 9 . 3 5 2 6 1 . 0 0 0 0 0 . 9 6 3 6 0 . 9 3 7 2 0 . 9 2 9 1 0 . 9 1 7 5 0.9074 0 . 6 9 7 0 0 . 8 8 9 8 0 . 8 B 2 9 0.8 766 0 . 8 7 1 4 0 . 8 6 4 9 0 . 8 5 8 0 0 . 8 5 0 1 0 . 6 4 1 6 0 . 8 3 3 1 0 . 8 2 4 3 0 . 8 1 5 2 0 . 8 0 6 3 0 . 7 9 7 2 0 . 7 8 8 0 0."7783 0 . 7 6 8 9 0 . 7 5 9 6 0 . 7 4 9 7 0 . 7 3 9 5 0 . 7 2 8 7 0 . 7 1 7 9 0 . 7 0 7 5 0 . 6 9 6 6 0 . 6 8 6 3 0 . 4 7 5 9 0 . 6 6 5 3 0 . 6 5 4 4 0 . 6 4 2 B 0 . 6 3 1 8 0 . 6 2 0 6 0 . 6 0 9 8 0 . 5 9 9 2 0 . 5 6 8 0 0 . 5 7 T 7 0 ^ 5 6 6 6 0.5~55 7 0 . 5 4 5 0 0 . 5 3 3 9 0 . 5 2 2 9 0 . 5 1 1 3 0 . 5 0 0 0 0 . 4 8 8 9 0 . 4 7 B 1 0 . 4 6 7 5 0 . 4 5 6 7 0 . 4 4 * 7 _ 0 . , * J 5 9 _ 0 . 4 2 5 B 0 . 4 1 4 9 0 . 4 0 6 0 0 . 3 9 7 5 0 . 3 8 9 6 0 , 3 8 2 7 0 . 3 7 5 1 0 . 3 7 0 2 0 . 3 6 4 6 0 . 3 6 1 1 0 . 3 5 8 1 0 . 3 5 5 8 0 . 3 5 4 9 0 . 3 5 3 1 0 . 3 5 3 6 0 . 3 5 2 3 0 . 3 5 3 0 . . 3 5 2 7 0.0 - 0 . 0 3 7 1 - 0 . 0 6 4 8 - 0 . 0 7 3 6 - 0 . 0 8 6 1 - 0 . 0 9 7 2 - 0 . 1 0 8 7 - 0 . 1 1 6 7 - 0 . 1 2 4 6 - 0 . 1 3 1 7 - 0 . 1 3 7 7 - 0 . 1 4 5 1 - 0 . 1 5 3 1 - 0 . 1 6 2 4 - 0 . 1 7 2 4 - 0 . 1 6 2 6 - 0 . 1 9 3 2 - 0 . 2 0 4 3 - 0 . 2 1 5 3 - 0 . 2 2 6 6 - 0 . 2 3 6 3 - 0 . 2 5 0 6 - 0 . 2 6 2 6 - 0 . 2 7 5 0 - 0 . 2 8 8 1 - 0 . 3 0 1 6 - 0 . 3 1 6 5 - 0 . 3 3 1 5 - 0 . 3 4 6 0 , - 0 . 3 6 1 5 - 0 . 3 7 6 5 - 0 . 3 9 1 7 - 0 . 4 0 7 5 - 0 . 4 2 4 0 - 0 . 4 4 2 0 - 0 . 4 5 9 2 - 0 . 4 7 7 1 - 0 . 4 9 4 6 - 0 . 5 1 2 2 - 0 . 5 3 1 0 - 0 . 5 4 8 7 - 0 . 5 6 8 1 - 0 . 5 8 7 4 - 0 . 6 0 70 - 0 . 6 2 7 5 - 0 . 6 4 8 3 - 0 . 6 7 0 7 - 0 . 6 9 3 1 - 0 . 7 1 5 6 - 0 . 7 3 7 9 - 0 . 7 6 0 3 - 0 . 7 8 3 6 - 0 . 8 0 5 9 - 0 , 6 3 0 ? - 0 . 8 5 3 8 - 0 . 8 7 9 7 - 0 . 9 0 1 3 - 0 . 9 2 2 7 - 0 . 9 4 2 6 - 0 . 9 6 0 4 - 0 . 9 8 0 6 - 0 . 9 9 3 6 - 1 . 0 0 R 8 - 1 . 0 1 8 7 - 1 . 0 2 6 9 - 1 . 0 3 3 4 - 1 . 0 3 6 0 - 1 . 0 4 1 0 - 1 . 0 3 9 6 - 1 . 0 4 3 1 - 1 . 0 4 1 2 - 1 . 0 4 2 2 3 6 0 . 0 0 . 2 1 7 9 0.JD799 - 0 . 0 2 3 7 0 . 0 7 8 6 0 . 0 2 0 5 0 . 3 5 3 3 0 . 3 5 3 9 - 1 . 0 3 8 7 3 6 5 . 0 0 . 2 1 2 4 0 . 0 7 9 3 - 0 . 0 1 9 2 0 . 0 7 6 2 0.0416 0 . 3 5 2 8 0 . 3 5 5 3 - 1 . 0 3 4 9 3 7 0 . 0 0.2C72 0 . 0 7 8 9 - 0 . 0 1 4 3 0 . 0 7 7 1 0 . 0 6 3 6 0 . 3 4 8 0 0 . 3 5 3 8 - 1 . 0 3 9 1 3 7 5 . 0 0 . 2 0 2 2 0.07B3 - 0 . 0 0 9 9 0 . 0 7 5 9 0 . 0 8 3 6 0 . 3 4 2 8 0 . 3 5 2 6 - 1 . 0 4 1 8 3 8 0 . 0 0 . 1 9 7 4 0 . 0 7 7 5 - 0 . 0 0 5 6 0 . 0 7 4 0 0 . 1 0 3 1 0.334<> 0 . 3 5 0 1 - 1 . 0 4 9 5 3 8 5 . 0 0 . 1 9 2 4 0.0765 - 0 . 0 0 1 6 0 . 0 7 2 3 0.1218 0.32 75 0 . 3 4 9 4 - 1 . 0 5 1 5 3 9 0 . 0 0 . 1 8 7 2 0 . 0 7 5 6 0 . 0 0 1 8 0 . 0 7 0 1 0 . 1 3 8 0 0 . 3 1 8 7 0 . 3 4 7 3 - 1 . 0 5 7 5 3 9 5 . 0 0 . 1 6 1 9 0 . 0 7 4 6 0 . 0 0 5 0 0 . 0 6 7 5 0 . 1 5 4 1 0 . 3 0 7 7 0 . 3 4 4 1 - 1 . 0 6 6 8 4 0 0 . 0 0 . 1 7 6 6 0 . 0 7 4 2 0 . 0 0 8 2 0 . 0 6 4 8 0.1705 0 . 2 9 5 2 0 . 3 4 0 9 - 1 . 0 7 6 2 4 0 9 . 0 0 . 1 7 1 4 0 . 0 7 3 9 0 . 0 1 1 0 0 . 0 6 2 0 0.1854 0 . 2 8 1 8 0 . 3 3 7 3 - 1 . 0 8 6 8 4 1 0 . 0 0 . 1 6 6 9 0 . 0 7 3 5 0 . 0 1 3 5 0 . 0 5 9 1 0 . 1 9 9 2 0 . 2 6 7 1 0 . 3 3 3 2 - 1 . 0 9 9 1 4 1 5 . 0 0 . 1 6 1 7 0 . 0 7 3 1 0 . 0 1 5 6 0 . 0 5 6 1 0 . 2 1 0 3 0 . 2 5 1 9 0 . 3 2 8 1 - 1 . 1 1 4 4 4 2 0 . 0 0 . 1 5 6 9 0 . 0 7 2 5 0 . 0 1 7 6 0 . 0 5 2 8 0 . 2 2 0 7 0 . 2 3 4 7 0 . 3 2 2 1 - 1 . 1 3 2 7 4 2 9 . 0 0 . 1 5 2 2 0 . 0 7 2 0 0 . 0 1 9 3 0 . 0 4 9 7 0 . 2 2 9 7 0 . 2 1 7 7 0 . 3 1 6 5 - 1 . 1 5 0 5 4 3 0 . 0 0 . 1 4 7 5 0 . 0 7 1 5 0 . 0 2 0 9 0 . 0 4 6 4 0 . 2 3 7 9 0. 1990 0 . 3 1 0 1 - 1 . 1 7 0 8 4 3 5 . 0 0 . 1 4 3 1 0 . 0 7 1 0 0 . 0 2 2 1 0 . 0 4 3 2 0 . 2 4 4 3 0 . 1 8 0 9 0 . 3 0 3 9 - 1 . 1 9 1 0 4 4 0 . 0 0 . 1 3 8 9 0 . 0 7 0 5 0 . 0 2 3 2 0.0399,. 0 . 2 4 8 9 0. 1608 0 . 2 9 6 3 - 1 . 2 1 6 5 4 4 5 . 0 0 . 1 3 4 9 0 . 0 6 9 9 0 . 0 2 4 1 0 . 0 3 6 9 0 . 2 5 2 5 0 . 1 4 2 4 0 , 2 8 9 9 - 1 . 2 3 8 3 4 9 0 . 0 0 . 1 3 1 1 0 . 0 6 8 9 0 . 0 2 4 7 0 . 0 3 3 7 0 . 2 5 3 8 0 . 1 2 3 8 0 . 2 8 2 4 - 1 . 2 6 4 5 4 5 5 . 0 0 . 1 7 7 1 0 . 0 6 7 7 0 . 0 2 5 2 0 . 0 3 0 6 0 . 2 5 5 1 0 . 1 0 6 3 0 . 2 7 6 4 - 1 . 2 8 5 9 4 6 0 . 0 0 . 1 2 3 0 0 . 0 6 6 4 0 . 0 2 5 5 0 . 0 2 7 9 0 . 2 5 5 3 0 . 0 6 8 7 0 . 2 7 0 3 - 1 . 3 0 8 4 4 6 5 . 0 0 . 1 1 8 7 0 . 0 6 5 3 0 . 0 2 5 8 0 . 0 2 5 2 0 . 2 5 6 1 0 . 0 7 1 0 0 . 2 6 5 7 - 1 . 3 2 5 3 4 7 0 . 0 0 . 1 1 4 5 0.0644 0 . 0 2 5 7 0 . 0 2 2 6 0.2 54 7 0 . 0 5 4 4 0 . 2 6 0 4 - 1 . 3 4 5 5 4 7 5 . 0 0 . 1 1 0 5 0 . 0 6 3 7 0 . 0 2 5 5 0 . 0 1 9 9 0 . Z 5 1 0 0 . 0 3 5 5 0 . 2 5 3 5 - 1 . 3 7 7 2 4 6 0 . 0 0 . 1 0 6 7 0 . 0 6 3 0 0 . 0 2 5 3 0 . 0 1 7 5 0 . 2 4 7 4 0 . 0 1 8 1 0 . 7 4 6 0 - 1 . 3 9 4 2 4 8 5 . 0 0 . 1 0 3 2 0 . 0 6 2 3 0 . 0 2 4 7 0 . 0 1 5 0 0 . 2 3 9 7 0 . 0 0 0 5 0 . 2 3 9 7 - 1 . 4 2 8 2 4 9 0 . 0 0 . 0 9 9 7 0 . 0 6 1 5 0 . 0 2 4 4 0 . 0 1 2 7 0.2 342 - 0 . 0 1 6 6 0 . 2 3 4 7 - 1 . 4 4 9 2 4 9 5 . 0 0 . 0 9 6 3 0 . 0 6 0 6 0 . 0 2 3 5 0 . 0 1 0 8 0 . 2 2 5 0 - 0 . 0 2 9 9 0 . 2 2 7 0 - 1 . 4 8 2 9 5 0 0 . 0 0 . 0 9 3 0 0 . 0 5 9 8 0 . 0 2 2 7 0 . 0 0 8 6 0 . 2 1 4 8 - 0 . 0 4 5 7 0 . 2 1 9 7 - 1 . 5 1 5 7 Table XXVII. Computer Output. Cold R o l l e d 75%. F o u r i e r C o e f f i c i e n t s f o r Ni-ThO r 220 D I S T A N C E ( L l PERCENT S T R A I N DOMAIN S I Z E C O E F F I C I E N T (ANGSTROMS 1 0.0 0.0 1.0000 5.0 0.0 0 . 9 6 3 6 * 10.0 0.0 0.9 3 7 2 15.0 0.0 0 . 9 2 9 1 2 0 . 0 0.0 0 . 9 1 7 5 7 5 . 0 O.0RR9 0. 9 1 0 2 30.0 0 . 1 3 0 8 0 . 9 0 5 9 35.0 0. 1461 0 . 9 0 4 8 +0.0 0 . 1 4 7 0 0 . 9 0 2 6 4 5 . 0 0 . 1 5 1 5 0.90 31 5 0 . 0 0 . 1 5 8 6 0 . 9 0 7 1 5 5 . 0 0. 1 5 8 9 0 . 9 0 8 ? 6 0 . 0 0 . 1 5 3 6 0 . 9 0 5 9 6 5 . 0 0. 1 4 7 9 0.9018 7 0 . 0 0 . 1 4 4 0 0 . 8 9 f t l 7 5 . 0 ' 0 . 1 4 0 3 0 . 8 9 4 ? 8 0 . 0 0 . 1 3 5 6 0 . 8 8 8 8 8 5 . 0 0 . 1 3 1 8 0 . 8 8 3 3 9 0 . 0 0 . 1 2 9 6 0 . 8 7 9 6 9 5 . 0 0 . 1 2 8 2 0 . 8 7 6 5 1 0 0 . 0 0. 1267 0 . 8 7 3 2 1 0 5 . 0 0 . 1 2 5 3 0.8694 1 10.0 0 . 1 2 3 9 0 . 8 6 5 9 1 1 5 . 0 0 . 1 2 2 1 0 . 8 6 1 7 1 2 0 . 0 0. 1 199 0 . 8 5 5 8 ' 1 2 5 . 0 0.1 178 0.8494 1 30.0 0 . 1 1 5 7 0 . 8 4 2 0 1 3 5 . 0 0. 1 1 36 0.8 344 U O . O 0 . 1 1 2 ? 0 . 8 7 3 4 1 4 5 . 0 0 . 1 1 1 7 0. 8 2 3 8 1 5 0 . 0 0.1 118 0 . 8 2 1 6 1 5 5 . 0 0 . 1 1 1 5 0 . 8 1 8 1 1 6 0 . 0 0 . 1 1 0 ? 0 . 8 1 1 6 1 1 6 5 . 0 0 . 1 0 8 8 0 . 8 0 4 1 1 7 0 . 0 0 . 1 0 8 0 0 . 7 9 7 4 1 7 5 . 0 0 . 1 0 7 5 0 . 7 9 2 3 1 8 0 . 0 0. 1063 0 . 7 9 4 2 1 8 5 . 0 0.104 7 0. 7 7 4 9 190.0 0 . 1 0 3 3 0 . 7 6 6 5 1 9 5 . 0 0 . 1 0 2 7 0.75 79 2 0 0 . 0 0 . 1 0 0 9 0 . 7 4 9 4 2 0 5 . 0 0 . 0 9 9 5 0 . 7 3 9 3 2 1 0 . 0 0 . 0 9 B 6 '0.7310 2 1 5 . 0 0 . 0 9 7 7 0 . 7 ? ? 6 2 2 0 . 0 0 . 0 9 6 0 0 . 7 1 0 1 2 2 5 . 0 0 . 0 9 3 9 0 . 6 9 5 5 2 30.0 0 . 0 9 2 3 0 . 6 9 2 1 2 3 5 . 0 0.0914 C.6718 2 4 0 . 0 0 . 0 9 0 5 0 . 6 6 0 9 2 4 5 . 0 0.CR91 0 . 6 4 6 4 7 5 0 . 0 0.0R78 0 . 6 3 6 1 2 5 5 . 0 0 . 0 8 6 9 0 . 6 ? 5 ? 2 6 0 . 0 0 . 0 6 6 4 0.616« 7 6 5 . 0 0 . 0 8 5 9 • 0 . 6 C 7 0 2 7 0 . 0 0 . 0 8 5 2 0 . 5 9 7 1 2 7 5 . 0 0 . 0 8 4 3 0 . 5 8 5 0 2 8 0 . 0 0 . 0 6 3 8 0 . 5 7 7 3 2 8 5 . 0 0 . 0 8 3 6 0 . 5 7 1 5 2 9 0 . 0 0.0835 0 . 5 6 6 7 2 9 5 . 0 0.0831 0 . 5 6 2 3 3 0 0 . 0 0 . 0 8 2 9 0 . 5 5 6 9 3 0 5 . 0 0 . 0 8 3 2 0.5586 3 1 0 . 0 0.0832 0 . 5 5 8 0 3 1 5 . 0 0 . 0 8 2 9 0.5585 3 2 0 . 0 0 . 0 8 2 6 0 . 5 5 9 8 3 2 5 . 0 0 . 0 8 2 6 0.5636 3 3 0 . 0 0.0826 0 . 5 7 0 5 3 3 5 . 0 0 . 0 8 2 3 0 . 5 7 4 1 3 4 0 . 0 0.0824 0.5839 345 . 0 0 . 0 8 2 5 0 . 5 9 1 2 3 5 0 . 0 0.0824 0.6006 3 5 5 . 0 0 . 0 8 1 9 0 . 6 0 5 8 3 6 0 . 0 0 . 0 8 1 8 0 . 6 1 6 4 3 6 5 . 0 0.0820 0 . 6 3 0 1 3 7 0 . 0 0 . 0 6 1 7 0 . 6 3 4 9 3 7 5 . 0 0 . 0 8 0 7 0 . 6 3 4 0 3 8 0 . 0 0 . 0 7 9 2 0.6243 3 8 5 . 0 0 . 0 7 8 0 0 . 6 2 2 2 3 9 0 . 0 0.0776 0 . 6 2 3 5 3 9 5 . 0 0 . 0 7 7 5 0 . 6 2 6 4 4 0 0 . 0 0 . 0 7 7 2 0 . 6 2 7 1 4 0 5 . 0 0 . 0 7 6 5 0.6230 4 1 0 . 0 0.0758 0 . 6 1 7 7 4 1 5 . 0 0 . 0 7 5 1 0 . 6 1 1 0 1 4 2 0 . 0 0 . 0 7 4 1 0 . 5 9 8 7 4 2 5 . 0 0 . 0 7 2 8 0 . 5 8 4 0 4 3 0 . 0 0 . 0 7 1 7 0 . 5 6 9 3 4 3 5 . 0 0 . 0 7 1 0 0 . 5 5 9 7 4 4 0 . 0 0 . 0 7 1 0 0 . 5 5 3 1 4 4 5 . 0 0 . 0 7 1 8 0 . 5 5 6 7 4 5 0 . 0 0 . 0 7 3 0 0 . 5 6 3 4 4 5 5 . 0 0 . 0 7 3 9 0.5694 4 6 0 . 0 0 . 0 7 3 7 • 0 . 5 6 3 5 4 6 5 . 0 0 . 0 7 3 7 0 . 5 6 2 8 4 7 0 . 0 0 . 0 7 4 8 0 . 5 7 4 5 4 7 5 . 0 0 . 0 7 6 ? 0 . 5 8 6 2 4 8 0 . 0 0 . 0 7 4 7 0.563B 4 8 5 . 0 0.0724 0 . 5 7 7 3 4 9 0 . 0 0 . 0 7 3 9 0 . 5 4 3 3 4 9 5 . 0 0 . 0 7 9 8 0 . 6 1 5 3 i 5 0 0 . 0 0 . 0 8 9 3 0 . 7 8 5 8 Table XXVIII. Computer Output. Variation of Lattice Strain and Domain Size Coefficient with Lattice Distance for Ni-Th0„ Cold Rolled 75%. 221 DOMAIN S I Z E I I I * 7 1 1 . 5 6 ANGSTROMS DOMAIN $1ZE (21 - 9+5.96 ANGSTROMS PIOT TAPE S U C C E S S F U L L Y WRITTEN DONE STOP 0 E X F C U T I O N TERMINATED Table XXIX. Computer Output. 'Domain Size i n Ni-ThO ? Cold Rolled 75%. t » 1 I NI POWDER ANNEALED ( l o o ) IRS RECORDED] (a) 222 NI POWDER flKNEBLED (2 0 0) (CORRECTED FOR LP RND F) (b) PXNEfllED (2 00) (CORRECTED FOR LP. F AND BACKGROUND) 4.1 4.18 4 . s 4 . h 4 . « 1.42 4.5 4. SB S I N E THETA (X10-' ) (c) NI POWDER ANNEALED ( a o o ) (CORRECTED FOR LP. F. BG AND DOUBLET] (d) Figure 58. Computer Graphs showing Sequence of Corrections for (200) Reflection from Annealed Nickel Powder Standard. 59. Computer Graphs showing Sequence of Corrections f o r (400) R e f l e c t i o n from Annealed N i c k e l Powder Standard. 22k TD Kl STRIP COLO ROLLED 7S PERCENT ( Z o o ) TD 1*1 STRIP COLD ROLLED 7S PERCENT ( 2 0 0 ) £CORREC*D FOR LP AND F) 72.0 76.0 0- » 0.44 0.4 (a) (b) O.i O.M a.e TO HI STRIP COLD ROLLED 75 PERCENT (aoo) 5J ICORRECED FOR LP. F AND BACKGROUND) p.fl O.M a.m (c) TD HI STRIP COLD ROLLED 73 PERCENT ( 2 0 0 ) (CORRECTED FOR LP. F. 0G HND DOUBLET) 9.30 D.4 0.44 0.4 0.6 0.64 0.0 (d) Figure 60. Computer Graphs showing Sequence of Corrections f o r (200) R e f l e c t i o n from Ni-Th02 Cold R o l l e d 75%. Figure 6.1. Computer Graphs showing Sequence of Corrections for (400) Reflection from Ni-Th0 9 Cold Rolled 75%. Figure 63. Computer Graph Showing variation of Domain Size Coefficient with Lattice Distance for Ni-Th0 2 Cold Rolled 75%. 22? BIBLIOGRAPHY 1. DuPont Metal Products, TD Nickel, Data Sheet No. A-27C&5, (1962). 2. 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