UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Structure and deformation characteristics of beta'AuZn Causey, Allan Robert 1967

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1967_A1 C39.pdf [ 19.18MB ]
Metadata
JSON: 831-1.0104683.json
JSON-LD: 831-1.0104683-ld.json
RDF/XML (Pretty): 831-1.0104683-rdf.xml
RDF/JSON: 831-1.0104683-rdf.json
Turtle: 831-1.0104683-turtle.txt
N-Triples: 831-1.0104683-rdf-ntriples.txt
Original Record: 831-1.0104683-source.json
Full Text
831-1.0104683-fulltext.txt
Citation
831-1.0104683.ris

Full Text

The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ALLAN ROBERT CAUSEY BoA.Sc, The Uni v e r s i t y of British/Columbia, 1958 MoA., The University of Toronto, 1959 MoA.SCo, The Univ e r s i t y of B r i t i s h Columbia, 1964 TUESDAY, SEPTEMBER 26, 1967, AT 3:30 P 0M 0 IN ROOM 210, METALLURGY BUILDING COMMITTEE IN CHARGE External Examiner: J.H. Westbrook Research and Development Center General E l e c t r i c Company Schenectady, New York Research Supervisor: E. Teghtsoonian Chairman: L McT. Cowan Ro Barrie L.Go Harrison A. M i t c h e l l . N.R., Risebrough Eo Teghtsoonian F i Weinberg "THE STRUCTURE AND DEFORMATION CHARACTERISTICS OF f> 'AuZn'1 ABSTRACT The deformation behaviour of the i n t e r m e t a l l i e C^Cl-structure compound fj'AuZn has been investigated over a wide range of m e t a l l u r g i c a l v a r i a b l e s . The .plastic deformation, s p e c i f i c a l l y the s t r e s s - s t r a i n r e l a t i o n , has been characterized in' terms of the e f f e c t s of composition, temperature, s t r a i n - r a t e , and grain s i z e . The c o n s t i t u t i o n a l defect structure was investigated using l a t t i c e parameter measurements and annealing experiments „-Po I y e r y s t a l l i n e AuZn was found to behave in a d u c t i l e manner over the temperature range 77 to 533 K and composition range 48.0 to 52.0 a/o Au. In addi-t i o n to s l i p on the planes of the <001> zone, s l i p on planes of the ^ L l l } zone was also suggested by the s l i p trace analyses. This may account for the observed d u c t i l i t y and high work hardening rate. The composition .dependence of the y i e l d stress exhibited the following behaviour; 1) a minimum at the stoichiometric composition, 2) a l i n e a r dependence of hardening on the deviation from stoichiometry, 3) approximately equal hardening due to both excess Au and Zn atoms, and 4) a temperature independent hardening-composition slope (except at 77 K where a hardening minimum was observed at 50..5 a/o Au) . The e x i s t i n g order strengthening theories and s o l i d s o l u t i o n harden-ing mechanisms were found to be unsatisfactory for AuZn. The temperature dependence of the y i e l d stress was s i m i l a r to that observed for bec metals and a l l o y s with a ragid increase i n y i e l d stress at temperatures below 200 Ko The excess Au; atoms decreased the temp-erature dependence s i g n i f i c a n t l y i n the composition range 50.1 to 51.6 a/o Au." The temperature dependence of the y i e l d stress was investigated using the thermally activated flow parameter analyses. The magnitude of the a c t i v a t i o n volume, a c t i v a t i o n energy, frequency factor and shear stress extrapolated to 0 K were consistent with the predictions of either the thermally activated c r o s s - s l i p mechanism developed by Escaig or the Peierls-Nabarro force mechanism proposed by Rajnak and Dorn. The P e i e r l s mechanism was found to provide a more- s a t i s f a c t o r y explanation of the s o l i d s o l u t i o n softening phenomena-The defect structure of AuZn was determined to be antistructural„ The larger Au atom expanded the l a t t i c e more than the smaller Zn atom con s t r i c t e d i t . The as-extruded Au-ricb. wire "exhibited an anomalous increase in r e s i s t i v i t y during annealing experiments. The increase and subsequent decrease were at t r i b u t e d to a v a r i a t i o n i n the degree of long-range order. GRADUATE STUDIES F i e l d of Study; Metallurgy M e t a l l u r g i c a l K i n e t i c s Properties of Ceramic Materials X-Rays and Electron Microscopy Nuclear Metallurgy Structure of Metals Topics i n Physical. Metallurgy D i f f u s i o n in Metals P r i n c i p l e s of Metal Fabrication E. Peters A.CDo Chaklader E. Teghtsoonian WoM. Armstrong E. Teghtsoonian J„A. Lund W.M. Armstrong JoA. Lund Related F i e l d s of Study: S t a t i s t i c a l Mechanics Plasma Physics Introduction to Low Temperature Physics Elementary Quantum Mechanics Physics of the S o l i d State RoF. Snider L. de Sobrino D. Osborne W. Opechowski R. Barrie PUBLICATIONS W.Mo Armstrong, A.R. Causey and W.R„ Sturrock, "Creep of S i n g l e - C r y s t a l UO , l, J. Nuclear Materials, 19 (1966), 42-49. A.R. Causey and E. Teghtsoonian, "The "Effects of a P o l y c r y s t a l l i n e Surface Layer on the Tensi l e Deformation of T i n Single C r y s t a l s " , Trans. Met. Soc. A.I.M.E.. 233 C1965K 1920-1923. THE STRUCTURE AND DEFORMATION CHARACTERISTICS OF 6*AuZn by ALLAN ROBERT CAUSEY B.AiSc, The Univ e r s i t y of B r i t i s h Columbia, 1958 M.A., The Univ e r s i t y of Toronto, 1959 M.A.Sc, The Univ e r s i t y of B r i t i s h Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1967 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 t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e 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 a nd S t u d y . 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 p u r p o s e s may be g r a n t e d b y t h e Head o f my D e p a r t m e n t o r b y 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 o f 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 n o t 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 . D e p a r t m e n t o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, C a n a d a - i i -ABSTRACT The deformation behaviour of the i n t e r m e t a l l i c CsCl-structure compound 3'AuZn has been investigated over a wide range of m e t a l l u r g i c a l v a r i a b l e s . The p l a s t i c deformation, s p e c i f i c a l l y the s t r e s s - s t r a i n r e l a t i o n , has been.characterized i n terms of the e f f e c t s of composition, temperature, s t r a i n - r a t e , and grain s i z e . The c o n s t i t u t i o n a l defect structure was investigated using l a t t i c e parameter measurements and annealing experiments. P o l y c r y s t a l l i n e AuZn was found to behave i n a d u c t i l e manner, over the temperature range 77 to 533°K and composition range 48.0 to 52.0 a/o Au. In add i t i o n to s l i p on the planes of the <001> zone, s l i p on planes of the <111> zone was also suggested by the s l i p trace analyses. This may account for the observed d u c t i l i t y and high work hardening rate. The composition dependence of the y i e l d stress exhibited the following behaviour; 1) a minimum at the stoichiometric composition, 2) a l i n e a r dependence of hardening on the deviation from stoichiometry, 3) approximately equal hardening due to both excess Au and Zn atoms, and 4) a temperature independent hardening-composition slope (except at 77°K where a hardening minimum was observed at 50.5 a/o Au). The e x i s t i n g order strengthening theories and s o l i d s o l u t i o n hardening mechanisms were found to be unsatisfactory f or AuZn. The temperature dependence of the y i e l d stress was s i m i l a r to that observed for bcc metals and a l l o y s with a rapid increase i n y i e l d stress at temperatures below 200°K. The excess Au.atoms decreased the temperature dependence s i g n i f i c a n t l y i n the composition range 50.1 to 51.6 a/o Au. - i i i -The temperature dependence of the y i e l d stress was investigated using the thermally activated flow parameter analyses. The magnitude of the a c t i v a t i o n volume, a c t i v a t i o n energy, frequency factor and shear stress extrapolated to 0°K were consistent with the predictions of either the thermally activated c r o s s - s l i p mechanism developed by Escaig or the P e i e r l s -Nabarro force mechanism proposed by Rajnak and Dorn. The P e i e r l s mechanism was found to provide a more s a t i s f a c t o r y explanation of the s o l i d s o l u t i o n softening phenomena. The defect structure of AuZn was determined to be antlstructural. The larger Au atom expanded the l a t t i c e more than the smaller Zn atom cons t r i c t e d i t . The as-extruded Zn-rich wire exhibited an anomalous increase i n r e s i s t i v i t y during annealing experiments. The increase and subsequent decrease were a t t r i b u t e d to a v a r i a t i o n i n the degree of long-range order. - i v -ACKNOWLEDGEMENT The author wishes to thank his research d i r e c t o r , Dr. E. Teghtsoonian, for h i s advice and encouragement. He also wishes to acknowledge the h e l p f u l and stimulating discussions with other f a c u l t y members and fellow graduate students. Thanks are also extended to the technical s t a f f f or t h e i r assistance. This research was financed i n part by a National Research Council studentship and by a Defence Research Board Research A s s i s t a n t s h i p . TABLE OF CONTENTS The Structure and Deformation C h a r a c t e r i s t i c s of g'AuZn Page Chapter 1 Introduction 1 1.1 Object of the Investigation 1 1.2 Pertinent L i t e r a t u r e 2 Chapter 2 Deformation Behaviour. 5 2.1 Experimental Procedure 5 2.1.1 Materials and Ingot Preparation 5 2.1.2 Specimen Preparation 6 2.1.3 Tensi l e Testing Procedures 11 2.2 S t r e s s - S t r a i n Relationship 11 2.2.1 Nature of the St r e s s - S t r a i n Curve 11 2.2.2 Luder's S t r a i n and Serrated Flow 19 2.2.3 D u c t i l i t y 21 2. 2.4, -Maximum Stress 26 2.2.5 S t r a i n Hardening Exponent 28 2.3 S t r u c t u r a l Observations 33 2.3.1 Deformation Modes 33 2.3.2 Deformation Markings 35 2.3.3 D i s l o c a t i o n Structure 46 2.4 Y i e l d Stress and Work Hardening 55 2.4.1 E f f e c t of Temperature 55 2.4.1.1 On the Y i e l d Stress 55 2.4.1.2 On the Flow Stress 60 2.4.2 E f f e c t of Composition 66 2.4.2.1 On the Y i e l d Stress 66 2.4.2.2 On the Flow Stress 68 2.4.3 E f f e c t of Strain-Rate 74 2.4.4 E f f e c t of Grain Size 74 2.4.5 Discussion. 82 2.4.5.1 < l l l > S l i p 82. 2.4.5.2 Work Hardening 85 - v i -Table of Contents (Cont) Page 2.4.5.3 E f f e c t s of Order on 88 A l l o y Strengthening 2.4.5.4 S o l i d Solution Hardening 92 2.4.5.4.1 D i s l o c a t i o n Locking Mechanisms 94 2.4.5.4.2 D i s l o c a t i o n F r i c t i o n Mechanisms 96 2.5 Thermally Activated Flow 98 2.5.1 Introduction 98 2.5.2 Thermally Activated Flow Parameters 103 2.5.2.1 Strain-Rate S e n s i t i v i t y 103 2.5.2.2 A c t i v a t i o n Volume 105 2.5.2.3 A c t i v a t i o n Enthalpy and Thermal Component of Stress 113 2.5.2.4 Frequency Factor 119 2.5.2.5 Cottrell-Stokes Law 122 2.5.3 Discussion 123 2.5.3.1 Impurity Mechanism 123 2.5.3.2 Thermally Activated Cross-S l i p 124 2.5.3.3 Peierls-Nabarro Force 126 Chapter 3 Defect Chemistry 132 3.1 Introduction 132 3.2 Experimental Procedure 132 3.3 Results 134 3.3.1 Annealed Powder Samples 134 3.3.2 As-extruded Zn-rich Wires 138 3.4 Discussion 138 - v i i -Table of Contents (Cont) Page. Chapter 4 Annealing Behaviour of As-Extruded Zn-Rich Wires 141 4.1 Introduction 141 4.2 Experimental Procedure 142 4.3 Results 143 4.3.1 E f f e c t of Composition on the, R e s i s t i v i t y 143 4.3.2 Isochronal Annealing 146 4.3.3 Isothermal Annealing 146 4.4 Discussion 156 Chapter 5 Electron Microscopy 160 5.1 Introduction 160 5.2 Experimental Procedure 160 5.3 Experimental Observations 161 5.4 Discussion 168 Chapter 6 Summary Discussion and Conclusions 171 6.1 Discussion 171 6.2 Summary and Conclusions 173 6.3 Suggestions for Future Work 176 Appendix A Bibliography 177 180 - v i i i -LIST OF FIGURES Page 6 -i 1.1 Phase diagram f o r Au-Zn .J 2.1 Schematic diagram of extrusion apparatus 9 2.2 AuZn wire i n as-extruded condition a) cross-section, b) l o n g i t u d i n a l section 10 2.3 Tensi l e t e s t i n g apparatus, a) p i n chucks for wire specimens, b) s p l i t jaw grips f o r s t r i p specimens 12 2.4 S t r e s s - s t r a i n curves f o r (a) Zn-rich at 295°K (b) Au-rich at 295°K 13,14 2.5 S t r e s s - s t r a i n curves as a function of temperature for various AuZn compositions 16,17,18 2.6 Comparison of the s t r e s s - s t r a i n curves for the as-extruded and annealed 48.92 a/o Au composition 20 2.7 Total Elongation as a.function of temperature 22 2.8 Microstructure of s t r i p specimen deformed 16% at 373°K shows c a v i t a t i e s at grain boundaries 24 2.9 Same specimen as i n Figure 2.8, showing grain boundary separation near the fr a c t u r e surface 25 2.10 Maximum stress as a function of temperature 26 2.11 Maximum stress as a function of composition 27 2.12 True s t r e s s - true s t r a i n p l o t s for various AuZn compositions 29,30,31 2.13 S t r a i n hardening exponent n as a function of temperature 32 2.14 Atomic motions during mechanical twinning of an AB a l l o y 34 2.15 Microstructure of a specimen deformed at 295°K to various s t r a i n s 36 2.16 Microstructure of specimen deformed 21.8% at 295°K shows multiple s l i p l i n e s near grain boundaries 37 L i s t of Figures (Cont) - i x -P a g e 2.17 Microstructure of specimen deformed 18.2% at 295°K, shows the severe deformation around an undeformed ce n t r a l region of a grain 37 2.18 Microstructure of specimen deformed 25% at 295°K (a) shows s l i p l i n e s passing through grain boundaries (b) shows severe deformation near the fra c t u r e surface 38 2.19 Microstructure of specimen deformed 6.8% at 295°K shows continuous reference l i n e s across grain. boundaries 40 2.20 Microstructure of specimen.deformed 12.3% at 77°C shows f i n e s t r a i g h t s l i p l i n e s 41 2.21 Microstructure and schematic diagram of sl i p , traces on specimen deformed at 295°K 43,44,45 2.22 El e c t r o n Micrographs of Au-rich specimen deformed 3% at. 295°K 47 2.23 Electron Micrographs of Au-rich specimen deformed 9% at 295°K 48 2.24 Electron Micrographs of Au-rich specimen deformed 5% at 77°K 50 2.25 El e c t r o n Micrographs of Au-rich specimen deformed 23% at 463°K 51 2.26' El e c t r o n Micrographs of Au-rich specimen annealed 1 1/2 hours at 473°K a f t e r r o l l i n g 52 2.27 Electron Micrograph showing s l i p traces of moving d i s l o c a t i o n s 52 2.28 Electron Micrographs showing s t r a i g h t d i s l o c a t i o n l i n e s i n specimen deformed 5% at 77°K 54 2.29 El e c t r o n Micrograph of Zn-rich specimen deformed 10% by r o l l i n g at 295°K 54 2.30 Y i e l d stress as a function of temperature for various AuZn compositions 56 2.31 I n i t i a l y i e l d stress of various p o l y c r y s t a l l i n e metals versus T / T M (after Conrad38) 57 2.32 Y i e l d stress as a function of the r e c i p r o c a l of the absolute temperature f or various AuZn compositions 58 L i s t of Figures (Cont) Comparison of the y i e l d stress-temperature v a r i a t i o n of the as-extruded and the annealed Zn-rich a l l o y s Flow stress as a.function of temperature for various AuZn compositions The v a r i a t i o n of the work hardening parameter for various AuZn compositions Flow Stress as a function of composition and s t r a i n at 295°K Comparison of the y i e l d stress-composition dependence of the as-extruded and annealed Zn-rich a l l o y s Y i e l d stress as a function of composition for Au-rich a l l o y s at several temperatures Flow stress as a function of composition at 77°K Flow stress as a function of composition for the as-extruded Zn-rich a l l o y s Flow stress as a function of s t r a i n - r a t e f or the 50.07 a/o Au composition at295°K E f f e c t of grain s i z e on the flow stress f or various AuZn compositions V a r i a t i o n of the Petch slope with s t r a i n V a r i a t i o n of o Q with s t r a i n E f f e c t of change i n l a t t i c e parameter on y i e l d stress at 295°K Plot of the hardening against the F l e i s c h e r modulus parameter ( n ' ) - ^ 2 T y p i c a l Force-Distance curve for a thermally activated deformation process The nature of the flow stress obtained during s t r a i n -rate change tests L i s t of Figures (Cont) - x i -Page 2.49 Str a i n - r a t e s e n s i t i v i t y as a function of s t r a i n f o r various AuZn compositions 106,107,108 2.50 Str a i n - r a t e s e n s i t i v i t y as a function of temperature 109 2.51 A c t i v a t i o n volume as a function of applied stress f o r various AuZn compositions 110,111,112 2.52 A c t i v a t i o n volume as a function of the thermal component of stress 114 2.53 Thermal component of stress as a function of temperature 116 2.54 A c t i v a t i o n enthalpy as a function of temperature 117 2.55 A c t i v a t i o n enthalpy as a function of the thermal component of stress 117 2.56 Y i e l d stress as a function of temperature 120 2.57 Comparison of the experimental data with the t h e o r e t i c a l curve of the thermal component of stress versus temperature 128 3.1 L a t t i c e parameters as a function of composition 136 3.2 Density as a function of composition 137 3.3 L a t t i c e parameters as a function of conposition f o r the as-extruded Zn-rich wires 139 3.4 Density as a function of composition f or the as-extruded Zn-rich wires 140 4.1 Schematic diagram of the resistance measuring c i r c u i t 144 4.2 R e s i s t i v i t y as a function of composition 145 4.3 Isochronal recovery of r e s i s t i v i t y following 5 minute anneals at the temperature ind i c a t e d 147 4.4 E f f e c t of annealing temperature on the isothermal annealing curves 148 4.5 Arrhenius p l o t of the r e c i p r o c a l of the time taken reach the maximum r e s i s t i v i t y against the r e c i p r o c a l of the annealing temperature 150 L i s t of Figures (Cont) - x i i -Page 4.6 T y p i c a l plot of fci/f against t ^ for an increase i n r e s i s t i v i t y 152 4.7 Arrhenius p l o t of the r e c i p r o c a l of the intercept i n Figure 4.7 against the r e c i p r o c a l of the annealing temperature 153 4.8 T y p i c a l p l o t of fci/f^ against t i f o r a decrease i n r e s i s t i v i t y 154 4.9 Arrhenius plot of the r e c i p r o c a l of the intercept i n Figure 4.8 against the r e c i p r o c a l of the annealing temperature 155 4.10 Atom arrangements i n Zn-rich wire 157 5.1 E l e c t r o n micrographs showing t y p i c a l s t r i p e d contrast on bright f i e l d and streaks on SAD pattern 162 5.2 Electron micrographs showing streaks, s a t i l l i t e s and double.zones on SAD pattern 163 5.3 Electron micrographs showing s t r i p e d contrast and bend contours, and SAD pattern 163 5.4 E l e c t r o n micrographs showing possible APB and SAD pattern 164 5.5 E l e c t r o n micrographs showing t y p i c a l area and SAD pattern 165 5.6 Electron micrographs showing t h i n twin-like markings and SAD pattern 166 5.7 E l e c t r o n micrograph showing possible APB 167 A - l Schematic i l l u s t r a t i o n of P e i e r l s ' mechanism 179 x i i i -LIST OF TABLES Page 2.1 Chemical compositions of the AuZn a l l o y s 7 2.2 The thermally activated deformation data f o r AuZn at y i e l d 118 2.3 The values of the shear stress at 0°K obtained by extrapolating the a-T and T - T curves 121 2.4 The thermally activated deformation parameters deduced by the Dorn-Rajnak analysis from the experimental data f o r AuZn . 129 3.1 Lines on the x-ray patterns 135 3.2 L a t t i c e parameter and density data f o r AuZn 135 3.3 L a t t i c e parameter and density data f o r as-extruded Zn-rich wires 141 4.1 The v a r i a t i o n of the maximum r e s i s t i v i t y increase with composition 149 - 1 -1. INTRODUCTION 1.1. OBJECT OF THE INVESTIGATION There i s considerable i n t e r e s t i n materials which can be used i n high temperature s t r u c t u r a l a p p l i c a t i o n s . Materials such as i n t e r s t i t i a l compounds, i n t e r m e t a l l i c compounds and primary m e t a l l i c s o l i d solutions are currently being investigated. The name 'i n t e r m e t a l l i c •. compound' i s usually given to those intermediate phases which exhibit long range order over the e n t i r e temperature range of stability."'" They usually occur,at a d e f i n i t e atomic r a t i o and often exhibit a narrow homogeneity range. Interm e t a l l i c s are of i n t e r e s t mainly because of t h e i r high temperature strength and useful p h y s i c a l properties, eg. semiconducting properties, oxidation resistance. Furthermore t h e i r a d d i t i o n i n f i n e despersion to d u c t i l e metals causes strong hardening. Current knowledge of the mechanical behaviour of i n t e r m e t a l l i c compounds i s very l i m i t e d compared with that of pure metals and primary m e t a l l i c s o l i d s o l u t i o n s . U n t i l the s i x t i e s , work on t h i s c l a s s of materials generally has been exploratory and ad hoc i n nature. Investigations, 2 such as those of Wood and Westbrook on AgMg, Marcinkowski and Chessin on FeCo, 4 5 B a l l and Smallman on N i A l , Mote, Tanaka and Dorn on Ag-Al, and several others, are contributions to the systematic documentation of the mechanical properties of i n t e r m e t a l l i c compounds. The object of the present i n v e s t i g a t i o n was to characterize the deformation behaviour of a simple ordered i n t e r m e t a l l i c over as wide a range as possible of the usual m e t a l l u r g i c a l v a r i a b l e s . The compound AuZn was selected f o r the following reasons, (1) the melting point of 725°C i s moderate and congruent,^ see Figure 1.1, (2) there i s a range of s o l i d s o l u b i l i t y from 47.5 to 52.0 a/o Au, (3) i t has a simple c r y s t a l 7 8 structure -CsCl, (B^ or L2o) ' and (4) the structure i s highly ordered 9 10 to the melting point. ' The f i r s t and second c r i t e r i a were expected to a i d i n the preparation of homogeneous s i n g l e phase specimens while the t h i r d and fourth would help s i m p l i f y the analysis of the test r e s u l t s . The range of s o l u b i l i t y also presents an opportunity to study the e f f e c t s of c o n s t i t u t i o n a l l a t t i c e defects on the deformation behaviour. To t h i s end a determination of the defect structure of AuZn was c a r r i e d out. A d d i t i o n a l information on the defect structure was obtained from an annealing study. 1.2. PERTINENT LITERATURE There are several comprehensive reviews of the mechanical proper-11-13 14 t . • c . j. . „„„„„„„,!„ and ordered a l l o y s with the most t i e s of i n t e r m e t a l l i c compounds J 11 I* extensive being those of Westbrook and S t o l o f f and Davies. A few of the studies on the mechanical properties of B2 s u p e r l a t t i c e s , with emphasis on the p o l y c r y s t a l l i n e materials, w i l l - b e mentioned here. Two f u l l y ordered i n t e r m e t a l l i c compounds that have been extensively investigated to date are AgMg^ '^ "** and NlAl^'^'"'"^, while of the materials 3 18 19 20 that order below the melting point, FeCo ' and 3 brass ' have been investigated. 2 15 Wood and Westbrook , and Terry and Smallman have investigated the t e n s i l e properties of AgMg a l l o y s covering a wide range of compositions - 3 -WEIGHT PER CENT ZINC 5 tO 15 20 30 40 50 60 70 80 90 0 10 20 30 40 SO CO 70 80 90 100 »u ATOMIC PER CENT ZINC Z» Fig. 142. Au-Zn Figure 1.1. Phase diagram for Au-Zn. - 4 -and temperatures. Mg-rich a l l o y s were found to be b r i t t l e helow 200°C while the Ag-rich a l l o y s were d u c t i l e to -196°C. Deformation occurred by s l i p on the planes of the <111> zone i . e . {110}, {112} and {123}, over the e n t i r e temperature and composition range. At temperatures below 0.6 of the melting point, the flow stress of the non-stoichiometric a l l o y s was higher than that of the stoichiometric a l l o y s . The reverse was true at higher temperatures. The observed y i e l d point and discontinuous y i e l d i n g phenomena i n the range 150° to 350°C was attributed by Westbrook and Wood to the i n t e r a c t i o n of d i s l o c a t i o n with solute atmospheres. However, Terry and Smallman did not observe any y i e l d points i n the same temperature range. 4 1 7 B a l l and Smallman and Rozner and Wasilewski have investigated the mechanical behaviour of N i A l , using compression and t e n s i l e t e s t i n g r e s p e c t i v e l y . At temperatures above 0.45 Tm, p o l y c r y s t a l l i n e N i A l has high d u c t i l i t y and low y i e l d strength; from room temperature to 0.45 Tm^NiAl has l i m i t e d d u c t i l i t y and high strength; below room temperature no d u c t i l i t y was detected before f r a c t u r e . Composition does not have as pronounced an e f f e c t as i n the AgMg system. The operative s l i p system 21 was found to be {110} <001>, thus accounting for the lack of d u c t i l i t y below 0.45 Tm. Above 0.45 Tm d i f f u s i o n c o n t r o l l e d deformation processes aid the .deformation. A minimum i n the flow stress was observed for the stoichiometric composition at low temperatures. Discontinuous y i e l d i n g was observed i n t e n s i l e t e s t i n g . 3 18 Marcinkowski and Chessin and S t o l o f f and Davies have investigated the mechanical properties of ordered and disordered - 5 -FeCo. The e f f e c t s of long-range order on y i e l d i n g , s t r a i n hardening, deformation modes and d u c t i l i t y were examined. The y i e l d stress exhibited a peak at a c r i t i c a l degree of order. The s t r a i n hardening 3 rate increased with increasing long—range order, while the d u c t i l i t y decreased. Both were co r r e l a t e d with the ordering a f f e c t i n g the mode of deformation by suppressing the amount of c r o s s - s l i p . Wavy s l i p r e s u l t i n g from g l i d e on a l l planes of the <111> zone occurs i n disordered FeCo whereas only planar s l i p i s observed i n ordered FeCo u n t i l dynamic recovery occurs. The deformation behaviour of 3 brass also exhibits a strong dependence on the long-range order. A d d i t i o n a l references w i l l be made i n the text. 2. DEFORMATION BEHAVIOUR 2.1.vi EXPERIMENTAL PROCEDURE 2.1.1. Materials and Ingot Preparation The Zn used i n t h i s i n v e s t i g a t i o n was obtained, from Cominco Ltd., T r a i l , B.C. i n the form of one-half inch diameter rods. The p u r i t y was 99.999% with the main impurities being Pb and Fe. The Au was obtained from two sources. The Au s p l a t t e r supplied by Cominco.Ltd. had a p u r i t y of 99.999+% With Ag as the major impurity. A Au bar of 99.999+% pu r i t y was obtained through the courtesy of the Canadian Metal Mining Association. The Zn rods were swaged down to 0.27 i n . d i a . and cleaned i n d i l u t e HNO^- Both the Au and Zn were thoroughly degreased before sealing i n vycor tubing which had been cleaned with an H»S0, - Cr„0„ s o l u t i o n . - 6 -Ingots of the desired compositions were prepared by melting accurately weighed amounts of Au and Zn under vacuo i n 11 mm I.D. vycor tubing. The materials were melted at 850°C i n a muffle furnace. The melts were turned end for end several times to ensure adequate mixing. The melt was quenched i n water to minimize d e - z i n c i f i c a t i o n during cooling. This resulted i n a small amount of coring at the top end which was cut o f f with a jeweller's saw before the extrusion or r o l l i n g process. The ingots were resealed i n larger diameter tubing and annealed under vacuo f or 48 hours at 650°C and a i r cooled. Ingots having the nominal compositions shown i n Table 2.1 were prepared. A wet analysis assaying procedure was used to determine the actual compositions with the r e s u l t s also shown i n Table 2.1. The quoted compositions are probably within - .05 atom percent (a/o) Au of the true values. 2.1.2. Specimen Preparation Specimens used i n a t e n s i l e deformation study must be sound, of s i g n i f i c a n t s i z e , and give reproducible r e s u l t s . The specimens used i n t h i s study were fabricated by hot extrusion and by r o l l i n g . The extrusion process was used because i t gave a large number of uniform specimens from a s i n g l e heat, thus minimizing material wastage. Extrusion permits the u t i l i z a t i o n of the three factors known to enhance deformability i n a b r i t t l e m aterial, namely, high temperature, low s t r a i n - r a t e and near hydrostatic stress state. It also helps break down the b r i t t l e as-cast structure. - 7 -Table 2.1 Chemical Composition of the AuZn A l l o y s Ingot Nominal Assayed Averaged a/o Au number w/o Au w/o Au w/o Au 1 73.21 73.54 73.54 47.66 2 73.71 73.88 73.83 73.85 48.38 3 74.20 74.26 74.25 74.26 48.92 4 74.78 74.79 74.78 74.79 49.54 5 74.99 74.95 74.95 49.88 6 75.50 75.44 75.43 75.49 50.55 7 76.00 76.21 76.21 51.30 8 76.50 76.54 76.57 76.51 51.94 9 75.10 75.17 75.09 75.13 50.07 10 76.50 76.32 76.24 76.28 51.63 11 74.97 74.88 74.86 74.87 49.78 12 75.45 75.42 75.42 75.42 50.45 13 75.82 75.80 75.77 75.79 50.96 14 76.51 76.42 76.50 76.46 51.88 - 8 -Wire 0.040 i n . d i a . was extruded by the i n d i r e c t extrusion technique using the s t e e l die i l l u s t r a t e d i n Figure 2.1. The die was heated by a Lepel Induction unit to ^ 500-525 oC as measured by a Cu-Constantin thermocouple which was inserted i n the ram. Pressures of 50,000-60,000 p s i gave an extrusion rate of 9-12 in./min. Approximately 40 specimens 2 i n . long were obtained from a 30 gm b i l l e t . The specimens were flaw free and had a smooth shiny surface. The grain s i z e was approximately 60-70 y as shown i n Figure 2.2. The grain structure shown i n Figure 2.2b indicates that uniform equiaxed grains were obtained. The material appeared to be i n a r e c r y s t a l l i z e d state. The specimens were annealed i n vacuo at 260°C for 12 hours and etched i n a KCN-water s o l u t i o n p r i o r to t e s t i n g . A number of t e n s i l e s t r i p specimens were prepared f o r microscopy and grain s i z e studies. To break down the as-cast structure the homogenized ingot was encapsulated i n a mild s t e e l sleeve and hot swaged at 400°C. A f t e r one swaging pass the ingot was hot r o l l e d i n four passes to 0.1 i n . thickness. The mild s t e e l was removed by grinding and the ingot was cold, r o l l e d to ^ 0.030 i n . Tensile specimens having a 0.8 i n gauge length and 0.20 i n . by 0.030 i n . cross-section were punched out. A layer ~.001 i n . was removed by e l e c t r o p o l i s h i n g at 12V i n a 5% KCN-water s o l u t i o n to remove the damage caused by punching. The specimens were annealed i n vacuo to the desired grain s i z e . Approximately 8-10 specimens were obtained from a 50 gm ingot. The e l e c t r o p o l i s h i n g s o l u t i o n gave the best r e s u l t s i f i t was warmed s l i g h t l y . The e l e c t r o p o l i s h i n g procedure produced a dark oxide layer WIRE - 9 -INDUCTION COILS EXTRUSION CYLINDER AuZn BILLET CYLINDER CAP SABRE STEEL PNEUMATIC JACK Figure 2.1. Schematic diagram of extrusion apparatus, (a) X100 - 11 -which was removed by, a 15 sec. etch at 1.5V. The etching procedure outlined the grain boundaries which aided the metallographic observations. 2.1.3 Tens i l e Testing Procedure The t e n s i l e t e s t i n g was c a r r i e d out on a Floor Model Instron. The t e n s i l e tests were conducted at a cross-head speed of 0.1 in./min., except where noted. The t e s t i n g was performed over the temperature range from 77° to 533°K using the following temperature baths: l i q u i d nitrogen, petroleum ether cooled by l i q u i d nitrogen (133 to 293°K), b o i l i n g water, and s i l i c o n e o i l (373 to 533°K). The bath temperature was co n t r o l l e d to within - 2°, The wire specimens were held i n small pin chucks which gave good a x i a l alignment. The gauge length was approximately 1 inch. Very few specimens f a i l e d within the g r i p s . The s t r i p specimens were tested using s p l i t jaw g r i p s . Both assemblies are shown i n Figure 2.3. 2.2 STRESS-STRAIN RELATIONSHIP 2.2.1 Nature of the S t r e s s - S t r a i n Curves Tensile tests were c a r r i e d out at temperatures from 77° to 533°K on a l l o y s covering the complete composition range of the phase f i e l d . The true s t r e s s - t r u e s t r a i n curves obtained at room temperature for the f u l l y annealed material as a function of composition are shown i n Figure 2.4. The curves are q u a l i t a t i v e l y s i m i l a r ; possessing a small Luder's s t r a i n followed by a short l i n e a r region, then a parabolic region which exhibited a serrated flow that tended to die out,after a short s t r a i n . The stoichiometric a l l o y had a smooth y i e l d and no evidence of serrated - 12 -CO oo oo vo o CO o VO o S7-X I I l _ I - • • i L 10 20 30 TRUE STRAIN €. % o Figure 2.4b. Stress-Strain curves for Au-rich at 295 K. - 15 -flow. I t was also observed that f o r t h i s temperature range the work hardening increased with increasing composition for the Au-rich a l l o y s but was e s s e n t i a l l y independent of composition for the Zn-rich material. A comparison with the s t r e s s - s t r a i n curves obtained by 3 Marcinkowski and Chessin for ordered FeCo suggests that the s t r e s s - s t r a i n curves for AuZn can be divided into three d i s t i n c t stages. Stage I i s a region of e s s e n t i a l l y zero work hardening, i . e . the Luder's s t r a i n , and i s absent i n the stoichiometric a l l o y . Stage II i s characterized by a very rapid l i n e a r work hardening rate, which i s quite short,at room temperature. Stage I I I i s a region of decreasing work hardening corresponding to dynamic recovery. This d e l i n e a t i o n of the s t r e s s - s t r a i n curves i s more e a s i l y detected at lower temperatures. The e f f e c t of the tes t i n g temperature on the true st r e s s - t r u e s t r a i n curves f o r t y p i c a l f u l l y annealed compositions i s shown i n Figure 2.5. P l a s t i c s t r a i n preceeding fr a c t u r e was observed at a l l temperatures and compositions with the exception of those a l l o y s containing le s s than 49.5 a/o Au at 77°K, which f a i l e d without,any appreciable p l a s t i c s t r a i n . At temperatures from 77° to 373°K d u c t i l i t y ranging from 10 to 50% was obtained followed by intergranular f r a c t u r e at the maximum str e s s . Above 373°K considerable s t r a i n beyond the maximum st r e s s , not associated with necking, was observed. The temperature of 373°K corresponds to an e f f e c t i v e temperature Th = 0.37 Tm, where Tm i s the melting point °K. Thus two regimes of deformation behaviour can be delineated, above,and below approximately 0.4 Tm. Below 0.4 Tm,observations i n d i c a t e that deformation procedes I 1 . I I L 0 10 20 30 4 0 TRUE STRAIN £ % Figure 2.5a. Stress-Strain curves as a function of temperature f o r the 48.92 a/o Au composition. 100 composition. 100 I I ; | . 1 0 " 2 0 30 40 TRUE STRAIN £ % i Figure 2.5c. Stress-Strain curves as a function of temperature for the 51.88 a/o Au °^ composition. - 19 -pri m a r i l y by s l i p while above 0.4 Tm the observation of grain boundary migration suggests that s l i p and d i f f u s i o n c o n t r o l l e d processes are act i v e . This d e l i n e a t i o n of deformation regimes has also been observed 17 2 3 i n N i A l and N i T i , AgMg, and FeCo at the appropriate temperature, 0.4-0.45 Tm. Tests were also performed on the as-extruded wires, with the r e s u l t that the Au-rich a l l o y s gave e s s e n t i a l l y the same s t r e s s - s t r a i n curves, including Luder's s t r a i n and ser r a t i o n s . The Zn-rich a l l o y s exhibited a pronounced increase i n flow stress as shown i n Figure 2.6. The as-extruded Zn-rich material had a smooth y i e l d and pronounced serrations. The work hardening rate was s l i g h t l y higher at low s t r a i n s . The extra hardening i n the as-extruded Zn-rich a l l o y s was dependent on the deviation from stoichiometry and was observed for a l l temperatures below 350°K. 2.2.2 Luder's S t r a i n and Serrated Flow A Luder's s t r a i n (Stage I) of approximately 0.5% was present i n f u l l y annealed compositions which were more than 0.2 a/o o f f stoichiometry r and tested at temperatures below 373°K. The s t r a i n decreased i n magnitude with decreasing temperature but was s t i l l present at 77°K. Serrations i n the flow curve were detected only at room temperature and exhibited the c h a r a c t e r i s t i c s of the Portevin-Le Chatelier phenomenon. The following observations were made i n support of t h i s claim. 1) The serrations were only observed i n non-stoichiometric a l l o y s . 2) An i n i t i a l p r e s t r a i n of approximately 1% occurred before / 10 20 30 ' to TRUE STRAIN cr % , Figure 2.6. Comparison of the s t r e s s - s t r a i n curves f o r the as-extruded and annealed 48.92 a/o Au composition. - l i -the serrations commenced. 3) The serrations were pe r i o d i c i n nature and tended to dampen down and die out a f t e r approximately 10% s t r a i n . 4) The serrations were detected only at room temperature. 5) At the -4 -1 s t r a i n - r a t e of 1.6 x 10 sec the serrations were larger and more c l e a r l y defined. 6) The serrations tended to increase i n magnitude with increasing grain s i z e . The Portevin-Le Chatel i e r e f f e c t has been r a t i o n a l i z e d as a strain-aging e f f e c t i n which the solute atoms move fa s t enough to 20 22 produce successive y i e l d points during a normal t e n s i l e test ' Further evidence of strain-aging a r i s e s from the observation that the Luder's s t r a i n could be recovered by aging a f t e r i t s removal by p l a s t i c s t r a i n . 2.2.3 D u c t i l i t y The d u c t i l i t y of the wire specimens used i n t h i s i n v e s t i g a t i o n was found to be a reproducible parameter. The true s t r a i n to f a i l u r e has been taken as a measure of the d u c t i l i t y since i t was e a s i l y obtained from the load-elongation curves and the measurement of the reduction i n area on wire specimens was not p r a c t i c a l . The temperature dependence of the d u c t i l i t y as a function of composition i s i l l u s t r a t e d i n Figure 2.7. There are three regions discemable; 1) from 77 to 273°K, the d u c t i l i t y increases with temperature, with the more pronounced peak occurring i n Zn-rich a l l o y s . 2) from 273 to 423°K a loss of d u c t i l i t y i s observed, 3) above 400°K the d u c t i l i t y increases s i g n i f i c a n t l y . The Au-rich a l l o y s are l e s s d u c t i l e than both Zn-rich and stoichiometric a l l o y s at almost a l l temperatures. - 22 -- 23 -The loss of d u c t i l i t y i n the intermediate temperature range j u s t below the r e c r y s t a l l i z a t i o n temperature has been observed i n almost 23 a l l d u c t i l e metals and; a l l o y s . For fee s u b s t i t u t i o n a l a l l o y s Rhines 23 and Wray have a t t r i b u t e d the d u c t i l i t y l o s s to the formation of c a v i t i e s at grain boundaries. The d u c t i l i t y l o s s i s l i m i t e d to temperatures above the beginning of recovery where grain boundary shearing becomes a c t i v e and below the r e c r y s t a l l i z a t i o n temperature where grain growth prevents any re a c t i o n with the c a v i t i e s . The temperature range of the d u c t i l i t y minimum observed i n t h i s work appears to agree with t h i s l i m i t a t i o n . C a v i t i e s mainly i n the v i c i n i t y of the grain boundaries are shown i n Figure 2.8 for a Au-iLch s t r i p t e n s i l e specimen deformed to fr a c t u r e at 373°K. A layer approximately .010 i n thick was removed by mechanical p o l i s h i n g , and the deformed layer removed by e l e c t r o l y t i c p o l i s h i n g . A l i g h t etch was given to o u t l i n e the grain boundaries without di s t u r b i n g the c a v i t y d i s t r i b u t i o n . However, no evidence of grain boundary shearing could be detected at magnifications up to llOOx, nor was any evidence of sub-grain formation or r e c r y s t a l l i z a t i o n detected at temperatures up., to 373°K. On the other hand, the example of grain boundary separation shown i n Figure 2.9, the observation of the granular i n t e r c r y s t a l l i n e type of fr a c t u r e and the observation that a decrease i n the grain s i z e resulted i n an increase i n d u c t i l i t y are a l l consistent with the "intermediate temperature embrittlement'' mechanism. (b) X100 Figure 2.8. Micrograph of s t r i p specimen deformed 16% at 373 K showing c a v i t i e s at grain boundaries. X250 Figure 2.9, Same specimen as i n Figure 2.8^showing grain boundary separation near the fracture surface. An a l t e r n a t i v e mechanism for the d u c t i l i t y loss has been suggested 24 by Koch and Troiano. They have pointed out that the existance of the Portevin-Le Chatelier phenomenon i n s u b s t i t u t i o n a l fee a l l o y s suggests that an analogy can be made with the spontaneous strain-aging embrittlement of i n t e r s t i t i a l bec a l l o y s . They have predicted that the temperature range i n which serrated flow occurs should coincide with the range of decreasing d u c t i l i t y , i n agreement with the observations i n t h i s work. The lack of spontaneous r e c r y s t a l l i z a t l o n i s also consistent with the strain-aging mechanism as i s the I n t r i n s i c property that the c r y s t a l structure i s b a s i c a l l y bcc. However, the observations concerning c a v i t i e s , grain boundary separation and i n t e r c r y s t a l l i n e f r a c t u r e do tend to suggest the p o s s i b i l i t y that both mechanisms considered may be operative i n the system. - 26 -2.2.4. Maximum Stress The maximum stress (or ultimate t e n s i l e stress) as a function of temperature for several t y p i c a l compositions i s shown i n Figure 2.10. There would appear to be a l i n e a r decrease i n the maximum stress with increasing temperature, with a peak superposed over the range 200 - 350°K. The peak would appear to be a consequence of the increased d u c t i l i t y over the same temperature range. A l i n e a r , or at most.two stage, decrease i n the maximum stress with increasing temperature has been observed for i 25 most metals. 100 80 •H CO cu .00 I o X b CO CO w Pi H CO 60 40 20 48.92 a/o Au 50.07 ° 50.96 A 51.88 4. 100 200 300 400 500 T ° K TEMPERATURE Figure 2.10. Maximum stress as a function of temperature. - 27 -The e f f e c t of the composition on the maximum stress at room temperature i s shown i n Figure 2.11. More pronounced hardening i s .•Obtained i n the Au-rich a l l o y s although the d u c t i l i t y i s e s s e n t i a l l y l e s s than or equal to that i n the Zn-rich and stoichiometric a l l o y s . 48 49 l 50 a/o Au 51 52 Figure 2.11. Maximum stress as a function of composition. - 28 -2.2.5. S t r a i n Hardening Exponent The empirical r e l a t i o n s o = Ke" has been used to approximate the behaviour of s t r e s s - s t r a i n curves of many metals. Logarithmic plots of the true s t r e s s - t r u e s t r a i n are shown i n Figure 2.12 for t y p i c a l compositions as functions of temperature. A l l specimens were found to conform to the empirical r e l a t i o n except at low temperatures and low s t r a i n s where l i n e a r hardening occurred and the empirical r e l a t i o n should be a = 0 j +Ke n where i s the y i e l d s t r e s s . The drop o f f at high temperatures i s r e l a t e d to necking. The v a r i a t i o n of the s t r a i n hardening c o e f f i c i e n t as a function of temperature obtained from the slope of the log-log p l o t s i s shown i n Figure 2.13. If a co r r e c t i o n f o r the temperature dependence of the e l a s t i c modulus were included ( i . e . n/E), the s t r a i n hardening c o e f f i c i e n t at temperatures<300°K would be a constant indpendent of temperature. The value of n ~0.5 i s comparable with the behaviour of many metals, e.g. at equivalent homologous temperature s i l v e r , 0.5; vanadium, 0.1; molybdenum, 0.25; tantalum, 0.2; tungsten 0.4; titanium, 0.5; and AgMg, 0.4. There would appear to be a decrease i n the s t r a i n hardening capacity as a function of composition at room temperature s i m i l a r to the observations of Wood and Westbrook on AgMg and i n agreement with previous work.^ J 1 1 10 20 50 \ TRUE STRAIN £ % Figure 2.12c. True stress-true s t r a i n plots f o r the 51.88 a/o Au composition. - 32 -H 25 W S5 O w o M. !Z5 W •a H CO V 48.92 a/o Au • 5 0 . 0 7 O 51.88 400 100 200 300 TEMPERATURE T°K Figure 2.13. S t r a i n hardening exponent n, as a function of temperature. 500 - 33 -2.3 STRUCTURAL OBSERVATIONS 2.3.1 Deformation Modes As already noted, the p o l y c r s t a l l i n e AuZn a l l o y s behave i n a d u c t i l e manner over the e n t i r e temperature range investigated. This behaviour i s at variance with the p r e d i c t i o n of Rachinger and 26 C o t t r e l l who found that the only s l i p system operative was { 110} 27 28 29 <001> which gives only three independent modes of s l i p . ' . von Mises c r i t e r i o n states that p l a s t i c deformation i n a p o l y c r y s t a l l i n e specimen requires that the stress and the material remain continuous. Continuity of the material ( i . e . no grain boundary shearing or separation) requires s l i p to take place on at l e a s t f i v e independent s l i p systems. If there are only three independent s l i p systems of the form {110} <001> then a d d i t i o n a l modes of deformatlion, such as twinning, or grain boundary shearing, are required.for a,general s t r a i n i n AuZn. Kinking and cross s l i p are often considered but i t can be shown,that even i f they do occur they do not contribute a d d i t i o n a l modes of deformation. Twinning as an extra mode of deformation was not observed at any temperature, s t r a i n - r a t e or composition i n t h i s work. This i s i n agreement with the p r e d i c t i o n by Laves that long-range order should 30 i n h i b i t mechanical twinning. Cahn and C o l l have pointed out that for the normal bcc twinning elements {112} <111> , a disordering of the l a t t i c e would r e s u l t . Figure 2.14 i l l u s t r a t e s the atomic motions during twinning for the disordered and ordered bcc l a t t i c e . The atomic.movement reconstructs the bcc l a t t i c e for the disordered state without any a d d i t i o n a l atomic rearrangement. However, i n the ordered case, the o r i g i n a l simple cubic structure with A atoms at cube corners and B atoms at cube centres becomes - 34 -Figure 2,14. Atomic motions during mechanical twinning of an AB a l l o y . Black symbols represent atoms i n the plane of proj e c t i o n , open symbols those on adjacent planes. The cross-section of the unit c e l l i s outlined. (a) disordered - a l l atoms equivalent,(b) ordered - c i r c l e s represent A atoms , squares represent B atoms 30 (from Cahn and C o l l ) . - 35 -an ordered tetragonal structure with 50% of the nearest neighbours unlike atoms. As i t i s considered e n e r g e t i c a l l y unfavourable f o r the atomic motion necessary to restore the l a t t i c e at low temperatures, twinning i s not expected to occur. Kinking was not detected i n the deformation of p o l y c r y s f a l l i n e A 31 32 AuZn. However, kinking has been observed i n N i A l , CsBr, and C s l i n compression along the <100> axes. Since kinking only occurs i f the s l i p vector of the s l i p plane i s eit h e r p a r a l l e l or at r i g h t angles to the compression axes, the only possible operational Burgers vector i s <001> which w i l l not increase the number of deformation modes. 2.3.2. Deformation Markings The development of the s l i p l i n e s with s t r a i n i n g i s shown i n Figure 2.15. For s t r a i n s of 5% or l e s s the s l i p l i n e s are extremely f i n e and d i f f i c u l t to detect even at high - magnifications. Figure 2.15a shows only a few grains with coarse s l i p l i n e s and no i n d i c a t i o n of cracking or grain boundary separation. At 9.4% s t r a i n ^ s l i p l i n e s are e a s i l y detected and appear both wavy and s t r a i g h t . Severe deformation i n the v i c i n i t y of the grain boundaries i s more apparent with sets of s l i p l i n e s along the grain boundaries with increasing s t r a i n . The presence of a d d i t i o n a l s l i p l i n e s i n the v i c i n i t y of the grain boundaries i s shown more c l e a r l y i n Figure 2.16. There are at l e a s t four sets of l i n e s along the edge of grain A, with profuse c r o s s - s l i p i n a l l regions. Figure 2.17 shows an example i n which the r e l a t i v e l y undeformed centre region of grain B i s surrounded by regions of severe deformation. Figure 2.18a shows the s l i p l i n e s passing through grain boundaries without a major change i n - 36 -Figure 2.16. Microstructure of specimen deformed 21.8% at 295iK, shows multiple s l i p l i n e s near grain boundaries. shows the severe deformation around an undeformed cent r a l region of a grain. Figure 2.18. Microstructure of a specimen deformed 25% at 295CK, (a) shows s l i p l i n e s passing through grain boundaries, (b) shows severe deformation near the frac t u r e surface. - 39 -or i e n t a t i o n or intensity. Figure 2.18b shows the severe deformation, wavy s l i p and elongation of grains without cracking that occurs near the fract u r e surface. Reference scratches were made (using a f i n e brush) on an electropolished t e n s i l e specimen before t e s t i n g i n an attempt to detect any grain boundary shearing or migration. The specimen was deformed only 6.8% as a d d i t i o n a l s t r a i n resulted i n an extremely uneven surface and d i f f i c u l t y i n focusing at high magnifications. Figure 2.19 shows that although the grains have become quite d i s t o r t e d the scratches are not discontinuous.at the grain boundaries. Figure 2.20 from a specimen deformed at 77°K to frac t u r e at 12.3% s t r a i n also shows no i n d i c a t i o n of grain boundary shearing or cracking. Figure 2.20c shows a set of fi n e s t r a i g h t s l i p l i n e s . Near the frac t u r e surface wavy s l i p l i n e s are common and the fr a c t u r e surface appears to be intragranular. The observation of f i n e s t r a i g h t s l i p l i n e s at low s t r a i n s and low 18 temperatures i s i n agreement with the expectation for ordered a l l o y s as observed i n FeCo. At higher s t r a i n s c r o s s - s l i p i s quite pronounced which i s also i n agreement with observations on FeCo. A.single surface trace analysis was performed i n an attempt to i d e n t i f y the operative s l i p planes. A s t r i p t e n s i l e specimen was annealed i n vacuo at 600°C for 24 hours to obtain grains approximately 1-2 mm i n diameter. A f t e r deforming the specimen to f a i l u r e i t was.observed that the s l i p l i n e s were mainly s t r a i g h t and most grains had several sets of . l i n e s . B a c k - r e f l e c t i o n Laue X-ray pictures were taken of s u i t a b l e grains and a trace analysis c a r r i e d out. Due to the rough nature of the surface and d i f f i c u l t y i n a l i g n i n g the surfaces p a r a l l e l to the X-ray pattern and (a) X260 (b) X700 Lgure 2.19. Microstructure of specimen deformed 6.8% at 295SK, shows continuous reference l i n e s across grain boundaries. - 41 -(c) X700 - 42 -micrograph, i t i s apparent that the technique has an inherent error which could be as much as - 5°. Thus to obtain rigorous r e s u l t s a s t a t i s t i c a l study would be required based on many observations. However, the r e s u l t s shown i n Figure; 2.21 tend to suggest that the main operative s l i p planes are {110} and {310} . The r e s u l t s also suggest that s l i p planes of the form {100} , {211} and{123} may be operative. These observations have been substantiated i n work 33 on sin g l e c r y s t a l s of AuZn. The presence of the {310} s l i p trace was found to be temperature dependent and r e s t r i c t e d to room temperature. At higher temperatures s l i p traces of the form {001} were observed. On s u i t a b l y oriented c r y s t a l s and at lower temperatures, s l i p traces of the form {211} and {123} were observed. The multiple c r o s s - s l i p that i s observed at higher s t r a i n s can be indexed as either {110} or {310} at room temperature. B a l l 2 l and Smallman have observed s i m i l a r c r o s s - s l i p on planes of the < 001> zone and they show that t h i s type of c r o s s - s l i p does not contribute to the independent modes of deformation. Therefore since twinning, kinking and c r o s s - s l i p are u n l i k e l y to supply a d d i t i o n a l modes of deformation and grain boundary shearing or migration i s not operative over the temperature range from 77 to 400°K, i t would appear,that the observations of s l i p planes of the form. {001 } , {123} and {211} i s s i g n i f i c a n t , and i n fact s l i p on these planes does occur supplying the required f i v e modes of deformation. Figure 2.21a. Microstructure and schematic specimen deformed at 295'K. diagram of s l i p traces on - 4 4 -X1Q0 P o s s i b i l i t i e s (within t 4} 1) (310) 2) OIQ) , (310) 3) (211) , (310) 4) (110) , (123) 5) (123) , (110) , (310) Best f i t underlined. Figure 2.21b. Microstructure and schematic diagram of s l i p traces on specimen deformed at 295 aK„ - 4 5 -Figure 2.21c. Microstructure and schematic diagram of s l i p traces on specimen deformed at 295 JK. - 46 -2.3.3. D i s l o c a t i o n i Structure An examination of the d i s l o c a t i o n d i s t r i b u t i o n obtained i n p o l y c r y s t a l l i n e AuZn was c a r r i e d out using transmission electron microscopy. Specimen preparation i s outlined i n Chapter 5. Representative d i s l o c a t i o n arrangements a f t e r 3 and., 9% s t r a i n i n tension at room temperature are shown i n Figures 2.22 and 2.23. In a p o l y c r y s t a l l i n e material , p a r t i c u l a r i l y at small s t r a i n s , i t i s impossible to accurately r e l a t e the l o c a l s t r a i n i n a region as small as that observed i n trans-mission microscopy to the measured average s t r a i n . The l o c a l stress f i e l d also varies from one region to another i n both magnitude and o r i e n t a t i o n . Therefore^the observed v a r i a t i o n i n d i s l o c a t i o n structure from one region to another i s not unexpected. The tendency towards tangling or c l u s t e r i n g of d i s l o c a t i o n s i s apparent even at small s t r a i n s with c e l l formation also evident. Sharp kinks are present on many of the i s o l a t e d d i s l o c a t i o n l i n e s . This suggests that d i s l o c a t i o n motion i s accompanied by i n t e r s e c t i o n between 34 d i s l o c a t i o n s of opposite Burgers vector. C r o s s - s l i p i s suggested by the formation of large numbers of i r r e g u l a r l y shaped closed d i s l o c a t i o n loops (Figures 2.22b and 2.23d). The development of a c e l l structure i n which regions of high d i s l o c a t i o n density are separated by regions of low d i s l o c a t i o n density i s evident from the lowest s t r a i n s . The average distance between c e l l walls i s approximately 0.5u and appears to decrease s l i g h t l y with increasing s t r a i n . The d i s l o c a t i o n l i n e s do not 35 have the joggy appearance exhibited by d i s l o c a t i o n s i n bcc metals. - 47 -Figure 2.23. Electron Micrographs of Au-rlch specimen deformed 9% at 295°K. - 49 -The e f f e c t of the deformation temperature on the d i s l o c a t i o n arrangement i s shown i n Figures 2.24 and 2.25. The specimen deformed at 77°K was strained only 5% and although tangles were observed, no evidence of c e l l formation was detected. I t has been reported that more s t r a i n i s required at lower temperatures before c e l l formation becomes 35 pronounced. Sharp kinks, tangles, loops, cusps and dipoles are a l l v i s i b l e i n Figure 2.24. The d i s l o c a t i o n d i s t r i b u t i o n appears to be more uniform from one grain to the next. During the deformation at 463°K^ dynamic recovery occurred and hence c e l l structure was r a r e l y observed. Regions r e l a t i v e l y free of d i s l o c a t i o n s are separated by tangles and the d i s l o c a t i o n s tend to be more joggy. Evidence of recovery i s shown i n Figures 2.25e and 2.25f with the subgrains s l i g h t l y l a r ger than 0.5u i n diameter. Figure 2.25f also shows d i s l o c a t i o n s i n the grain boundaries. The recovered structure of a specimen r o l l e d to a reduction i n thickness of 90% and annealed at 473°K for 1 1/2 hours i s shown in. Figure 2.26. A hexagonal d i s l o c a t i o n network i s v i s i b l e i n Figure 2.26a while the average s i z e of the sub-grains remains the same as that of the c e l l present i n the deformed condition. Some general observations can be made on the d i s l o c a t i o n structures. Piled-up groups of d i s l o c a t i o n s were never observed. Some i n d i v i d u a l d i s l o c a t i o n s moved during observation i n the microscope due to the thermal stress introduced by the electron beam. Figure 2.27 shows the traces l e f t on the two surfaces of the f o i l . Following deformation at,77°K, very s t r a i g h t l i n e structures were observed, as shown i n Figure 2.28. Evidence of c r o s s - s l i p at point A suggests that these l i n e s are long screw 36 d i s l o c a t i o n s s i m i l a r to those.observed by Swann i n Al-4% Cu. Figure 2.24. Electron Micrographs of Au-rich specimen deformed 5% at 77°K. - 52 -Figure 2.26. Electron Micrographs of Au-rlch specimen annealed 11/2 hrs. at 473°K a f t e r r o l l i n g . Figure 2.27. Electron Micrograph showing s l i p traces of moving d i s l o c a t i o n s . - 53 -The d i s l o c a t i o n arrangement t y p i c a l of a Zn-rich specimen reduced 10% i n thickness by r o l l i n g i s shown i n Figure 2.29. An analysis 37 of the dark f i e l d micrographs using the i n v i s i b i l i t y c r i t e r i o n , i . e . g.b = 0 where g i s the vector of the r e f l e c t i n g plane and b i s the Burgers vector, showed that the Burgers vector was consistent with [001]. The double images can probably be a t t r i b u t e d to double d i f f r a c t i o n rather than s u p e r l a t t i c e d i s l o c a t i o n s . The d i s l o c a t i o n structures observed i n the Au-rich^stoichiometric and Zn-rich material appeared to be i d e n t i c a l , and also s i m i l a r to those observed f or bcc metals and a l l o y s . -54 -(a) L - * ^ (b) U ^ J Figure 2.28. Electron Micrographs showing s t r a i g h t d i s l o c a t i o n l i n e s i n specimen deformed 5% at 77°K. - 55 -2.4 YIELD STRESS AND WORK. HARDENING 2.4.1 E f f e c t of Temperature 2.4.1.1 On the Y i e l d Stress The s t r e s s - s t r a i n curve i s most amenable to analysis at the y i e l d s t r e s s . For the purposes of t h i s work the macroscopic y i e l d s tress has been a r b i t r a r i l y taken as the 0.1% proof s t r e s s , with no d i s t i n c t i o n being made as to the nature of the y i e l d phenomena. The v a r i a t i o n of y i e l d stress with temperature i s shown in,Figure 2.30 for several t y p i c a l compositions. At 373°K a d i s c o n t i n u i t y occurs for the Au-rich due to the change i n the nature of the y i e l d phenomenon. The Zn-rich, stoichiometric and extreme Au-rich a l l o y s a l l display s i m i l a r temperature dependence of y i e l d , that i s , a r e l a t i v e l y small dependence down to approximately 200°K and then a gradual increase with decreasing temperature. Au-rich a l l o y s i n the range 50.1 to 51.4 a/o Au showed the temperature dependence i l l u s t r a t e d by the 50.96 a/o Au composition. The y i e l d stress-temperature dependence can be compared with other metals by noting that since the melting point of 3*AuZn i s 725°C, the temperature i n °K i s d i r e c t l y proportional to the homologous temperature. 39 Figure 2 31, taken from Conrad, shows the y i e l d stress-temperature dependence of several other metals. In general the behaviour,is comparable with the bcc metals although the dependence i s not as strong. This may be p a r t i a l l y explained by the observation by Johnston, Davies and S t o l o f f that ordered FeCo-V.had a smaller temperature dependence 39 ' than the disordered material. In addition the temperature dependence , . „ 2,15,40,41 ..... 4,17 , „..„,. 17 . of AgMg , N i A l , and N i T i i s comparable over the same temperature range. A l l these i n t e r m e t a l l i c compounds are f u l l y ordered - 56 -•H CO a CO i o CO to w Di E-i to O w 60 -50 A O 30 20 10 _ L 100 400 Figure 2.30. . 200 300 TEMPERATURE T°K Y i e l d Stress as a function of temperature for various AuZn compositions. 500 - 57 -Figure 2.31. I n i t i a l y i e l d stress of various p o l y c r y s t a l l i n e metals 38 versus T/Tm (after Conrad ). to the melting point. The d i f f e r i n g behaviour of the 50.1 to 51.4 a/o Au a l l o y s w i l l be commented on i n section 2.5.3. The y i e l d stress-temperature curve was found to f i t the -Q. 42 kT empirical Zener-Hollomon r e l a t i o n a a e as shown i n Figure 2.32 for the temperature 77 to 500°K. The anomalous behaviour of the as-extruded Zn-rich material c ompared to the annealed material i s quite apparent i n the y i e l d s t r e s s -temperature dependence as shown i n Figure 2.33. The extra hardening of as extruded material i s only present below 350°K. 500 400 300 200 150 100 77 T TEMPERATURE T°K •H CO P, CO I o r H CO CO w H CO O 30 20 15 10 O 48.92 a/o Au & 50.07 Q 50.96 w 51.88 8 10 12 14 00 10 /T°K Figure 2.32. Y i e l d Stress as a function of the r e c i p r o c a l of the absolute temperature f o r various AuZn compositions. o 70 ~ 6 0 5 0 -4 0 -3 0 -2 0 1 0 - 5 9 -4 8 . 9 2 a / o A u A s - e x t r u d e d A n n e a l e d ± _L 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 T E M P E R A T U R E T ° K F i g u r e 2 . 3 3 . C o m p a r i s o n o f t h e y i e l d s t r e s s - t e m p e r a t u r e v a r i a t i o n o f t h e a s - e x t r u d e d a n d a n n e a l e d Z n - r i c h a l l o y s . 2.4.1.2. On the Flow Stress - 60 -The e f f e c t of the temperature on the flow stress f or several t y p i c a l compositions i s shown.in Figure 2.34. The decrease i n flow stress with increasing temperature i s more rapid at higher s t r a i n s and much more pronounced for the non-stoichiometric a l l o y s . An assessment of the e f f e c t of temperature on the work hardening can be obtained by subtracting the y i e l d stress from the flow stress at each s t r a i n . Figure 2.35 shows the work hardening parameter (a - a ) flow 0.1% as a function of temperature. The parameter i s independent of temperature up to a c r i t i c a l temperature, which decreases with the amount of p l a s t i c s t r a i n imposed. The dashed l i n e separates the two regions of work hardening behaviour. Only i n the stoichiometric a l l o y i s the work hardening perfect 43 l i n e a r i n the region below the dashed l i n e . Russell and J a f f r e y have correlated the lower region with Stage II hardening i n si n g l e c r y s t a l s and the upper region with Stage I I I , on the basis of comparable values 0 T T 9 9 of — — and (—) l i n e a r hardening. A value of — for the stoichiometric 1 6 a l l o y of — i s obtained from Figure 2.35a using a shear modulus of 2.32xl0 a o 45 a p s i and the assumption that T= -j . This value i s at l e a s t 2 orders of magnitude higher than that obtained for stage II hardening i n si n g l e 33 c r y s t a l s of AuZn . Grain boundaries i n p o l y c r y s t a l l i n e metals are expected to have a pronounced hardening e f f e c t . A comparison between the l i n e a r work hardening rates, where obtainable, and the stage II hardening rates i n fee, hep and'bec metals show that reasonable quantitative c o r r e l a tions are observed. Thus, the r e s u l t s obtained for AuZn are s i g n i f i c a n t i n terms of the grain boundary e f f e c t s . 80 - 61 -I 1 1 1 U 1 100 200 300 400 500 TEMPERATURE T°K Figure 2.34a. Flow Stress as a function of temperature for the 48.92 a/o Au,composition. - 62 100. 200 300 TEMPERATURE T°K 400 Figure 2.34b. Flow Stress as a function of temperature f 50.07 a/o Au composition. L I I I 1 u 100 200 300 400 500 TEMPERATURE T°K Figure 2.34c. Flow Stress as a function of temperature f o r the 51.88 a/o Au composition. - 64 -% S t r a i n 100 400 500 200 300 TEMPERATURE T°K Figure 2.35a. The v a r i a t i o n of the hardening parameter f o r the 50.07 a/o Au composition. 100 200 300 400 500 TEMPERATURE T°K Figure 2.35b. The v a r i a t i o n of the hardening parameter for the 51.88 a/o Au composition. - 66 -The observation of ( i l l ) zone s l i p i n p o l y c r y s t a l s , and i n su i t a b l y oriented s i n g l e c r y s t a l s at higher stress l e v e l s , and lower temperatures suggests that stress concentrations present i n the v i c i n i t y of grain boundaries are necessary to a c t i v a t e s l i p on plane of the <111> zone. Although a quantitative agreement i s not observed between the l i n e a r hardening of p o l y c r y s t a l s and stage II hardening of si n g l e c r y s t a l s , a q u a l i t a t i v e assessment can be made for the stoichiometric a l l o y . The region below the c r i t i c a l temperature i s a region of l i n e a r work hardening while above,T £ dynamic recovery i s occurring and decreasing the hardening rate. T £ v a r i e s with composition, increasing with increasing deviation from stoichiometry. Except at the lowest temperatures^the work hardening rate f or the non—stoichiometric a l l o y s , while not l i n e a r , i s independent of temperature i n the lower.region and i s approximately the same as for the stoichiometric composition. At temperatures below 150°K the work hardening rate increases s i g n i f i c a n t l y with decreasing temperature for the non-stoichiometric a l l o y s . Also at 77°K the Au-rich a l l o y has a l i n e a r work hardening rate which i s s i g n i f i c a n t l y higher than the stoichiometric value. 2.4.2 Effect of Composition 2.4.2.1 On the Y i e l d Stress ' The v a r i a t i o n of the y i e l d stress with composition over the range 47.96 to 51.94 a/o Au at room temperature i s shown i n Figure 2.36. The minimum i n y i e l d stress at the stoichiometric composition i s a commonly observed c h a r a c t e r i s t i c of ordered a l l o y s at low temperatures. The composit-ion dependence"of the y i e l d i s l i n e a r on both sides of the stoichiometric - 67 -Figure 2.36. Flow Stress as a function of composition and s t r a i n at 295 °K. - 68 -composition, with a deviation at the extreme Zn-rich composition tested. The hardening i s almost,equal on both sides of stoichiometry with s/ 9,000 psi/a/o for the Zn-rich material and ~ 7,500 p s i / a/o for the Au-rich material. The as-extruded Zn-rich material also exhibits a l i n e a r dependence of hardening on the deviation from stoichiometry, as shown i n Figure 2.37. Linear r e l a t i o n s h i p s between the hardening and deviation from stoichiometry were obtained from 133 to 533°K for both Au and Zn-rich material. The behaviour at 77°K was d i f f e r e n t for both materials. The Zn-rich specimens were b r i t t l e and exhibited l e s s than 0.5% d u c t i l i t y i n compositions containing l e s s than 49.5 a/o Au. This b r i t t l e n e s s may be a t t r i b u t e d to the low temperature phase transformation reported by Pops 45 and Massalski. They observed that the transformation temperature varied with the composition decreasing with increasing a/o Au. Furthermore, they did not i d e n t i f y the low temperature c r y s t a l l o g r a p h i c structure. The behaviour of the Au-rich material at 77°K i s shown i n Figure 2.38 along with t y p i c a l higher temperature curves. At 77°K a pronounced minimum exi s t s at approximately 50.5 a/o Au. Similar minima have 46 - 47 been reported i n d i l u t e a l l o y s of Ta-Re, Fe-Ni and Fe-Pt at low temperatures. 2.4.2.2 On the Flow Stress The flow stress at 295°K for various s t r a i n s i s also shown as a function of composition i n Figure 2.36. On the Zn-rich side the only e f f e c t of the composition i s to increase the flow s t r e s s , whereas on the Au-rich side there i s an a d d i t i o n a l work hardening e f f e c t . - 69 -ro I eg P. o rH 62 b 0 CO co w »i H CO Q W 60 50 -40 30 20 10 48 Figure 2.37. 295 °K As-extruded 49 50 a/o Au Comparison of the y i e l d stress-composition dependence of the as-extruded and annealed Zn-rich a l l o y s . - 70 -77°K 133 295 473 50 gure 2.38. 51 a/o Au 52 Y i e l d Stress as a function of composition for the Au-rich a l l o y s at several temperatures. Similar r e s u l t s were obtained at a l l test temperatures. The r e s u l t s at 77°K shown i n Figure 2.39 in d i c a t e that the e f f e c t of composition on the flow stress at a given s t r a i n i s a l i n e a r function with the slope increasing with s t r a i n . At temperatures above 77°K the l i n e a r r e l a t i o n s h i p was observed although there i s a marked increase i n the f i r s t 0.1-0.3 a/o A u a s shown i n Figure 2.36. The extrapolated value at 50.0 a/o Au was d i f f e r e n t from the stoichiometric value. The y i e l d stress data, the Zn-rich flow stress data and the low temperature Au-rich data can be represented by an empirical r e l a t i o n of the form a- = 0 - + RA where a- i s the flow s t r e s s , a, i s the f fs f f s flow stress at 50.0 a/o.Au, A i s the deviation from stoichiometry i n a/o and K i s a constant. The a_ value was almost i d e n t i c a l to the flow stress f s of the 50.07 a/o Au a l l o y , except as already noted, f o r the Au-rich a l l o y s above 77°K. The l i n e a r dependence of flow stress on composition was also observed for the as-extruded Zn-rich material, as shown i n Figure 2.40. These data suggest that the concentration of quenched-in defects giving r i s e to the extra hardening i s a d i r e c t function of the composition and serve mainly to increase the flow stress and not the work hardening 2 s rate. Wood and Westbrook have used a r e l a t i o n of the form ac =a r +KA r r s to represent t h e i r data on AgMg. The exponent was observed to be 1 approximately 0.5 - 0.1. - 72 -- 73 -48 49 50 a/o Au Figure 2.40. Flow Stress as a function of composition for the as-extruded Zn-rich a l l o y s . - 74 -2.4.3 E f f e c t of Strain-Rate A d i r e c t study of the e f f e c t of the s t r a i n - r a t e on the y i e l d and flow stress was c a r r i e d out only at room temperature, with the r e s u l t s shown i n Figure 2.41 only f o r the stoichiometric a l l o y . The -4 -1 -2 -1 range of s t r a i n - r a t e s used was from 1.6 x 10 sec to 1.6 x 10 sec At room temperature the y i e l d stress and flow stress of the non-stoichiometric a l l o y s was s t r a i n - r a t e insensitive The s t r a i n - r a t e s e n s i t i v i t y of the stoichiometric a l l o y was low but increased with s t r a i n . The region of low s t r a i n — r a t e s e n s i t i v i t y corresponds to the low temperature s e n s i t i v i t y over the same temperature range. 2.4.4 E f f e c t of. Grain Size An i n v e s t i g a t i o n was c a r r i e d out on the e f f e c t of grain s i z e on the y i e l d stress and flow stress of AuZn. Tensile s t r i p specimens were used to permit a range of grain sizes from 30p to 300y. The specimens had a gauge length of 0.8 inch, a width of 0.2 inch and a thickness of 0.030 inch (~760u). The desired grain s i z e was obtained by annealing i n vacuo over the temperature range from 250 to 350°C for 3 hours. The grains were f a i r l y uniform i n s i z e and the average grain s i z e was determined by the l i n e a r intercept method. 48 49 " ~ 1 / 2 The empirical Hall-Petch ' type equation o^= K ^ l was found to f i t the data for the y i e l d stress and flow st r e s s ; where a i s the flow stress for a given s t r a i n e, a and K are constants e oe e for that s t r a i n and 1 i s the average grain diameter. Figure 2.42 shows. -1/2 the p l o t s , o f versus 1 for Zn-rich, stoichiometric and Au-rich specimens -3 -1 tested at room temperature and at a s t r a i n rate of 2.0 x 10 sec DIAMETER ^ mm - 76 -1.0 .25 .11 .063 .04 .026 .02 ~ i 1 1 T r~—i 1— - 77 -DIAMETER V mm 1.0 .25 .11 .063 .04 .026 .02 ~I I 1 1 1 1 1 -- 78 -DIAMETER £_ mm 1.00 .25 .11 .063 .04 .026 .02 .016 1 1—; 1 1 1 1 1 i % S t r a i n \ • i I i. i | i r i 1 2 3 4 5 6 7 8 0-1/2 ( ,-1/2 ji (mm) Figure 2.42c. E f f e c t of grain s i z e on the flow stress for the 51.1 a/o Au composition. - 79 -The grain s i z e s e n s i t i v i t y of the y i e l d stress for the stoichiometric a l l o y i s quite low and i s not s i g n i f i c a n t l y higher for the non-stoichiometric a l l o y s . The presence of a Luder's s t r a i n i n the non-stoichiometric a l l o y s contributed to the s c a t t e r . The values of K £ a n d a Q e were approximately the same for the Zn-rich and Au-rich a l l o y s . The Petch slope increased with s t r a i n for a l l compositions, with the slope of the non-stoichiometric a l l o y s , i n c r e a s i n g s l i g h t l y f a s t e r than that of the stoichiometric a l l o y . I t has been observed by Marcinkowski and F i s h e r " ^ on FeCo that K £ for the ordered a l l o y i s i n general higher than that for the disordered a l l o y . This i s not i n agreement with the r e s u l t s here, since a deviation from stoichiometry has the e f f e c t of decreasing the degree of order. The Hall-Petch equation has been studied and reviewed by several authors e.g. C o t t r e l l , " ^ Armstrong, Codd, Douthwaite and P e t c h , L i , " ^ and 54 Jaswon and Richman. Armstrong et a l have derived an equation of-the 2 1/2 -1/2 form.o, = mx + m x f 1 where a,. i s the t e n s i l e flow s t r e s s , x f o e f o i s the applied shear stress r e s i s t i n g d i s l o c a t i o n motion, 1 i s the average grain diameter, m i s an o r i e n t a t i o n factor and x £ i s the stress to generate d i s l o c a t i o n s loops at a distance r from the grain boundaries. The 51 a or mx term has been v a r i o u s l y a t t r i b u t e d to the Peierls-Nabarro force o o or impurity atoms. Armstrong et a l have proposed that the Petch slope 2 K i s proportional to m x , i . e . the factors c o n t r o l l i n g the ease of spreading s l i p across grain boundaries. Thus the s e n s i t i v i t y to grain s i z e depends on the number of s l i p systems, the shear modulus and any d i s l o c a t i o n locking.- The low value of the Petch slope.implies i n i t i a l l y that locking - 80 -of d i s l o c a t i o n s by impurity atoms ( i . e . excess Au or Zn atoms) or other point defects i s small. This i s i n agreement with the observation that y i e l d occurs either i n a smooth manner.or with a small Luder's s t r a i n , but with no upper y i e l d point phenomenon. The larger Petch slope i n the non-stoichiometric a l l o y s can be a t t r i b u t e d to d i s l o c a t i o n locking by the excess Au or Zn atoms. The increase i n the Petch slope with s t r a i n can be a t t r i b u t e d to the work hardening i n the v i c i n i t y of the grain boundaries r e s u l t i n g i n higher applied stresses needed to operate d i s l o c a t i o n sources. Marcinkowski and F i s h e r h a v e proposed a contribution to the Petch slope of the form / o n i 2 1/2 m 3 / 2a „ , , N l / 2 (2.1) k f = m x c r + j — G (eb) to account for the e f f e c t of the i n t e r n a l stresses oh the s t r a i n hardening. Here a i s a constant approximately equal.0.4 and G i s the shear modulus. The f i r s t term corresponds to the Petch slope for the y i e l d stress and the second term increases p a r a b o l i c a l l y with s t r a i n . Figures 2.43 and 2.44 show the v a r i a t i o n of K and aQ with s t r a i n . The Petch slope increases p a r a b o l i c a l l y with increasing p l a s t i c s t r a i n supporting the above mechanism. The aQ values at zero s t r a i n are comparable with the y i e l d stress values for si n g l e c r y s t a l s . The low value of the Petch slope for the y i e l d stress suggests that m, the o r i e n t a t i o n f a c t o r , may also be quite low. The minimum possible value of m i s 2 for the case where an i n f i n i t e number of s l i p systems are operative. Since i t has already been proposed that s l i p occurs on planes of the <111> zone.as well as the <001> zone i t appears reasonable to further assume that m approaches 2 for AuZn i n agreement with the above observations. CD ro I o rH X CO CO w Pi H CO 10 15 20 STRAIN £ % Figure,2.43. V a r i a t i o n of, the Petch slope with s t r a i n . 30 20 h 10 Figure 2.44. 5 10 STRAIN € % V a r i a t i o n of (T7 with s t r a i n . 15 20 - 82 -2.4.5 Discussion The discussion of the y i e l d stress and work hardening behaviour as a function of the experimental variables must be, by necessity, an attempt to characterize the behaviour i n terms of ex i s t i n g theories and mechanisms. It can be said before hand that no ex i s t i n g theory completely describes the deformation behaviour of AuZn s a t i s f a c t o r i l y . I t i s proposed to discuss,the following observations i n terms of the e x i s t i n g theories; (1) the existence of <111^ s l i p as required for the low temperature d u c t i l i t y ; (2) the high rate of work hardening; (3) the ef f e c t s of order on the a l l o y strengthening; and (4) the a p p l i c a b i l i t y of s o l i d s o l u t i o n hardening theories. 2.4.5.1 <111> S l i p 9 10 AuZn i s f u l l y ordered r i g h t up to i t s melting point. ' Like most ordered a l l o y s AuZn i s anisot r o p i c , with an isotropy f a c t o r , given by ^4 , equal to 3.3. This value compares with 8.8 for \ (C11-C12). 26 g-brass, 3.28 for N i A l , and 11.7 for AuCd. Rachinger,and c o ' t t r e l l determined the operative s l i p system for AuZn to be {110} <001> and kTr attempted to explain t h i s observation using a c r i t e r i o n i n which — ^>0.06 ev. implied that a <100> d i s l o c a t i o n s were preferred for deformation, where k i s Boltzmann's constant and Tc i s the disordering temperature. The Burgers vectors a v a i l a b l e to unit perfect d i s l o c a t i o n s i n the ordered CsCl l a t t i c e are a [ l l l ] , a[110] and a[100]. These are perfect d i s l o c a t i o n s and do not disorder the l a t t i c e . I f they do not dissociate into imperfect d i s l o c a t i o n s , they can be expected to s l i p along the perfect d i s l o c a t i o n a<100> . This follows from the fac t that d i s s o c i a t i o n to <100> involves - 83 -no change of e l a s t i c energy and a stress acting more strongly on one component, e.g. a[100] of an a[110] or a [111] d i s l o c a t i o n , can move th i s component independently of the others. S l i p i s possible by.<lll> Burgers vector only i f d i s s o c i a t i o n into imperfect d i s l o c a t i o n s occurs, Si 3 v i z , a [111] —> - j f l l l ] +"2 s i n c e . t h i s reaction prevents d i s s o c i a t i o n into [Q01]. The reduction i n e l a s t i c energy of the <111> d i s l o c a t i o n i s opposed by the surface tension of the ribbon of stacking f a u l t i n the s u p e r l a t t i c e . On the basis of a rough c r i t e r i o n i n which i t i s assumed that the c r i t i c a l surface energy of the stacking f a u l t i s that which exerts a force on the d i s l o c a t i o n s equal to the t h e o r e t i c a l shear strength of the l a t t i c e , Rachinger and C o t t r e l l derived the above r e l a t i o n kT 5 7 where i s the ordering energy from the Bragg and Williams theory of long range order. According as.the energy i s larger or smaller than 0.06 ev, so the d i r e c t i o n of s l i p i s <100> or <111>. Using the metling point as the disordering temperature, the ordering energies of N i A l , AgMg, and AuZn can be calculated to be.0.04 ev, 0.023 ev, and 0.022 ev r e s p e c t i v e l y . Rachinger and C o t t r e l l observed <111> s l i p i n AgMg as predicted but not i n AuZn. 21 B a l l and Smallman have observed only <001> s l i p for N i A l contrary to p r e d i c t i o n s . However, observations i n t h i s work on the presence of <111> s l i p i n AuZn are i n agreement with expectations. Rachinger and C o t t r e l l considered that AuZn was a borderline case for <001> s l i p and <111> s l i p , based on,observations of the d i f f u s e nature of the punch markings i n t h e i r o r i g i n a l work. - 84 -The existence of Burgers vectors of the form <111> i s c r u c i a l to a discussion of the e f f e c t s of order i n the AuZn a l l o y . D i s l o c a t i o n s having <100> Burgers vectors do not create disorder with the passage of a d i s l o c a t i o n , whereas d i s l o c a t i o n s having <111> Burgers vectors do create disorder, and I t has been predicted and observed that they move i n pairs to minimize the e f f e c t s of disorder."' 7 The two — [ I l l ] d i s l o c a t i o n s which form the s u p e r l a t t i c e d i s l o c a t i o n are separated by an antiphase boundary or stacking f a u l t . The antiphase boundary can only be tolerated i f the ordering energy i s low, a condition which has already been shown to be s a t i s f i e d for AuZn. On the basis of the observations from s l i p trace analysis 26 33 of AuZn s i n g l e c r y s t a l s , ' , the contr i b u t i o n to the t o t a l shear s t r a i n from s l i p on the {110} <001> system would appear to be larger than from the s l i p systems of the <111> zone. In f a c t , since the existence of <111> s l i p requires the high stresses created by the constraints of the grain boundaries, i t i s reasonable to assume that they make l i t t l e con-t r i b u t i o n to the shear s t r a i n . The main contribution of, <111> s l i p to the deformation a r i s e s through the increase i n the number of operative s l i p systems to s a t i s f y von Mises c r i t e r i o n . The observation that super-dislocations were never detected in.the transmission electron microscopy work i s i n agreement with the idea that t h e i r contribution to the t o t a l shear s t r a i n i s small. It should be noted that the observed d i s l o c a t i o n pairs i n Figure 2.29 can be.ruled out,as possible super-dislocations due to t h e i r wide spacing. - 85 -58 Marcinkowski and Brown have given an equation for the equilibrium width of antiphase boundary separating two d i s l o c a t i o n s i n a super-dislocation a s 2 2 2 2 2 2 a D b (h +k +1 ) r . 2, _,_ cos » , w - [ s i n * + 1 ^ ~ 1 2TT kT h c where a Q i s the l a t t i c e parameter, u i s the shear modulus, b i s the Burgers vector y [ H I ] ,• T £ i s the disordering temperature, k i s the Boltzmanns constant, v i s the Poissons r a t i o , ij; =0 for edge, components and i|-90° for screw components and {hkl} i s the s l i p plane. The calculated o value of w i s approximately 30A as compared with the measured width of o ^ 80A. The predominant s l i p system i n AuZn at temperatures below 0.4Tm appear to be on planes of the <001> zone. The observation of {310} planes at room temperatures i s i n agreement with s l i p trace analyses on sing l e c r y s t a l s of AuZn. I t would appear that the observed {110} , {112} and{123} planes at room temperature are associated with the <111> s l i p d i r e c t i o n . 2.4.5.2 Work Hardening P o l y c r y s t a l l i n e bcc metals have non l i n e a r work hardening rates i n the range 400< \ < 900,^ much larger than the value of 8 observed here. It appears l o g i c a l to associate the increased work hardening rate i n p o l y c r y s t a l l i n e AuZn to the long-range order. The sharp increase i n the work hardening rate at temperatures below 150°K for the non-stoichiometric a l l o y s however, cannot be a t r r i b u t e d to the e f f e c t s of composition on the long-range order.. The extremely high, l i n e a r work hardening rate observed for the stoichiometric a l l o y i s comparable with that observed by Marcinkowski 3 and Ghessin for ordered FeCo. - 86 -Deformation of p o l y c r y s t a l l i n e material requires s l i p on i n t e r s e c t i n g planes to r e l i e v e stress concentrations at grain boundaries. In ordered AuZn t h i s type of s l i p r e s u l t s i n a high work hardening rate since the i n t e r s e c t i n g s l i p i s probably of the <111> form which moves by the creation of antiphase boundaries. The observed grain boundary f r a c t u r e at low temperatures and the lower d u c t i l i t y at large grain sizes i s associated with the large stresses at the grain boundaries. 59 F l i n n has proposed a model for work hardening i n ordered a l l o y s which i s dependent on the domain s i z e . A l l o y s with very large domains should show only a slow increase i n work hardening rate contrary to the 60 observation. Vidoz and Brown have proposed a work hardening theory based on Hirsch's jog t h e o r y ^ . The mechanism i s independent of the domain s i z e . Jogs created by the i n t e r s e c t i o n of super-dislocations of screw o r i e n t a t i o n require extra energy to drag the associated antiphase boundary. The jog mechanism i s expected to become more important with increasing s t r a i n and hardening i s independent of temperature. The jog model also predicts that c r o s s - s l i p w i l l be more d i f f i c u l t and s t r a i g h t s l i p l i n e s should be observed at lower temperatures. . Marcinkowski and Chessin have reported a l i n e a r work hardening region i n ordered FeCo. Their electron microscopy observations of the d i s l o c a t i o n structure i n which no well defined c e l l structure was present lead them to the conclusion that long range stress f i e l d s were not present or responsible for the rapid rate of l i n e a r work hardening. They proposed the jog theory of Vidoz and Brown to explain t h e i r r e s u l t s . Having noted that ordering tended to decrease c e l l formation during l i n e a r work hardening, they also noted •.that the c e l l formation which commenced with - 87 -the onset of dynamic recovery was le s s marked as the degree of order increased. Electron microscopy observations on AuZn deformed at 77°K showed a tendency towards s t r a i g h t d i s l o c a t i o n s and no c e l l formation up to 5% s t r a i n . The amount of wavy s l i p was considerably reduced. The specimens deformed at room temperature exhibited less than 2% l i n e a r hardening, thus the well defined c e l l structure at 3% s t r a i n and the occurrence of considerable wavy s l i p at low s t r a i n s was to be expected since dynamic recovery was already occurring. It would appear that the temperature indpendent work hardening theory of Vidoz and Brown i s i n reasonable agreement with the observations for AuZn,for the stoichiometric a l l o y and the non-stoichiometric a l l o y i n the region below the dashed l i n e . The higher work hardening rate i n the non-stoichiometric a l l o y s below 150°K can be a t t r i b u t e d to the increased stress l e v e l r e s u l t i n g i n more <111> s l i p . Linear work hardening has not, to the authors knowledge, been reported i n p o l y c r y s t a l l i n e disordered bcc metals or a l l o y s . Instead, 1/2 the flow stress i s a parabolic function of the s t r a i n , v i z o=a^ + ke The non-linear hardening i s AuZn i s parabolic and can probably be a t t r i b u t e d to.the same work hardening mechanism, namely, the thermally a c t i v a t e d c r o s s - s l i p of screw d i s l o c a t i o n s . The d i s l o c a t i o n structure observed i n the transmission electron microscopy i s q u a l i t a t i v e l y very s i m i l a r to that f or bcc metals. At room temperature, tangles and c e l l s formed early i n the deformation and became more pronounced with increasing s t r a i n . As the deformation temperature was decreased the d i s l o c a t i o n s had a tendency to become str a i g h t e r and either c e l l formation i s i n h i b i t e d or the s t r a i n necessary for a,given c e l l structure i s considerably increased. - 88 -2.4.5.3 E f f e c t s of Order.on A l l o y Strengthening The main experimental observations which the various theories of order strengthening must explain are; 1) the minimum i n flow stress at the stoichiometric composition, 2) the l i n e a r r e l a t i o n between the increase i n flow stress Aa and the deviation from stoichiometry A, 3) the approximately equal hardening due to excess Au and Zn atoms, and 4) the constancy of the slope of the hardening versus A curve with temperature over the range from 133 to 373°K. The degree of order i n ordered.compounds can be varied i n two ways; 1) thermally, by quenching i n disorder from high temperatures, and 2) chemically, by varying the composition.. The degree of order can a f f e c t the strength, i n several ways, namely; 1) the contribution of anti-phase boundaries, 2) the influence of departure from long-range order on the s u p e r l a t t i c e d i s l o c a t i o n structure through the antiphase boundaries, and 3) the influence of departure from stoichiometry upon l o n g -range order. There have been several mechanisms proposed to account for the strengthening e f f e c t s observed i n ordered a l l o y s as a function of the degree of order. I t should f i r s t be noted that AuZn has a B2 (or L20) c r y s t a l structure which i s CsCl . (ordered bcc) with the Au atoms at the cube corners and the Zn atoms at the body centres, or v i c e versa. Since t h i s structure has only two interpenetrating s u b - l a t t i c e s , domain 6 2 growth i s very rapid and.no stable antiphase domain structure can be formed, Ordering i n the AuZn compound i s a homogeneous reaction and hence no s i g n i f i c a n t amount of disorder.has been quenched i n from above the melting - 89 -point, which i s the c r i t i c a l ordering temperature. Thus hardening mechanisms based on a v a r i a t i o n of the degree of long-range order due to thermal treatment are not applicable f o r AuZn. 63 Ardley's mechanism proposes that the e f f e c t of the decreasing order of the l a t t i c e with increasing temperature causes an increase i n flow stress near the c r i t i c a l temperature. Fli n n ' s 59 model i s based on an increasing rate of d i f f u s i o n with increasing temperature allowing d i s l o c a t i o n climb to occur. And thus creating g l i d e resistance due to the t r a i l i n g antiphase boundaries associated with the d i s l o c a t i o n s that have moved ou t : o f the super l a t t i c e configuration. Both.of these models are i n a p p l i c a b l e to AuZn. Marcinkowski and M i l l e r ' s 64 model involves an i n t e r a c t i o n between the s u p e r l a t t i c e d i s l o c a t i o n s and massive short-range order and i s not applicable to a homogeneously ordered s u p e r l a t t i c e i n which there are no d i s t i n c t regions of short-range order. 65 The mechanism of domain hardening f i r s t proposed by C o t t r e l l , 63 66 67 and extended by Ardley, , Logie, and Marcinkowski and Fisher, i s not.possible i n B2 structures since stable small domains cannot e x i s t . 18 S t o l o f f and Davies, model a t t r i b u t e s the strengthening to the antiphase boundary t r a i l s from the unit d i s l o c a t i o n s which form as a r e s u l t of the decomposition of the super-^dlslocations as the long-range order decreases. This model cannot apply i n a l l o y s which are ordered to the melting point - 90 -The deviation of the composition from stoichiometry can lower the degree of order and/or produce two phase (ordered and disordered) structures. A minimum i n strength as a function of composition should be observed at the stoichiometric composition, as i s observed here for AuZn. The strength minimum w i l l correspond to a minimum super-dislocation spacing i n which case the quenched material should not show any such minimum. The deviations from the stoichiometric composition which occur i n the i n t e r -m e t a l l i c compounds can produce vacant l a t t i c e s i t e s rather than a decrease i n the degree of o r d e r , e . g . N i A l . " ^ At low temperatures a minimum i n 2 strength was also observed for AgMg. In addition, Wood and Westbrook observed that the hardening on the Mg-rich side of stoichiometry was greater than on the Ag-rich side. I t was determined that AgMg was 69 a n t i s t r u c t u r a l , i . e . s u b s t i t u t i o n a l on both sides of stoichiometry. The excess hardening was at t r i b u t e d to a greater l a t t i c e d i s t o r t i o n from the Mg atoms than from Ag atoms. Hence, the observed low temperature strength minimim in AgMg was a t t r i b u t e d to point defects of c o n s t i t u t i o n a l o r i g i n which conferred s o l i d s o l u t i o n strengthening pr i m a r i l y by l a t t i c e d i s t o r t i o n . 16 Lautenschlager, Kiewit and B r i t t a i n also observed a minimum i n flow stress at the stoichiometric composition f o r NiAl at 69 700°C. The defect l a t t i c e of NiAl has s u b s t i t u t i o n a l Ni atoms above 50 a/o Ni and s u b s t i t u t i o n a l A l atoms down to —'49 a/o Ni. Below 49 a/o Ni the l a t t i c e contains Ni vacancies rather than s u b s t i t u t i o n a l A l atoms. Lautenschlager et a l observed a s l i g h t l y higher hardening rate on the A l - r i c h side as compared with the N i - r i c h side of stoichiometry. At the high temperatures studied vacancies were not as - 91 -e f f e c t i v e hardeners as the s u b s t i t u t i o n a l A l atoms and the flow stress decreased below 48.5 a/o Ni. They ascribed the increase i n strength to an i n t e r a c t i o n between the d i s l o c a t i o n s and excess point defects. A s t r a i g h t forward proportional r e l a t i o n between the degree of long-range order and the composition can be assumed as a f i r s t 2 approximation. If the hardening i s d i r e c t l y related to the degree of long-range order, i t would be expected that an antiscructural i n t e r -m e t a l l i c compound such as AgMg or AuZn would exhibit equal rates of hardening on both,sides of the equiatomic composition. This was not observed for«AgMg, but i s almost the case for p o l y c r y s t a l l i n e AuZn, see Figure 2.36. Results on si n g l e c r y s t a l s of AuZn also displayed equal 33 rates of hardening on both sides of stoichipmetry. The s l i g h t excess hardening on the Zn-rich side could be a t t r i b u t e d to the grain boundaries, since Zn i s the re a c t i v e compound, i n a manner s i m i l a r 70 to that suggested by Westbrook and Wood for AgMg and Seybolt and Westbrook for N i G a . ^ The l i n e a r r e l a t i o n between the hardening and the decrease i n long-range order due to a deviation from stoichiometry has been 72 predicted by Shibuya on the basis of an e l a s t i c a n a l y s i s . The d e t a i l s of a hardening mechanism based on the decrease i n long-range order due to the deviation from stoichiometry are lacking. However on a s t r i c t l y q u a l i t a t i v e basis, the main experimental r e s u l t s are explained. Thus, the flow stress minimum, the l i n e a r dependence of Aa on A, the equal hardening due to excess Au and Zn atoms, and the temperature independence of the hardening slope are a l l i n agreement with such a model. - 92 -2.4.5.4 So l i d Solution Hardening A strengthening model based on long-range order would appear to s a t i s f y the experimental observations on p o l y c r y s t a l l i n e AuZn. However, i t i s necessary to consider the p o s s i b i l i t y that e x i s t i n g s o l i d s o l u t i o n hardening theories may be a p p l i c a b l e . The mechanisms of s o l i d s o l u t i o n strengthening can be divided into two groups; 1) mechanisms based on d i s l o c a t i o n locking with the observation of a pronounced y i e l d point, and 2) mechanisms based on d i s l o c a t i o n f r i c t i o n , which tends to s h i f t the whole s t r e s s - s t r a i n curve to higher stresses and cause a gradual y i e l d . An evaluation of the various theories i s usually based on; 1) the observed strengthening Ad as a function of the solute composition; 2) the v a r i a t i o n of the s i z e m i s f i t with composition, given by 1 da 6 = — — ; and 3) the v a r i a t i o n of the shear modulus with composition, a dc given by n = 1 dy y dc The observed strengthening as a function of the deviation from stoichiometry was found to be l i n e a r and independent of temperature over the range from 133 to 373°K. The s i z e m i s f i t was determined i n Chapter 3 using p r e c i s i o n l a t t i c e parameter measurements. The values -4 -4 of 6 obtained were 4.1.x 10 per a/o and 7.9 x 10 per a/o for the Zn-rich. and Au-rich a l l o y s r e s p e c t i v e l y . The increase i n stress as a function of the change i n l a t t i c e parameter i s shown i n Figure 2.45. The hardening i s l i n e a r i l y r e l a t e d to the v a r i a t i o n i n l a t t i c e parameter but i s not equal on both sides of stoichiometry. The v a r i a t i o n of the shear modulus with composition was not measured i n t h i s work and i s not a v a i l a b l e i n the l i t e r a t u r e . However, an approximation of the r e l a t i v e e f f e c t s of the Au and Zn atoms 73 on the shear modulus can be obtained using a r e l a t i o n given by F l e i s c h e r , . For e l a s t i c spheres of modulus u(, imbedded i n a matrix of modulus y, the dependence on composition i s given by (2.2) V=- -where a= — ; — a n d v i s Poissons r a t i o . The appropriate values are; ^AuZn = ^'^xlO ^ dynes/cm , " ^ u = 2.8x10"^ dynes/cm^, y ^ n = 3.7x10 ^" 2 74 dynes/cm , and v = 0.4. The value of the Poissons r a t i o i s not c r i t i c a l to the comparison. The calculated ^ values are 0.98x10"'"''" dynes/cm^ per 11 2 a/o and 1.5x10 dynes/cm per a/o for excess Au and Zn r e s p e c t i v e l y . The corresponding modulus v a r i a t i o n s are 0.61 per a/o and 0.94 per a/o - 94 -for the excess Au and Zn r e s p e c t i v e l y . The magnitude of the n values i s comparable with those f o r copper a l l o y s observed by F l e i s c h e r and H i b b a r d . 7 5 2.4.5.4.1 D i s l o c a t i o n Locking Mechanisms The s o l i d s o l u t i o n hardening mechanisms based on d i s l o c a t i o n locking which can,be considered are; 1) the chemical locking mechanism 76 65 of Suzuki; 2) the e l a s t i c locking mechanism due to C o t t r e l l ; 3) the e l e c t r o s t a t i c locking mechanism due to C o t t r e l l , Hunter and 77 74 Nabarro , and F r i e d e l ; and 4) the stress induced order locking 78 mechanism of Schoeck and Seeger. 7 6 The chemical locking mechanism f i r s t proposed by Suzuki for fee metals, i s based on the d i f f e r e n c e i n s o l u b i l i t y between the matrix l a t t i c e and the stacking f a u l t s . The composition dependence of the (f - f )^ increase i n stress i s given by (2.3) Ao = c ( l - c ) §. k where f bhRT c i s the free energy per unit area of the matrix a and the solute b, c i s the solute concentration of the matrix, h Is the stacking f a u l t thickness, R i s the gas constant, and T £ Is the heat treatment temperature, not.the t e s t i n g temperature. A l i n e a r r e l a t i o n Is predicted at low concentrations and the hardening Is Independent of temperature. The hardening i s expected to be strongly dependent on the d i f f e r e n c e i n free energy between the matrix and the solute atoms. However, t h i s mechanism i s not.applicable to AuZn since i t would predict a d i f f e r e n t hardening e f f e c t f or either excess Au or Zn atoms. - 95 -6 5 The e l a s t i c locking mechanism of C o t t r e l l ( C o t t r e l l cloud mechanism) i s based on the concept of the impurity atoms segregating to edge d i s l o c a tions i n order to minimize the energy diffe r e n c e created by s i z e e f f e c t s . The stress necessary to tear the d i s l o c a t i o n loose i s given by (2.4) Aa = ~"/^ c where c i s the saturated impurity concentration. Although the mechanism predicts the observed temperature independence and composition dependence, the predicted r e l a t i o n between Aa and 5 i s not observed for AuZn and the predicted hardening i s an order of magnitude too low. The e l e c t r o s t a t i c locking mechanism proposed by C o t t r e l l , 77 74 Hunter and Nabarro, and F r i e d e l i s based on the i n t e r a c t i o n between the permanent charge on a d i s l o c a t i o n (due to the e l e c t r i c dipole caused by a v a r i a t i o n of the hydrostatic pressure around the d i s l o c a t i o n ) and 73 the nuclear charge of the impurity. I t i s estimated (Fleischer) that the s i z e e f f e c t i s 3-6 times larger than the e l e c t r o s t a t i c e f f e c t and hence i t has been neglected as a hardening mechanism In metals. The stress-induced order locking mechanism of Schoeck and 78 Seeger, Is based on the Snoek ordering of i n t e r s t i t i a l impurities i n the stress f i e l d of a d i s l o c a t i o n . For i n t e r s t i t i a l impurities the hardening i s l i n e a r i l y dependent on the composition and independent of temperature below the temperature for rapid d i f f u s i o n . For s u b s t i t u t i o n a l a l l o y s the e f f e c t should be q u a d r a t i c a l l y dependent on 79 the composition and independent of temperature. - 96 -It would appear that none of the d i s l o c a t i o n locking mechanism outlined are applicable to AuZn. However, the existence of a Luder's s t r a i n and the Portevin-Le Chatleier phenomenon are. suggestive that some form of d i s l o c a t i o n pinning i s occurring, with the most probable mechanism being C o t t r e l l ' s impurity cloud model. 2.4.5.4.2 D i s l o c a t i o n F r i c t i o n Mechanisms Several theories of s o l i d s o l u t i o n hardening are based on the d i s l o c a t i o n f r i c t i o n a r i s i n g when the solute atoms act on moving d i s l o c a t i o n s . Three of the more well known theories which w i l l be discussed b r i e f l y are; 1) the Mott-Nabarro theory of the mean i n t e r n a l 80 81 73 stre s s ; '2j the F l e i s c h e r theory of shear modulus i n t e r a c t i o n ; and 82 3) the Fisher theory of l o c a l order f r i c t i o n . The f i r s t theory of s o l i d s o l u t i o n hardening s t i l l i n use was 80 81 proposed and developed by Mott and Nabarro. ' Their model was based on the idea that the m i s f i t between the foreign atoms and. the matrix created Internal s t r a i n s . To enable a d i s l o c a t i o n to pass through the regions of i n t e r n a l stresses the applied stress must be at lea s t equal to the average i n t e r n a l stress given by a^= ^o~c . In a homogeneous s o l i d s o l u t i o n the distance between atoms i s given by A = - 2 ^ . j where a i s the interatomic spacing. The non-vanishing average 1 <r4/3 stress a on a d i s l o c a t i o n of length L i s given by Ao = r pb c x c2/3 ! 4 1/3 [g (In —) ] . The bracketed term i s a slowly varying function of c and can be assumed constant. Hence the increase i n strength due to a l l o y i n g .4/3 can be written as (2.5) Aa = Ay5 c, where A i s a constant. The model predicts the observed temperature independence and compos i t i o n dependence. - 97 -However, the s i z e m i s f i t for the Au-rich material i s s i g n i f i c a n t l y greater than that of the Zn-rich material while the hardening i s approximately equal. 73 F l e i s c h e r has developed a theory based on the e l a s t i c modulus mismatch as well as the s i z e m i s f i t . On the basis of.the symmetry of the defects F l e i s c h e r has c l a s s i f i e d two types of hardening; 1) a rapid hardening associated with defects having a l a r g e . t e t r a g o n a l i t y , such as i n t e r s t i t i a l s ; and 2) a gradual hardening associated with symmetrical defects, such as s u b s t i t u t i o n a l atoms. The gradual hardening involving p a r t i a l l y f l e x i b l e d i s l o c a t i o n s i s given by (2.6) (n ) 3 / V / 2 Ax = u — — . i ) s i s a combined s i z e m i s f i t and modulus parameter 700 given by n g = /n'-a6/ where a ^ 16 for edge d i s l o c a t i o n s and < 16 for screw i _ 1 1 d i s l o c a t i o n s and l \ — 7 Jn~T\ Since 6<<n i t can . l / + 2/ . 3/2 be neglected and a plot of versus (n ) i s shown i n Figure Ac 2.46. I t i s apparent that the modulus mismatch i s not responsible for the hardening although the composition dependence of the moduli must be determined to be c e r t a i n . In addition, F l e i s c h e r ' s model does not predict the observed cpmposition dependence. 82 The l o c a l order f r i c t i o n model of Fisher i s based on the extra stress necessary to propagate s l i p through regions of short-range order or c l u s t e r i n g i n a non-ideal s o l u t i o n . The extra stress i s given by AT = — where A i s the increase i n binding energy across the s l i p plane. The hardening i s expected to be.quadratically dependent on the composition thus d i s q u a l i f y i n g the model. - 98 -Figure 2.46. Pl o t of the hardening against the F l e i s c h e r modulus . ../\3A-parameter (VJ The preceeding discussion j u s t i f i e s the conclusion that e x i s t i n g s o l i d s o l u t i o n hardening theories cannot explain the a l l o y strengthening behaviour of AuZn. 2.5 THERMALLY ACTIVATED FLOW 2.5.1 Introduction The study of the e f f e c t s of the te s t i n g temperature on the y i e l d or flow stress i s one,of the more fundamental aspects of the 83 84 deformation of metals. Many workers (Seeger, Conrad ) have found i t convenient to separate the macroscopic y i e l d or flow stress into two components according to the expression (2.7) r= I * , ( T 3 Y )+T^ , where - 99 -X* i s a thermal component which depends on the temperature T and s t r a i n -rate ~jf , and 71^ i s an athermal component which depends on the temperature only through the shear modulus^u . The athermal component i s presumed to represent long-range obstacles or stress f i e l d s due to such obstacles as d i s l o c a t i o n on p a r a l l e l or i n t e r s e c t i n g s l i p planes, large jogs and possibly impurity atoms. The thermal component i s presumed to be associated with shortrrange obstacles or stress f i e l d s which thermal f l u c t u a t i o n s aid the applied stress to overcome. Examples of thermal obstacles are the Peierls-Nabarro s t r e s s , f o r e s t d i s l o c a t i o n s , resistance to the motion of small jogs, resistance to c r o s s - s l i p , and impurity atoms. The mechanism of thermally activated flow can be most conveniently investigated using temperature and s t r a i n - r a t e d i f f e r e n t i a l 85 86 change t e s t s . ' In the d i f f e r e n t i a l t e s t s , flow stress values at d i f f e r e n t temperatures and s t r a i n - r a t e s can be obtained from one test specimen. The use of instantaneous type.changes enables the d i r e c t comparison of the e f f e c t s of two d i f f e r e n t temperatures or s t r a i n - r a t e s on the same athermal d i s l o c a t i o n structure. Unfortunately only s t r a i n - r a t e change tests can be made quasi-instantaneously since a short period of time i s always required for temperature e q u i l i b r a t i o n and the ensuing stress r e l a x a t i o n r e s u l t s i n a change i n the d i s l o c a t i o n structure. P a r t l y for t h i s reason, and also to si m p l i f y experimental procedures, the ef f e c t s of the temperature on the thermal stress component have been obtained by te s t i n g f u l l y annealed v i r g i n specimens at each temperature. Of course t h i s means that the analysis i s r e s t r i c t e d to the mechanisms of the macroyield s t r e s s . - 100 -The thermodynamic analysis of thermally activated flow 87 88 89 90 has been studied by many workers, see for example Conrad et a l ' ' ' 91 92 93 C h r i s t i a n and Masters, Schoek, and Risebrough, . It i s c l e a r that most.disloca t i o n i n t e r a c t i o n s w i l l have d i f f e r i n g a c t i v a t i o n energies at d i f f e r e n t points i n a c r y s t a l . To s i m p l i f y the analysis i t has been necessary to assume that a s i n g l e equivalent a c t i v a t i o n energy can be used to replace the d i s t r i b u t i o n of energies a c t u a l l y i n existence. This i s s t r i c t l y true only for a d i s t r i b u t i o n of thermally activated processes which occurs i n s e r i e s , with the a c t i v a t i o n energy for the slowest or rate c o n t r o l l i n g mechanism being equal to the s i n g l e equivalent value. For given temperature and applied stress d i s t r i b u t i o n s only one process w i l l be c o n t r o l l i n g . However, over the complete temperature and stress range of i n t e r e s t i t i s quite, possible to have more than one process involved i n thermally activated deformation. For the case i n which a s i n g l e thermally activated d i s l o c a t i o n mechanism i s c o n t r o l l i n g the rate of p l a s t i c deformation,.the macroscopic — AP / t e n s i l e strain-rate. z i s given by (2.8) i =vexp (~ kT). The frequency factor v i s given by (2.9) v = ^ Ab^v Q where p i s the density of moving d i s l o c a t i o n s , 1* i s the length of the d i s l o c a t i o n segment involved i n the thermal a c t i v a t i o n , A i s the area of g l i d e plane swept, by a d i s l o c a t i o n l i n e a f t e r a successful a c t i v a t i o n , b i s the Burgers vector of the d i s l o c a t i o n , IJJ i s an o r i e n t a t i o n factor of the order 0.5 for t e n s i l e s t r a i n , and V q i s the frequency of v i b r a t i o n of the d i s l o c a t i o n segment 1*. AG i s the Gibbs free energy associated with the thermal a c t i v a t i o n given by AG = AH-T AS where AH i s the enthalpy and AS the entropy of a c t i v a t i o n . In order to have equation 2.8 v a l i d for - 101 -p l a s t i c s t r a i n i n g the pre-exponential term y must be independent of stress and temperature, a requirement that does not appear to be s a t i s f i e d , b and y> are not expected to vary with a change i n s t r a i n - r a t e or temperature during a t e n s i l e t e s t , but small changes could occur i n p , 1*, and A implying a v a r i a t i o n i n the e f f e c t i v e stress and d i s l o c a t i o n structure. For constant s t r a i n - r a t e tests equation 2.8 has been expanded 87-93 to give useful mathematical expressions by many authors and the re l a t i o n s h i p s to be used i n t h i s work are b r i e f l y outlined here. The a c t i v a t i o n enthalpy AH can be obtained from equation 2.8 i f i t i s assumed that the temperature v a r i a t i o n of the e l a s t i c constants may be neglected i n comparison with that of the flow s t r e s s , ^ i . e . yi > then A H a AG. Hence the enthalpy i s given by The equation can be written with t e n s i l e stresses since the stress appears i n both numerator and denominator. The a c t i v a t i o n volume can be.defined i n a formal sense as (2.11) I T = "['frftjj. » which from equation (2.8) gives (2 12) ~ 2KT( ) * ^ t ^ a s k e e n found experimentally that the stress v a r i a t i o n of AG and A H i s i d e n t i c a l and the a c t i v a t i o n enthalpy can also be Written as (2.13) £U = _ VlX f—Ml) 2- K. dT le/j A l t e r n a t i v e l y the a c t i v a t i o n volume has been defined from the work done.by the stress f i e l d during the a c t i v a t i o n . The work done by a stress to move an element d l of a d i s l o c a t i o n a distance dd during th overcoming of an obstacle, i s given by (2.14) f(-f) = b£*<j(*'£* = where 1 - 102 -FORCE Figure 2.47. Typ i c a l Force-Distance curve for a thermally activated deformation process. A G = ABCA vi?- A C ^ i , A AtS*l ~ * 0 A 6 C * * * * -103 -i s the t o t a l length of the d i s l o c a t i o n l i n e involved i n the a c t i v a t i o n , x* i s the mean e f f e c t i v e stress acting on t h i s length, d* i s c a l l e d the a c t i v a t i o n distance and<v i s the a c t i v a t i o n volume. The t o t a l f ree energy required for a d i s l o c a t i o n to overcome an obstacle i s given by (2.15) AG Q = AG + t*V* where AG i s the thermal free energy and i s the free energy supplied by the stress f i e l d . Figure 2.47 shows the force-distance curve for the t o t a l energy involved i n overcoming an obstacle. The terms marked with the a s t e r i c k may be functions of s t r e s s . If the shape of the F-d curve i s not a function of stress then -u- = and the a c t i v a t i o n volume can be determined experimentally from equation 2.12. The a c t i v a t i o n enthalpy, a c t i v a t i o n volume and frequency fa c t o r have been determined for p o l y c r y s t a l l i n e AuZn using the temperature dependence of the y i e l d stress and s t r a i n - r a t e change tests at constant temperature. 2.5.2 Thermally Activated Flow Parameters 2.5.2.1 Strain-Rate S e n s i t i v i t y S t r a i n - r a t e change tests were c a r r i e d out on specimens having the compositions 48.38, 50.07 and 51.63 a/o Au. The s t r a i n - r a t e -3 -1 -2 - 1 was varied by a factor of 10 from 1.6x10 sec to 1.6x10 .sec The stress change Ao associated with increasing and decreasing s t r a i n - r a t e changes 'are i l l u s t r a t e d i n Figure 2.48. I t was observed that the stress increment on increasing the s t r a i n - r a t e Ao-^  was instantaneous with y i e l d points occurring for the non-stoichiometric a l l o y s at a l l temperatures tested. The flow stress at the higher s t r a i n - r a t e was taken at the - 104 -Figure 2.48. The nature of the flow stress obtained during s t r a i n - r a t e change t e s t s . tS-^  "> £r| . - 105 -95 deviation from l i n e a r i t y , following Basinski and C h r i s t i a n , and 94 Risebrough. The stress decrements obtained f o r the decrease i n s t r a i n -rate were not obtainable by the above c r i t e r i o n and were not analysed. The stress increments, expressed by the s t r a i n - r a t e s e n s i t i v i t y / -. f^ T ^ , as a function of s t r a i n are shown i n Figure 2.49. The {A&*e Jr stoichiometric material has a two stage behaviour at lower temperatures, ACT decreases during the f i r s t few % £ and then either increases or remains constant with tr . The non-stoichiometric specimens displayed an increase i n ££T with cr , with a leveling-rof f trend at higher cr. and lower temperature. The v a r i a t i o n i n ^CT~ with cr and the influence of the actual s t r a i n - r a t e on A T may be correlated with the temperature v a r i a t i o n of / 4< T \ I A C T \ I ~T"75—Ti shown i n Figure 2.50. The / —— r—— — values were obtained by extrapolating back to zero s t r a i n . The di f f e r e n c e i n behaviour between the stoichiometric and non-stoichiometric material i s r e a d i l y apparent. The observed broad maximum i n the range of 125°K exhibited by the 84 91 94 non-stoichiometric a l l o y s i s s i m i l a r to that observed for bcc metals. ' ' The temperature at which the maximum occurs i s considerably higher for the non-stoichiometric a l l o y s . 2.5.2.2 A c t i v a t i o n Volume The a c t i v a t i o n volume v was calculated using equation (2.12) and the v a r i a t i o n with the applied t e n s i l e stress i s shown in,Figure 2.51. In order to c a l c u l a t e v using equation 2.12 i t i s necessary to assume that the shear stress i s rel a t e d to the t e n s i l e stress by the r e l a t i o n L ~" ^  and the shear s t r a i n i s rel a t e d to the t e n s i l e s t r a i n by Y-Q7'l£ •rl (0 P. 14 H H CO W CO w H I S3 H H CO 800 r 600 L 400 200 Figure 2.49b. 10 STRAIN t£ % Strain-rate s e n s i t i v i t y as a function of s t r a i n f o r the 50.07 a/o Au composition. - 109 -Figure 2.50 S t r a i n - r a t e s e n s i t i v i t y as a function of temperature. 80 60 40 20 48.38 a/o Au A 133°K • 169 ° 226 -A A-—A—A—A-40 50 60 70 ,-3 80 90 APPLIED STRESS Q] x l O ~ J p s i Figure 2.51a. A c t i v a t i o n volume as a function of applied stress f o r the 48.38 a/o Au composit - I l l -600 500 h 400 \-300 *5Q 200 5 1 0 0 o •> o M H H 1 5 u J"J < i o h 5h 10 Figure 2.51b. 50.07 a/o Au 20 30 40 . APPLIED STRESS 50 (Tl xlO p s i 60 A c t i v a t i o n volume as a function of applied stress f o r the 50.07 a/o Au composition. o > 53 O M H < > M H U <C 100 -80 60 40 20 0 ^ 20 51.63 a/o Au V—v~ 30 40 50 60 70 80 90 _3 APPLIED STRESS (J~j xlO p s i Figure 2.51c. Ac t i v a t i o n volume as a function of applied stress for the 51.63 a/o Au composition.^ - 113 -The 2 value i s an o r i e n t a t i o n f a c t o r which takes into consideration the number of s l i p systems a v a i l a b l e f or deformation. In bcc metals there are 48 possible s l i p systems and hence the value 2 i s a good approximation. In addition* the o r i e n t a t i o n factor i s re l a t e d to the degree of preferred o r i e n t a t i o n and the grain s i z e . The v values calculated represent the minimum possible since the o r i e n t a t i o n factor increases with decreasing number of s l i p systems. The magnitude of v and i t s v a r i a t i o n with a are s i m i l a r for the non-stoichiometric a l l o y s but d i f f e r s i g n i f i c a n t l y from the,values obtained for the stoichiometric composition. The low temperature values of the a c t i v a t i o n 3 volume for y i e l d i n g range from 13 to 45 b and are comparable with values 87 obtained for bcc metals over the same stress range. The v a r i a t i o n of the a c t i v a t i o n volume with T* i s shown i n Figure 2.52. The composition does not appear to have a s i g n i f i c a n t e f f e c t on the i v - x * curve. 2.5.2.3,, A c t i v a t i o n Enthalpy and Thermal Component of Stress In order.to evaluate the a c t i v a t i o n enthalpy using equation (2.10) the v a r i a t i o n with temperature of the thermal component x * of 84 equation. 2.7 must be known. Conrad has suggested that t h i s can be accomplished by s u b t r a c t i n g the stress at some reference. temperature T Q from that at a given temperature, i . e . T t - x T = r * ( T , y ) - T * ( T Q , Y ) = AT *(T, Y) o The reference temperature i s a r b i t r a r i l y taken as the temperature where x * (T Q,y) = 0 which i s equivalent to ^ ^ and (2-15) x * = T„ - T M ^ . The l e v e l region of the y i e l d stress versus temperature T T o H,T 0 for the 50.07 a/o Au a l l o y shown,in Figure 2.30 has been taken as - 114 -0 1 2 3 4 5 THERMAL COMPONENT OF STRESS T^xloT p s i Figure 2.52. A c t i v a t i o n volume as a function of the thermal component of s t r e s s . - 115 -representing the temperature dependence of the athermal stress component iy through the temperature dependence of the shear modulus. An extra-polation of t h i s slope to 0°K gives an increase i n y of 15% over the value at 300°K which i s reasonable. The reference temperature has been a r b i t r a r i l y chosen as 250°K. I t i s necessary to assume that the temperature dependence of y i s r e l a t i v e l y independent of the composition. Plots of X* f ° r y i e l d i n g versus temperature for a s t r a i n - r a t e - 3 - 1 of 1.6x10 sec. derived i n the above manner are given i n Figure 2.53. The v a r i a t i o n of T*.with temperature i s c l e a r l y dependent on the composition.' The decrease i n temperature dependence at low temperatures exhibited by the Au-rich a l l o y s i s s i m i l a r to the e f f e c t s of a l l o y i n g or impurities 90 on the x*-T curve for many bcc metals. Values of AH calculated from.equation 2.10 are shown,in Figure 2.54. There i s a l i n e a r r e l a t i o n between AH and T, the slope of which 91 i s dependent on composition. According to C h r i s t i a n and Masters a str a i g h t l i n e plot may be regarded as j u s t i f y i n g the use of a simple rate equation i n which V i s nearly constant and AH i s dependent only on s t r e s s . Since the thermal free energy i s approximately equal to the enthalpy, neglecting the.entropy term as being <.01 ev., the t o t a l free energy i s given by (2.16) AG = AH + t * u , and i s shown,in Table 2.2 This i s only the apparent t o t a l free energy since the areas at the corners of the base of the F-d curve have not been considered. AG i s not a a constant over the temperature range investigated, suggesting that more than one thermally activated deformation mechanism i s operative< - 116 -Figure 2.53. Thermal component of stress as a function of temperature. > 01 X <1 3 H Is w o H H H H O < 0 50 200 100 150 TEMPERATURE T°K Figure 2.54. A c t i v a t i o n enthalpy as.a function of temperature. 250 5 0.6 X 5S o M H H <! 0.4 0.2 .o D 48.38 a/o Au O 50.07 — o THERMAL COMPONENT OF STRESS "C* x l 0 _ 3 p s x Figure 2.55. A c t i v a t i o n enthalpy as a function of the thermal component of s t r e s s . - 118 -TABLE 2.2 The Thermally activated deformation data for AuZn at y i e l d . (Symbols are defined i n the text) 48.38 a/o Au T(°K) ( ^ j ) T ( p s i ) ' U 7 b 3 % ( p S ± ^ t V <ev> A H (ev> &Ga <ev> 133 765 22.2 3700 .11 .23 .34 169 625 34.6 2000 .09 .28 .37 226 380 76.2 500 .05 .40 .45 30.07 a/o Au 77 730 13.5 4300 .08 .15 .23 146 215 87 680 .08 .28 .36 166 150 142 420 .08 .30 .38 227 70 415 100 .06 .40 .46 295 25 1510 0 31.63 a/o Au 77 495 19.9 4600 .12 .10 .22 133 630 27.0 2300 .08 .14 .22 171 485 45.3 1350 .08 .19 .27 232 195 152 200 .04 .62 .66 - 119 -Conrad et a l ^ ^ obtained AG from the equation AG = 3. 3 A H + t*t> by taking f * = 0 and defined i t as A H q . Figure 2.55 shows that A H q ~is approximately 0.43- .04 ev. depending on the composition. 3 87-90 For bcc metals A H q has been found,to be approximately equal to 0.1 ^ ub . —8 11 2 Thus using b = a Q [100] ":here a Q = 3.15x10 cm and JUL. = 1.6 x 10 dynes/cm 3 91 a value of 0.1 ^ b of 0.31 ev i s obtained i n f a i r agreement. The dependence of AH on "£* appears to be dependent on the composition, although the stoichiometric and Zn-rich both extrapolate to s i m i l a r values of AH . o The low stress value f o r the Au-rich a l l o y i s probably questionable on.the grounds that the temperature s e n s i t i v i t y used i n equation 2.10 maybe too large. The values of Z* a t 0 9K were obtained by extrapolating the X*-T curves as shown in,Figure 2.53. Similar extrapolations were c a r r i e d out on the 0~-T curves shown.in Figure 2.56. The —- values obtained are /° L *-2 shown in.Table 2.3. The —2. value f o r stoichiometric AuZn of .0.6x10 • • • • / « • _ 2 i s comparable with values ranging from 0.5 to 1.5x10 for bcc metals and 90 91 alloys., ' The excess Zn does not.appear to have a detectable e f f e c t on ~£Q* whereas the excess Au reduces i t considerably i n the f i r s t 0.5 a/o. 2.5.2.4 Frequency Factor The observed p r o p o r t i o n a l i t y between dH and T shown i n Figure 2.54 can be used to determine the frequency factor V from the r e l a t i o n (2.17) A H = -kT In e/v. The value of ^= 2.6xl0 6 s e c " 1 obtained for the stoichiometric and Zn-rich material i s comparable with that 90 91 -3 commonly obtained for bcc p o l y c r y s t a l s . ' However, the value of 2x10 sec,''' obtained for the Au-rich material i s low. If the t y p i c a l values f o r Figure 2.56. Y i e l d stress as a function of temperature. - 121 -TABLE 2.3 The values of the shear stress at 0°K obtained by extrapolating the CT-T and %-T curves. a/o Au 48.38 48.92 50.07 50.45 50.55 50.96 51.30 51.63 51.88 51.94 xlU p s i L 0 L2I 14.0 14.5 14.0 1.2 1.5 I. 7 3.2 10.0 I I . 0 9.8 T .060 .062 .060 .005 .006 .007 .014 .043 .047 .042 assumed to be 2.3 x 10^ p s i - 122 -the terms i n the expression (2,9) s) = 4b^<j are taken as 1* «i 30b, A = Lb where L i s the average length of a d i s l o c a t i o n loop ci 10 ^cm, b = 3x10 ^ cm and V = 10"*"2 sec \ then \) ~ -B-The frequency factor v a r i a t i o n indicates that d i f f e r i n g proportions of the t o t a l d i s l o c a t i o n density are taking part i n the deformation i n the stoichionetricand Zn-rich and the Au-rich m a t e r i a l . A d i s l o c a t i o n density 7 - 2 of 2.6x10 cm i n the stoichiarjetric and Zn-rich material during y i e l d i n g i s reasonable. 2.5.2.5 Cottrell-Stokes Law Obeyance of the "Cotrell-Stokes Law" was investigated using 85 the s t r a i n - r a t e change data. C o t t r e l l and Stokes showed that the r a t i o of flow stresses at two temperatures i s approximately a constant independent of s t r a i n for A l s i n g l e c r y s t a l s . Subsequent work has v e r i f i e d t h i s f i n d i n g for many fee and hep metals, although i n many 84 cases the r e l a t i o n s h i p i s more nearly given by AT=a + b% • Both temperature and s t r a i n - r a t e change tests have been u t i l i z e d i n the study of the Cottrell-Stokes law. The constancy of the or r a t i o implies that Z /tju. i s also constant. This further implies that "Z? and X.J*. r e s u l t from the same type of d i s l o c a t i o n i n t e r a c t i o n s . The constancy r e s u l t s i f during deformation the geometry of d i s l o c a t i o n s remains constant and only the scale changes. In bcc metals, however, the Cottrell-Stokes law i s not obeyed, instead A<V «. • J j *• o 90,91,95,96 £\ C constant independent of s t r a i n . The s t r a i n - r a t e s e n s i t i v i t y p l o t s shown i n Figure 2.49 i l l u s t r a t e that several v a r i a t i o n s i n behaviour e x i s t for AuZn. - 123 -At low temperatures, i . e . <C 150°K, A(T i s e s s e n t i a l l y constant. For the stoichiometric a l l o y at higher temperatures /(f i s nearly constant a f t e r a few % s t r a i n . The approximate constancy of AT at low temperatures suggests that the obstacles to flow are not created during s t r a i n i n g but are r e l a t e d to the inherent resistance of the l a t t i c e . The increase i n ACT may be a t t r i b u t e d to.an increase i n the frequency factor caused either by an increase i n the mobile d i s l o c a t i o n density j> or the length of d i s l o c a t i o n loops L. 2. 5, 3 Discussion Various o r i g i n s have been attributed to the strong thermal v a r i a t i o n of the y i e l d stress of bcc metals at low temperatures. 97 Many t h e o r e t i c a l models, eg, that of Schoeck are inconsistent with _2 the observed magnitude of the low temperature s t r e s s , ca. 10 JUL at 0°K. The only d i s l o c a t i o n i n t e r a c t i o n s which w i l l be considered here are those with dispersed impurities or with the c r y s t a l l a t t i c e (including P e i e r l s -Nabarro forces and c r o s s - s l i p p i n g processes). 2.5.3.1 Impurity Mechanism? The pronounced e f f e c t of the deviation from stoichiometry on.the X*-T curves c e r t a i n l y suggests that impurity i n t e r a c t i o n s are important. However the following consideration w i l l show that the impurity e f f e c t i s not d i r e c t . 91 If i t i s assumed that the d i s l o c a t i o n bends so as to make nearest neighbour contacts with the impurity i n the s l i p plane, then i 1/2 ijL ~ ° where 1 i s the separation of pinning points and c i s the - 124 -atomic concentration of obstacles. For a 1 a/o Au or Zn a l l o y t h i s gives 14b. The stress needed to bend the d i s l o c a t i o n between the obs s t a c l e s given by t = j^- i s of the order of and i s considerably larger 95 than the stress at 0°K. Mordike and Haasen have assumed that the d i s l o c a t i o n makes three-dimensional nearest neighbour contacts, so that b 1/3 u — at c . The corresponding s t r e s s , i s i n excess of the t h e o r e t i c a l A-shear s t r e s s . I t i s also apparent from Figure 2.52 that the a c t i v a t i o n volume does not vary much with excess Au or Zn concentration. In addition a decrease i n v would be expected with increasing temperature rather than the observed increase. This i s r e l a t e d to the decrease i n the a c t i v a t i o n distance d* i n the expression -v* = b d * l * . Although the impurities of most i n t e r e s t i n t h i s work are s u b s t i t u t i o n a l , an i n t e r s t i t i a l impurity content of ^ 1 ppm i s present. Using the same arguments as above i t can be seen that the T*-T curve for the stoichiometric a l l o y can not be a t t r i b u t e d to.these i n t e r s t i t i a l impurities. Thus the temperature v a r i a t i o n i s probably due to the l a t t i c e and not impurities. 2.5.3.2 Thermally Activated Cross-Slip The i n t r i n s i c hardening at low temperatures i n bcc metals has been analysed i n terms of either the thermally activated c r o s s - s l i p of screw d i s l o c a t i o n s or the Peierls-Nabarro force. Thermally activated s e s s i l e - g l i s s i l e t r a n s f o r m a t i o n s of,screw d i s l o c a t i o n s have been suggested 98 by M i t c h e l l , F o x a l l and Hirsch as being responsible for the hardening. 99 Several authors, including Kossowsky and Brown, Escaig, Fontaine and F r i e d e l , a n d Kroupa and Vitek"^"'" have developed the model further. - 125 -The s e s s i l e nature of the ^ H i ) d i s l o c a t i o n s comes about due to t h e i r s p l i t t i n g on [ l io) and [ 1 1 2 ] planes with the recombination necessary for g l i d e possible through thermal a c t i v a t i o n . The <^  100^ d i s l o c a t i o n s i n AuZn would not be affected by t h i s process except i n the case of an i n t e r s e c t i o n between (100s} and ( i l l ) d i s l o c a t i o n s • The presence of s u p e r l a t t i c e d i s l o c a t i o n s i n ordered a l l o y s would greatly enhance the effectiveness of such a c r o s s - s l i p model. Escaig has given r e l a t i o n s f o r the s t r a i n - r a t e of recombined p a r t i a l s g l i d i n g on the (^lio) plane which f i t measurements on bcc i r o n and tungsten. If the distance between p a r t i a l s i s ~1.6b, then the a c t i v a t i o n energy and a c t i v a t i o n volume calculated from Escaig's r e l a t i o n s are i n good agreement with the values obtained here for AuZn. • The temperature dependence of as predicted by the r e l a t i o n T b 3 ~pL ~ ^ ^ T " w a S aPP r o x :'- m a t e-'-y s a t i s f i e d over the temperature range, considered, v i z 77 to 250°K. Below 77°K the y i e l d stress i s expected to deviate from the above expression and tend to a f i n i t e limits given by T 0 ~ 10 yu-. The theory appears to f i t the data reasonably well except for an adequate explanation of the s o l i d s o l u t i o n softening observed, at 77°K i n the Au-rich a l l o y . . Since i t i s expected that the a l l o y i n g w i l l decrease the stacking f a u l t energy, an add i t i o n a l , a p p l i e d stress w i l l be required to aid the thermal a c t i v a t i o n i n the c o n s t r i c t i o n process. A decreased temperature dependence would imply that the stress l e v e l due to a l l o y i n g has been raised beyond that required to compensate for the increased stacking f a u l t width. Since i t i s not clear j u s t how such a - 126 -mechanism would work i t i s f e l t that the model i s not s a t i s f a c t o r y for the temperature region below, say 100°K, although i t may be applicable above that temperature. However, the main reason for discarding t h i s model is that the amount of ^111^ s l i p i s probably not s u f f i c i e n t to e f f e c t the thermallyjactivated flow to the extent observed here. 2.5.3.3 Peierls-Nabarro Force The most widely accepted thermally activated deformation 90 91 mechanism i n bcc metals ' , involves the i n t e r a c t i o n of d i s l o c a t i o n s with the i n t r i n s i c resistance of the bcc l a t t i c e or P e i e r l s - ' h i l l s ' . The v a r i a t i o n of the core energy of a d i s l o c a t i o n l i n e with i t s exact p o s i t i o n gives r i s e to a f r i c t i o n a l resistance to motion. The Peierls-Nabarro (P-N) stress lip i s the stress required to move a. d i s l o c a t i o n from i t s postion of minimum energy over the P e i e r l s ' h i l l s ' mechanically. The p o s i t i o n of minimum energy i s along a 'valley' p a r a l l e l to close-packed rows of atoms on the g l i d e plane. In c r y s t a l s i n which the P-N stress i s high the d i s l o c a t i o n s are frequently observed to be,long,and s t r a i g h t and l i e p a r a l l e l to the more c l o s e l y packed rows of atoms. When the thermal component of stress 7T * i s less than p , motion of the d i s l o c a t i o n can s t i l l occur through energy supplied by thermal f l u c t u a t i o n s . The d i s l o c a t i o n moves forward by the formation of a pair of kinks which move sideways a f t e r the: thermal nucleation under the stress 7J" *. The height.and shape of the P e i e r l s h i l l influence the equilibrium configuration of a sing l e kink thus a f f e c t i n g the kink energy. 102 Guyot and Dorn have given a review of the types of P e i e r l s h i l l s , the mechanisms for nucleating p a i r s of kinks, and the assumptions and d e t a i l s of estimating the macroscopic s t r a i n - r a t e i n terms of nucleation and - 127 -migration of kink p a i r s . Appendix A contains a b r i e f o u t l i n e of the 103 equations of the Dorn-Rajnak theory from Guyot and Dorn. V e r i f i c a t i o n of the P-N mechanism can be c a r r i e d out either by d i r e c t determination of v e l o c i t i e s of d i s l o c a t i o n s or by macroscopic deformation experiments. The y i e l d stress obtained from the deformation experiments can be used to evaluate the P-N mechanism i n two ways; 1) the experiemntal dependence of the flow stress with temperature can be compared with t h e o r e t i c a l curves; and 2) the experimentally determined a c t i v a t i o n energies and a c t i v a t i o n volumes can be compared with t h e o r e t i c a l values. The experimentalTj-T curves of AuZn have been compared O - K in* 103 with the t h e o r e t i c a l u /  cp versus T/T £ curve given by Dorn and Rajnak, where T £ i s the c r i t i c a l temperature. Using the extrapolated T^* a value of T £ was deduced. I t was necessary to assume that the shear stress t * obtained by extrapolating the t-T curves back to 0°K was equal o to the P-N stress X Figure 2.57 i l l u s t r a t e s the f i t of the experimental data to the t h e o r e t i c a l curve. The s l i g h t deviation of the experimental data at high temperatures suggests that some u n i d e n t i f i e d thermally activated deformation mechanism takes the place of the P e i e r l s m e c h a n i s m . T h e extrapolated 7? and deduced T values obtained v po c here are shown i n Table 2.4. At T = T , T * = 0 for the P e i e r l s mechanism and U n = 2U^ where i s the experimentally determined thermal a c t i v a t i o n energy for the nucleation of a pair of kinks and U^ i s the kink energy. The values obtained from equation 2.10 have already been shown i n Figure 2.54. The 2Uk values taken from Figure 2.54 at the c r i t i c a l - 129 -TABLE 2.4 The thermally a c t i v a t i o n deformation parameters deduced by the Dorn~R ajnak analysis from the experimental data for AuZn a/o Au 48.38 50.07 51.63 t p (psi) 14,000 14,000 10,000 T (°K) 240 150 210 (ev) 0.43 0.27 0.25 ^(cm 2) 9 11 4 x 10* - 10 X 9 1 1 4 x 10 - 10 6 x 10 3 - 8 x 10 7 temperatures are also shown i n Table 2.4. These values can be compared with a value of <^0.2 ev calculated from equation A.3 of Appendix A, 1 2 assuming that the l i n e tension J""^ i s given by = "jyUb . The most c r i t i c a l judgement of the operation of the P-N mechanism i s obtained from the experimentally determined a c t i v a t i o n 3 volume. The magnitude of 1>* ranging from 13-45b obtained for AuZn i s i n good agreement, as i s the observation that the composition a f f e c t s iy only through the s t r e s s . The r e l a t i v e invariance of the a c t i v a t i o n volume with s t r a i n i s also predicted by the P e i e r l s mechanism. The upper and lower bound of the d i s l o c a t i o n d e n s i t i e s can be obtained from the preexponential terms of equation A . l . The 102 density i s obtained by assuming that L can vary from the s i z e of the -1/2 Frank network, i.e.D to the c r i t i c a l kink width w. The c r i t i c a l - 130 -kink width can be obtained from equation A.6 and i s 20 b. The values of p obtained are shown i n Table 2.4. The values have reasonable orders of magnitude although they are on the high side for the Zn-rich and stoichiometric ompositions. 106 Arsenault has considered a t y p i c a l expression for the P-N stress (2.18) I = ^ j^— exp (-"~") where ex" i s a constant, y i s the 'width' of a d i s l o c a t i o n x na where n i s an integer and a i s the / l a t t i c e constant, and c i s a consianfasb for bcc metals. Solute additions i can effeet , the parameters that change the P e i e r l s stress by; 1) changing the shear modulus; 2) causing l o c a l d i s t o r t i o n i n the l a t t i c e near the core of the d i s l o c a t i o n j and/or 3) changing the d i s l o c a t i o n width. Unfortunately the moduli of AuZn as a function of composition were not measured here and are not a v a i l a b l e i n the l i t e r a t u r e . The moduli of both Au and Zn are twice that of AuZn so that no d i s t i n c t i o n i n behaviour can be made. The addit i o n of. 1 a/o Au increased the l a t t i c e parameter by 0.025% whereas the addition.of 1 a/o Zn decreased the l a t t i c e parameter by 0.013%. Furthermore, s o l i d s o l u t i o n softening was not observed i n the Zn-rich a l l o y s at 77°K and the extrapolated X* value did not appear to have decreased. The e f f e c t of the excess Au on the P-N stress probably a r i s e s from either a l o c a l disturbance around the core of the d i s l o c a t i o n s or a change i n the stacking f a u l t energy. M i t c h e l l and R a f f o ^ have r a t i o n a l i z e d the minimum i n the stres6-concentration curve i n terms of the r e l a t i o n "C ~ TTp + T c where T i s the flow s t r e s s , T, i s a contr i b u t i o n which decreases with increasing a l l o y content, and T i s a contribution which increases with increasing a l l o y content. X. i s analogous to the Pr-N stress and - 131 -decreases due to ei t h e r the P e i e r l s h i l l s becoming d i f f u s e or the solute atoms acting as s i t e s f o r the nucleation of kinks. Thus from the above discussion of the three proposed mechanism of low temperature thermally activated flow, i t appears that impurities and c r o s s - s l i p of screw d i s l o c a t i o n s are u n l i k e l y explanations for AuZn. The predictions of the Peierls-Nabarro mechanism give reason-able agreement with the experimental observations and q u a l i t a t i v e l y explain the s o l i d s o l u t i o n softening phenomena. - 132 -3. DEFECT CHEMISTRY 3.1 INTRODUCTION A knowledge of the defect chemistry of c r y s t a l l i n e s o l i d s i s necessary for the understanding of s o l i d state processes such as d i f f u s i o n rates, transport mechanism and a l l o y hardening mechanisms. The usual method for i n v e s t i g a t i n g the defect structure i s to measure 107 the l a t t i c e parameter and density as a function of composition, van Gool has given a theory f o r the r e l a t i o n between density, l a t t i c e parameter and generalized d e s c r i p t i o n of the defect chemistry for pure binary phases. A more commonly used approach involves the c a l c u l a t i o n of the t h e o r e t i c a l d e n s i t i e s assuming c e r t a i n s t r u c t u r a l models and comparison of these calculated d e n s i t i e s with the experimental d e n s i t i e s . Defect models based on s u b s t i t u t i o n s } i n t e r s t i t i a l s and vacancies can be used. A study of the composition dependence of the l a t t i c e parameter g and density of AuZn was c a r r i e d out by Ages/ and Shoykhet. However, th e i r data were not extensive enough and preliminary tests indicated s i g n i f i c a n t differences i n the experimental values of a Q and D. 3.2 EXPERIMENTAL PROCEDURE Powders for the p r e c i s i o n l a t t i c e parameter determinations were prepared from f i l i n g s of the homogenized ingots. The f i l i n g s were" passed through a 200 mesh screen. The powders were s t r a i n - r e l i e v e d by sealing i n pyrex tubes under vacuo and annealing at 350°C for 30 min. The powders were a i r cooled i n a l l cases except one which was furnace cooled to confirm that the cooling rate had no e f f e c t on the measurements. - 133 -A Noreleo Type 52058 symmetrical focussing back r e f l e c t i o n camera was used to obtain the precise l a t t i c e parameters. The camera has a radius of 60 mm and provides excellent r e s o l u t i o n between 9 = 5j) 9 and 9 = 88J°. The powder sample was mixed with a small quantity of Dow-Corning silicone,grease and applied to the camera target as a t h i n f i l m . The as-extruded Zn-rich wires were bent to the curvature of the camera and held i n front of the camera target by masking tape. The d i f f r a c t i o n patterns were obtained at ~ 23°C using 2-8 hour exposures O 0 with u n f i l t e r e d Cu r a d i a t i o n ( k ^ = 1.54051A, = 1.54433A, and k^ = o 1.39217A) at 30 KV and 15 ma. The films were developed on one side only to minimize parallax e r r o r s . The patterns from the powder samples were of uniformly good, q u a l i t y with a l l l i n e s from the r a d i a t i o n , including the s u p e r - l a t t i c e l i n e s , sharp and c l e a r . The l i n e s from the r a d i a t i o n were weaker and le s s d i s t i n c t . The patterns from the as-extruded wires were spotty i n appearance and the l i n e s were quite broad. Table 3.1 gives the r e f l e c t i n g planes find t h e i r r e l a t i v e i n t e n s i t i e s . + The positions of the l i n e s were measured to - 0.1 mm, f i l m shrinkage or expansion was considered i n a l l c a l c u l a t i o n s . The l a t t i c e constants 108 were calculated by the method of Cohen using the extrapolation function —•° = K <pL»A».^ P where A a^ i s the error i n the, l a t t i c e parameter K i s a constant and ( p = ^ - 9 where 9 i s the Bragg angle. The v a r i a t i o n i n l a t t i c e parameter due to temperature was neglected. - 134 -The d e n s i t i e s were obtained by the conventional water d i s p l a c e -ment »technique. A drop of Photo-Flo was added to the d i s t i l l e d water to act as a wetting agent and the water temperature was measured to the nearest 0.1°C. Weighings were made on chain balances. The bulk samples used for the annealed material were obtained from the homogenized ingots. The density of the as-extruded Zn-rich wire was also determined. 3.3 RESULTS 3.3.1 Annealed Powder Samples the l a t t i c e parameter measurements are presented i n Table 3.2 and Figure 3.1 as a function of composition. The larger Au atom expanded the l a t t i c e s u b s t a n t i a l l y more than the smaller Zn atom contracted i t . The l a t t i c e constant for stoichiometric AuZn may be determined by i n t e r -+ ° polation to be 3.1477 - .0003A. This value does not compare well with the 3.122A value given by Ageev and Shoykhet*but i s close to the value ° 109 of 3.145A given by Pearson. The l a t t i c e parameter of a pure gold f o i l o was determined as a c a l i b r a t i o n and found to be 4.0789A. This compares ° 109 reasonably w e l l with the value of 4.0783A at 25°C given by Pearson and suggests that the values obtained i n t h i s work are r e l i a b l e . Figure 3.2 shows the r e s u l t s of the density measurements as a function of composition. The density values are compared with the calculated d e n s i t i e s using the s u b s t i t u t i o n a l , vacancy, and i n t e r s t i t i a l defect models. The calculated d e n s i t i e s are obtained using the r e l a t i o n D = !• 6602 ^£A)— ^ £ A i s the sum of the atomic weights of the con-V. centration of the Au and Zn atoms per unit c e l l for each model and V i s the atomic•volume given by a 3 . - 135 -TABLE 3.1 Lines on the X-ray patterns ( hkl) Line k V + i 2 Type Relative Intensity 1 13 320 Supe r l a t t i c e Medium 2 13 320 Weak 3 17 410,322 Very Weak 4 14 321 Fundamental Very strong 5 14 321 I I Strong 6 18 411,330 I I Weak 7 16 400 I I Weak 8 16 400 M Weak 9 20 420 I I Very Weak TABLE 3.2 L a t t i c e parameter and Density Data f or AuZn Composition L a t t i c e D r i f t Density a/o Au, Parameter A Constant g/cc 48.38 3.1454 2x l 0 ~ 4 13.70 48.38 3.1455 2 48.92 311464 3 13.82 49.59 3.1471 4 13.90 49.59 3.1471 3 49.88 3.1475 4 13.93 50.07 3.1482 2 13.96 50.07 3.1476 3 50.45 3.1487 4 14.02 50.55 - - 14.03 -50.96 3.1499 4 -.51.30 3.1511 3 14.11 51.63 3.1517 1 -51.63 3.1518 3 -51.88 3.1524 3 14.18 The d r i f t constant i s a measure of,the t o t a l systematic error involved i n the determination. - 136 -- 137 -/ Au I n t e r s t i t i a l s / Z n Substitutions -L -L 48 49 51 52 50 a/o Au Figure 3.2. Density as a function of composition. S o l i d l i n e s are calculated d e n s i t i e s from X-ray data using a s u b s t i t u t i o n a l defect model. Broken l i n e s are for s i m i l a r c a l c u l a t i o n using vacancy and i n t e r s t i t i a l models. - 138 -3.3.2 As-extruded Zn-rich Wires The l a t t i c e parameter measurements of the as-extruded Zn-rich wires are shown i n Figure 3.3 and tabulated i n Table 3.3. The systematic error involved i n the parameter determinations i s much larger due to the poorer q u a l i t y of the x-ray patterns. The density of the as-extruded Zn-rich wire as a function of composition i s shown i n Figure 3.4. The calculated d e n s i t i e s assuming Zn s u b s t i t u t i o n s , Au vacancies and Zn i n t e r s t i t i a l s are shown also. 3.4 DISCUSSION a r i t i s t r u c t u r a l ; i e s u b s t i t u t i o n a l defects on both sides of stoichiometry. The larger excess Au atoms have expanded the AuZn l a t t i c e while the smaller Zn atoms have contracted i t . The r e l a t i v e d i s t o r t i o n per a/o of excess atom i s greater f o r Au than f o r Zn, v i z 0.025 versus 0.013 percent. The distance 3 ° of c l o s e s t approach given by aQ i s 2.726A and i s smaller than the mean value fo r Au and Zn atoms, viz,2-884 + 2.664 _ 2.774A implying a high binding energy f o r AuZn. Figure 3.3 indicates that at high Zn concentrations some Au vacancies of c o n s t i t u t i o n a l o r i g i n are present, otherwise any vacancies or i n t e r s t i t i a l defects present are mainly those of thermal o r i g i n . s l i g h t l y d i f f e r e n t .from the annealed material. The increase i n l a t t i c e parameter shown i n Figure 3.4 suggests that i n t e r s t i t i a l atoms are present. The density values are j u s t above the calculated values and are i n the r i g h t d i r e c t i o n to be accounted for by excess i n t e r s t i t i a l s . Apparently some of the Zn s u b s t i t u t i o n a l atoms have been displaced from the Au s u b - l a t t i c e and placed i n i n t e r s t i t i a l postions, probably by the deformation of the hot extrusion process. These r e s u l t s show that the defect structure of AuZn i s The defect structure of the as-extruded Zn-rich wires i s - 139 -Figure 3.3. L a t t i c e parameter as a function of composition for the as-extruded Zn-rich wires. - 140 -14.2 -14.0 -13.8 -13.6 -Zn I n t e r s t i t i a l s 48.5 50 Figure 3.4. 49 49.5 a/o Au Density as a function of composition for the as-extruded Zn-rich wires. - 141 -TABLE 3.3 L a t t i c e Parameter and Density Data f o r As-extruded Zn-rich Wires Composition L a t t i c e 0 D r i f t Density a/o Au Parameter A Constant g/cc 48.38 3.1533 l O x l O - 4 13.71 3.1515 11 48.92 3.1590 7 13.78 3,1501 8 49.59 " 3.1492 7 13.90 3.1494 7 49.78 - - 13.94 49.88 - - 13.95 / 4. ANNEALING BEHAVIOUR OF AS-EXTRUDED ZN-RIQH WIRES 4.1 INTRODUCTION The as-extruded Zn-rich wire specimens were found to have a higher flow stress than the f u l l y annealed material. The flow stress was a l i n e a r function of the deviation from stoichiometry i n d i c a t i n g that the hardening of the as-extruded wire i s associated with the excess Zn concentration. The l a t t i c e parameter and density measurements have suggested that the as-extruded wire has i n t e r s t i t i a l Zn atoms and Au vacancies. E l e c t r i c a l r e s i s t i v i t y measurements during annealing were used i n an attempt to determine' the a c t i v a t i o n energies for the migration of the atom species responsible for the hardening. The r e s i d u a l r e s i s t i v i t y , of a,metal or a l l o y i s very s e n s i t i v e to the presence of imperfections.because any disturbance of the i d e a l l y p e r iodic l a t t i c e r e s u l t s i n sca t t e r i n g of the conduction electrons and hence an increase i n the r e s i d u a l r e s i s t i v i t y . At low defect concentrations the increase i n the r e s i d u a l . r e s i s t i v i t y i s expected to be proportional to the concentration of defects. The change in.the thermal component - 142 -of the r e s i s t i v i t y depends on the change i n the v i b r a t i o n a l spectrum i n the s o l i d caused by the defect. Measurements are u s u a l l y made at s u f f i c i e n t l y low temperatures to minimize the e f f e c t s of the thermal component. The r e s i d u a l r e s i s t i v i t y of an ordered a l l o y i s expected to be a minimum at the f u l l y ordered condition. Increases i n r e s i s t i v i t y a r i s e through a decrease i n the degree of long-range order caused by deviations from stoichiometry. The presence of i n t e r s t i t l a l s and vacancies can also contribute to changes i n the r e s i s t i v i t y . 4.2 EXPERIMENTAL PROCEDURE The material used was the as-extruded Zn-rich wire t e n s i l e specimens. The 0.040 i n . diameter wire was extruded at 500°C at a rate of ~ 9-12 in/min and a i r cooled. The wire was cut into 2 i n . lengths for use as t e n s i l e specimens and these samples were used for the r e s i s t i v i t y measurements. The annealing was c a r r i e d out i n a mechanically s t i r r e d s i l i c o n e o i l bath. The bath was heated by an immersion heater and the temperature was c o n t r o l l e d to within - 0.5°C by a thermister and thermistemp heating c o n t r o l l e r . The actual bath temperature was measured by a thermometer. The specimen was supported i n a 1 1/2 i n . long copper tube and immersed by hand into the bath. For anneals of le s s than 2 min. the specimen was held by tweezers. Following the anneal the specimen was manually extracted and quenched to room temperature i n chlorethane. In addition to quenching the chlorethane dissolved the s i l i c o n e o i l on the specimen. - 143 -The resistance measurements were made by the n u l l probe method using a Pye Potentiometer. The specimen was supported i n a simple j i g which had a constant distance of 4.0 cm. between the knife edged copper probes. The current leads were attached to the specimen by small a l l i g a t o r c l i p s . An aluminum c l i p maintained a good contact between the probe and the specimen. The resistance measuring c i r c u i t i s shown i n Figure 4.1. The resistance of the specimen was obtained by measuring the voltage drop across the specimen for a given current supplied by a 12v battery. The current was determined by measuring the voltage drop across a standard r e s i s t o r of 0.01-ft-. Readings were taken for current flowing i n both d i r e c t i o n s through the specimen and averaged. 4" —6 The resistance was determined to within - 2x10 _n_ at room temperature and - 1x10 ^  -fu at l i q u i d nitrogen temperature. Measurements were made at l i q u i d nitrogen temperature by immersing the specimen and j i g i n a dewar of l i q u i d nitrogen. The r e s i s t i v i t y was calculated using the equation JO = — R where A i s the cross-section area of the wire and L i s the distance between the probes. The r e p r o d u c i b i l i t y of the r e s i s t i v i t y + -9 / \ values was within - 2x10 (—H-cm) for two consecutive measurements. 4.3. RESULTS 4.3.1 E f f e c t of Composition on the R e s i s t i v i t y The v a r i a t i o n of the r e s i s t i v i t y with composition i s shown i n Figure 4.2. The composition dependence of the annealed specimens i s higher at l i q u i d nitrogen temperature than at room temperature. The values of 2.45 and 1.35 xlO jn_cm per a^o are comparable with the e f f e c t s of various defects on the r e s i s t i v i t y of metals and alloys."'""'"^ I t should be noted that the r e s i s t i v i t y of the specimens annealed at 260°C for 12 hrs. i s higher than that of as-extruded material. - 144 -12V BATTERY VARIABLE RESISTOR STANDARD RESISTOR SPECIMEN Figure 4.1. Schematic diagram of the resistance measuring c i r c u i t . - 145 -48 48.5 49 49.5 50 a/o Au Figure 4.2. R e s i s t i v i t y as a function of composition. - 146 -4.3.2 Isochronal Annealing To plan a s e r i e s of isothermal annealing experiments i t i s necessary to know the range of annealing temperatures f o r which the v a r i a t i o n of r e s i s t i v i t y takes place i n a reasonable time. I t i s therefore useful to i n v e s t i g a t e the resis t i v i t y v a r i a t i o n using an isochronal annealing procedure. Figure 4.3 shows the isochronal annealing curve fo r a 49.59 a/o Au specimen which was annealed 5 min. at increasing temperatures i n steps of 10°C. The r e s i s t i v i t y was measured at l i q u i d nitrogen temperature. For t h i s p a r t i c u l a r composition a drop i n r e s i s t i v i t y was not indicated at the higher temperatures. However, isothermal annealing tests at temperatures below 120°C did show a decrease with longer annealing times. The most pronounced increase i s i n the temperature range from 70 to 120°C. 4.3.3 Isothermal Annealing The object of the isothermal annealing tests was to determine the dependence of the r e s i s t i v i t y change on the annealing temperature and thus determine the order of the r e a c t i o n and the a c t i v a t i o n energy of the phenomena. A s e r i e s of tests were c a r r i e d out over the temperature range from 85 to 135TC on wires of the a v a i l a b l e compositions. Figure 4.4 shows a seri e s of t y p i c a l isothermal curves for the 49.59 a/o Au composition i n which the change i n r e s i s t i v i t y Ap has been plotted against time. The maximum Ap values varied with the composition as shown i n Table 4.1. No consistent trend i n A p max, values with annealing temperature was observed. The tests at the higher temperatures were continued u n t i l the values became constant. Again, no consistent trend of the Zlj)^ values with annealing temperature was apparent. In some of the tests theAj^ values were negative. 20 40 60 80 100 120 140 TEMPERATURE T°C Figure 4.3. Isochronal recovery of r e s i s t i v i t y following 5 minute anneals at the temperature indicated. Measured i n l i q u i d nitrogen 80 49.59 a/o Au • 85°C A 95 O 105 • 115 A p xlO (JLcm 10 100 1000 TIME (min.) Figure 4.4. E f f e c t of annealing temperature on the isothermal annealing curves. - 149 -TABLE 4.1 The v a r i a t i o n of the maximum r e s i s t i v i t y increase with composition 9 a/o Au AjDxlO Acm 49.59 60-70 48.92 500-600 48.38 1100-1200 An i n i t i a l increase i n r e s i s t i v i t y has been observed i n systems where p r e c i p i t a t i o n occurs and has been associated with the cl u s t e r i n g of solute atoms during annealing.-'-•'--'-»-'--'-2 Dugdale has reported an increase i n r e s i s t i v i t y during the annealing of Cu^Au 113 and had a t t r i b u t e d i t to a change i n the ordering rates. An a c t i v a t i o n energy f o r the motion of the defects responsible for the i n i t i a l increase i n r e s i s t i v i t y can be deduced simply by p l o t t i n g the r e c i p r o c a l of the time taken to reach the maximum r e s i s t i v i t y against the r e c i p r o c a l of the absolute temperature. The maximum r e s i s t i v i t y can be assumed to represent the case where the concentration of i n t e r s t i t i a l Zn atoms has been exhausted by recombination at each temperature. An a c t i v a t i o n energy of 1.16 ev. i s obtained from slope of the l i n e i n Figure 4.5. A more.detailed analysis can be made which w i l l consider ! 114 the e n t i r e annealing curve. I f i t can be assumed that a sing l e activated process i s rate c o n t r o l l i n g then the change of r e s i s t i v i t y can be expressed by a chemical rate equation","^4.1) ^ = - V jS*" e E/kT where o< i s the order of the reaction, \> i s the frequency f a c t o r , and E i s the a c t i v a t i o n energy. Integration between zero and t. gives (4.2) ( l - f i ) 1 " < * = 1+ fc-1) c 2 t ± . 0.5 _1 I I I 1 1— 2.55 2.6 2.65 2.7 2.75 2.8 1 0 3 / T ° K Figure 4.5. Arrhenius plot of the r e c i p r o c a l of the time taken to reach the maximum r e s i s t i v i t y against the r e c i p r o c a l of the annealing temperature . D . _ D - 151 -f. i s the f r a c t i o n reacted at time t..-, v i z f. = —j->- j—3— wherejD Q, j>^ and JD^ are the r e s i s t l v t i e s at zero time, time t ^ and at i n f i n i t e time or at the maximum. C2 i s a constant given by \)C^* ^ e ^/kT where i s a constant. If (4.2) i s expanded using the binomial theorem and terms higher than second order are neglected, the following equation becomes (4.3) £i = ^ + ^ t . . The order f. L2 1 1 of the reac t i o n i s obtained from a plo t of t i versus ~t; . Figure 4.6 shows a t y p i c a l p l o t of _±. versus t ^ for the i n i t i a l r e s i s t i v i t y increase wh f i ere has been taken as J^max' ^ n e specimens were 49.59 a/o Au and the resistance was measured at l i q u i d nitrogen temperature. The order of the reac t i o n was found to be 2.0 - 0.1. The a c t i v a t i o n energy obtained from the Arrhenius p l o t shown i n Figure 4.7 compares very well with that obtained.from the maximum Ap a n a l y s i s . A s i m i l a r analysis was c a r r i e d out for the decrease i n r e s i s t i v i t y on a se r i e s of 48.92 a/o Au specimens with the r e s i s t i v i t y measurements made at room temperature. The j50 value was taken at the maximum jO and was.obtained from the value a f t e r long times. A . t y p i c a l p l o t of t l / f ^ versus t ^ i s shown i n Figure 4.8 from which i t can be seen that the order of the reaction i s again 2.0-0.1. The a c t i v a t i o n energy obtained from the Arrhenius plot of versus ^ shown i n Figure 4.9 i s 0.50 ev. i The isothermal annealing experiments have shown that the en t i r e annealing process was a second order reaction. The a c t i v a t i o n energy for the increase i n r e s i s t i v i t y was 1.15 ev and for the decrease i n r e s i s t i v i t y was 0.5 ev. 5.0" L | I I I 1 :—I i 2.55 2.60 2.65 2.70 2.75 2.80 & 3 1 10 /T°K Figure 4.7. Arrhenius plot of the r e c i p r o c a l of the intercept i n Figure 4.6 against the r e c i p r o c a l of the absolute annealing temperature. - 154 -1000 2000 t (min.) Figure 4.8. T y p i c a l p l o t of t^/f^against t ^ for a decrease i n r e s i s t i v i t y . 0.10 0.05 0.02 (mln.) -1 0.01 E = 0.50 ev. .005 .002 _L Figure 4.9. 2.5 2.6 2.7 10 /T°K Arrhenius p l o t of the r e c i p r o c a l of the intercept i n Figure 4.8 against the r e c i p r o c a l of the annealing temperature . Ul - 156 -4.4 DISCUSSION The e l e c t r i c a l r e s i s t i v i t y almost always decreases as the annealing temperature and time increases. The exceptions so f a r noted , . ^ . 111,112, . fc . J 114,115 occur i n cases where c l u s t e r i n g or short-range ordering occurs. Since the a l l o y s used i n t h i s work were a l l within the s o l i d s o l u t i o n phase region, the c l u s t e r i n g of solute atoms i s not l i k e l y . 114 Kim and Flanagan have shown that the destruction of short-range order by cold-working causes a decrease i n the r e s i s t i v i t y of Cu-Pd and.Au-Pd a l l o y s . The increase i n r e s i s t i v i t y during annealing i s due to the r e s t o r a t i o n of short-range order with the subsequent decrease due to the disappearance of point defects. An explanation of the r e s u l t s obtained f o r AuZn would not appear to be related to a change i n the degree of short-range order since the subsequent decrease i n r e s i s t i v i t y would imply a s i g n i f i c a n t increase i n long—range order and AuZn i s already very nearly completely ordered. » An explanation of the anomalous r e s i s t i v i t y increase i n AuZn based on a n . i n i t i a l decrease i n long-range order i s outlined here. The annealed equilibrium structure of a,Zn-rich a l l o y i s shown i n Figure 4.10a i n which the excess Zn atoms are accommodated on the Au s u b l a t t i c e . The atom arrangement of the as-extruded material i s i l l u s t r a t e d i n Figure 4.10b. A given number of the excess Zn atoms are now i n cube edge i n t e r s t i t i a l p ositions leaving an equal number of vacancies on the Au s u b l a t t i c e . It i s suggested that the Zn i n t e r s t i t i a l s are created during the deformation involved i n the hot extrusion process. This also implies that the energy to create vacancies on the Au s u b l a t t i c e i s only s l i g h t l y lower than that required to create unfavourable nearest neighbour bonds. di X o - 157 -O Au atoms \ Zn atoms a) The normal arrangement of Au and Zn atoms i n an annealed Zn-rich a l l o y . / O Au atoms ^ Zn atoms ^ Au vacancies b) The atom arrangement of the as-extruded wires, the excess Zn atom i s i n the cube edge i n t e r s t i t i a l p o s i t i o n leaving a vacancy on the Au s u b l a t t i c e . O Au atoms X Zn atoms QAu composition vacancies O Au thermal vacancies A Zn thermal c) Atom arrangement during the decrease i n r e s i s t i v i t y vacancies Zn.atoms on the Au s u b l a t t i c e and Zn thermal vacancies combine and Au composition vacancies are created. Figure 4.10. Atom arrangements i n Zn-rich wires. - 158 -( i . e . between l i k e atoms). The degree of long-range order i n the as-extruded specimens w i l l be higher than i n the f u l l y annealed specimens since vacant l a t t i c e s i t e s or i n t e r s t i t i a l atoms do not a f f e c t the 14 degree of long-range order. A bimolecular recombination of Au vacancies and Zn i n t e r s t i t i a l s , as suggested by the 2nd order k i n e t i c s law,"*""*"^  i s proposed as the rate c o n t r o l l i n g process during the r e s i s t i v i t y increase. The r e s i s t i v i t y increases due to the decrease i n long-range order caused by the Zn atoms occupying the Au s u b l a t t i c e s i t e s . The a c t i v a t i o n energy of 1.15 ev. represents the a c t i v a t i o n energy for the migration of a Zn i n t e r s t i t i a l . The maximum r e s i s t i v i t y occurs when the atom arrangement shown i n Figure 4.10a i s achieved. The decrease i n r e s i s t i v i t y i s associated with an increase i n the degree of long-range order caused by a removal of the Zn atoms from 116 the Au s u b l a t t i c e . Mukherjee, Lieberman and Read have reported that the concentration of thermal vacancies which can be retained i n AuZn quenched from the melting point i s 0.60 - .08 a/o. This i s an order of magnitude larger than that f or pure metals."''''""'" At the temperatures used i n t h i s work the concentration of thermal vacancies ranges from 10 7 to 10 ^ a/o. The d i f f u s i o n of the Au and Zn vacancies on t h e i r respective s u b l a t t i c e s w i l l eventually r e s u l t i n a recombination between a. migrating Zn vacancy and the Zn atom on the Au s u b l a t t i c e and thereby increase the degree of long-range order as shown i n Figure 4.10c. The second order k i n e t i c s are re l a t e d to the recombination reaction. The a c t i v a t i o n energy of 0.5 ev should be that for the d i f f u s i o n of Zn vacancies. Mukherjee et al''"^ have reported an a c t i v a t i o n energy for the - 159 -motion of vacancies i n a AuZn a l l o y (51.1 a/o Au) of 0.47-.05 ev. The anomalous r e s i s t i v i t y increase observed during the annealing of as-extruded Zn-rich wire specimens can probably be att r i b u t e d to a decrease.in long-range order, caused by a recombination of i n t e r s t i t i a l Zn atoms.and Au vacancies. The subsequent decrease i n r e s i s t i v i t y i s then due to the recombination of Zn thermal vacancies and Zn atoms from the Au s i t e s . There are two competing processes, the f a s t one involving the d i f f u s i o n of the i n t e r s t i t i a l Zn atoms and the slower one involving the d i f f u s i o n of Zn vacancies. The slower one takes over and increases the long-range order when the concentration of i n t e r s t i t i a l Zn atoms i s depleted. - 160 -5. ELECTRON MICROSCOPY 5.1 INTRODUCTION The electron microscope has proved to be a valuable t o o l i n the study of the deformation behaviour of metals and a l l o y s . The Purpose of t h i s electron microscopy.study was an examination of the d i s l o c a t i o n structure i n deformed p o l y c r y s t a l l i n e AuZn as a function of temperature, composition, and s t r a i n . The i n v e s t i g a t i o n has been exploratory i n nature and was hampered by d i f f i c u l t i e s i n obtaining a s u i t a b l e e l e c t r o p o l i s h i n g s o l u t i o n and procedure for the deformed material. 5.2 EXPERIMENTAL PROCEDURE It was found that the thinning of p o l y c r y s t a l l i n e f o i l s was greatly aided i f the s t a r t i n g material was of the order of 0.005 i n . thick. In the thicker specimens the edges tended to become rounded very r a p i d l y and p r e f e r e n t i a l p o l i s h i n g occurred at the grain boundaries. , Tensile s t r i p specimens 0.030 i n . thick were r o l l e d to 0.005 i n . and r e c r y s t a l l i z e d at 250°C. The r o l l i n g process resulted i n a c e r t a i n degree of preferred o r i e n t a t i o n as shown by back r e f l e c t i o n x-ray photographs of the r o l l e d m aterial. The specimen was cut to rectangular a shape of 1x2 cm for thinning. The f i n a l thinning was achieved by e l e c t r o p o l i s h i n g i n a mixture of 40% concentrated hydrochloric a c i d , 50% ethyl alcohol 117 and 10% g l y c e r i n using the Bollman method. The specimen was held i n s t a i n l e s s s t e e l tweezers and the edges of the specimen and the tweezers were stopped-off.with Microstop lacquer. The temperature of the po l i s h i n g bath was held at about -20°C by surrounding the bath with ethyl alcohol - 161 -cooled by s o l i d CC^. Pointed electrodes were placed 1mm from the centre of the specimen.' The voltage (*> 20-25 V) was c o n t r o l l e d by a hand held microswitch and only applied for a few seconds at a time. As soon as a hole.appeared the specimen was removed and c a r e f u l l y washed with ethyl alcohol. The probes were repositioned about 3 mm from the surface to cause edge perfo r a t i o n . When two or more holes joined up the regions near the jo were s u i t a b l e for observation. The specimen was removed, dipped i n ethyl alcohol and c a r e f u l l y washed with methanol from a wash b o t t l e . After drying, the specimen was kept i n a dessicator u n t i l viewed. The rate of attack during e l e c t r o p o l i s h i n g was extremely rapid and great care was required to prevent the l o s s of the thinned areas. Observations.were made on an.Hitachi Hu 11A operating at L00KV. The specimens could only be t i l t e d with respect to the electron beam through a.range of i 10° i n order to vary the contrast. Corresponding selected area d i f f r a c t i o n patterns were,taken of a l l areas photographed. 5.3 EXPERIMENTAL OBSERVATIONS Electron micrographs of t y p i c a l d i s l o c a t i o n structures have already been presented i n Chapter 2. In t h i s section some representative .micrographs of other phenomena are shown. Figures 5.1 to 5.5 show examples of various selected area d i f f r a c t i o n patterns and the. associated bright f i e l d micrographs. SAD patterns with more,than one tfone present were common.and may be-due to either a phase transformation or the bend,contours. A l l the SAD patterns exhibited'streaking of the spots. If the r o t a t i o n d i f f e r e n c e between the.SAD patterns and the bright - 162 -< 001^ zone - 163 -Figure 5.2. Electron Micrographs showing streaks, s a t i l l i t e s and double zones on SAD pattern. Figure 5.3. Electron Micrographs showing s t r i p e d contrast and bend contours, and SAD pattern. - 164 -- 165 -- 166 -Figure 5.6. Electron Micrographs showing th i n twin-like markings and SAD pattern. - 167 -Figure 5.7. Electron Micrograph showing possible APB. - 168 -f i e l d was corrected f o r , the streaks were observed to be perpendicular to the s t r i p e d contrast appearing i n the bright f i e l d micrographs. The streaks appear to be.along the [110] and [100] d i r e c t i o n s suggesting that the planar regions giving r i s e to the streaks and st r i p e d contrast l i e along ( 110) and (l00) planes. The t h i n twin-like marking shown i n Figure 5.6 were observed near the edge of the t h i n f o i l . They are s i m i l a r i n appearance to i n t e r n a l twinning in.material which has undergone a m a r t i n s i t i c phase transformation. The high r e s o l u t i o n d i f f r a c t i o n technique was used i n a attempt,to determine the transformed structure. The high r e s o l u t i o n patterns could a l l be indexed as planes of the |3' AuZn phase with the d + ° spacings within - 0.01 A. A thorough,search for antiphase boundaries was not c a r r i e d out. However, structures which were s i m i l a r i n appearance to those 118 shown i n the l i t e r a t u r e for APB were occasionally observed. Figures 5.3, 5.A and 5.7 are t e n t a t i v e l y suggested as showing APB. The v a r i a t i o n i n constrast shown,in Figure 5. 7 across the bend contours supports the suggestion. However, i t was not established whether or not the r e f l e c t i n g planes were s u p e r l a t t i c e r e f l e c t i o n s . 5.4 DISCUSSION The presence of streaks and/or s a t e l l i t e spots on the SAD 117 patterns has been v a r i o u s l y a t t r i b u t e d to one of the following; 1) c r y s t a l shape e f f e c t , 2) e l a s t i c s t r a i n e f f e c t , 3) l a t t i c e imperfections, 4) periodic l a t t i c e v a r i a t i o n s , 5) twinning, and 6) the presence of a second jphase. Some of the above w i l l give r i s e to - 169 -extra or forbidden r e f l e c t i o n s by double d i f f r a c t i o n . If the c r y s t a l has a p l a t e - l i k e sturcture, the r e c i p r o c a l l a t t i c e point w i l l become a spike. The r e f l e c t i n g sphere w i l l thus pass through r e c i p r o c a l l a t t i c e points which otherwise would not.be present. I f the r e c i p r d c a l l a t t i c e spikes are perpendicular to the electron beam they lead to the formation of streaks through each d i f f r a c t i o n spot l y i n g close to the c i r c l e of i n t e r s e c t i o n , but no descrete spots. In a l l other cases the r e c i p r o c a l l a t t i c e spikes lead to the displacement or s p l i t t i n g of the spots. The SAD pattern shown i n Figure 5.1 shows streaks and no s p l i t spots. The streaks a r i s e from [110] r e c i p r o c a l l a t t i c e spikes which cause streaks along the [OlO] d i r e c t i o n for a (100) d i f f r a c t i o n pattern. This would suggest that the p l a t e - l i k e structures causing the streaks l i e along the [110] d i r e c t i o n s . An analysis of the spacing of the s a t e l l i t e spots such as those shown o i n Figure 5.2, indicates that the p l a t e r l i k e structures are 15-20 A apart. However, the spacing of the str i p e d contrast shown i n the bright o f i e l d micrographs i s considerably larger (of the order of 500-1000A). This would appear to suggest that double d i f f r a c t i o n was responsible for the s a t e l l i t e spots. The double d i f f r a c t i o n could occur from the in t e r f a c e between the plate structures. Twinning can also be considered since i n t e r n a l twinning i n m a r t i n s i t i c phase transformations can occur whereas i t would not be possible i n the ordered phase. I t was not possible to determine a system which might give r i s e to the t h i n markings i n Figure 5.6. The two zones shown i n Figure 5 . 2 ? ( l l l ^ and <^21L\ cannot be related by a 180° r o t a t i o n around the common twinning d i r e c t i o n i n bcc structures, <^lll}> . - 170 -119 B a l l and Smallman have reported the r e s u l t s of an i n v e s t i g a t i o n of a martensitic phase transformation i n P' AuZn i n which they observed a spontaneous transformation at the edge of the t h i n f o i l s . They a t t r i b u t e d t h i s observation to an increase i n the transformation 45 temperature from that found i n bulk material by Pops and Massalski (from ~100°K to, ~300°K). B a l l and Smallman have suggested that a d e f i n i t e c r y s t a l l o g r a p h i c r e l a t i o n e x i s t s between the parent and product phases. They observed that the s t r a i g h t edges of the martensitic plates l a y close to the QLIO^J d i r e c t i o n i n the ft' phase and the i n t e r n a l twinning has a twin plane which also l i e s close.to the JJLIOJ d i r e c t i o n s i n the parent matrix. They note that these observations conform to the habit 120 and twin r e l a t i o n s h i p s predicted for the bcc,to orthorhombic transformation such as that observed for |3 AuCd for the 52.5 a/o Au composition. The high r e s o l u t i o n d i f f r a c t i o n patterns for a 51.0 a/o Au a l l o y did not give any i n d i c a t i o n of the presence of an orthorhombic phase. It i s therefore suggested that the t h i n f o i l transformation i n . p AuZn i s analgous to the bcc to.body centered.tetragonal transformation observed ' 1 2 2 ' 121 i n |3 AuMn ,or |3 AuCd for the 50 a/o Au composition Pe r i o d i c l a t t i c e v a r i a t i o n s such as a p e r i o d i c v a r i a t i o n i n the interplanar spacings or a regular p e r i o d i c arrangement of APB lead to the formation of subsidiary maxima or sidebands. The main feature of these e f f e c t s i s the r e g u l a r i t y of the spacing of the s a t e l l i t e s i n the same d i r e c t i o n around each main spot. However, the i n t e r p r e t a t i o n of such e f f e c t s i s confused by the possible presence of double d i f f r a c t i o n . The other mentioned sources of streaks and s a t e l l i t e s are not applicable for obvious reasons. It would appear that the c r y s t a l shape e f f e c t , twinning, or periodic l a t t i c e v a r i a t i o n can.be considered as possible explanations for the streaks, s a t e l l i t e s , s t r i p e d contrast, and t h i n markings. - 171 -6. SUMMARY DISCUSSION AND CONCLUSIONS 6.1 DISCUSSION P o l y c r y s t a l l i n e AuZn has been found to be,ductile at temperatures below 0.40-0.45 TV ,contrary to predictions based on the reported operative s l i p systems. The d u c t i l i t y can be a t t r i b u t e d to ( i l l ) s l i p activated by stresses high enough to overcome the ordering energy. At temperatures above 150°K , the stress l e v e l i s attained only i n the v i c i n t y of the grain boundaries. S l i p on the \llo] ( 0 0 l ) system tends to concentrate the stress at the end of s l i p bands, blocked by grain boundaries. The concentrated stress nucleates ( l l l ^ s l i p . The a l l o y i n g additions tend to r a i s e the i n t e r n a l stress l e v e l also. Since the a l l o y i n g also decreases the long-range order i t might be expected that the spacing of the ( i l l ) superdislocations would be increased, however, the decrease i n LRO due to a l l o y i n g i s too small to produce an observable e f f e c t . The high work hardening rate can be att r i b u t e d to ( l l l ^ superdislocations and t h e i r attendent antiphase boundaries, i . e . Vidoz and Brown's jog theory. The sharp increase i n hardening rate below 150°K i s explained by the f a c t that the lower temperature prevents multiple c r o s s - s l i p on the planes of the ( O O l ) zone. Stress concentrations w i l l be greatly increased and the amount of ( i l l ) s l i p w i l l be appreciably more. Mechanisms of work hardening based on i n h i b i t i o n of deformation modes due to long—range order do not appear applicable f o r AuZn. The operative ( i l l ) s l i p i n the v i c i n i t y of the grain boundaries also explains the observed increase i n work hardening with decrease i n grain s i z e , i . e . smaller grains, more grain boundary area , more stress concentration , more ( l l l ^ s l i p , and more work hardening. The second term - 172 -of equation 2.1 represents the increasing density of ( i l l ) d i s l o c a t i o n s . The observation that the hardening e f f e c t s of the Au-rich and Zn-rich a l l o y s prepared for the grain s i z e study.were i d e n t i c a l suggests that the. phenomena of grain boundary hardening, as emphasized by Westbrook, was not. a complicating factor i n t h i s grain s i z e study. The a l l o y hardening observed i n i n t e r m e t a l l i c compounds should be explanable by mechanisms operating i n primary m e t a l l i c s o l i d s o l u t i o n s . Previous discussion has shown that the e x i s t i n g theories are not applicable to AuZn. The d i f f i c u l t y i s undoubtedly re l a t e d to the ordering, possibly there i s some non-random arrangement of the s u b s t i t u t i o n a l atoms,on the host s u b l a t t i c e . An order strengthening model which depends s o l e l y on the e f f e c t s of deviation from stoichiometry, as suggested by the present r e s u l t s , has not been developed. I t i s not clear how such a model would explain the large hardening for 1 a/o solute on.the basis of a decrease i n the long-range order from 1.0 to 0.98. Also, the p r i n c i p l e s l i p system at temperatures above 150°K i s ^110] (001) which does not require s u p e r l a t t i c e d i s l o c a t i o n s . The c o m p o s i t i o n dependence of the hardening.in the as-extruded Zn-rich wire i s s i g n i f i c a n t l y higher than that for either the Au or Zn substitutions. The hardening i s due.to the Zn i n t e r s t i t i a l s which are assymmetrical and hence produce 'rapid' hardening. The hardening i s probably a d d i t i v e on the Zn-rich side with a contribution from the s u b s t i t u t i o n a l Zn atoms and from the i n t e r s t i t i a l atoms. It i s apparent that the a l l o y hardening i n AuZn i s a complicated process. S o l i d s o l u t i o n e f f e c t s have also been found to depend on the stoichiometry of the base material and upon whether the samples are sin g l e or p o l y c r y s t a l s . Since the amount of hardening was found to be.the same i n - 173 -sin g l e c r y s t a l s f o r both excess Au and Zn atoms, no a d d i t i o n a l complications a r i s e from t h i s consideration. However, l o c a l v a r i a t i o n s i n the composition are suggested by the st r i p e d contrast i n the electron microscopy and may further complicate the an a l y s i s . 6.2 SUMMARY AND CONCLUSIONS The observations and int e r p r e t a t i o n s of the structure and deformation c h a r a c t e r i s t i c s of p o l y c r y s t a l l i n e |3'AuZn may be summarized as follows; 1) P o l y c r y s t a l l i n e AijZn was observed to behave i n a d u c t i l e manner over the temperature range 77 to 533°K and composition range 48.0 to 52.0 a/o Au. Below 400°K deformation occurred by s l i p while above 400°K d i f f u s i o n c o n t r o l l e d processes were also operative. 2) At temperatures below 400°K the s t r e s s - s t r a i n curves f o r the stoichiometric a l l o y exhibited a.smooth y i e l d , and a region of l i n e a r work ; hardening followed by a region of parabolic hardeningi The region of l i n e a r hardening decreased with increasing temperature. The non-stoichiometric a l l o y s exhibited Luder's s t r a i n s and serrated flow. The work hardening was parabolic throughout the en t i r e s t r e s s - s t r a i n curve. 3) A loss of d u c t i l i t y with increasing temperature was observed over the temperature range 273 to 423°K, a r i s i n g from either the intermediate temperature embrittlement or the spontaneous strain-aging embrittlement . mechanisms. 4) The observations of the o p t i c a l microscopy and the s l i p trace analyses were consistent with the p r e d i c t i o n that planes of the ^QOl) - 174 -zone were operative. The trace analyses also suggested that s l i p on planes of the ^111^ zone was occurring, p r i m a r i l y i n the v i c i n i t y of the grain boundaries. The occurrence of ^111^ s l i p was re l a t e d to the higher s t r e s s " l e v e l . " " 5) The d i s l o c a t i o n structure observed i n the electron microscope was s i m i l a r to that reported for bcc metals and a l l o y s . 6) The temperature dependence of the y i e l d stress of the stoichiometric and Zn-rich a l l o y s was s i m i l a r to that of bcc metals. The excess Au decreased the temperature dependence s i g n i f i c a n t l y i n the composition range 50.1 to 51.6 a/o Au, 7) A region of temperature independent work hardening was observed for a l l compositions at temperatures below 300°K. The non-stoichiometric a l l o y s displayed a sharp increase i n the hardening rate with decreasing temperature below 150°K. Vidoz and Brown's jog theory of work hardening was suggested as the hardening mechanism. The sharp r i s e below 150°K was a t t r i b u t e d to the enhanced frequency of ( l l l ^ s l i p . 8) The composition dependence of the y i e l d stress exhibited the following behaviour; a minimum at the stoichiometric composition, a l i n e a r dependence of hardening on the deviation from stoichiometry, equal hardening due to excess Au and Zn atoms, and a temperature independent hardening-composition slope,(except at 77°K where a pronounced hardening minimum at 50.5 a/o Au was observed). The composition dependence of the flow stress was s i m i l a r . E x i s t i n g order strengthening theories and s o l i d s o l u t i o n hardening mechanisms cannot explain the above r e s u l t s . 9) Zn-rich a l l o y s containing ^49.5 a/o Au were b r i t t l e at 77°K. The b r i t t l e n e s s may be due to a low temperature m a r t i n s i t i c phase transformation. 10) The s t r a i n - r a t e s e n s i t i v i t y at room temperature was small f o r the stoichiometric a l l o y and non-existent for the non-stoichiometric a l l o y s . 11) The grain size-flow stress data f o r AuZn were found to follow the Hall-Petch r e l a t i o n , v i z 0^  = + K l" 1^ 2 . The intercept was comparable with the y i e l d stress f o r s i n g l e c r y s t a l s . The Petch slope was low and increased with s t r a i n . The Au and Zn-rich materials exhibited i d e n t i c a l behaviour. 12) The magnitude of the a c t i v a t i o n volume, a c t i v a t i o n energy, frequency f a c t o r , and shear stress extrapolated to 0°K were consistent with either Escaig's model of thermally activated s e s s i l e - g l i s s i l e transformations or the Peierls-Nabarro Force mechanism for the temperature dependence of the y i e l d s t r e s s . The P e i e r l s mechanism was found to provide a more s a t i s f a c t o r y explanation of the s o l i d s o l u t i o n softening phenomena. 13) The defect structure of f u l l y annealed AuZn was determined to be a n t i -s t r u c t u r a l , i . e . s u b s t i t u t i o n a l on both sides of stoichiometry. The larger Au atom expanded the AuZn l a t t i c e 0.025% per a/o while the smaller Zn atom constricted the l a t t i c e only 0.013% per a/o. The as-extruded Zn-rich material was found to contain Zn i n t e r s t i t i a l atoms and vacancies on the Au s u b l a t t i c e . 14) The strength of the as-extruded Zn-rich a l l o y s was s i g n i f i c a n t l y greater (~3X) than that of the annealed material. In addition the composition dependence of the strength was found to be l i n e a r . 15) The as-extruded Zn-rich wire exhibited an anomalous.increase i n e l e c t r i c a l r e s i s t i v i t y during annealing experiments. The e n t i r e annealing - 176 -process followed a second order k i n e t i c rate law. The increase i n r e s i s t i v i t y was at t r i b u t e d to a decrease i n long-range order caused by the recombination of the Zn i n t e r s t i t i a l s with vacancies on the Au s u b l a t t i c e . The subsequent decrease was at t r i b u t e d to an increase i n long-range order r e s u l t i n g from the removal of wrong Zn atoms from the Au s u b l a t t i c e by thermal vacancies. 6.3 SUGGESTIONS FOR FUTURE WORK This project could undoubtedly be extended i n many d i r e c t i o n s , however, the most obvious and desireable continuations are; 1) a more thorough i n v e s t i g a t i o n of the a l l o y hardening phenomena. Single c r y s t a l s having both deviations from stoichiometry and ternary solute additions to a stoichiometric base a l l o y should be used. The hardening, s i z e m i s f i t , and modulus v a r i a t i o n with composition should be determined and an e f f o r t made to separate out the e f f e c t s of ordering. 2) d i r e c t experimental evidence f o r the/existence of ^,111^ s l i p . This would require the use of both the t i l t i n g stage.and beam t i l t i n g devices i n the electron microscope. 3) a more.extensive i n v e s t i g a t i o n of the s o l i d s o l u t i o n softening phenomena. This i s of s p e c i a l i n t e r e s t since the phenomena appears to be quite general i n bcc a l l o y s . A thermally activated flow parameter study of more Au-rich a l l o y s within the 50.1 to 51.6 a/o Au range may be useful i n t h i s respect. 177 -Appendix A 104 B r i e f o u t l i n e of the equations of the Dorn-Rajnak analysis of the P e i e r l s mechanism, as given by Guyot and Dorn. 103 A . l where The shear s t r a i n rate for the forward motion of d i s l o c a t i o n s r e s u l t i n g from the nucleation of p a i r s of kinks has been given by Guyot and Dorn as 2 * , p Lab V / U . \ y = p b v = r - ^ r - ex P ( - n / k T ) • T o t a l length of a l l thermally activated d i s l o c a t i o n segments per unit volume b - Burgers vector V - The average v e l o c i t y of a d i s l o c a t i o n moving as a r e s u l t of nucleation of a.pair of kinks L - the average, length of a . d i s l o c a t i o n that might be swept out by a pair of kinks following t h e i r nucleation. a - spacing between p a r a l l e l rows of c l o s e l y spaced atoms of the s l i p plane - Debye frequency w - the width of the c r i t i c a l pair of kinks k - Boltzman constant T - absolute temperature U - the energy to nucleate a pair of kinks n The P e i e r l s stress for P e i e r l s h i l l s which are nearly s i n u s o i d a l i s given by <r b = (Hr to) A + I 1 + 8c*2 \ m 2 - 2+2 J 1+8 2 ) ^ 16a/ / / A.2 - 178 -where = energy per unit length of d i s l o c a t i o n a t . p o s i t i o n ABC on the P e i e r l s h i l l and at the bottom A a B 0 C 0 c< - constant which depends on the shape of the P e i e r l s h i l l , when o< =0, the kink energy i s given by A. 3 D. = K T N and depends .primarily on VQ and ^ p . The value of 2U^ i s equal to U when X. * = 0 thus The a c t i v a t i o n volume should be independent of d i s l o c a t i o n density and the work hardened state and i s given by A . 5 = ->Ja - - 2 u k ) <V 2 uk while the experimental a c t i v a t i o n volume UJ , i s rela t e d to the above by - V a =kT ( ^ ) T - 2 k T ( ^ ) +V* The width of the c r i t i c a l ; p a i r of kinks i s given by W = 2 ( b ^ " } Figure A - l . Schematic i l l u s t r a t i o n o f . P e i e r l s ' mechanism. The d i s l o c a t i o n l i n e l i e s at A B C i n i t i a l l y . Under / O O o an applied stress i t moves to ABC. Thermal f l u c t u a t i o n s of s u f f i c i e n t energy nucleate loops which move,the it d i s l o c a t i o n -to AB*C. The kinks AB' and B'C move appart for a l l configurations exceeding the c r i t i c a l one,and the d i s l o c a t i o n advances to the next equilibrium p o s i t i o n ABC . - 180 -BIBLIOGRAPHY 1) J . H. Wernick, 'Physical Metallurgy', Ed. by R.W. Cahn, John Wiley and Sons Inc, New York, p. 213 (1965). 2) D. L. Wood and J . H. Westbrook, Trans. A.I.M.E., 224, 1024, (1962). 3) M. J . Marcinkowski and H. Chessin, P h i l . Mag., 10, 837, (1964). 4) A. B a l l and R. E. Smallman, Acta Met., 14, 1349, (1966). 5) J . D. Mote, K. Tanaka, and J . E. Dorn, Trans. A.I.M.E., 221, 858, (1961). 6) M. Hansen, Const i t u t i o n of Binary A l l o y s , McGraw-Hill, New York, p. 241, (1958). 7) A. Westgren and G. Phragmen, P h i l . Mag., 50, 311, (1925). 8) N. V. Ageev and D. N. Shoykhet, Izvest. Sektora,Fiz-Khim. Anal. 13, 165, (1940). 9) E. A. Owen and J . G. Edmunds, Proc. Roy. Soc. (London), _50, 389, (1938). 10) R. W. Carpenter, R. L. Orr, and R. Hultgren, Trans. A.I.M.E., 239, 107, (1967). 11) J . H. Westbrook, 'Mechanical Properties of Inte r m e t a l l i c Compounds' Ed. by J . H. Westbrook, John Wiley and Sons Inc., New York, p. 1, (1960). 12) P. Stark, J . Metals, 16, 252, (1964). 13) J . H. Westbrook, "High-Strength Materials'', Ed. by V. F. Zackay, John Wiley, and Sons Inc., New York, p. 724, (1965). 14) N. S. S t o l o f f and R. G. Davies, Prog, i n Mat. S c i . , 13 #1, 1, (1966). 15) J . C. Terry and R. E. Smallman, P h i l Mag., 8., 1827, (1963). 16) E. P. Lautenschlager, D. A. Kiewit, and J . 0. B r i t t a i n Trans. A.I.M.E., 233, 1297, (1965). 17) A. G. Rozner and R. J . Wasilewski, J . Inst. Metals, 9h_, 169, (1966). 18) N. S. S t o l o f f and R. G. Davies, Acta Met., 12, 473, (1964). 19) N. Brown, P h i l . Mag. j4, 693, (1959). - 181 -20) G. W. Ardley and A. H. Cottr.ell, Proc. Roy. S o c , 219A, 328, (1953). 21) A. B a l l and R. E. Smallman, Acta. Met., 14, 1517, (1966). 22) A. H. C o t t r e l l , P h i l . Mag., 44, 829, (1953). 23) F. N. Rhines and P. J . Wray, ASM Trans. Quart., 54, 117, (1961). 24) C. C. Koch and A. R. Troiano ASM Trans. Quart., _57, 519 (1964). 25) D. McLean, ,'Mechanical Properties of Metals' John Wiley and Sons Inc., New York, (1962). 26) W. A. Rachinger and A. H. C o t t r e l l , Acta Met., 4_, 109, (1956). 27) G. W. Groves and A. K e l l y , P h i l Mag., 8., 877, (1963). 28) S. M. Copley, P h i l . Mag. 8., 1599, (1963). 29) R. von Mises, Z. angew. Math. Mech., 161, (1928). 30) R. W. Cahn and J . A. C o l l , Acta. Met., 9.. 1 3 8 » (1961). 31) L. D. Johnson and J . A. Pask, J . Am. Cer. S o c , 47., 437, (1964). 32) M. V. Klassen-Neklyudova,and A. A. Urusovskaya, Tr. Inst. K r i s t a l l o g r . Akad. Nauk. SSSR, #11, 146, (1955). 33) E. M. Schulson, P r i v a t e Communication, (1967). 34) R. Benson, G. Thomas and J . Washburn, 'Direct Observations of Imperfections i n C r y s t a l s ' , Ed. by J . B. Newkirk and J . H. Wernick, Interscience, New York, pV 375, (1962). 35) A. S. Keh., Ibi d , p. 213. 36) P. R. Swann, 'Electron Microscopy and Strength of C r y s t a l s ' , Interscience New York, p. 131, (1963). 37) P. B. Hirsch, A. Howie and M. J . Whelan, P h i l . Trans. R. S o c , 252A, 499, (I960). 38) H. Conrad, 'Mechanical Behaviour of Materials at Elevated Temperatures' McGraw-Hill, p. 185, (1961). 39) T. L. Johnston, R. G. Davies and N. S. S t o l o f f , P h i l . Mag. 12, 305, (1965). - 182 -40) A. K. Mukherjee and J . E. Dorn, Trans. A.I.M.E., 230, 1065 (1964). 41) A. K. Mukherjee, W. G. Ferguson, W. L. Barmore and J . E. Dorn, J . Appl. Phys., 37, 3707, (1966). 42) G. E. Dieter, 'Mechanical Metallurgy' McGraw-Hill, New York, (1961). 43) B. Ru s s e l l and D. Jaff.rey, Acta Met., _13, 1 (1965). 44) M. Schwartz.and L.. Muldawer, J . Appl. Phys., 29, 1561 (1958). 45) H. Pops and T. B. Massalski, Trans. A.I.M.E., 233, 728, (1965). 46) T. E. M i t c h e l l and P. L. Raffo, Can. J . Phys., 45, 1047, (1967). 47) H. H. Kranzlein, M. S. Burton, and G. V. Smith, Trans. A.I.M.E., 233, 64, (1965). 48) E. 0. H a l l , Proc. Roy. Soc* (London), 64B, 747, (1951). 49) N. J; Petch, J . Iron Steel.Inst., 174, 25, (1953). " 50) M. J . Marcinkowski and R. M. Fisher, Trans. A.I.M.E., 233, 293, (1965). 51) A. H. C o t t r e l l , Trans. A.I.M.E. 212, 192, (1958). 52) R. Armstrong, L Codd, R. M. Douthwaite and N. J . Petch, P h i l . Mag., 1, 45, (1962). 53) J . C. M. L i , Trans. A.I.M.E., .227.. 239, (1963) . 54) M. A. Jaswon and M. H. Richman, Appl. Mech. Rev., 17., 857, (1964). 55) D. F. Stein, J . R. Low, J r . , and A. U. Seybolt, Acta Met., 11, 1253, (1963). 56) W. L. Bragg and E. : J . Williams, Proc. Roy. S o c , A151, 540, (1935). 57) A. H. C o t t r e l l , 'Dislocations and P l a s t i c Flow i n C r y s t a l s ' , Oxford Clarendon Press, (1953). 58) M. J . Marcinkowski and N. Brown, J . Appl. Phys. 33., 537, (1962). 59) P. A. F l i n n , Trans. A.I.M.E., 218, 145, (1960). 60) A. E. Vidoz and L. M. Brown, P h i l . Magi, ]_, 1167, (1962). 61) P. B. Hirsch and D. Warrington, P h i l . Mag. 6., 735, (1961). 62) W. L. Bragg, Proc. Phys. Soc. (London! V, 52, 195,- (1940). - 183 -63) G. W. Ardley, Acta Met., 3., 525, (1955). 64) M. J . Marcinkowski and D. S. M i l l e r , P h i l . Mag. 6., 871, (1961). 65) A. H. C o t t r e l l , Seminar on Relation of Properties to Microstructure, ASM p 151, (1954). 66) H. J . Logie, Acta Met., 5_, 106, (1957). 67) M. J . Marcinkowski and R. M. Fisher, J . Appl. Phys. 34, 2135, (1963). 68) W. C. Hagel and J . H. Westbrook, Trans. A.I.M.E. 221, 951, (1961). 69) M. J . Cooper, P h i l . Mag. 8., 805, (1963). 70) J . H. Westbrook and D. L. Wood, J . Inst. Met., 91, 174, (1962-3). 71) A. U. Seybolt and J . H. Westbrook, Acta Met., 12, 449, (1964). 72) Y. Shibuya, Tohoku Univ. S c i . Repts. Res. Inst., 1A, 161, (1949). 73) R. L. F l e i s c h e r , 'The Strengthening of Metals' Ed. by D. Peckner, Reinhoded Publ. Corp. New York, p. 93, (1965). 74) J . F r i e d e l , 'Dislocations', Addison-Wesley Pub., (1964). 75) R. L. F l e i s c h e r and W. R. Hibbard, J r . , 'The Relation between the Structure and Mechanical Properties of Metals' NPL Conference HMSO London, p. 261, (1963). 76) H. Suzuki, 'Dislocations and Mechanical Properties of C r y s t a l s ' , John Wiley and Sons, New York, p. 172, (1957). 77) A. H. C o t t r e l l , C. S. Hunter, and F. R. N. Nabarro, P h i l . Mag. 44, 1064, (1953). 78) G. Schoeck and A. Seeger, Acta. Met., ]_, 469, (1959). 79) P. Haasen, 'Physical Metallurgy', Ed. by R. W. Cahn, John Wiley and Sons Inc., New York, p. 821, (1965). 80) N. F. Mott and F. R. N. Nabarro, B r i s t o l Conf. Strength of S o l i d s , Phys. Soc! London, p. 1, (1948). 81) N. F. Mott, Imperfections i n Nearly Perfect C r y s t a l s , Ed. by W. Schockley, John Wiley and Sons Inc., New York, p. 173, (1952). 82) J . C. Fisher, Acta Met., 2, 9, (1954). - 184 -83) A. Seeger, 'Dislocations and Mechanical Properties of C r y s t a l s ' John Wiley and Sons Inc., New York, p. 243, (1957). 84) H. Conrad, 'High-Strength-Materials', Ed. by V. E. Zackey, John Wiley and Sons Inc., New York, p. 436, (1965). 85) A. H. C o t t r e l l and R. J . Stokes, Proc. Roy. S o c , 233, 17, (1955). 86) Z. S. Basinski, Aust. J . Physics, 13, 284, (1960). 87) H. Conrad and W. Hayes, Trans. Quart. ASM, ,56, 249, (1963). 88) H. Conrad, R. Armstrong, H. Wiedersich and G. Schoeck, P h i l . Mag., 6., 177, (1961). 89) H. Conrad and H. Wiedersich, Acta. Met., 8., 128, (1960). 90) H. Conrad, NPL Conf. Relations between the Structure and Mechanical Properties of Metals, H.M.S.0. London, p. 475, (1963). 91) J . W. C h r i s t i a n and B. C. Masters, P r o c Roy. S o c , 281, 240, (1964). 92) G. Schoeck, Phys. Stat. S o l . , 8., 499, (1965). 93) N. R. Risebrough, Ph.D. Thesis, University of B r i t i s h Columbia, (1965). 94) Z. S. Basinski and J . W. C h r i s t i a n , Aust. J . Phys., 13, 299, (1960). 95) B. L. Mordike and.P. Haasen, P h i l . Mag. ]_, 459, (1962). 96) D. F. Stein, Acta Met., 14, 99, (1966). 97) G. Schoeck, Acta Met., 9, 382, (1961). 98) T. E. M i t c h e l l , R. A. F o x a l l and P. B. Hirsch, P h i l . Mag. 8., 1895, (1963). 99) R. Kossowsky and N. Brown, Acta. Met., 14, 131, (1966). 100) B. Escaig, G. Fontaine and J . F r i e d e l , Can. J . Phys., 45, 481, (1967). 101) F. Kroupa and V. Vitek, Can. J . Phys., 45, 945, (1967). 102) P. Guyot and J . E. Dorn, Can. J . Phys., 45, 983, (1967). 103) J . E. Dorn and S. Rajnak, Trans. A.I.M.E., 230, 1052, (1964). 104) A. S. Keh and Y. Nakada, Can. J . Phys., 45,, 1101, (1967). 105) P. Wynblatt and J . E. Dorn, Trans. A.I.M.E., 236, 1451, (1966). 106) R. J . Arsenault, Acta Met., 15, 501, (1967). - 185 -107) W. van Gool, J . Mater. S c i . , 1, 261, (1966). 108) B. D. C u l l i t y , 'Elements of X-ray D i f f r a c t i o n ' , Addison-Wesley Publ. Co. Inc., New York, p. 338, (1956). 109) W. B. Pearson, 'Handbook of L a t t i c e Spacings and Structures of Metals', Pergamon Press, (1967). 110) A. C. Damask and G. J . Dienes, 'Point Defects i n Metals', Gordon and Breach, New York, (1963). 111) D. Turnbull, H. S. Rosenbaum, and H. N. T r e a f t i s , Acta Met., _8, 277, (1960). 112) C. Panseri and T. Federighi, Acta Met., 8., 217, (1960). 113) R. A. Dugdale, P h i l . Mag. JL, 537, (1956). 114) M. J . Kim and W. F. Flanaghan, Acta. Met., 15, 753, (1967). 115) Van Den Beukel, P. C. J . Coremans, and M. A. Vryhoff, Phys., Stat. S o l . , 19, 177, (1967). 116) K. Mukherjee, D. S. Lieberman and T. A. Read, J . Appl. Phys. 35, 857, (1964). 117) P. B. Hirsch, A . Howie, R. B. Nicholson, D. W. Pashley and M. J . Whelan, 'Electron Microscopy of Thin C r y s t a l s ' , Butterworths, London, (1965). 118) M. J . Marcinkowski, 'Electron Microscopy and Strength of C r y s t a l s ' Ed. by G. Thomas and J . Washburn, Interscience, New York, p. 333, (1963) 119) A. B a l l and R. E. Smallman, Acta Met., 13, 1011, (1965). 120) J . K. McKenzie and J . S. Bowles, Acta. Met., 5.. 137, (1957). 121) D. S. Leiberman, M.S. Wechsler, and T. A. Read, J . Appl. Phys., 26, 473, (1955). 122) J . H. Smith, and P. Gaunt, Acta Met., 9., 819, (1961). 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0104683/manifest

Comment

Related Items