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Plastic deformation of lithium fluoride. Street, Kenneth Norman 1964

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PLASTIC DEFORMATION OF LITHIUM FLUORIDE BY KENNETH NORMAN STREET B. A . S c . , The U n i v e r s i t y of B r i t i s h Columbia, 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR.THE DEGREE OF MASTER OF APPLIED SCIENCE ifh the Department of METALLURGY We accept t h i s t h e s i s as. conforming to the standard r e q u i r e d from candidates f o r the degree of MASTER OF APPLIED SCIENCE. Members of the Department of M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA J u l y , 196^ In present ing t h i s t h e s i s i n p a r t i a l f u l f i l m e n t - o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the 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 reference and study. -I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department o r by h i s r e p r e s e n t a t i v e s . It i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n permiss ion . Department of Meta l lurgy The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date July 17. I9£k ABSTRACT A nonuniform annealing rate of. c o l o r centers i n L i F i s a t t r i -buted to a nonuniform densi ty of d i s l o c a t i o n s which, i n t u r n , i s a d i r e c t consequence of the c l e a v i n g process . The t e n s i l e deformation p r o p e r t i e s of annealed L i F c r y s t a l s were o o determined over the temperature range - 196 C . to +60 C. Several t e s t s were a l s o c a r r i e d out on ^ - i r r a d i a t e d specimens at ambient temperatures. A t r a n s i t i o n occurs i n the work hardening rate d u r i n g stage II deformation. Experiments i n v o l v i n g both s t r a i n - r a t e and temperature c y c l i n g were performed over the l i m i t e d temperature range of - 60 to +60 C . The r e s u l t s were analyzed i n terms of rate theory expressions and i n d i c a t e d that the rate c o n t r o l l i n g mechanism f o r d i s l o c a t i o n motion i n stage IIA i s probably the nonconservative motion of jogs i n screw d i s l o c a t i o n s . Stage IIB hardening i s more l i k e l y c o n t r o l l e d by d i s l o c a t i o n i n t e r s e c t i o n s . Evidence i s presented which i n d i c a t e d that s t ress r e l a x a t i o n 12 experiments may provide an extremely easy technique f o r the determination of the i n t e r n a l f low s t r e s s . Values obtained from such experiments on L i F agree remarkably w e l l with those obtained from rate theory experiments. ACKNOWLEDGEMENT The author would l i k e to express h i s thanks to h i s research d i r e c t o r , D r . E . Teghtsoonian, f o r h i s suggestions and guidance throughout the course of study and i n the preparat ion of t h i s t h e s i s . Thanks are a l s o extended to R. J . R-ichter f o r . h i s t e c h n i c a l ass is tance and to f e l l o w grad-uate students and other f a c u l t y members f o r t h e i r h e l p f u l d i s c u s s i o n s . P a r t i c u l a r thanks are extended to D r . J . Proverbs of the Ento-mology Laboratory, Canadian Department of A g r i c u l t u r e , Summerland, B. C . f o r h i s co -opera t ion and a s s i s t a n c e . i n the ^ - i r r a d i a t i o n of the L i F b l o c k s . F i n a n c i a l support was rece ived from The Consol idated Mining" and Smelting Company i n the form of a graduate research f e l l o w s h i p and from The N a t i o n a l Research C o u n c i l under 'Grant A - lUo3» This support i s .most g r a t e f u l l y acknowledged. TABLE OF CONTENTS Page I . INTRODUCTION AND PREVIOUS WORK 1 A. In t roduct ion 1 •B. Previous Work 1 I I . EXPFJRIMENTAL 8 A. M a t e r i a l . . . . . . 8 B. Specimen Preparat ion • • 8 ( a ) C l e a v i n g . . . . . 8 (b) Anneal ing 9 (c) Chemical P o l i s h i n g . . . . 9 (d) Mounting H C. M e t a l l o g r a p h i c Examination 12 D. Pulse Anneal ing of I r r a d i a t e d C r y s t a l s 12 E . Deformation Experiments . . . . . 13 (a) Continuous T e n s i l e and Microhardness Tests . 13 (b) S t r a i n - r a t e Change Tests 1^  (c) Temperature Change Tests 1^  (d) Stress R e l a x a t i o n 15 F . Temperature Measurement 15 I I I . RESULTS I 6 A. Cleaved and P o l i s h e d Specimens l6 B. O p t i c a l Densi ty and Pulse Anneal ing 18 (a) Absorpt ion Measurements 18 (b) Microscopy 20 TABLE OF CONTENTS Continued Page C. T e n s i l e Deformation 23 (a) Flow s t ress T dependence); Microhardness 23 (b) S t r a i n - r a t e Change Tests 30 (c) Temperature-Change Tests 33 (d) Rate Theory . . • 33 (e) Stress Relaxat ion ^0 ( f ) Frac ture ^3 IV. DISCUSSION ." . ' . . . 5^ A . Cleaved Specimens. . . . . B . C o l o r Centers C. Pulse Anneal ing of I r r a d i a t e d C r y s t a l s D. T e n s i l e P r o p e r t i e s (a) S l i p Systems 52 ' ( b ) Flow Stress 52 (c) S t r e s s - s t r a i n Curve . . . ^ (d) E f f e c t of Media 57 (e) Shape E f f e c t 57 E . ' Microhardness Measurements . . 59 F . A c t i v a t i o n Volume ^1 (a) Stress dependence of the a c t i v a t i o n volume . . (b) S t r a i n - r a t e dependence of a c t i v a t i o n volume (c) A c t i v a t i o n volume and the s t ress dependence of d i s l o c a t i o n v e l o c i t y . . . . TABLES OF CONTENTS Continued Page (d) A c t i v a t i o n volume of i r r a d i a t e d c r y s t a l s ' 66 G. • Thermally A c t i v a t e d Deformation Mechanisms . . . (a) P e i e r l s - N a b a r r o Stress . . . . 67 (b) Impurity In terac t ions 67 (c) Forest d i s l o c a t i o n s i n t e r s e c t i o n s and charge e f f e c t s 68 (d) Cross g l i d e of screw d i s l o c a t i o n s 69 (e) Nonconservative motion of jogs i n screw d i s l o c a t i o n s . . . 70 ( f ) Rate C o n t r o l l i n g Mechanism. 73 H. Stress Relaxat ion 73 (a) I n t e r n a l and relaxed f low s t ress 73 (b) Strain- and s t r a i n - r a t e dependence o f " ? ^ . e i 7^ (c) Stress dependence of the re laxed f low s t ress 76 (d) Flow Stress 77 I . F rac ture . . . : 78 V. CONCLUSIONS . 7 9 V I . SUGGESTIONS FOR FURTHER WORK . . 80 V I I . APPENDICES | 8 l V I I I . , REFERENCES 99 LIST OF FIGURES Page 1. Force - d is tance curve f o r d i s l o c a t i o n motion 1 2 . C l e a v i n g apparatus • • 10 3- Specimen p o l i s h i n g holder 10 k. Mounted L i F t e n s i l e specimen 11 5 . A r r e s t e d cleavage crack i n ' L i F 290 x 17 6. Grown-in d i s l o c a t i o n s t ruc ture of p o l i s h e d . L i F . . . specimen : 25 x 17 ' 7 - M - band o p t i c a l d e n s i t y v . s . d is tance along specimen . 19 8. C h i s e l end of c leaved and pulse annealed specimen 70 x. 21 9- N o n - c h i s e l end of c leaved and pulse annealed specimen (etch p i t rows) lk-0 x 21 10. N o n - c h i s e l end of cleaved and pulse annealed specimen (no etch p i t rows) kOO x 22 11. Diagramatic r e p r e s e n t a t i o n of F i g . 10 • 22 12. T y p i c a l s t r e s s - s t r a i n curves 23 13- S t r e s s - s t r a i n behavior of annealed c r y s t a l s . at var ious temperature 25 l i l - . S t r e s s - s t r a i n behavior of annealed c r y s t a l s at var ious s t r a i n - r a t e s . 26 15- S t r e s s - s t r a i n curves f o r i r r a d i a t e d L i F at 2 1 ° C . ( a i r ) 27 16. Temperature dependence of the y i e l d s t ress 28 17- Temperature dependence of the c r i t i c a l t e n s i l e s t ress • 28 18. Macroscopic deformation behavior of t e n s i l e specimens . 29 19- M i c r o h a r d n e s s ' v . s . indenter load f o r annealed and i r r a d i a t e d L i F 30 20. A s t r a i n - r a t e change t e s t 30 21. Basic s t r a i n - r a t e dependence of A V T1 32 a 22. Flow s t ress r a t i o v . s . . t e n s i l e s t r a i n f o r G /S, = 1 0 . 32 LIST OF FIGURES .Continued Page 23- Temperature s e n s i t i v i t y of ~£~ a v . s . s t r a i n : f o r var ious temperatures 3^ -2k. A c t i v a t i o n volume v . s . f low s t ress f o r annealed L i F . . 35 25. A c t i v a t i o n volume v . s . a p p l i e d s t ress f o r annealed and i r r a d i a t e d L i F 37 26. Temperature s e n s i t i v i t y of the f low s t ress v . s . temperature 37 27- Temperature s e n s i t i v i t y of "2^  v . s . s t r a i n - r a t e s e n s i -t i v i t y of f or e 2/e 1 = 5 • • 38 28. S t r a i n - r a t e s e n s i t i v i t y of "Z" v . s . temperature f o r eje2 - 5 • • . . 38 29. Temperature s e n s i t i v i t y of v . s . s t r a i n - r a t e s e n s i t i v i t y of > i f or £ _ / • a = 100 39 *- a <->' g 30. S t r a i n - r a t e s e n s i t i v i t y of "2" v . s . temperature f o r e2li.! = 100 39 31. S t r e s s - r e l a x a t i o n curve . . . 32. Relaxed f l o w s t ress v . s . f low s t ress . . . . kl 33- Relaxed f low s t ress v . s . s t r a i n ^1 3^. Change i n f low s t ress f o l l o w i n g r e l a x a t i o n k2 35' I n t e r n a l s t ress and re laxed f low s t ress v . s . a p p l i e d s t ress k2 36. S t r e s s - b i r e f r i n g e n c e of f r a c t u r e d t e n s i l e specimens . . kk 37. E q u a l l y s t r e s s e d j l i o j <CP-°y s l i P systems 53 38. D i s l o c a t i o n motion on obl ique ^ l l o " | . ^ l l O / 1 s l i p systems . 53 39- General s t r e s s - s t r a i n curve 55 kO. E f f e c t of specimen shape on operat ive £ll0~j ^-10^ s l i p systems kl. Stages of a c t i v a t i o n volume v . s . s t ress curves . . . . 6 l k2. D i s l o c a t i o n i n t e r s e c t i o n s on obl ique and orthogonal g l i d e planes i n MgO. 66 ^3' Moving screw d i s l o c a t i o n s i n MgO 71 kk. A p p l i e d and i n t e r n a l s t resses v . s . s t r a i n 76 LIST OF TABLES Page I . Spectrographic A n a l y s i s of L i F C r y s t a l s 8 I I . C o n t r o l l e d Temperature Baths f o r Deformation Experiments 13 I I I . Summary of True A c t i v a t i o n Energies 36 IV. C o l o r centers i n L i F U6 T * T r e l e £ sat 0 \T b A N e • s H A Q H * LIST OF SYMBOLS a p p l i e d t e n s i l e s t r e s s ; f low s t ress ( C . T . S . ) (F/Ao) long range I n t e r n a l t e n s i l e s t ress e f f e c t i v e t e n s i l e s t ress (M~ - V. ) re laxed t e n s i l e f low s t ress change i n f low s t ress f o l l o w i n g r e l a x a t i o n a p p l i e d shear s t ress (.5 V~a); s i m i l a r l y f o r * ~ £ " j ^ "C*, t e n s i l e s t r a i n (A l / l o ) s a t u r a t i o n s t r a i n (end-point of stage I work-hardening) shear s t r a i n (£/»5) t e n s i l e s t r a i n - r a t e ( t i m e - ^ ) shear s t r a i n - r a t e ((S/..5) s t r a i n - h a r d e n i n g slope ( F / A© / u n i t t e n s i l e s t r a i n ) frequency of v i b r a t i o n of a d i s l o c a t i o n ( ^ l O ^ ^ s e c - ^ ) burgers vector of d i s l o c a t i o n (2.85 A f o r L i F ) area swept-out-by d i s l o c a t i o n / s u c c e s s f u l a c t i v a t i o n number of a c t i v a t i o n s i t e s / u n i t volume d i s l o c a t i o n d e n s i t y (cm/cm3) average d i s l o c a t i o n v e l o c i t y t o t a l energy b a r r i e r height (see F i g . l ) thermal component of the a c t i v a t i o n energy a c t i v a t i o n energy-a c t i v a t i o n volume r e l I . INTRODUCTION AND PREVIOUS.WORK A. I n t r o d u c t i o n Studies of the mechanical proper t ies of i o n i c c r y s t a l s have been g r e a t l y enhanced d u r i n g the past few y e a r s . Much of the work has been f o -cussed around L i F . Comprehensive reviews of t h i s work have appeared i n 1 2 3 s e v e r a l recent p u b l i c a t i o n s . ' Thus, a vast amount of informat ion has been gathered on the fundamental proper t ies of i n d i v i d u a l d i s l o c a t i o n s i n L i F . However, the d e t a i l e d p h y s i c a l mechanism producing r e s i s t a n c e to t h e i r movement d u r i n g s t r a i n hardening remains to be understood. The a p p l i c a t i o n of rate theory techniques has g r e a t l y a s s i s t e d i n v e s t i g a t o r s i n the determination of the thermally a c t i v a t e d f low mech-anisms c o n t r o l l i n g deformation. To date , t h i s method has been only a p p l i e d to m e t a l l i c s t r u c t u r e s . Hence, a l o g i c a l step would be the extension to i o n i c s o l i d s , i n p a r t i c u l a r L i F . Over the past few years , the vast improvement i n the p u r i t y of commercially a v a i l a b l e L i F has r e s u l t e d i n a d r a s t i c decrease i n the hard-ness of t h i s m a t e r i a l . Consequently, i t has become extremely d i f f i c u l t to cleave these c r y s t a l s i n t o small specimens without severely damaging them. Nadeau and Johnston^ introduced the idea of H - i r r a d i a t i o n hardening as a means of o b t a i n i n g c r y s t a l s that could be cleaved without damage. They a lso observed that the i r r a d i a t i o n e f f e c t s could be completely removed by anneal ing ahd the o r i g i n a l p r o p e r t i e s r e s t o r e d . The c r y s t a l s u s e d . i n the present work were i r r a d i a t e d mainly to f a c i l i t a t e c l e a v i n g i n t o s lender t e n s i l e specimens. However, as the nature of the hardening had not been thoroughly i n v e s t i g a t e d , i t was thought - 2 -d e s i r a b l e to carry out a p re l im in ary study of the proper t ies of i r r a d i a t e d L i F . A d i r e c t consequence of the ^ - i r r a d i a t i o n of L i F i s the produc-t i o n of var ious c o l o r centers coupled with a very large increase i n hard-ness, i . e . r e s i s t a n c e to p l a s t i c deformation. Thus a l i k e l y course of study of the hardening would.be a determination of the dependence or r e l a t i o n between the mechanical proper t ies and the c o l o r . c e n t e r concentra t ions . Such observations combined with the annealing k i n e t i c s of var ious c o l o r centers could p o s s i b l y lead to informat ion regarding the r e l a t i v e importance of var ious d e f e c t s . A l s o , such a study may l e a d . t o a more thorough undert= s tanding of the p l a s t i c deformation of u n i r r a d i a t e d . L i F c r y s t a l s . Inherent i n a study of t h i s type would be the a b i l i t y to o b t a i n a homogeneous concentrat ion of c o l o r centers throughout specimens subjected to deformation. This was not a t t a i n a b l e i n the present experiments. Hence a p r e l i m i n a r y i n v e s t i g a t i o n i n t o the source of inhomogeneous anneal ing of c o l o r centers was performed. B. Previous Work A large amount of informat ion on the deformation p r o p e r t i e s of 1 , 2 , " L i F has been made a v a i l a b l e through the experiments of Gilman and Johnston. Most of t h e i r work has been concerned with the proper t ies of i n d i v i d u a l d i s l o c a t i o n s;jsuch as t h e i r o r i g i n ' ' and m u l t i p l i c a t i o n , e t c h - p i t t i n g Char-CD a c t e r i s t i c s and m o b i l i t y . 9 , 1 0 The p o s s i b l e ra te c o n t r o l l i n g deformation mechanisms proposed f o r the thermally a c t i v a t e d motion of d i s l o c a t i o n s i n m e t a l l i c substances are a l s o b e l i e v e d to h o l d . f o r i o n i c c r y s t a l s . However the charged nature of i o n i c c r y s t a l s leads to one a d d i t i o n a l mechanism which i s r e l a t e d t o the e l e c t r o s t a t i c analogue of the C o t t r e l l i m p u r i t y - p i n n i n g mechanism. Hence - 3 -the f o l l o w i n g mechanisms are considered p o s s i b l e i n L i F ; ( i ) charge e f f e c t s ( i i ) overcoming P e i e r l s - N a b a r r o s t ress ( i i i ) i m p u r i t i e s ( i v ) c r o s s - s l i p of screw d i s l o c a t i o n s (v) i n t e r s e c t i o n of d i s l o c a t i o n s ( jog formation) ( v i ) motion of jogs i n screw d i s l o c a t i o n s The a p p l i c a t i o n of ra te theory to p l a s t i c deformation has been 11 i p o u t l i n e d by many workers. Assuming that d i s l o c a t i o n motion w i t h i n a m a t e r i a l under s t ress requires thermal a c t i v a t i o n to overcome o b s t a c l e s , ( F i g . l ) , the rate of deformation or the d i s l o c a t i o n v e l o c i t y can be des-c r i b e d by the f a m i l i a r Arrehenius equat ion , where ^ - £ bs = \ T b A N e x p ( - _ Q/kT) ( l ) = shear s t r a i n rate ( s e c _ l ) >^ = d i s l o c a t i o n d e n s i t y (cm/cm3) b = B u r g e r ' s vector = 2.85 x ,10"8cm f o r L i F s = average d i s l o c a t i o n v e l o c i t y (cm/sec) V~ = frequency of v i b r a t i o n of a d i s l o c a t i o n ( lCT^sec"-") A = area swept out by a d i s l o c a t i o n per thermal f l u c t u a t i o n (cm^) . IT = numberc.of a c t i v a t i o n s i t e s per u n i t volume (cm"3) A Q = thermal component of the a c t i v a t i o n energy A term with the dimensions of ( length)3 a r i s e s when one introduces the assumption that the a c t i v a t i o n can be a s s i s t e d by the a p p l i e d s t r e s s , " ? ^ , i . e . A Q = H - v* ^ ~ a (2) where H i s the t o t a l energy b a r r i e r height and v* i s the " a c t i v a t i o n volume". The dis tance moved.by a d i s l o c a t i o n i n overcoming a p o t e n t i a l energy b a r r i e r i s designated as the a c t i v a t i o n dis tance " d " . (See F i g . l ) - k -0) o u o En A Q = Area BCD H = Area OABCDFG H*= Area ABCDF d = a c t i v a t i o n distance Distance (x) F i g . 1 Force - dis tance curve for, d i s l o c a t i o n motion 13 Henceforth t h i s f i g u r e w i l l be r e f e r r e d to as the F - x curve. Seeger proposed that a c o n s i s t s of two components, ' C i . and which a s s i s t a c t i v a t i o n as f o l l o w s , the s t ress necessary to overcome the i n t e r n a l s t ress f i e l d s , reduces the b a r r i e r height through v * . Hence, when the thermal energy r e q u i r e d f o r a c t i v a t i o n i s A Q = H * = H - v * (3) Under these condi t ions d i s l o c a t i o n s w i l l not move unless very high temp-eratures e x i s t . When > the thermal a c t i v a t i o n energy can be reduced by the e f f e c t i v e shear s t r e s s , * A Q = H * - v* f * (10 In otherwards H = H * + v* "Z"± (5) and • Ta = !:* + 7r± (6) I t can be seen that f o r a round-topped F - x curve , H , H * , and d are f u n c -t i o n s of s t ress ( " £ " * ) . This would not be true f o r a square-topped F - x curve. Fur ther mathematical manipulat ion leads to the f o l l o w i n g equations , (see Appendix I) v* = kT ( ) m = -k ln (yrb A H / y ) (7) H = v* T"a - v * T (dfo. T T (8) A Q = - k T 2 ( _ ) 7 y 2 T ) ( 9 ) The main parameters of i n t e r e s t are thus v * , H and A Q- The value 'of a c t i v a t i o n energy we are i n t e r e s t e d i n i s that c h a r a c t e r i s t i c of the rate c o n t r o l l i n g process . This i s independent of the i n t e r n a l s t ress of the l a t t i c e and hence i s represented by H * at"£T* = 0 . This value i s to be compared with the c a l c u l a t e d . a c t i v a t i o n energies f o r the var ious p o s s i b l e mechanisms. The rate c o n t r o l l i n g deformation mechanisms proposed by var ious Ik 1 5 workers f o r m e t a l l i c c r y s t a l s have been reviewed by Simpson and Gregory. Rate theory has not been a p p l i e d to i o n i c s o l i d s to date and hence any p r e -d i c t e d mechanisms have been i n f e r r e d from other types of experiments. In order to e x p l a i n the strong temperature dependence of the f low s t ress observed i n e a r l y work on L i F , Gilman X D p o s t u l a t e d that the P e i e r l s -Nabarro s t ress was the rate c o n t r o l l i n g deformation mechanism. However, t h i s dependence can now be a t t r i b u t e d to impuri ty e f f e c t s as recent work on pure c r y s t a l s (->-• 2 ppm Mg) has shown that L i F does not e x h i b i t a very strong temperature dependence f o r c o o l i n g rates l e s s . t h a n 50 deg. C/minute. In f a c t the work on impure L i F ( ^ 80 ppm Mg) agreed-well with F l e i s c h e r ' s -i Q t h e o r e t i c a l c a l c u l a t i o n s on impuri ty c o n t r o l l e d d i s l o c a t i o n m o b i l i t y . ° - 6 -Gilmarr has a l s o s tated that C o t t r e l l i n t e r a c t i o n s may be r a t e -c o n t r o l l i n g i n impure L i F . Johnston-*-? has placed an upper l i m i t of 50 gm/mn}^  on the room - temperature f low s t ress c o n t r i b u t i o n of the P e i e r l s -Nabarro s t r e s s . Johnston and Gilman^-9 have a l s o c a l c u l a t e d that a con-servat ive estimate of the lower l i m i t f o r drag due to jogs i n a c r y s t a l with a y i e l d s t ress o f — • 500 gm/mfcp would be about 75 - 150 gm/mfe? Gilman 2 ® has proposed that s t r a i n hardening at low s t r a i n s —-10$) i s caused b y . " d e b r i s " produced by m u l t i p l e c r o s s - g l i d e of screw d i s -l o c a t i o n s . The. debr is c o n s i s t s of edge d i s l o c a t i o n d i p o l e s which i n h i b i t the motion of subsequent d i s l o c a t i o n s on the same or near ly g l i d e p lanes . However, the a c t u a l hardening mechanism.involving the d e b r i s s t i l l remains u n c e r t a i n . The f i r s t s tudies of the i r r a d i a t i o n hardening.of L i F were c a r r i e d out by Gilman and Johnston 21. They observed, that f o l l o w i n g neutron i r r a -d i a t i o n , hardening e f f e c t s d i d not appear u n t i l the 450 xcji (M center) absorp-t i o n band was observed. Even though heavy p a r t i c l e i r r a d i a t i o n was used, they postula ted that the major e f f e c t was one of i o n i z a t i o n . Very r e c e n t l y , Nade,au22 ^ a s proposed that the defec t i n v o l v e d i n hardening of - i r r a -d i a t e d L i F i s the i n t e r s t i t i a l f l u o r i n e i o n . He observed that the hardening i s r e l a t e d to the c r e a t i o n of F centers but that F centers alone cannot account f o r the magnitude i n v o l v e d . He proposed that the F centers are c reated ,as a r e s u l t of Varleys mechanism23 of F r e n k e l p a i r product ion whereby the i n t e r s t i t i a l F ions act as the hardening d e f e c t s . V a r l e y proposed that negative ions which have l o s t s e v e r a l e l e c t r o n s w i l l experience strong r e -p u l s i v e e l e c t r o s t a t i c f o r c e s due to the s u r r o u n d i n g . c a t i o n s . Hence, they w i l l tend to move i n t o i n t e r s t i t i a l s i t e s where they are then surrounded by negative i o n s . • - 7 -'Seatz and Koehler b e l i e v e that such a mechanism would not be of great p r a c t i c a l i n t e r e s t i n the c r e a t i o n of F centers . They proposed that the i n t e r s t i t i a l anions should be able to capture f r e e e l e c t r o n s and move back i n t o the assoc ia ted vacancies . Johnston and G i l m a n ^ have shown that the f low s t ress of L i F i s determined by the r e s i s t a n c e to motion of f r e s h d i s l o c a t i o n s produced dur ing deformation. Hence, p i n n i n g e f f e c t s , although present i n i r r a d i a t e d c r y -s t a l s , are not important i n determining the r e s i s t a n c e to d i s l o c a t i o n motion. Thus, the point defects c r e a t e d . d u r i n g i r r a d i a t i o n r e s u l t i n l o c a l -i z e d s t r a i n f i e l d s which impede d i s l o c a t i o n movement. ! Johnston, Nadeau, and F l e i s c h e r ^6 have shown that the observed hardening i n L i F can be a t t r i b u t e d to the non-symmetrical s t r a i n f i e l d s assoc ia ted with i n t e r s t i t i a l F i o n s . - 8 -I I . EXPERIMENTAL A . M a t e r i a l The s i n g l e c r y s t a l s used in'tthe present work were obtained from the Harshaw Chemical Company i n the form of rec tangular b l a n k s , 1" x 1" x 2", with £ l O O j ' plane e x t e r n a l s u r f a c e s . The a s - r e c e i v e d m a t e r i a l was descr ibed as having been slow-cooled to room temperature over a one week p p e r i o d . a f t e r growth. The o v e r a l l s toichiometry of Harshaw L i F c r y s t a l s has been checked by Gilman and.Johnston^ and found to be w i t h i n 0.2 percent of i d e a l . They a l s o observed s u b - g r a i n m i s o r i e n t a t i o n s averaging about 5 minutes of a r c . Spectrographic a n a l y s i s of the present m a t e r i a l revealed t race amounts of d i v a l e n t i m p u r i t i e s as shown i n T a b l e . I . TABLE I Spectrographic A n a l y s i s * of L i F c r y s t a l s (ppm) C r y s t a l Fe A l S i Ca Mg A 0-3 0.1 0.2 0.3 1.0 • ; . B 0.3- o . i 0.05 0.2 2.0 * T e s t e d . a t Coast E l d r i d g e L t d . , Van. , B . C . B . Specimen Preparat ion (a) C l e a v i n g The r e l a t i v e l y s o f t L i F b l o c k s were exposed to o' - i r r a d i a t i o n from a c y l i n d r i c a l , b i r d - c a g e type C o ^ source (20 hours @ 60,000 r a d s / h r ) © . T h i s was c a r r i e d out to f a c i l i t a t e c l e a v i n g with a minimum amount of p l a s t i c deformation. Guide l i n e s were s c r i b e d onto one face of the i r r a d i a t e d c r y s t a l u s i n g . a v e r n i e r layout marker. Slender t e n s i l e specimens were then cleaved ® I r r a d i a t e d at the Entomology Laboratory , Canadian Department of A g r i c u l t u r e Summerland, B . C. - 9 -u t i l i z i n g the j i g shown i n F i g . 2. The r e s u l t i n g specimens had .j~10o"^  ex-t e r n a l faces and nominal dimensions of 1" x . 1" x .1" or .05". A mounted s ingle-edge razor blade appeared to be more s a t i s f a c t o r y i n the f i n a l stages of c l e a v i n g . A hardened s t e e l , c h i s e l - t y p e c leaver (R 60, 30 deg. ) was used i n the . i n i t i a l and a l s o sometimes i n the f i n a l s tages . (b) Anneal ing The cleaved specimens were placed on L i F supports and annealed i n a i r at 650 deg C. (*~ .75 T m.p . ) f o r 2k hours to remove the i r r a d i a t i o n e f f e c t s and to ensure homogeneity. Furnace heat ing and c o o l i n g rates aver-aged/about . 50 deg. C. per hour;.' (c) Chemical P o l i s h i n g ' A l l specimens were chemical ly p o l i s h e d p r i o r to deformation i n order to remove any surface l a y e r damage. They were placed i n a t e f l o n p o l i s h i n g holder ( F i g . 3) and subjected to the f o l l o w i n g treatment-: i ) 2 minutes i n 50$ EBFI+ (slow r o t a t i o n of j i g ) i i ) 3 cyc les o f : - 1 minute d i p i n 50$ HF - 5 minutes i n a s o l u t i o n of 3$ NH^OH and d i s t i l l e d H2O (slow r o t a t i o n of j i g combined with r a p i d r o t a t i o n of magnetic s t i r r e r i n s o l u t i o n ) Each step was fo l lowed by an e t h y l a l c o h o l r i n s e w i t h . t h e f i n a l step having an a d d i t i o n a l d r y - e t h e r r i n s e . The treatment removed about 50 microns from the s u r f a c e . A f t e r p o l i s h i n g , they were handled only by t h e i r end p o i n t s . F i g . 3 Specimen p o l i s h i n g holder - 11 -(d) Mounting T e n s i l e specimens were prepared by cementing the p o l i s h e d c r y s t a l s i n t o m i l d s t e e l g r i p s with epoxy r e s i n . * A mounted specimen i s shown i n F i g . k. is | rTTTT 4 m 5 mmm F i g . l t Mounted L i F t e n s i l e specimen The g r i p s contained d r i l l e d holes which were s l i g h t l y l a r g e r than the speci -men c r o s s - s e c t i o n a l area . The technique c o n s i s t e d of p l a c i n g a g r i p con-t a i n i n g epon i n t o a c lose f i t t i n g d r i l l e d hole i n a l u c i t e b l o c k , s l i d i n g the specimen i n t o the epon, and p l a c i n g a dummy g r i p over the upper end of the specimen. No elaborate measures were taken to assure p e r f e c t a x i a l alignment as the setup was, to a c e r t a i n degree, s e l f - a l i g n i n g . Curing time f o r the epoxy r e s i n w a s ^ 2 f hours at 200 deg. F . f o r each g r i p . The mounted specimens were then c a r e f u l l y placed on a V-block and the dimensions measured with a Gaertner t r a v e l l i n g microscope. * Epon 828 + c u r i n g agent Z; weight r a t i o = 5 / l « - 12 -C. Meta l lographic Examination Examination of cleavage f a c e s , f r a c t u r e surfaces , e t c . was c a r r i e d out on a Reicher t Meta l lographic Microscope u s i n g both t ransmit ted.and r e -f l e c t e d l i g h t . Etch p i t techniques were u t i l i z e d to observec' .dislocation d e n s i t i e s , crack propagation and g l i d e band format ion . Gilman and John-ston's etch W was found s a t i s f a c t o r y (~ 2 x 10'^ molar F e d . i n d i s t i l l e d H 2 0 ) . Stress b i r e f r i n g e n c e observations proved extremely u s e f u l as a non-defetructive technique i n the e v a l u a t i o n of specimen p e r f e c t i o n . G l i d e band d i s t r i b u t i o n was a l s o r e a d i l y revealed by t h i s technique which simply consisted- of viewing between crossed p o l a r i z e r s with t ransmit ted l i g h t . D. Pulse Anneal ing of I r r a d i a t e d C r y s t a l s The absorpt ion spectrum of the o/- i r r a d i a t e d c r y s t a l s was d e t e r -mined with a Beckman D U Spectrophotometer. Absorpt ion band maxima were i. measured f o r specimens subjected to pulse anneal ing treatments at ~ 325 deg. C . During anneal ing^severa l specimens were arranged on L i F supports such that t h e i r cleavage d i r e c t i o n s opposed, one another. Q u a l i t a t i v e observations were made f o r specimens annealed i n the f o l l o w i n g s t a t e s : ( i ) asT-cleaved ( i i ) cleaved and p o l i s h e d ( i i i ) c leaved, annealed at 650 deg. C. f o r 2k hours, and r e - i r r a d i a t e d ( i v ) c leaved i n opposite d i r e c t i o n s with respect to the parent c r y s t a l E t c h - p i t t i n g techniques were a l s o u t i l i z e d . r 13 -E . Deformation Experiments (a) Continuous T e n s i l e and Microhardness Tests Both i r r a d i a t i o n hardened and annealed specimens were s t r a i n e d continuously to f r a c t u r e on an Instron t e n s i l e machine. The i r r a d i a t e d c r y s t a l s were deformed i n .a i r at room temperature whereas the annealed c r y s t a l s were deformed over a range of temperatures ( - I96 deg. C . to +60 deg. C . ) . The' var ious environments used i n a l l the t e n s i l e experiments are l i s t e d i n Table I I . . TABLE.II C o n t r o l l e d Temperature Baths f o r Deformation Experiments• Temperature Range Environment -I96 deg. C. L i q u i d Nitrogen - l60' d e g . C . to + 10 deg. C. C A i r \ P e t r o l e u m Ether + L i q . N 2 + 22 deg.C to 60 deg. C . / A i r (. S i l i c o n e O i l The Inst ron setup was designed to a l low complete immersion of the specimen and g r i p p i n g arrangement i n t o the c o n t r o l l e d b a t h s . For t e s t s c a r r i e d out i n a i r at non-ambient temperatures, a copper p r o t e c t i o n - j a c k e t was placed around the assembly before immersion i n t o the temperature medium. The s t r a i n - r a t e s i n v o l v e d corresponded to constant crosshead speeds ranging from 0.002 i n / m i n . to 0.2 i n / m i n . The major i ty of t e s t s were car -r i e d out at the slower speed which produced a s t r a i n - r a t e of about l O ' ^ / s e c . A l o a d s e n s i t i v i t y of - .01 pounds was maintained i n the major i ty of experiments by b a c k i n g o f f the f u l l - s c a l e load d e f l e c t i o n v i a the c a l i b r a -t i o n adjustment. Load and e longat ion parameters were cont inuously recorded on a moving s t r i p - c h a r t r e c o r d e r . - Ik -A Tukon hardness t e s t e r was u t i l i z e d to determine KNOOP Hardness Numbers (KHH) of f u l l y i r r a d i a t e d and annealed c r y s t a l s . Indenter loads used i n the measurements ranged from.5 to 100 grams. (b) S t ra in-Rate Change Tests The s t r a i n - r a t e dependence of the f low s t ress was determined by c y c l i n g the cross-head speed by f a c t o r s of 5, 25, and 100 f o r a b a s i c speed of 0.002 i n / m i n . over the temperature range -60 to + 60 deg. C . Room temp-erature t e s t s were a l s o c a r r i e d out u s i n g the a d d i t i o n a l f a c t o r s of 2-5 and 10 from the same b a s i c speed. ~.'..\ Room temperature experiments u s i n g . a f a c -t o r of 5 were conducted at b a s i c speeds of .01 and .02 i n / m i n . The major i ty of the experiments were performed on a n n e a l e d . c r y s t a l s i n a i r . However, one room temperature t e s t was c a r r i e d . o u t on an i r r a d i a t e d c r y s t a l . S t r e s s - b i r e f r i n g e n c e observations were made duiing both continuous and i n t e r r u p t e d t e s t s . In the l a t t e r case, specimens were unloaded and reloaded d u r i n g the b a s i c s t r a i n - r a t e p o r t i o n of the c y c l e . (c) Temperature Change Tests The temperature dependence of the f low s t ress was determined u t i l i z i n g a constant s t r a i n - r a t e corresponding to 0.002 i n / m i n . The t e c h -nique i n v o l v e d s t r a i n i n g a specimen a given amount at one temperature, rej-< moving 90 percent of the l o a d , e q u i l i b r a t i n g at a new temperature and rep s t r a i n i n g at the same s t r a i n - r a t e . This procedure was repeated mainta ining the same end point temperatures. Approximately 20 to 40 minutes e q u i l i b r a t i o n time was allowed depending upon the temperature medium. The abnormal e q u i l i b r a t i o n times r e q u i r e d by t e s t s c a r r i e d out i n a i r n e c e s s i t a t e d the use of the temperature baths descr ibed i n Table I I . - 15 -(d) Stress Relaxat ion The experimental method i n v o l v e d was to deform a specimen to some s t r a i n , stop the cross-head motion f o r " \ - 30 s e c , and then r e s t r a i n the specimen at the same i n i t i a l s t r a i n - r a t e . T h i s was repeated u n t i l f r a c t u r e , f o r cross-head speeds ranging from .005 " -5 i n / m i n . A l l t e s t s were c a r r i e d out at room temperature. F . Temperature Measurement A l l temperatures were measured with a copper-constantan thermo-couple . P e r i o d i c checks were made against another thermocouple or a mer-c u r y - g l a s s thermometer. E a r l y s t r a i n - r a t e change t e s t s i n which the specimen temperature was taken to be equal to the measured a i r temperature ' « re b e l i e v e d to be s l i g h t l y inaccurate although e x t r a o r d i n a r i l y long e q u i l i b r a t i o n periods were a l l o w e d . • In the more s e n s i t i v e temperature change experiments, the thermocouple was wrapped around a dummy L i F c r y s t a l which was placed beside the c r y s t a l b e i n g deformed. When l i q u i d environments were u t i l i z e d , the temperature of the specimen was taken to be equal to the measured temperature of the b a t h . T h i s was checked u s i n g dummy specimens. - 16 -I I I . RESULTS A. Cleaved and P o l i s h e d Specimens Immediately f o l l o w i n g )(- i r r a d i a t i o n , the L i F blanks were observed to be greenish-yel low i n c o l o r , d i f f e r i n g , f r o m t h e i r i n i t i a l c l e a r , t r a n s -parent s t a t e . However, they transformed to a b r i g h t ye l low c o l o r a f t e r a short time at near ambient temperatures. I t was d i f f i c u l t to maintain constant cleavage condi t ions due to v a r i a t i o n s i n alignment and cleavage crack v e l o c i t y . The as -c leaved specimens e x h i b i t e d v a r y i n g numbers and s i z e s of cleavage s teps . Specimens of uneven dimensions were o f t e n obtained when s p l i t t i n g a t h i n c r y s t a l i n t o unequal p o r t i o n s . Use of the r a z o r - b l a d e c leaver appeared to help r e c t i f y t h i s problem. However, i t was only useable on , very t h i n sec t ions of t h e ' c r y s t a l ^ i . e . only i n the f i n a l stages of c l e a v -i n g . A c e r t a i n amount of end damage was v i s i b l e , i n a l l specimens due to penetra t ion of the .blade i n t o the c r y s t a l . This depth was minimized to about l / l 6 inches . Incorrec t alignment or namm'er blow to the blade r e s u l t e d i n chipped o f f pieces or i n .cleavage cracks terminat ing w i t h i n the c r y s t a l . F i g . 5 was obtained by e t c h i n g a specimen i n which the cleavage crack had propagated part way through the specimen. I t can be seen that d i s l o c a t i o n formation and m u l t i p l i c a t i o n has resul ted , i n the formation of s e v e r a l microcracks at k5 deg. to the cleavage crack which has jumped between planes . - 17 -F i g . 6 Grown-in d i s l o c a t i o n s t ructure of p o l i s h e d L i F specimen 25 x - 18 -A t y p i c a l p o l i s h e d and etched specimen i s shown i n F i g . 6 and d i s p l a y s an average grown-in d i s l o c a t i o n densi ty o f " J x 10^/cm^. A l s o v i s i b l e are subgrain boundaries and s e v e r a l prominent cleavage s teps . B. O p t i c a l Densi ty and Pulse Anneal ing (a) Absorpt ion Measurements Over the range of wavelength 220 - 770 mp., two absorpt ion maxima were observed, one at kk5 my. and one at 250 mn. The l a t t e r peak (F band) was about three times higher and wider than the former peak (M band), r e s u l t i n g i n an area d i f f e r e n t i a l of about ten: t imes. A very small peak at 375 nip was observed i n some i n s t a n c e s . This band disappeared d u r i n g the e a r l y stages of the annealing treatments. Except f o r the determination of the c h a r a c t e r i s t i c wavelength, the F band.was not s tudied i n the present work. F i g . 7 shows the M band height ( o p t i c a l d e n s i t y ) as a f u n c t i o n of dis tance along the specimen. F i g . 7a corresponds to specimens i n the a s - i r r a d i a t e d and r e -i r r a d i a t e d s t a t e s . I t can be seen that the o p t i c a l densi ty i s constant » . ! a long each specimen. The absorpt ion peaks have not been normalized to a constant specimen thickness (—• .1 inches) to prevent over lapping of the value s. F i g s . 7h and "Jc are s i m i l a r p l o t s f o r c r y s t a l s which were pulse annealed at —» 325 deg. C . i n the as -c leaved and p o l i s h e d s ta tes , r e s -p e c t i v e l y . In both cases i t may be seen that the o p t i c a l densi ty no longer remains constant over the specimen length as annealing proceeds; 1, x the rate of decrease increases along the cleavage d i r e c t i o n of the - 19 -Cleavage d i r e c t i o n •30_ .20. o M fl >> , -P •H M fl d) nd H o •H -P Oi o (a) a s - i r r a d i a t e d and r e - i r r a d i a t e d A — — * — X • 0 _®! @_ — e — © " i (b) as -c leaved and pulse-annealed (325 C . ) .20 .1© 2^ hrs 3t 4 44 •30 .20 .10 (c) P o l i s h e d and pulse annealed (325 C . ) _0_ -0- -©-© B 29 , ( re-ir . ) B 25 B.' .24 B 23 ( p o l . ) 0 5 Distance (mm) 20 25 F i g . 7 M-band o p t i c a l d e n s i t y v . s . dis tance along specimen - 20 -specimen. The o v e r a l l decrease of o p t i c a l d e n s i t y with annealing time i s a l s o reduced i n the p o l i s h e d c r y s t a l s . Such gradients r e l a t i v e to the cleavage d i r e c t i o n were observed f o r a l l specimens t e s t e d . (b) Microscopy F i g . 8 and 9 are photographs showing the d i s l o c a t i o n etch p i t d i s t r i b u t i o n on a cleavage face at the " c h i s e l " and " n o n - c h i s e l " ends of a t y p i c a l specimen. The cleavage d i r e c t i o n was f r o m . l e f t to r i g h t i n both cases. Note the high etch p i t densi ty a l o n g , a ( n o ) plane at the c h i s e l end. This was introduced i n the c l e a v i n g o p e r a t i o n . Cleavage steps are a l s o p l a i n l y v i s i b l e emanating from the s truck corner . The n o n - c h i s e l end d i s p l a y s s e v e r a l i n t e r e s t i n g f e a t u r e s . F i r s t , the etch p i t d e n s i t y c lose to the end of the specimen i s very high and second, tows of e tch p i t s are observed l y i n g approximately p a r a l l e l to the end of the specimen. The l a t t e r a l so appear to become p r o g r e s s i v e l y c l o s e r together along the cleavage d i r e c t i o n . An abundance of micro-cracks can be seen along the end of the c r y s t a l . F i g . 10 i s a s i m i l a r photograph of the cleavage face of the n o n - c h i s e l end of another specimen. F i g . 11 i s a diagramatic represen-t a t i o n of F i g . 10. Again the high d i s l o c a t i o n densi ty at the very end of the,specimen i s present . However, the rows of etch p i t s o b s e r v e d . i n F i g . 9 are absent. The presence of "grooves" was a l s o observed through-out the length of the p a r t i a l l y annealed specimen. These.•were not present i n the a s - i r r a d i a t e d specimens. ^Cleavage steps and a sub-boundary are a l s o v i s i b l e i n the above photograph. I t was a l s o observed that the etch p i t d e n s i t y was much l a r g e r (-10x) on the n o n - c h i s e l end than en the c h i s e l end. F i g . 9 N o n - c h i s e l end* of cleaved and pulse annealed specimen (etch p i t rows) lUo x * Cleavage crack : L e f t to Right F i g . 10 N o n - c h i s e l end of cleaved and pulse-annealed specimen (no e tch p i t rows) kOO x F i g . 11 Diagramatic representa t ion of F i g . 10 - 23 -The p r o p o r t i o n of the high densi ty regions on the cleavage faces v a r i e d between faces and specimens. However, a l l specimens e x h i b i t e d such a region across the base of the n o n - c h i s e l end. C. T e n s i l e Deformation « (a) Flow s t ress (tS , £ , T dependence); Microhardness The parameters determined i n the t e n s i l e experiments are d e f i n e d i n F i g . 12 f o r the various types of curves : c .T . s . V "3 / 1 j C.T.S. / lA^y^C-- C.T.S. / 1 / 1 i ! I I / r \ I I /! ! . S t r a i n £ s a t F i g . 12 T y p i c a l s t r e s s - s t r a i n curves The y i e l d s t ress ( Y . S . ) i s def ined as the f i r s t d e v i a t i o n from l i n e a r i t y of the e l a s t i c s l o p e . The c r i t i c a l t e n s i l e s t ress ( C . T . S . ) or f low s t ress represents the s t ress necessary to produce large scale d i s -- 2k -l o c a t i o n motion. £ s a t represents the s t r a i n at the end of stage I i n the deformation curve. B i r e f r i n g e n c e e f f e c t s were detected near the gr ips of a l l s p e c i -mens observed p r i o r to deformation. Due to ambiguity i n the choice of gauge l e n g t h , the .absolute values of s t r a i n may be anomalously h i g h . The major i ty of the t e n s i l e experiments were performed on r e c -tangular specimens (.05 x .1 x 1. inches) as opposed to square specimens (.1 x . 1 x 1 i n c h e s ) . The l a t t e r were u s e d . i n s e v e r a l instances d u r i n g some of the i n i t i a l experiments. I t was found that specimens s l i p p e d out of the epon cement i f t e n s i l e l o a d s ^ 20 l b s . were surpassed. P l a s t i c deformation of the i r -r a d i a t e d c r y s t a l s at loads l e s s than t h i s value necess i ta ted the smaller c r o s s - s e c t i o n a l area of the rec tangular specimens. S t r e s s - s t r a i n curves f o r both annealed and i r r a d i a t e d rec tang-u l a r c r y s t a l s are shown i n F i g s . 13, lk and.15- The flow s t ress has been increased approximately f i v e times by i r r a d i a t i o n whereas the s t r a i n to f r a c t u r e has been considerably decreased. The s a t u r a t i o n s t r a i n , tS s a t> of the i r r a d i a t e d c r y s t a l s i s 3 - k times greater than that of the annealed c r y s t a l s . The annealed c r y s t a l s d i s p l a y an i n c r e a s e . i n f low s t r e s s , i n -crease i n work-hardening rate §Q ), and decrease i n s t r a i n to f r a c t u r e with decreasing temperature. A rather i l l - d e f i n e d t r a n s i t i o n i n slope occurred d u r i n g stage II hardening, c h a r a c t e r i z e d by a change ln-0 from an i n i t i a l constant value to a gradual ly i n c r e a s i n g v a l u e . The t r a n s i t i o n was a l s o more apparent at higher temperatures where d u c t i l i t y was i n c r e a s e d . OJ w w <u u -p CO [fl T e n s i l e S t r a i n F i g . 15 S t r e s s - s t r a i n curves f o r i r r a d i a t e d L i F at 2 1 d d e g . C . ( a i r ) ro —] - 28 -500 1+00 h 300 200 100 X A i r © Pet . Ether A O i l A (.002"/min) 1 .200 250 T 300 350 Temperature ° K F i g . l6 Temperature dependence of" the y i e l d s t ress 8 0 0 h 600h koo\ 200 11 Gilman and Johnston (.005 " / m i n ) y - head speed, " /min  005 .002 •'. • O Pet . Ether A O i l X A i r (.002, .005 "/min) 50 100 200 300 Temperature K F i g . 1? Temperature dependence of the c r i t i c a l t e n s i l e s t ress - 29 -I n i t i a l and f i n a l values of Q f o r stage II hardening are recorded i n the above f i g u r e s . i Several anomalous b l i p s were observed i n many of the t e h s i l e curves. The temperature dependence of the y i e l d and c r i t i c a l t e n s i l e stress i s shown i n F i g s . l 6 and 17 f o r strain-rates of ~ .6 x 10"^/sec. and 2. x 10~^/sec. re s p e c t i v e l y . Gilman and Johnston' 1's^ r e s u l t s f o r c r y s t a l s of s i m i l a r p u r i t y are also shown f o r comparison. Some of the above data points represent the i n i t i a l properties of specimens subjected to s t r a i n - r a t e or temperature-change t e s t s . < The macroscopic deformation behaviour of rectangular specimens was characterized by e i t h e r non-uniform or uniform s l i p ( F i g . 18). No r e l a t i o n was found between the active s l i p systems and the c r y s t a l shape. However, specimens e x h i b i t i n g good d u c t i l i t y (^ 10$>) usually deformed uniformily on e>ither the wide or t h i n s l i p systems. I t was observed that innany one section of the gauge length, the majority of s l i p took place on'only one set of orthogonal s l i p planes. wide t h i n Non-uniform Uniform -on Non-uniform " t h i n " system F i g . 18 Macroscopic deformation behaviour of t e n s i l e specimens - 30 -F i g . 19 i s a pl o t of the K.H.N, v.s. indenter load f o r i r -radiated and . annealed specimens. I t i s observed that the hardness appears to increase with decreasing indenter load i n a s i m i l a r fashion f o r both types of specimen. 25 50 75 100 Indenter Load (gms) F i g . 19 Microhardness v.s. Indenter Load (b) Strain-rate Change Tests A section of a typical, instantaneous s t r a i n - r a t e change curve i s shown i n F i g . 20. Time F i g . 20 A s t r a i n - r a t e change t e s t - 31 -Tests were conducted such that approximately equal amounts of s t r a i n (^-\_ O.Wfo) were induced at both high and low s t r a i n - r a t e s . Pseudo y i e l d points were observed under c e r t a i n experimental condi t ions when the s t r a i n -rate was greater than the s e n s i t i v i t y of the recorder pen r e l a t i v e to the chart speed. Values of ^ were obtained by e x t r a p o l a t i n g back through the y i e l d point to the e f f e c t i v e e l a s t i c s lope . The change i n f low s t r e s s , A ~ _ , was always measured f o r an increment i n s t r a i n - r a t e to avoid p o s s i b l e recovery or r e l a x a t i o n e f f e c t s which might e x i s t d u r i n g a decrement i n s t r a i n - r a t e . A l s o , the f low s t ress was not w e l l d e f i n e d f o l l o w i n g a decrease i n s t r a i n - r a t e . P l o t s of A^T_,.v.s. ~ii, are shown i n Appendix I I I f o r the var ious temperatures and s t r a i n - r a t e change f a c t o r s . The dependence of _ \ N | o . upon the b a s i c s t r a i n - r a t e f o r a con-stant ^"2/^-.- ' = 5 i s shown i n F i g . 2 1 . I t can been seen that A N a. increases with the average s t r a i n - r a t e . The r a t i o of the f low s t resses , V"2/^ f±> corresponding to tZ. 2 / €j_ = 1 0 , v . s . t e n s i l e s t r a i n i s shown i n F i g . 2 2 . The r e s u l t i n g curve i s very s i m i l a r to that which may be obtained from the compressive s t r a i n - r a t e change t e s t s of Johnston and S t e i n . 2 7 Only the general shapes of the curves can be compared as the b a s i c s t r a i n r a t e , w a s n o ^ reported by the above workers. I t should a l s o be noted that a l a r g e r specimen gauge length would t r a n s l a t e the present r e s u l t s towards those of John-ston and S t e i n . - 32 -- 33 -(c) Temperature-Change Tests The change i n f l o w s t r e s s was determined only f o r a decrease i n temperature so as t o avoid Annealing e f f e c t s . The deformation curves were analogous t o those of F i g . 20 f o r the s t r a i n - r a t e change experiments. The'temperature s e n s i t i v i t y of the f l o w s t r e s s as a f u n c t i o n of s t r a i n i s shown i n F i g . 23- jAC\.) increases w i t h hoth i n c r e a s i n g CAT / s t r a i n and decreasing temperature. Due t o the low s t r a i n s i n v o l v e d , the r e s u l t s represent only stage HA s t r a i n - h a r d e n i n g . (d) Rate Theory The a c t i v a t i o n volume, v*, was determined from equation (7) and i s p l o t t e d as a f u n c t i o n of s t r e s s i n F i g . 2k. v* tends to increase r a p i d l y d u r i ng i n i t i a l s t r a i n i n g , remains r e l a t i v e l y constant f o r a period of time, and then decreases l i n p a r l y w i t h s t r e s s to f r a c t u r e . These c h a r a c t e r i s t i c s are inverse t o those of the curves.(see Appendix I I I ) The t r a n s i t i o n i n v* (constant t o decreasing) g e n e r a l l y occurred almost simultaneously w i t h a sharp t r a n s i t i o n I n the work-hardening slope, Q , from a constant to an i n c r e a s i n g value. These l a t t e r t r a n s i t i o n p o i nts are designated toy v e r t i c a l arrows on the v* v.s. T ^ _ a | curves ( F i g . 2k) and a l s o on the A^"~ v.s. 'ST p l o t s i n Appendix I I I . However, i n many cases, Q only increased g r a d u a l l y w i t h ^J~ a )and d i d not e x h i b i t an obvious t r a n s i t i o n p o i n t . This s i t u a t i o n e x i s t e d mainly i n the high s t r a i n - r a t e experiments ( £"2/£~1 = 100 ) • O B 121 X B Ilk & B 112 O B 113 « B 122 • B 12k Tensi le s t r a i n - € . - $ . . 23 Temperature s e n s i t i v i t y of Z ^ v . s . s t r a i n f o r var ious temperatures. - 35 -F i g . 2k A c t i v a t i o n volume v . s . f low s t r e s s . f o r annealed L i F - 36 -The room temperature v* values f o r an i r r a d i a t e d c r y s t a l are shown i n F i g . 25 along with the corresponding values f o r annealed c r y s t a l s . I t can be seen that the former l i e very close to the extrapolated values of the l a t t e r . F i g . 26 i s a plo t of ( -ttTt/ A T ) V . S . T at G = .02 obtained from the temperature change experiments (Fig. 23)- Values of A " 2 * /AT corresponding to the.temperatures of the A G experiments were then deter-mined and plotted v.s. the s t r a i n - r a t e s e n s i t i v i t y of the flow stress for•-'< ^1 = 5 as shown i n F i g . 2$. From equation (l), i t can be seen that the slope of such a p l o t i s equal to In /\T ]. A value of the true a c t i v a t i o n energy, A Q = H* at * = 0, was then determined u t i l i z i n g a value of Tc obtained from F i g . 28 (see Appendix 1(b)). » • This procedure was also c a r r i e d out f o r ^ r ' p Y ^ i = 100 with the r e s u l t s shown i n F i g . 29 and 30-The r e s u l t s are summarized i n Table I I I . TABLE.Ill Summary of True A c t i v a t i o n Energies • / A £ 2 / 6 1 T c ln(±L ) A Q = H * ( I ? * = G) : (°K) — A J L Z (ev) 5 350 2k .72 100 380 19 .62 The s t r a i n dependence o f A Q , H, and In f^L- ) was. determined \ <r / according to equations (7)> (8) and (9)> The r e s u l t s are shown i n Appendix K c ) . B81+ (annealed .002"- .01"/min. T.= 22 C. i r r a d i a t e d ) XXXX 500 1000 ^ - gm/i 1500 mra^  2000 F i g . 25 A c t i v a t i o n volume v.s. a p p l i e d s t r e s s f o r annealed and i r r a d i a t e d L i F 1-5 .02 bO OJ 1.0 EH 200 250 o Temperature K 300 F i g . 26 Temperature s e n s i t i v i t y of the f l o w s t r e s s v.s. temperature. (e) Stress R e l a x a t i o n The parameters of i n t e r e s t " a r e shown i n the sequence of events i n F i g . 31- The m a j o r i t y of the t e s t s were perfcammed on square specimens. Due t o the low f r a c t u r e s t r a i n s , only stage ItAhardening was observed. S t r a i n F i g . 31 S t r e s s - r e l a x a t i o n curve Upon stopping the cross-head motion, the load was observed to r e l a x to a near constant value a f t e r 30 seconds. The m a j o r i t y (f^&Qffo) f . of the r e l a x a t i o n occurred w i t h i n the i n i t i a l 10 seconds. F i g s . 32 and 33 are p l o t s of the r e l a x e d f l o w s t r e s s , V r e ^ , v.s. "^~~a, and € , r e s p e c t i v e l y , f o r various s t r a i n - r a t e s . I t can been seen-that a f t e r a few percent s t r a i n , ^ ~ r e l becomes a l i n e a r f u n c t i o n of N , r e l a t i v e l y independents -of the . " ^ e i als° v a r i e s l i n e a r l y w i t h s t r a i n , w i t h no i n i t i a l d e v i a t i o n s , but ••is dependent upon the s t r a i n - r a t e of the t e s t . 200 kOO 600 800 1OQ0 Flow St r e s s - gm/mm2 F i g . 32 Relaxed f l o w s t r e s s v.s. f l o w s t r e s s F i g . 33 Relaxed f l o w s t r e s s v.s. s t r a i n Symbols: same as F i g . 32 - U2 -80 ho. OJ < -ho O -®- •57 min. • ^ i —t— * X I "X 57~ A A •2"/min. . l M / m i n . .05"/min. 2 W Too feo " BSO App l i e d S t r e s s - ^JJ- gm/rnm^  CUUo-F i g . 3^ Change i n f l o w s t r e s s f o l l o w i n g r e l a x a t i o n . 1200 " 800 CM 1+00 CQ CO .<U U •P CO Ambient Temperature ( c a l c u l a t e d from r a t e theory f o r £ 2 / 6 1 =5)* X - V r e l 200 ' kOO 600 800~~ *» A p p l i e d s t r e s s -^ J^ -,.tgm/mm2 1000 F i g . 35 I n t e r n a l s t r e s s and r e l a x e d f l o w s t r e s s - v . s . a p p l i e d s t r e s s - ^3 The slopes of these curves are observed to increase w i t h i n c r e a s i n g s t r a i n -r a t e . The change i n the f l o w s t r e s s f o l l o w i n g r e l a x a t i o n , A~~ , w i t h i s shown i n F i g . 3^- Curves of i d e n t i c a l form were observed when T^__ was replaced by G- . Values of the i n t e r n a l s t r e s s , at room temperature d e t e r -mined from the AG. and A T experiments for~-Tp/^-j. = 5 are super-imposed upon a p l o t of M r e i v.s. ^T^.in F i g . 35. V~ was determined from equation (5) f o r values of H (see Appendix 1(c)) and f o r H* = .rJ2ev (see F i g . 28). The values ofV^ "ei correspond t o the mean values of the s c a t t e r band of F i g . 32- I t can be seen t h a t good agreement e x i s t s between ^ F^  and Vrel-( f ) F r a c t u r e Stress b i r e f r i n g e n c e techniques were u t i l i z e d to observe the f r a c t u r e c h a r a c t e r i s t i c s of deformed L i F specimens. In a l a r g e number of cases, specimens f r a c t u r e d i n the g r i p s , making p o s s i b l e observation of only one p o r t i o n of the deformed c r y s t a l . Fig;.. .'3_ d i s p l a y s examples of specimens which have broken i n the center of the gauge le n g t h . Note t h a t f r a c t u r e has propagated along both j l O o | and j l i o j planes and a l s o the presence of major s l i p bands c u t t i n g through the f r a c t u r e surface. Both of these c h a r a c t e r i s t i c s were observed i n the m a j o r i t y of cases i n v e s t i g a t e d . F i g . 36 Stress b i r e f r i n g e n c e of f r a c t u r e d t e n s i l e specimens. IV DISCUSSION - 1+5 -A. Cleaved Specimens The v a r i a t i o n s observed i n specimens a f t e r c l e a v i n g are, pro-bab l y , a major source of the d i s c r e p a n c i e s i n the deformation r e s u l t s ( v a r i a b l e work hardening r a t e , e l o n g a t i o n , e t c . ) . I t i s v i r t u a l l y impossible t o c o n t r o l , such f a c t o r s as the cleavage-crack v e l o c i t y (depends on sharpness of c h i s e l , sharpness and weight of blow, e t c . ) and the c r y s t a l alignment. Chemical p o l i s h i n g was c a r r i e d out to reduce cleavage e f f e c t s , i The formation of cleavage steps i s w e l l understood and i s , i n 28 f a c t , r e l a t e d , t o the i n t e r n a l d i s l o c a t i o n s t r u c t u r e of the c r y s t a l . Small steps formed by the passage of a cleavage crack through a screw d i s l o c a -t i o n may u n i t e t o form macrosteps i f the screw d i s l o c a t i o n s are of the same s i g n . Other sources of cleavage steps are r e l a t e d t o the c r y s t a l alignment d u r i n g cleavage. B. Color Centers Models of the v a r i o u s c o l o r centers of i n t e r e s t i n the present work are described a f t e r Dekker 2^ i n Table IV. The wavelengths and the r e l a t i v e i n t e n s i t i e s of the a b s o r p t i o n maxima observed.in the present work agree f a v o r a b l y w i t h those observed by Delbecq and.Pringsheim^O f o r the F,M, and c o l o r center bands. The mechanisms i n v o l v e d i n the formation of c o l o r centers have been e x t e n s i v e l y d escribed and w i l l not be discussed here. U6 -TABLE IV Color centers i n L i F C o l o r center F M Ro Model e' plus - ve i o n vac. e' plus - ve i o n vac. plus vac. p a i r 2e' plus 2 - ve i o n vacs. 2e' plus - ve i o n vac. ^ (mp.) ^ (nyu) Delbecq & Pringsheim Present Work 250 250 1+50 UU5 , 380 375 62b Not s t u d i e d The c o l o r centers and hence the r e s u l t i n g a b s o r p t i o n bands i n L i F have s e v e r a l unique p r o p e r t i e s . The F band occurs at a r e l a t i v e l y -short wavelength and i s very s t a b l e at room temperature. The M band.is formed by the room temperature decay of the F' band. I n f a c t , t h i s was probably the source^of the observed c o l o r t r a n s i t i o n from greenish-yellow (d u r i n g i r r a d i a t i o n ) t o y e l l o w s h o r t l y a f t e r i r r a d i a t i o n . The M band ( i . e . y e l l o w c o l o r ) i s a l s o known t o be very s t a b l e at room temperature, even when exposed to b l u e l i g h t (or d a y l i g h t ) . The s t a b i l i t y of the c o l o r centers i n L i F , which i s not observed i n other a l k a l i h a l i d e s , meant that c l e a v i n g could be c a r r i e d out over a p e r i o d of time without l o s s of hardness. This s t a b i l i t y would a l s o make these c r y s t a l s very amenable to c o l o r center s t u d i e s . C. Pulse Annealing of I r r a d i a t e d C r y s t a l s There are s e v e r a l p o s s i b l e sources of non-uniform annealing of c o l o r centers which may be r e l a t e d to the f o l l o w i n g : ( i ) d i s t r i b u t i o n of p o i n t d e f e c t s ( i m p u r i t i e s , vacancies) ( i i ) i r r a d i a t i o n treatment ( i i i ) d i s l o c a t i o n d e n s i t y - ^7 -The present r e s u l t s cannot be explained by the f i r s t two possi-b i l i t i e s . Since both the as-received and the r e - i r r a d i a t e d specimens were f u l l y annealed, a homogeneous d i s t r i b u t i o n of point defects would e x i s t . I t i s also u n l i k e l y that the non-uniformity i s r e l a t a b l e to the i r r a d i a t i o n treatment due to the symmetrical nature of the C o ^ source. The most conclusive evidence i n r e j e c t i n g these two fa c t o r s i s the obser-vation that the annealing gradient r e l a t i v e to the cleavage d i r e c t i o n i s the same i n specimens cleaved i n opposite d i r e c t i o n s from the same bulk c r y s t a l . It should be rioted that annealing temperatures o f ~ 8 0 0 ° C . (Tm.p. -- QkO C.) are required to a l t e r the surface d i s l o c a t i o n structure of cleaved LiF. 3 1 The p o s s i b i l i t y of a temperature d i f f e r e n t i a l along the speci-men length was ruled out by the r e l a t i v e o r i e n t a t i o n of specimens i n the annealing furnace -Metallographic observations tend to point to the presence of a non-uniform d i s l o c a t i o n density as the major f a c t o r . Also, the evidence suggests that the cleavage operation i s the fundamental source of the non-uniformity. Nonuniform annealing probably existed on a much smaller, scale at the c h i s e l end of the specimens. This was observable i n one case where a specimen had been .very severely damaged at the c h i s e l end. However, i n t h i s case, the non-uniformity was s t i l l greater at the non-chisel end. The high d i s l o c a t i o n density on the base of the nonrchisel end i s probably due to contact of the c r y s t a l block with the base (I . / 3 2 " f e l t ) - k8 -of the cleaving apparatus. This i s not unreasonable as recently i t has been suggested that surface d i s l o c a t i o n loops can be introduced i n t o L i F 32 even by impinging dust p a r t i c l e s . The non-uniform density may be due to the non-elastic motion, of the cleavage crack. Gilman et a l J J has shown that a c e r t a i n incubation time, which i s characterized by a c r i t i c a l crack v e l o c i t y , v ( ~ 1 0^cm/sec), i s required f o r d i s l o c a t i o n nucleation by moving cleavage cracks. In t h i s region, the crack v e l o c i t y was observed to o s c i l l a t e ' about v , r e s u l t i n g i n rows of etch p i t s along the crack f r o n t . Profuse dis.locva,-t i o n nt/c'leation took, place when the v e l o c i t y remained, below v and hence decreased to zero. The rows of etch p i t s observed at the non-chisel end of speci-mens i n the present work strongly suggests the above mechanism. However, as such rows were not observed i n a l l cases, t h i s mechanism i s probably not the only one operating. 31) S e i t z has observed an increase i n the rate of color canter depletion at deformation bands. Although the present r e s u l t s are not re l a t a b l e to deformation bands, they do emphasize the importance of a high d i s l o c a t i o n density. The rate of formation of color centers- has been observed to be enhanced.in quenched i o n i c c r y s t a l s . ^ P r a t t ' ^ concluded that t h i s e f f e c t may be due to the quenched-in vacancies or to the d i s l o c a t i o n s created by quenching s t r a i n s . The apparent uniformity of the color cen- . te r concentration i n the r e - i r r a d i a t e d specimens i n f e r s that the d i s l o -c ation arrangement' i s r e l a t i v e l y unimportant i n the formation of color - k9 -centers. Hence the vacancies were probably the major f a c t o r . This i s true, provided, we assume that any such gradient i n the r e - i r r a d i a t e d specimens was measurable. I t i s well known that vacancies must be produced i n large num-bers during ^ - i r r a d i a t i o n . This i s evident from several f a c t s : (1) observations of decreases in density of a l k a l i h a l i d e s during i r r a d i a t i o n . •J 1 ( 2 ) comparison o f calculated color center concentrations with e q u i l i -brium vacancy concentrations. Using.Smakula's formula, we can determine the order o f raagni-0 0 tude of the color center concentration i n the present c r y s t a l s . Nadeau has used t h i s fomqjfla i n the following form f o r X - i r r a d i a t e d L i F , f n F = .87 x IO 1? H oCrnax /cm.3 where f = o s c i l l a t o r strength (~»-1.0) np = number o f F centers / cm^ H = h a l f width of absorption, maximum (ev) °Snax = absorption c o e f f i c i e n t at peak (cm"l) The present measurements gave n-p 6 x.lO^/cm^. The M center peak having an a r e a ^ l / l O that o f the F center peak would r e s u l t i n rj^ ~ 6 x 10^ / cm3. As both o f these color centers are b a s i c a l l y composed o f negative i on vacancies, the i r r a d i a t e d c r y s t a l s must contain"" 10-^ /•cm3 o f such vacancies. The existence o f dival e n t impurities requires the formation o f p o s i t i v e . i o n vacancies t o maintain the charge balance. Thermal, equilibrium also contributes an i n t r i n s i c vacancy concentration ( p o s i t i v e and negative) o f ~ 10^ /cm^ a t room temperature38. Hence, for a - 5 0 . -d i v a l e n t impuri ty concentrat ion of -—• lOppm ( ~ 1 0 x 8 / c m 3 ) , the t o t a l vacancy concentrat ion at room temperature i s n + = 1 0 6 - + 1 0 1 8 £ 1 0 l 8/cm 3 6 ^ . n_ = 10 / crcP Thus the negative i on vacancy concentra t ion must he increased by a f a c t o r of 1 0 l 8 / l 0 6 = 1 0 1 2 by i r r a d i a t i o n . vacancies of both. sign, must, of course, be produced to preserve charge n e u t r a l i t y . The exact mechanism ( d r i v i n g force) of vacancy production i n a l k a l i h a l i d e s d u r i n g i r r a d i a t i o n i s not known. However, d i s l o c a t i o n s are b e l i e v e d t o p l a y a major r o l e . Seitz"1-' -postulates that i t i s reasonable to expect jogs on d i s l o c a t i o n s to act as ei t h e r sources or sinks f o r vacancies . Such jogs i n the present c r y s t a l s must r e s u l t from thermo-dynamic e q u i l i b r i u m as the c r y s t a l s vere tundeforraed. The number of such jogs per un i t length of d i s l o c a t i o n can be calcula t e d , a f t e r Van Buren , as follows: n = n Q exp (-Uj/kT) where n 0 - number of atomic s i t e s per u n i t length of d i s l o c a t i o n l i n e (~10^/cm) and Uj = jog format ion 'energy . Taking Uj - jib3/l.o - ..5ev (see K e f . 7 0 ), we obta in n == 10~r~ jogs /cm dislocation, at room temperature. Estimated values of = 10^cm/cm3 and 1 0 8 .cm/cm^ i n the uniform and non-uniform regions r e s p e c t i v e l y of the present c r y s t a l s then correspond to jog d e n s i t i e s of lO-^/cm 3 and 10 /c'm.3. As the specimens used i n the present experiments contained a 'volume 1 0 ~ 3 c n r 5 , the number of jogs i n the uniform r e g i o n was - v 8 0 . Also, the number of vacancies created per jog d u r i n g , i r r a d i a t i o n was 10 "-'('IO /lO?) i n the uniform and 1 0 " • i n the non-uniform r e g i o n s . - 51 -The annealing of color centers requires d i s s o l u t i o n of l a t t i c e vacancies. Hence the a c t i v a t i o n energy must be r e l a t e d to the d i f f u s i o n of such vacancies to sinks ( i . e . jogs). I t i s reasonable to expect that the d i s s o l u t i o n rate w i l l be c o n t r o l l e d by the distance between color centers and the nearest jogs. The present r e s u l t s can thus be explained i n terms of the high jog density of the non-chisel end of the .specimens. Also the slow d r i f t of vacancies toward t h i s end of the c r y s t a l would r e s u l t i n the observed annealing gradient along the specimen. An i n t e r e s t i n g experiment to.observe whether vacancies are created.at jogs may be,possible u t i l i z i n g e l e c t r o n microscopy. The el e c -tron beam would act as the i o n i z i n g r a d i a t i o n and vacancies should be observed t o " b o i l o f f " from jogs. The formation of vacancy c l u s t e r s i n KC1 has been observed,by H i b i and Yada^ x. Although highly speculative, perhaps the presence of the d i s -l o c a t i o n "grooves" observed i n the annealed specimens but not i n the a s - i r r a d i a t e d specimens i s r e l a t e d to the absorption of vacancies by jogs. Eventually, t h i s would r e s u l t i n the j o g . i n t e r s e c t i n g the surface of the c r y s t a l and perhaps leaving a defect which is , r e v e a l e d by etching. The study of non-uniform annealing e f f e c t s i n i r r a d i a t e d L i F c r y s t a l s was terminated at t h i s point as i t was not the o r i g i n a l intent of the present program. The work i s by no means considered to be com-plete . - 52 -D. T e n s i l e P r o p e r t i e s (a) S l i p Systems L i F has NaCl s t r u c t u r e c o n s i s t i n g of two i n t e r p e n e t r a t i n g f . c . c . l a t t i c e , , one of each i o n i c s p e c i e , . Tne s l i p s y s t e m {l!0~} and |l00^ ^110^ the l a t t e r b e i n g a c t i v e only above 400°C ^  and hence unimportant i n the present work. Each ^110^ Burgers vector of a d i s l o -c a t i o n i n L i F has only one ^ ^ - ^ j plane a s s o c i a t e d w i t h i t , u n l i k e the s i t u a t i o n .in . f . c . c . metals. Hence c r o s s - g l i d e of screw d i s l o c a t i o n s can only take place along some other plane, g e n e r a l l y ^10oj . When a specimen i s s t r e s s e d under t e n s i o n along a <^ 001^ > d i r e c -t i o n , f o u r of the s i x p o s s i b l e s l i p systems experience an equal shear s t r e s s . These f o u r systems are shown i n F i g . 37 separated.into two sets of orthogonal £ l l o | planes. D i s l o c a t i o n motion on e i t h e r , set of orthogonal planes gives r i s e to orthogonal i n t e r s e c t i o n s . S i m i l a r motion on both sets of planes produces oblique i n t e r s e c t i o n s as shown i n F i g . 3 8 ' I t should be noted,from these f i g u r e s t h a t the edge component of a d i s l o c a t i o n i n t e r s e c t s a ^lOO^j- face along a <^ 11C))> d i r e c t i o n compared t o a <^100^ f o r the screw component. (b) Flow s t r e s s The present r e s u l t s i n d i c a t e t h a t the f l o w s t r e s s of L i F i s increased f i v e times by: .Sub j e c t i n g i t t o a t o t a l Y-ray dose of 1 . 2 x left rads. Gilman and Johnston^ have observed that the hardening i s not a r e s u l t of a d i s l o c a t i o n - d e f e c t p i n n i n g mechanism but i s s o l e l y due to the dynamic i n t e r a c t i o n of moving d i s l o c a t i o n s and r a d i a t i o n d e f e c t s . - 53 -- 54 -o p Nadeau" has shown that the F center i s c l o s e l y r e l a t e d to the defect involved i n i r r a d i a t i o n hardening. He proposed that i n t e r s t i t i a l F ions are produced by Varley's^ 3 mechanism whereby F" ions stripped of several< of t h e i r electrons become e l e c t r o s t a t i c a l l y unstable with respect to t h e i r neighbors and are forced i n t o i n t e r s t i t i a l s i t e s . The f e a s i b i l i t y of such a mechanism occuring i n a l k a l i halides has been s e r i o u s l y ques-p k tioned by Seitz and Koehler . They postulated that the anion should be completely capable of capturing free electrons and moving back in t o the l a t t i c e vacancy. The f a c t that F centers are stable at room temperature under a l l wavelengths of l i g h t tends to disprove Nadeau's theory i f the above reasoning of Seitz and Koehler i s correct. The l i m i t e d d u c t i l i t y of the i r r a d i a t e d specimens may be due to the f a c t that the very high stresses necessary to move d i s l o c a t i o n s i n such c r y s t a l s are s u f f i c i e n t to cause neai* in s t a n t propagation of microcracks. Such cracks may e x i s t i n the t e n s i l e specimens (perhaps 28 at the c h i s e l end) or may~ r e s u l t from the deformation i t s e l f . The temperature dependence of the flow stress of L i F i s very 43 close to that of f . c . c . metals. The agreement between the present observations and those of Gilman and Johnston-'-''' f o r "pure". L i F ind i c a t e that pre-deformation heat treatment was not important. (c) S t r e s s - s t r a i n curves A generalized deformation curve f o r L i F specimens i s shown i n Fi g - 39- Three stages are apparent. - 55 -w w <U u +> CQ I I A | IIB ;at S t r a i n F i g . 39- General s t r e s s - s t r a i n curve. Stage I represents a r e g i o n i n which g l i d e "band widening i s t a k i n g place and where the s t r a i n hardening i s "-^  zero. A t r a n s t i o n from stage I t o IIA occurs when the surface of the c r y s t a l becomes completely covered w i t h deformation bands. The t r a n s i t i o n i s c h a r a c t e r i z e d by a "saturation"- s t r a i n , £ , the p r e c i s e value of sat which i s dependent upon s e v e r a l f a c t o r s . An e x t r i n s i c factor:'.is the per-f e c t i o n of the specimen surface i . e . the number of surface d i s l o c a t i o n sources. A l a r g e number of such sources would decrease G. , as the ° sat r e s u l t i n g deformation bands would only have to move a short d i s t a n c e before impinging upon one another. The most important i n t r i n s i c f a c t o r i s the hardness of the c r y s t a l . The present r e s u l t s i n d i c a t e that ^" s a^ at room temperature was f o r the i r r a d i a t e d specimens as compared to-f o r the annealed specimens. The l a t t e r value agrees w e l l w i t h t h a t observed by other workers f o r L i F . A l s o , the hardness dependence i s i n agree-9 ment w i t h the r e s u l t s of Gilman and Johnston who observed t h a t C. sat f o r L i F i s p r o p o r t i o n a l t o the hardness ( y i e l d s t r e s s ) . They explained - 56 -t h i s dependence through further experimental observations that the s t r a i n per glide band increases with hardness, i . e . the i n d i v i d u a l glide bands become more densely populated with d i s l o c a t i o n s . Hence, fewer glide bands can accomodate a f i x e d amount of s t r a i n . L i F apparently undergoes a t r a n s i t i o n during stage II hardening which i s characterized by the onset of a gradually increasing work hard-ening slope. Such a t r a n s i t i o n i s also apparent i n several of the p u b l i -cations on the deformation of L i F crystals.^5^46 However, i n most instances i t has e i t h e r been overlooked or neglected and the work hardening rate has been described.as l i n e a r to f r a c t u r e . Limited d u c t i l i t y has masked t h i s e f f e c t i n many in v e s t i g a t i o n s . Impurities may have also been a major f a c t o r as i t i s known f o r f . c . c . metals that stage I hardening (stage IIA i n L i F ) i s extended by impurity additions. Gilman and Johnston"^ ascribe the l i n e a r region to the inter/-, action of l a t t i c e defects produced by moving screw d i s l o c a t i o n s with sub-sequent dislocations'' on c l o s e l y associated glide planes. Westwood^, who f i r s t brought a t t e n t i o n to the t r a n s i t i o n point, suggests that e i t h e r increasing numbers of l a t t i c e defects are produced with s t r a i n or that a d d i t i o n a l mechanisms, such as d i s l o c a t i o n - d i s l o c a t i o n interactions may become more prevalent at higher s t r a i n s . Very recently, Alden^? has observed a s i m i l a r t r a n s i t i o n i n NaCl and KC1 but only the i n i t i a t i o n of sfcage IIB i n L i F . However, an important feature of t h i s l a t t e r observation i s that his maximum compressive s t r a i n was only -^3$>- Hence, the t r a n s i t i o n point was probably masked by the l i m i t e d d u c t i l i t y . As w i l l be discussed i n d e r a i l , the t r a n s i t i o n i s - 57 -b e l i e v e d to be due t o the onset of s u b s t a n t i a l d i s l o c a t i o n movement on oblique s l i p ; systems. This has a l s o been proposed by AlderA?. (d) E f f e c t of Media Westwood suggested t h a t the petroleum ether temperature environment used i n the present work be f i l t e r e d through both a c t i v a t e d s i l i c a g e l and alumina t o remove any surface a c t i v e i m p u r i t i e s . He has observed t h a t a c o n c e n t r a t i o n o f 1 0 " ^ M of such agents w i l l a f f e c t the y i e l d s t r e s s of L i F . ^ However, two f a c t o r s of h i s work are important, here j ( i ) the maximum increase i n y i e l d s t r e s s due to a h i g h l y surface o a c t i v e reagent ( s t e a r i c a c i d ) was - ^ 2 0 - ^ 0 gm/mm'. ( i i ) the e f f e c t was only observed i n as-cleaved specimens which would contain a r e l a t i v e l y l a r g e number of surface d i s l o c a t i o n sources. In the present work, no recognizable e f f e c t was found over the temperature range i n v e s t i g a t e d probably because a l l specimens t e s t e d were chemically p o l i s h e d . A l s o , the s c a t t e r band found f o r the " a i r tests' alone was ~ 50 gms/mm2 and would thus tend to mask any surface adsorption phenomena. The o i l r e s u l t s look d o u b t f u l i n so f a r as the f l o w s t r e s s e s f a l l s l i g h t l y above the s c a t t e r band f o r the a i r and petroleum ether • r e s u l t s . However, only a few t e s t s were performed w i t h t h i s medium and hence the evidence i s f a r from c o n c l u s i v e . (e) Shape E f f e c t P r e l i m i n a r y experiments u t i l i z i n g square L i F specimens (0.1 x 0.1 x 1.0") gave i n f e r i o r p r o p e r t i e s when compared t o r e c t a n g u l a r s p e c i -mens (0.05 x 0.1 x 1 . 0 " ) . The lower d u c t i l i t y and the wider s c a t t e r - 58 -of deformation p r o p e r t i e s e x h i b i t e d by the former could be r e l a t e d to the smaller l e n g t h / t h i c k n e s s r a t i o . Hence end e f f e c t s may have been more prevalent. The major reason.in going to r e c t a n g u l a r specimens was t o t r y to o b t a i n completely uniform deformation on one set of orthogonal s l i p planes. I t had been reported e a r l i e r " ^ and a l s o observed, i n the present work, that deformation of square L i F specimens tended to take place i n " b l o c k s " , each b l o c k b e i n g characterized.by deformation on only one set of orthogonal planes. F u r t h e r u n i f o r m i t y was expected t o r e s u l t from the w e l l known "shape" e f f e c t whereby d i s l o c a t i o n s tend to move on s l i p systems e x h i b i t i n g the s h o r t e s t o v e r a l l s l i p d i s t a n c e i . e . the- " t h i n " system shown i n F i g . kO s l i p system - 59 -51 This e f f e c t was f i r s t reported by Wu and Smoluchowski(Al) and has been observed f o r other metals-' and also f o r NaCl . The complete disagreement between the present observations and the above predictions was f i r s t thought to be due to extraneous factors hi such as specimen alignment, etc. However, the very recent work of Alden has indicated that the shape e f f e c t i s observed f o r NaCl and KC1 but not f o r L i F , i n agreement with the present r e s u l t s . This phenomenon cannot be explained at present. He also observed that the work hardening rate f o r L i F was the same f o r deformation on the thin or wide s l i p systems. E. Microhardness Measurements The apparent dependence of microhardness upon indenter load has also been reported by Krantz-^ 55 B u c k l e r > y states that the discrepancy i s simply a . r e f l e c t i o n of the r e l a t i v e inaccuracies involved.in the measurement of indentations of varying s i z e s . However, i t may also have a more fundamental o r i g i n r e lated.to the r e l a t i v e amounts of work hardening induced by the indenter penetrating to varying depths. An important feature of the present r e s u l t s i s the constancy of the hardness r a t i o of i r r a d i a t e d and annealed specimens indenpendent of the indenter load. Microhardnesses can thus be compared at constant indenter loads Nadeau^ has observed the f o l l o w i n g relation.between the flow stress and the microhardness of impurity hardened L i F : - 6oc-'^~2 = k ^2 where k = c o n s t a n t s 2. and and H-^  are f l o w s t r e s s and hardness of the annealed m a t e r i a l r e s p e c t i v e l y . The f l o w s t r e s s i s a measure of the r e s i s t a n c e t o d i s l o c a -t i o n , motion whereas the hardness c o n s i s t s of t h i s r e s i s t a n c e p l u s the e f f e c t of work-hardening d u r i n g the i n d e n t a t i o n . Assuming we can rel a t e " , hardness t o work hardening r a t e , 0 , we can w r i t e For c r y s t a l s e x h i b i t i n g the . same annealed f l o w s t r e s s and hardness and a l s o the same"^"2 w e have f o r an i r r a d i a t e d and ai i m p u r i t y hardened c r y s t a l k. ^  . i r r = imp kimp Q i r r p r o v i d i n g f("<?"^) i s dependent only upon * ? ^ . The present r e s u l t s i n d i c a t e t h a t k^ r r=^and hence the r a t e of work hardening i n i m p u r i t y hardened L i F should be about three times greater than i n i r r a d i a t i o n hardened L i F . This would then be- evidence of a d i f f e r e n t work hardening mechanism i n the two m a t e r i a l s . The present r e s u l t s a l s o i n d i c a t e @±TT ^ 1-5 x 10+^gm/mm2. Nadeau^ has observed a value of & o f ( k-l6)x 10^ gm/mm2 which i s i n agreement w i t h the present p o s t u l a t i o n . o n I t i s i n t e r e s t i n g t h a t Gilman and Johnston observed a k f a c -t o r of 1 . 1 - 2 . 0 over l a r g e ranges of neutron i r r a d i a t e d L i F . This suggests t h a t the hardening produced by neutron i r r a d i a t i o n i s s i m i l a r to t h a t due to i m p u r i t i e s . P h i l l i p s ^ observed a room temperature work hardening r a t e of 3-6 x 10^ gm/mm2 ( t e n s i l e ) f o r L i F c o n t a i n i n g - 61 -60 ppm of Mg impurity. This i s also i n agreement with the predicted trend. F. A c t i v a t i o n Volume In terms of a dis l o c a t i o n - o b s t a c l e i n t e r a c t i o n , the a c t i v a t i o n volume i s generally defined by the r e l a t i o n v* = b i d . where l . i s the distance between obstacles, b i s the burgers vector, and d . i s the a c t i v a t i o n distance. In order to attach t h i s physical s i g n i f i c a n c e to the a c t i v a t i o n volume, the F' - x 58 curve must remain constant with temperature and s t r a i n - r a t e . (a) Stress dependence of the a c t i v a t i o n volume. The c h a r a c t e r i s t i c regions of the v* v.s. curves w i l l be designated as shown i n F i g . kl. F i g . kl Stages of a c t i v a t i o n volume v.s. stress curves The occurrence of the three stages suggests that they correspond to the deformation stages observed.in the curves (see F i g . 3 9 ) . - 62 -Any dependence of v* upon stress or s t r a i n can be a t t r i b u t e d to a corresponding dependence of the components of the frequency f a c t o r , V*', i n p a r t i c u l a r A and N, (see equation ( 7 ) ) or the a c t i v a t i o n length, 1, providing d remains constant. At present, t h i s i s assumed to be true Hence, stages I, IIA,and IIB can be interpreted i n terms of an increasing, constant, or decreasing v~' or 1. This follows simply from the mathematical r e l a t i o n s h i p s . The phy s i c a l s i g n i f i c a n c e of such v a r i a t i o n s w i l l be discussed l a t e r i n terms of the possible rate c o n t r o l l i n g deformation mechanisms. ( i ) Stage.I In a d d i t i o n to the above mentioned f a c t o r s , stage I can also be a t t r i b u t e d to an increasing d . As w i l l be discussed l a t e r , * decreases during t h i s period and hence, f o r a constant F --x curve, d would increase. Stage I was not observed i n a l l cases as no attempt was made to i n i t i a t e the s t r a i n - r a t e change experiments i n t h i s region. (ii:'.) Stage IIA The dependences of the extent of stage IIA upon temperature or s t r a i n - r a t e i s not obvious from the present r e s u l t s . The i n a b i l i t y to reproduce the t r a n s i t i o n point (IIA to IIB) i n terms of stress or s t r a i n to b e t t e r than + 20$ can be a t t r i b u t e d to the f a c t that d i f f e r e n t specimens were used f o r each t e s t and also to the variable uniformity of deformation. The trend f o r stage IIA to extend over the e n t i r e stress range to fracture at lower temperatures could be due to the f a c t that the f r a c -- 63 -ture s t r a i n was, e q u i v a l e n t t o t h a t ' o f the t r a n s i t i o n p o i n t at higher temperature s (4 - 6 $). Conrad and F r e d e r i c k - ^ have observed s i m i l a r trends i n b.c.c. i r o n . At low temperatures they a l s o observed a constant v*. However, at higher temperatures v* increased l i n e a r l y w i t h s t r e s s or s t r a i n . ( i i i ) Stage IIB The b i r e f r i n g e n c e observations of e i t h e r deforming or deformed L i F c r y s t a l s i n d i c a t e d t h a t the formation of k i n k bands or l a r g e s c a l e d i s l o c a t i o n movement on oblique s l i p systems may be r e l a t e d t o the t r a n s i -t i o n from stage I I A t o stage I IB,. I t should be r e c a l l e d t h a t t h i s t r a n s i -t i o n was accompanied by a change i n the work hardening slope from constant to i n c r e a s i n g w i t h M . a I t i s u n l i k e l y t h a t the t r a n s i t i o n r e s u l t e d d i r e c t l y from the formation of k i n k bands. Pratt60 and Nabarro6l have reported a decrease i n the work hardening slope i n NaCl c r y s t a l s at the onset of k i n k i n g . They observed t h a t d i s l o c a t i o n g l i d e occurred on a p a i r of orthogonal s l i p systems and t h a t kinlcing' r e s u l t e d i n the t e r m i n a t i o n of s l i p on one of the i n t e r s e c t i n g systems. Ther e a f t e r , deformation took place by s i n g l e s l i p . This i s contrary to what i s u s u a l l y found i n f . c . c . m e t a l l i c s i n g l e c r y -go s t a l s , where k i n k i n g occurs simultaneously w i t h the onset of secondary s l i p and hence an increase i n the work hardening r a t e . Washburn et al^3 have observed (see F i g . 42) t h a t i n MgO only those i n t e r s e c t i o n s between d i s l o c a t i o n s on non-orthogonal planes r e s u l t e d i n a dense tangled network of d i s l o c a t i o n s . T h e i r observations lend 64 support t o the p o s t u l a t i o n by Kear e t a l t h a t the only d i s l o c a t i o n i n t e r a c t i o n i n NaCl - type c r y s t a l s which would produce a decrease i n - 6k -the o v e r a l l e l a s t i c s t r a i n energy occurs between d i s l o c a t i o n s on oblique s l i p planes, i . e . | a |loi] + i a joli]— > - \ a Jlio] The new d i s l o c a t i o n formed, \ ra Qlipj , is pure' edge i n character and l i e s on the ^ 1 1 2 ^ plane. " Since t h i s is not one of the normal s l i p planes, it w i l l be r e l a t i v e l y immobile. The s e s s i l e d i s l o c a t i o n s formed by such i n t e r a c t i o n s may oppose subsequent d i s l o c a t i o n movement on both . orthogonal and oblique s l i p systems. This may be r e l a t e d to the increasing work hardening rate observed during stage IIB. I t i s noted that exactly the same s i t u a t i o n regarding, work hardening rate was^Dbserved i n the con-tinuous s t r e s s - s t r a i n curves. The i n i t i a t i o n of d i s l o c a t i o n movement on oblique planes may be i n d i r e c t l y r e l a t e d to the formation of kink bands on orthogonal planes. Haasen^ has observed f o r f . c . c . n i c k e l single c r y s t a l s that the stress dependence of A"£" obtained from temperature change tests exhibited an i n i t i a l , constant region which corresponded to stage I defor-mation ( 'sj -- £ ) and an increasing A^T region which corresponded to stage II deformation. Also, at low temperatures a l a r g e r amount of s i n -gle s l i p was obtainable r e s u l t i n g . i n a larger constant A*"^ region. (b) Strain-rate dependence of a c t i v a t i o n volume A s t r a i n - r a t e dependence of v* has also been observed by Basinski and C h r i s t i a n ^ f o r p o l y c r y s t a l l i n e i r o n , Mordike and Haasen^ /TO f o r single c r y s t a l i r o n , and by Causey f o r single c r y s t a l t i n . The majority of researchers performing s t r a i n - r a t e experiments have neglected to investigate t h i s phenomenon. This i s probably due to the f a c t that - 65 -i t s existence places some doubt on the v a l i d i t y of the rate theory equa-t i o n s . However, i n cases where i t has been observed, rate theory has been applied anyway.^>^7 The present r e s u l t s (see Appendix VI) show that the m n o n - l i n e a r i t y i n A ^ T w i t h A l n £ may be a t t r i b u t e d to the s t r a i n - r a t e dependence of AST • However, due to the few r e s u l t s available, and the f a c t that no s a t i s f a c t o r y explanat ion e x i s t s , t h i s phenomenon w i l l not be discussed f u r t h e r . (c) A c t i v a t i o n volume and the stress dependence of d i s l o c a t i o n  v e l o c i t y The absolute values of a c t i v a t i o n volume can be compared at room temperature to those obtained from the stress dependence of d i s l o -10 cation v e l o c i t y as determined by Gilman and Johnston. ' !Equation ( l ) can be written i n the f o l l o w i n g form s = s c exp (-A<9/kT) where now S G = v~bAN/^  b. I t also follows that the a c t i v a t i o n volume i s given by S-^ \ /S v* =: kT ( d In s) = kT / Jin S \ a w /mm From the slope of Gilman and Johnston's curves, a value f o r a i n ' t ~ was obtained, which y i e l d s v* = 2.3 x,10" cm-3 f o r = 200 gm/ri and v* = . 9 x lO'^cm^.for 500 'gjtn/mm2 at room temperature. These are i n good agreement with the presently observed values of 6.2 and 4.2 x 10 cm r e s p e c t i v e l y , f o r tS — 1.8 x 10 sec" , con-s i d e r i n g the v a s t l y d i f f e r e n t techniques that were used. - 66 -I t i s i n t e r e s t i n g that Gilman and Johnston's r e s u l t s make no suggestion of a region of constant v* with stress. However, t h i s could simply be due to the f a c t that t h e i r experiments were c a r r i e d out at very low s t r a i n s ( O s a - t ) ' (d) A c t i v a t i o n volume of i r r a d i a t e d c r y s t a l s . The f a c t that the few values of v* obtained f o r i r r a d i a t e d L i F f a l l very close to the extrapolated v* v.s. VJ^ curve f o r annealed c r y s t a l s may indicate that the stress dependence of d i s l o c a t i o n v e l o c i t y i s unaltered by i r r a d i a t i o n , except f o r a higher i n i t i a l flow s t r e s s . Johnston and G i l m a n ^ observed t h i s to be approximately true f o r neutron i r r a d i a t e d c r y s t a l s . The s l i g h t deviation could be due to s t r u c t u r a l damage caused by the heavy p a r t i c l e neutron i r r a d i a t i o n . Thus, the same deformation mechanism could possibly be rate c o n t r o l l i n g i n both annealed and i r r a d i a t e d L i F at room temperature. F i g . 42 D i s l o c a t i o n i n t e r s e c t i o n s on oblique (upper photo) and orthogonal (lower pshoto) glide planes i n MgO(after Washburn et a l -') - 6 7 -G. Thermally A c t i v a t e d Deformation Mechanisms The p o s s i b l e r a t e c o n t r o l l i n g mechanisms f o r d i s l o c a t i o n motion i n L i F w i l l be discussed i n d i v i d u a l l y . I t should be r e c a l l e d t h a t the experimentally determined a c t i v a t i o n energy i s b e l i e v e d to be character-i s t i c of stage IIA hardening only. However, the v* r e s u l t s extend over both deformation stages, IIA and I I B ^ p r o v i d i n g the temperature i s suf-f i c i e n t l y high. (a) P e i e r l s - H a b a r r o s t r e s s I f the P e i e r l s - N a b a r r o mechanism i s r a t e - c o n t r o l l i n g v* i s not expected to be d i r e c t l y a f f e c t e d by s t r a i n . 5 9 • Instead, \J~' or more s p e c i f i c a l l y w i l l be the major s t r a i n dependent f a c t o r . Hence, t h i s mechanism may be important'only d u r i n g stage I IA of the deformation of L i F . T h e o r e t i c a l c a l c u l a t i o n s have not been advanced to the stage where comparisons can be made w i t h experimentally determined a c t i v a t i o n energies, e t c . Ge n e r a l l y , s e l e c t i o n of t h i s mechanism as r a t e - c o n t r o l l i n g i s based l a r g e l y on disagreement-between experimental r e s u l t s and a l l other a v a i l a b l e mechanisms. • (b). Impurity I n t e r a c t i o n s Gilman and Jo h n s t o n 1 ^ have shown that i m p u r i t i e s do not a f f e c t the f l o w s t r e s s of L i F i f they e x i s t only i n t r a c e amounts ( few. ppm),. The c r y s t a l s used.in the present work would be i n c l u d e d i n t h i s c l a s s i f i -c a t i o n . Assuming t h a t on the average the i m p u r i t i e s are uniform l y spaced, an a c t i v a t i o n l e n g t h can be estimated as follows.' A u n i t c e l l i n L i F - 68 -c o n t a i n s k L i - : - and F i p n s . A n i m p u r i t y l e v e l o f 10 ppm (maximum) 1+ w o u l d g i v e 1 i m p u r i t y p e r 2.5 x 10 u n i t c e l l s . The a v e r a g e s p a c i n g b e t w e e n i m p u r i t i e s w o u l d t h e n b e (2.5 x 10^)"^^ a = 1.2 x 10 ^cm. T h i s a c t i v a t i o n l e n g t h . i s a b o u t two o r d e r s o f m a g n i t u d e s m a l l e r t h a n t h e o b s e r v e d v a l u e o f 1.2 x 10~c"m o b t a i n e d f r o m t h e r e l a t i o n 1 = v * / b d , where -20 3 v * s= 10 x 10 c m J and d = b . ( c ) F o r e s t d i s l o c a t i o n i n t e r s e c t i o n s a n d c h a r g e e f f e c t s I t i s , u n l i k e l y t h a t t h i s m e c h a n i s m i s r a t e - c o n t r o l l i n g i n s t a g e s I o r I I A o f d e f o r m a t i o n . E v i d e n c e t h a t d i s l o c a t i o n r e a c t i o n s i n g e n e r a l do n o t p l a y a n i m p o r t a n t r o l e i n s t a g e I h a s b e e n r e v e a l e d b y e t c h -10 p i t t i n g t e c h n i q u e s . A s i m i l a r c o n c l u s i o n c a n b e r e a c h e d f r o m t h e d i s -Q l o c a t i o n v e l o c i t y e x p e r i m e n t s o f J o h n s t o n a n d G i l m a n ^ . S t r e s s p u l s e s o f ~ 1 0 s e c were u t i l i z e d t o p r o d u c e maximum d i s l o c a t i o n v e l o c i t i e s o f k i -2 10 c m / s e c . H e n c e , d i s l o c a t i o n s were moved ~.10 cm w h i c h i s o f t h e same o r d e r o f m a g n i t u d e as t h e a v e r a g e s p a c i n g b e t w e e n d i s l o c a t i o n s , r e s u l t i n g i n l i t t l e o r no i n t e r s e c t i o n . As t h e c a l c u l a t e d v a l u e s o f v * f r o m t h e i r w o r k a g r e e f a v o r a b l y w i t h t h o s e o f t h e p r e s e n t e x p e r i m e n t s , t h i s m e c h a n i s m d o e s n o t a p p e a r t o b e r a t e c o n t r o l l i n g . A c o n s t a n t v * w i t h € i s a l s o u n l i k e l y i f f o r e s t i n t e r s e c t i o n s i n L i F a r e i m p o r t a n t as d e f o r m a t i o n g e n e r a l l y o c c u r s on a t l e a s t two o r t h o g o n a l s l i p s y s t e m s . The f o r e s t s p a c i n g w o u l d t h e n d e c r e a s e as w o u l d v * w i t h s t r a i n . H e n c e , t h i s m e c h a n i s m may p o s s i b l y b e i m p o r t a n t o n l y .1 d u r i n g s t a g e I IB. h a r d e n i n g . The e x p e r i m e n t a l l y o b s e r v e d v a l u e of 1 — 1.2 x 10"^cm i s i n good a g r e e m e n t w i t h t h e e s t i m a t e d d i s l o c a t i o n d e n s i t y d u r i n g s t a g e I I B - 6 9 -Q ^ hardening (~10 /cm ). I t should he noted that such a value of 1 would hold true f o r e i t h e r orthogonal or oblique i n t e r s e c t i o n s . D i s l o c a t i o n i n t e r s e c t i o n would r e s u l t i n the formation of jogs. Estimates of the required a c t i v a t i o n energy to form such jogs are usually 69 based upon Seegers p r e d i c t i o n , E jog= jLib 1 where 1 = length of jog. For 1 = b = 2.85 x 10"° cm and jl = 6 x 10"dynes/cm , E jog - .72 ev which i s i n good agreement with the present r e s u l t s . However, considerable d i f f e r e n c e i n opinion e x i s t s regarding 70 the exact form of t h i s t h e o r e t i c a l equation . Stage IIB may also be a t t r i b u t e d to e l e c t r o s t a t i c e f f e c t s . Experimental and t h e o r e t i c a l work has shown that d i s l o c a t i o n s i n deformed a l k a l i halide c r y s t a l s are p o s i t i v e l y charged.with the charge e x i s t i n g at jogs. I t has also been shown that oblique d i s l o c a t i o n i n t e r s e c t i o n s 72 r e s u l t i n the formation of charged'jogs. The increase i n the jog den* s i t y may then r e s u l t i n an increase i n the e l e c t r o s t a t i c drag on a d i s l o -cation. This follows from the predictions of Prat t3^ anr\ Eshleby et a l ^ ^ that the motion of a d i s l o c a t i o n w i l l be impeded by a surrounding cloud of p o s i t i v e - i o n vacancies. A large number of such vacancies already e x i s t s i n an undeformed impure c r y s t a l (see Section IVC) (d) Cross Glide of screw d i s l o c a t i o n s Cross-glide of screw d i s l o c a t i o n s has been observed to occur r e a d i l y i n L i F and has been postulated to be the fundamental source of d i s l o c a t i o n m u l t i p l i c a t i o n ? . Only screw d i s l o c a t i o n s are involved as they are not characterized by a single g l i d e plane and hence can move along v a r i o u s planes i . e . between (1.10J planes. In doing so, edge jogs are formed which cannot move i n the d i r e c t i o n of motion of the o r i g i n a l screw d i s l o c a t i o n . Depending upon t h e i r height, they may remain immobile or can be dragged along w i t h the screw d i s l o c a t i o n producing l a t t i c e -1 7 de f e c t s . Johnston and Gilman have shown that the m u l t i p l e c r o s s - g l i d e mechanism n e c e s s i t a t e s the formation of jogs of height given by d -- y t i b 8 1 1 ( 1 -J) V I where f o r L i F ^ j? = Poissons r a t i o = .27 ,jj = shear modulus = 6 x 1 0 + ^ Xdynes/cm 2 b = Burgers vector ^a. - a p p l i e d . s t r e s s | _ A maximum value of U^j= 1200 gm/mm observed i n the present work would give a minimum j o g height of 280 b. This height i s s e v e r a l orders of • magnitude greater than any which could be due to the thermal a c t i v a t i o n of d i s l o c a t i o n s between ^110 ) planes. This does not preclude the p o s s i b i l i t y t hat jogs of l e s s than t h i s height are created by c r o s s - g l i d e . Such jogs simply do not l e a d t o d i s l o c a t i o n m u l t i p l i c a t i o n . (e) Nonconservative motion of jogs in/screw d i s l o c a t i o n s L a t t i c e vacancies are expected to be the prime r e s u l t of the . nonconservative motion of jogs i n screw d i s l o c a t i o n s . Oblique d i s l o c a t i o n i n t e r s e c t i o n s r e s u l t - i n the formation of charged j o g s ^ 2 of height b/2'. I n t e r s e c t i o n of orthogonal d i s l o c a t i o n s produces n e u t r a l jogs of height 'b'. - 71 Vacancy producing jogs may a l s o r e s u l t from c r o s s - s l i p of screw d i s l o c a t i o n s . Johnston and Gilman? conclude that such a process w i l l occur i n such a f a s h i o n as to observe the energy d i f f e r e n c e s between opp o s i t e l y charged jogs i . e . lower energy jogs w i l l dominate. Movement of jogs i n screw d i s l o c a t i o n s i s expected to create cusps or dragging p o i n t s . These have i n f a c t been observed i n Mg0^3 ( F i g . 43). F i g . 43 Moving screw d i s l o c a t i o n s i n MgO ( a f t e r Washburn et a l ~) I n d i r e c t evidence f o r the movement of jogs i n screw d i s l o c a t i o n i s evident from observations t h a t the v e l o c i t y of edge d i s l o c a t i o n s i s approximately twenty-five times f a s t e r than that of screw d i s l o c a t i o n s , f o r a constant s t r e s s . This m o b i l i t y d i f f e r e n c e i s probably due t o the drag e f f e c t of jogs. - 72 -Mott?^ has po s t u l a t e d t h a t a temperature dependence of flo w s t r e s s w i l l only occur i f the vacancies created by j o g motion d i f f u s e away from the jog.immediately a f t e r formation. Jog.movement w i l l then.be charac-t e r i z e d by the energy f o r s e l f d i f f u s i o n of vacancies, provided the temperature i s s u f f i c i e n t l y high. 1 The observed a c t i v a t i o n energy i s very c l o s e t o e i t h e r t h a t f o r the s e l f d i f f u s i o n of L i + vacancies, .65 e v ^ or .70 e v ^ , or the d i f f u s i o n of vacancy p a i r s , . 5 8 e v . The l a t t e r may d i f f u s e by e i t h e r p o s i t i v e or negative ions jumping i n t o . t h e corresponding vacant s i t e of • the p a i r . Thus, the present r e s u l t s could i n d i c a t e t h a t such p a i r s d i f f u s e by the movement of p o s i t i v e i o n vacancies. The observed A Q i s i n good agreement w i t h the value of .7 ev determined by Gilman and Johnston^ from measurements of the temperature dependence of d i s l o c a t i o n v e l o c i t y . The temperature range studied was - 50 t o 25 deg. C. which i s w i t h i n the l i m i t s of the present work. The r e g i o n of constant v* w i t h ^Xi. would mean t h a t jogs are being a n n i h i l a t e d at a rate, equal t o th a t of t h e i r formation r a t e . Such a 17 mechanism has, i n f a c t , been proposed f o r L i F . Stage IIB would be i n t e r p r e t e d t o mean t h a t jogs are now b e i n g produced at a greater r a t e than they are b e i n g a n n i h i l a t e d . This would n e c e s s i t a t e the onset of another production mechanism, probably oblique s l i p . - 73 -( f ) Rate c o n t r o l l i n g mechanism Impurity i n t e r a c t i o n s and c r o s s - g l i d e of screw d i s l o c a t i o n s do not appear t o be of importance i n determining the f l o w of d i s l o c a t i o n s i n "pure" L i F . The r e s u l t s i n d i c a t e the f o l l o w i n g : ( i ) Due t o the general d e f i c i e n c y of q u a n t i t a t i v e r e s u l t s f o r the P e i e r l s mechanism, the nonconservative motion of jogs appears t o be r a t e c o n t r o l l i n g i n stage IIA deformation. ( i i ) Thi s mechanism may a l s o h o l d f o r stage I I B . However, i t appears more l i k e l y t h a t t h i s stage i s due t o a f o r e s t i n t e r s e c t i o n mechanism. E l e c t r o s t a t i c e f f e c t s could a l s o be important d u r i n g t h i s stage of deformation. H. S t r e s s r e l a x a t i o n S t r e s s r e l a x a t i o n r e s u l t s were obtained only i n stages I-and IIA Larger specimens ( . 1 x .1 x .1") were u t i l i z e d which e x h i b i t e d l e s s duct-i l i t y than the r e c t a n g u l a r specimens and hence stage IIB was not observed. St r e s s relaxation.experiments have been c a r r i e d out by s e v e r a l 77 worteisincluding Feltham on p o l y c r y s t a l l i n e copper and cC - brass and Chang' on p o l y c r y s t a l l i n e uranium car b i d e . There i s general agreement th a t the mechanism involved, i s t h a t of l i m i t e d c o n t i n u a t i o n of d i s l o c a t i o n g l i d e i n i t i a t e d d u r i n g y i e l d i n g . (a) I n t e r n a l and r e l a x e d f l o w s t r e s s e s As d escribed e a r l i e r , the a p p l i e d s t r e s s a . m a t e r i a l s u s t a i n s i s composed of two separate terms given by ^ j e ,e , T ) = ? i ( 6 ) T ) Before d i s l o c a t i o n movement w i l l occur, a s t r e s s greater than '^ '^  must be a p p l i e d . Thus "2" * can be d i r e c t l y r e l a t e d to the d i s l o c a t i o n v e l o c i t y . - 74 -Upon stopping the cross head motion, > and hence some d i s l o c a t i o n s w i l l continue to move. The a d d i t i o n a l s t r a i n hardening w i l l then r e d u c e ^ " * according t o the f o l l o w i n g r e l a t i o n proposed by Conrad?^. where ^~^ 0 = i n i t i a l i n t e r n a l s t r e s s of c r y s t a l h = s t r a i n hardening c o e f f i c i e n t Assuming t h a t equatiion(l) i s a p p l i c a b l e , a decrease i n " ^ " * w i l l r e s u l t i n an increase i n & Q, and hence, an e x p o n e n t i a l decrease i n V • This would then r e s u l t i n an e x p o n e n t i a l decrease i n the s t r e s s This i s e x a c t l y as observed. E v e n t u a l l y the p o i n t i s reached where ""t^ ~= (~t"io+ hS ) = '2r^  and h e n c e = 0 (s = 0 ) . At t h i s p o i n t the a p p l i e d s t r e s s which equals the r e l a x e d f l o w s t r e s s i s e x a c t l y balanced by the opposing i n t e r n a l s t r e s s of the c r y s t a l . The present r e s u l t s f o r L i F show very good agreement between an approximate " ? " r e i and ca l c u l a t e d , from r a t e theory (see Fig.3 5 ) - I t is•emphasized t h a t t h i s comparison i n v o l v e s e n t i r e l y d i f f e r e n t specimens and experimental procedures. (b) S t r a i n and s t r a i n - r a t e dependence of " ^ e i -The p r o p e r t i e s o f ^ p e i f o l l o w e x a c t l y those expected of w i t h respect t o t£ and £ f o r L i F (and i n gen e r a l , a l l m a t e r i a l s ) . For example, the £ dependence of would be expected t o be dependent upon the s t r a i n - r a t e and temperature through h as shown i n the above equation. Hence, i t should increase w i t h . i n c r e a s i n g € (and decreasing T) as observed experimentally i n F i g . 33-A l i n e a r dependence of d i s l o c a t i o n d e n s i t y upon s t r a i n has been observed i n L i F ^ . Hence, the present r e s u l t s p r e d i c t a s i m i l a r depen-dence upon This i s contrary to a l l e x i s t i n g t h e o r i e s f o r metals 75 -but i s b e l i e v e d t o hold f o r L i F , a t l e a s t during stage IIA hardening. Gilman and Johnston"^ have noted t h a t the.increment of s t r e s s due t o s t r a i n hardening.is p r o p o r t i o n a l to the d i s l o c a t i o n d e n s i t y . This i s a l s o i n agreement w i t h the above p o s t u l a t i o n . B e l l and B Q n f i e l d 8 ^ performed a very l i m i t e d number of e x p e r i -ments on germanium and a l s o observed fa'fir agreement between'~^ r ei L "2^  c a l c u l a t e d , and *~£~y s The curves o f " ? ^ v.s. tZ should e x t r a p o l a t e t o a common i n t e r -cept "£~j_0 which represents the i n t e r n a l s t r e s s of the annealed, undeformed c r y s t a l . The present r e s u l t s i n d i c a t e that = 210 - kO gm/mm2. I t i s expected t h a t any measurable y i e l d s t r e s s would be s l i g h t l y greater than the s t r e s s r e q u i r e d t o i n i t i a t e d i s l o c a t i o n movement. Hence "?^j_0 should be l e s s than the temperature independent y i e l d s t r e s s observed a t high temperatures ( ~ 230 gm/mm2). This l a t t e r s t r e s s i s o f t e n taken as an approximate value f o r 2-.. To date, a value f o r "2""^  i s o f t e n obtained u t i l i z i n g e l e c t r o n microscopy. This technique i s not without u n c e r t a i n t i e s due t o the nec-essary e x t r a p o l a t i o n of i n f o r m a t i o n t o b u l k samples. Probably a more important source of e r r o r i n t h i s method l i e s i n the necessary assumption regarding the r e l a t i o n between and the measured d i s l o c a t i o n d e n s i t y . Most t h e o r i e s propose t h a t ^ = c C pj,./b (^ > where o< i s a constant ( .1 - .5). Such a r e l a t i o n i s not observed t o hold f o r L i F . Moreover, the u n c e r t a i n i t y i n OC would l e a d to a considerable e r r o r i n - 76 -(c) S t r e s s dependence of the r e l a x e d f l o w s t r e s s The n o n l i n e a r i t y of trex e x h i b i t e d i n the f l o w s t r e s s dependence and not i n the s t r a i n dependence i s an i n t e r e s t i n g f e a t u r e . The i n i t i a l n o n l i n e a r r e g i o n corresponds to stage I of the deformation curve. G i l -man and Johnston^ have observed t h a t the r a t e of widening of g l i d e bands during t h i s r e g i o n was p r o p o r t i o n a l t o the p l a s t i c s t r a i n and the d i s l o -c a t i o n d e n s i t y remained constant w i t h i n the g l i d e bands. Hence, the o v e r a l l d i s l o c a t i o n d e n s i t y was p r o p o r t i o n a l to the s t r a i n . " ? ^ e ^ ( measured under these conditions,corresponds t o the d i s l o c a t i o n d e n s i t y and hence the s t r a i n w i t h i n the g l i d e bands. Therefore, i t would a l s o be expected t o vary l i n e a r l y w i t h s t r a i n over the e n t i r e deformation r e g i o n . However, as n e a r l y constant: f o r £ — £ s at.> a p l o t of "£rel v.s. "£* would be expected t o increase r a p i d l y d u r i n g stage I . This i s shown d i a g r a m a t i c a l l y i n F i g . kk which p r e d i c t s the observed results^.; S t r a i n F i g . kk A p p l i e d and i n t e r n a l s t r e s s e s v.s. s t r a i n - 77 -(d) Flow s t r e s s Any e x p l a n a t i o n of the change i n f l o w s t r e s s f o l l o w i n g r e l a x a -t i o n must account f o r the f o l l o w i n g f e a t u r e s : ( i ) the magnitude and i t s dependence upon s t r a i n - r a t e ( i i ) the r a p i d . i n c r e a s e from negative values a t low s t r a i n s f o l l o w e d by the r e l a t i v e l y constant r e g i o n . R7R7 Present t h e o r i e s ' of s t r e s s r e l a x a t i o n p r e d i c t values f o r the increase, i n f l o w s t r e s s a f t e r r e l a x a t i o n which are about two orders of magnitude l e s s than observed i n the present experiments. Wo e x p l a n a t i o n can be found.for the observed r e s u l t s . M a r t i n s o n ^ has a r r i v e d , a t the same c o n c l u s i o n a f t e r observing s i m i l a r r e s u l t s . I t was noted t h a t f o r a l l cases where the f l o w s t r e s s f o l l o w i n g r e l a x a t i o n was l e s s than t h a t p r i o r t o r e l a x a t i o n , r e l a x a t i o n had been i n i t i a t e d s h o r t l y after;; y i e l d i n g but before the c r i t i c a l t e n s i l e s t r e s s had been reached i . e . before l a r g e s c a l e d i s l o c a t i o n motionjihad taken place. I t i s known th a t the s a t u r a t i o n d e n s i t y of d i s l o c a t i o n s w i t h i n 9 g l i d e bands has not yet been reached at t h i s p o i n t . Thus, d u r i n g r e l a x a -t i o n , the r e l a t i v e l y s m a l l number of d i s l o c a t i o n s present move e a s i l y i n the v i r t u a l l y undeformed m a t e r i a l causing m u l t i p l i c a t i o n . In f a c t , Johnston and Gilman^ have shown t h a t the t o t a l number of d i s l o c a t i o n loops w i t h i n a g l i d e band incr e a s e s e x p o n e n t i a l l y w i t h time when a constant s t r e s s s u f f i c i e n t l y high to cause m u l t i p l i c a t i o n ( i . e . >> y i e l d s t r e s s ) i s a p p l i e d . An i n c r e a s e i n d i s l o c a t i o n d e n s i t y d u r i n g s t r e s s r e l a x a t i o n would then r e s u l t i n a decrease i n the d i s l o c a t i o n v e l o c i t y and hence the 78 -f l o w s t r e s s , i f the s t r a i n - r a t e i s c o n s t a n t ^ . Apparently when S ^ ^ s a t ' a s t r a i n hardening mechanism takes over and d r a s t i c a l l y decreases tO during s t r e s s r e l a x a t i o n . The d i s l o c a -t i o n s must then move at greater v e l o c i t i e s r e q u i r i n g an increase i n ^~a_ . I t appears t h a t the mechanism i s independent of s t r a i n f o r £ > £ s a f I F r a c t u r e The present r e s u l t s i n v o l v i n g p o s t - f r a c t u r e observations tend t o emphasize the importance of orthogonal j^llO^ i n t e r s e c t i o n s as a source of f r a c t u r e n u c l e a t i o n . S i m i l a r observations have been made by 82 ( Johnston et a l i n MgO. However, no c o r r e l a t i o n between f r a c t u r e ; and the Do presence of k i n k bands was observed as. i n the case of MgO. The importance of g l i d e band i n t e r s e c t i o n s i n f r a c t u r e n u c l e a t i o n was a l s o i n d i r e c t l y observed i n so f a r as c r y s t a l s e x h i b i t i n g l a r g e s t r a i n s t o f r a c t u r e g e n e r a l l y deformed on one p a i r of ^ " l l O ^ planes f o r a l a r g e percentage of the gauge l e n g t h . Theiinumeroua cases of f r a c t u r e w i t h i n the epon may have been d i r e c t l y r e l a t e d t o the presence of s m a l l cracks formed at the c h i s e l end of specimens. This would be evidence t h a t : a c e r t a i n amount of defor-mation occurred w i t h i n the p o r t i o n of the specimen- immersed i n the epon. - 79 -V CONCLUSIONS 1. The increased annealing r a t e of c o l o r centers a t the " n o n - c h i s e l " end of a cleaved i r r a d i a t e d L i F c r y s t a l i s a t t r i b u t e d t o an abnormally high j o g d e n s i t y . 2. A t r a n s i t i o n p o i n t appears to e x i s t i n the stage I I s t r a i n - h a r d e n i n g of annealed L i F . It. becomes evident at r e l a t i v e l y high s t r a i n s and i s c h a r a c t e r i z e d by the onset of a s t e a d i l y i n c r e a s i n g work hardening slope. D i s l o c a t i o n motion on oblique g l i d e planes i s b e l i e v e d t o c o n t r o l the t r a n s i t i o n p o i n t . 3. The a c t i v a t i o n energy f o r d i s l o c a t i o n motion over the temperature range - . 6 0 to +60 °C. i s .6 - .7 ev. This i s i n good agreement w i t h . tha t f o r the,,, d i f f u s i o n of L i * vacancies o r vacancy p a i r s . The movement of vacancy producing jogs i n screw d i s l o c a t i o n s appears t o be' the'..rate.,, con-t r o l l i n g mechanism d u r i n g stage I I A hardening- D i s l o c a t i o n i n t e r s e c t i o n s •f. • • • 1 and perhaps e l e c t r o s t a t i c charge e f f e c t s probably c o n t r o l deformation i n stage I I B . k. The i n t e r n a l f l o w s t r e s s of L i F determined from r a t e theory agrees remarkably w e l l w i t h the r e l a x e d f l o w s t r e s s . These s t r e s s e s are b e l i e v e d t o be analogous. 5. L i F e x h i b i t s an anomalous increase i n f l o w s t r e s s f o l l o w i n g r e l a x a t i o n which cannot be explained by current t h e o r i e s . - 80 -VI SUGGESTIONS FOR FURTHER WORK 1. High speed cinematography coupled w i t h s t r e s s b i r e f r i n g e n c e tech-niques could very e a s i l y be u t i l i z e d t o study the importance of s l i p band d i s t r i b u t i o n ' upon the t r a n s i t i o n i n work hardening r a t e ducing stage I I t 2. ' Such techniques along w i t h e t c h - p i t t i n g pould be used to study f r a c t u r e phenomena . i n i r r a d i a t e d c r y s t a l s . These are w e l l s u i t e d f o r such a study due t o t h e i r low s t r a i n s t o f r a c t u r e and hence low d e n s i t y of deformation bands. 3- Rate theory experiments could be extended t o lower temperatures very e a s i l y ; extension t o high temperature may prove troublesome. k. The r e l a t i o n between the r e l a x e d f l o w s t r e s s and the i n t e r n a l s t r e s s should be more thoroughly i n v e s t i g a t e d . This would be a good t o p i c t o study as i t could be of major importance. 5. An e l e c t r o n microscopy study of deformed L i F c r y s t a l s would prove very i n t e r e s t i n g as very l i t t l e work has been done on i o n i c c r y s t a l s i n general. - 81 -V I I . APPENDICES - 82 -APPENDIX I RATE THEORY ( a ) E q u a t i o n s P u t t i n g V ' = v ~ b A N , t h e A r r e h e n i u s e q u a t i o n ( s e e e q u a t i o n ( l ) o f t e x t ) c a n b e - w r i t t e n i n t h e f o r m A. Q = k T I n ( A 1 ) . H e n c e - <S)AQ = -fe AQ ) ft T ) = - k lnAc^\ a** t ^ U r J _ k J (A2) a T p r o v i d i n g \ f ' / V" ' ( T) I t a l s o f o l l o w s f r o m e q u a t i o n ( A l ) t h a t -d A Q . = k T 9 I n ^ a ^ * (A3) p r o v i d i n g V T * / V (?T*) F r o m t h e r e l a t i o n A Q = H * - v * t * (See F i g . 1 o f t e x t ) we o b t a i n v * = " ^ A Q ( A 4 ) a s s u m i n g ~c) H * •="* * ?d v * \ ( a good a p p r o x i m a t i o n i f t h e a * * ^ {& * ) s h a p e o f F - x c u r v e r e m a i n s c o n s t a n t w i t h s t r e s s ) I f . ? * ! f f±(X, T ) , t h e n (2>mY\ ~(hsJ\ ana / 3 ? - * A ~ ^ ^ > 7 T " U W T ( a T A w T h u s v * = k T (ci lxijf\ = - k I n Ac!_\ I t s h o u l d b e n o t e d t h a t d~£"a. i s n e g a t i v e f o r T < Tc ( t e m p e r a t u r e a T where = 0 ) . C o m b i n i n g e q u a t i o n s ( A l ) a n d (A5) w i t h t h e r e l a t i o n - 83 H = A Q + v * 7~a ( s e e F i g . 1 o f t e x t ) , we o b t a i n H = v * ? " ' - v* , T / < ^ ? " a A (A6) • I t a l s o f o l l o w s f r o m e q u a t i o n s ( A l ) a n d ( A 5 ) i t h a t The d e t e r m i n a t i o n o f v * , H , a n d A Q f r o m A £ a n d A T e x p e r i -ments n e c e s s i t a t e s t h e f o l l o w i n g a p p r o x i m a t i o n s : e q u a t i o n ( A 6 ) : 9 I n V ~ I n {Xo/Ki) ~ I n ^ / l f 1 2>7a 37a . A 7k a n d 37a = A T L 2> T A T e q u a t i o n ( A 7 ) : 7" a n < ^ ^ e c l u a l a v e r a g e v a l u e s d u r i n g A T t e s t : = * ? " a i + "?*ag ; T = T n + T 2 2 o ( b ) True . A c t i v a t i o n E n e r g y I t can b e s e e n f r o m t h e e q u a t i o n A Q = H * - v * 7* ( e q u a t i o n (k) o f t e x t ) t h a t A Q = H * a t 7* = 0 . T h i s r e p r e s e n t s t h e t o t a l a c t i -v a t i o n e n e r g y o f t h e r a t e - c o n t r o l l i n g . p r o c e s s i . e . t h e s t r e s s u n - a s s i s t e d v a l u e . I n t e r m s o f t h e t e m p e r a t u r e d e p e n d e n c e o f t h e f l o w s t r e s s , t h i s 27a c o r r e s p o n d s ; t o t h e p o i n t where — - = 0 . The t e m p e r a t u r e a t w h i c h t h i s :•: f i r s t o c c u r s , T c , c a n b e - d e t e r m i n e d u t i l i z i n g t h e r e l a t i o n '27. ~^r~l T~7T~ I " — ^ i * T (. see e q u a t i o r t e x t ) 1 / j 7 a f Ia i n • ) " AQ~ ( ^ T ^ ) ' T ( s e e e q u a t i o n j 7 ) ^ o f E x t r a p o l a t i o n o f t h e t e m p e r a t u r e d e p e n d e n c e o f — ^ I n y / z e r o wou-'-^  mean t h a t = 0 a n d h e n c e T = T c . T h i s t e m p e r a t u r e , c a n t h e n b e U T/ . v i n s e r t e d i n t o e q u a t i o n ( A l ) a l o n g w i t h t h e p r e v i o u s l y d e t e r m i n e d l n A T ' \ U / t o g i v e t h e t o t a l o r t r u e a c t i v a t i o n e n e r g y . (c) £ dependence of A. Q, H, and. In (v"/y The s t r a i n dependence of the. parameters AQ> and l n A C l J was determined u t i l i z i n g equations (j), (8) and (9) from the t e x t . This necess i ta ted e x t r a p o l a t i n g the v* values at var ious s t r a i n s to temperatures corresponding to the A T t e s t s (see, f o r example, F i g . 26 of t e x t ) . The r e s u l t s are shown i n F i g , k-2. 2 > 1 1.0. > 30 20 ^ m V 0 * A < 4 1 — k — • B 122 31k:° K O B 113 265°K X B 1 1 4 216°K O B 1 2 1 2l6°K A B 112 236°K % fa *0 « •A-O Strain Fig-Al Strain dependence of H, A Q, and In 00 - -APPENDIX II TENSILE EXPERIMENTS Specimen X-head in/min Temp. ,°C. Gauge Length (mm) V-sectioi area (mm2) B 80 .005 72 13.00 2.20 B 81 .005 22 12.68 2.21 B 100 .005 6 13.07 2.68 B 101 .005 6 14.06 2.89 B 103 .005 - 55 13-21 3-05 B 104 .005 - 68 13.01 3-33 B 109 .005 -196 12.12 3-93 B 110 .005 - 89 11.74 3-25 B 111 .005 - -122 11.41 3-22 B 118 .002 - 62 "'11.42 2.76 A' 1 .002 21 14.17 2.89 A 2 .005 21 14.11 2.86 A .3 . 02 21 14.08 2.19 A 4 . 05 21 13.98 3-14 Appendices I I I and IV contain data f o r specimens where only the i n i t i a l deformation properties were u t i l i z e d . APPENDIX III - 87 -STRAIN-RATE CHANGE EXPERIMENTS Specimen T = -63°'C (210°K) <\ G in/min. Gauge Length ( l j (mm) x-sec' (A.) ( nAArea Q( mm2) kgm/' mm2" 0* kgm mm2 B 120 ( E ) * . 0 0 2 - . 2 13.87 2.98 12. 10. B 96 (A) .002- .2 13.56 2.69 8. 8. B 95 (A) .002-.05 13.22 2.56 10. 10. B 116 (E) .002-.05 13.89 2-33 11. 9 B 115 (E) .002-.01 l i l . 65 2.78 12. 11. B 9k (A) .002-.01 . 13-62 2.70 11. 8 0 , 0 . T = -22 C (251 K) B 98 (A) . 0 0 2 - . 2 1U.30 2.61+ 7- 8. B 97 (A) .002-.05 12.59 2.68 6. 9-B 99 (A) .002-.01 13-52 2.83 7- 9-T = k°C. (277°K) B 89 (A) .002- .2 13-80 2.00 7- 8. B 88 (A) .002-.05 13.05 3-24 6. 8. B 87 (A) . 0 0 2 r , 0 1 13-20 2-75 6. 9-T = 22°C. (295°K) B 86 (A) . 0 0 2 - . 2 13-13 2.6k h. 6. B 123 (0) .002-,05 13-76 2.90 Single Test B 93 (A) .002-.05 13.8 2.52 6. 11. B125 (A) .002-.05 13.87 2.67 6. 10. B128 (A) .002-.05 2.53 7- 7-B 129 (A) .002-.05 Ik.Ql 2.k-2 5- 8. * Petroleum,.Ether (E), A i r (A), O i l (0) - 88 -Specimen A S Gauge Length V-sec' n Area 0t' in/min (lo) (mm) (A.) ( mm2) kgm mm^  • kgm mm^  B 127 (A) .02 - . 1 13-01 2.17 N.D.* N.D. B 82 (A) . 0 0 2 - . 0 2 13-19 1.58 N.D. ' N.D. B 126 (A) .01 - . 0 5 12.95 2.41 N.D. N.D. B ,84 (A) . 0 0 2 - . 0 1 12.91 2.56 6. 13. B 83 (A) . 0 0 2 - . 0 0 5 11.95 2.40 N.D. N.D. 0 ), 0 . T = 57.C (330 K) B 90 (A) . 0 0 2 - . 2 13-63 2.54 5- 9-B 91 (A) .002-v05 13.80 2.87 6. 22 . C r i t i c a l s t r a i n s are recorded i n brackets on the p l o t s . a a The t r a n s i t i o n i n 0 i s a l s o marked w i t h v e r t i c a l arrows (Figs. A2 - A6) * Not Determined (N.D.) A A 30 L B 1 2 0 r\ • -. 0 (k.k) O (5-7) 0 B 95 a - — ^ & a - G T A — - " ~ * h A B 116 © A A (U .2) ' (^) B 115 © • © © _ © 0 —>r —- & - - £ A * . B 9U A A A A I T * ? * (6-3) (1+.6) ( 6 . 1 ) • 1 : _J _i 1 1— 200 1+00 600 O 0 O • 1000 : 1200 - gm/mm2 / T = -63°C. (210°K) F i g . A 2 A ^ r v.s. F i g . A3 AST V . S . ST a a - 9 4 -APPENDIX IV TEMPERATURE-CHANGE EXPERIMENTS cross-head = .002 " / m i n . f o r a l l tes ts Specimen A T ~T~avp- Gauge Length y - s e c ' n area (•C?) (mm) (mm2) B 112 ( E ) * -23 to -52 -37 12.20 3.78 B:..113 (E) + 9 to -25 - 8 12.49 2.88 B 114 (E) -40 to -74 -57 12.61 3.28 B 121 (E) -22 to -92 -57 12.05 3-62 B 122 (A-E) +72 to +11 +42 13-38 3.16 B 124 (0) +73 to +52 +62 14.61 2.62 * Petroleum Ether (E ) , A i r ( A ) , O i l (0) - 95 -APPENDIX V STRESS RELAXATION EXPERIMENTS A l l t e s t s performed i n a i r at ambient temperatures Specimen x-head speed ("Mn.) Gauge Length (mm) Y - s e c ' n area (mm2) A 6 .005 13-07 2.49 A 5 •05 12.72 2.34 B 63 .1 13-66 4.95 B 64 .2 ,13.66 6.77 B 65 .2 14.23 5.48 B 67 >5 13.97 5-97 B 68 •5 \ 14.02 6.26 B 71 •5 12.90 5.42 - 96 APPENDIX VI S t r a i n - r a t e Dependence of The d e v i a t i o n from l i n e a r i t y of the observed values A ^ l v . s . A In G may be due to a dependence of A^T^ upon the average s t r a i n - r a t e . Experiments were performed at ambient temperature f o r A l n £ = constant = 5, over a range of average s t r a i n - r a t e s ( s e e F i g . 2 l ) . The c a l c u l a t i o n s are shown i n the Table below: T = 22 ° C . , = 500 gm/mm2 JJexp. ) mm2 • avg / m m A ^ t h e o r . ) gm/mm2 D i f f e r e n c e gm/mm2 23 .006 23 0 56 .026 U6 + 10 86 . 101 • 66 + 20 / J ( a v § ) gm/mm^ .—• + 10 ^ v - + 20 To study t h i s e f f e c t f u r t h e r , the f o l l o w i n g experiments should be c a r r i e d out . ( i ) e f f e c t of average s t r a i n - r a t e on AW f o r var ious a A In {S = constant v a l u e s . ( i i ) e f f e c t of ^ In r S on AU~" f o r a constant average £1 s t r a i n - r a t e . APPENDIX VII ESTIMATES OF ERROR (a) Specimen•Dimensions The Gaertner t r a v e l l i n g microscope read to 10"3mm. However, due to the rounding o f f of corners d u r i n g p o l i s h i n g , the accuracy was ^10~ 2 mm. For a minimum specimen thickness of 1 . 0 mm, the maximum e r r o r would equal . O l / l . O = 1 . $ . (b) Inst ron chart parameters ( i ) T e n s i l e Tests Maximum f u l l scale load = 2 0 l b s . Accuracy of chart reading = + 0 . 2 of smallest d i v i s i o n = 0.0k l b s . For a minimum load of 2 . 0 l b s . , e r r o r = 0.0k/2 = 2$. ( i i ) A 6 and A T Tests Maximum f u l l scale load = 5 l b s . , Accuracy of chart reading = 0 . 0 1 l b . For a minimum load of 1 l b . , e r r o r = O . O l / l = 1 $ . (c) Deformation Parameters ( i ) Stress I t f o l l o w s from the r e l a t i o n F ( load) A (area) that d ^ = ^ F + ^ A = d F + g d x xr^ F " A F " x From ( i ) and ( i i ) above, the maximum e r r o r equals e ) ^ = 0 . 0 2 + 2 ( 0 . 0 1 ) = 0.0k = 4 $ . ( i i ) Stress change ( AVI) The accuracy i n A^3«. can be estimated by p u t t i n g 2 ( A^rJ = ^ ^ " 2 ± 2 CTi - 98 -The minimum value of A ^ ^ was .1 l b . Hence ~g) (A^ /I) = 0-01 + 0-01 = 0.20 = 20$. i s the maximum e r r o r , (d) Rate Theory I t i s d i f f i c u l t to estimate the maximum e r r o r i n the rate theory c a l c u l a t i o n s . However, i t i s not expected to be much b e t t e r than 25$. - 99 -V I I I . BIBLIOGRAPHY 1. Gilman, J . J . , Johnston, W. G . , " S o l i d State Physics 1 , ' V . 13, T u r n b u l l , D . , ed . (1962) 2. Gilman, J . J . , "Progress i n Ceramic Sc ience" , V. 1, Burke, J . E . , ed . (i960) 3. Johnston, W. G . , "Progress i n Ceramic S c i e n c e " , V . 2, Burke, J . E . , ed . (i960) ' k. Nadeau, J . S . , Johnston, W. G . , J . A p p l . Phys. 32, 2563,(1961) 5. Gilman, J . J . , J . A p p l . Phys. 30, 158k (1959) 6. Gilman, J . J . , Johnston, ¥ . G . , " D i s l o c a t i o n s and Mechanical P r o p e r t i e s of C r y s t a l s " , F i s h e r , J . C. e d . , W i l e y , N.Y. I l 6 (1957) 7. Johnston, W. G . , Gilman, J . J . , J . A p p l . Phys. 31, 632 (i960) 8. Gilman, J . J . , Johnston, W. G . , Sears , G. W., J . A p p l . Phys. 29_, 7^7, (1958) ' 9. Gi lman, J . J . , Johnston, W. G . , J . A p p l . Phys. 30, 129 (1959) 10. Gilman, J . J . , Johnston, W. G . , J . A p p l . Phys, 31, 687 (i960) 11. B a s i n s k i , Z . S . , P h i l Mag. k, 393 (1959) 12. Conrad, H . , J . Iron and S t e e l I n s t . 198, 36k (1961) 13. Seeger, A . , D i s l o c a t i o n s , Ref . 6 p. 272 Ik. Simpson, L . A . , M.Sc . T h e s i s , U n i v . of B . C. (1963) 15. Gregory, D. P . , Acta M e t . , 11, U55 (1963) 16. Gilman, J . J . Ref . (6), p.5kk 17.. Johnston, W. G . , J . A p p l . Phys. 33, 2050 (1962) 18. F l e i s c h e r , R. L . , J . A p p l . Phys. 33, 350^ (1962) 19. Johnston, W. G . , J . A p p l . Phys. 33_, 27l6 (1962) 20. Gilman, J . J . , J . A p p l . Phys. 33_, 2703 (1962) 21. Gilman, J . J . , Johnston, W. G. J . ' A p p l . Phys. 2£, 877 (1958) 22. Nadeau, J . S . , J . A p p l . Phys.. 33_, 3^80 (1962) 23. V a r l e y , J . H. 0 . , Nature 17_4, 886 .(195*0 - 100 -2k. S e i t z , F . , Koehler , J . S . , " S o l i d State P h y s i c s " , V. 2, kk2 (1956) 25. Johnston, W. G . , Gilman, J . J . , J . A p p l . Phys, 3_0, 129 (1959) 26. Johnston, W. G . , Nadeau, J . S . , F l e i s c h e r , R. L . , J . Phys. Soc. Japan, 18, 7 (1963) 27. Johnston, W. G . , S t e i n , D . F . Acta Met 11, 317 (1963) 28. Low, J . R . , "Progress i n M a t e r i a l s S c i e n c e " , V . 12, (1963) 29. Dekker, A . J . , " S o l i d State P h y s i c s " , (1957) 30. Delbecq., C . J . , Pr ingsheim, P . , J . Chem. Phys. 21, 79^ (1953) 31. S c h u l t z , J . M., Washburn, J . , J . A p p l . Phys. 3_1, 1800 (i960) 32. M a c k l i n , E. S . , "Strengthening Mechanisms i n S o l i d s " , A . S . M . Seminar, 375(1962) 33- Gilman, J . J . , Knudsen, C , Walsh, W. , J . A p p l . Phys. £2, 601 (1958) 3k. S e i t z , F . , Adv. i n Phy. 1, H-3 (1952) 35- See Ref . (36), P. 116 36. P r a t t , P . L , I n s t , of Metals Monograph (1958) 37- Estermann, I . , Phy. Rev. 75, 627 U9 k9) 38. Dekker, A . J . , Ref .(29), p. 178 39- S e i t z , F . , Phy. Rev. 80, 239 (1950) kO. Van Buren, H . G . , "Imperfect ions i n C r y s t a l s " , (i960) kl. H i b i , H . , Yada, K . , J . A p p l . Phys. 3J}, 3530 (1962) k2. Gilman, J . J . , " F r a c t u r e " , M . I . T . Tech. Press H-3. Conrad, H . , Hayes, W. Trans A . S . M . 56, 2k9 (1963) kk. Hoover, D . , Washburn, J . , J . A p p l . Phys. 33, 11 (1962) H-5- F e u e r s t e i n , S . , Parker , E . R . , M i n e r a l s Research Laboratory , U n i v . of C a l i f . , Ser ies # 150, #5 (1962) 46. Westwood, A . R . C . , P h i l Mag. 5, 981 (i960) kT. A l d e n , T . H . , Trans A . I . M . E . , 230, 6U9 (196U) - 101 -k-8. Westwood, A . R . C . , p r i v a t e communication k9. Westwood, A . R. C , P h i l Mag, £ , 633 (1962) 50. Mar t inson , R. H . , M . A . S c . T h e s i s , U n i v . of B . C . (1963) 51. Wu, T . L . , Smoluchowski, R . , Phy. R e v . , 78, 468 (1950) 52.".. Gilman, J . J . , Trans A . I . M . E , 1217 (1953) 53. H i k a t a , A . , Elbaum, C , J . A p p l . Phys. 34, 2151+ (1963) 54. Krantz , T . , M . A . Sc T h e s i s , U n i v . of B . C . (1964) 55. B u c k l e r , H . , Proc . Powder Met. C o n f . , N.Y. 221 (i960) 56. Nadeau, J . S . , P h . D . T h e s i s , U n i v . of C a l i f , (1959) ( a v a i l a b l e i n U . B . C . L i b r a r y - u f i l m - #562) 57- P h i l l i p s , W. L . , Trans . A . I . M . E . , 224, 434 (1962) 58. Conrad, H . , Trans A . S . M . 5j5, 945 (1963) 59- Conrad, H . , F r e d e r i c k , S . , Ac ta Met 10, 1013 (1962) 60. P r a t t , P . L . , Acta Met. 1, 103 (1953) 61. Nabarro, F . R . N . , Ref . (6), p. 235 62. Van Buren, H . G . , Ref . (40), p. l66 63. Washburn, J . , Grooves, J . , Kelby , A . , W i l l i a m s o n , G . K . , P h i l Mag, 5, 991 (i960) 64. Kear , B . H . , T a y l o r , A . , P r a t t , P . L . , P h i l Mag. 4, 665 (1959) 65. Haasen, P . , P h i l Mag 3, 38U (1958) 66. B a s i n s k i , Z . S . , C h r i s t i a n , J . W., A u s t . J . Phys. 13, 299 (i960) 67. Mordike, B . L . , Haasen, P . , P h i l Mag 7, ^59 (1962) 68. Causey, A . , M . A . Sc T h e s i s , U n i v . of B . C . (1963) 69. Seeger, A . , "Conference i n Defects i n C r y s t a l l i n e S o l i d s " , Phy. Soc. London (195*0 70. F r i e d e l , J . , " I n t e r n a l Stresses and Fat igue i n M e t a l s " , 220 (1958) 71. Gilman, J . J . , Ref . (2), p. l66 72. P r a t t , P . L . , I n s t . Metals Monograph 23, 99 (1957) - 102 -73- Eshleby, J. D., Newey, C , Pratt, P.L., Lidiard, A.B., Phil. Mag. 3, 75 (1958) 7 k . N.F. Mott, Trans A.I.M.E. 218, 962 (i960) 75. Haven, Y. Rec. trav. chim. Pays - Bas, 6_£, 1V71. (1950) 76. Breckenridge, R.G., "Imperfections on Nearly Perfect Crystals", p. 219 (1952), Wiley, N.Y. 77. Feltham, P., J . Inst. Metals, 8j?, 210 (1960/61) 78. R. Chang, J. Appl. Phys. 3JJ, 858 (1962) 79. Conrad, H., Hays, G., Schoeck, G.-., Wiedersick, H., Acta Met. 367 (1961) 80. B e l l , R.L., Banfieia, W., Phil Mag. % 9 (196k) 81. McLean, D., "Mechanical Properties of Metals", (1962) Wiley, N.Y. 82. Johnston, T.L., Stbkes, R.J., L i , C.H., Phil. Mag, h, 1316 (1959) 83. Stokes, R.J., Johnston, T.L., L i , C.H., J. Appl. Phys. 3jJ, 62 (1962) 

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