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UBC Theses and Dissertations

The growth and deformation of cobalt crystals Davis, Keith Gordon 1961

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THE GROWTH AND DEFORMATION OF COBALT CRYSTALS by KEITH GORDON DAVIS A THESIS SUBMITTED IN PARTIAL FMLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of MINING AND METALLURGY We accept t h i s t h e s i s as conforming t o the standard r e q u i r e d from candidates f o r the -degree of DOCTOR OF PHILOSOPHY Members of the Department of Mining and M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA October, 1961 In presenting 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 a t 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 o f t h i s t h e s i s f o r s c h o l a r l y purposes may be 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 . I t 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 permission. Department of r ) t ^ ~ ^ st rU.fcU\Jv><iy Tho U n i v e r s i t y o f B r i t i s h Columbia, Vancouver £>, Canada. D a t e 8 K K r m A f ^ ^ r 1 9 6 1  PUBLICATIONS I V f i "The Growth of Cobalt Crystals for Deformation Studies," K G Davis, E Teghtsooman, Trans A I M E , in the press FACULTY OF GRADUATE STUDIES * PROGRAMME OF THE F INAL O R A L E X A M I N A T I O N FOR THE DEGREE OF D O C T O R OF PH ILOSOPHY of KEITH GORDON DAVIS B Sc University of Birmingham M A Sc University of British Columbia EV ROOM 201, MINING BUILDING MONDAY, NOVEMBER 6, 1961, at 1 pan. COMMITTEE IN CHARGE Chairman F H SOWARD W M ARMSTRONG R BARRIE C A BROCKLEY F A FORWARD L G HARRISON J A H LUND K D NAEGELE E TEGHTSOONIAN External Examiner B CHALMERS Harvard University GROWTH AND DEFORMATION OF COBALT CRYSTALS ABSTRACT Cobalt crystals of commercial purity have been grown in an electron beam zone refiner They were tested in tension at tempera-tures between 150°C and -196°C The resolved shear stress—shear strain curves are similar in form to those for the high stacking-fault energy hexagonal metals zinc, cadmium, and magnesium There is an initial linear region for shear strains up to around 150%, with a ratio of work hardening slope to shear modulus of about 2 x 10 This is followed by an upturn, which is, however, smaller in magni-tude for cobalt than for the other metals Values for the critical re-solved shear stress vary from 97 Kg/cm at room temperature to approximately 170 Kg/cm 2 at -196°C Two crystals of high purity cobalt were also tested, giving a critical resolved shear stress at room temperature of 65-70 Kg/cm 2 The Cottrell-Stokes law is not obeyed, either for temperature changes between -196°C and 18°C or for changes in the strain rate at room temperature An explanation in terms of dislocation theory has been put forward Activation energies for plastic flow have been tentatively evaluated to be of the order of 35 kr ', Twinning was neve^  observed m crystals pulled at room tem-perature Deformation twins produced by bending a crystal at -196°C took two forms, very thin'ones similar in appearance to Neumman bands in iron, and more .usual lenticular twins The thin twins have a 1121 habit plane Metallographic examination of crystals pulled to large extensions and' electropolished to remove slip lines showed small needle-like markings, probably fine twins In addition to the deformation work, certain observations have been made concerning transformation markings which supplement the work of previous investigators It was found that secondary transformation markings are not a necessary part of the transforma-tion, and that primary markings form on cooling as well as on heating GRADUATE STUDIES Field of Study Metallurgy Nuclear Metallurgy Phase Transformations Gram Boundaries Theory of Alloys Metallurgical Themodynamics Metallurgical Kinetics Structure of Metals Diffusion Other Studies Statistical Mechanics Sohd State Physics Chemical Kinetics Introductory Quantum Mechanics V Griffiths, D R Wiles W M Armstrong E Teghtsoonian V Griffiths C S Samis . E Peters V Griffiths E Teghtsoonian V Gntfitns L G Harrison J B Gunn J Halpern, G B Porter W Opechowskt Techniques in Low Temperature Physics J B Brown ABSTRACT C o b a l t c r y s t a l s o f c o m m e r c i a l p u r i t y h a v e b e e n grown i n a n e l e c t r o n beam zone r e f i n e r . T h e y w e r e t e s t e d i n t e n s i o n a t t e m p e r a t u r e s b e -t w e e n 150°C and -196°C, The r e s o l v e d s h e a r s t r e s s — s h e a r s t r a i n c u r v e s a r e s i m i l a r i n f o r m t o t h o s e f o r t h e h i g h s t a c k i n g - f a u l t e n e r g y h e x a g o n a l m e t a l s z i n c , c admium, a n d m a g n e s i u m . T h e r e i s a n i n i t i a l l i n e a r r e g i o n f o r s h e a r s t r a i n s up t o a r o u n d 150%, w i t h a r a t i o o f w o r k h a r d e n i n g s l o p e t o s h e a r -4-modulus o f a b o u t Z x J O . T h i s i s f o l l o w e d b y a n u p t u r n , w h i c h i s , h o w e v e r , s m a l l e r i n m a g n i t u d e f o r c o b a l t t h a n f o r t h e o t h e r m e t a l s . V a l u e s f o r t h e c r i t i c a l r e s o l v e d s h e a r s t r e s s v a r y f r o m 97 K g / c m 2 a t room t e m p e r a t u r e t o a p p r o x i m a t e l y 170 K g / c m 2 a t -196°C. Two c r y s t a l s o f h i g h p u r i t y c o b a l t w e r e a l s o t e s t e d , g i v i n g a c r i t i c a l r e s o l v e d s h e a r s t r e s s a t room t e m p e r a t u r e o f 65-70 K g / c m 2 . The C o t t r e l l - S t o k e s l a w i s n o t o b e y e d , e i t h e r f o r t e m p e r a -t u r e changes b e t w e e n -196°C a n d l 8 ° C . o r f o r changes i n t h e s t r a i n r a t e a t room t e m p e r a t u r e . A n e x p l a n a t i o n i n t e r m s o f d i s l o c a t i o n t h e o r y has b e e n p u t f o r - w a r d * A c t i v a t i o n e n e r g i e s f o r p l a s t i c f l o w have b e e n t e n t a t i v e l y e v a l u a t e d t o be o f t h e o r d e r o f 35 k T . T w i n n i n g was n e v e r o b s e r v e d i n c r y s t a l s p u l l e d a t room t e m p e r a t u r e . D e f o r m a t i o n t w i n s p r o d u c e d b y b e n d i n g a c r y s t a l a t -196°C. t o o k two f o r m s , v e r y t h i n ones s i m i l a r i n a p p e a r a n c e t o Neumman b a n d s i n i r o n , a n d more u s u a l l e n t i c u l a r t w i n s . The t h i n t w i n s have a {ll2l}h a b i t p l a n e . M e t a l l -o g r a p h i c e x a m i n a t i o n o f c r y s t a l s p u l l e d t o l a r g e e x t e n s i o n s a n d e l e c t r o -p o l i s h e d t o remove s l i p l i n e s showed s m a l l n e e d l e - l i k e m a r k i n g s , p r o b a b l y f i n e t w i n s . I n a d d i t i o n t o t h e d e f o r m a t i o n w o r k , c e r t a i n o b s e r v a t i o n s have b e e n made c o n c e r n i n g t r a n s f o r m a t i o n m a r k i n g s w h i c h s u p p l e m e n t t h e w o r k o f p r e v i o u s i n v e s t i g a t o r s . I t was f o u n d t h a t s e c o n d a r y t r a n s f o r m a t i o n m a r k i n g s a r e n o t a n e c e s s a r y p a r t o f t h e t r a n s f o r m a t i o n , a n d t h a t p r i m a r y m a r k i n g s f o r m o n c o o l i n g as w e l l as o n h e a t i n g . ACKNOWLEDGEMENT The a u t h o r i s g r a t e f u l f o r t h e a d v i c e a n d encouragement g i v e n b y h i s r e s e a r c h d i r e c t o r , D r . E . T e g h t s o o n i a n , f o r t e c h n i c a l a s s i s t a n c e g i v e n b y M r . R . G . B u t t e r s , a n d f o r h e l p f u l d i s c u s s i o n s w i t h f e l l o w g r a d u a t e s t u d e n t s . F i n a n c i a l a s s i s t a n c e was r e c e i v e d f r o m t h e D e f e n c e R e s e a r c h B o a r d a n d i n t h e f o r m o f a n I n t e r n a t i o n a l N i c k e l C o . F e l l o w s h i p . TABLE OF CONTENTS Page INTRODUCTION THE DEFORMATION OF HEXAGONAL METAL CRYSTALS - A LITERATURE SURVEY . . . 2 3_. I n t r o d u c t i o n .oof l««oo. . . .Bo«« .««o . o . . . . . . . . . . . . . . . . . 0 2 2. Modes o f S l i p . . . . . . . a . . . . . . . . . . . • • • • • • • • • « « • • • • • • • • 3 3. V a l u e s f o r t h e C r i t i c a l R e s o l v e d S h e a r S t r e s s . . . . . . . . 3 k„ R e s o l v e d S h e a r S t r e s s - S h e a r S t r a i n C u r v e s 6 5. S h e a r T e s t s 10 6. The R e c o v e r y o f P r o p e r t i e s on A n n e a l i n g 10 7. L a u e A s t e r i s m 11 8. The E f f e c t o f S u r f a c e C o n d i t i o n 11 9. The N a t u r e o f " P r e - Y i e l d " S t r a i n 12 10. C h a n g e - m - s t r a i n - r a t e a n d C h a n g e - m - T e m p e r a t u r e . . . . . T e s t s o n M a g n e s i u m 12 H • C OITJIlSri"bS ooo«oo»«««oooo*oo.>a<ioooooo«>.»ooo.>o»o«©»>**.>oo« 13 ANALYSIS OF THE MATERIAL . . . . . . . . . . . . . . . . . . . . . . . . . . J.6 GROWTH OF THE CRYSTATS • •ooooooo«»ec-ooo«**eo»ooooo«*oco«o<>«e«.>«e(>.>eo UJ EXPERIMENTAL PROCEDURE 23 1. E l e c t r o p o l i s h i n g 23 2. E t c h i n g .25 3. E l e c t r o m a c h i n i n g 25 • O l * l SXl"fc £li"t 1 O H O f "fcllS CX*yS"fccllS o**»eo.>o0«oQao»oo«ooQooo»*o 5 • T G n S l l S TSS"blXl^ »a«oo*ooa»ao«««««oB«ot>*«aaa««oaeoa<i«* 9^ a) Measurement o f C r o s s - S e c t i o n 29 b ) G r i p p i n g 29 c ) T e s t i n g P r o c e d u r e 30 d) T e m p e r a t u r e C o n t r o l 32 e) D e t e r m i n a t i o n o f t h e F l o w - S t r e s s T e m p e r a t u r e C u r v e s 32 TABLE OF CONTENTS CONTINUED Page RESULTS OF THE TENSILE TESTS 35 1. S t r e s s - S t r a i n Curves 35 2. Values f o r the C r i t i c a l Resolved Shear S t r e s s 35 3. V a r i a t i o n of the Flow S t r e s s w i t h Temperature kl h. V a r i a t i o n of the Flow S t r e s s w i t h S t r a i n Rate k2 5. Work Hardening Slope kty a) At Room Temperature k$ b) V a r i a t i o n w i t h Temperature L9 c) V a r i a t i o n w i t h S t r a i n Rate 52 6. O r i e n t a t i o n E f f e c t s 5^  METALLOGRAPHIC OBSERVATIONS 56 1. S l i p Lines and Deformation Markings 56 2. Twinning 59 3 • F r a c t u r e 62 LAUE ASTER ISM AND RECOVERY 66 DISCUSSION OF THE TENSILE TEST DATA 69 1. Theories of G l i d e and Work-Hardening i n Metals 69 2. I n t e r p r e t a t i o n of the Re s u l t s of the Present Work .... 70 a) V a r i a t i o n of the Work-Hardening Slope w i t h Temperature 70 b) Non-Observance of the C o t t r e l l - S t o k e s Law .. 71 THE COBALT TRANSFORMATION 77 1. I n t r o d u c t i o n 77 2. Observations and D i s c u s s i o n 78 SUMMARY AND CONCLUSIONS 86 SUGGESTED FUTURE WORK 88 TABLE OF CONTENTS CONTINUED Page APPENDICES I . E l e c t r o p l a t i n g Cobalt on Cobalt 89 I I . Determination of Resolved Shear Stress-Shear S t r a i n Curves 90 I I I . Determination of the Habit Plane f o r Deformation Twins. 92 IV. Shear Moduli f o r C o b a l t - C r y s t a l s 99 V. A c t i v a t i o n Energy f o r S l i p 101 1. Theory 101 2. Experimental Determination 10k BIBLIOGRAPHY 110 FIGURES No,. Page 1. Variation of the C r i t i c a l Resolved Shear Stress with Temperature for Magnesium 5 2. Variation of the C r i t i c a l Resolved Shear Stress with Temperature for Zinc 5 3. Variation of the C r i t i c a l Resolved Shear Stress with Temperature for Cadmium 5 k. Resolved Shear Stress-Shear Strain Curves for Zinc at Room Temperature 7 5- Variation of the Work-Hardening Slope with Temperature for Z i n c 8 6. Typical Stress-Strain Curve for a Hexagonal Metal Ik 7. AS versus £ for Magnesium at 200°K, from Change-in-Strain-Rate Experiments 15 8. Results of Change-in-Stram-Rate Experiments for Magnesium .... 15 9. Axes of the Zoned Cobalt Crystals 21 10. Standard Cubic Stereogram, Showing Areas containing no Pole more than 60° from one of the ( i l l ) Poles 22 11. Surface Spirals after a Hydrochloric Acid-Methyl Alcohol Electropolish 2k 12. The Electromachining Apparatus 26 13. The Testing Assembly showing a Crystal mounted m the Rotating Grips 31 ik. Derivation of the Load-Elongation Plot for a Typical Crystal 33 15- Load-Extension Plot for Crystal 10 during the First-Cycle 3^ 16. Stress-Strain Curves for Cobalt Crystals at Room Temperature .. 36 17. Resolved Shear Stress-Shear Strain Curves for Cobalt Crystals .. 37 18. Resolved Shear Stress-Shear Strain Curves for the series S-H Crystals 38 19. C r i t i c a l Resolved Shear Stress for Cobalt Crystals 39 20. C r i t i c a l Resolved Shear Stress for the Cobalt Series S-H Crystals ^0 FIGURES CONTINUED No. Page 21. V a r i a t i o n of the Flow Stress with Temperature 43 22. f o r Change-in-Temperature Tests between Room Temperature * « x and -196°C 44 23. Load-Elongation P l o t f o r C r y s t a l 12 45 24. at Room Temperature f o r Changes m Cross-Head Speed between 0.2 and 0.002 ms/min 47 25. ^ - ^ 3 at Room Temperature f o r Changes m Cross-Head Speed between 0.2 and 0.002 ins/min. p l o t t e d against 3 . . 48 2 6 . Values f o r the Work-Hardening Slope f o r C r y s t a l 10 51 27. Resolved Shear Stress-Shear S t r a i n P l o t s , and Curves f o r Change-m-Temperature Tes t s , f o r Magnesium 53 28. C r y s t a l s 12, 23 a f t e r Extension 55 29. "Deformation Markings" i n deformed Cobalt 57 30. Specimen Extended, E l e c t r o p o l i s h e d , and Annealed f o r \ hour at 600°C 58 31. Twins i n C r y s t a l 7 60 32. Twins at a Sub-boundary i n C r y s t a l 9 60 33. Two Types of Twin Traces i n a C r y s t a l bent at -196°C 6l 34. Twin " r e f l e c t i n g " from a Pa i r of Grain boundaries 6l 35- Positions of the { i l l ] Planes i n a standard Octahedral Pr o j e c t i o n f o r a Cubic Structure 63 36. The Two Possible Positions f o r a Twin Plane Derived from a Cubic C r y s t a l by the Cubic — > Hexagonal transformation. 64 37• Fracture Surface of a Cobalt-Crystal 65 38. Laue P i c t u r e of a C r y s t a l extended to around 200$ Shear S t r a i n . . 67 39. Laue back-reflect!on P i c t u r e of a C r y s t a l extended to the order of 200$ Shear S t r a i n followed by an Anneal f o r £ hour at 600°C 68 40. Two Hypothetical States f o r the D i s t r i b u t i o n of Dis l o c a t i o n s i n the S l i p Plane 75 41. Transformation Markings i n P o l y e r y s t a l l i n e Cobalt 79 FIGURES CONTINUED N o . h2. ' A s - G r o w n S u r f a c e o f a Z o n e - R e f i n e d R o d . S e c o n d a r y T r a n s f o r m a t i o n M a r k i n g s n e a r a G r a i n B o u n d a r y 79 U3. A s - G r o w n S u r f a c e o f a Z o n e - R e f i n e d R o d . P r i m a r y a n d S e c o n d a r y T r a n s f o r m a t i o n M a r k i n g s n e a r a S u b - B o u n d a r y 80 hk. A s - G r o w n S u r f a c e o f a Z o n e - R e f i n e d R o d . . . . . 80 U5. S e c t i o n a l V i e w o f A p p a r a t u s f o r T a k i n g X - R a y B a c k -R e f l e c t i o n P i c t u r e s o f t h e H i g h T e m p e r a t u r e P h a s e . . . . 8l k6. Laue B a c k - R e f l e c t i o n P i c t u r e s o f t h e same I C r y s t a l t a k e n a t Room T e m p e r a t u r e and a t a p p r o x i m a t e l y 600°C 82 V7. H e a t i n g a n d C o o l i n g C u r v e s f o r t h e A n n e a l e d C r y s t a l s 84 hQ. A S t a n d a r d (0001) S t e r e o g r a m f o r H e x a g o n a l C o b a l t , s h o w i n g t h e P o s i t i o n s o f t h e { l l l \ C u b i c P l a n e s a n d t h e >{ll2l} H e x a g o n a l P l a n e s 85 k$. The C r y s t a l G o n i o m e t e r , w i t h a S p e c i m e n i n P o s i t i o n 93 50. A r r a n g e m e n t o f t h e G o n i o m e t e r i n f r o n t o f t h e X - R a y U n i t and u n d e r t h e B e n c h M i c r o s c o p e 95 51. P l o t o f t h e D i r e c t i o n s o f t h e T w i n T r a c e s 96 52. The T w i n H a b i t P l a n e s i n a s t a n d a r d (OOOl) C o b a l t P r o j e c t i o n . . 97 53« Laue B a c k - R e f l e c t i o n X - R a y P i c t u r e o f t h e C r y s t a l u s e d f o r T w i n O r i e n t a t i o n 98 54. I l l u s t r a t i o n o f t h e A c t i v a t i o n E n e r g i e s R e q u i r e d t o f r e e a D i s l o c a t i o n f r o m a L o c k i n g M e c h a n i s m w i t h F o r c e C u r v e F ( x ) 102 55• F l o w S t r e s s V e r s u s T e m p e r a t u r e f o r C r y s t a l 10, w i t h a n E s t i m a t e d C u r v e f o r a s t r a i n R a t e 100 x G r e a t e r 105 56. — v e r s u s l o g ^ Q £ > t h e V a l u e s b e i n g t a k e n f r o m F i g u r e 55 •••• 106 57. P l o t o f u/k V e r s u s T 108 TABLES Wo. Page I Work Hardening Slopes f o r Zinc C r y s t a l s at -l83°C 9 II Values f o r 6/G ~9 I I I Orientations f o r the Large C r y s t a l s 28 IV Orientations f o r the Johns on-Mat they Crystals 28 V Orientations f o r the Series S-H Crystals 29 VI C r i t i c a l Resolved Shear Stress at -196°C hi VII E f f e c t of S t r a i n Rate on Flow Stress i n C r y s t a l 12 h6 VT.H Values f o r the Work-Hardening Slope i n F i g . 7 h$ IX Work-Hardening Slopes f o r Cr y s t a l s 3, 11 50 X Work-Hardening Slopes f o r C r y s t a l 10 50 XI V a r i a t i o n i n Work-Hardening Slope with S t r a i n Rate 52 XII C a l c u l a t i o n of Resolved Shear S t r a i n Corresponding to 10.inches on the S t r a i n Axis of the Instron Chart 91 XIII Measurements Corresponding to F i g . 5° 9 2 XIV S t i f f n e s s C o e f i c i e n t s f o r Cobalt at 25°C 99 XV A c t i v a t i o n Energies of S l i p i n Cobalt 107 -1-I1WR0DUCTI0N P l a s t i c d e f o r m a t i o n i n m e t a l s i n g l e c r y s t a l s w i t h c l o s e -p a c k e d s t r u c t u r e s ha s b e e n f o u n d s t r o n g l y d e p e n d e n t on s t a c k m g - f a u l t e n e r g i e s . A l o w s t a c k i n g - f a u l t e n e r g y a l l o w s d i s l o c a t i o n s t o d i s s o c i a t e i n t o w i d e l y s e p a r a t e d p a r t i a l s , r e s u l t i n g m two i m p o r t a n t e f f e c t s : -a) i t i s d i f f i c u l t f o r a d i s l o c a t i o n t o e s c a p e f r o m i t s s l i p p l a n e b ) g r e a t e r s t r e s s e s a r e n e e d e d f o r d i s l o c a t i o n i n t e r s e c t i o n s . B o t h e x p e r i m e n t and t h e o r y a r e f a i r l y w e l l a d v a n c e d i n t h e c a s e o f f a c e -c e n t r e d c u b i c m e t a l s , b u t f o r h e x a g o n a l m e t a l s t h e f i e l d i s l e s s w e l l d e v e l o p e d . The h i g h s t a c k i n g - f a u l t e n e r g y h e x a g o n a l m e t a l s m a g n e s i u m , z i n c , a n d cadmium, have b e e n q u i t e e x t e n s i v e l y t e s t e d , b u t up t o now no d a t a have b e e n a v a i l a b l e f o r a c o m p a r a b l e l o w s t a c k m g - f a u l t e n e r g y h e x a g o n a l m e t a l . A n i n v e s t i g a t i o n i n t o t h e p l a s t i c d e f o r m a t i o n o f c o b a l t , w h i c h has a v e r y l o w s t a c k m g - f a u l t e n e r g y , has t h e r e f o r e b e e n u n d e r t a k e n . -2-THE DEFORMATION OF HEXAGONAL METAL CRYSTALS A LITERATURE SURVEY 1. Introduction There is a large body of data on deformation behaviour i n the hexagonal metals, a complete survey of which would be impracticable. In the following the principal experimental results w i l l be outlined, leaving theory for the discussion. For the sake of completeness, some data are included that do not apply directly to the present work. The notation used is as follows:-© = the work hardening slope the resolved shear stress 6 = the shear strain € = the strain rate % = the angle between the tension axis and the normal to the s l i p plane The following are the c/a ratios for the common hexagonal metals--Metal Be Ti Re Co Mg Zn Cd Ideal c/a 1.568 1.600 1.615 1.623 1.624 I.856 1.886 1.633 Only magnesium, zinc and cadmium have been studied i n any detail for their single crystal p l a s t i c i t y , and the discussion w i l l be largely restricted to these metals. They a l l have high stacking-fault energies. From data on creep at low temperatures, Thornton and Hirsch"*" have derived minimum energies of 130 ergs/cm^ for cadmium and 250 ergs/cm^ for zinc; from similar data on cobalt they obtained a stackmg-fault energy of around 25 ergs/cm^. The existence of a phase transformation from .close-packed hexagonal to face-centred cubic at 400°C. demonstrates that the stacking-fault energy m cobalt at room temperature must be very small. - 3 -2 . Modes o f S l i p M a g n e s i u m , z i n c a n d cadmium a l l s h e a r mos t e a s i l y a c r o s s t h e i r b a s a l p l a n e s , w i t h s l i p e l e m e n t s (OOOl) <(ll20) . I n g e n e r a l , a c / a r a t i o l o w e r t h a n i d e a l l e a d s t o e a s i e r s l i p i n n o n - b a s a l p l a n e s . W i t h c / a above i d e a l , t h e atoms a r e c l o s e - p a c k e d i n t h e i r b a s a l p l a n e s . p Magnes ium R e e d - H i l l a n d R o b e r t s o n , t e s t i n g c r y s t a l s u n s u i t e d t o b a s a l g l i d e , f o u n d p r i s m a t i c s l i p {lOlo} { l l 2 0 ) i s d o m i n a n t a t l o w t e m p e r a t u r e s . A t h i g h t e m p e r a t u r e s p y r a m i d a l {1013} (1120) s l i p t a k e s o v e r . Z i n c B e l l a n d Cahn3 p u l l e d z i n c c r y s t a l s w i t h % - 8 5 - 8 8 0 . A n o n - b a s a l s l i p s y s t e m {1122} ^1123^ was o b s e r v e d . T h i s i s r a t h e r r e m a r k a b l e , f o r n e i t h e r t h e s l i p p l a n e n o r t h e s l i p d i r e c t i o n a r e u n u s u a l l y c l o s e - p a c k e d . I t has b e e n s u g g e s t e d t h a t t h e s l i p p l a n e i s i n f a c t i r r a t i o n a l . A t h i g h e r t e m p e r a t u r e s b o t h p r i s m a t i c a n d p y r a m i d a l s l i p t a k e p l a c e . Cadmium B r o w n has o b t a i n e d e v i d e n c e ^ f o r n o n - b a s a l s l i p i n cadmium, o b -s e r v i n g c o n n e c t i n g s l i p b y e l e c t r o n m i c r o s c o p y . B e r y l l i u m , r h e n i u m a n d t i t a n i u m I n t h e s e m e t a l s , w i t h l o w c / a r a t i o s , n o n - b a s a l s l i p i s common.5 3 . V a l u e s f o r t h e C r i t i c a l R e s o l v e d S h e a r S t r e s s C r i t i c a l r e s o l v e d s h e a r s t r e s s e s a r e s e n s i t i v e t o s t r u c t u r e and t o s m a l l q u a n t i t i e s o f i m p u r i t y ; w i d e v a r i a t i o n s a r e f o u n d i n r e p o r t e d v a l u e s . A l t h o u g h d a t a g i v e n m t h i s s e c t i o n r e f e r t o h i g h - p u r i t y m e t a l s , t h e y s h o u l d b e t a k e n o n l y as a r o u g h g u i d e . Magnes ium B u r k e and H i b b a r d ^ f o u n d a s t r e s s o f k.6 K g / c m 2 f o r b a s a l s l i p . R e e d - H i l l and R o b e r t s o n 2 f o u n d t h e r a t i o o f n o n - b a s a l s l i p s t r e s s t o b a s a l s l i p s t r e s s t o b e f a i r l y c o n s t a n t b e l o w 0 ° C , w i t h a v a l u e o f 8 5 . The r a t i o d r o p s t o a r o u n d 3 at"* 2 8 6 °C . -Im-p u r e s h e a r t e s t s g i v e ? a c r i t i c a l s h e a r s t r e s s f o r b a s a l s l i p o f 3-5 K g / c m 2 . Z i n c B a s a l s l i p 3 , 5.0 K g / c m 2 (1122} (1123) s l i p 3 , 100 t o 150 K g / c m 2 8 ? P u r e s h e a r t e s t , b a s a l s l i p , 2.1 K g / c m Cadmium B a s a l slip9 ->»1.5 K g / c m 2 8 2 P u r e s h e a r t e s t , 3-9 K g / c m V a r i a t i o n o f t h e c r i t i c a l r e s o l v e d s h e a r s t r e s s w i t h t e m p e r a t u r e — D a t a on t h e c r i t i c a l r e s o l v e d s h e a r s t r e s s have b e e n s u m m a r i s e d i n F i g u r e s 1, 2, 3« V a l u e s d r o p w i t h r i s e i n t e m p e r a t u r e , t h e r a t e o f d e c r e a s e b e i n g l o w e r a t h i g h e r t e m p e r a t u r e s . k. R e s o l v e d S h e a r S t r e s s - S h e a r S t r a i n C u r v e s I n g e n e r a l , f o r h e x a g o n a l m e t a l s w i t h "X b e l o w a b o u t 55° g e o m e t r i c a l s o f t e n i n g i s g r e a t e r t h a n w o r k h a r d e n i n g a n d a n u n s t a b l e s l i p p r o c e s s r e s u l t s , w i t h t h e f o r m a t i o n o f a k i n k band- ' - 3 . V a l u e s o f "X so l a r g e t h a t t h e b a s a l p l a n e s . a r e e n t i r e l y h e l d i n t h e g r i p s a r e t o b e a v o i d e d i f b a s a l s l i p i s t o b e i n v e s t i g a t e d . A r a n g e o f "X. b e t w e e n 50° and 80° i s t h e r e f o r e n o r m a l l y u s e d i n d e r i v i n g t h e f o l l o w i n g d a t a . The s t r e s s - s t r a i n c u r v e s f o r z i n c , cadmium and magnes ium a l l show a n i n i t i a l l i n e a r r e g i o n , f o l l o w e d a t s h e a r s t r a i n s b e t w e e n 100$ a n d 200$ b y a s h a r p b e n d u p w a r d s . I t s h o u l d be n o t e d t h a t , c o n t r a r y t o t h e r e v i e w a r t i c l e s b y S e e g e r - ^ and b y C l a r e b r o u g h and H a r g r e a v e s ^ t h e t w o - s t a g e c u r v e i s n o t r e p l a c e d b y a l i n e a r c u r v e a t l o w t e m p e r a t u r e . I n f a c t Boas and S c h m i d o b s e r v e d a t w o - s t a g e c u r v e i n cadmium a t 20°K and B a s i n s k i - ' - ^ shows a t w o - s t a g e c u r v e f o r magnes ium a t 60°K. T h e r e i s no s y s t e m a t i c o r i e n t a t i o n d e p e n d e n c e , e x c e p t t h a t i n z i n c t h e w o r k h a r d e n i n g s l o p e i n t h e f i r s t l i n e a r r e g i o n i s i n c r e a s e d and t h e u p t u r n i n t h e s t r e s s - s t r a i n c u r v e r e a c h e d e a r l i e r i f two s l i p F i g . 1 -5-F i g . 2 F i g ..3 F I G S . 1, 2, 3* V a r i a t i o n o f t h e C r i t i c a l R e s o l v e d S h e a r S t r e s s w i t h T e m p e r a t u r e . F i g . 1 magnes ium R e p r o d u c e d f r o m . R e f . 10 F i g . 2 z i n c R e p r o d u c e d f r o m R e f . 11 F i g . 3 Cadmium R e p r o d u c e d f r o m . R e f . 12 directions are equally, favoured . (see figure k) Seeger has indicated that for the hexagonal metals v is constant below the recovery range of temperature. There is l i t t l e evidence for this. Scatter i n the data is very large (see for example table 1, taken from ref. 17). Only for zinc are a high number of values available, and i t can be seen from f i g . 5 that the constancy of 9 is debatable. The ratio where 8 is the slope of the f i r s t linear stage below the recovery range of temperature and G is the r i g i d i t y modulus, has been found to have a similar value for zinc, cadmium and magnesium, of the order 1.5 X 10"^ ". Actual figures are given i n table 2. Very similar values for ®/G obtain for face-centred cubic crystals i n the easy glide region. Strain Rate Effects Magnesium No tests have been carried out on the effect of strain rate on the stress-strain curve. Tests i n which the change m flow stress with a change m strain rate was measured during a test w i l l be described i n a later section. Cadmium At room temperature and above an increase m the strain rate 12 raises both the work hardening slope and the flow stress . At room temperature a hundred-fold increase m the strain rate causes an increase i n flow stress of 20-30$. At -l85,-253°C. the effect i s very much smaller, an increase of approximately a 100 times having no signi-ficant effect on the stress-strain curves. Zinc At room temperature, similarly to cadmium, the strain rate has a very c r i t i c a l effect both on 6 i n both linear regions and on the flow stress 1^. No strain rate variation experiments have been done at low temperature. -7-[mo] i 6 i > r" / ^112 31 . 103 ,128 i i i e 92-.* .157, 21. 38 HO* HI 15. 4 1 . ' 3 ' « l t 2 V „ , 62 0 115 B 3 111 / / / 116B/6 j J 62C/V I ffy™— /// ,7v /fas / V - —^^t /A/f/U / 1,7 FIG. k. Resolved Shear Stress--Shear S t r a i n Curves f o r Zinc at Room Temperature. The Orientations of the Axes of the Cr y s t a l s are shown i n the Stereogram at the L e f t . Reproduced from Ref. 5. -8-0 23 123 173 223 Temperatur in *K FIG. 5. V a r i a t i o n of Work Hardening Slope 6 with Temperature f o r Zinc. Taken From Ref. 2 , . U n i t s of 8 are gm/m.m. / Unit Shear S t r a i n . -9-TABLE I Work H a r d e n i n g S l o p e s f o r Z i n c C r y s t a l s a t -l83 °C, m K g / c m 2 , t a k e n f r o m R e f . "17. 3^ .3 35.8 .40.7 35-6 30.9 38.9 37-7 33-9 34.5 28.2 34.6 35-0 38.8 46.6 TABLE II V a l u e s f o r 9/G ( x l O ) , G i s t a k e n as 1 / 3 E , u s i n g K o s t e r ' s 3 4 v a l u e s f o r Youngs m o d u l u s . M e t a l M e t h o d o f t e s t i n g R e f . 18°C -82°C -185°C -I96°c -253°C Mg t e n s i l e 10 1.4 - - - -Mg s h e a r 7 1.0 - - - -Z n t e n s i l e 35 0.5 1-5 1.2 - 1.2 Z n s h e a r 8 - - - 0.5 -Z n s h e a r 7 0.5 - - - -C d t e n s i l e 12 - - 0.9 - 1-5 C d s h e a r 8 - - - 0.7 --10-5. S h e a r T e s t s Q E d w a r d s , W a s h b u r n a n d P a r k e r 0 h a v e t e s t e d b o t h z i n c a n d c a d i u m , i n p u r e s h e a r , up t o a b o u t 25$ s h e a r s t r a i n . T h e y f o r m e d ' f i v e m a i n c o n c l u s i o n s : -a) R e v e r s a l o f t h e d i r e c t i o n o f s h e a r c a u s e s a d r o p i n f l o w s t r e s s , b u t no change i n 0 . b ) A change i n t h e d i r e c t i o n o f s h e a r c a u s e s a r i s e m t h e f l o w s t r e s s , a g a i n w i t h no change i n 0 . c ) I f two d i r e c t i o n s o f s l i p a r e e q u a l l y f a v o u r e d , b o t h 0 a n d t h e c r i t i c a l f l o w s t r e s s a r e g r e a t l y i n c r e a s e d . d) t h e p r e s e n c e o f a l o w a n g l e b o u n d a r y p u t i n b y l o c a l d e f o r m a t i o n f o l l o w e d b y a n n e a l i n g c a u s e s a n i n c r e a s e m t h e f l o w s t r e s s . e) A t TT K , t h e v a l u e f o r 6 i s a p p r o x i m a t e l y f i v e t i m e s g r e a t e r t h a n a t room t e m p e r a t u r e . P h i l l i p s ^ ha s r e c e n t l y c a r r i e d o u t s i m i l a r t e s t s o n magnes ium c r y s t a l s a t room t e m p e r a t u r e . T h e i r b e h a v i o u r f o l l o w e d t h a t o f z i n c a n d cadmium v e r y c l o s e l y . 6. The R e c o v e r y o f P r o p e r t i e s o n A n n e a l i n g L u c k e e t a l . " ' " D d i d r e c o v e r y t e s t s o n z i n c a t room t e m p e r a t u r e . I f t h e t e s t s w e r e s t o p p e d i n t h e f i r s t l i n e a r s t a g e , r e c o v e r y o f t h e m e c h a n i c a l p r o p e r t i e s was c o m p l e t e a f t e r 2k h o u r s . A f t e r one h o u r c o n -s i d e r a b l e r e c o v e r y h a d o c c u r r e d . I f t h e t e s t s w e r e s t o p p e d i n t h e s e c o n d l i n e a r s t a g e , c o m p l e t e r e c o v e r y n e v e r o c c u r r e d , a n d , on r e - t e s t i n g , t h e c r y s t a l s a l w a y s r e s u m e d a w o r k h a r d e n i n g s l o p e c h a r a c t e r i s t i c o f t h e s e c o n d s t a g e . I t i s c o n c l u d e d t h a t a new, more s t a b l e o b s t a c l e must f o r m i n t h e s e c o n d s t a g e . A t e l e v a t e d t e m p e r a t u r e no s e c o n d s t a g e i s s e e n ; t h e o b s t a c l e s p r e s u m a b l y a n n e a l o u t as t h e y a r e f o r m e d . -11-Edwards et al. 0" found for cadmium and zinc that repeated shear strains up to 25$ could be completely recovered by a one hour anneal at 260°C. L i et a l . ^ have shown that the yield stress i s extremely sensitive to cooling rate after annealing, while 0 is not greatly affected. 19 Conrad et a l . found that for the case of magnesium shear strains of up to 100$ were completely annealed out by holding the crystal at U50°C for one hour. 7. Laue Asterism It has been shown that a crystal of cadmium-can be extended well over 100$ at room temperature with no accompanying asterism21-1. Lucke et a l . " ^ found l i t t l e asterism due to the room temperature deformation of zinc during the f i r s t linear stage, but severe asterism was given i n the second stage. 8. The Effect of Surface Condition Surface effects have been very well summarised by Clarebrough and Hargreaves y . While the rise i n c r i t i c a l flow stress produced by a surface layer has been extensively investigated, only two pieces of work have treated the effect on 8 . Gilman and Read2-L found that copper plated onto a zinc crystal increased the i n i t i a l value of 0 up to 1 0$ shear strain but had l i t t l e effect at greater strains. Lipsett and K i n g 2 2 found.that a layer of gold plated onto a cadmium crystal had l i t t l e effect on 0 during the f i r s t linear stage, but rather surprisingly increased 0 for the second stage. Lucke et a l . ^ 6 found an oxide layer to have l i t t l e effect on the room temperature stress-strain curve for zinc, but the curves are not very precise. It has been shown that an oxide layer can have a very profound effect on creep rates i n zinc and i n cadmium. -12-9. The M a t u r e o f ' P r e - Y i e l d " S t r a i n F i g . 6 shows a t y p i c a l s t r e s s - s t r a i n c u r v e f o r a h e x a g o n a l m e t a l . The y i e l d s t r e s s i s d e f i n e d f o r t h e p u r p o s e s o f t h i s s e c t i o n as t h e s t r e s s a t w h i c h l i n e a r f l o w commences. I n t h e c u r v e d r e g i o n i m m e d i a t e l y p r o -c e e d i n g t h i s , t h e r e i s a v e r y h i g h v a l u e f o r 0 . T h i s does n o t r e p r e s e n t a h i g h w o r k h a r d e n i n g r a t e , b u t i s a p a r t l y e l a s t i c r e g i o n . The movement o f d i s l o c a t i o n s w i t h i n t h e c r y s t a l i s p r o b a b l y r e t a r d e d b y s u b -b o u n d a r i e s . P r a t t 2 3 ha s shown t h a t i n s o d i u m c h l o r i d e c r y s t a l s t h e p r e -y i e l d s t r a i n i s a c c o m p a n i e d b y l o c a l s l i p p r o c e s s e s u n a b l e t o c r o s s s u b s t r u c t u r e b o u n d a r i e s , w h e r e a s a t t h e y i e l d s t r e s s t h e d e f o r m a t i o n s p r e a d s r i g h t a c r o s s t h e s l i p p l a n e . 10. C h a n g e - i n - S t r a i n - R a t e a n d C h a n g e - i n - T e m p e r a t u r e T e s t s on Magnes ium B a s i n s k i " ' " ^ has c a r r i e d o u t a s e r i e s o f t e s t s o n magnes ium c r y s t a l s i n w h i c h t h e s t r a i n r a t e was s u d d e n l y c h a n g e d b y a f a c t o r o f t e n d u r i n g t h e t e s t a n d t h e c o r r e s p o n d i n g change i n t h e f l o w s t r e s s n o t e d . The C o t t r e l l - S t o k e s l a w , f o u n d t o ' h o l d f o r t h e f a c e - c e n t r e d c u b i c m e t a l s c o p p e r a n d a l u m i n u m d u r i n g s e c o n d s t a g e h a r d e n i n g , s t a t e s t h a t f o r t h e same change i n s t r a i n r a t e t h e r a t i o o f t h e change i n f l o w s t r e s s t o t h e f l o w s t r e s s , , i s a c o n s t a n t i n d e p e n d e n t o f s t r a i n . B a s m s k i f o u n d t h e C o t t r e l l - S t o k e s l a w t o b e o b e y e d f o r t e m p e r a t u r e s up t o 90°K a n d s t r a i n s up t o 200$. A t h i g h e r t e m p e r a t u r e s t h e i n c r e a s e i n w i t h 3 was somewhat l o w e r t h a n t h a t p r e d i c t e d b y t h e C o t t r e l l - S t o k e s l a w . The p l o t o f ^ v e r s u s <5 f o r 200°K i s r e p r o d u c e d - i n F i g . 7- R e s u l t s f r o m c h a n g e - i n - t e m p e r a t u r e t e s t s w e r e s i m i l a r t o t h o s e f r o m t h e s t r a i n r a t e t e s t s . i n ph C o n r a d e t a l . y> h a v e r e c e n t l y o b t a i n e d r e s u l t s t h a t a p p e a r t o c l a s h w i t h t h o s e o f B a s i n s k i . T h e y d e f i n e a p a r a m e t e r B , e q u a l t o -13-) as f o u n d f r o m change i n - s t r a i n r a t e t e s t s . B was f o u n d c o n s t a n t f o r t h e t e m p e r a t u r e s i n v e s t i g a t e d (85°K a n d a b o v e ) , a n d n e a r l y i n d e p e n d e n t o f s t r a i n r a t e . F i g u r e 8 shows some o f t h e i r r e s u l t s . Wow i f B i s c o n s t a n t , A S i n B a s i n s k i ' s p l o t s s u c h as g i v e n i n F i g u r e 6 s h o u l d be i n d e p e n d e n t o f 8 . We have t h e r e f o r e t h e u n u s u a l c i r c u m s t a n c e o f two d i r e c t l y c o n f l i c t i n g p i e c e s o f e v i d e n c e . The answer may l i e i n t h e f a c t t h a t most o f B a s i n s k i ' s d a t a was o b t a i n e d f o r s h e a r s t r a i n s between.20% and 300fo> w h e r e a s t h e maximum s h e a r s t r a i n s r e a c h e d i n C o n r a d ' s w o r k were a r o u n d kofc. I t c o u l d be t h a t t h e r e i s a change i n mechani sm b e t w e e n l o w s t r a i n s and h i g h s t r a i n s , b u t t h e r e i s no o t h e r e v i d e n c e f o r t h i s . I n v i e w o f t h e much w i d e r r a n g e o f s t r a i n i n B a s i n s k i ' s w o r k , we s h a l l f o r t h e p r e s e n t d i s c o u n t C o n r a d ' s r e s u l t s as n e e d i n g f u r t h e r v e r i f i c a t i o n . 11. Comments T h i s b r i e f s u r v e y o f t h e c h i e f e x p e r i m e n t a l f a c t s c o n c e r n e d w i t h d e f o r m a t i o n i n h e x a g o n a l m e t a l s d e m o n s t r a t e s t h a t t h e f i e l d i s n o t y e t w e l l d e v e l o p e d . The p a u c i t y o f r e l i a b l e d a t a make i t i m p r a c t i c a l t o p r e s e n t a d e t a i l e d t h e o r y ; s u c h t h e o r y as does e x i s t s e r v e s c h i e f l y t o o u t -l i n e t h e d i r e c t i o n w h i c h f u r t h e r e x p e r i m e n t a l w o r k s h o u l d t a k e . _ l k -Figure 6. T y p i c a l Stress - S t r a i n Curve f o r a Hexagonal Metal. -15-a- / 2 0 0 ' V / / / > 1 / '/ ; O - G ' 2 / , ' / 1 i C o-o io 1 / ' * o-ooe '•/ * • / / " ' / / / 1 / - \ O O Z / -/ ' / ' / ' 1 i i i i . . . i i . c •2 ct-<> o s o-e i-o 1-6 O ' K G / M . M 2 -F i g u r e 7. A v e r s u s 3 f o r Magnes ium a t 200°K, f r o m C h a n g e - i n - S t r a i n -R a t e e x p e r i m e n t s . T a k e n f r o m . R e f e r e n c e 15. c^x> 1 1 1 1 1 \ 1.0 E - 0 0 0 0 O O O O 0 0 0 c 0 c 0 ° 0 0 160 - n - Mg 15 e \ 1 2 0 _ r- n O" 1/1 to 0 - in CO O OJ CO •3- in CO ^ 8 0 O <li C in ID O CM •0-i— min '7 4 0 — J O ' 2 1 — 10 -3 m m ' 1 1 0 ' 1 — / .1 I I I I I ' ° 0 .10 . 2 0 . 3 0 F i g u r e 8. R e s u l t s o f C h a n g e - i n - S t r a i n - R a t e e x p e r i m e n t s f o r M a g n e s i u m . T a k e n f r c m R e f e r e n c e 2k. -16-AHALYSIS OF THE MATERIAL The bulk of the experiments were carried out on l/8 inch diameter cobalt rod supplied by the A.D. Mackay Co. The following i s the suppliers spectrographs analysis:-cooalt 99-5 ft nickel 9, .3 f> copper traces iron .005 $ carbon .02 calcium oxide .03 $ manganese .02 $ sulphur .002 <f0 s i l i c o n .02 <f0 Two samples, one of the as-received material and the other cut from a zone-refined rod, were sent to Ledoux and Co. for gas analysis. The following analysis was furnished:-as received zoned oxygen 200 p.p.m. 130 p.p.m. nitrogen h-3 p.p.m. 18 p.p.m. hydrogen 1.8 p.p.m. 5.1 p.p.m. Gas bubbles observed to be given off from the molten zone during refining were probably nitrogen. In addition to the Mackay cobalt, a small quantity of Johnson Matthey high purity cobalt with the following spectrograph!c analysis was used. element quantity i n p.p.m. nickel 3 iron 2 manganese 2 sil i c o n 2 magnesium 1 calcium, silver less than 1 -17-GROWTH OF THE CRYSTALS The p r e p a r a t i o n o f c o b a l t c r y s t a l s o f f e r s p r o b l e m s , f o r on c o o l i n g t h r o u g h 400°C. a p h a s e t r a n s f o r m a t i o n t a k e s p l a c e , t h e s t r u c t u r e c h a n g i n g f r o m f a c e - c e n t r e d c u b i c t o t h e l o w t e m p e r a t u r e c l o s e - p a c k e d h e x a g o n a l f o r m . T h e r e a r e a few r e f e r e n c e s i n t h e l i t e r a t u r e w h i c h d e s c r i b e t h e 25 26 p r e p a r a t i o n o f c o b a l t c r y s t a l s f o r m a g n e t i c w o r k , ^ ' w h e r e m e l t - s o l i d i -f i c a t i o n methods were u s e d . R e a s o n s w i l l b e g i v e n why t h i s m e t h o d was f o u n d u n s u i t a b l e . C r y s t a l s f o r d e f o r m a t i o n s t u d i e s must f u l f i l c e r t a i n r e q u i r e -ments . T h e y s h o u l d b e ( 1 ) o f r e a s o n a b l e s i z e ( e . g . 5 cm. l o n g a n d 3 mm. i n d i a m e t e r ) ( i i ) h a v e u n i f o r m s e c t i o n ( n i ) b e f r e e of' ' c o n s t r a i n t s A t t e m p t s t o p r e p a r e s u c h c r y s t a l s a r e d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n s . S o l i d S t a t e Methods I t i s h i g h l y d e s i r a b l e t o grow c r y s t a l s t h a t c a n be t e s t e d d i r e c t l y , w i t h no i n t e r m e d i a t e m e c h a n i c a l s h a p i n g , e s p e c i a l l y i n t h e c a s e o f c o b a l t w h i c h t w i n s e a s i l y and i s d i f f i c u l t t o c u t . A n y m e c h a n i c a l s h a p i n g w o u l d l e a d t o u n c e r t a i n t y w i t h r e g a r d t o m e c h a n i c a l s t r a i n . W i t h t h i s i n m i n d , f o l l o w i n g K a y a , 2 ? g r a i n g r o w t h methods w e r e e x t e n s i v e l y i n v e s t i g a t e d . C o m m e r c i a l p u r i t y c o b a l t powder s u p p l i e d b y S h e r r i t t G o r d o n M i n e s L t d . was c o m p a c t e d a n d s i n t e r e d a t 1200°C f o r 12 h o u r s u n d e r h y d r o g e n . The compact s w e r e c o l d - r o l l e d t o t h m s t r i p . I n one c a s e a compact was m e l t e d a n d c a s t u n d e r vacuum b e f o r e c o l d r o l l i n g . Wo more t h a n 10$ r e d u c t i o n i n r o l l i n g c o u l d b e g i v e n b e f o r e s e v e r e c r a c k i n g s e t i n . The r e q u i r e d r e -d u c t i o n s i n s e c t i o n w e r e i m p a r t e d b y r e p e a t e d r o l l i n g and vacuum a n n e a l i n g . R e c r y s t a l l i s a t i o n t e m p e r a t u r e s f r o m 650°C t o 1100°C w e r e t r i e d , w i t h t h e s t r a i n g i v e n b y c o m p r e s s i o n m r o l l i n g o r b y e x t e n s i o n i n a t e n s i l e m a c h i n e . -18-I n no case was s i g n i f i c a n t g r a i n growth accomplished. One specimen was annealed at lU00°C, but again w i t h no success. A small q u a n t i t y of purer (99'95$) c o b a l t s u p p l i e d by the Cobalt Research I n s t i t u t e was a l s o t r i e d , but no improvement i n g r a i n growth r e s u l t e d . A v a r i a t i o n on the Andrade method, which has been s u c c e s s f u l f o r s e v e r a l r e f r a c t o r y m e t a l s ' ^ w a s a i s o t r i e d . Thin c o b a l t s t r i p was h e l d at one end i n a water-cooled copper clamp, w i t h the lower end d i p p i n g i n t o a low m e l t i n g p o i n t indium-gallium a l l o y , l i q u i d at room temperature. Current was passed through the s t r i p u n t i l i t s centre heated up t o a few degrees below the m e l t i n g p o i n t , and c o n d i t i o n s were kept steady f o r s e v e r a l hours. The method was t r i e d w i t h atmospheres of hydrogen and helium, and a l s o under vacuum. Grains w i t h diameters around one mm. r e s u l t e d , but u s e f u l s i n g l e c r y s t a l s never. The t r a n s f o r m a t i o n boundaries, which are c r y s t a l l o g r a p h i c a l l y s i m i l a r t o twin.boundaries, are probably v e r y s t a b l e and i n h i b i t g r a i n growth. Growth from the Melt S o l i d s t a t e methods having f a i l e d , growth of c r y s t a l s fromothe melt was t r i e d . Cobalt was h e l d i n h i g h - p u r i t y r e c r y s t a l l i s e d alumina c r u c i b l e s and boats purchased from the Morgan Co. of Canada. They were heated i n a molybdenum-wound furnace u t i l i s i n g a hydrogen atmosphere. The c r u c i b l e was h e l d at the end of a water-cooled copper probe t o provide a sharp temperature gradient i n the melt, and the probe was withdrawn 1 from the furnace at a c o n t r o l l e d r a t e . Cobalt of various p u r i t i e s was t r i e d , both i n open boats w i t h the furnace h o r i z o n t a l and i n tubes w i t h the furnace v e r t i c a l . The f o l l o w i n g d i f f i c u l t i e s were encountered. ( i ) Gas was evolved when the metal s o l i d i f i e d . I n the case of -19-l o n g narrow tubes, around l / 2 cm. i n diamter, metal was a c t u a l l y e x p e l l e d from the tube. I n n e a r l y a l l cases some p o r o s i t y was observed. ( i i ) Only a s m a l l p r o p o r t i o n of the runs gave s i n g l e c r y s t a l s . Contrary t o previous r e p o r t s ^ 0 , c o n t r o l of the r a t e of growth from the melt or of t r a v e l through the t r a n s f o r m a t i o n temperature d i d not appear very e f f e c t i v e . (111) The c r y s t a l s stuck t o the alumina. To remove them i t was u s u a l l y necessary t o crack o f f the c r u c i b l e , g i v i n g p o s s i b l e deformation t o the c r y s t a l . I n an attempt to e l i m i n a t e p o r o s i t y , a furnace o p e r a t i n g under a vacuum of around 1 0 " 4 mm. of mercury was b u i l t ; p o r o s i t y s t i l l remained a problem. On the premise t h a t c r u c i b l e r e s t r a i n t s were r e s p o n s i b l e f o r the break-up of the c r y s t a l s at the tr a n s f o r m a t i o n , a few runs were t r i e d u s i n g a "s o f t mould" t e c h n i q u e 2 ^ . Cobalt rods were packed i n alumina powder and melted under vacuum by i n d u c t i o n h e a t i n g . Gas e v o l u t i o n always took p l a c e , u p s e t t i n g the w a l l s of the mould. C r y s t a l s w i t h a very i r r e g u l a r contour r e s u l t e d . Growth i n the Zone-Refiner Much the best r e s u l t s have been obtained u s i n g an e l e c t r o n -beam f l o a t i n g zone r e f i n e r , d e t a i l s of which may be found i n reference 33• Commercial grade Mackay c o b a l t r od 1/8" diameter was given one pass at a r a t e of zone t r a v e l normally 25 cms. per hour, under a vacuum approxi-mately 10~5 mm. of mercury. C r y s t a l s up t o 20 cms. long w i t h good u n i f o r m i t y of c r o s s - s e c t i o n and s t r a i g h t n e s s have been grown i n t h i s way. Sub-boundaries are few, and Laue X-ray spots are sharp. The success of the method i s be-l i e v e d t o l i e i n two f a c t o r s : --20-( i ) The a b s e n c e o f c r u c i b l e r e s t r a i n t s d u r i n g t h e t r a n s f o r m a t i o n , and ( i i ) e x t r e m e a x i a l i t y o f h e a t f l o w d u r i n g c o o l i n g . . Some J o h n s o n M a t t h e y h i g h p u r i t y c o b a l t was d r a w n down t o a p p r o x i m a t e l y 1/8" d i a m e t e r a n d z o n e d a t 25 cms . p e r h o u r . The gas c o n t e n t a p p e a r e d t o be h i g h , f o r gas e v o l u t i o n f r o m t h e m o l t e n zone made t h e p r o d u c t i o n o f c r y s t a l s w i t h u n i f o r m s e c t i o n r a t h e r d i f f i c u l t . Two c r y s t a l s g o o d enough f o r t e n s i l e t e s t i n g were o b t a i n e d . The axes o f t h e z o n e d c r y s t a l s were c l u s t e r e d a r o u n d a {10I0} p o l e , t h e p o l e o f t h e b a s a l p l a n e b e i n g a t l e a s t 60° f r o m t h e s p e c i m e n a x i s . C r y s t a l s g rown a t l o w e r r a t e s o f zone t r a v e l showed t h e same o r i e n -t a t i o n r a n g e ( F i g . $))• T h i s o r i e n t a t i o n i s s i m i l a r t o t h a t f o r o t h e r h e x a g o n a l m e t a l s g rown f r o m t h e m e l t , w h i c h i s a l i t t l e s u r p r i s i n g when t h e mode o f f o r m a t i o n o f t h e h e x a g o n a l p h a s e i s c o n s i d e r e d . The p r e f e r r e d o r i e n t a t i o n may be c a u s e d b y a n i s o t r o p y o f h e a t c o n d u c t i o n , i . ' e . t h a t c r y s t a l w h i c h c a n most e f f e c t i v e l y c o n d u c t h e a t away f r o m t h e t r a n s f o r m a t i o n i n t e r f a c e w i l l be f a v o u r e d . F i g u r e 10 shows t h e a r e a on a l i s t a n d a r d c u b i c s t e r e o g r a m i n w h i c h t h e r e a r e no p o l e s g r e a t e r t h a n 60° f r o m one o f t h e f o u r ^111^ d i r e c t i o n s . T h i s a r e a b e i n g s m a l l , a p r e f e r r e d o r i e n t a t i o n i n t h e c u b i c phase i s n o t n e c e s s a r y t o g i v e t h e o b s e r v e d h e x a g o n a l o r i e n t a t i o n s . -21-0001 IOTO Figure 9» Axes of the zoned cobalt c r y s t a l s . -22-F i g u r e 10. Standard Cubic Stereogram, showing Areas (shaded) con-t a i n i n g no Pole more than 60° from one of the 1^11^  Poles ( A ) . -23 EXPERIMENTAL.PROCEDURE C r y s t a l s g rown as d e c r i b e d i n t h e p r e v i o u s s e c t i o n w e r e s u b j e c t e d t o t h e f o l l o w i n g p r o c e d u r e s . 1. E l e c t r o p o l i s h i n g A l l c r y s t a l s were e l e c t r o p o l i s h e d b e f o r e t e s t i n g . V a r i o u s e l e c t r o p o l i s h i n g s o l u t i o n s s u g g e s t e d i n t h e l i t e r a t u r e w e r e t r i e d , none w i t h g r e a t s u c c e s s . The f o l l o w i n g m o d i f i c a t i o n s w e r e f o u n d s a t i s f a c t o r y . l ) e l e c t r o l y t e 15$> p e r c h l o r i c a c i d i n a c e t i c a c i d v o l t s 25 t o 35 t e m p e r a t u r e 15 t o 25°C t i m e 1 t o 2 m i n u t e s c a t h o d e c o p p e r Use a v e r y s l o w s t i r . S w i t c h o f f t h e s t i r r e r f o r a p p r o x i m a t e l y 20 s econds b e f o r e c u t t i n g o f f t h e c u r r e n t a n d r e m o v i n g t h e s p e c i m e n s f r o m t h e b a t h . i i ) E l e c t r o l y t e 25$ h y d r o c h l o r i c a c i d i n m e t h y l a l c o h o l v o l t s 12 t e m p e r a t u r e 30 t o ^0°C c a t h o d e s i l v e r Do n o t s t i r . The f i r s t p r o c e d u r e was u s e d a l m o s t e x c l u s i v e l y i n t h e p r e s e n t w o r k . I n some c a s e s t h e s e c o n d e l e c t r o l y t e gave a s u r f a c e c o v e r e d w i t h s t e p s , o f t e n i n s p i r a l f o r m , v e r y s i m i l a r t o g r o w t h s p i r a l s . Example s a r e shown i n F i g u r e 11. Figure 11. Surface S p i r a l s a f t e r a H y d r o c h l o r i c Acid-Methyl A l c o h o l E l e c t r o p o l i s h . I n A the S p i r a l s are S i n g l e , i n B they are Double. Mag. X 600. -25--2 . Etching The zone-refined rods were macro-etched in the following manner:-5 minutes m a solution of 21$ H 2S0h., 15$ H C 1 , 21$ H N 0 3 , 21$ HF, 21$ H 2 0 , followed by 5 minutes i n a solution of Uo$ H C 1 , 20$ HF, and Uo$ of a solution with one gram CUCI-2.2H2O per 5 cc. H 2 0 . Micro-etching was carried out by immersion for approximately one minute i n a solution with 60 cc. H C 1 , 15 cc. HNO^ , 15 cc. HAc, 15 cc. HgO. Both procedures were suggested by the Cobalt Information Centre. 3. Electromachining To produce tensile specimens with reduced cross-section between the grips, various electrothinning methods were tried. I n i t i a l l y the crystal was held v e r t i c a l l y m the electrolyte, with a l l but i t s test section masked with e l e c t r i c a l tape or a coating of paraffin wax. A taper usually developed. Next an apparatus with the specimen rotated i n the horizontal plane was tried. Problems of taper were reduced, but there was a strong tendency for a groove to form at the interface where the crystal was masked off. Finally an electromachining apparatus was b u i l t based on a design supplied by H.W. Schadler of the G.E. research laboratories. A photograph is shown i n Fig. 1 2 . An aluminum wheel, carrying a film of electrolyte^was rotated at the same speed as the crystal, approximately 20 r.p.m. The gap between the wheel and the crystal was reduced u n t i l a continuous meniscus was formed between them. As machining progressed the crystal had to be periodically lowered to retain the meniscus. An equal current passed from the crystal to the wheel and from the wheel to the electrolyte bath, preventing build-up of cobalt on the wheel. Perchloric acid-acetic acid electrolytes were found quite unsuit-able for any form of electrothinning, giving a specimen with an e l l i p t i c a l -26-Figure 12. The Electromachining Apparatus. -27-cross-section. Methyl alcohol-hydrochloric acid electrolytes leave a black layer which builds up on the wheel. Most satisfactory results have cane using methyl alcohol-nitric acid mixtures, with some urea i n the baths as a safety factor. Specimens with a gauge length around 1 " and diameter approxi-mately l / l 6 " could be manufactured from l / 8 " diameter rod i n about 3 / 4 of an hour. In some cases a taper was produced but the method was i n general satisfactory for the reduction of cross-section i n straight crystals with an i n i t i a l l y uniform section. Variations i n cross-section could not be eliminated. k. ' Orientation of the Crystals Before testing, each crystal was oriented by the back-reflection Laue technique, with an accuracy estimated at + 2 ° . In two cases crystals were oriented after deformation. The rotations of the axes of the crystals across a standard stereogram were m accord with those expected from (0001) <1120> s l i p . In the tables below, orientations of the crystals are expressed in terms of two angles. % i s the angle between the specimen axis and the sl i p plane pole, and the c< 's are the angles between the specimen axis and the three ( l l 2 0 ^ s l i p directions. Dimensions for these crystals can be found i n Appendix 2 . -28-TABLE III Orientations for the Large Crystals crystal 71° QL 1 85 26, 35. 85 2 62 ko,,4l, 89 3 70 36, 36, 90 k 7B 27, 37, 86 5 77 31. 35, «« 6 78 25, 39, 83 7 85 27, 33, 87 8 65 37, kO, 88 9 78 25, 39, 83 10 70 32, 41, 85 11 65 36, kl, 86 12 63 kO, kl, 89 13 73 30, 39. 85 Ik 81 30, 31, 79 TABLE IV Orientations for the Johnson Matthey Crystals crystal *° *° J-M 1 Qk 7, 56, 6k J-M 2 80 22, la, 8o To distinguish them from the other crystals, the short, electro-machined crystals, with test sections approximately 2.5 cm. long and 0.15 cm. i n diameter, w i l l be designated by the prefix S-H followed by the number of the crystal. TABLE V Orientations for the Series S-H Crystals crystal %° o 1 73 28, la. 82 2,3 68 ?>h, ho. 86 ^5 77 26, 1+0, 83 6,7,a, 76 27, 1+0. 83 9,io 83 22, 1+1, 81 n 76 26, 1+0, 83 12 65 38, 39, 89 13 83 18, 1+1+, 77 14, 15 88 29, 32, 88 lb, 17, 10 79 26, 38, 83 19 79 27, 38, 3h 20,21 71 35, 35, 90 22,23,24 63 hi, 39, 89 5» Tensile Testing a) Measurement of Cross-Section Some crystals had a slight taper, quite frequently so after electro-machining. Each crystal was therefore measured across two perpendicular diameters at both ends and at the centre, using a travelling microscope. T^e largest deviation from the average for the large crystals was usually within 3$> of the average, and for the series S-H electromachined crystals i t was within 5fo. b) Gripping Single crystal testing is bedevilled with grip effects (see for example references 30, 31) • To minimise these, the length to diameter ratio should be kept as great as possible. The cobalt crystals prepared i n the zone-refiner were f a i r l y short, and to reduce grip effects i t was con-sidered desirable to use rotatDng grips. Figure 13 shows the grips used, which were based on a design by Rosi3 2„ They each incorporated two sets of ro l l e r bearings, allowing the gripped portions of the test specimen to be -3Q-rotated about any horizontal axis, eliminating most of the grip restraints. Details of their construction are given i n reference 33• The crystals were soldered into brass adapters, which threaded into the grips. D i f f i c u l t y was occasioned by the crystals reducing i n section and pulling out of the solder after a small extension. To overcomes this the later crystals were electroplated with a layer of cobalt for about 3/4 cm. at each end (for details see appendix 1.). . The solder adhered very strongly to the plated layer, but tests were terminated when the crystal pulled out from i t s plated., covering. Crystals with f a i r l y low flow stresses could be extended up to a maximum of around 150$ shear strain, but stronger crystals fa i l e d at much lower strains. To obtain tests with higher extensions the electromachined series S - H specimens were used. The thick ends were soldered into brass adapters which were held securely i n r i g i d grips. Extensions of up to 350$ shear strain could be obtained in crystals with low flow stresses. c) Testing Proceedure The tensile machine used was a 10,000 pound capacity Instron screw-driven unit, with the grips mounted below the cross-head so that the whole gripping assembly could be contained i n a dewar (Figure 13). Mounted specimens were allowed to remain i n the temperature bath for at least 10 minutes prior to testing. With the specimen under stress, variations in temperature could be easily detected by a rise or f a l l in the applied load. Crosshead speeds were varied between 2" per minute and .002" per minute. For each load scale and rate of crosshead movement, the specimen was replaced by a short brass rod of large diameter which was threaded into the grips at both ends. Extension of this rod under the loads used in the present investigation was taken as negligible. A load- "elongation" Figure 13. The Testing Assembly showing a Crystal Mounted in the Rotating Grips. The Shelf is used to Hold the Dewar of Liquid Nitrogen i n Place. Approximately l/h actual Size. -32-plot was taken to the maximum of each load scale, and this was used as a calibration curve. The indicated "elongations" were subtracted from the values indicated m an actual test to give a true load-extension plot. (Figure Ik). d) Temperature Control Temperature changes were effected by lowering the gripping assembly into a Dewar flask f i l l e d with the following liquids :-Temperature Range Liquid l8°C+-l40°C Petroleum Ether -196 C Liquid Nitrogen 18°C -» + 150°C Silicons O i l A s t i r r e r kept the l i q u i d agitated. Temperature was measured with a copper-constantan thermocouple held near to the surface of the specimen. The petroleum ether was cooled by pouring l i q u i d nitrogen into a copper vessel immersed in the bath. The o i l was heated by an immersion heater, and i t s temperature checked with a normal mercury-m-glass thermometer. e) Determination of Flow Stress-Temperature Curves To examine the variation of flow stress with temperature, crystals 8 and 10 were tested as follows. The mounted specimen was pulled at room tem-perature to i t s c r i t i c a l flow stress and given a small extension. The load was then removed and a temperature bath placed around the specimen. When thermal equilibrium had been established, testing was repeated at the new temperature. The load-extension curve for crystal 10 is shown i n figure 15. Work hardening was kept to a low value,and the c r i t i c a l flow stress that would be present i n the virgin crystal was found by subtracting the increase i n flow stress arising from work hardening from the measured flow stress. After each series of tests, a room temperature test was again made and i f the^value for' c r i t i c a l flow stress obtained m the way described agreed with that for the virgin crystal the values were considered satisfactory. 300 CO Extension i n Inches Figure Ik. Derivation of the Load-Elongation Plot for a Typical Crystal. 120 100 -0 .02 .Ok .06 .08 .10 .12 .11+ .16 .18 .20 .22 .2k Extension i n inches Figure 15. Load-Extension P l o t f o r C r y s t a l 10 during the F i r s t Cycle, -35-RESULTS OF THE TENSILE TESTS 1. Stress-Strain Curves Figure 16 shows stress-strain curves for crystals 1, 2, 3, 5, 6, and 12. In figure 17 the same data have been replotted i n terms of resolved shear stress and resolved shear strain (see appendix 2 for details). It can be seen that Schmid's law is f a i r l y closely obeyed. The curves are linear after an i n i t i a l curved portion, with approximately the same work hardening slope. Curves for the two Johnson-Matthey high-purity cobalt crystals and for two crystals (9, 4) tested entirely at l i q u i d nitrogen temperature are also shown. Resolved shear stress-shear strain curves for the series S-H crystals are given i n figure 18. Of 23 crystals pulled, only a few with favourable orientations extended to high strains, and curves are shown only for these. The general form of the curves i s similar to that for zinc, caomium or magnesium (see figure k). They are S-shaped with an i n i t i a l lowering of the work hardening slope followed by a nearly linear region up to shear strains of about 150$. There is a definite upturn at shear strains of around 200$, although the increase m slope is not so great as is the case for the other hexagonal metals. 2. Values for the C r i t i c a l Resolved Shear Stress The c r i t i c a l resolved shear stress. was taken as that value given by extrapolating the early linear region of the stress-strain curves to zero strain. The main source of error was inaccuracies in the orientation, especially with respect to OC • Figure 19 shows values for c r i t i c a l resolved shear stress plotted against 7L , with errors that could be expected from errors in «x alone. Values are well within the confidence limits. The average value for 3c = 97 kg./cm.2. Elongation, $ ^urel6. S t r e s s - S t r a i n Curves f o r Cobalt Crystals at Room Temperature. Resolved Shear S t r e s s , Kg/cm 2 250 200 -150 100 . •~ Johnson-Matthey High Purxty Cobalt t e s t e d a t Liquxd Nitrogen Temperatures 3 k ilm^Jl. Resolved 9 10 11 Shear S t r a i n (#) Shear Stress-Shear S t r a i n Curves 1 2 13 14 15 16 17 f o r Cobalt C r y s t a l s . -39-F i g u r e 19. C r i t i c a l Resolved Shear S t r e s s e s , ^ , f o r Cobalt C r y s t a l s . I i s the V a r i a t i o n from3 C r = 100 Kg/cm 2 Caused by a + 2° Change i n J( . -1+0-130 I 120 110 co, 3 ioo cc u 0^ OC F i g u r e 2 0 . C r i t i c a l R e s o l v e d S h e a r S t r e s s e s , 3 C r > f o r t h e C o b a l t S e r i e s S - H C r y s t a l s . I i s t h e V a r i a t i o n f r o m B p = 100 k g . / c m 2 C a u s e d b y a + 2 ° Change m 9C . Figure 20 shows similar values for the S-H series• Here some of the specimens had a taper after electromacblriing, and i n these cases the minimum cross-sectional area was used. If % is very high, above about 85°, some sli p planes w i l l enter the grips at both ends. Thisj probably explains the rise i n 3 g~ at very high?* values. When averaging, values for 9 ^ for 'crystals ~lk- and 15 were^heglected for this reason. Mean £ Q t for the S-H series = 97 Kg/cm2, fable VI shows values of2 ^ at l i q u i d nitrogen temperature. TABLE Wt C r i t i c a l Resolved Shear Stress at =196°C Crystal 3 C I , i n Kg/cm2 T 17k i 18? 8 161 1.1- , 162 10 165 9 164 Average 3 ^ = 168 Kg/cm2 From Figure I'J, 3 ~- for Johnson-Matthey cobalt is 65 to 70 Kg/cm2 The high values for 9C in these two crystals cause this figure to be hot very reliable, but the consistency between the values for the two crystals indicates that some significance can be put on i t . In^ummary $p~ for commercial cobalt at 18°C = 97 Kg/cm2 for commercial cobalt at al96°C = 168 Kg/cm2 for Johnson-Matthey high purity cobalt s 65-70 Kg/cm2 |. Variation of the Flow Stress with Temperature Variations from crystal- to crystal are too great for stress-strain curves for different crystals pulled at various temperatures to be -42-easily compared. Temperature change tests, as previously described, have been carried out on crystals 8 and 10. Plots of flow stress versus temperature are shown i n figure 21. The flow stresses for crystal 8 at 133, 17T°K are anomalously low. To l i e on a smooth curve with the other points, their temperatures would have to be raised approximately 10°K. This suggests that either (l) thermal equilibrium between the specimen and the temperature bath had not been established or ( i i ) the thermocouple junction was displaced from the crystal surface. The Cottrell-Stokes law for temperature states that i f the temperature i s changed abruptly during flow, the reversible change i n flow stress ^3 is a linear function of the total flow stress 3 , l.e.^^ is a constant throughout the test. This has been confirmed for the face-centred cubic metals copper, aluminum and silver, 36 • an^ f o r the hexagonal metalc magnesium-^. Some tests were therefore made in which the specimen was pulled alternately at room temperature and m li q u i d nitrogen. Figure 22 demonstrates that i n the case of cobalt -5IT. I S not a constant, but steadily decreases as the specimen extends. ^ does however appear to be function of ^ , i n that points from three different crystals f a l l on the same curve. 4. Variation of the Flow Stress with Strain Rate During several tests the rate of crosshead travel was changed ab-ruptly, and the effect on flow stress noted. Figure 23 shows the load-elongation curve for one such test. Data extracted from the curve is presented m table VII. 50 j i  100 200 300 k~00 Temperature °K Figure 21. V a r i a t i o n of the Flow Stress with Temperature. Resolved Shear S t r a i n , $, f o r C r y s t a l 3 12.6 107 113 Figure 23 Load-Elongation Plot for Crystal 1 2 . Effect of Changes i n Cross- Head Speed between .002"/Min. and 0.2"/Min* at various Temperatures. -46-TABLE V I I E f f e c t o f S t r a i n R a t e on F l o w S t r e s s m C r y s t a l 12. A3= t h e change m f l o w l o a d when t h e r a t e o f c r o s s h e a d t r a v e l i s changed "between .002" p e r m i n u t e and 2" p e r m i n u t e . € = R e s o l v e d s h e a r s t r a i n . T°C S i n lbs . load A c J i n lbs . + 18 45. 4 2.6 .057 • 2.1 + lB 47.0 2.8 .055 2.9 + 18 4Q.O 2.8 .057 4.6 + 18 49.6 2.8 .053 5.8 + 18 50.2 2.8 .052 6.6 - 196 80.6 4.0 .052 8.4 - 196 82.2 4.0 .046 9.3 - 196 84.0 4.0 .046 10.1 - 196 85.O 4.0 .049 11.2 - 196 88.4 4.0 .043 13.2. - 196 90.4 4.0 .047 14.3 + 18 62.2 3.2 .048 17.4 + ikl 55.0 1.8 .029 18.2 + 147 56.2 1.6 .025 20.7 + i4o 56.4 1.6 .032 21.3 + l4o 57.0 1.6 .025 22'. 0 + 18 65.6 2.8 .043 23.7 + 18 66.2 .^2 .051 24.8 + 18 67.6 2.6 .038 25.6 The s t r a i n r a t e e f f e c t i s much s m a l l e r t h a n t h e t e m p e r a t u r e e f f e c t , and a c c u r a c y f o r i s c o r r e s p o n d i n g l y l o w e r . A 3 i n t a b l e V I I c o u l d be measured t o no b e t t e r t h a n p l u s o r minus .2 l b s . Two mam con-c l u s i o n s may be drawn•-1) A 5 i s g r e a t e r f o r l o w e r t e m p e r a t u r e s 2) ^ ^ ^ t e n d s t o l o w e r v a l u e s as t h e e x t e n s i o n i n c r e a s e s . To examine t h e v a r i a t i o n o f ^ ^ j w i t h 3 a t room t e m p e r a t u r e more f u l l y , c r y s t a l 13 was p u l l e d up t o l60$ s h e a r s t r a i n a t a l t e r n a t e c r o s s h e a d speeds o f .002 and .2 i n c h e s p e r m i n u t e . F i g u r e 24 shows ^ as a f u n c t i o n o f t h e l o a d . V a l u e s f r o m t h e smoothed c u r v e were t a k e n , and p l o t t e d a g a i n s t r e s o l v e d s h e a r s t r e s s ( f i g u r e 25). As m t h e t e m p e r a t u r e e f f e c t s , - 47-ko > 60 80 100 Load i n Pounds. Figure 2k. At Room Temperature, f o r Changes i n Cross-Head Speed Between . 2 " and .002"/Mm. F i g u r e 2 5 . <2 f o r Changes i n the Crosshead Speed Between . 2 " and .002 "/Min. Values are p l o t t e d against Resolved Shear S t r e s s , . - -1+9-A ^ d r o p s steeply as the test continues. 5. Work-Hardening Slopes ( 8 ) . a) At room Temperature Work-hardening slopes for single crystals are notoriously un-reproducible (see for example Table I ) . Values for work-hardening slope cal-culated from Figure 17 are given m Table VIII.Average6 = 135 Kg/cm2/unit shear strain. TABLE VIII. Values for Work-Hardening Slopes in, Fig. 7« Crystal Q m Kg/cm^/unit shear strain 2 200 1 175 12 113 3 119 6 loo 5 100 From Figure 18 the slope of the f i r s t linear region for the S-H crystals i s 143 Kg/cm2/unit shear strain. The value for 8 is therefore subject to wide variations, and has a mean value around l40 Kg/cm2/unit shear strain. b) Variation with Temperature The slopes for crystals 9 and 4,pulled entirely at li q u i d nitrogen temperature, are from Figure 17 equal to 240 and 250 Kg/cm2/unit shear strain respectively. Crystals 3 and 11, tested alternately at room temperature and m liq u i d nitrogen, gave work-hardening slopes shown in Table IX. -50-TABLE IX Work-Hardening Slopes f o r C r y s t a l s 3 and 11 C r y s t a l 3 ' C r y s t a l 11 18°C -196°C 18°C -196°C F i r s t Cycle 95 i l l 73 136 Second Cycle 95 143 51 165 T h i r d Cycle 119 159 46 225 An attempt was made to measure the work-hardening slopes f o r c r y s t a l 10, p u l l e d at various temperatures. The" regions where slope could be measured were not very extensive (see f i g u r e 15), and the values are not very accurate. Even so some rather anomalous values were obtained. The values forO, i n Kg/cm 2/unit shear s t r a i n are given i n Table X. . Values from Table X are p l o t t e d i n Figure 26. TABLE X Work-Hardening Slopesfor C r y s t a l 10 F i r s t Cycle Second Cycle T°C o T K 0 o T C 0 T K 9 + 18 291 13 + 17 290 126 - 12 261 85 - 10 263 99 - 48 225 40 - 47 226 142 - 92 181 155 - 102 171 176 - 132 141 158 - 135 138 147 - 196 77 163 - 196 77 160 + 19 292 70 + 17 290 75 + Bo 353 43 + 47 320 48 + 143 416 13 + 102 _375 . . 13. _ + 17 290 86 •^196 77 225 a H u -p CO 160 240 220 i crj 2 0 0 W •P H OJ 180 1 160 J 140 <*> 120 J 100 80 -6o 40 20 0 0 o o o a Values from the F i r s t Cycle O Values from the Second Cycle 8 0 S N O v 100 200 300 tob" I h-1 I Figure 26. Temperature K Values for the Work-Hardening SlopeQfor Crystal 10. -52-The scatter i n values for 9 taken from abrupt change in temperature flow curves is probably caused partly by work-softening phenomena. Figure 27 shows Basinski's (reference 15) change-in-temperature stress-strain curves for magnesium. In seme cases the slope is actually negative after a drop i n flow stress. Work-softening effects were less marked in cobalt. In summary, there i s no striking change in 9 with temperature. While values were not very consistent, there was a definite trend towards higher 9 values at low temperatures. c) Variation with strain rate The strain rate has sometimes been changed during a test. Figures are given i n Table XI-TABLE XI Variation m 9 with Strain Rate (* = tested i n l i q u i d nitrogen) Units Kg/cm2/unit shear strain Crystal .02 .2 2 Inches per Mm. Extension 5 107 117 2 169 205 6 13^ 173 3* 159 167 10* 225 179 10 56 77 8 3h 41 The effect i s small, with a slight tendency towards greater hardening slopes at higher strain rates. Crystal 13 was tested specifically to examine variations i n flow stress and work-hardening slope with strain rate. Repeated changes i n strain rate by a factor of 100 showed no measurable consistent effect on the work-hardening slope. - 5 3 -Resolved Shear Stress-Shear Strain Plots, and Curves For Change-in-Temperature Tests, for Magnesium. Reproduced from Reference 15. -5k-6. Orientation Effects In accord with previous work on other hexagonal metals, no systematic orientation dependence of the stress-strain curves was found. It had been noted^ that for zinc the work-hardening slope was increased and the upturn in the stress-strain curve reached earlier i f two s l i p directions were equally favoured. No such dependence was detected in cobalt. For instance, crystals 3 and 12, both have two s l i p directions nearly equally favoured, and Figure 17 shows that this has produced no anomalous work hardening slope. The same applies for cystals S-H 12, 22, 23. Crystals with two directions nearly equally favoured appear to glide in large packets on one s l i p system only, often giving rise to a macroscopic twist i n the crystal. Figure 28 shows an example where the crystal has folded along a line parallel to i t s axis. -55-Figure 2 8 . Crystals S-H 1 2 , 2 3 , after Extension. Crystal S-H 12 (Right) has Slippped on two Systems and Folded along i t s Axis. Mag: Approx. actual size. -56-' METALLOGRAPHIC OBSERVATIONS 1. Slip Lines and Deformation Markings The polished crystals examined after pulling i n tension showed a s l i p structure typical of hexagonal metal crystals, i.e. long straight lines f a i r l y uniformly spaced. In no case was clear evidence for s l i p on non-basal planes obtained. When the tested crystals were electropolished and etched, the more severely deformed ones showed a system of twin-like markings (see Figure It has not been possible to ide n t i f i y these markings unambiguously, and they w i l l be referrred to simply as "deformation markings". X-ray analysis is impossible m a highly deformed crystal, and other methods have proved inconclusive There was i n i t i a l l y some doubt i f the markings were produced during the deformation or during the period of heating when the crystal was soldered into or removed from the grips. Examination of crystals pulled i n simple f r i c t i o n jaws showed the same markings, proving that they are produced by the deformation. Attempts have been made to identify them with small platelets of transformed material. Figure 30 shows the deformation markings in a crystal that has been extended to the order of 200fo shear strain and then annealed at 600°C for half an hour to give small regions with a new orientation. There is no clear correlation between directions of the outlines of the small regions of new orientation, lying on •fill}, cubic planes, and the deformation markings. It should however be kept i n mind that there are six twin planes and four { i l l ] cubic planes, and i f the deformation1- markings are twins some correlation i n direction of surface markings was sure to occur. One crystal was stretched to around 200$ shear strain, electro-polished, and bent at li q u i d nitrogen temperature to give twins. A definite identification of deformation markings with the twins could not be made, but Figure 29. Deformation Markings i n Deformed Cobalt. Specimens Eleerropolished and Etched after Extension. -58-Figure 3 0 . Specimen Extended, Electropolished, and Annealed for l/2 hr. at 600°C. Etched. Mag: Aprox. kOO x 1 -59-they were of ve r y s i m i l a r appearance. In summary, the deformation markings are probably f i n e mechanical twins, but t h i s has not been confirmed. 2. Twinning Except f o r the deformation markings, i n only two of the c r y s t a l s t e s t e d (nos. 7,9) were twins observed (see f i g u r e 31). Both these were t e s t e d at -196°C. I n no case was there a r e l a x a t i o n of l o a d i n the l o a d -e l o n g a t i o n p l o t c h a r a c t e r i s t i c of a twinning process. I n general twins are formed during t e n s i l e deformation only near sub-boundaries, f o r example see Fig u r e 32, or g r a i n boundaries, which probably act as stress r a i s e r s . The twins appear i n some cases t o be able to " r e f l e c t " from g r a i n boundaries (Figure, 34). ; • ., . I t w i l l be noted t h a t the twins shown i n Figures 31, 3*S are extremely t h i n , s i m i l a r in appearance t o Neumann bands i n i r o n . When a c r y s t a l i s subjected t o a more complex s t r e s s s system , e.g. compression i n a v i c e , more t y p i c a l l e n t i c u l a r deformation twins are formed. There i s a tendency f o r wider twins t o form at room temperature and t h i n ones at l i q u i d n i t r o g e n temperature, but both can occur at e i t h e r temperature. F i g u r e 33 shows the two types of twin formed i n a c r y s t a l bent at -196°C. Cobalt twins r e l u c t a n t l y compared w i t h z i n c or magnesium. I t has not been p o s s i b l e t o o b t a i n a c r y s t a l w i t h a s u f f i c i e n t volume of twins t o giv e a c l e a r X-ray p i c t u r e of the twinned s t r u c t u r e , f o r the deformation r e q u i r e d gave r i s e t o too much as t e r i s m i n the Laue spots. O p t i c a l goniometric determinations of the h a b i t plane f o r the t h i n type of tw i n have been c a r r i e d out f o r two c r y s t a l s (by iVhabit p l a n e " i s meant the plane of the m a t r i x c r y s t a l on which the t w i n l i e s , - . ( I t w i l l be the same as the composition plane of the m a t r i x c r y s t a l , which i s the i n t e r f a c e between two tw i n c r y s t a l s ) . In both cases the h a b i t plane was w i t h i n a few degrees of {ll2l} . Appendix 3 gives d e t a i l s of the determination. Figure 32» Twins at a Sub-Boundary in Crystal 9. Mag: X 300 -6i-Figure 3k. Twin 'Reflecting"from a P a i r of G r a i n Boundaries. C r y s t a l Bent at -196°C. Mag: X 200 - 62-{ll2i} is a rather unusual twin plane for a hexagonal metal, the only other case being titanium^. Further, H a l l ^ reports a more usual {1012} composition plane for "annealing twins" m cobalt. Hall's specimens were coarse-grained cobalt prepared by a slow cool from the melt. His "twins" were presumably the result of crystals i n the cubic form giving hexagonal structures with two different orientations. Figure 35 shows the positions of the four £lll} planes for a cubic l a t t i c e on a sterogram, the planes being numbered 1, 2, 3, and 4. It can be seen that only two types of transformation twin could form, type A where planes 1-2, 1-3, 1-4 give basal planes i n the hexagonal form, or type B from planes 2-3, 3-4, 4-2. The \ position of the twin planes (i.e. the planes of symmetry) for the two types of twin are shown m a standard hexagonal cobalt stereogram i n Figure 36. It may be that the twins analysed by Hall were actually type A twins, although they are some 8° from the {1012}planes. 3. Fracture Tensile testing was often terminated by fracture near one grip. The fracture surface was always stepped, with small shiny facets. A large area of shiny surface such as i s observed m the cleavage of zinc was never obtained. Figure 37 shows a typical fracture i n a crystal pulled at room temperature. - 63-Figure 35. Positions of the { i l l } Planes i n a Standard Octahedral Projection for a Cubic Structure. = f i l l } Poles »—+ = {110> Directions -6k-0 0 0 1 10 10 F i g u r e 36. The two'Possible P o s i t i o n s f o r Twin Plane Derived from a Cubic C r y s t a l by the Cubic •—• Hexagonal Transformation. -65-Figure 37. Fracture Surface on a Cobalt Crystal Mag: X Ik. -66-LAUE ASTERISM A M D RECOVERY Crystals with extensions up to around 100$ shear strain showed l i t t l e asterism. Crystals with very high strains showed extreme, asterism, such that the orientation of the crystals was d i f f i c u l t to recognise, the spots consisting in many cases of short arcs of Debye ring (Fig. 38). One crystal was severely deformed and then heated to 600°C for half an hour followed by a rapid cool.Its Laue back reflection picture i s shown m Figure 39- A high degree of la t t i c e distortion was obviously present. A further anneal at 600°C for 3 hours gave l i t t l e change. The microstructure showed that while small areas with a new hexagonal orientation had formed, no macroscopic recrystallisation had taken place. The transformation, i t appears, does not lead to a total elimination of a l l l a t t i c e strain. -67-F i g u r e 3 8 . Laue Picture of a Crystal Extended Around 200$. Molybdenum Radiation. -68-Figure 39• Laue Back Reflection. Picture of a Crystal Extended to the Order of 200$ Shear Strain followed by an Anneal at 600°C for \ hour. -69-DISCUSSION OF THE TENSILE TEST DATA 1. Theories of Glide and Work-Hardening m Metals. Seeger has developed a detailed theory for plastic deformation i n iretal crystals with close-packed structures. His ideas have been expressed m a series of papers, the most comprehensive of which is given as reference Ik. Basically he assumes the flow stress 3 to be made up of two parts, and 3 ~ . S P » "the stress from long range elastic interactions , G U is independent of temperature except for variations i n the elastic modulus. "3g arises from dislocations that thread the glide plane. It i s the stress needed to push dislocations through such "forest" dislocations. When dislocations of density N and strength b each move over an area of glide plane A , the shear strain produced is given by6= bAn. the strain rate may then be expressed by the equation-6 = bAN^o JlMl -equation 1 where^is a frequency factor, U ( ^  ) i s an activation energy and 3 is the applied shear stress. U (3) is the energy needed to tear a locked dislocation away from i t s locking point. This i s taken as U ) = U Q - v (<§ - 3Q). U q is the energy of thermal vibration that would be needed to free a dislocation from i t s locking point i f there were no applied stress. It i s independent of temperature, v is the "activation volume", equal to bdl, where b i s the strength of the glide dislocation, d is the effective "thickness" of a forest dislocation, and 1 is the mean distance between forest dislocations. -70-Now the flow stress for a certain temperature w i l l be given by U D - kT i n (NAbV o /£) <5 =dG + - equation 2. Ug Above a c r i t i c a l temperature Tc = L. i n (Nftb^/g), ° w i l l be independent of temperature. Differentiating with respect to €, the work-hardening slope w i l l be given by ^ = " " ^ " l e v2 [ U ° " k T l n ( M b^o/e|] equation 3-When there i s basal glide only, 1 and thereforev w i l l be independent of strain. This gives Q = ^ w h i c h i s nearly independent of temperature Basinski 3^ has since formulated some ideas which differ from Seeger's i n several important aspects. Where Seeger assumes uniformly distributed obstacles a l l of which are capable of breaking down, Basmski takes the number of sources activated to be dependent on temperature. He obtains an expression for the strain rate L kT~ -equation k € = NkT.AbV0 exp, which differs from Seeger's expression (equation l ) in the pre-exponential temperature term. 2. Interpretation of the Results of the Present Work There i s l i t t l e difference m the general shape of the stress-strain curves from those for the other hexagonal metals. Some important differences i n the flow behaviour were however revealed, and w i l l be discussed separately. a) Variation of the work-hardening slope with temperature The work hardening slope is_ a function of temperature. The variation i s much greater than can be explained on the basis of variation m the elastic moduli, for Young's modulus changes only from 20.5 x 10 5 to 22cO x 10' Kg/cm2 when cobalt is cooled from 150°C to l i q u i d nitrogen temperature. According to Seeger, for basal glide = Insertion of Seeger's expression for U (3 ) into Basinski's rate equation (k) would not alter this result. Below the recovery range, (i.e. N a constant with time), 6 should be independent of temperature. It is extremely unlikely that recovery would take place i n cobalt at any of the testing temperatures used i n this investigation. The most l i k e l y explanation (see next section) is that 1 is not constant with & ,but that the forest density increases. — — is therefore negative, giving u 0 v kT WBbVn . i n . v^ e As the temperature rises © w i l l decrease , which is i n accord with observations.. The evidence for a temperature-independent work-hardening slope i n the other hexagonal metals i s not m fact so clear as Seeger claims, and more extensive experimental data may well prove this contention unwarranted. b) Non-Observance of the Cottrell-Stokes law. The Cottrell-Stokes law is not followed, either for temperature changes or for changes in the strain rate. Before this result can be dis-cussed, the meaning of the Cottrell-Stokes law must be considered. The constant I2L ratio implies a proportionality between the stress due to elastic i n t e r a c t i o n s , ^ G , and that connected with dislocation inter-sections or other thermally activated processes,£ . That such a proportionality leads to a Cottrell-Stokes law can be seen as follows:-- 7 2 -Let^,, and^jjbe the flow stresses before and after a change i n temperature or i n strain rate. 3 1 = ^ G + £ S i <5 2 = C^ G + ^ s 2 T f ^ s l £ s2 r ~3 C l ' "S - 2 <5G 1 © G Then = * S 1 ^ 5 g =  C\*r~ C g*> = °J^l = Constant <*. ^ s i + ^ G CI^G + a G 1 + C l Several explanations for the constant ratio have been put forward, the most thorough treatment being that given by B a s i n s k i 3 ^ who reached the following conclusions. The elastic and thermally activated portions of the flow stress both arise from interactions between the same dislocation groups, i.e. the forest dislocations give rise to both £ Q. an<3- ^ (this differs from Seeger's interpretation of 3 ^ , but does not alter his equations). On this model, work-hardening i s caused by an increase i n the forest density, r9 _ and ^ ris i n g i n the same u s ratio. Non-observance of the Cottrell-Stokes law indicates that deformation i n cobalt may be controlled by a mechanism different from that i n magnesium. Arguments w i l l now be put forward that suggests this i s unlikely. It i s perhaps significant that the Cottrell-Stokes law appears not to be followed by face-centred cubic metals i n the easy glide region, i t being during easy glide that the deformation behaviour of face-centred cubic metals is most similar to that for hexagonal metals. -73-The lowest easy glide slope observed i n copper-^ gives ^/G = 1.7 X 10~\ Stress- strain curves for cadmium, magnesium and zinc a l l have 0/G around !•.§ x 10"^. In the case of cobalt, G for shear across the basal plane is 7-5 x 105 Kg/cm2 (see appendix 4). Taking 0 at room temperature as 140 Kg/cm2/ unit shear strain, ®/G = 1.8 x 10"^, which is of the expected order. From combined data on the temperature and strain rate dependence of the i n i t i a l flow stress, activation energies for s l i p , U, of around 35 kT have been determined (see appendix 5)« This may be compared to a value of 17 kT obtained by Basinski 1^ f o r magnesium. It can be shown (appendix 5, p. IO9) that for the same locking mechanism U should be approximately proportional to G. G for polycrystalline cobalt i s around three times that for magnesium. Considering the large experimental scatter i n both investigations, the two values for U are reasonably consistent. In summary, the similarity i n the general form of the stress-strain curves and the similar values for work hardening slope and activation energy for s l i p make i t l i k e l y that the basic flow mechanisms in cobalt are similar to those for the other hexagonal metals and for face-centred cubic metals i n their region of easy glide. An explanation is therefore nee-4 / ded to explain why, with the same flow mechanism,3 Q and should be proportional to one another for magnesium but not for cobalt. The difference i n Cottrell-Stokes behaviour probably l i e s in the ease with which magnesium can s l i p on non-basal planes. In the present investigation s l i p on a second plane has never been observed, even m the severely stressed region around a hardness indentation. The absence of non-basal glide is probably a function of the low stackirg fault, energy, which makes i t very d i f f i c u l t for a dislocation to change i t s s l i p plane. -Ik-In magnesium the forest dislocations build up m number as the specimen extends, whereas in cobalt the increase m the number of forest dislocations w i l l be very small compared to the increase m the number of dislocations lying m the basal plane. The following mechanism i s suggested. Figure kO depicts two possible situations. In A the number of forest dislocations i s of the same order as the number i n the basal plane. We shall take this to be the case for magnesium. In B the density of s l i p dislocations i s much greater than the forest density. In case A the flow stress is determined largely by the forest density, which increases as the specimen deforms. In case B the forest density increases very l i t t l e . If i n case A the forest density did not increase, the flow stress would be lowered with strain, for deformation would simply give more glide dislocations moving through the same forest. In case B, however, an increase m the number of glide dislocations does not lead to any large change i n 3 s• To see this consider the glide dislocations 1, 2, 3, i n Figure kO B, locked by a forest dislocation cA . Dislocations 1, 2 cannot move forward u n t i l dislocation 3 has cut throughCX. They take no part i n the kinetics of flow, except i n so far as they help to push dislocation 3 through the barrier. In other words, i n the rate ex-pressions of equations 1 and k dislocations 1, 2 do not contribute to N. In case B, therefore,^ s and so A^ s w i l l be constant with strain. Cobalt tends towards this state. But we are l e f t with the problem of why should the crystal work harden? The only dislocations that can give rise to flow are the "leading" ones such as 1 m figure kO, and their elastic interactions with the forest dislocations w i l l not vary with strain. We must assume m this case that hardening is caused by some form of elastic interaction between groups of dislocations held between the trees, as well as the constant forest-glide dislocation interaction. -75-Direction of Dislocation Movement Two Hypothetical States for- the Distribution of Dislocations i n the Slip Plane. o = V A Forest Dislocation A Glide Dislocation -76-The conclusions may now be summarised:-i ) In cobalt, unlike magnesium, the forest density rises very slowly with strain and is always small compared with the density of glide dislocations. This means that 3 s should rise only very slowly with ^ t o t a l * w n i c n 1 S i - n accord with observation. i i ) The work-hardening slope i s caused by two factors -a) the slow increase m forest density. This gives rise to the small but definite temperature-dependence of 0 . b) an elastic interaction between groups of dislocations held up by the forest. In general, the properties of cobalt seem to l i e much closer to the model proposed by Seeger than to that of Basinski. One further point concerning the Cottrell-Stokes law for temperature changes should be mentioned. The experimental observation that^5/^ appears to be the same function of 3 for different crystals, i.e that ^s/$G + 3 s) ~ ^ ( ^ s + 5 Q) means that at each stress ^|/3G for different crystals i s a constant, merely indicating an identical dis-location arrangement for different crystals. While of l i t t l e theoretical significance, i t does give a useful correlation of data from different crystals for this type of measurement. -77-THE COBALT TRANSFORMATION 1. Introduction During the course of the present work certain observations have been made of transformation markings in cobalt that supplement the work of others. The most comprehensive paper on deformation markings i s that of Bibring et a l . 39^ and i t is to this paper that the present findings w i l l be related. Bibring et a l . formed the following conclusions:-1. When heated and cooled through the transformation temperature coarse-grained cobalt returns to a wholly hexagonal room temperature structure. 2 . The individual grains retain the same hexagonal orientation. 3. There i s some break-up of the structure into small areas of new orientation. h. Two types of transformation marking occur-a) "Primary" markings consisting of fine parallel striations that run almost completely across each grain and are by far the most numerous and most highly developed. They appear on heating (^ -» c* transformation). b) A "secondary" system made up of shorter striations. which are much less numerous and thicker than the others, and follow several directions on the specimen surface. They are formed on cooling. Figure hi, reproduced from the Bibring paper, shows both types of transformation marking. 5. The striations observed are in every case traces of -[ill"} planes of the cubic l a t t i c e or of i t s twin formed from the same hexagonal crystal. The primary markings always correspond to the trace of the ( l l l ) ^ (OOOl)^ transformation plane. -78-6. If the specimen surface i s polished, the primary markings do not become visible again when the metal is etched, whereas the secondary markings reappear. 2. Observations and Discussion Examination of the as-grown surfaces of cobalt crystals grown in the zone-refiner reveals clear primary markings, but i n general, secondary markings appear only near sub-boundaries or grain boundaries. Figures 42, 43, 44 show such markings. Two main conclusions can be drawn:-1) The primary markings form on cooling as well as on heating. 2) The secondary markings are not a necessary feature of the transformation. They occur only i n those areas where stresses arise through conformation forces between grams during the transformation. A few experiments have been done with an apparatus designed so that X-ray pictures of both the high-and low-temperature phases could be taken. A diagram of the set-up is shown i n Figure 45• The crystal was situated i n a slic&—glass tube wound with Chromel-A ribbon. A hole approximately 1/4 inch diameter served as an X-ray port. The film-holder was cooled by a fan, to prevent this from also cooling the furnace winding, a second glass tube with larger diameter was placed over the f i r s t . Helium was passed up the inside tube to prevent oxidation of the crystal. The temperature was measured by a chromel-alumel thermocouple with i t s junction i n contact with the specimen surface opposite the X-ray port. Laue X-ray back-reflection pictures of the same crystal taken at room temperature and at approximately 500°C are shown in figure 46. It can be, seen that, as previously reported, the (0001) plane of the hexagonal phase corresponds to a ( i l l } of the cubic phase. In agreement with Bibnng et a l . , crystals heated into the high temperature phase always returned to their -79-Figure 42. As-Grown Surface of a Zone-Refined Rod. Secondary Transformation Markings near a Grain Boundary. Etched. Mag: X 100. Figure hh. As-Grown Surface on a Zone-Refined Rod. Etched. Mag: X 100. - 8 1 -Film Holder Silica-Glass Tubing Furnace Winding Crystal Collimator ^X-Ray Beam Thermocouple Leads Figure 4j5. Sectional View of Apparatus for Taking X-Ray Back-Reflection Pictures of the High Temperature Phase. Actual Size. -82-A B Figure 46. Laue Back-Reflection Pictures of the same Crystal Taken at Room Temperature, A, and at Approx. 500°C, B. The Original Pictures did not Reproduce WeLI, and so the Positions of Their Spots have been Drawn. -83-original room temperature orientation. One crystal was cycled between room temperature and 500°C six times, with l i t t l e break-up of the structure. To further examine the metallographic features of the transformation, some crystals were heated to 600°C for a half hour under high vacuum, and cooled slowly. The heating and cooling curves are shown i n figure 1+7• Subsequent metallographic observation revealed some small regions of new orientation, normal primary markings, and a few secondary markings near the regions of new orientation. A water-quench from 600°C gave rather more break-up of the structure, but the bulk of the crystal remained unchanged. The only point of possible controversy is the nature of the secondary markings. They look i n some cases extremely lik e mechanical twins, for example compare Figures 1+1, 1+1+, with Figures 31- 3^ > However their orientations as given by Bibring et a l . rule out this p o s s i b i l i t y (see figure 1+8). It must be assumed that they are very small regions with different orientation given by transformation on a {ill]plane of the face-centred cubic phase other than the principal transformation shear plane. - 8 5 -Figure 48. A Standard (OOOl) Stereogram for Hexagonal Cobalt, Showing the Positions of the {"111} Cubic Planes (&) and the { l l 2 l } Hexagonal Planes (0). -86-SUMMAEY AND CONCLUSIONS An investigation into the tensile properties of commercial purity-cobalt crystals at temperatures between -196°C and 150°C has given the following results : -1. The resolved shear stress-shear strain curves for cobalt are similar i n general form to those for the other hexagonal metals zinc, cadmium, and magnesium, with an i n i t i a l linear region up to around 150$ shear strain followed by an up-turn. The value for e/G i n the i n i t i a l linear region i s very similar for a l l four of these metals. In cobalt the upturn tends to come later and is of smaller magnitude. 2. The room temperature c r i t i c a l resolved shear stress for commercial purity cobalt has been evaluated at 97 Kg/cm2. At liq u i d nitrogen temperature the value rises to around 170 Kg/cm2. Values for high purity cobalt are a l i t t l e lower, 65-70 Kg/cm at room temperature. 3. Unlike magnesium, the Cottrell-Stokes law i s not followed, either for temperature changes between room temperature and -196°C or for hundred-fold changes i n the strain rate at room temperature. An explanation for this on the basis of the relative ease of non-basal glide has been put forward. k. Cobalt twins reluctantly compared to zinc and magnesium. Twinning was never observed during room temperature tensile tests. There are two types of twin, very thin ones similar m appearance to Neumman bands i n iron, and more normal twins of lenticular form. The thin twins have a {ll2l} habit plane. 5« After large extensions, of the order of 200$ shear strain, metall-ographic observation revealed the presence on an etched surface of small needle-like markings. They were not definitely identified, but were probably fine twins. -87-6. An activation energy for plastic flow i n cobalt has been tentatively determined to be around 35 kT. 7- A crystal extended to the order of 200$ shear strain does not recrystallise when annealed at 600°C, nor does the transformation remove a l l the l a t t i c e strain. One of the primary purposes of the investigation was to compare the deformation characteristics of the low stacking fault energy hexagonal metal cobalt with those for the high stacking fault energy hexagonal metals magnesium, cadmium and zinc. As noted above, the stress-strain curves for cobalt are very similar to those for the other metals, and differences i n plastic behaviour which have been found cannot be ascribed directly to a difference i n stacking fault energy. It appears that stacking fault energy is a much less c r i t i c a l parameter i n the deformation of hexagonal metals than i t is for face-centred cubic metals. Some metallographic and X-ray studies of the cobalt transformation led to the following conclusions -1. The primary transformation markings, as defined by Bibring et a l . 39. occur during the cooling transformation as well as on heating. 2. The secondary markings are not a necessary part of the transformation, occuring on cooling only near grain boundaries or sub-boundaries. 3- In agreement with Bibring et al.39, a crystal of cobalt returns to i t s original room temperature hexagonal orientation when i t is heated and cooled through the transformation temperature. A small amount of break-up of the structure always occurs. .88-SUGGESTED FUTURE WORK The p r e s e n t i n v e s t i g a t i o n , t h e f i r s t on t h e m e c h a n i c a l p r o p e r t i e s o f s i n g l e c r y s t a l s o f c o b a l t , has been t o some e x t e n t e x p l o r a t o r y i n n a t u r e . I t has been d e m o n s t r a t e d t h a t t h e d e f o r m a t i o n c h a r a c t e r i s t i c s a r e s i m i l a r i n o u t l i n e t o t h o s e f o r t h e o t h e r h e x a g o n a l m e t a l s t h a t s l i p p r i m a r i l y on b a s a l p l a n e s , namely cadmium, magnesium, and z i n c . B a s i c p a r a m e t e r s s u c h as t h e c r i t i c a l r e s o l v e d s h e a r s t r e s s , and t h e v a r i a t i o n o f t h e f l o w s t r e s s and o f t h e work h a r d e n i n g s l o p e w i t h t e m p e r a t u r e , have been d e t e r m i n e d . F u t u r e d e v e l o p m e n t s , w i t h t h i s as b a s i s , s h o u l d l i e m t h e f o l l o w i n g d i r e c t i o n s --1) An a n a l y s i s o f t h e l e n t i c u l a r d e f o r m a t i o n t w i n s and o f t h e " d e f o r m a t i o n m a r k i n g s " . T h i s w i l l b e s t be done w i t h a m i c r o - f o c u s X - r a y u n i t . 2) An i n v e s t i g a t i o n i n t o t h e e f f e c t o f p u r i t y on t h e d e f o r m a t i o n c h a r a c t e r -i s t i c s . 3) A more d e t a i l e d s t u d y o f t h e C o t t r e l l - S t o k e s b e h a v i o u r , e x t e n d i n g t h e s t u d i e s down t o l i q u i d h e l i u m t e m p e r a t u r e s . h) A s t u d y o f t h e d e f o r m a t i o n c h a r a c t e r i s t i c s as t h e t e m p e r a t u r e i s r a i s e d t o n e a r t h e t r a n s f o r m a t i o n t e m p e r a t u r e , where t h e p a r t i a l s o f t h e e x t e n d e d d i s l o c a t i o n s s h o u l d be w i d e l y s e p a r a t e d . -89-APPENDIX I ELECTROPLATING COBALT ON COBALT The following electrolyte, given m Mantel, "Industrial Electrochemistry", p. 2 3 6 , was used. CuSO, .7H20 504 grams/litre Na CI 17 grams/litre 45 grams/litre A cobalt plate was used as anode. For plating approximately one centimeter at the end of a crystal, the following procedure was found to give a coating with good adherence and a rough surface that was easily wetted by solder 1) Reverse the current at 120 m. a. for 15 mms. 2) Lower the current to around ^ m. a., then reverse the polarity. 3) After 10 mins., increase the current to 90 m.a. 4) Plate at 90 m. a. for 1 1/2 hours. 5) Plate at 125 m. a. for l/2 hour. -90-APPENDIX II THE DETERMINATION OF RESOLVED SHEAR STRESS-SHEAR STRAIN CURVES Boas UO gives the following relations between resolved shear stress and load, and between resolved shear strain and elongation. resolved shear stress 3 resolved shear strain £ — c o s «*o — sin 2o( Q where F = load, A Q = i n i t i a l cross sectional area, 1Q l-j_, are the i n i t i a l and f i n a l specimen lengths,9C*Q, 0( Q, are the i n i t i a l values for these two angles as defined previously (page 27 ). It should be noted that 3 is not a linear function of F/A0, nor € of 1, therefore one cannot simply change the scales lo on the axes of a stress-strain plot. The calculations must be repeated for each point on the curve. As an example, i n table 12 are reproduced calculations for the resolved shear strain corresponding to ten inches on the strain axis of the stress-strain plot on the Instron chart. \ TABLE XII Calculation of Resolved Shear Strain Corresponding to 10 Inches on the Strain Axis of the Instron Chart.Cross Head Speed taken as 0.02"/Mm. dumber of Crystal A cm^  o l 0 m s chart-s peed ms/mm ^ f o r 10" on chart 1 C O S " * © € for 10" on Chart 1 .0697 2.03 5 ,0157 .9206 11.47 0.250 2 .0658 1.34 5 .0299 .8046 2.13 .0822 3 .0658 2.97 5 .0135 .8306 2.92 .0483 4 .0684 1.97 2 .0508 .9477 4.81 .273 5 .06Qk 1.96 5 .0204 .8852 4.44 .105 6 .0671 2.00 5 .0200 .9283 4.81 .106 7 .0703 1.99 5 .0201 .9211 u 11.47 .256 8 .0693 2.55 2 .0392 .8473 2.66 .130 9 .0660 2.28 2 .0436 .9542 4.81 .230 10 .0707 2.25 2 .Okkk .9000 2.92 .152 11 .0707 3-35 2 .0299 .8457 2.37 .0868 12 .0726 3-40 2 .0294 .8094 2.20 .0833 13 2.18 2 .OU59 .9187 3.42 .180 l4 .0736 2.06 2 .0485 .9191 6.39 • 332 J-M 1 .0731 1.60 2 .0625 1.0555 9.57 .603 J-M 2 .O67U 1.63 2 .0613 • 9930 5.76 • 379 -92-APPENDIX III DETERMINATION OF THE HABIT PLANE FOR DEFORMATION TWINS The procedure used was as follows. A one-circle goniometer with a b a l l joint for mounting the crystal axially was b u i l t , and is shown m Figure 49. The crystal was eleetropolished, bent at l i q u i d nitrogen temperature to give twins, and then straightened and mounted i n the goniometer. The goniometer was clamped to a stand on the track of an X=-ray unit, i n such a manner that the crystal was vertical, and a back-reflection X-ray picture taken. The goniometer was then placed undera bench microscope, where measurements were made of the angle's between the axis of the crystal and the twin traces as seen on the crystal surface, using a protractor eyepiece. Measurements were taken for a series of positions of the crystal, which was rotated about i t s axis. Details of the arrangement are shown i n Figure 50. 0 is a measure of the rotation of the crystal and measures the slope of the twin traces relative to the axis of the crystal. Two crystals have been analysed m this manner. F u l l details of the measurements for one crystal are given i n table XIII. TABLE.XIII . • Measurements Corresponding to Fig. 50. e ° 0 -33, -33 27, 27, 28 17.5 -36 22 31 47.5 -35 77.5 -28 107.5 -27 137.5 -33 167.5 -29, -30 -21, -21 197.5 -30, -29 -24, -23 227.5 -31, -30 -8, -7 257.5 -23 14 287.5 -29 -10 26 317.5 -35 -13, -12 +32, "35 337-5 -36 -24 -93-Figure U9. The C r y s t a l Goniometer, w i t h a Specimen i n P o s i t i o n . Approximately h a l f a c t u a l S i z e . -9k-These values are plotted i n the form of a stereogram (Figure 51) and the poles of four twin habit planes are found. In Figure 52 the twin plane poles are replotted i n the stereogram given by the Laue X-ray back-reflection picture, reproduced i n Figure 53, which i n this case has the basal plane almost exactly at the centre, thus simplifying the procedure. It should be noted that the film must be viewed from the side opposite to the crystal. It can be seen that the twin habit planes correspond to {ll2l} planes to within a few degrees, i n fact the correlation i s closer than could have been expected from the experimental procedure. '-93-u Film Holder -X-Ray Beam Collimator Crystal Protractor Microscope Eyepiece Goniometer Scale Figure 5Q° Arrangement of the Goniometer i n -front A'., of the X-Ray Unit and under the Bench Microscope. The Zero for Measure-ments of 9 was taken at the Value when the X-Ray was Taken. -96-r ot ation cr y st a I ax i s Figure 51. Plot of the Directions of the Twin Traces. Values taken from Table 13. o = Directions of the Twin Traces A = Poles of the Twin Habit Planes -97-F i g u r e 52. Twin Habit Planes i n a Standard (0001) Cobalt Projecti A= Twin Habit Plane Poles O = {1121} Poles. -98-Figure 53 Laue Back-Reflection X-Ray Picture of the Crystal used for Twin Orientation. The Crystal Position Corresponds to 9 = 0 in Figure 50--99-APPENDIX IV SHEAR MODULI FOR COBALT CRYSTALS Crystals with hexagonal symmetry require only five independent elastic constants to specify completely the relations between stress and strain. In terms of stiffness coefficient, these are C-^, Cj_2, C]_3> O33, and C ^ Values for these, taken from Reference 41, are given i n Table XIV. TABLE XIV STIFFNESS COEFFICIENTS FOR COBALT At 25°C i n Kg/cm2 c l l 3.131 x 10 6 C12 1.682 x 106 C13 1.047 x 106 C33, 3.647 x 10 c44 O.769 x 10 6 Two values for the shear modulus G w i l l be calculated, one for shear stresses across the basal plane ani the other for shear stresses par a l l e l to the hexagonal axis (there i s only one value for each because the elastic properties of hexagonal crystals have rotational symmetry about the six-fold axis). G i s related to S , the compliance coefficients, by the relation (Reference 42, P. 21) VG = + [ ( s u -s 1 2 ) - I s J (1-tf 2 ) + 2 . ( S u + s 3 3 - s 1 3 -s^)^ 2 ( i-^) where ^ = the cosine of the angle between the direction considered and the hexagonal axis. For the two cases considered:-l ) Shear parallel to the hexagonal a x i ^ . Y - 1. l/G = S^. From Reference 43. s41). =  1/Chh' Therefore G = C, , = 7.69 x 10^ Kg/cm2. -100-2. Shear across the "basal .plane. Y= o. l/G = 1/2. Shh + ( S 1 X - S 1 2) S l l " S12 =" 1/(C 1 1-C 1 2) = 1/1.449 x 10"5 l/G = (1/1.538 + 1/1.449) x 10"6 = 1/0.746 x 10_6 G = 7-46 x lO^ Kg/cm2 A value for polycrystalline cobalt, taken for comparison from Reference 44, is given as G - 7«73 x 105 Kg/cm2„ It appears, therefore, that cobalt i s f a i r l y isotropic i n i t s shear modulus. -101-APPENDIX V ACTIVATION ENERGY FOR SLIP . 1. Theory Seeger's rate expression (equation 1, P°69 ) will firs t "be examined. 6 := bANVexp kT or In 6 = In b A N V + V(<?-<3G-) _ Uo u o kT k'T When the strain rate is changed at constant temperature. In \> AN. V + • V(. $,-<$&) k T u0/: kT In €, = la 6, = In b AN. V + V - U^/ In 6, — •• In € a = j^p* A ^ , where A ^ is the measured change in flow stress. Therefore the same change in cross-head travel rate, for the same value of In 6, - l n € j , ^ ^j-should retain the same value for change in strain rate experiments carried, out at different temperatures. At lower temperatures, A£ should be lower. This is opposite to observations •. It seems unlikely that Seeger's assumed form for the stress-dependence of the activation energy is so grossly untrue that i t is wrong in sense. More likely his assumption that U Q is temperature (or stress) independent is invalid. Let us look at the true meaning of U Q more closely. Refer to Figure 54 A. Let F (oc) be the function followed by the force F acting on a dislocation at distance oc from the centre of its locking mechanism. The locking may be considered a dislocation cutting process although the treatment given here may be applied to other barriers. The activation energy U needed from thermal vibrations to free the dis-location is given by --U = (F-FA) \oc If'-?* where F^ is the .applied force on the dislocation. Fig. 5 4 A F(x) 'Max Area i n Dotted Rectangle imx Fig. 5 4 B X, 'f to Area Shaded -f F = F« Area Shaded . ' :- ii.. Figure 5 4 . Illustration of the Activation Energies Required';, to free a Dislocation from a Locking Mechanism with Force Curve F (x). -103-U = j p ^ ( P - P A ) ^ - J ^ (F-F A ) \ ' ^fi 4x+ (F.-P) \ >r~-o JF--0 )f-.Q  R }f--  This i s ill u s t r a t e d i n Figure 54 B« We may equate the f i r s t term with.Seeger's U , and the second with his '~ ~v ac Let / F-f* - a G ) v , giving u = u 0 - a - a G ) v + (F -F) ^ ( F~f* # (F.-F) ^  = U" If the applied stress i s raised either by temperature or strain rate changes, (see Figure 54 c), U , v are unaffected, and u ' gets larger. The strain rate i s now given by x £ =\ AWV exp. ["- uo-(^"'^5)V + U j L kT J Using this modified Seeger equation, we w i l l treat the case as before when the strain rate i s changed at constant temperature. kT In €, = lnbAN^ u 0 kT + kT _ c5tV kT In Gx = InbANV _. u D kT kT kT In 6, - In 6 2 - , kT (a, - 3* ) K - < ) kT 2 For €,>€x j 3 , > gXf A 3 is positive U^ >^ U 2 (Ug - U^ ; i s negative In €, - l n € a = J L - . (v ' A U J ) For the same change i n strain rate but at different temperatures, jjr°( V ~ A ( J — ) j[ S a constant, neglecting changes i n the function F (oc) through variations i n the elastic modulus with temperature. Now refer to Figure 54 C. As the temperature is raised, Y-^ and F2 are lowered. The area representing (v A £ - A U ) w i l l therefore become longer. Since this -104-area should, from t h e above r e l a t i o n , remain constant i n magnitude, i t f o l l o w s t h a t A 3 must decrease. This i s i n accord w i t h experimental observations. I t i s concluded t h a t Seeger's expression U = U Q -(£ - 5 Q ) . V must be mod i f i e d t o U 4 J 0 + U - ( 2 - 3 Q ) ' V J i n order t o f i t the experimental observations. I t i s not p o s s i b l e t o c a l c u l a t e values f o r U D^ U', without ,a d e t a i l e d knowledge of the f o r c e f u n c t i o n F (x). 2. Experimental Determination 36 B a s i n s k i has d e r i v e d a formula r e l a t i n g a c t i v a t i o n energy w i t h C o t t r e l l -Stokes parameters f o r both temperature and s t r a i n r a t e . As the method i s o b v i o u s l y i n a p p l i c a b l e t o c o b a l t , i t w i l l not be de s c r i b e d here. Approximate values f o r U have been determined i n the f o l l o w i n g manner. Fig u r e 55 gives the i n i t i a l r e s o l v e d shear s t r e s s versus temperature curve f o r c r y s t a l 10. Superimposed on t h i s curve i s the s t r a i n r a t e data from c r y s t a l 12 (Table 7), f o r which a r i s e i n s t r a i n r a t e by a f a c t o r of 100 x gave the f o l l o w i n g averaged increases i n r e s o l v e d shear s t r e s s . 418° K 3.5 Kg/cm 2 293°K 6.1 Kg/cm 2 77°K 8.75 Kg/cm 2 These gave three p o i n t s on a flow s t r e s s curve at a s t r a i n r a t e 100 x higher than t h a t f i r s t p l o t t e d . A new flow stress-temperature curve f o r the higher s t r a i n r a t e was drawn through the three p o i n t s , u s i n g the assumption t h a t the shape of the curve was not a l t e r e d . Wow 6 = const, e" U ( 3 ) kT For the same s t r e s s , but d i f f e r e n t s t r a i n r a t e s U ( $ ) w i l l be the same. In,a p l o t of I n 6 versus l / T , f o r the same s t r e s s , the slope of the curve w i l l be -U/K. From F i g u r e 55 w e have two p o i n t s on such a curve f o r each s t r e s s . Temperature °K Figure.55- Flow Stress Versus Temperature for Crystal 10 (First Cycle), with an Estimated Curve for a Strain Rate 100X Greater, €, = 100e 2 , Taken from Strain Rate Data fny C.T'VRT.PI 1 I P . . . . _ - 106-o r-{ w o H 90 104. 5 1 -.3.3 13t .002 .004 .006 .008 .010 .012 .014 Figure, 56 are g l V e n on each Lane. Units f o r £ -107-The In 6-l/T relationship was assumed linear and slopes were taken for a series of stresses represented "by the horizontal joining lines i n Figure 55. Values are plotted i n Figure 56. The strain rate units are arbitrary, taken straight from the cross-head travel rate, but this i s immaterial as only the change in strain rate determines the slope. In each case the slope should be -U (3 ) / 2 ^  For a given strain rate should be a constant. Values for the slope divided by temperature kT for either strain rate should therefore give a constant value. Figure 57 demonstrates that this i s so within the accuracy of the data. A complete set of values is given i n Table XV below. TABLE XV ACTIVATION ENERGIES FOR SLIP IN COBALT. CALCULATED FROM FIGURE 56 . Kg/cm2 -slope u/k T °K 1 U/kT-L T 2°K U/kT 2 172 1,110 2,553 70 36.5 80 31.9 159 1,670 3,841 88 43.6 100 38.4 139 2,530 5,819 134 43.4 150 38.8 124.5 3,125 7,188 177 40.6 200 35-9 113.5 3,846 8,846 221 40.0 250 35.4 104.5 4,348 10,000 264 37-8 300 33.3 90 8,333 19,166 365 52.5 400 47.9 The value for 3 = 9 ° Kg/cm is unreliable, for the slope of the l/T versus log€ line (Figure 54) i s very high and the difference (l/T^ - l/Tg) used i n calculating the slope i s so small that errors i n T-|_ and T 2 w i l l be magnified. Basmski 0 , using the Cottrell-Stokes parameters, has obtained values for U/kT of around 13 for copper, silver and aluminum, and of 17 for magnesium. At f i r s t sight, therefore, the present values seem a l i t t l e high. The discrepancy i s believed to l i e i n the large difference i n elastic modulus. We shall follow Basmski, (Reference 36, p. 40l) i n assuming 2o.ooa Figure 57. P l o t of U/k Versus T, Taken from Table 15, x = , o = T 2. From the Slope of the Curve, u/ k T =37-1 -109-u = a l l retarding forces proportional to G, the shear modulus. Now i f F (,x) = G F ° (-DC), where F ° (x) is a function independent of temperature. / F - F MAX (F-F A ) \ X 0 6 \F (OC) (F-Frt f lx OCGAF°(X) O C \ F ° ( K ) = G If, as appears l i k e l y , the form of F° (x) is similar for different metals, U w i l l be proportional to G. The following are standard values for G i n polycrystalline material. copper 4.2 x 10+5 Kg/cm2 aluminum 2.4 x 10+5 Kg/cm2 silver 3.8 x 10+5 Kg/cm2 magnesium 2.4 x 10+5 Kg/cm2 cobalt 7.7 x 10+5 Kg/cm2' In view of these values, i t i s not surprising that cobalt has an activation energy considerably higher than those for the other metals. It should be emphasised, however, that the values obtained m the present work are quite tentative. To get more reliable values a whole series of crystals would have to be tested. Furthermore the method is i n t r i n s i c a l l y inaccurate, depending on the measurement of small variations of flow stress with the strain rate. -110-BIBLIOGRAPHY 1. P.R. Thornton, P.B. H i r s c h , P h i l . Mag. 3, 1958, 738 2. R.E. R e e d - H i l l , W.D. Robertson, J o u r n a l of Metals 9, 1957, 496 3. R.L. B e l l , R.W. Cahn, Proc. Phys. Soc. A239, 1957, 494 4. A.F. Brown, Advances i n Physics 1, 1952, 427 5. L.M. Clarebrough, M.E. Hargreaves, Progress i n Metal Physics 8, 1959, 1 6. E.C. Burke, W.R. Hibbard, J o u r n a l of Metals k, 1952, 301 7. W.L. P h i l l i p s , Trans. A.S.M. 5^ , 1961, 50 8. E.H. Edwards, J . Washburn, E.R. Parker, J o u r n a l of Metals 5., 1953, 1525 9. A.H. C o t t r e l l , D.P. Gibbons, Nature l62, 1948, 488 10. H. Conrad, W.D. Robertson, J o u r n a l of Metals 9, 1957, 503 11. A. Seeger, H. Trauble, Z. f u e r Metallkunde 51, i960, 44l 12. W. Boas, E. 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