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The deformation of copper whiskers Saimoto, Shigeo 1960

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THE DEFORMATION .OF COPPER WHISKERS by SHIGEO SAIMOTO .A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE IN THE DEPARTMENT OF MINING AND METALLURGY We accept t h i s thesis as conforming to the ' standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE Members of the Department of Mining and Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA March, i960. In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f th e r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I 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 r e f e r e n c e and s t u d y . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by t h e Head o f 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 u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department Of Mining anrl Ifatuniirgy The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 3, Canada. Date A p r i l kf i<?6o.  i ABSTRACT The d e f o r m a t i o n o f c o p p e r w h i s k e r s was s t u d i e d by t e s t i n g them a t room and low t e m p e r a t u r e s i n a s p e c i a l l y b u i l t t e n s o m e t e r . The w h i s k e r s were g rown b y t h e s t a n d a r d method o f h y d r o g e n r e d u c t i o n o f c u p r i c c h l o r i d e . X - r a y s t u d i e s o f s t r a i g h t and k i n k e d w h i s k e r s showed t h a t c r y s t a l l o g r a p h i c d i r e c t i o n s o f t h e w h i s k e r a x i s o t h e r t h a n < 1 0 0 X < ( 1 1 0 > , and < ( l l l ) > a r e p o s s i b l e . I n a d d i t i o n t h e f o r m a t i o n o f c o h e r e n t t w i n s i s p o s s i b l e i n c o p p e r w h i s k e r s g rown by t h e above m e t h o d . T e n s i l e t e s t s a t v a r i o u s t e m p e r a t u r e s r e v e a l e d a s t e p e f f e c t , a h e s i t a n t f l o w and y i e l d p o i n t s i n t h e f l o w r e g i o n w h i c h were e x -p l a i n e d by p r o p o s i n g d i s l o c a t i o n mechan isms . T e n s i l e t e s t s i n d i l u t e s u l p h u r i c a c i d showed t h a t t h e o x i d e c o a t i n g i s n o t s o l e l y r e s p o n s i b l e f o r t h e s t r e n g t h o f w h i s k e r s . i i ACKNOWLEDGEMENT The a u t h o r g r a t e f u l l y acknowledges D r . V . G r i f f i t h s and D r . E. T e g h t s o o n i a n f o r t h e i r s u p e r v i s i o n and e n c o u r a g e m e n t . I t i s a p l e a s u r e t o acknow ledge M r . K. G. D a v i s f o r t h e many p r o f i t a b l e d i s c u s s i o n s . The a u t h o r i s i n d e b t e d t o M r . . R. G. B u t t e r s and M r . R. R i c h t e r f o r t h e i r t e c h n i c a l a d v i c e and a s s i s t a n c e . The w o r k was f i n a n c e d by R e s e a r c h G r a n t 7510-33 p r o v i d e d by t h e D e f e n c e R e s e a r c h Boa rd o f Canada . t9 6 a SUMMARY OF STAFF COMMENTS ON THESIS EXAMINATION OF S . SAIMOTO A p r i l k, I960. T h i s .was c o n s i d e r e d t o be a good t h e s i s . I t r e p r e s e n t s a l a r g e a m o u n t - o f w o r k , and i f t h e r e i s any a p p a r e n t l a c k o f c o n c l u s i v e r e s u l t s , i t s h o u l d - b e b o r n e i n mind t h a t a g r e a t d e a l o f p r e l i m i n a r y i n s t r u m e n t a t i o n , c a l i b r a t i o n and t e c h n i q u e d e v e l o p m e n t has been n e c e s s a r y . No m a j o r . c r i t i c i s m .o f t h e w o r k was made. A p o i n t w a s . r a i s e d c o n c e r n i n g t h e r a t e o f d i s s o l u t i o n . o f CU2O i n . s u l p h u r i c a c i d , and hence o f t h e adequacy o f t h e p r o c e d u r e u s e d . H o w e v e r , i n s p i t e o f such p o s s i b l e d o u b t s , i t was f e l t t h a t t h e c o n c l u s i o n s d rawn f r o m t h i s . p a r t o f t h e w o r k w e r e b a s i c a l l y s o u n d . A few m i n o r t y p o g r a p h i c a l e r r o r s :were o v e r l o o k e d s i n c e t h e mean ing was n e v e r i n . s e r i o u s q u e s t i o n . The c a n d i d a t e ' s o r a l p r e s e n t a t i o n was g o o d . He answered q u e s t i o n s d u r i n g t h e d i s c u s s i o n p e r i o d w e l l . H i s t o t a l p e r f o r m a n c e i n d i c a t e s t h a t he has a good g r a s p o f h i s s u b j e c t . The s t a f f was unanimous i n f i n d i n g t h e t h e s i s c o m p l e t e l y a c c e p t a b l e . i i i TABLE OF CONTENTS Page I . INTRODUCTION . . . . 1 A * G e n e r a l . . . . . . . . • * • • • • « . • • • • » » • • 1 B . P r e v i o u s Work . . . . . 0 . . . . . . . . . . . . . 3 1* Growth • • . . • « « . . . . « « . . » « » . 3 2 . P h y s i c a l P r o p e r t i e s . . . . . . . . . . . . 6 C . Purpose o f P r e s e n t I n v e s t i g a t i o n . . . . . . . . . . 11 I I . EXPERIMENTAL . . 12 A . G r o w t h and S e l e c t i o n 12 B . Spec imen H a n d l i n g A p p a r a t u s . . . . . . . lk C . T e n s i l e T e s t i n g A p p a r a t u s . . . . . . . . 18 1. C o n s t r u c t i o n . . . . . . . . . . . . . . . . l 8 2 . C a l i b r a t i o n . 21 D. The A c i d and C o l d T e m p e r a t u r e B a t h . . . . . . . . . 22 E . Spec imen M o u n t i n g . . . . . . . . . . . 2k F . O r i e n t a t i o n D e t e r m i n a t i o n 2k G. Measurement o f Spec imen L e n g t h . . . . . . . . . . . 25 H . C r o s s S e c t i o n a l A r e a D e t e r m i n a t i o n . . . . . . . . . 25' I . E x p e r i m e n t a l P r o c e d u r e . . . . . . . . . . . . . . . 27 1 . G rowth S t u d y . . . . . . . . . . . . . . . . 27 2 . A c i d T e s t s 27 3 . C o l d T e m p e r a t u r e T e s t s . . . . . . . . . . . 28 i v TABLE OF CONTENTS (continued) Page I I I . EXPERIMENTAL OBSERVATIONS.AND RESULTS ... . * 29 A. Growth Observations . . . . . . . . . . . . . . . . 29 B. Orientation Determination . . . . . . . . . . . . . . . 30 C. .Cross Sectional Area ..................... 3^ D. Growth Kinks . . . . . . . . . . . . . . . . . . . . . . 35 E. Tensile Tests k2 1. The R e l i a b i l i t y of the Quantitative Measurements k-2 2. Effect of Oxide Layer . . . . . . . . . . . . ^3 3. Tensile Tests at Room and Low Temperatures ^7 IV. DISCUSSION . . . . - • . » . . . • « • < * . . . . . . . o . . « . . . 6^ A. Growth Kinks B. . Effect of Oxide Layer 68 C. Tensile Tests . . . . 68 1 . The Yield Phenomenon . 68 2 . P l a s t i c Flow . . . . . . . . . . 73 3. Propagation of Luders Band . . . . . . . . . 78 V. CONCLUSIONS . . . . . . . . . . . . » • « . . . . . . . . . 80 VI. RECOMMENDATIONS FOR FURTHER WORK . . . . . . . . . . . . . . 8 l V I I . APPENDIX 8.2 V I I I . BIBLIOGRAPHY 90 V LIST OP FIGURES No. Page 1. Schematic diagram of the whisker growing furnace . . . . . . . 12 2 . Whisker s e l e c t i n g setup . . . . . . . . . . . . . . . . . . . lk 3 . Schematic diagram of the whisker tensometer . . . . . . . . . l 6 h. Whisker tensometer . . . . . . . . . . . . . . . . . . . . . . . . . 17 5. Whisker mounted on U-bent tungsten filaments . . . . . . . ..-.«. 19 6. E l e c t r i c a l c i r c u i t f o r the l i n e a r d i f f e r e n t i a l transformer . . 20 7. E l e c t r i c a l c i r c u i t f o r the impedance transducer . . . . . . . . . .20 8 . Schematic diagram of the acid bath . . . . . . . . . . . . . . 22 9 . Cross s e c t i o n a l diagram of the cold temperature bath . . . . . . 23 10. Laue transmission picture of a <110> whisker with, the,X?ray.. beam p a r a l l e l to a <100> «100> picture) . . . . . . . . . . 31 11 . Laue transmission picture of a <110> whisker with the X-ray beam p a r a l l e l to a <110> (<110) picture) . . . . . . . . . . 32 12. Laue transmission picture of a <110> whisker with the X-ray beam p a r a l l e l to a <111> (<(111> picture) . . . . . . . . . . 33 13 . Cross sections of whiskers . . . . . . . . . . . . . . . . . . J>k •1^. Whisker with 90° kink . . . . . . . . . . . . . . . . . . . . .36 . 15. Whisker with 4^-5° kink . . . . . . . . . . . . . . . . . . . . 36 • l6. Whisker with 120° kink . . . . . . . , . . . . . . ... . . . . . ..#. 37 17. H e l i c a l l y twisted whisker with 150° kink . . . . . . . . . . . . 37 18. Laue transmission < l l l ) picture of b-c kink showing dual spots 38 19. H e l i c a l l y twisted whisker . . . . . . . . . . . . . . . . . . . 39 2 0 . Kinked whisker with ridges . » . « . . . . . . . . ... . . . . . .k0 2 1 . Large kinked .whisker with ridges . . . . . . . . . . . . . . . . U l 2 2 . Laue transmission <100> picture of the whisker shown i n Figures 20 and 21 * ^1 2 3 . Load-extension p l o t of Sample A9 tested i n d i l u t e sulphuric 2k. Load-extension p l o t of Sample B15 . . . . . . . . . . . . . . .^9 v i LIST .'OF FIGURES (continued) Page No. 25. Load-extension pl o t of the p l a s t i c region of Sample B9 tested a l t e r n a t e l y at room temperature and -68°C . . . . . . 53 26. Load-extension plot of the p l a s t i c region of Sample Bl8 tested at -1^3°C . . . . . . . . . . . . . . . . . . . . . . 5^ 27. Load-extension p l o t of the p l a s t i c region of Sample B22 tested at —8 C .......0 «»#««.«-«.«.«..«-«. * « • 55 28. Load-extension pl o t of the p l a s t i c region.of Sample B21 tested at room temperature . . . . . . . . . . . . .56 29. Load-extension p l o t of the p l a s t i c region of Sample B17 tested at —153 0 . . . . * « « « . . . * . * « - . . « . . « - . . . « « . . 57 30. Formation of Luders band at -153°C, Sample B17 » • » . . . . . 6° 3 1 . Formation of conjugate s l i p at ~153°C, Sample B17 . . . . » » • 60 32. Laue transmission picture of undeformed portion of Sample B17 • 6 l 33. Laue transmission p i c t u r e of deformed portion of Sample B17 » • 6 l 3 -^* Formation of Luders band at room temperature i l l u s t r a t i n g cross s l i p . * . a . . . . . . . . . • . . . * a * . . o cS2 35» Mechanical equilibrium i n s i d e c r y s t a l (a) and at (100) surface (b) i n a face-centred cubic l a t t i c e . . . . . . . . . . . . . 71 36. Schematic diagram of a beam under a bending moment . . . . . . 75 37 • Current-force r e l a t i o n f o r the bent pyrex arms . . . . . . . . 83 38. Current-force r e l a t i o n f o r the s t r a i g h t pyrex arms . . . . . . 8^4-39« C a l i b r a t i o n of h e l i c a l springs (small and large) . . . . . . . 85 ko. Determination .of the r e s t o r i n g force of the suspended rod . » . -86 hit .Current-force r e l a t i o n at low current f o r the s t r a i g h t pyrex arms . » . . . . . . . . ..... . . . ... . . . . ... . . • . . 87 h20 C a l i b r a t i o n of the r e s t o r i n g force of the suspended rod with the s t r a i g h t pyrex arms . . . . . . . . . . . . . . . . . . . 87 4^-3. Relaxation of the bent pyrex arms . . . . . . . « . « » . « . . 88 v i i LIST OF TABLES No. Page I. Comparison of the Areas Determined by the Three Methods . . . . 35 I I . T e n s i l e Tests Carried Out i n D i l u t e Sulphuric Acid . . . . . . kk I I I . T e n s i l e Tests at Room and Low Temperatures . . . . . . . . . . ^8 IV. C a l i b r a t i o n of the Impedance Transducer * . ... . . . • « « , . 89 THE DEFORMATION OF COPPER WHISKERS I. INTRODUCTION A. General The property which gives metals t h e i r great engineering value i s p l a s t i c i t y . However, i t i s t h i s property which i s responsible f o r t h e i r r e l a t i v e l y low strength. Furthermore, bulk s i n g l e c r y s t a l s are weaker than p o l y c r y s t a l s . Hence when filamentary metal growths were discovered to possess strength comparable to that t h e o r e t i c a l l y predicted, t h e i r study became of great i n t e r e s t . These filamentary growths are c a l l e d metal whiskers. H i s t o r i c a l l y metal whiskers are not new. For example, h a i r s i l v e r , i t s n a tural occurrence and i t s a r t i f i c i a l production, has been known f o r centurieso Whiskers are not confined only to metals. Whiskers of oxides, minerals, hydrocarbons and s a l t s have been observed and noted i n c r y s t a l l o -graphic works such as Dana . In general whiskers range i n diameter from about 0.01 micron (/*,) to 5 0 a n d i n length from about l/<- to a few centimeters (cm). A comprehensive h i s t o r i c a l review of filamentary growth 2 of metals and non-metals has been given by Hardy . Whiskers f i r s t came under d e t a i l e d study i n the l a t e nineteen f o r t i e s and e a r l y nineteen f i f t i e s , since t h e i r presence i n engineering 3 materials was undesirable. .Compton, Mendizza and Arnold i n i n v e s t i g a t i n g f a i l u r e s of e l e c t r o p l a t e d capacitors discovered that whiskers growing from the p l a t i n g had s h o r t - c i r c u i t e d . t h e c a p a c i t o r s . In t h e i r growth study of - 2 -p r o p e r w h i s k e r s ( w h i s k e r s g rown f r o m t h e s o l i d ) o f Zn and C d , t h e s e w o r k e r s o b s e r v e d t h a t s t r a i g h t w h i s k e r s a r e u s u a l l y s i n g l e c r y s t a l s and t h a t t h e w h i s k e r a x i s was a l w a y s p a r a l l e l t o [ l O l . O ] o r \ll2.0]. L a t e r w o r k 4 showed t h a t p r o p e r w h i s k e r s were c y l i n d r i c a l w i t h i r r e g u l a r c r o s s s e c t i o n , o c c a s i o n -a l l y i r r e g u l a r l y t w i s t e d o r s h a r p l y k i n k e d . The s u r f a c e s o f some were m i c r o -s c o p i c a l l y p e r f e c t , o t h e r s were f l u t e d . U s i n g s p e c i m e n s u p p l i e d by A r n o l d e_t al, G a i t and H e r r i n g 5 p e r f o r m e d a s i m p l e bend t e s t on Sn w h i s k e r s . They f o u n d t h a t t h e s e w h i s k e r s c o u l d w i t h -s t a n d e l a s t i c s t r a i n as h i g h as 2 p e r c e n t ($>), whereas f o r b u l k t i n , f l o w b e g i n s a t s t r a i n s l o w e r t h a n 0.01$. T h i s s t r e n g t h o f w h i s k e r s i s c l o s e t o t h e t h e o r e t i c a l v a l u e o f p e r f e c t c r y s t a l s . Y i e l d i n w h i s k e r s p roduced s h a r p k i n k s . Two p o s s i b l e e x p l a n a t i o n s f o r t h e h i g h s t r e n g t h o f w h i s k e r s were s u g g e s t e d by G a i t and H e r r i n g ; a ) w h i s k e r s a r e f r e e o f d i s l o c a t i o n s , b ) w h i s k e r s c o n t a i n o n l y few d i s l o c a t i o n s and t h e s e a r e i n s u f f i c i e n t t o cause m u l t i p l i c a t i o n . S i n c e t h e f i r s t i n v e s t i g a t i o n i n g r o w t h and p h y s i c a l p r o p e r t i e s o f w h i s k e r s , . m a n y r e s e a r c h e r s have e n t e r e d t h i s f i e l d o f s t u d y f o r e i t h e r o f two r e a s o n s : a ) - a c a d e m i c , t o s t u d y t h e f u n d a m e n t a l n a t u r e o f c r y s t a l g r o w t h and p l a c t i c i t y o f c r y s t a l s , b ) a p p l i e d r e s e a r c h , t o i n v e s t i g a t e t h e n a t u r e o f w h i s k e r g r o w t h i n o r d e r t o e l i m i n a t e w h i s k e r s f r o m o c c u r r i n g i n e n g i n e e r i n g m a t e r i a l s . - 3 -B . P r e v i o u s Work 1. Growth The d i f f e r e n t methods o f g r o w t h and s u g g e s t e d t h e o r e t i c a l e x p l a n a t i o n s have b e e n e x t e n s i v e l y c o v e r e d by N a b a r r o and. J a c k s o n . The m a j o r means o f g r o w t h o f w h i s k e r s i n t h e l a b o r a t o r y a r e l i s t e d be low b u t o n l y t h a t method w h i c h has b e e n used i n t h e p r e s e n t i n v e s t i g a t i o n w i l l be d e a l t w i t h i n d e t a i l . The m a j o r means o f w h i s k e r g r o w t h a r e : : l ) Growth f r o m s o l i d , — S n , . C d . 2) G rowth f r o m s o l u t i o n s , — KC1, N a C l . 3) G rowth by c o n d e n s a t i o n o f a s u p e r s a t u r a t e d v a p o u r , — S i , H g , Z n , C d , A g , C . h) G rowth by r e d u c t i o n o f m e t a l h a l i d e , — C u , A g , . F e , N i , . C o . The g r o w t h o f Ag and .Cu w h i s k e r s by h y d r o g e n r e d u c t i o n o f c h l o r i d e has been r e p o r t e d . s o m e t i m e a g o 7 . H o w e v e r , i n t e r e s t i n t h i s method o f g r o w t h was n o t a r o u s e d u n t i l t h e f i n d i n g s o f H e r r i n g and G a i t were r e p o r t e d . S i n c e h a l i d e r e d u c t i o n i s an easy and q u i c k method o f p r o d u c i n g w h i s k e r s , g r o w t h by 8 9 IO t h i s means r e c e i v e d . r e n e w e d a t t e n t i o n ' * B r e n n e r i n h i s d e t a i l e d s t u d y grew C u , A g , P e , N i , Co b y . h y d r o g e n r e d u c t i o n , and A u , P t by t h e r m a l r e d u c t i o n . He r e p o r t s t h a t c o p p e r w h i s k e r s a r e most r e a d i l y g rown f r o m . C u C l , CuBr , and C u l . I n a l l cases he c o u l d n o t grow w h i s k e r s f r o m s t a b l e f l u o r i d e s . B r e n n e r ' s o b s e r v a t i o n s on c o p p e r w h i s k e r s a r e t a b u l a t e d b e l o w . a ) .Copper w h i s k e r s can be g rown i n . t h e t e m p e r a t u r e r a n g e o f ^30° t o 850°C. -k -b ) W h i s k e r s g rown a t t e m p e r a t u r e s b e t w e e n 430° and 700°C were i n g e n e r a l s t r a i g h t , n a r r o w and f r e e f r o m o v e r g r o w t h . On t h e o t h e r h a n d , a t 700° t o 850°C t h e w h i s k e r s were c o a r s e and i r r e g u l a r l y -d i s t o r t e d . c ) Growth k i n k s w e r e f r e q u e n t l y o b s e r v e d and t h e p r e d o m i n a n t a n g l e o f k i n k was 90°. d ) The s t r a i g h t , u n t a p e r e d w h i s k e r s u s u a l l y were h e x a g o n a l i n c r o s s s e c t i o n . When w h i s k e r s w e r e exposed t o l o n g p e r i o d s o f r e d u c t i o n a t t e m p e r a t u r e s be low 600°C, t h e w h i s k e r s w e r e i n c l i n e d t o b r o a d e n i n t o b l a d e s . I n g e n e r a l a h e x a g o n a l c r o s s - s e c t i o n a l shape i n d i -c a t e s a [ i l l ] o r i e n t a t i o n o f t h e a x i s and s q u a r e c r o s s - s e c t i o n , a [100]11. e ) The h y d r o g e n f l o w r a t e d i d n o t have an a p p r e c i a b l e e f f e c t on • w h i s k e r g r o w t h , p r o v i d e d - t h a t i t was above a m in imum. f ) Copper w h i s k e r s g rown f r o m . C u l a t 630°C grow a x i a l l y a t ~100/«/sec and . r a d i a l l y a t -^ 5X10 / * . / sec . g ) The s u r f a c e s o f some w h i s k e r s were e x t r e m e l y smooth and h i g h l y r e f l e c t a n t , a l t h o u g h e x p o s u r e t o humid a i r soon t a r n i s h e d t h e m . h ) The g r o w t h t i p o f t h e w h i s k e r t e r m i n a t e d e i t h e r i r r e g u l a r l y • l i k e a t w i s t e d cane h a n d l e o r p y r a m i d a l l y . i ) W h i s k e r g rown f r o m C u l a t 570°C e x h i b i t e d g r o w t h f r o m t h e t i p . - 5 -j ) X - r a y Laue a n d . r o t a t i o n p i c t u r e s show t h a t s t r a i g h t , d e f e c t - f r e e w h i s k e r s a r e s i n g l e c r y s t a l s and t h e i r axes a r e u s u a l l y p a r a l l e l t o one o f t h r e e d i r e c t i o n s , [ l O O ] , [ l l O ] , [ i l l ] . A l t h o u g h i t i s n o t w i t h i n t h e scope o f t h i s t h e s i s t o s t u d y w h i s k e r g r o w t h mechan isms , a b r i e f o u t l i n e o f v a r i o u s p r o p o s a l s i s i n c l u d e d f o r t h e sake o f c o m p l e t e n e s s . The t h e o r y o f w h i s k e r g r o w t h by c h e m i c a l r e d u c t i o n i s s t i l l n o t w e l l e s t a b l i s h e d . The t h e o r y o f c r y s t a l g r o w t h f r o m 13 v a p o u r p r e d i c t s t h a t an e q u i l i b r i u m .shape i s r e a c h e d a t w h i c h t h e b o u n d i n g f a c e s a r e t h o s e o f low i n d e x p l a n e s . O n l y v e r y h i g h s u p e r s a t u r a t i o n w i l l i n d u c e f u r t h e r g r o w t h by two d i m e n s i o n a l n u c l e a t i o n . The g r o w t h b y . c o n d e n -s a t i o n o f a s u p e r s a t u r a t e d v a p o u r , where s u p e r - s a t u r a t i o n i s i n s u f f i c i e n t t o 14 cause t w o d i m e n s i o n a l n u c l e a t i o n , has b e e n r a t i o n a l i z e d by Sears by i n v o k -i n g t h e F r a n k mechanism o f a sc rew d i s l o c a t i o n . B r e n n e r 1 0 . s u g g e s t s t h a t t h e r e q u i r e d , s u p e r s a t u r a t i o n o f 10 f o r two d i m e n s i o n a l g r o w t h i s p o s s i b l e i n t h e case o f h a l i d e r e d u c t i o n w i t h h y d r o g e n . I n o r d e r t o e x p l a i n u n i d i r e c t i o n a l g r o w t h , he s u g g e s t s t h a t s u r f a c e a b s o r p t i o n o f r e a c t a n t s m i g h t h i n d e r s u r f a c e 15 16 17 n u c l e a t i o n . H o w e v e r , W i e d e r s i c h , Webb and R e i b l i n g , and Gorsuch i n t h e i r t h e r m o d y n a m i c s t u d i e s s u g g e s t t h a t s u p e r s a t u r a t i o n i s much l o w e r t h a n 10 4. A l t h o u g h sc rew d i s l o c a t i o n mechanism has been p roposed t o p r o v i d e 18 a g r o w t h s t e p t o s t a r t w h i s k e r g r o w t h , t h i s mode l does n o t e x p l a i n two o b s e r v a t i o n s : \ 19 a ) b a s a l g r o w t h o f Ag f r o m l i q u i d . A g C l , b ) b a s a l and t i p g r o w t h o f c o p p e r w h i s k e r s f r o m l i q u i d CuCl . - 6 -The o b s e r v e d f a c t t h a t w h i s k e r s grow u n i d i r e c t i o n a l l y seems t o demand a 21 c e n t r a l sc rew d i s l o c a t i o n . However , . X - r a y d i f f r a c t i o n e v i d e n c e o f w h i s k e r s p r o d u c e d by h y d r o g e n r e d u c t i o n does n o t show any t w i s t i n t h e l a t t i c e as 22 p r e d i c t e d by E s h e l b y . A n o t h e r mechan ism s u g g e s t e d by F r a n k r a t i o n a l i z e d u n i d i r e c t i o n a l g r o w t h b y p r o p o s i n g t h a t t h e l i q u i d h a l i d e f i l m p r o t e c t i n g t h e s i d e s o f t h e w h i s k e r was c a t a l y t i c a l l y decomposed a t t h e t i p and a l s o a c t s as t h e t r a n s -p o r t i n g med ium. G o r s u c h ' s o b s e r v a t i o n t h a t p u r e FeCl2 m ixed w i t h Fe2C-3 d i d grow w h i s k e r s i s s t r o n g a rgument i n d e f e n c e o f t h i s m e c h a n i s m . H o w e v e r , w h e t h e r t h e c a t a l y t i c a g e n t i s a d i s l o c a t i o n o r i m p u r i t y i s u n c e r t a i n . . I n summary, a l t h o u g h t h e mechanism o f w h i s k e r g r o w t h i s n o t y e t c l e a r , e x p e r i m e n t a l o b s e r v a t i o n s i n d i c a t e t h e f o l l o w i n g c o n c l u s i o n s : . a ) t h e mechanism o f w h i s k e r g r o w t h by h y d r o g e n r e d u c t i o n i s d i f f e r e n t f o r d i f f e r e n t m e t a l s and h a l i d e s , b ) t h e p r o p o s e d mechanisms must e x p l a i n u n i d i r e c t i o n a l g r o w t h . 2. P h y s i c a l P r o p e r t i e s I n t h e f o r e g o i n g d i s c u s s i o n , t h e s e p r o p e r t i e s o f s t r a i g h t w h i s k e r s were r e v e a l e d : a ) t h e w h i s k e r i s u s u a l l y p o l y g o n a l i n c r o s s s e c t i o n , . b ) t h e b o u n d i n g f a c e s a r e m i c r o s c o p i c a l l y p e r f e c t , and a r e p l a n e s . o f low i n d i c e s , c ) t h e a x i s i s p a r a l l e l t o a s p e c i f i c p r o m i n e n t c r y s t a l l o g r a p h i c d i r e c t i o n , d ) t h e e x i s t e n c e o f an a x i a l sc rew d i s l o c a t i o n has n o t been d e f i n i t e l y e s t a b l i s h e d . H e r e a f t e r a l l p r o p e r t i e s d i s c u s s e d w i l l p e r t a i n o n l y t o s t r a i g h t , u n t a p e r e d , - f r e e f r o m - s u r f a c e d e f e c t s w h i s k e r s u n l e s s o t h e r w i s e n o t e d . As m e n t i o n e d e a r l i e r , b e n d i n g t e s t s i n S n 5 and F e 8 ; w h i s k e r s a t room t e m p e r a t u r e f i r s t e x h i b i t e d t h e p h e n o m e n a l l y l a r g e e l a s t i c s t r a i n . I n o r d e r t o e l i m i n a t e t h e inhomogeneous s t r a i n caused b y . b e n d i n g t e s t s , . t e n s i l e 24,25,26,27 2^ pa t e s t s w e r e d e v i s e d . T e n s i l e t e s t s o f C u , A g , Fe , Cd and Zn a t room t e m p e r a t u r e c o n f i r m e d t h a t w h i s k e r s can w i t h s t a n d h i g h e l a s t i c s t r a i n s . X 2 D e v i a t i o n s f r o m H o o k e ' s law w e r e o b s e r v e d i n Fe b u t n o t i n Cu . S t r e s s s t r a i n c u r v e s a r e r e v e r s i b l e f o r f a s t s t r a i n r a t e s . H o w e v e r , . f o r s l o w s t r a i n 5 2a& 3 0 r a t e s , C a b r e r a and P r i c e ' o b s e r v e d . i r r e v e r s i b i l i t y i n some Zn w h i s k e r s . T h i s i r r e v e r s i b i l i t y was a t t r i b u t e d t o m i c r o c r e e p . B r e n n e r 1 2 , t o c o n f i r m t h e r e s u l t s o f C a b r e r a and P r i c e , p e r f o r m e d . c r e e p t e s t s on Zn and Cu w h i s k e r s b u t d i d n o t d e t e c t any c r e e p . T h i s d i s c r e p a n c y o f r e s u l t s has n o t y e t been r e s o l v e d . The most s i g n i f i c a n t a s p e c t . w h i c h t e n s i l e t e s t s r e v e a l e d i s t h a t a v e r y h i g h y i e l d s t r e s s (<jp ) i s r e a c h e d . B r e n n e r 2 6 r e p o r t s r e s o l v e d s h e a r s t r e s s e s f o r y i e l d o f c o p p e r w h i s k e r s w h i c h r a n g e f r o m 10 t o ko k i l o g r a m s p e r s q u a r e m i l l i m e t e r ( k g / m m 2 ) . The t h e o r e t i c a l s h e a r s t r e n g t h i s e s t i m a t e d 3 1 t o be o n e - t h i r t i e t h o f t h e s h e a r modu lus by M a c k e n z i e . F o r t h e c a s e ' o f c o p p e r t h i s amounts t o .about 100 k g / m m 2 . Beyond t h i s p o i n t t h e s t r e s s r e q u i r e d . f o r p l a s t i c f l o w (<£f. ) i s many t i m e s l o w e r t h a n t h e y i e l d p o i n t , some w h i s k e r s possess ..iS. r a t i o w h i c h i s as h i g h as ~80, u s u a l l y ~25. A t room t e m p e r a t u r e , t h e s h a r p y i e l d phenomenon i s c h a r a c t e r i s t i c o f d u c t i l e - 8 -m e t a l s such as C u , A g , C d , Z n . I n n o r m a l l y b r i t t l e m a t e r i a l s such as S i , AI2O3, S102, c l e a v a g e - t y p e f r a c t u r e t a k e s p l a c e beyond t h e e l a s t i c l i m i t . The mode o f f r a c t u r e o f Pe w h i s k e r s i s u n u s u a l . B r e n n e r 2 5 d e s c r i b e s t h e f r a c t u r e o f Pe by s a y i n g " t h e y s u d d e n l y snapped w i t h o u t any o b s e r v a b l e a m o u n t . o f p l a s t i c d e f o r m a t i o n and wrapped t h e m s e l v e s a r o u n d " . A l s o some Cu w h i s k e r s were o b s e r v e d t o f r a c t u r e i n t h i s manner . Mos t Cu and a l l Ag w h i s k e r s f r a c t u r e d a f t e r c o n s i d e r a b l e p l a s t i c f l o w . L a t e r w o r k 1 2 on Pe w h i s k e r s r e v e a l e d p l a s t i c d e f o r m a t i o n b u t t h e t o t a l p l a s t i c f l o w h a r d l y e v e r exceeded;10$. A l t h o u g h s c a t t e r i s l a r g e , t h e s i z e e f f e c t i n t h e s t r e n g t h o f 32 25 w h i s k e r s has been i n d i c a t e d i n NaCl , Pe and Cu . F o r d i a m e t e r s l e s s t h a n 25/«., t h e a v e r a g e s t r e n g t h s , i . e . t h e y i e l d s t r e s s , a r e i n v e r s e l y p r o p o r t i o n a l t o t h e i r d i a m e t e r s . B e n d i n g t e s t s on S i w h i s k e r s a t . r o o m and e l e v a t e d t e m p e r a t u r e 33 w e r e p e r f o r m e d b y . P e a r s o n , R e a d , and Fe ldman . T h e i r f i n d i n g s a r e as f o l l o w s : a ) From room t e m p e r a t u r e t o 600°C, t h e w h i s k e r s f r a c t u r e d . b ) From 600° t o 650°C, w h i s k e r s may f l o w a f t e r e x h i b i t i n g y i e l d p o i n t o r f r a c t u r e w i t h l i t t l e o r no f l o w . . c ) From 650 0 t o 800°C,. w h i s k e r f l o w e d a p p r e c i a b l y . d ) The y i e l d s t r e s s and f l o w s t r e s s b o t h d e c r e a s e d w i t h i n c r e a s e i n t e m p e r a t u r e . e ) 6y was s m a l l , ~K, f ) Some w h i s k e r s r e c o v e r e d . u p . t o l / 2 t h e i r o r i g i n a l y i e l d s t r e s s a f t e r a g i n g a t 800°C f o r t w o h o u r s . On t h e o t h e r hand b u l k c r y s t a l s cut to approximately the same dimensions as whiskers recovered completely under s i m i l a r conditions. Comparing r e s u l t s of S i whiskers and cut S i rods of comparable s i z e , these workers concluded that S i whiskers had high strength due to t h e i r small s i z e . At room temperature the f r a c t u r e strength of c r y s t a l s l e s s than 50/*, i n diameter and over lOO/o i n diameter i s independent of s i z e . The drop i n f r a c t u r e strength from < 50/*. to >100 /u, i s about 0.6. 34 I t i s suggested that the sharp y i e l d i n g i s due to the C o t t r e l l mechanism with boron and oxygen impurities as the locking s o l u t e s . A f t e r recovery of y i e l d point of S i whiskers became known,.other 12 36 whiskers were i n v e s t i g a t e d . No such recovery was observed i n Cu and Zn . * 35 Coleman, P r i c e and Cabrera have investigated s l i p i n Zn and Cd whiskers b y . t e n s i l e t e s t s at low temperatures. Below ,l60°K, Zn fractured without s l i p . Cd, on the other hand, did not f r a c t u r e t i l l 20°K. The increase i n y i e l d s t r e s s or f r a c t u r e s t r e s s of Zn was twofold below l60°K.. Cd also showed t h i s increase i n strength at 20°K. The high strength of whiskers may be a t t r i b u t e d . t o surface f i l m s . 25 Brenner , i n t e s t i n g whiskers which were heated i n a i r at 100° to 150°C, :30 did not observe large decrease i n strength. Cabrera and Priee 9 i n t e s t i n g Zn whiskers, found that strength increased .with increase i n oxide l a y e r thickness. A f t e r an optimum thickness was reached, strength f e l l with increasing thickness. This was a t t r i b u t e d to non-uniformity of oxide t h i c k -37 ness beyond the optimum. Mott suggested that rather than the thickness of the oxide f i l m , the surface with only a few atom l a y e r s of oxide may be 38 s u f f i c i e n t to act as a b a r r i e r to d i s l o c a t i o n s . Brenner , to investigate - 10 t h i s p o s s i b i l i t y , p u l l e d Au w h i s k e r s w h i c h p r e s u m a b l y have no o x i d e c o a t i n g and f o u n d t h a t Au w h i s k e r s a l s o possessed h i g h s t r e n g t h and t h e s h a r p y i e l d p o i n t . He c o n c l u d e d t h a t t h i s e x p e r i m e n t i n d i r e c t l y showed t h a t t h e h i g h s t r e n g t h o f w h i s k e r s was n o t s o l e l y due t o t h e p r e s e n c e o f an o x i d e l a y e r . I n a l l d u c t i l e m e t a l s t e s t e d , p l a s t i c f l o w i s a s s o c i a t e d w i t h n u c l e a t i o n and p r o p a g a t i o n o f L u d e r s b a n d s . The shape o f t h e s t r e s s - • e x t e n s i o n c u r v e i s u n i q u e f o r each w h i s k e r . However , t h e r e a r e two d i s t i n c t c a t e g o r i e s . I n one t y p e , where t h e f l o w r e g i o n i s e x t e n s i v e , t h e L u d e r s band spans t h e t o t a l l e n g t h o f t h e spec imen b e f o r e w o r k h a r d e n i n g s t a r t s . I n t h e o t h e r t y p e , , where t h e f l o w r e g i o n i s s h o r t , w o r k h a r d e n i n g t a k e s p l a c e t i l l a second L u d e r s band i s g e n e r a t e d . I n t h e l a t t e r c a s e , f r a c t u r e u s u a l l y t a k e s p l a c e b e f o r e t h e w h o l e l e n g t h has s l i p p e d . A l t h o u g h t h e r e s o l v e d f l o w s t r e s s i s dependen t on t h e c r y s t a l l o g r a p h i c a x i s o f t h e w h i s k e r , i n a l l cases i t i s h i g h e r t h a n t h a t f o r b u l k c r y s t a l s . F o r C u , t h e a v e r a g e v a l u e i s 0.75 k g / m m 2 f o r [ l i o ] , 1.05 k g / m m 2 f o r f i l l ] and.1.35 k g / m m 2 f o r [ l O O ] w h i s k e r s , compared w i t h 0.10 k g / m m 2 f o r b u l k c r y s t a l s 2 6 . B r e n n e r 2 r s u g g e s t s t h a t f l o w s t r e s s i s n o t t h e s t r e s s r e q u i r e d t o i n i t i a t e " e a s y g l i d e " b u t r a t h e r t h a t s t r e s s r e q u i r e d t o p r o p a g a t e t h e f r o n t o f t h e L u d e r s b a n d . H o w e v e r , he does n o t p r o p o s e any m e c h a n i s m - w h i c h r a t i o n a l i z e s t h i s o b s e r v a t i o n . E a r l i e r , d e f o r m a t i o n k i n k i n g o f w h i s k e r s u n d e r b e n d i n g t e s t s .was 39 33 r e c o r d e d . By a n n e a l i n g , k i n k e d . w h i s k e r s o f F e , Cu , S i s t r a i g h t e n o u t . 4o N a b a r r o advanced a t h e o r y t o q u a l i t a t i v e l y e x p l a i n t h e k i n e t i c s o f d e k i n k i n g . . I n t h i s m o d e l t h e a r r a y o f d i s l o c a t i o n s i n t h e k i n k e d r e g i o n i s r e p r e s e n t e d by p o l y g o n i z e d . w a l l s . The d e k i n k i n g i s p roposed as t h e m a c r o s c o p i c m a n i -f e s t a t i o n o f d i s l o c a t i o n s g l i d i n g o u t t o t h e s u r f a c e d u r i n g t h e p o l y g o n i z a t i o n p r o c e s s . - 11 -C . Purpose o f P r e s e n t I n v e s t i g a t i o n The p u r p o s e o f t h e p r e s e n t i n v e s t i g a t i o n i s t o s t u d y t h e d e f o r m a t i o n o f c o p p e r w h i s k e r s . The p r i m a r y s t e p - w a s t o d e t e r m i n e t h e e f f e c t o f t h e o x i d e l a y e r on t h e t e n s i l e p r o p e r t i e s . An e f f e c t o f o x i d e l a y e r has been d e t e r m i n e d 41' f o r b u l k c r y s t a l s . However , w h e t h e r t h e h i g h s t r e n g t h and t h e y i e l d p h e n o -menon' o f w h i s k e r s a r e due t o s u r f a c e l a y e r s has n o t y e t been d i r e c t l y a s c e r -t a i n e d . I t was p roposed t h a t w h i s k e r s be t e s t e d i n d i l u t e s u l p h u r i c a c i d ..which 4 2 p r e s u m a b l y removes c u p r o u s o x i d e b u t n o t c o p p e r . I f t h e y i e l d .phenomenon was n o t due t o t h e p r e s e n c e o f t h e s u r f a c e l a y e r , t h e n t h e d e f o r m a t i o n o f c o p p e r w h i s k e r s was t o be s t u d i e d b y t e s t i n g w h i s k e r s a t v a r i o u s low t e m p e r a t u r e s . I n i t i a l l y , t e s t s s i m i l a r t o Adams and 4 3 . C o t t r e l l w e r e p roposed t o - o b s e r v e i f t h e change o f f l o w , s t r e s s w i t h t e m p e r a -t u r e i s c l o s e l y . p r o p o r t i o n a l t o t h e f l o w s t r e s s . By t h i s s t u d y , a b e t t e r u n d e r s t a n d i n g o f t h e mechanism f o r L u d e r s band p r o p a g a t i o n may be r e a c h e d . •••12 •* I I . Experimental A. Growth and S e l e c t i o n Copper whiskers were grown by the standard method of halid e reduction by hydrogen 1 0. The halid e used i n t h i s i n v e s t i g a t i o n was anhydrous cupric c h l o r i d e , standard reagent grade supplied by Baker and Adamson. The quoted maximum l i m i t s of impurities are: Insoluble 0.01$ N i t r a t e (N0 3) 0.005$ Sulphate (S0 4) 0.005$ Iron (Fe) 0.010$ Substances not p r e c i p i t a t e d 0.20$ by hydrogen sulphide (as Sulphates) Boat f i l l e d with cupric c h l o r i d e Sample T.C. •Furnace ^ V y ° ° r Tube Copper Rod Chamber Flow Meter < He H 2 Figure 1. Schematic diagram of the whisker growing furnace. The w h i s k e r s w e r e g rown i n a t u b e f u r n a c e s c h e m a t i c a l l y shown i n F i g u r e 1 . .Bo th h e l i u m and h y d r o g e n w e r e d r i e d w i t h s i l i c a g e l and p r e c e d i n g t h i s d r y i n g chamber , h y d r o g e n was passed t h r o u g h a c a t a l y t i c p u r i f i e r . Care was t a k e n t o r e d u c e t h e a tmosphere gases f r o m c o n t a m i n a t i n g t h e h o t f u r n a c e . A f t e r t h e V y c o r t u b e was t h o r o u g h l y c l e a n e d w i t h a c i d , i t was d r i e d and r i n s e d w i t h a c e t o n e . The f u r n a c e was f i r s t f l u s h e d w i t h h e l i u m a t room t e m p e r a t u r e . A t a l l t i m e s , even when t h e f u r n a c e was n o t i n u s e , a s l i g h t p o s i t i v e p r e s s u r e o f h e l i u m was m a i n t a i n e d . The t i m e r e q u i r e d t o i n s e r t o r remove t h e b o a t f r o m t h e f u r n a c e was k e p t t o a m in imum. The t e m p e r a t u r e o f r e d u c t i o n was measured by a c h r o m e l - a l u m e l t h e r m o c o u p l e . A s u i t a b l e f i r e c l a y b o a t was f i l l e d w i t h c u p r i c c h l o r i d e and i n s e r t e d i n t o t h e c o o l i n g chamber o f t h e f u r n a c e , w h e r e u p o n t h e f u r n a c e was f l u s h e d w i t h h e l i u m f o r a t l e a s t 30 m i n u t e s . A f t e r f l u s h i n g , t h e b o a t was pushed i n t o t h e f u r n a c e and t h e h e l i u m was r e p l a c e d w i t h h y d r o g e n f l o w . Upon c o m p l e t i o n o f r e d u c t i o n , . w h i c h i s i n d i c a t e d by t h e c l e a r n e s s o f t h e b u b b l i n g b o t t l e , a m a t t e r o f 20 t o ko m i n u t e s , t h e h y d r o g e n was r e p l a c e d w i t h h e l i u m f l o w and t h e b o a t was d rawn o u t o f t h e h o t chamber i n t o t h e c o o l i n g chamber . B o a t s w i t h w h i s k e r s were examined w i t h a R e i c h e r t s t e r e o s c o p i c m i c r o s c o p e u n d e r 36 m a g n i f i c a t i o n as shown i n F i g u r e 2, Upon l o c a t i n g a s u i t a b l e w h i s k e r i t ,was removed f r o m t h e b o a t w i t h a m i c r o m a n i p u l a t o r , Which i s 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 . A f t e r t h e w h i s k e r was p l a c e d on a w h i t e c a r d p l a t e , i t .was t h e n examined u n d e r a R e i c h e r t m e t a l l o g r a p h i c m i c r o s c o p e a t ,110 and 390.m a g n i f i c a t i o n . I f t h e w h i s k e r passed e x a m i n a t i o n i t was s t o r e d i n a d e s s i c a t o r f o r f u t u r e u s e . A l l w h i s k e r s w h i c h were used f o r t e s t s were a t l e a s t 8 h o u r s o l d b u t n e v e r o v e r 48 h o u r s o l d . - 14 -F i g u r e 2. W h i s k e r s e l e c t i n g s e t u p . The c r i t e r i a used f o r w h i s k e r s e l e c t i o n w e r e t h e s e : a ) s t r a i g h t , u n t a p e r e d and a t l e a s t 1 l/2 mm. l o n g ; b ) no s u r f a c e d e f e c t s such as l i n e d e f e c t s , p i t s , v e r y s h o r t b r a n c h g r o w t h ; c ) t h e s u r f a c e s must be f l a t ; d ) t h e edges o f t h e s u r f a c e must be s t r a i g h t and p a r a l l e l } e ) t h e s u r f a c e f a c e must n o t s u d d e n l y change i t s c r y s t a l l o g r a p h i c p l a n e . B . Specimen H a n d l i n g A p p a r a t u s A m i c r o m a n i p u l a t o r w i t h 4 t o 1 r e d u c t i o n i n l a t e r a l m o t i o n i s shown i n F i g u r e 2. To t h i s i n s t r u m e n t was c lamped a t w e e z e r . T h i s t w e e z e r accom-modated a h e l i c a l s p r i n g and a d e f l a t e d e l a s t i c b a g . The c o n s t r u c t i o n was - 15 -such t h a t upon i n f l a t i n g t h e bag w i t h a f o o t l e v e r t h e t w e e z e r w h i c h n o r m a l l y was c l o s e d o p e n e d . i t s c l a w s . W i t h t h i s s e t u p , when a s u i t a b l e w h i s k e r was l o c a t e d , t h e w h i s k e r was h e l d .a t t h e base and p u l l e d . o f f t h e s u b s t r a t e . The d i f f i c u l t y i n r e m o v i n g t h e s e w h i s k e r s f r o m t h e t w e e z e r was overcome by m e t a l l o g r a p h i c a l l y . p o l i s h i n g t h e i n s i d e s o f t h e c l a w s and d e -g r e a s i n g i t each t i m e b e f o r e u s e . On o c c a s i o n s t h a t a w h i s k e r d i d n o t f a l l f r o m t h e c l a w s , . i t was pushed o f f w i t h t h e a i d o f a f i n e p o i n t e d n e e d l e . A l t h o u g h o r d i n a r y t w e e z e r s m e t a l l o g r a p h i c a l l y p o l i s h e d and d e -g r e a s e d w e r e f i r s t t r i e d f o r m o u n t i n g w h i s k e r s on t h e t e n s i l e a p p a r a t u s and on t h e g o n i o m e t e r , . t h e f a i l u r e r a t e was e n o r m o u s . Hence a p y r e x p r o b e w i t h a t u n g s t e n f i l a m e n t a t t h e t a p e r e d end .was c o n s t r u c t e d . The a . c . c u r r e n t t o t h e f i l a m e n t was c o n t r o l l e d by means o f a f o o t . s w i t c h . The compound d i p h e n y l c a r b a z i d e was used as t h e g l u e t o mount t h e s p e c i m e n . T h i s s u b s t a n c e has a low m e l t i n g p o i n t o f 1 7 3 ° C A g l o b u l e o f t h i s compound was f r o z e n o n t o t h e U-bend o f t h e f i l a m e n t t i p . The w h i s k e r was t r a n s p o r t e d f r o m t h e c a r d p l a t e t o - t h e mounts b y . m e l t i n g t h e g l u e , t o u c h i n g one end o f t h e w h i s k e r and f r e e z i n g t h e g l u e . .To remove t h e w h i s k e r f r o m t h e p r o b e , t h e f i l a m e n t was h e a t e d and t h e h o t p r o b e was c a r e f u l l y removed so t h a t t h e w h i s k e r r e m a i n e d . w i t h t h e s o l i d i f i e d . r e g i o n o f t h e g l u e . T h i s t e c h n i q u e g r e a t l y d e c r e a s e d m o u n t i n g f a i l u r e . Bridge Ammeter Figure 3. Schematic diagram of the whisker tensometer • OA I Figure Whisker tensometer - 18 -C. T e n s i l e T e s t i n g A p p a r a t u s 1 . . C o n s t r u c t i o n A h o r i z o n t a l w h i s k e r t e n s o m e t e r was . c o n s t r u c t e d s i m i l a r t o t h a t o f 26 B r e n n e r . T h i s a p p a r a t u s i s s c h e m a t i c a l l y i l l u s t r a t e d i n F i g u r e 3 and shown i n F i g u r e 4 . As i l l u s t r a t e d t h e a l l a luminum t e n s o m e t e r i s based on t h e pendu lum p r i n c i p l e . The r i g h t p y r e x arm i s h e l d r i g i d . w h i l e t h e l e f t i s a t t a c h e d t o t h e suspended r o d . The f o r c e i s a p p l i e d t h r o u g h a s o l e n o i d a c t i v a t e d by a d . c . s o u r c e whose f i e l d a t t r a c t s . t h e A l n i c o permanent magnet imbedded a t a s u i t a b l e p o s i t i o n i n t h e suspended r o d . T h i s c u r r e n t was measured w i t h a S e n s i t i v e R e s e a r c h I n s t r u m e n t ammeter , U n i v e r s i t y m o d e l . T h i s suspended r o d . i s s t a b i l i z e d by two damping arms immersed i n m i n e r a l o i l . The e x t e n s i o n i s measured w i t h an impedance t r a n s d u c e r . The m i c r o m e t e r s t o p i s u s e d . t o c a l i b r a t e t h e t r a n s d u c e r and t o p r e v e n t e x t e n s i v e p l a s t i c d e f o r -m a t i o n when t h e w h i s k e r y i e l d s . The p o s i t i o n i n g o f t h e v a r i o u s p a r t s was easy s i n c e most o f t h e s e p a r t s a r e a d j u s t a b l e . On b o t h t h e f i x e d and mov ing p y r e x arms a r e f i x e d U - b e n t t u n g s t e n f i l a m e n t s w h i c h can be h e a t e d b y an a . c . s o u r c e c o n t r o l l e d • b y a f o o t s w i t c h . The t i p s o f t h e s e f i l a m e n t s a r e c o a t e d w i t h S a u e r e i s e n cement t o p r e v e n t s h o r t c i r c u i t i n g by t h e w h i s k e r . D i p h e n y l c a r b a z i d e was used on t h e t i p s t o a c t as g r i p s . An . i l l u s t r a t i o n o f t h e t i p s w i t h a mounted s p e c i m e n i s shown i n F i g u r e 5« The t e n s o m e t e r was p l a c e d on a c o n c r e t e p i l l a r w h i c h s a t on k r u b b e r c o r k s . T h i s a r r a n g e m e n t e l i m i n a t e d t r a n s m i s s i o n o f v i b r a t i o n s t o t h e t e n s o m e t e r . The w h o l e s e t u p was c o v e r e d e x c e p t f o r one w o r k i n g s i d e w i t h a p o l y t h e n e s h e e t t o r e d u c e m o t i o n o f t h e suspended r o d due t o d r a u g h t s . A - 19 -F i g u r e 5« W h i s k e r mounted on U - b e n t t u n g s t e n f i l a m e n t s . t a b l e was b u i l t a round t h e a p p a r a t u s so t h a t t h e s t e r e o s c o p i c m i c r o s c o p e c o u l d be p l a c e d on i t . I n t h i s way a s p e c i m e n c o u l d be mounted and t e s t e d w i t h j a r r i n g o r t o u c h i n g o f t h e t e n s o m e t e r r e d u c e d t o a m in imum. I n i t i a l l y t h e e x t e n s i o n was t o be measured w i t h a l i n e a r d i f f e r e n t i a l t r a n s f o r m e r , A t c o t r a n t y p e 6208-A. A H e w l e t t Packard vacuum t u b e v o l t m e t e r mode l kOOD was used t o measure t h e d e f l e c t i o n . The a d v a n t a g e o f t h i s s y s t e m i s t h a t l i n e a r i t y o v e r 3 mm r a n g e on e i t h e r s i d e o f n u l l was a s s u r e d by t h e m a n u f a c t u r e r . W i t h g r e a t d i f f i c u l t y t h i s sys tem became o p e r a b l e w i t h a n u l l v o l t a g e o f 0.5 m i l l i v o l t s (mv) and s e n s i t i v i t y o f 0.1 mv p e r p e r 5 v o l t s ( v ) i n p u t . The c i r c u i t used i s shown i n F i g u r e 6. U n f o r t u n a t e l y t h i s r e m a r k -a b l y s t a b l e , l i n e a r and s e n s i t i v e s y s t e m had t o be abandoned s i n c e a v o l t a g e z e r o i n g d e v i c e was n o t a v a i l a b l e . 20 -T r a n s i s t o r O s c i l l a t o r w = 1350 cps £5 -O VTVM - G L i n e a r D i f f e r e n t i a l T r a n s f o r m e r F i g u r e 6. E l e c t r i c a l c i r c u i t f o r t h e l i n e a r d i f f e r e n t i a l t r a n s f o r m e r . o O s c i l l a t o r f r o m B r i d g e w = kOQO c p s . - O B r i d g e -o -o Impedance T r a n s d u c e r F i g u r e 7. E l e c t r i c a l c i r c u i t f o r t h e impedance t r a n s d u c e r . The s y s t e m used i n t h e p r e s e n t i n v e s t i g a t i o n was an impedance t r a n s d u c e r i n c o n j u n c t i o n w i t h a P h i l l i p s PR 9300 D i r e c t M e a s u r i n g B r i d g e . S i n c e t h i s b r i d g e i s n o r m a l l y used w i t h s t r a i n g a u g e s , d i f f i c u l t y . w a s e n -c o u n t e r e d w i t h phase a n g l e c h a n g e s . However , t h i s was overcome by i n s e r t i n g l a r g e r e s i s t a n c e s , H e a t h K i t decade r e s i s t a n c e b o x e s , i n p a r a l l e l w i t h t h e i m p e d a n c e s . The c i r c u i t i s shown i n F i g u r e 7« The impedance t r a n s d u c e r i t s e l f was home b u i l t . - 2 1 2. C a l i b r a t i o n The d.c. solenoid was c a l i b r a t e d with h e l i c a l springs. Two ranges were used, one from 0 to 350 milligrams (mg), the other from 0 to 3 grams (gm). •To determine the absolute current-force r e l a t i o n , the current-extension r e l a t i o n had to be compensated f o r the r e s t o r i n g force of the suspended rod. Hence the r e s t o r i n g force of the rod had.to be determined and.it was assumed to be symmetrical about n u l l . . The springs were f i r s t c a l i b r a t e d with weights and a t r a v e l l i n g microscope. The extension of the springs a f t e r being h o r i -z o n t a l l y mounted between the fixed and mobile pyrex arms were measured e i t h e r with the impedance transducer or the micrometer stop. A l l the c a l i b r a t i o n curves are found i n Appendix I. Although three s l i g h t l y , d i f f e r e n t , r e l a t i v e positions between the solenoid and the A l n i c o permanent magnet were t r i e d during c a l i b r a t i o n , a l l three were wit h i n 2fo of each other. Also, the r e l a x a t i o n i n the pyrex arms :was measured, In the case where the bent arms were used, the r e l a x a t i o n was appreciable and t h i s was compensated f o r i n the t e s t s . On the other hand the r e l a x a t i o n with s t r a i g h t arms was n e g l i g i b l e even at a t o t a l force of 7 gm* The impedance transducer was c a l i b r a t e d with the micrometer stop and i t was found' to be l i n e a r f o r 0.5 mm on e i t h e r side of n u l l . The smallest d i v i s i o n on the 10/c scale represented ~0.42 / u - and the smallest d i v i s i o n on the 3/"- s c a l e , ~0.2l^u- . A sample c a l i b r a t i o n table i n Appendix I shows - 6$ deviation from the average. However t h i s value i s misleading since the micrometer could not be positioned accurately. Nevertheless, the c a l i b r a t i n g procedure was such that the p o s i t i o n i n g errors of the micrometer tended to cancel and therefore the calculated s e n s i t i v i t y i s probably accurate'to within . l e s s than •* 2fo. * 22 -D. The A c i d and C o l d T e m p e r a t u r e B a t h The a c i d b a t h was v e r y s i m p l y b u i l t . The p y r e x arms were b e n t as shown s c h e m a t i c a l l y i n F i g u r e 8. The d i s h was p l a c e d i n p o s i t i o n b e f o r e t h e w h i s k e r was m o u n t e d . A f t e r m o u n t i n g t h e s p e c i m e n , t h e s o l u t i o n was poured i n t o t h e d i s h v e r y g e n t l y by means o f a wash b o t t l e u n t i l t h e w h i s k e r was c o m p l e t e l y i m m e r s e d . D i s h F i g u r e 8. S c h e m a t i c d i a g r a m o f t h e a c i d b a t h . The c o l d t e m p e r a t u r e b a t h was c o n s t r u c t e d f r o m s t y r o f o a m . As shown s c h e m a t i c a l l y i n F i g u r e 9, i t c o n s i s t e d . o f two b a t h s , one above and t h e o t h e r b e l o w t h e t e s t s p e c i m e n . T h i s b a t h was p l a c e d a r o u n d t h e spec imen p i e c e - w i s e * F i r s t t h e b o t t o m b a t h was c e n t r a l l y p l a c e d u n d e r t h e s p e c i m e n on a s h e l f w h i c h d i d n o t t o u c h t h e frame o f t h e t e n s o m e t e r . Then t h e two s p a c e r s were p l a c e d c l o s e t o t h e p y r e x a r m s , and f i n a l l y t h e t o p b a t h on t o p o f t h e s p a c e r s . S i n c e t h e s p e c i m e n c o u l d n o t be immersed i n l o w t e m p e r a t u r e s o l u t i o n s , s p e c i -men t e m p e r a t u r e as low as t h e b a t h c o u l d n o t be r e a c h e d and a l s o t h e c o o l i n g p r o c e s s was s l o w . H o w e v e r , w i t h t h e a i d o f t h e s e c o n d a r y b r a s s b a t h a r e a s o n a b l y s t a b l e t e m p e r a t u r e c o u l d be r e a c h e d . The t e m p e r a t u r e was measured w i t h a c o p p e r - ^ c o n s t a n t a n t h e r m o c o u p l e p l a c e d on t h e t u n g s t e n f i l a m e n t o f t h e - 2 3 -F i g u r e 9° C r o s s s e c t i o n a l d i a g r a m o f c o l d t e m p e r a t u r e b a t h . f i x e d p y r e x a r m . The b a t h was d e s i g n e d so t h a t i n t r o d u c t i o n o f low t e m p e r a -t u r e s o l u t i o n i n t h e t o p b a t h f i r s t removed most o f t h e w a t e r v a p o u r i n t h e c o o l i n g c h a m b e r p r e v e n t i n g i c i n g on t h e s p e c i m e n when t h e b o t t o m b a t h was f i l l e d . The b a t h was e q u i p p e d w i t h d u c t s t o d e f l e c t t h e c o l d a i r away f r o m t h e body o f t h e t e n s o m e t e r . T h i s p r e c a u t i o n e l i m i n a t e d t h e a m b i e n t t e m p e r a -t u r e changes n e a r t h e a p p a r a t u s . - 24 -E. Spec imen M o u n t i n g The m o u n t i n g o f t h e w h i s k e r o n t o t h e t e n s o m e t e r w i t h o u t d e f o r m i n g o r c o n t a m i n a t i n g i t w i t h g l u e o r t h i c k o x i d e l a y e r was a v e r y d e l i c a t e j o b . The g l u e on t h e f i l a m e n t s o f t h e p y r e x arms was h e a t e d c o n s i d e r a b l y above t h e m e l t i n g p o i n t . The m o u n t i n g t i p s were t h e n s u b j e c t e d t o a h i g h f l o w o f d r y h e l i u m . T h i s c o o l e d t h e g l u e somewhat . The d i s t a n c e b e t w e e n t h e g l u e and t h e s o u r c e o f h e l i u m was a d j u s t e d , s o t h a t t h e g l u e had a v e r y t h i n s k i n . F o r b e s t r e s u l t s t h e g l u e s h o u l d be f r e e o f b u b b l e s . The w h i s k e r was t r a n s -p o r t e d t o r t h e mounts as p r e v i o u s l y d e s c r i b e d . Once t h e w h i s k e r was p l a c e d on t h e mounts and r e l e a s e d f r o m t h e p r o b e , t h e suspended r o d was r e t r a c t e d 10JUL t o i n s u r e a x i a l a l i g n m e n t . Then t h e g l u e was c o o l e d . A f t e r t h e t e s t t h e w h i s k e r was removed and mounted on a g o n i o m e t e r f o r o r i e n t a t i o n d e t e r m i n a t i o n . F o l l o w i n g t h i s i t .was mounted i n t h i x o t r o p i c p o l y e s t e r t o be c r o s s s e c t i o n e d . The r e m o v a l o f w h i s k e r s w i t h o u t damaging them was d i f f i c u l t and hence f a i l u r e r a t e was h i g h . F o r w h i s k e r s w i t h s p e c i m e n l e n g t h s h o r t e r t h a n 1 mm o r d i a m e t e r l e s s t h a n 3/*-, i t was v i r t u a l l y i m p o s s i b l e t o r e m o u n t w i t h s u c c e s s . Where p o s s i b l e a l o n g w h i s k e r was c u t i n t w o , one p a r t f o r t h e t e n s i l e t e s t and t h e o t h e r f o r o r i e n t a t i o n d e t e r -m i n a t i o n . F . O r i e n t a t i o n D e t e r m i n a t i o n The o r i e n t a t i o n o f t h e w h i s k e r was d e t e r m i n e d b y . m o u n t i n g a spec imen on a Un icam S 2 5 S i n g l e C r y s t a l G o n i o m e t e r and by t a k i n g Laue t r a n s m i s s i o n p h o t o g r a p h s . Once s t a n d a r d p i c t u r e s o f t h e low i n d e x d i r e c t i o n s were o b t a i n e d , s u b s e q u e n t a n a l y s i s was p e r f o r m e d . b y c o m p a r i s o n . G . Measurement o f Spec imen L e n g t h Spec imen l e n g t h was measured by t h e g r a t i c u l e i n one o f t h e 6x e y e p i e c e s . o f t h e s t e r e o s c o p i c m i c r o s c o p e . The s m a l l e s t d i v i s i o n , o f w h i c h t h e r e a r e one h u n d r e d , w i t h 10X o b j e c t i v e c o r r e s p o n d e d t o 16/*.; . w i t h 6x o b j e c t i v e , t o 26„7yu- . S i n c e t h e g l u e d i d n o t n e c e s s a r i l y g r i p t h e spec imen p r e c i s e l y a b o u t 'one d e f i n i t e c i r c u m f e r e n t i a l l i n e , t h e l e n g t h measurements may be i n e r r o r up t o 2 s m a l l d i v i s i o n s i n a g i v e n m e a s u r e m e n t . T h e r e f o r e t h e e r r o r i n l e n g t h measurement i s l e s s t h a n t 5 $ . H. Cross S e c t i o n a l Area. D e t e r m i n a t i o n The c r o s s s e c t i o n a l a r e a was d e t e r m i n e d by t h r e e means : a ) m i c r o s c o p e , t h i s was t h e most a p p r o x i m a t e method b u t mos t f e a s i b l e . The o u t s i d e d i a m e t e r was measured and a c i r c u l a r c r o s s - s e c t i o n assumed. F o r a h e x a g o n a l c r o s s - s e c t i o n t h i s a p p r o x i m a t i o n i s q u i t e s a t i s f a c t o r y . The d i a m e t e r c o u l d be measured by t h e v e r n i e r t o a b o u t i 0.3^. b ) c r o s s s e c t i o n i n g o f t h e w h i s k e r and t h e measurement o f t h e m a g n i f i e d a r e a . The t e c h n i q u e used-was s i m i l a r t o t h a t o f B r e n n e r and More lock" 1 The b r a s s w a s h e r was n o t used s i n c e b r a s s f i l i n g s made t h e l o c a t i n g o f t h e w h i s k e r d i f f i c u l t . I n s t e a d , t h e w h i s k e r was l a i d on t h e s u r f a c e o f a j u s t g e l l e d p o l y e s t e r and some n o t - y e t g e l l e d p o l y e s t e r was p o u r e d on t o p . T h i s s a n d w i c h i n g o f t h e w h i s k e r gave r e a s o n a b l y good r e s u l t s . A f t e r n o r m a l m e t a l l o g r a p h i c p o l i s h , t h e spec imen was p o l i s h e d on a s t a t i o n a r y f i n a l l a p w i t h a l u m i n a s l u r r y . A v e r y s h o r t e t c h i n g w i t h ammonium h y d r o x i d e , h y d r o g e n p e r o x i d e and w a t e r - 26 s o l u t i o n and t h e n r e p o l i s h i n g l i g h t l y w i t h t h e s l u r r y r e s u l t e d i n an unsmeared c r o s s s e c t i o n a l s h a p e . The m i c r o p h o t o g r a p h o f t h e c r o s s s e c t i o n was measured w i t h a p l a n i m e t e r . a r e a f r o m Y o u n g ' s M o d u l u s / E . Prom t h e s l o p e o f t h e l o a d - e x t e n s i o n p l o t and E , t h e a r e a was c o m p u t e d . Where t h e o r i e n t a t i o n o f t h e w h i s k e r was not , d e t e r m i n e d , i t was assumed t o be t h a t whose E v a l u e was c l o s e s t t o t h e computed E v a l u e f r o m t h e o p t i c a l d i a m e t e r . The 44 E v a l u e used was computed f r o m t h e r e l a t i o n | = s n - 2 .(sn - s 1 2) - 1/2 s 4 4 ( tfi2 r2 2+ ^ 2 2 ^ 2 + *3 2&i 2) where t h e S j^ a r e t h e e l a s t i c c o m p l i a n c e c o n s t a n t s and Yx, Yz, 3^ r e p r e s e n t t h e c o s i n e s o f t h e a n g l e s fo rmed by t h e a x i s o f t h e s p e c i -men, w i t h t h e t h r e e edges o f t h e u n i t c u b e . The v a l u e s o f S n , S12 and S44 f o r v a r i o u s low t e m p e r a t u r e s were computed f r o m O v e r t o n and G a f f n e y ' s v a l u e s 4 5 o f C n , C12, and C44. - 27 -I . E x p e r i m e n t a l P r o c e d u r e 1 . Growth S t u d y G e n e r a l g r o w t h t e n d e n c i e s w e r e o b s e r v e d . Whenever good s h a r p g r o w t h k i n k s were f o u n d , t h e k i n k a n g l e was d e t e r m i n e d by t a k i n g m i c r o p h o t o g r a p h s o f t h e w h i s k e r . Laue p i c t u r e s were t h e n t a k e n t o d e t e r m i n e w h e t h e r i t was a s i n g l e c r y s t a l and i f so what was i t s o r i e n t a t i o n . 2. A c i d T e s t s The t e n s i l e t e s t s i n d i l u t e s u l p h u r i c a c i d were c o n d u c t e d a t room t e m p e r a t u r e w i t h t h e s p e c i m e n c o m p l e t e l y i m m e r s e d . A f t e r t h e spec imen was m o u n t e d , b o i l e d o r n i t r o g e n b u b b l e d d i s t i l l e d w a t e r was poured i n t o t h e d i s h as p r e v i o u s l y d e s c r i b e d . The w h i s k e r was t h e n t e s t e d i n c r e m e n t a l l y / t o some p o i n t be low i t s y i e l d p o i n t and t h e l o a d i n c r e m e n t a l l y r e l e a s e d . T h i s i n i t i a l t e s t was p e r f o r m e d t o check t h a t t h e i m m e r s i o n p r o c e s s d i d n o t i n t r o d u c e d e f e c t s i n t h e w h i s k e r . Then some 10$ s o l u t i o n o f r e a g e n t g r a d e s u l p h u r i c a c i d was i n t r o d u c e d . A f t e r i t ,was p i c k l e d f o r a b o u t t e n m i n u t e s , t h e w h i s k e r was t e s t e d t o and beyond t h e y i e l d p o i n t . A f t e r y i e l d i n g o c c u r r e d , , t h e l o a d was r e l e a s e d t o a v a l u e j u s t s u f f i c i e n t t o m a i n t a i n t h e w h i s k e r t a u t and t h e m i c r o m e t e r s t o p was s e t back 1 0 / ^ . The l o a d was a p p l i e d a g a i n and t h e f l o w s t r e s s was d e t e r m i n e d . Upon c o m p l e t i o n o f t h e t e s t , t h e a c i d s o l u t i o n was s i p h o n e d o u t . A f t e r t h e w h i s k e r was r i n s e d i n d i s t i l l e d w a t e r , i t was removed f o r o r i e n t a t i o n d e t e r m i n a t i o n and c r o s s s e c t i o n i n g . - 28 -3 . -Cold T e m p e r a t u r e T e s t s F o r t e m p e r a t u r e dependence s t u d i e s , t h e c o l d t e m p e r a t u r e b a t h e a r l i e r d e s c r i b e d was u s e d . The c o l d t e m p e r a t u r e s o l u t i o n s used were l i q u i d n i t r o g e n , and c a l c i u m c h l o r i d e - i c e s o l u t i o n . The measured t e m -p e r a t u r e s were w i t h i n 1 3 °K . A f t e r t h e w h i s k e r was mounted and t e s t e d a t room t e m p e r a t u r e , t h e b a t h was b u i l t a round t h e spec imen and t h e c o l d t e m -p e r a t u r e s o l u t i o n i n t r o d u c e d . U s u a l l y 4 5 t o 60 m i n u t e s were r e q u i r e d t o r e a c h . e q u i l i b r i u m t e m p e r a t u r e . Upon d e t e r m i n i n g t h e f l o w s t r e s s a t t h i s t e m p e r a t u r e , t h e l o a d was r e l e a s e d t o n e a r z e r o . The m i c r o m e t e r was t h e n d i s p l a c e d a s u i t a b l e d i s t a n c e t o accommodate e x p a n s i o n o f t h e p y r e x a r m s , and t h e n t h e b a t h was c a r e f u l l y r e m o v e d . A t a l l t i m e s t h e p o s i t i o n o f t h e suspended r o d . f r o m n u l l was r e c o r d e d i n o r d e r t h a t t h e o b t a i n e d l o a d -e x t e n s i o n p l o t may be c o r r e c t l y compensated f o r t h e r e s t o r i n g f o r c e . T h i s p r o c e d u r e was r e p e a t e d f o r v a r i o u s d i f f e r e n t s e q u e n c e s . o f t e s t s . - 29 -I I I . E x p e r i m e n t a l O b s e r v a t i o n s and R e s u l t s A . Growth O b s e r v a t i o n s W h i s k e r s were g rown i n t h e t e m p e r a t u r e r a n g e o f 550° t o 700°C. The opt imum t e m p e r a t u r e f o r g r o w t h o f w h i s k e r s l e s s t h a n 10^ i n d i a m e t e r was a round 600°C w i t h h y d r o g e n f l o w . o f 200 c u b i c c e n t i m e t e r s p e r m i n u t e ( c c / m i n ) . S i n c e w h i s k e r g r o w t h i s n o t r e a d i l y r e p r o d u c i b l e , even t h o u g h a p p a r e n t l y same c o n d i t i o n s a r e u s e d , o n l y g e n e r a l t e n d e n c i e s a r e l i s t e d b e l o w . a ) A t t e m p e r a t u r e s c l o s e t o 700°C w h i s k e r s were few i n number , c o a r s e ( o v e r l C y ^ i n d i a m e t e r ) and l o n g , 1 t o 2. cm were common. b ) . A t t e m p e r a t u r e s c l o s e t o 550°C w h i s k e r s grew i n c l u s t e r s b u t w e r e ' n o t h e a v i l y e n t a n g l e d t o i n t e r f e r e w i t h e x a m i n a t i o n and r e m o v a l . c ) H i g h h y d r o g e n f l o w o f 300 c c / m i n gave e r r a t i c g r o w t h r e s u l t s . L o w . f l o w o f 100 c c / m i n u s u a l l y . d i d n o t r e s u l t i n w h i s k e r g r o w t h . d ) When new f i r e c l a y b o a t s w e r e u s e d , w h i s k e r s d i d n o t g r o w . However , r e u s e o f t h e b o a t a f t e r t h e c o p p e r m a t t e was removed gave good r e s u l t s . e ) The most i m p o r t a n t f a c t o r i n w h i s k e r g r o w t h seemed t o be t h e c l e a n l i n e s s o f t h e r e d u c i n g a t m o s p h e r e . W i t h a c l e a n a tmosphere good w h i s k e r s were more a b u n d a n t . G e n e r a l l y a l l t h e g r o w t h c h a r a c t e r i s t i c s r e p o r t e d by B r e n n e r 1 0 were a g a i n o b s e r v e d . Segments o f most w h i s k e r s were s t r a i g h t w i t h b r a n c h e s o r -30 -surface defects. However c i r c u l a r h e l i c e s , polygonal h e l i c e s , f i n e l y threaded.whiskers, sharply kinked whiskers were also observed. A s t r a i g h t non-tangled whisker usually terminated pyramidally. P i t s s i m i l a r to those described.by Brenner 1 2 were usually found .in large whiskers (~15/<.in diameter). Although a facet did not seem to change i t s crystallographic plane, i t s plane occasionally was not f l a t but rippled. Also, in large whiskers very slight bevelling and/or ridging were common, such as shown in Figure 20. B. Orientation Determination Good interpretable Laue transmission photographs were obtained .using a molybdenum tube at 50 kv and 15 mllli-amperes (ma).with an exposure time of two hours. Even at this high irradiation, very few spots were detectable. The scarcity of spots caused d i f f i c u l t y in Interpretation but With the aid of standard gnomonic projections, standard pictures .were, obtained. Three standard photographs are shown in Figures 10, 11 and.12. These pictures were obtained from a whisker whose axis was parallel to a <110>. The rings which appear on the picture are due to a collimator effect. As seen from these pictures the <110> pattern is not very distinct. Hence ^ l l l ) a x i s deter-minations were most d i f f i c u l t to perform. If the whisker axis .was not parallel to one of the three common low index directions, orientation deter-mination was not always possible. Figure 10b, Schematic representation of Figure 10a. Figure 1 1 a . Laue transmission picture of a ^ 1 1 0 > whisker with the X-ray beam p a r a l l e l to a <110> « 1 1 0 > picture) Figure l i b . Schematic representation of Figure 1 1 a . - 5 3 -Figure 12b. Schematic representation of Figure 12a. C . C ross S e c t i o n a l A r e a Some m i c r o p h o t o g r a p h s o f c r o s s s e c t i o n e d w h i s k e r s a r e shown i n F i g u r e 13. S h a r p p o l y g o n a l c r o s s s e c t i o n s were d i f f i c u l t t o o b t a i n , e s p e c i a l l y i f t h e w h i s k e r s had p r e v i o u s l y undergone t e n s i l e t e s t s . T a b l e I l i s t s t h e r e s u l t s f r o m t h e t h r e e methods t h a t were e m p l o y e d . I n most c a s e s , t h e o p t i c a l method i s i n good agreement w i t h t h e o t h e r t w o . Sample A9 i s t h e e x c e p t i o n s i n c e t h e c r o s s s e c t i o n i n t h i s case was r e c t a n g u l a r . I n a l l t h e s t r e s s c a l c u l a t i o n s t h e a r e a computed f r o m t h e Y o u n g ' s Modu lus and t h e s l o p e o f t h e l o a d - e x t e n s i o n c u r v e was u s e d . Where o r i e n t a -t i o n was n o t d e t e r m i n e d , i t was assumed t o be one o f t h e t h r e e common ones w h i c h possessed t h e modu lus c l o s e s t t o t h a t computed f r o m t h e a r e a d e t e r -mined b y t h e o p t i c a l m e t h o d . ( a ) <100> w h i s k e r ( b ) <100> w h i s k e r ( c ) <110> w h i s k e r a r e a 33/t2. a r e a 20^. a r e a 38A 2 . F i g u r e 13« Cross s e c t i o n s o f w h i s k e r s . -35 -T a b l e I . Compar i son o f t h e A reas D e t e r m i n e d by t h e T h r e e Methods Measured .Area I n /uJ 2 Sample O p t i c a l C ross S e c t i o n i n g E A3 A6 A7 A9 A10 25 65 21 7^  33 59 38 20 29 35 22 22 D. Growth K i n k s The most i n t e r e s t i n g a s p e c t s o f w h i s k e r g r o w t h w e r e o b s e r v a t i o n s o f g r o w t h k i n k s . The t e r m g r o w t h k i n k s r e f e r s t o t h o s e w h i s k e r s w h i c h possess a v e r y w e l l d e f i n e d . k i n k and u s u a l l y two segments have t w o f a c e t s i n common. Examples o f t h e s e a r e shown i n F i g u r e s 1^, 15, l6 and 17. The k i n k a n g l e s i l l u s t r a t e d by t h e s e m i c r o p h o t o g r a p h s a r e 90°, ^ 5°120° and 150° w i t h i n i 2° r e s p e c t i v e l y . Those k i n k s w h i c h have common f a c e t s , as i s r e a d i l y seen i n F i g u r e s .1^- and-15, a r e assumed t o be s i n g l e c r y s t a l s 4 ^ . U n f o r t u n a t e l y , o r i e n t a t i o n o f t h e s e t w o k i n k e d w h i s k e r s c o u l d n o t be o b t a i n e d due t o d i f f i c u l t y e n c o u n t e r e d d u r i n g m o u n t i n g on t h e g o n i o m e t e r . The s u r f a c e m a r k i n g s on t h e s e k i n k e d w h i s k e r s a r e v e r y s h o r t b r a n c h g r o w t h s . O p t i c a l d i a m e t e r measurement o f t h e w h i s k e r shown i n F i g u r e l^ t- r e v e a l e d t h a t t h e two segments were a p p r o x i m a t e l y t h e same b u t t h e t r a n s i t i o n p o r t i o n was a b o u t 2% t h i c k e r . F i g u r e l6 i s a u n i q u e w h i s k e r i n t h a t a l l t h e segments o f t h e k i n k l i e on t h e same p l a n e . F o r d i s c u s s i o n p u r p o s e s , segments a r e d e n o t e d a , b , c , d , e , s t a r t i n g f r o m t h e b o t t o m u p w a r d s . The bend i n t h e e arm was i n c u r r e d Figure 15. Whisker with ^5° kink. Figure 17. H e l i c a l l y twisted whisker with 150° kink. - 38 -d u r i n g t h e r e m o v a l f r o m t h e b o a t . The measured i n t e r i o r a n g l e s a r e 60°, 120°, 120°, 120°. Under m i c r o s c o p i c i n s p e c t i o n b , c and d have a common f a c e t b u t no d i s t i n c t ma tch o f f a c e t s c o u l d be f o u n d b e t w e e n e i t h e r a and b o r d and e . X - r a y d e t e r m i n a t i o n s r e v e a l e d t h a t d and b , w h i c h a r e p a r a l l e l , possessed t h e same ^110} o r i e n t a t i o n and i n f a c t d , c , and b were segments o f t h e same s i n g l e c r y s t a l , a and e b o t h had a <110> o r i e n t a t i o n and t h e r e l a t i v e a n g l e w h i c h e had t o be r o t a t e d a b o u t i t s a x i s f o r p e r f e c t c r y s t a l -l o g r a p h i c c o i n c i d e n c e w i t h a was a b o u t h°. C o n s i d e r i n g t h e h a n d l i n g and i n t e r p r e t a t i o n a l e r r o r , i t can be c o n c l u d e d t h a t t h e s e e x t e r i o r segments a and e were i d e n t i c a l i n o r i e n t a t i o n i n e v e r y r e s p e c t , b and a have a measured o r i e n t a t i o n d i f f e r e n c e o f a b o u t 73° a b o u t a <110^. X - r a y s t u d y showed t h a t i n a l l segments one s e t o f { i l l were p a r a l l e l . H o w e v e r , b o t h a - b and b - c k i n k s e x h i b i t e d u n u s u a l d u a l s p o t s . T h i s i s shown i n F i g u r e l 8 . The r e a s o n f o r t h i s t y p e o f a s t e r i s m c o u l d n o t be s a t i s f a c t o r i l y e x p l a i n e d . T h i s m u l t i -k i n k e d w h i s k e r was h e a t t r e a t e d f o r one h o u r u n d e r h e l i u m a t m o s p h e r e a t 910°C. No o b s e r v a b l e d e k i n k i n g had t a k e n p l a c e . F i g u r e l 8 . Laue t r a n s m i s s i o n < l l l ) p i c t u r e o f b - c k i n k s h o w i n g d u a l s p o t s . - 39 -F i g u r e 17 i l l u s t r a t e s a h e l i c a l l y t w i s t e d w h i s k e r w h i c h i s k i n k e d w i t h an i n t e r i o r a n g l e o f 150°. Upon k i n k i n g , t h e w h i s k e r s t o p p e d i t s h e l i c a l g r o w t h and s t a r t e d t o grow i n a r e g u l a r c y l i n d r i c a l m a n n e r . The e x a c t n a t u r e o f t h e h e l i c a l g r o w t h i s b e t t e r seen i n F i g u r e 19. The p e r i o d i c i t y o f g r o w t h i s o u t s t a n d i n g and t h e f l a t o v a l - s h a p e d f a c e s o f t h e w h i s k e r seem t o be c r y s t a l l o g r a p h i c a l l y i d e n t i c a l . X - r a y s t u d y r e v e a l e d t h a t t h e c y l i n d r i c a l p o r t i o n o f t h e w h i s k e r has an o r i e n t a t i o n w h i c h i s 15° o f f a <110>. The p l a n e o f t h e k i n k a n g l e was c l o s e t o a {l00}. The h e l i c a l p o r t i o n e x h i b i t e d t h e same p a t t e r n as t h a t f o u n d on t h e c y l i n d r i c a l p o r t i o n b u t some e x t r a s p o t s were super imposed on i t . From t h i s s t u d y i t was c o n c l u d e d t h a t t h e h e l i c a l p o r t i o n c o n s i s t e d o f a t l e a s t two o r i e n t a t i o n s , one c o i n c i d e n t w i t h t h a t o f t h e c y l i n d r i c a l p o r t i o n . F i g u r e 19. H e l i c a l l y t w i s t e d w h i s k e r - ho -Figure 2 0 displays a large kinked whisker with an i n t e r i o r angle of 9 7 ° and 1 7 ^ ° , This whisker, as i s re a d i l y d i s c e r n i b l e , has low ridges around most of i t s perimeter. The cross-section i s approximately rectangular, the dimensions being 2 by 1 3 / * . . Figure 2 1 i s the same whisker at a lower magni-f i c a t i o n . The whisker has many high angled kinks, almost curves. X-ray studies revealed that the t o t a l whisker i s a single c r y s t a l . The orientation of the straight portion (bottom part i n Figure 2 0 ) i s about 1 2 ° o f f a < 1 1 0 ) . A sample (l00} picture i s shown i n Figure 2 2 . This i d e n t i c a l pattern was obtained whether the whisker was irradiated at the top, middle or bottom portion. The photographed face i s close to a { l 0 0 } . The above-mentioned X-ray picture indicates a 1 2 ° deviation to the l e f t but the kinks were to the rig h t when the whisker was ir r a d i a t e d . Figure 2 0 . Kinked whisker with ridges. Figure 22. Laue transmission ( 1 0 0 ^ picture of the whisker shown in Figures 20 and 2 1 . The indicated l i n e i s p a r a l l e l to a < 1 1 0 / . The axis of the whisker i s v e r t i c a l . - k2 -E. T e n s i l e T e s t s 1 . The R e l i a b i l i t y o f t h e Q u a n t i t a t i v e Measurements The f o r c e c a l i b r a t i o n o f t h e a p p a r a t u s and t h e c r o s s s e c t i o n a l a r e a d e t e r m i n a t i o n o f t h e w h i s k e r a r e t h e two m a j o r s o u r c e s o f e r r o r . The p r o b a b l e e r r o r o f each c a l i b r a t i o n has been computed s t a t i s t i c a l l y and d e n o t e d on t h e g r a p h s . The p e r c e n t a g e e r r o r i n t r o d u c e d due t o t h e c o m p e n s a t i o n f o r t h e r e s -t o r i n g f o r c e i s v e r y s m a l l f o r t h e y i e l d s t r e s s b u t t h e same amount o f e r r o r g i v e s a h i g h p e r c e n t a g e e r r o r f o r t h e f l o w s t r e s s . The e s t i m a t e d maximum e r r o r i s a b o u t 10 mg. Hence i f t h e l o a d f o r f l o w . i s i n t h e 200 mg r a n g e , , t h e p e r c e n t a g e e r r o r i s a b o u t 5$« T h e r e f o r e t h e p r o b a b l e e r r o r f o r t h e l o a d m e a s u r e m e n t s , w h i c h i n c l u d e s c a l i b r a t i n g and. c o m p e n s a t i n g e r r o r , i s a b o u t 15$. The c r o s s s e c t i o n a l a r e a d e t e r m i n a t i o n may be a l a r g e s o u r c e o f e r r o r . F i r s t l y i t was assumed t h a t t h e Y o u n g ' s M o d u l u s f o r w h i s k e r s i s t h e same as t h a t f o r b u l k c r y s t a l s . T h e r e a r e two p o s s i b l e r e a s o n s why t h i s may n o t be s o ; .a) t h e s u r f a c e t o vo lume r a t i o i s much h i g h e r f o r w h i s k e r s t h a n f o r b u l k c r y s t a l s , b ) t h e d i s l o c a t i o n d e n s i t y may be d i f f e r e n t . The f i r s t f a c t o r i s n e g l i g i b l e s i n c e , a l t h o u g h w h i s k e r s a r e s m a l l t h e y a r e n e v e r t h e l e s s more t h a n 10 atoms t h i c k , and t h e n o n - s y m m e t r i c a l b o n d i n g o f t h e s u r f a c e l a y e r c a n n o t a p p r e c i a b l y change t h e e l a s t i c c o n s t a n t s . The second f a c t o r can a c c o u n t f o r a t most o n l y a few p e r c e n t d i f f e r e n c e i n t h e 4 7 e l a s t i c c o n s t a n t s . T h e r e f o r e t h e a s s u m p t i o n t h a t Y o u n g ' s Modu lus o f w h i s k e r s i s t h e same as t h a t f o r b u l k c r y s t a l s i s a r e a s o n a b l e o n e . The use of Young's Modulus f o r the area determination i s very.accurate f o r the cases where the o r i e n t a t i o n Is known. .The e r r o r occurs when an o r i e n t a t i o n i s assumed from the modulus computed from the area determined.by the o p t i c a l method. .However, evidence shown i n Table I indicates that t h i s method i s quite good.. The e r r o r i s introduced when a whisker with an axis o r i e n t a t i o n other than the three common ones i s encountered. In t h i s case a s l i g h t l y higher or lower modulus i s assumed. However, since X-ray determination i n t h i s i n v e s t i g a t i o n has shown that whiskers which possess axes o f f the low index ones do so by about 15°, the maximum erro r introduced i s ~10$ . .Prom the above discussion i t i s apparent t h a t the absolute stress values may be as much as 25$ i n e r r o r . However, the e r r o r i n r e l a t i v e stress values f o r any p a r t i c u l a r t e s t i s a great deal l e s s . Hence the observed phenomena i n the following sections are t r u l y a property of the whisker and are s i g n i f i c a n t . .2. E f f e c t of Oxide Layers T e n s i l e t e s t s i n d i s t i l l e d water and d i l u t e sulphuric acid were complicated by the r e l a x a t i o n of the bent.pyrex arms and some d i s s o l u t i o n of the diphenyl carbazide by,water. The l a t t e r e f f e c t was n e g l i g i b l e , even b e n e f i c i a l , , since i t washed away any adhering t h i n glue f i l m on the specimen. However, the former was undesirable since the s e n s i t i v i t y of the t e s t .was reduced. Nevertheless t h i s f a c t o r did not mask the r e s u l t of the t e s t s . The t e s t s which were performed are tabulated i n Table I I . A t y p i c a l load-extension plot i s shown i n Figure 23. The slope of the e l a s t i c region was independent of the s o l u t i o n . i n which the whisker was immersed. Tableit« T e n s i l e T e s t s C a r r i e d Out i n D i l u t e S u l p h u r i c A c i d (Try -= r e s o l v e d s h e a r s t r e s s f o r y i e l d 6~rf ; i = r e s o l v e d s h e a r s t r e s s f o r f l o w 6 .= maximum e l a s t i c t e n s i l e s t r a i n Sample H 2S0 4 . Concentration molar (m) (NH4)2S04 Concentration (m) Determined Orientation Assumed Vmnrv Computed Cross Sectional Area from E /JL 2 <Try \mm / 6"rf \mm / C r f em A l 0.43 — 6,800 51.5 13*5 .2.37 ' 5.7 • 0.45 A2 0.25 — 6,800 .27.6 4.4i 4.4i 1.0 0.10 A3 d i s t i l l e d water only [110] 13,^00 21.8 22.5 — — 0.37 A4 0,48. — 13,400 ,18.7 24.1 6.62 3.6 — A5 0.33 O.71 6,800 3.7 55.1 — — 1.75 A6 .0.44 0.34 6,800 58.7 4.85 ,3.48 /L.4 0,15 A7 .0.45 0.34 [110] 13,400 35.4 -22.0 2,90 7.6 0.19 A8 0.49 6,800 20.4 24.1 __. 0.69 A9 0.A1 — [lOO] 6,800 22.4 26,7 3.64 7-3 0.90 loading c u r v e in d i s t i l l e d w a t e r - x - x - x - x — unloading curve in d i s t i l l e d w a t e r load ing cu rve in 0.41m. s u l p h u r i c ac id J I L curve c o m p e n s a t e d f o r the re laxat ion of the py rex a rms specimen length 1.84 mm c r o s s s e c t i o n a l area 2 2 / v i I I L 0.4 0.8 1.2 1.6 2.0 E x t e n s i o n (%) 2.4 2.8 3.2 3.6 F igu re 2 3 . L o a d - e x t e n s i o n p lo t o f S a m p l e A 9 t e s t e d in d i l u te s u l p h u r i c a c i d . -46 -A l l t h e t e s t s e x c e p t o n e , A2, d i s p l a y e d t h e sudden y i e l d phenomenon. Those t e s t s i n w h i c h f l o w s t r e s s e s a r e m i s s i n g f r a c t u r e d upon y i e l d i n g . The f r a c t u r e t o o k p l a c e i n t h e y i e l d e d r e g i o n . • A l t h o u g h a s h e a r s t r e s s o f 26.6 ^ 0 was a p p l i e d on s p e c i m e n A2 i n mm 2 • d i s t i l l e d . w a t e r , no y i e l d . p o i n t was f o u n d when t e s t e d i n d i l u t e s u l p h u r i c . a c i d . I t s y i e l d s t r e s s was o n l y h.hl M , . T h i s r e s u l t i n d i c a t e s t h a t a d e f e c t was mm^ i n t r o d u c e d i n t h e w h i s k e r d u r i n g t h e a c i d . p o u r i n g p r o c e s s . The i n t e r e s t i n g a s p e c t o f t h i s t e s t was t h a t s u b s e q u e n t r i n s i n g , d r y i n g and t e s t i n g o f t h e s p e c i m e n i n a i r showed no a p p r e c i a b l e change i n f l o w s t r e s s . -Sample Ah d i f f e r e d f r o m t h e o t h e r t e s t s i n t h a t a t o n e - h a l f t h e y i e l d , s t r e s s c r e e p was o b s e r v e d . No v i s i b l e s l i p . l i n e s were e v i d e n t u n d e r l o w m a g n i f i c a t i o n b u t p i t t i n g was n o t e d a t t h e t i m e t h a t t h e c r e e p was f i r s t o b -s e r v e d . Upon y i e l d i n g , t h e u s u a l L u d e r s bands were g e n e r a t e d . C r i t i c a l e x a m i n a t i o n o f t h e g r i p s i n d i c a t e d . t h a t t h e s l i p p i n g o f t h e g l u e was u n l i k e l y . I n o r d e r t o d e t e r m i n e t h e n a t u r e o f t h e above observed , . c r e e p , ammonium s u l p h a t e s o l u t i o n was used i n s t e a d o f p u r e d i s t i l l e d . w a t e r . T h i s i n t r o d u c t i o n , w h i c h r a i s e d t h e pH o f t h e a c i d s o l u t i o n , w o u l d t e n d t o r e d u c e t h e p i t t i n g a c t i o n . A l s o , t h e s o l u t i o n was d e - a e r a t e d w i t h n i t r o g e n b u b b l i n g r a t h e r t h a n b o i l i n g . F u r t h e r t e s t s u n d e r t h e s e c o n d i t i o n s d i d n o t e x h i b i t c r e e p o r o b s e r v a b l e p i t t i n g . Sample A9 was a w h i s k e r w i t h l i n e s u r f a c e d e f e c t s , i . e . s h o r t l e n g t h s o f r i d g e s . T e s t i n g o f t h i s w h i s k e r w i t h o u t b u f f e r i n g w i t h ammonium s u l p h a t e d i d n o t m a n i f e s t c r e e p . 3. T e n s i l e T e s t s a t Room and Low. T e m p e r a t u r e s The r e s u l t s o f t h e t e n s i l e t e s t s a r e t a b u l a t e d i n T a b l e I I I . The samples a r e g r o u p e d a c c o r d i n g t o t h e i r o r i e n t a t i o n s . Those 'which a r e marked w i t h a s t e r i s k s a r e samples on w h i c h s u b s e q u e n t l o a d i n g t e s t s have been p e r -f o r m e d . These t e s t s a r e t r e a t e d i n t h e f o l l o w i n g s e c t i o n . The one s i g n i f i c a n t p o i n t w h i c h i s e v i d e n t f r o m t h i s t a b l e i s t h a t t h e r e s o l v e d f l o w s t r e s s e s a r e t w o t o t h r e e t i m e s h i g h e r t h a n t h o s e r e p o r t e d by B r e n n e r 2 6 . The l o a d - e x t e n s i o n c u r v e o f w h i s k e r s w h i c h w e r e p u l l e d t o y i e l d a t room t e m p e r a t u r e and t h e n p u l l e d a t l o w t e m p e r a t u r e e x h i b i t e d two p r o p e r t i e s . F i r s t l y t h e o~*fT r a t i o s were n o t c o n s t a n t b u t e r r a t i c . T h i s i s . i n a c c o r d a n c e 6"fT, low 43 w i t h Adams and C o t t r e l l , who r e p o r t e d t h a t i n b u l k c o p p e r s i n g l e c r y s t a l s a c o n s t a n t v a l u e was n o t a t t a i n e d u n t i l t h e spec imen was e x t e n d e d 10 t o 15$* H o w e v e r , w h e t h e r t h e e r r a t i c n a t u r e o f t h e f l o w s t r e s s i n b o t h cases i s due t o t h e same r e a s o n i s q u e s t i o n a b l e . S e c o n d l y , t h e f l o w s t r e s s was n o t d i s t i n c t . S m a l l amounts o f f l o w u s u a l l y p r e c e d e d a l a r g e r f l o w w h i c h t o o k p l a c e a t a h i g h e r s t r e s s , c r e a t i n g a s t e p e f f e c t . T h i s s t e p o c c u r r e d more f r e q u e n t l y a t l o w t e m p e r a t u r e s . I n d e e d a t low t e m p e r a t u r e s t h i s s t e p somet imes o c c u r r e d a t a s t r e s s , l o w e r t h a n t h e p r e c e d i n g f l o w s t r e s s a t room t e m p e r a t u r e . T h i s s t e p e f f e c t i s c l e a r l y e x h i b i t e d i n F i g u r e 2 4 b . a t A . The e x t e n s i o n s b e t w e e n l o a d -i n g s w e r e caused d u r i n g t h e c h a n g i n g o f t h e b a t h s and r e s e t t i n g o f t h e m i c r o -m e t e r s t o p . The low t e m p e r a t u r e r e a c h e d i n t h i s t e s t was -150° i 5°C» T h i s o b s e r v e d s t e p e f f e c t i s n o t s i m i l a r t o t h e o b s t r u c t e d f l o w r e p o r t e d by B r e n n e r 1 2 , B r e n n e r ' s o b s t r u c t e d f l o w d i s p l a y e d c o n s i d e r a b l e w o r k h a r d e n i n g , whereas t h e s t e p e f f e c t d e s c r i b e d above d i d n o t . T a b l e I I I . T e n s i l e T e s t s a t Room and Low T e m p e r a t u r e s Sample D e t e r m i n e d O r i e n t a t i o n Assumed E Vmm2/ .Computed Cross S e c t i o n a l A r e a f r o m E <T r y \mm2/ < T r f v mm2' €(*) T e m p e r a t u r e o f T e s t B l 6,800 8.4 50.0 5.15 9.7 1 .70 room B2 6,800 5.1 47.0 — c u r l e d .1.57 room B3 6,800 35.7 45.0 2 .40 18.8 1.57 room BIO 6,800 34.2 27.O — 0.97 room B l l 6,800 .11.4 35.8 — c u r l e d 1.42 room B12 6,800 10.3 58.5 — , - - 2.10 room B 1 3 f t 6,800 39.7 .34.2 2.45 13.9 •1.23 room Bl4 6,800 7.2 49.0 — — 1.78 room Bl8* 7,300 19.4 52.6 2.79 18.9 1.82 -1^ -3° C B19 7,150 5.7 66.6 c u r l e d 2.10 -78°C B2G* 6,800 16.0 11.5 3.00 3.9 0.36 room B21& [100] 6,800 11.8 39.6 3..7v .10.-7 •1.33 room B 2 2 * 6,850 16.7 44.2 2.96 14.9 1 .70 -8°C B24 7,300 12.2 23.O .•" — — 0.71 -l49°c ... B 1 7 * 12° o f f [lOO] 7,550 48.6 56.O 2 . 0 0 28.0 1.33 -153°C B7 13,400 76.6. 16.7 I.67 10.0 0.31 room 19,400 37.2 21.4 2.52 8.5 0.4i room B5* [111] 19,400 24.0 24.0 3.02 7.9 0.39 room - • B6 19,^00 ,lh.3 48.5 1.91 25.3 0.92 room B 8 O 19,400 8.1 19.9 2.91 6.8 0.38 room i9 ,4oo 17.8 42.5 2.86 14.9 0.71 room B15 [111] 19,400 19.9 26.0 3.16 8.2 ,0.47 room Bl6 . 19,^00 14.4 13.8 3.29 . 4.2 0 .24 room B23 20,000 5.1 33.8 .-- — 0.55 -153°c E x t e n s i o n (%) F i g u r e 2 4 a . L o a d - e x t e n s i o n p lo t o f t h e e l a s t i c r e g i o n . o f Sample B 15 t e s t e d a t r o o m t e m p e r a t u r e . - 50 -48 0 -0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 E x t e n s i o n (%) Figure 2 4 b. Loo d - e x t e n s i o n plot of the t e s t e d alternately at r o o m plastic reg ion of temperature and Sample B 15 - I 5 0 ° C . - 51 -F i g u r e 24a i s a p l o t o f t h e e l a s t i c r e g i o n . The e x t r e m e l y , l i n e a r p l o t o f t h e p o i n t s i s most s i g n i f i c a n t . . W i t h o u t e x c e p t i o n a l l t h e t e s t s p e r f o r m e d d i s p l a y e d t h i s r e m a r k a b l e l i n e a r r e l a t i o n s h i p . Upon y i e l d i n g o f sample B15, L u d e r s band n u c l e a t e d a t one o f t h e g r i p s . Subsequen t l o a d i n g t o d e t e r m i n e t h e f l o w s t r e s s a t room t e m p e r a t u r e p r o p a g a t e d . t h i s , b a n d . . A f t e r t h e f i r s t low t e m p e r a t u r e l o a d i n g and t h e second room t e m p e r a t u r e l o a d i n g , o n l y t h e one band was o b s e r v e d . However , a f t e r t h e s e c o n d . l o w t e m p e r a t u r e l o a d i n g , two o t h e r r e g i o n s o f L u d e r s band a p p e a r e d . A f t e r t h e t h i r d .low t e m p e r a t u r e l o a d i n g , no a p p a r e n t e x t e n s i o n o f t h e t h r e e d e f o r m e d . r e g i o n s had t a k e n p l a c e . F i g u r e 24b c l e a r l y i l l u s t r a t e s t h e work ' h a r d e n e d r e g i o n . T h i s t y p e o f b e h a v i o u r has been d e s c r i b e d as o b s t r u c t e d . f l o w by. B r e n n e r . T h i s p l o t c l e a r l y shows t h a t t h e s t e p e f f e c t and o b s t r u c t e d f l o w a r e two q u i t e d i f f e r e n t phenomena. The n e g a t i v e s l o p e w h i c h i s i n d i c a t e d . o n a l l t h e l o a d - e x t e n s i o n g r a p h s i s due t o t h e c o m p e n s a t i o n o f t h e measured v a l u e s f o r t h e r e s t o r i n g f o r c e o f t h e suspended r o d . . A l t h o u g h w i t h t h i s a p p a r a t u s s m a l l y i e l d p o i n t s c a n n o t be p r e c i s e l y d e t e r m i n e d , t h e d e c r e a s e o f l o a d w i t h e x t e n s i o n , an i n h e r e n t p r o p e r t y o f t h e a p p a r a t u s , i s a good i n d i c a t i o n t h a t a t i n i t i a t i o n o f f l o w a s m a l l y i e l d p o i n t e x i s t s . 33 P e a r s o n , Read and Fe ldman r e p o r t e d . t h a t a y i e l d p o i n t i n s i l i c o n w h i s k e r s i n t h e f l o w r e g i o n . w a s o b s e r v e d b u t was e l i m i n a t e d by t a p p i n g t h e a p p a r a t u s . B r e n n e r 1 2 n o t e d t h a t s m a l l f l u c t u a t i o n s i n f l o w s t r e s s were o b s e r v e d b u t he d i d n o t g i v e any. d e t a i l s . The f a c t t h a t y i e l d p o i n t s a r e o b s e r v e d s t r e n g t h e n s t h e b e l i e f t h a t t h e f l o w r e g i o n i n t h e w h i s k e r i s n o t 48 c o m p a r a b l e t o t h e easy g l i d e r e g i o n o b s e r v e d i n s i n g l e b u l k c r y s t a l s . .Makin , - 52 -i n c o n d u c t i n g i n t e r r u p t e d t e n s i l e t e s t s on c o p p e r s i n g l e c r y s t a l s a t low • t e m p e r a t u r e s , r e p o r t e d t h a t s m a l l y i e l d p o i n t s were o b s e r v e d o n l y d u r i n g S t a g e I I and S tage I I I o f t h e s t r e s s - s t r a i n c u r v e . He a t t r i b u t e s t h i s e f f e c t t o t h e f o r m a t i o n o f L o m e r - C o t t r e l l s e s s i l e s d u r i n g u n l o a d i n g . T h e r e f o r e , i f t h e d e f o r m a t i o n o f w h i s k e r s i s a n a l o g o u s t o t h a t o f b u l k s i n g l e c r y s t a l s , t h e p l a s t i c f l o w o f w h i s k e r s s h o u l d c o r r e s p o n d t o S tage I I . The v e r y low s t r a i n h a r d e n i n g i n t h e p l a s t i c f l o w r e g i o n i s e x p l a i n e d by t h e f a c t t h a t t h e r e g i o n o f d e f o r m a t i o n grows a t t h e expense o f t h e undeformed m a t e r i a l . W h e t h e r such a d e d u c t i o n i s r e a s o n a b l e i s d i s c u s s e d i n a l a t e r s e c t i o n . The r a t e o f e x t e n s i o n once f l o w i s i n i t i a t e d , o f c o u r s e , depends on how much t h e f l o w s t r e s s i s e x c e e d e d . S i n c e t h e l o a d i s s l o w l y i n c r e a s e d , b y i n c r e m e n t s o f 5 mg, t h e c o n t r o l l i n g mechanism f o r f l o w . t o t a k e p l a c e i s e x t r e m e l y s e n s i t i v e t o t h e a p p l i e d s t r e s s . When f l o w i s i n i t i a t e d , o c c a s i o n a l l y i t h e s i t a t e s a f t e r f l o w i n g some d i s t a n c e and t h e n c a r r i e s on t i l l t h e m i c r o -m e t e r s t o p i s r e a c h e d . . F i g u r e 25 i s t h e l o a d - e x t e n s i o n . p l o t f o r sample B9. . T h i s sample was a l t e r n a t e l y t e s t e d be tween room t e m p e r a t u r e and -69° i 3°C« T h i s g r a p h e x h i b i t s two i n t e r e s t i n g phenomena. F i r s t l y t h e f l o w s t r e s s a t room t e m p e r a t u r e f o l l o w -i n g l o a d i n g a t -69°C i s l o w e r t h a n t h e p r e v i o u s f l o w s t r e s s a t room t e m p e r a t u r e , i . e . f l o w s t r e s s a t c i s l o w e r t h a n t h a t f o r a . S e c o n d l y t h e f l o w s t r e s s o f t h e t h i r d r e l o a d i n g a t t h e same ( room) t e m p e r a t u r e ( e ) i s l o w e r t h a n t h a t o f t h e second ( d ) . T h i s sample g e n e r a t e d o n l y one L u d e r s b a n d . I n o r d e r t o d e t e r m i n e t h e n a t u r e o f t h e s t e p e f f e c t and t h e f l u c t u -a t i o n o f t h e f l o w s t r e s s , . w h i s k e r s were t e s t e d a t one g i v e n t e m p e r a t u r e w i t h o u t t h e r m a l c y c l i n g . The r e s u l t s o f t h e s e t e s t s a r e shown i n F i g u r e s 26, 27 and 28. 320 -280 tested at room temperature ^O^^Q^ tested at — 6 9 ° C . specimen length 1.86 mm cross sec t ional area 17.8 yfc1 E o o 240 2 0 0 160 120 80 4 0 0-o- 9— J L I I I L J L 1.0 2.0 3 0 Extension (%) 4.0 5 0 Figure 25 . L o a d - e x t e n s i o n plot of the p las t ic region of Sample B 9 t e s t e d al ternately at room temperature and - 6 9 ° C . 160 h » 120 E •o o Z 8 0 4 0 specimen length 2.13 mm cross sectional a r e a 19.4 1 I 1 I I I I I I I I I I I L 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 E x t e n s i o n (%) F i g u r e 2 6 . L o a d — extens ion plot of the p l a s t i c region of Sample BI8 t e s t e d at - I 4 3 ° C . VJl •1=-- 5 6 -Figure 2 8 . L o a d - e x t e n s i o n plot of the plastic region of Sample B2I tes ted at room temperature. - 57 360 3 2 0 2 8 0 2 4 0 E 2 0 0 specimen length 142 mm o o 160 120 c ross s e c t i o n a l a r e a 48.6 9-d 94 80 4 0 V-J 1 I L i.o 2.0 3.0 E x t e n s i o n (%) 4.0 F i g u r e 29. L o a d - e x t e n s i o n plot of the p l a s t i c reg ion of Sample BI7 t e s t e d at - I 5 3 * C . - 58 -The r e s p e c t i v e t e s t i n g t e m p e r a t u r e s were -1^3°C,-8°C and room t e m p e r a t u r e * S i n c e t h e s p e c i m e n was e n c l o s e d i n t h e b a t h f o r a l l t h e t e s t s e x c e p t f o r t h o s e a t room t e m p e r a t u r e , t h e o b s e r v a t i o n o f L u d e r s band n u c l e a t i o n and p r o p a g a t i o n was n o t p o s s i b l e . Sample Bl8 n u c l e a t e d f i v e L u d e r s band r e g i o n s ; -sample B22, t w o ; .sample B21, t h r e e . The manner I n w h i c h f l o w p r o p a g a t e d i s i n t e r e s t i n g . Prom t h e g r a p h s , i t i s seen t h a t p o i n t s l y i n g on t h e n e g a t i v e s l o p e i n d i c a t e a " c r e e p " t e s t . The o b s e r v e d " c r e e p " , h o w e v e r , i s n o t c r e e p i n t h e c o n v e n -t i o n a l s e n s e . The " c r e e p " h e r e d e s c r i b e d i s n o t g r a d u a l b u t s p o r a d i c , i . e . e x t e n s i o n t a k e s p l a c e i n s p u r t s . T h i s " c r e e p " phenomenon w i l l h e n c e f o r t h be c a l l e d h e s i t a n t f l o w . S i n c e f l o w a t room t e m p e r a t u r e i s v e r y s e n s i t i v e t o . l o a d i n g , t h e l o a d . w a s i n c r e a s e d t o j u s t be low t h e e s t i m a t e d f l o w s t r e s s and h e l d t h e r e f o r s e v e r a l m i n u t e s . I f no f l o w was o b s e r v e d i n f i v e m i n u t e s t h e l o a d was i n c r e a s e d . A t a s p e c i f i c l o a d , h e s i t a n t f l o w w i l l t a k e p l a c e a f t e r a few m i n u t e s . A t low t e m p e r a t u r e s i f f l o w d i d n o t t a k e p l a c e w i t h i n t h e f i r s t 20 s e c o n d s , f l o w d i d n o t t a k e p l a c e even i f h e l d f o r a l o n g t i m e . T h i s i n d i c a t e s t h a t a t low t e m p e r a t u r e s t h e t h e r m a l a c t i v a t i o n f o r f l o w i s n e g l i -g i b l e . T h i s o b s e r v a t i o n i s s i g n i f i c a n t s i n c e sc rews g l i d e much e a s i e r t h a n edges i n t h e room t e m p e r a t u r e r a n g e w h i l e t h e r e v e r s e case i s t r u e a t low t e m p e r a t u r e s . Hence L u d e r s bands may be t h e r m a l l y a c t i v a t e d a t room t e m p e r a -t u r e due t o c r o s s s l i p , whereas t h i s i s u n l i k e l y a t low t e m p e r a t u r e s . However t h e s p o r a d i c n a t u r e o f g l i d e has y e t t o be e x p l a i n e d . ' Sample B17, w h i c h was t e s t e d a t -153°C, n u c l e a t e d . t h r e e L u d e r s band r e g i o n s . The l a r g e s t r e g i o n was a d j a c e n t t o one o f t h e g r i p s , t h e o t h e r t w o r e g i o n s were e q u a l l y spaced i n t h e r e m a i n i n g undeformed p a r t o f t h e w h i s k e r . The l o a d - e x t e n s i o n p l o t f o r t h i s sample i s shown i n F i g u r e 29. A t t h e com-p l e t i o n o f t h e t e s t , t h e sample was c a r e f u l l y removed f r o m t h e g r i p s and - 59 -m i c r o s c o p i c a l l y i n s p e c t e d . . F i g u r e 30 shows t h e L u d e r s band i n t h e l a r g e d e f o r m e d . r e g i o n . No c o n j u g a t e s l i p was v i s i b l e . On the ' e x t r e m e l e f t o f t h e m i c r o p h o t o g r a p h t h e undeformed w h i s k e r can be s e e n . The f i n e s t r u c t u r e o f L u d e r s band i s . n o t l i k e t h e o r d i n a r y s l i p b a n d . L u d e r s band c o n s i s t s o f s l i p p e d r e g i o n s i n t e r s p a c e d w i t h u n s l i p p e d r e g i o n s . Thus u n d e r low m a g n i f i -c a t i o n t h e s l i p p e d r e g i o n s a p p e a r as b a n d s . T h i s s t r u c t u r e o f L u d e r s bani^. i s r e v e a l e d i n F i g u r e 30, where s m a l l p o r t i o n s o f t h e banded r e g i o n do n o t d i s p l a y s l i p . l i n e s . Where s l i p l i n e s a r e p l a i n l y e v i d e n t , a n o t i c e a b l e r o t a t i o n o f l a t t i c e i s a p p a r e n t . F i g u r e 31 shows a n o t h e r de fo rmed r e g i o n o f t h e . w h i s k e r . .Here c o n j u g a t e s l i p i s v i v i d l y m a n i f e s t e d . From t h e m i c r o -p h o t o g r a p h i t i s a p p a r e n t t h a t t h e l i n e s w i t h o u t o f f s e t a r e t h e c o n j u g a t e s l i p m a r k i n g s . The s p a r s e n e s s o f c o n j u g a t e s l i p m a r k i n g s i n d i c a t e s t h a t t h e d i s -l o c a t i o n s o u r c e s on c o n j u g a t e s l i p p l a n e s a r e s c a r c e . Laue p i c t u r e s o f sample B17 .were a l s o t a k e n . The u n d e f o r m e d . p a r t o f t h e spec imen when i r r a d i a t e d showed p r e c i s e c l e a r s p o t s as i l l u s t r a t e d i n F i g u r e 32. The same p a t t e r n w h i c h was t a k e n on t h e de fo rmed p a r t showed s t r e a k y s p o t s as i l l u s t r a t e d i n F i g u r e 33. T h i s i s s u p p o r t i n g e v i d e n c e t h a t l a t t i c e r o t a t i o n t a k e s p l a c e when w h i s k e r s a r e de fo rmed a t low t e m p e r a t u r e s . D e t a i l e d m i c r o g r a p h i c s t u d i e s o f t h e d e f o r m e d . w h i s k e r s were n o t p o s s i b l e s i n c e t h e w h i s k e r s c o u l d n o t be examined u n d e r h i g h m a g n i f i c a t i o n i n s i t u . However two a s p e c t s o f d e f o r m a t i o n were o b s e r v e d : .a ) d e f o r m a t i o n m a y . t a k e p l a c e i n t h e manner d i s c u s s e d i n r e l a t i o n t o F i g u r e 30, b ) d e f o r m a t i o n may t a k e p l a c e w i t h o u t s m a l l i n t e r s p a c i n g s o f good . m a t e r i a l . Figure 31. Formation of conjugate s l i p at -153°C. Sample BIT. - 6 i Figure 35« Laue transmission picture of deformed portion of Sample B17. -62-I n t h i s i n v e s t i g a t i o n t h e f o r m e r t y p e was more common. F i g u r e 3^ i l l u s t r a t e s a sample w h i c h d e v e l o p e d L u d e r s bands when b e i n g removed f r o m t h e s u b s t r a t e . The c e n t r e o f t h e m i c r o p h o t o g r a p h shows t h e p o i n t where L u d e r s bands s t o p p e d p r o p a g a t i n g . Here t h e good and t h e deformed a r e a s a r e d i s t i n c t l y o b s e r v a b l e . The o b s t r u c t i o n o f band f o r m a t i o n seems t o be due t o c r o s s - s l i p a t t h e band b o u n d a r y w i t h t h e f o r m a t i o n o f s e s s i l e d i s -l o c a t i o n s , as s u g g e s t e d by B r e n n e r 1 2 . The d a r k bands a r e a r e a s where a l a r g e amount o f s l i p and r o t a t i o n had t a k e n p l a c e . F i g u r e 54. F o r m a t i o n o f L u d e r s bands a t room t e m p e r a t u r e i l l u s t r a t i n g c r o s s s l i p . - 6-3 -The mode o f f r a c t u r e o b s e r v e d .were o f two t y p e s : a ) f r a c t u r e upon y i e l d i n g w i t h l i t t l e p l a s t i c d e f o r m a t i o n , b ) f r a c t u r e a f t e r y i e l d i n g . The f i r s t t y p e o f f r a c t u r e was n o t common and was d e s i g n a t e d " c u r l e d " i n T a b l e I I I . The samples w h i c h f r a c t u r e d i n t h i s manner had one p r o p e r t y i n common. Over h a l f t h e spec imen l e n g t h was s t i l l s t r a i g h t . The b e n d i n g b a c k on i t s e l f a b o u t t h e g r i p t o o k p l a c e r i g h t a t o r v e r y c l o s e t o i t . T h i s b e n d -i n g o r c u r l i n g was n o t smooth b u t a n g u l a r . The d e f o r m a t i o n o f t h e w h i s k e r i n t h i s manner i s due t o t h e r e l e a s e o f t h e e l a s t i c e n e r g y when t h e w h i s k e r b r e a k s . The f l u c t u a t i n g s t r e s s w h i c h i s s e t up a l o n g t h e w h i s k e r l e n g t h has t h e l a r g e s t a m p l i t u d e a t t h e f i x e d e n d . The maximum a m p l i t u d e i s as l a r g e as t h e s t r e s s r e q u i r e d t o i n i t i a l l y f r a c t u r e t h e w h i s k e r . Hence t h i s " s h o c k " wave i s l a r g e enough t o a c t i v a t e o t h e r s o u r c e s n e a r t h e f i x e d e n d , c a u s i n g o b s e r v e d .bend ing o f w h i s k e r s . .The e f f e c t o f r e t a r d e d r e l e a s e o f e l a s t i c e n e r g y when t h e w h i s k e r y i e l d s and L u d e r s band p r o p a g a t e s i s d i f f i c u l t t o a s s e s s . H o w e v e r , d e p e n d i n g on t h e r a t e o f L u d e r s band p r o p a g a t i o n , i t i s c o n c e i v a b l e t h a t i t may n u c l e a t e s o u r c e s f r o m w h i c h o t h e r L u d e r s band r e g i o n s may g r o w . T h i s w i l l e x p l a i n t h e m u l t i - n u c l e a t i o n o f L u d e r s b a n d . r e g i o n i n t h e p r e s e n t i n v e s t i g a t i o n . The s e c o n d . t y p e o f f r a c t u r e t o o k p l a c e i n t h e de fo rmed r e g i o n c l o s e t o t h e b o r d e r o f t h e de fo rmed .and good m a t e r i a l . T h i s t y p e o f f r a c t u r e i s s i m i l a r t o t h e d u c t i l e f r a c t u r e c h a r a c t e r i s t i c o f f a c e c e n t r e d c u b i c m e t a l s . - 6h -I V . D i s c u s s i o n A . Growth K i n k s I n an e a r l i e r s e c t i o n g r o w t h mechanisms w e r e d i s c u s s e d . H o w e v e r , d o u b t .was c a s t on t h e i d e a t h a t a c e n t r a l sc rew d i s l o c a t i o n i s p r i m a r i l y r e s p o n s i b l e f o r w h i s k e r g r o w t h by h a l i d e r e d u c t i o n . T h i s d o u b t a r o s e f r o m t h e f a c t t h a t w h i s k e r s p roduced by h a l i d e r e d u c t i o n d i d n o t e x h i b i t l a t t i c e t w i s t 4 9 w h i c h i s a s s o c i a t e d w i t h a c e n t r a l sc rew d i s l o c a t i o n . However , Webb has s u g g e s t e d t h a t t h e absence o f d e t e c t a b l e t w i s t may be due t o two p o s s i b i l i t i e s : a ) Two sc rew d i s l o c a t i o n s o f e q u a l and o p p o s i t e s i g n , w h i c h has been shown t o e x i s t i n sod ium c h l o r i d e 5 0 , may e x i s t i n m e t a l w h i s k e r s . These t w o c o u l d g l i d e t o g e t h e r and a n n i h i l a t e t h e m s e l v e s . b ) The screw- d i s l o c a t i o n i n t h e w h i s k e r may c l i m b o u t o f t h e w h i s k e r by a b s o r b i n g t r a p p e d v a c a n c i e s d u r i n g o r a f t e r t h e g r o w t h p r o c e s s . H i r t h and P r a n k 5 1 have c o n s i d e r e d t h e p o s s i b i l i t y o f d i s l o c a t i o n s l e a v i n g t h e w h i s k e r by t h e r m a l l y a c t i v a t e d . s l i p . They c o n c l u d e d t h a t t h i s was p o s s i b l e and s u g g e s t e d . t h a t t h e t h e r m a l l y a c t i v a t e d s l i p mechanism may e x p l a i n g r o w t h k i n k s and t e r m i n a t i o n o f w h i s k e r g r o w t h . The o b s e r v a t i o n s o f g r o w t h k i n k s w i t h ' d e f i n i t e k i n k a n g l e s i n d i c a t e t h a t a d i s l o c a t i o n mechanism i s h i g h l y l i k e l y . The o n l y , o t h e r p o s s i b i l i t y i s s u r f a c e e n e r g y . A l t h o u g h s u r f a c e e n e r g y c e r t a i n l y i s an i m p o r t a n t f a c t o r g o v e r n i n g w h i s k e r m o r p h o l o g y , i t i s u n l i k e l y t h a t s u r f a c e e n e r g y a l o n e can k i n k w h i s k e r s i n such a r e g u l a r m a n n e r . T h e r e f o r e i n t h e f o l l o w i n g d i s c u s s i o n o f o b s e r v e d g r o w t h k i n k s o n l y d i s l o c a t i o n mechanism w i l l be c o n s i d e r e d . F o r m a l 5 2 mode ls o f g r o w t h k i n k s have been s u g g e s t e d . b y A m e l i n c k x and N a b a r r o .and J a c k s o n 6 . The f o r m e r assumes t h a t t h e g r o w t h d i r e c t i o n i s n o r m a l t o t h e f a c e t - 6 5 -i n w h i c h t h e d i s l o c a t i o n emerges* T h i s does n o t n e c e s s a r i l y mean t h a t t h e g r o w t h d i r e c t i o n i s a l w a y s c o i n c i d e n t w i t h t h e d i s l o c a t i o n l i n e . H i s a rgument i s t h a t t h e d i s l o c a t i o n w i l l d e c r e a s e i t s e n e r g y by a t t a i n i n g a c o n f i g u r a t i o n w h i c h w i l l possess minimum l e n g t h . On t h e o t h e r hand N a b a r r o and J a c k s o n assume t h a t t h e d i r e c t i o n o f g r o w t h i s p a r a l l e l t o t h e B u r g e r s v e c t o r . B o t h o f t h e s e t h e o r i e s assume g r o w t h f r o m t h e t i p . F i g u r e s 15 and -l6 a r e t h e t y p e o f k i n k p o s t u l a t e d by N a b a r r o and J a c k s o n . A c c o r d i n g t o t h e i r t h e o r y a [ lOO] d i s l o c a t i o n i s i n n e u t r a l e q u i l i -b r i u m f o r t h e d i s s o c i a t i o n r e a c t i o n a [ l O O ] = l/2a [ l!0] + l/2a[ll0] Hence o n l y a o r 90° k i n k i s p o s s i b l e . A l s o , when j l l O ] w h i s k e r k i n k s ^5° t o [l00] , t h e d i a m e t e r mus t i n c r e a s e by \(~2~. F i g u r e 15 shows a n o t i c e a b l e change i n d i a m e t e r . As p r e d i c t e d by N a b a r r o and J a c k s o n , F i g u r e lk e x h i b i t s a ^5° t r a n s i t i o n segment w h i c h i s a b o u t 25$ w i d e r t h a n t h e two s e g m e n t s . These o b s e r v a t i o n s seem t o i n d i c a t e t h a t a t l e a s t i n some cases t h e N a b a r r o and J a c k s o n t h e o r y i s p o s s i b l e . H o w e v e r , s i n c e t h e o r i e n t a t i o n s o f t h e s e w h i s k e r s were n o t o b t a i n a b l e , no d e f i n i t e c o n c l u s i o n can be r e a c h e d . On t h e o t h e r hand t h e w h i s k e r d i s p l a y e d i n F i g u r e 17 seems t o i n d i -c a t e an A m e l i n c k x t y p e o f k i n k . S i n c e t h e w h i s k e r i s n o t o r i e n t e d p a r a l l e l t o • e i t h e r a ^ l i o ) o r a <^ 100), t h e N a b a r r o - J a c k s o n mode l i s n o t a p p l i c a b l e . The A m e l i n c k x mode l p r e d i c t s t h a t t h e h e l i c a l p o r t i o n s h o u l d be a s i n g l e c r y s t a l . I n t h i s p a r t i c u l a r w h i s k e r t h i s Was n o t t r u e . The h e l i c a l p o r t i o n c o n t a i n e d a t l e a s t two o r i e n t a t i o n s . I n t h e m u l t i - k i n k e d w h i s k e r shown i n F i g u r e l 6 , b , c and d . w e r e segments o f a s i n g l e c r y s t a l . The o c c u r r e n c e o f 60° k i n k s ( e q u i v a l e n t t o 120°) - 6 6 -5 3 were o b s e r v e d b y C o u r t n e y i n s i l v e r w h i s k e r s g r o w n by c h e m i c a l r e d u c t i o n o f A g ( l ) w i t h P e ( l l ) f r o m aqueous p e r c h l o r a t e s o l u t i o n . A m e l i n c k x and D a s h 5 4 s u g g e s t e d t h a t t h e m u l t i p l e 60° k i n k s r e p o r t e d by C o u r t n e y i n d i c a t e t h a t t h e segments o f t h e w h i s k e r l i e i n a - [ i l l } p l a n e . T h e i r r e a s o n f o r t h i s b e l i e f i s t h e f o l l o w i n g . I f t h e B u r g e r s v e c t o r o f t h e d i s l o c a t i o n r e s p o n s i b l e f o r g r o w t h i s a [ l l O ] and l i e s o n t h e ( i l l ) p l a n e , t h e d i s s o c i a t i o n o f t h i s d i s l o c a t i o n i n t o S h o c k l e y p a r t i a l s w o u l d p r o h i b i t c r o s s s l i p t o a n o t h e r c l o s e packed p l a n e . T h i s r e s t r i c t i o n on t h e d i s l o c a t i o n t o r e m a i n on t h e ( i l l ) p l a n e w i l l e x p l a i n t h e p l a n a r p a t t e r n . C o u r t n e y , h o w e v e r , . w a s n o t a b l e t o d e t e r m i n e t h e o r i e n t a -t i o n s o f t h e s e g m e n t s . The segments b, c , d o f t h e m u l t i - k i n k e d w h i s k e r o b s e r v e d i n F i g u r e l 6 do p o s s e s s a < ( l l O ) t y p e o r i e n t a t i o n . T h i s i n d i c a t e s t h a t t h e B u r g e r s v e c t o r o f t h e d i s l o c a t i o n r e s p o n s i b l e f o r g r o w t h i s a ^110^. Hence t h e A m e l i n c k x and Dash mode l ^ r a t i o n a l i z e s t h e o b s e r v a t i o n s e x c e e d i n g l y w e l l . H o w e v e r , - the above mode l does n o t e x p l a i n t h e o r i e n t a t i o n d i f f e r e n c e o f 73° a b o u t a 0-10} b e t w e e n a and b , . d and e . S i n c e 73° i s w i t h i n e x p e r i m e n t a l e r r o r v e r y c l o s e t o 7 0 ° 3 2 ' , t h e a - b and d - e g r o w t h k i n k s can be shown t o be f i r s t - o r d e r c u b i c t w i n s . The o b s e r v e d t w i n c a n n o t be s a t i s f a c t o r i l y r a t i o n a l i z e d by a d i s l o c a t i o n mechanism w h i c h i s c o n s i s t e n t w i t h t h e p r e s e n t t h e o r y on g r o w t h . o f w h i s k e r s . I f t h e B u r g e r s v e c t o r o f t h e c e n t r a l d i s l o c a t i o n i s assumed t o be i n t h e [lio] and t h e d i s -l o c a t i o n l i n e l i e s on t h e (111), i t i s p o s s i b l e t h a t t h e d i s l o c a t i o n r e a c t i o n l / 2 a [ l l 0 ] l / 3 a [ l l l ] + l / 6 a [ l l 2 ] t a k e s p l a c e n e a r t h e g r o w i n g t i p . I f t h e g l i s s i l e S h o c k l e y p a r t i a l sweeps t h e (111), i t can o n l y do so o v e r one p l a n e because t h e s e s s i l e p a r t i a l l i e s on t h a t same p l a n e . Hence o n l y a s t a c k i n g f a u l t i s p o s s i b l e . F o r a c o h e r e n t t w i n - 67 -t o f o r m , s u c c e s s i v e p l a n e s m u s t . b e s w e p t b y a s i m i l a r p r o c e s s . • S i n c e t h e c l i m b o f t h e S h o c k l e y and t h e g l i d e o f t h e P r a n k p a r t i a l i n t h e [ i l l ] i s h i g h l y i m p r o b a b l e , t h e hope o f e x p l a i n i n g t h e g r o w t h t w i n b y t h i s mechanism .seems v e r y f a i n t . A p o s s i b l e cause f o r t h e t w i n f o r m a t i o n i s i n t u i t i v e r a t h e r t h a n r i g o r o u s . I t i s ^ c o n c e i v a b l e t h a t once t h e s t a c k i n g f a u l t has been i n i t i -a t e d a t t h e g r o w i n g t i p , t h e v a p o u r d e p o s i t i o n p r o c e s s may c o n t i n u e t h e m i s -s t a c k i n g and p r o d u c e a t w i n r a t h e r t h a n a s t a c k i n g f a u l t . H o w e v e r , . s u c h a mechanism ; W i l l r e q u i r e a l a r g e amount o f a t o m i c r e a r r a n g e m e n t and f r o m t h i s p o i n t o f v i e w i t seems p r o h i b i t i v e . The o r i e n t a t i o n o f t h e w h i s k e r shown i n F i g u r e 20 i s d e f i n i t e l y , n o t a <110). T h i s s u g g e s t s t h a t w h i s k e r s do n o t a l w a y s have t o grow p a r a l l e l t o t h e B u r g e r s v e c t o r o r t o one o f t h e t h r e e common o r i e n t a t i o n s . The o r i e n t a t i o n o f t h e b o t t o m p o r t i o n o f t h e w h i s k e r i s mos t l i k e l y [320j * The neck p o r t i o n where a 17^ -° k i n k i s o b s e r v e d i s p a r a l l e l t o [210~]. The r e a s o n f o r t h e s e d e d u c t i o n s i s t h a t [320] and [210] r e s p e c t i v e l y make l l 0 1 9 ' andl8 ° 2 6 » w i t h t h e [lio] and b o t h l i e on t h e (100). The o r i e n t a t i o n o f t h e n e a r r i g h t a n g l e k i n k i s [23d]. A c c o r d i n g t o H i r t h and F r a n k 5 1 t h e d i s l o c a t i o n r e s p o n s i b l e f o r t h i s g r o w t h i s s t a b l e . H o w e v e r , t h e y do n o t g i v e any d e t a i l e d mechanism f o r k i n k i n g * The k i n k s a r e p r o b a b l y due t o changes i n t h e s u r f a c e e n e r g y Which f o r c e t h e d i s l o c a t i o n l i n e t o change i t s d i r e c t i o n i n o r d e r t o m a i n t a i n a minimum l e n g t h 5 2 as s u g g e s t e d by A m e l i n c k x • . The f o r m a t i o n - o f r i d g e s may be a t t r i b u t e d t o t h e n o n - u n i f o r m s u p e r s a t u r a t i o n a t t h e c o r n e r s , s i n c e c o r n e r s p o s s e s s h i g h e r super"* 5 6 s a t u r a t i o n s t h a n t h e s i d e s . - 68 -B . E f f e c t o f Ox ide L a y e r T e n s i l e t e s t s c a r r i e d . o u t . i n d i l u t e s u l p h u r i c a c i d and d i l u t e s u l p h u r i c a c i d b u f f e r e d . w i t h ammonium s u l p h a t e d e f i n i t e l y showed t h a t t h e sudden y i e l d m a n i f e s t e d b y . w h i s k e r s i s n o t due t o t h e p r e s e n c e o f an o x i d e l a y e r . A l t h o u g h one s a m p l e , . k k , d i s p l a y e d an anomalous c r e e p , s u b s e q u e n t t e s t s u n d e r s i m i l a r c o n d i t i o n s d i d n o t m a n i f e s t t h i s c r e e p . Hence i t i s c o n c l u d e d t h a t t h e c r e e p o b s e r v e d i n sample Ah- i s due t o some s p u r i o u s c a u s e . S i n c e sample A2 showed no a p p r e c i a b l e change i n . t h e f l o w s t r e s s when t e s t e d • f i r s t i n d i l u t e s u l p h u r i c a c i d a n d - t h e n i n a i r , i t seems t h a t t h e t h i n o x i d e l a y e r has l i t t l e e f f e c t on t h e f l o w s t r e s s . The r e s o l v e d s h e a r s t r e s s e s f o r y i e l d a r e c o m p a r a b l e t o t h o s e t e s t e d i n a i r w i t h o u t t h e r e m o v a l o f t h e o x i d e l a y e r , as seen by c o m p a r i n g T a b l e s I I and I I I . Hence o x i d e l a y e r does n o t seem t o c o n t r i b u t e t o t h e s t r e n g t h o f w h i s k e r s . A t a b o u t t h e same t i m e t h i s c o n c l u s i o n was . r e a c h e d - b y t h e w r i t e r , 5 7 Webb.and S t e r n r e p o r t e d , t h a t t h e y had p e r f o r m e d bend t e s t s .on o x i d e - f r e e c o p p e r w h i s k e r s . T h e i r f i n d i n g s l e d them t o t h e same c o n c l u s i o n s as above.-s t a t e d . C . . T e n s i l e T e s t s 1. The Y i e l d Phenomenon The f a c t t h a t c o p p e r w h i s k e r s d i s p l a y a sudden y i e l d p o i n t w h i c h i s i r r e c o v e r a b l e i n d i c a t e s one o f t h e f o l l o w i n g s t r u c t u r e s : a ) w h i s k e r s a r e p e r f e c t , b ) w h i s k e r s c o n t a i n d i s l o c a t i o n s s i m i l a r i n d i m e n s i o n s t o t h o s e o f b u l k c r y s t a l s w h i c h a r e l o c k e d by i m p u r i t i e s , - 69 -o) w h i s k e r s c o n t a i n d i s l o c a t i o n s o f u n u s u a l d i m e n s i o n s and d i s t r i b u t i o n s . The 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 and t h e o b s e r v a t i o n s o f d i s l o c a t i o n s i n some w h i s k e r s by X - r a y t e c h n i q u e s and d e c o r a t i o n methods i n d i c a t e t h a t w h i s k e r s a r e n o t p e r f e c t . F u r t h e r m o r e , s i l v e r and c o p p e r w h i s k e r s were f o u n d t o d i s s o l v e 5 8 l e s s s l o w l y t h a n b u l k c r y s t a l s i n c o n c e n t r a t e d a c i d s . The w h i s k e r t i p . d i s -s o l v e d more r a p i d l y , t h a n t h e s i d e s . A l s o p r e f e r e n t i a l a t t a c k was n o t e d a t m e c h a n i c a l l y de fo rmed r e g i o n s . T h i s p i e c e o f e v i d e n c e s t r o n g l y i n d i c a t e s t h a t w h i s k e r s may c o n t a i n d i s l o c a t i o n s b u t t h e i r d i s t r i b u t i o n may be u n i q u e and t h e i r d e n s i t y i s l o w e r t h a n t h a t o f b u l k c r y s t a l s . I f w h i s k e r s c o n t a i n d i s l o c a t i o n s o f s i m i l a r d i m e n s i o n s t o t h o s e o f b u l k c r y s t a l s , w h i c h a r e l o c k e d by i m p u r i t i e s , t h e y i e l d p o i n t s h o u l d be r e p r o d u c e d upon a n n e a l i n g , b u t t h i s i s n o t o b s e r v e d . A l s o C o t t r e l l o r S u z u k i a t m o s p h e r e s w i l l b r e a k down b e f o r e t h e h i g h y i e l d p o i n t s as t h o s e possessed by w h i s k e r s a r e r e a c h e d . Hence t h e t h i r d . s u g g e s t i o n seems most l i k e l y . The two c o n t e m p o r a r y t h e o r i e s on t h 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 a r e t h e Seeger h y p o t h e s i s 5 9 and t h e " c r i t i c a l l e n g t h o f t h e F r a n k - R e a d . s o u r c e " h y p o t h e s i s . Seeger assumes^a random d i s t r i b u t i o n . o f d i s l o c a t i o n s w h i c h r e t a r d t h e m o t i o n o f each o t h e r t h r o u g h t h e i r m u t u a l i n t e r a c t i o n . He d e f i n e s t h e f l o w s t r e s s as t h a t a p p l i e d • s t r e s s w h i c h i s j u s t s u f f i c i e n t t o overcome t h e r e t a r d i n g a c t i o n o f t h e s u r r o u n d i n g d i s l o c a t i o n s and p e r m i t s t h e movement o f d i s l o c a t i o n s over , l a r g e d i s t a n c e s on t h e p r i m a r y p l a n e . Such a t h e o r y r e q u i r e s t h a t t h e w h i s k e r s possess a h i g h e r d i s l o c a t i o n d e n s i t y t h a n t h a t f o u n d . i n b u l k c r y s t a l s t o a c c o u n t f o r t h e h i g h e r f l o w , s t r e s s o f w h i s k e r s . T h i s i s n o t c o n -s i s t e n t w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n t h a t d i s l o c a t i o n d e n s i t y i n w h i s k e r s i s p r o b a b l y s m a l l e r t h a n i n b u l k c r y s t a l s . On t h e o t h e r hand t h e F rank -Read s o u r c e h y p o t h e s i s s u g g e s t s t h a t t h e l o n g e s t s o u r c e w h i c h i s f i r s t t o o p e r a t e d e t e r m i n e s t h e f l o w s t r e s s . The s h e a r s t r e s s r e q u i r e d . t o o p e r a t e a s o u r c e can be computed f r o m t h e e x p r e s s i o n r - -2£ / " T where G i s t h e s h e a r m o d u l u s j b , t h e B u r g e r s v e c t o r , and 1, t h e l e n g t h o f t h e p i n n e d d i s l o c a t i o n segmen t . Hence i n s e r t i n g <*~y f o r "Cy, t h e l e n g t h o f t h e s o u r c e r e q u i r e d f o r s l i p t o o c c u r i n w h i s k e r s i s computed t o be ~10 6 c m . 2 Whethe r a d i s l o c a t i o n s o u r c e o f t h i s s i z e can o p e r a t e i s q u e s t i o n a b l e . B r e n n e r s u g g e s t s t h a t some o t h e r unknown mechanism may be r e s p o n s i b l e f o r s l i p a c t i v a -t i o n . Assuming t h a t d i s l o c a t i o n s o u r c e s o f ~10 cm can o p e r a t e , t h e p o s s i b l e o r i g i n o f such s o u r c e s w i l l be d i s c u s s e d i n t h i s s e c t i o n . N o n - a x i a l d i s l o c a t i o n s w h i c h a r e fo rmed d u r i n g t h e g r o w t h o f t h e w h i s k e r w i l l t e n d - t o m i g r a t e t o t h e s u r f a c e s . The image f o r c e w i l l be t h e d r i v i n g f o r c e f o r t h e p r o c e s s . The m i g r a t i o n o f a d i s l o c a t i o n w h i c h w i l l d e c r e a s e i t s t o t a l l e n g t h w i l l t a k e p l a c e w i t h o u t f o r m i n g new s u r f a c e s , s i n c e t h i s p r o c e s s i s most e n e r g e t i c a l l y f a v o u r a b l e . As t h e l e n g t h d i m i n i s h e s , a t some c r i t i c a l l e n g t h d e p e n d i n g on . the g e o m e t r y o f t h e s l i p . p l a n e , i t w i l l e i t h e r f o r m a new s u r f a c e and move o u t .of t h e w h i s k e r o r r e a c h an e q u i l i b r i u m c o n d i t i o n w i t h t h e s u r f a c e . B e f o r e t h e p o s s i b i l i t y -o f an e q u i l i b r i u m c o n d i t i o n can be c o n s i d e r e d S h a l e r ' s s u r f a c e mode l w i l l be b r i e f l y r e v i e w e d . H i s mode l i s r e p r o d u c e d i n F i g u r e 35. S h a l e r assumes t h a t atoms i n c r y s t a l l i n e s o l i d s r e p e l one a n o t h e r when t h e y a r e c r o w d e d . a n d t h e y a t t r a c t one a n o t h e r when p u l l e d a p a r t . F o r e x a m p l e , an atom i n s i d e a f a c e - c e n t r e d c u b i c c r y s t a l a t t h e o r i g i n P o f t h e r e c t a n g u l a r c o o r d i n a t e s i n t h e [ lOCf] d i r e c t i o n s o f t h e l a t t i c e must be i n m e c h a n i c a l e q u i l i b r i u m . The x y p l a n e w h i c h i s an (GOl) i s shown i n F i g u r e 35. - 71 -y - l y y+1 y - i y O 0 atoms i n p l a n e s a d j a c e n t and p a r a l l e l t o p l a n e x y c o o r d i n a t e s x , y a r e i n t h e ^ 1 0 0 } d i r e c t i o n atoms i n p l a n e o f f i g u r e The F i g u r e 35» M e c h a n i c a l e q u i l i b r i u m i n s i d e c r y s t a l ( a ) and a t (100) s u r f a c e ( b ) i n a f a c e - c e n t r e d c u b i c l a t t i c e * L e t t h e n e a r e s t (A) and t h e second n e a r e s t (B) n e i g h b o u r s o f a tom P r e s p e c t i v e l y r e p e l P w i t h a f o r c e a and a t t r a c t P w i t h a f o r c e b . Thus f o r m e c h a n i c a l I f t h e c r y s t a l i s c u t b e t w e e n t h e yz p l a n e and t h e n e x t (100) p l a n e , i . e . b e t w e e n y and y + 1 ( F i g u r e 3 5 b ) , t h e d i s t a n c e b e t w e e n t h e y and y - 1 p l a n e s r e m a i n s u n d i s t u r b e d , s i n c e t h e sum o f t h e f o r c e s i n t h e x d i r e c t i o n on P i s u n c h a n g e d . M o r e o v e r , t h e atoms i n t h e y p l a n e a r e c o n s t r a i n e d t o r e m a i n i n t h e s u r f a c e l a y e r by c o h e r e n c y r e q u i r e m e n t s . Hence t h e f o r c e on P i n t h e y d i r e c t i o n i s now e q u i l i b r i u m ( F i g u r e 35a) i n t h e x d i r e c t i o n b + ka, cos - j j - = 0 , o r b = -2 /2 ' a b + 3a cos S i n c e a i s / a f o r c e o f r e p u l s i o n , - t h e f t a ^ i p < ; : ! l ^ ^ i ' . e . a ( 1 0 0 ) f a c e , a r e i n t e n s i o n i n t h e [IOO] d i r e c t i o n . . A l s o a (100) s u r f a c e has a t e n s i o n i n t h e [HO]. The t y p e o f s u r f a c e , t e n s i o n d e s c r i b e d above i s c a l l e d " s u r f a c e s t r e s s " . I t must be b o r n e i n mind t h a t t h i s s u r f a c e s t r e s s e x i s t s o n l y i m m e d i a t e l y a f t e r a c r y s t a l i s c u t . T h i s c o n f i g u r a t i o n i s p r o b a b l y u n s t a b l e and changes i n a t o m i c a r r a n g e m e n t w i l l t a k e p l a c e t o r e d u c e i t s f r e e e n e r g y . Some o f t h e ways i n w h i c h t h i s s u r f a c e s t r e s s can be r e l i e v e d a r e e l a s t i c s t r e s s r e l i e f , m i g r a t i o n o f i n t e r s t i t i a l atoms o r l a t t i c e v a c a n c i e s t o t h e s u r f a c e , and t h e movement o f d i s l o c a t i o n s t o o r away f r o m t h e s u r f a c e . I f a p a r a l l e l p r o c e s s o f s u r f a c e s t r e s s r e l i e f i s assumed, i n t h e case o f w h i s k e r g r o w t h , t h e n an e q u i l i b r i u m s i t u a t i o n b e t w e e n t h e image f o r c e s a t t h e d i s l o c a t i o n and t h e s u r f a c e s t r e s s i s c o n c e i v a b l e . A l s o , i f the. s u r f a c e i s i n t e n s i o n , t h e ends o f t h e d i s l o c a t i o n t h a t t e r m i n a t e a t t h e s u r f a c e s " • K i l l be i n p u r e edge o r i e n t a t i o n s . T h i s i s c o n s i s t e n t w i t h t h e e a r l i e r i d e a t h a t d i s l o c a t i o n s w i l l g l i d e w i t h o u t f o r m i n g . s u r f a c e s t i l l a c r i t i c a l l e n g t h i s r e a c h e d . I t i s e v i d e n t f r o m S h a l e r ' s m o d e l t h a t s u r f a c e s t r e s s e s w i l l a f f e c t o n l y t h o s e atoms q u i t e c l o s e t o t h e s u r f a c e . Hence t h e e q u i l i b r i u m l e n g t h o f t h e d i s l o c a t i o n s i n t h e w h i s k e r s a r e n e c e s s a r i l y v e r y s h o r t . So f a r t h e p o s s i b i l i t y o f h a v i n g s h o r t l e n g t h s o f d i s l o c a t i o n s a r o u n d t h e s u r f a c e s o f t h e w h i s k e r has been i n v e s t i g a t e d . A s i d e f r o m d i s -l o c a t i o n s , a p i n n i n g a g e n t i s n e c e s s a r y t o f o r m Prank -Read s o u r c e s . To s a t i s f y t h i s r e q u i r e m e n t t h e m i g r a t i o n o f v a c a n c i e s , d u r i n g t h e c o o l i n g o f t h e g rown w h i s k e r s , t o t h e d i s l o c a t i o n s i s p r o p o s e d . I f t h e s u r f a c e s a r e i n t e n s i o n , w h i c h i s t h e u s u a l c a s e , v a c a n c i e s w i l l n o t be welcome t h e r e and hence t h e y - 73 -w i l l have t o condense on d i s l o c a t i o n s , o r i n t o c l u s t e r s t o f o r m c i r c u l a r F r a n k p a r t i a l s , Thus i n t h i s s e c t i o n on t h e y i e l d phenomenon t h e p o s s i b l e mechanism w h i c h w i l l e x p l a i n t h i s y i e l d i n g has been c o n s i d e r e d . The p o s s i b i l i t y o f w h i s k e r s p o s s e s s i n g F r a n k K R e a d . s o u r c e s o f t h e o r d e r o f 10 cm i s l i k e l y . 2. P l a s t i c F low I n t h i s s e c t i o n the . p o s s i b l e mechanisms f o r p l a s t i c f l o w o f w h i s k e r s w i l l be c o n s i d e r e d . The low t e m p e r a t u r e t e s t s c o n d u c t e d , i n t h e p r e s e n t i n v e s -t i g a t i o n i n c r e a s e d t h e d i s l o c a t i o n i n t e r a c t i o n c o n t r i b u t i o n t o t h e f l o w . s t r e s s , g i v i n g r i s e t o t h e s t e p e f f e c t and h e s i t a n t f l o w . . These two e f f e c t s and t h e y i e l d i n g i n t h e f l o w r e g i o n w i l l be r a t i o n a l i z e d by s u g g e s t i n g p o s s i b l e d i s -l o c a t i o n m e c h a n i s m s . To a c c o u n t f o r t h e " f i n e s l i p " a s s o c i a t e d w i t h L u d e r s band a d o u b l e 59 c r o s s s l i p mechanism seems i m p e r a t i v e . F o r c r o s s s l i p t o t a k e p l a c e , h o w e v e r , some o b s t a c l e t o r e t a r d p r i m a r y s l i p and hence p romote c r o s s s l i p i s r e q u i r e d . .The f i r s t o b v i o u s s u g g e s t i o n f o r such an o b s t a c l e i s t h e f o r e s t o f d i s l o c a t i o n s . The c o n t r i b u t i o n o f t h e r e t a r d i n g f o r c e o f t h e f o r e s t t o t h e f l o w s t r e s s i s w e l l k n o w n , e s p e c i a l l y a t low t e m p e r a t u r e s . However , i t s i n f l u e n c e on t h e c r o s s s l i p p i n g o f t h e g l i d i n g d i s l o c a t i o n s i n t h e p r i m a r y p l a n e i s u n c e r t a i n . Q u a l i -t a t i v e l y i t seems t h a t g l i d i n g d i s l o c a t i o n s w i l l c u t t h r o u g h f o r e s t s w i t h r e l a t i v e e a s e , e s p e c i a l l y i n w h i s k e r s where t h e f o r e s t d e n s i t y i s s m a l l . Hence i t seems t h a t f o r e s t s i n w h i s k e r s a r e i n s u f f i c i e n t t o p romote c r o s s s l i p . T h i s a p p a r e n t d i lemma may be overcome i f i t i s r e c a l l e d t h a t f o r common w h i s k e r o r i e n t a t i o n s t w o s l i p p l a n e s a r e e q u a l l y p r e f e r r e d . Hence i f a "•lk -d i s l o c a t i o n o f a sc rew o r i e n t a t i o n s h o u l d f i n d i t s e l f i n a g e o m e t r i c a l l y s u i t a b l e p o s i t i o n , i t w i l l c r o s s s l i p i f i t i s s l i g h t l y h e l d up f r o m s l i p p i n g f r e e l y on t h e p r i m a r y p l a n e b y t h e f o r e s t . A l s o t h e r e e x i s t t h r e e o t h e r p o s s i b l e o b s t a c l e s : a ) i m p u r i t i e s , b ) p a r a l l e l w a l l s o f d i s l o c a t i o n s , c ) f o r m a t i o n o f C o t t r e l l - L o m e r s e s s i l e s . F i r s t l y t h e e f f e c t o f i m p u r i t i e s w i l l t e n d t o p r o m o t e c r o s s s l i p . S i n c e s p h e r i -c a l s o l u t e atoms r e s i s t t h e m o t i o n o f edges g r e a t e r t h a n s c r e w s , . s l i p on t h e p r i m a r y p l a n e w h i c h g e n e r a l l y t a k e s p l a c e by means o f m ixed d i s l o c a t i o n s w i l l be r e t a r d e d - b y t h e i m p u r i t i e s . On t h e o t h e r h a n d , c r o s s s l i p w h i c h i s a p u r e sc rew p r o c e s s w i l l n o t be g r e a t l y a f f e c t e d . S e c o n d l y , due t o t h e l a t t i c e r o t a -t i o n o f t h e de fo rmed r e g i o n , p a r a l l e l w a l l s o f d i s l o c a t i o n s w i l l s e t up i n t e r n a l s t r e s s e s s u f f i c i e n t t o p romote c r o s s s l i p . T h i r d l y , i f L o m e r - C o t t r e l l s e s s i l e s f o r m , t h e n c r o s s s l i p . w i l l have t o t a k e p l a c e . The r e a s o n f o r t h i s i s t h a t , as 62 S t r o h has c a l c u l a t e d , a t room t e m p e r a t u r e ~ 1 5 0 p i l e d - u p d i s l o c a t i o n s u n d e r 1 s t r e s s a r e n e c e s s a r y t o b r e a k up t h i s s e s s i l e . A s i m p l e c a l c u l a t i o n 6 1 mm 2 w i l l show t h a t o n l y ~ 1 0 d i s l o c a t i o n s can be packed i n t o a s l i p p l a n e o f w h i s k e r d i m e n s i o n s . Hence b r e a k up o f L o m e r - C o t t r e l l s e s s i l e d i s l o c a t i o n i s h i g h l y i m p r o b a b l e . H o w e v e r , as p o i n t e d o u t i n t h e e a r l i e r s e c t i o n , d i s l o c a t i o n s on c o n j u g a t e s l i p p l a n e s a r e s c a r c e and hence f o r m a t i o n o f L o m e r - C o t t r e l l s e s s i l e s i s n o t f r e q u e n t . Because o f t h e above r e a s o n s c r o s s s l i p p i n g i s h i g h l y p o s s i b l e i n t h e d e f o r m a t i o n o f w h i s k e r s . A l t h o u g h d o u b l e c r o s s s l i p may s a t i s f a c t o r i l y e x p l a i n f i n e s l i p , i t does n o t e x p l a i n t h e p r e s e n c e o f t h e i n t e r s p a c i n g s o f good m a t e r i a l as shown i n F i g u r e 3 0 . . T h i s i s a p p a r e n t s i n c e t h e w i d t h s o f t h e i n t e r s p a c i n g s a r e somet imes w i d e r t h a n t h e d i a m e t e r o f t h e w h i s k e r and t h e r e f o r e c r o s s s l i p o v e r * ' 7 5 -t h i s d i s t a n c e seems i m p r o b a b l e . T o - d e t e r m i n e how Prank-Read s o u r c e s . p r e s u m a b l y ~10 cm c a n be a c t i v a t e d by t h e f l o w s t r e s s an e s t i m a t e o f t h e s h e a r s t r e s s d e v e l o p e d a t some d i s t a n c e ahead o f t h e de fo rmed r e g i o n w i l l be made. I t i s p roposed t h a t a l t h o u g h t h e s l i p p e d . r e g i o n o f t h e w h i s k e r undergoes l a t t i c e r o t a t i o n t o m a i n t a i n a l i g n m e n t o f t h e g r i p s , a b e n d i n g w i l l t a k e p l a c e n e a r t h e heads o f t h e s l i p p e d r e g i o n . T h i s b e n d i n g w i l l g i v e r i s e t o a b e n d i n g moment w h i c h w i l l be most c o n c e n t r a t e d a t t h e head o f t h e L u d e r s b a n d . The b e n d i n g 63 moment can be r e l a t e d - t o t h e s h e a r s t r e s s on t h e d i s l o c a t i o n ' M M F i g u r e 36. S c h e m a t i c d i a g r a m o f a beam u n d e r a b e n d i n g moment . I n F i g u r e 36, a d i s l o c a t i o n i s l o c a t e d a t a d i s t a n c e S Q f r o m t h e n e u t r a l p l a n e o f a c y l i n d r i c a l beam. The s h e a r s t r e s s on t h e d i s l o c a t i o n when t h e beam i s u n d e r a b e n d i n g moment M i s g i v e n b y - ?6 -Z, = _ 2 ^ s i n X 0 MD . „ where = -j- s i n c o s x o and I i s t h e moment o f i n e r t i a o f t h e c r o s s s e c t i o n . A r e a s o n a b l e e s t i m a t e o f M can be made i f t h e moment arm i s t a k e n t o be — l O ^ 4 cm and t h e f o r c e 300 mg. Assuming a s q u a r e c r o s s s e c t i o n w i t h s i d e —4 ~* h x 10 cm a n d . X 0 t o be ~35°.> a s h e a r s t r e s s o f ~10 can be d e v e l o p e d . mm 2 A l t h o u g h t h i s v a l u e i s somewhat l o w e r t h a n t h e a v e r a g e r e s o l v e d y i e l d s t r e s s , i t i s w i t h i n t h e o r d e r o f m a g n i t u d e . Hence t h e a c t i v a t i o n o f d i s l o c a t i o n s o u r c e s i n t h e u n s l i p p e d . p o r t i o n o f t h e w h i s k e r i s n o t beyond p o s s i b i l i t y . So f a r i n t h i s s e c t i o n on p l a s t i c f l o w t h e p o s s i b i l i t y o f d o u b l e c r o s s s l i p and a c t i v a t i o n o f d i s l o c a t i o n s o u r c e s i n t h e u n s l i p p e d . p o r t i o n o f t h e w h i s k e r has been d i s c u s s e d . The q u e s t i o n a r i s e s w h e t h e r t h e s t e p e f f e c t can be e x p l a i n e d by e i t h e r o f t h e s e p r o c e s s e s . The d o u b l e c r o s s s l i p p r o c e s s f o r m s a new d i s l o c a t i o n each t i m e i t c r o s s s l i p s t o a p a r a l l e l p l a n e . C o n s i d e r a t i o n o f t h e l i n e t e n s i o n and t h e _ a p p l i e d s t r e s s e q u i l i b r i u m i n d i c a t e s t h a t ' t h e - l e n g t h o f t h e s e d i s l o c a t i o n s o u r c e s w i l l p r o b a b l y be c o m p a r a b l e t o t h o s e f o u n d i n b u l k c r y s t a l s . T h e r e f o r e , s i n c e t h e a p p l i e d s t r e s s f o r t h e a c t i v a t i o n .of t h e n e w l y fo rmed s o u r c e s w i l l be q u i t e l o w , i t i s r e a s o n a b l e t o a t t r i b u t e t h e s t e p e f f e c t t o t h e " d o u b l e c r o s s s l i p p r o c e s s and t h e s t r e s s r e q u i r e d f o r a l a r g e amount o f f l o w t o t h e a c t i v a t i o n o f d i s l o c a t i o n s o u r c e s ' ( ^ 1 0 " 6 cm) i n t h e good m a t e r i a l , as p r e v i o u s l y d e s c r i b e d . The mechanism o f c r o s s s l i p depends on t h e m o b i l i t y o f screw d i s -l o c a t i o n s . The f a c t t h a t s c r e w s a r e l e s s m o b i l e t h a n edges a t l ow t e m p e r a t u r e s and v i c e v e r s a a t room t e m p e r a t u r e i s c o n s i s t e n t w i t h t h e o b s e r v a t i o n t h a t t h e s t e p e f f e c t i s more f r e q u e n t l y m a n i f e s t e d a t . low t e m p e r a t u r e s t h a n a t room t e m p e r a t u r e . T h i s can be r e a l i z e d by t h e f o l l o w i n g a r g u m e n t . A t l ow . t e m p e r a t u r e s when t h e a p p l i e d s t r e s s a c t i v a t e s a d i s l o c a t i o n s o u r c e f o r m e d - b y t h e d o u b l e c r o s s s l i p mechan ism, d i s l o c a t i o n s w i l l n o t c r o s s s l i p e x t e n s i v e l y due - to - the r e t a r d e d m o t i o n o f t h e s c r e w . On t h e o t h e r h a n d , a t room t e m p e r a t u r e sc rews a r e v e r y m o b i l e and hence e x t e n s i v e s l i p w i l l t a k e p l a c e . Thus t h e s t e p e f f e c t i s n o t o b s e r v e d . T h i s t e m p e r a t u r e dependence o f sc rew d i s l o c a t i o n s a l s o . s a t i s f a c t o r i l y e x p l a i n s h e s i t a n t f l o w . A t room t e m p e r a t u r e movement o f sc rews can be t h e r m a l l y a c t i v a t e d , . -whi le a t low t e m p e r a t u r e s a sc rew can g l i d e o n l y i f i t has t h e n e c e s -s a r y a p p l i e d s t r e s s . The s p o r a d i c n a t u r e o f h e s i t a n t f l o w can be a t t r i b u t e d . , t o t h e dynamic f o r m a t i o n o f d i s l o c a t i o n , w h i c h w i l l be d i s c u s s e d i n t h e f o l l o w i n g p a r a g r a p h . Once a s o u r c e has been t h e r m a l l y a c t i v a t e d i t w i l l g e n e r a t e d i s l o c a -t i o n s t i l l i t i s s t o p p e d e i t h e r by t h e b a c k s t r e s s o r by a p p r o a c h i n g tot? c l o s e t o t h e s u r f a c e . Once t h i s t a k e s p l a c e , c r o s s s l i p w i l l a g a i n have t o be t h e r -m a l l y a c t i v a t e d . The l a r g e amount o f f l o w w h i c h t a k e s p l a c e a t a r a t h e r h i g h f l o w s t r e s s has been a t t r i b u t e d t o t h e a c t i v a t i o n o f P rank -Read s o u r c e s i n t h e u n -s l i p p e d p o r t i o n o f t h e w h i s k e r . T h i s i s r e a s o n a b l e s i n c e a l a r g e f l o w s t r e s s i s n e c e s s a r y t o d e v e l o p t h e l a r g e s h e a r s t r e s s t o a c t i v a t e s o u r c e o f ~10 cm. S i n c e t h e s e s o u r c e s v a r y i n l e n g t h w i t h i n t h i s g i v e n o r d e r o f m a g n i t u d e , t h e f l u c t u a t i o n o f f l o w s t r e s s i s o b s e r v e d . The e x p l a n a t i o n o f y i e l d p o i n t s o b s e r v e d i n t h e f l o w r e g i o n i s most d i f f i c u l t . M a k i n ' s s u g g e s t i o n o f t h e f o r m a t i o n o f L o m e r - C o t t r e l l s e s s i l e s d u r i n g u n l o a d i n g and s u b s e q u e n t b r e a k up o f t h e s e upon l o a d i n g , r e s u l t i n g i n a y i e l d p o i n t , i s n o t c o m p a t i b l e . w i t h t h e e a r l i e r d i s c u s s i o n on t h e f o r m a t i o n o f L o m e r - C o t t r e l l s e s s i l e s . The f o r m a t i o n o f s e s s i l e s , w h i c h i s n o t abundan t u n l e s s e x t e n s i v e c o n j u g a t e s l i p t a k e s p l a c e , w i l l o n l y p romote c r o s s s l i p s i n c e - 18 -b r e a k up i s n o t p o s s i b l e . The o n l y c o n v e n t i o n a l mechanism w h i c h w i l l r a t i o n a l i z e 6 4 t h e y i e l d p o i n t i s t h e d y n a m i c a l f o r m a t i o n o f s l i p - b a n d . I n t h i s t h e o r y i t i s s u g g e s t e d t h a t once a Prank -Read s o u r c e i s a c t i v a t e d i t w i l l g e n e r a t e d i s -l o c a t i o n s u n t i l t h e b a c k s t r e s s o f p i l e d - u p d i s l o c a t i o n s s t o p s i t s o p e r a t i o n . • A l s o , t h e minimum s t r e s s r e q u i r e d t o m a i n t a i n o p e r a t i o n o f t h e s o u r c e i s a b o u t 0 .7 o f t h e s t r e s s r e q u i r e d t o a c t i v a t e i t . I n b u l k c r y s t a l s t h e number o f d i s -l o c a t i o n s g e n e r a t e d b e f o r e b a c k s t r e s s e s s t o p i t s o p e r a t i o n i s a b o u t 500. I f t h i s mechanism o f b u r s t o p e r a t i o n o f F rank -Read s o u r c e i s i n v o k e d f o r w h i s k e r d e f o r m a t i o n , due t o t h e f a c t t h a t s t r e s s e s l o w e r t h a n t h e a c t i v a t i o n s t r e s s w i l l keep t h e s o u r c e o p e r a t i n g , a y i e l d p o i n t as o b s e r v e d i n t h i s p r e s e n t i n -v e s t i g a t i o n w i l l be m a n i f e s t e d . 3. L u d e r s Band P r o p a g a t i o n From t h e mechanisms d i s c u s s e d i n t h e p r e c e d i n g s e c t i o n on p l a s t i c d e f o r m a t i o n o f w h i s k e r s t h e L u d e r s band p r o p a g a t i o n may be s u m m a r i z e d . The a c t i v a t i o n o f a F rank -Read s o u r c e i n t h e undeformed w h i s k e r r e s u l t s i n d o u b l e c r o s s s l i p , w h i c h g i v e s r i s e t o f i n e s l i p . I f d o u b l e c r o s s s l i p c a n n o t t a k e p l a c e , t h e n a t some some s t r e s s F rank -Read s o u r c e s a t some d i s t a n c e ahead o f t h e s l i p p e d r e g i o n w i l l be a c t i v a t e d and f i n e s l i p w i l l a g a i n t a k e p l a c e . T h i s p r o c e s s w i l l c o n t i n u e t i l l t h e w h o l e w h i s k e r i s d e f o r m e d . Some p o s s i b l e o b s t a c l e s w h i c h w i l l c u r b d o u b l e c r o s s s l i p a r e a ) ' r e g i o n s o f p e r f e c t c r y s t a l s b ) c i r c u l a r F r a n k p a r t i a l s c ) c o n c e n t r a t e d r e g i o n s o f i m p u r i t i e s . - 79 -The f i r s t m e n t i o n e d i s n o t a good o b s t a c l e b u t w i l l t e n d t o r e t a r d c r o s s s l i p i n t h e f o l l o w i n g f a s h i o n . I f a d i s l o c a t i o n s o u r c e i s fo rmed i n t h e p e r f e c t c r y s t a l by t h e d o u b l e c r o s s s l i p mechan ism, t h e d i s l o c a t i o n s i n t h e p r i m a r y p l a n e w i l l f i n d i t d i f f i c u l t t o c r o s s s l i p s i n c e o b s t a c l e s such as f o r e s t s and i m p u r i t i e s a r e a b s e n t . The o n l y a g e n t w h i c h w i l l p romote c r o s s s l i p I s t h e p a r a l l e l w a l l s o f d i s l o c a t i o n s w h i c h may e x i s t i n t h e a l r e a d y s l i p p e d r e g i o n . S i n c e t h e s e d i s l o c a t i o n w a l l s w i l l have t o b u i l d up b e f o r e t h e i r i n t e r n a l s t r e s s i s g r e a t enough t o p r o m o t e c r o s s s l i p , t h e f r e q u e n c y o f c r o s s s l i p w i l l d i m i n i s h . T h e r e f o r e i t i s l i k e l y t h a t r e g i o n s o f p e r f e c t c r y s t a l s w i l l r e t a r d c r o s s s l i p . The second o b s t a c l e w i l l be v e r y e f f e c t i v e i f i t i s p r e s e n t . S ince c i r c u l a r F r a n k p a r t i a l s w h i c h a r e s e s s i l e s s u r r o u n d an a r e a o f s t a c k i n g f a u l t , and s i n c e t h e d i s l o c a t i o n movement t h r o u g h a f a u l t e d a r e a i s e n e r g e t i c a l l y p r o h i b i t i v e , c r o s s s l i p i s i m p r o b a b l e . The t h i r d o b s t a c l e w i l l b e v e r y e f f e c t -i v e s i n c e d i s l o c a t i o n s w i l l n o t be a b l e t o pass t h r o u g h and w i l l be f o r c e d t o go a r o u n d t h i s r e g i o n o f h i g h s t r a i n . These t h r e e o b s t a c l e s a r e p o s s i b i l i t i e s b u t a r e d i f f i c u l t t o d e t e r m i n e - e x p e r i m e n t a l l y . - 80 -Y . C o n c l u s i o n s Prom t h e p r e s e n t i n v e s t i g a t i o n on t h e d e f o r m a t i o n o f c o p p e r "wh iske rs two g e n e r a l c o n c l u s i o n s may be d r a w n : a ) The p r o p a g a t i o n o f L u d e r s band d e t e r m i n e s t h e f l o w s t r e s s . S i n c e t h e advance o f L u d e r s band depends on r a n d o m l y d i s t r i b u t e d o b s t a c l e s i n t h e w h i s k e r g i v i n g r i s e . t o f l u c t u a t i o n s i n t h e f l o w s t r e s s , t h e ' t e m p e r a t u r e dependence o f t h e f l o w s t r e s s i n t h i s r e g i o n d i d n o t g i v e c o n s i s t e n t r e s u l t s . b ) The p r e s e n c e o f t h e o x i d e l a y e r i s n o t r e s p o n s i b l e f o r t h e h i g h s t r e n g t h o f w h i s k e r s . The o x i d e l a y e r . i s n o t t h e b a r r i e r t o t h e movement o f d i s l o c a t i o n s . The b a r r i e r t o t h e u n r e s t r i c t e d movement o f d i s l o c a t i o n s i s t h e p r e s e n c e o f t h e m e t a l s u r f a c e i t s e l f . -•81 -V I . Recommendat ions f o r F u r t h e r Work The d i s l o c a t i o n s t r u c t u r e o f w h i s k e r s (~15/<-. i n d i a m e t e r ) may be s t u d i e d by t h e m i c r o s c o p i c e x a m i n a t i o n o f t h e r m a l e t c h p i t s on a l l t h e b o u n d -i n g f a c e s . The e t c h p i t a r r a y n e a r t h e r o o t s o f d i s t i n c t b r a n c h e s and p y r a m i d a l t i p s may g i v e a c l u e t o t h e mechanisms o f w h i s k e r g r o w t h . A l t h o u g h a n n e a l i n g and t e s t i n g o f de fo rmed w h i s k e r s have been . p e r -fo rmed i n p a s s i n g b y a few w o r k e r ' s , no d e t a i l e d s t u d y has been d o n e . T h e r e i s r e a s o n t o b e l i e v e t h a t t h e w h i s k e r s w i t h v e r y s m a l l L u d e r s band r e g i o n s when a n n e a l e d w i l l g i v e an u n u s u a l s t r e s s - s t r a i n c u r v e . Hence t h i s i n v e s t i g a t i o n , c o u p l e d w i t h m i c r o c r e e p s t u d y , , w o u l d be v e r y i n t e r e s t i n g . The t e m p e r a t u r e dependence o f t h e f l o w s t r e s s may be d e t e r m i n a b l e i n a w h i s k e r w h i c h has fo rmed a s i n g l e L u d e r s band t h r o u g h o u t i t s l e n g t h . S i n c e t h e de fo rmed w h i s k e r w i l l possess a d i s l o c a t i o n p a t t e r n r a d i c a l l y d i f f e r e n t f r o m t h a t o f t h e b u l k c r y s t a l c a s e , a d e t e r m i n a t i o n o f t h e t e m p e r a t u r e d e p e n d -ence o f t h e f l o w s t r e s s w i l l t h e r e f o r e add t o t h e u n d e r s t a n d i n g o f w o r k h a r d e n i n g . — 82 -APPENDIX I A . P r o c e d u r e f o r t h e C a l i b r a t i o n o f t h e Tensomete r The t e n s o m e t e r was c a l i b r a t e d w i t h a h e l i c a l s p r i n g . The s p r i n g , w h i c h was p r e v i o u s l y c a l i b r a t e d w i t h w e i g h t s , . w a s g l u e d h o r i z o n t a l l y on t h e f i l a m e n t - h o l d e r s o f t h e p y r e x a r m s . T h i s was done w i t h t h e suspended r o d p o s i t i o n e d a t n u l l . Then t h e c u r r e n t - e x t e n s i o n r e l a t i o n was d e t e r m i n e d by i n c r e a s i n g t h e c u r r e n t by i n c r e m e n t s o f 1 ma . The r e s t o r i n g f o r c e was d e t e r m i n e d by g l u e i n g t h e s p r i n g on t h e f i l a m e n t s a t v a r i o u s p o s i t i o n s f r o m n u l l and by r e l e a s i n g t h e s u s p e n d e d r o d t o p e r m i t i t t o r e a c h e q u i l i b r i u m . .A t t h e e q u i l i b r i u m p o s i t i o n s t h e d i s t a n c e s f r o m n u l l and t h e e x t e n s i o n s o f t h e s p r i n g were r e c o r d e d . I n t h i s way t h e d i s t a n c e - f r o m - n u l l - e x t e n s i o n r e l a t i o n was o b t a i n e d . The r e l a x a t i o n o f t h e p y r e x arms was d e t e r m i n e d b y g l u e i n g a s h o r t l e n g t h o f f i n e t u n g s t e n w i r e on t h e f i l a m e n t s a t n u l l p o s i t i o n . The c u r r e n t -e x t e n s i o n r e l a t i o n was o b t a i n e d b y i n c r e a s i n g t h e c u r r e n t by 1 ma i n c r e m e n t s . The s t r a i g h t p y r e x arms d i s p l a y e d no r e l a x a t i o n . The c u r r e n t - f o r c e r e l a t i o n was d e t e r m i n e d by c o m p e n s a t i n g t h e c u r r e n t -e x t e n s i o n r e l a t i o n f o r t h e r e s t o r i n g f o r c e o f t h e suspended r o d and t h e r e l a x a -t i o n o f t h e p y r e x arms, and t h e n by r e l a t i n g t h e e x t e n s i o n t o t h e f o r c e . The above p r o c e d u r e was p e r f o r m e d f o r t h e b e n t p y r e x arms and t h e s t r a i g h t p y r e x arms w i t h t h e l a r g e s p r i n g . F o r l ow c u r r e n t s t h e p r o c e d u r e was r e p e a t e d f o r t h e s t r a i g h t p y r e x arms u s i n g t h e s m a l l s p r i n g . - 83 -B . C a l i b r a t i o n Curves and T a b l e 0.4 0.8 .1.2 1.6 2.0 2.4 F o r c e (gm) F i g u r e 37. - C u r r e n t - f o r c e r e l a t i o n f o r t h e b e n t p y r e x a r m s . n 84 -0.4 0.8 1.2 1.6 2.0 2.4 Force (gm) Figure g8. Current-force r e l a t i o n f o r the s t r a i g h t pyrex.arms. -•85 -0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.20 1.30 Extension (mm) Figure 39• C a l i b r a t i o n of h e l i c a l springs (small and.large). Force-extension p l o t . F i g u r e ~ 4 Q a . D e t e r m i n a t i o n o f t h e r e s t o r i n g f o r c e o f t h e suspended r o d w i t h t h e b e n t p y r e x a r m s . The l a r g e s p r i n g was u s e d . F i g u r e 0.10 0.20 E x t e n s i o n (mm) D e t e r m i n a t i o n o f t h e r e s t o r i n g f o r c e o f t h e suspended r o d w i t h t h e s t r a i g h t p y r e x a r m s . The l a r g e s p r i n g was u s e d . - 87 -100 150 F o r c e (mg) 250 F i g u r e Kl» C u r r e n t - f o r c e r e l a t i o n a t l o w c u r r e n t f o r t h e s t r a i g h t p y r e x a r m s . The s m a l l s p r i n g was u s e d . 0.05 0.10 0.15 D i s t a n c e f r o m N u l l (mm) 0.20 F i g u r e k-2. C a l i b r a t i o n ,of t h e r e s t o r i n g f o r c e o f t h e suspended . r o d w i t h t h e s t r a i g h t p y r e x a r m s . The s m a l l s p r i n g was used , - 8 8 Extension (fx.) Figure 4 -5 . Relaxation of the bent pyrex arms. T a b l e I V . C a l i b r a t i o n o f Impedance T r a n s d u c e r N u l l a t 11.48 mm M i c r o m e t e r 10 .^, s c a l e M i c r o m e t e r 3/o s c a l e M i c r o m e t e r 3/1- s c a l e R e a d i n g ( B r i d g e ) R e a d i n g ( B r i d g e ) R e a d i n g 11,4o _ 11.40 11.55 _ 11.42 10.0 11 .4i 4.95 .11.56 4.8 11.44 9-5 11.42 4.9 11.57 4,8 11.46 9.4 11.43 4.7 11.58 4.7 11.48 9.6 11.44 4.6 11.59 4,8 11.50 9.6 11.45 .4.6 11,60 4.5 11.52 9-3 11.46 4.9 11.61 4,8 11.54 10.0 11.47 4.8 .11.62 4.6 11.56 9.3 11.48 4.9 11,63 4.5 11.58 .9.4 11.49 4.5 .11,64 4.7 I I . 6 0 9.5 11.50 • 4.8 •11.65 4.3 11.62 9.6 11.51 4.6 11,66 4 , 8 11.64 9.7 11.52 4.8 11,67 4,4 11,66 .9.5 11.53 4.9 11.68 4.7 11.68 .9.0 11.54 4.6 11.69 4.1 11.70 9.5 11.55 4.6 11.70 4.5 0.2. = one s m a l l d i v i s i o n 0.1 = one s m a l l d i v i s i o n S e n s i t i v i t y - 0.422 /« . /d iv S e n s i t i v i t y - 0 .2 l4 / ^ / d i v 90 -BIBLIOGRAPHY 1. D a n a , J . P . , . " T h e System o f M i n e r a l o g y o f James D w i g h t Dana and Edward S a l i s b u r y D a n a " , 7th e d . , John W i l e y and S o n s , I n c . , New Y o r k (1946). 2. H a r d y , H . K . , P r o g . M e t a l P h y s i c s , V o l . 6, 45 (1956). 5. Compton , K. G . , M e n d i z z a , A . , and A r n o l d , S . M . , C o r r o s i o n , Vo l . .7, 327, (1951). 4. K o o n c e , S . E l o i s e , and A r n o l d , S . M . , J . A p p l . P h y s . , V o l . 25,.134 (1954). 5. G a i t , J . K . , and H e r r i n g , C , P h y s . . R e v . , V o l . 85, 1060 (1952). 6. N a b a r r o , P . R. N . , and J a c k s o n , P. J . , "Growth and P e r f e c t i o n .of C r y s t a l s " , e d i t e d by Doremus e t a l , John W i l e y and S o n s , I n c . , New Y o r k , p..11 (1958). 7. . K o h l s c h u t t e r , H . W . , Z» f . E l e c t r o c h e m i e , V o l . 38, 345 (1932). 8. S e a r s , G. W . , G a t t i , A . , and P u l l m a n , R . . C . , A c t a M e t . , . V o l . 2, 727 (1954). 9. E v e r e t t , E . R . , and A m i c k , W. A . , J . A p p l . P h y s . , Vo l ..25, 1204 (1954). 10. B r e n n e r , S . S . , A c t a M e t , , . V o l . 4, 62 (1956). 11. B r e n n e r , S . S . , and M o r e l o c k , , C . R . , R e v . S c i , I n s t . , V o l . 2.8, 652 (1957). 12. B r e n n e r , . S . S . , " G r o w t h and P e r f e c t i o n o f C r y s t a l s " , . e d i t e d by Doremus e t a l , John W i l e y and S o n s , I n c . , New Y o r k , p , 157 (1958). 13* B u r t o n , W. K . , C a b r e r a , . N . , and P r a n k , F . C , P h i l . T r a n s , R o y . S o c , V o l . A243, 299 (1951)a 14. S e a r s , G. W . , A c t a M e t . , V o l . 3, 361 (1955). 15. W i e d e r s i c h , H . , J . E l e c t r o c h e m . S o c , V0I..IO6, 810 (1959). 16. .Webb, W. W . , and R i e b l i n g , E . F . , J . Chem. P h y s . , V o l . 28, 1242 (1958). 17. G o r s u c h , P. D . , G e n e r a l E l e c t r i c R e p o r t N o . 57-RL-1840 (1957). 18. B r e n n e r , S . S . , and S e a r s , G. W . , A c t a M e t , , V o l . 4, 268 (1956), 19. B r e n n e r , S . S., A c t a M e t . , . V o l . 7, 677 (1959). 20. . A l l a n , . W . J . , and Webb, .W, W . , A c t a M e t . , . V o l . 7, 648 (1959). 21. Webb, W . W . , " G r o w t h and P e r f e c t i o n o f C r y s t a l s " , e d i t e d by Doremus e t a l , John W i l e y and S o n s , I n c . , New Y o r k , p . 230 (1958). 22. E s h e l b y , J , D . , J . A p p l . P h y s , , V o l . 24, 176 (1953). - 91 -23. p r a n k , F . C . , q u o t e d R e f e r e n c e N o . 17. 24. E i s n e r , R . S . , . A c t a M e t . , V o l . 3, 4l9 (1955). 25. B r e n n e r , S . S . , J . A p p l . P h y s . , V o l . 27, l484 (1956). 26. B r e n n e r , S . S . , J . A p p l . P h y s . , V o l . 28, 1023 (1957), 27. M a r s h , D . M . , J . S c i . I n s t r u m e n t s , Vo l .-36, 165 (1959). 28. .Co leman, R. V . , P r i c e , P. B . , and C a b r e r a , Ne , J . A p p l , P h y s , , V o l . .28, 1360 (1957). 29. C a b r e r a , N . , and P r i c e , . P . B . , "Growth and P e r f e c t i o n o f C r y s t a l s " , e d i t e d by Doremus e t a l , John W i l e y and S o n s , I n c . , New Y o r k , p . 204 (1958) 30. C a b r e r a , N . , Cambr idge C o n f e r e n c e on W h i s k e r s and T h i n F i l m s , (1958), 31. M a c k e n z i e , J . K . , T h e s i s ( U n i v e r s i t y o f B r i s t o l ) (1949). 32. G y l a i , Z , , Z , f . F h y s i k , V o l . 138, 317 (1954). 33. P e a r s o n , G. L , , R e a d , W. T . , and F e l d m a n , W. L . , A c t a M e t , , V o l . 5, l 8 l , (1957) . 34. C o t t r e l l , A . H . , " D i s l o c a t i o n s and P l a s t i c F low i n C r y s t a l s " , C l a r e n d o n P r e s s , O x f o r d , p . 139 (1953). 35. C o l e m a n , R, V . , P r i c e , P. B . , and C a b r e r a , N . , J . o f A p p l . P h y s . , V o l . 28, 1360 (1957). 36. C a b r e r a , N . , and P r i c e , P. B . , " G r o w t h and P e r f e c t i o n o f C r y s t a l s " , e d i t e d b y Doremus e t a l , John W i l e y and S o n s , I n c . , New. Y o r k , p . 204, (1958). 37- M o t t , W. F . , Cambr idge C o n f e r e n c e on S t r e n g t h o f W h i s k e r s and T h i n F i l m s , (1958) . 38. B r e n n e r , S , S . , J . A p p l . P h y s . , V o l . 30, 266 (1959). 39. B r e n n e r S . S . , and M o r e l o c k , C . R . , A c t a M e t . , Vol.,4,.87 (1956). 40. N a b a r r o , F . R , N « , " D i s l o c a t i o n s and M e c h a n i c a l P r o p e r t i e s o f C r y s t a l s " , e d i t e d by F i s h e r e t a l , John W i l e y and S o n s , I n c . , New Y o r k , p . 521 (1956), 41. A n d r a d e , E . N . da C , M e t a l s Monograph N o . . 13 (1953). 42. A r m s t r o n g , A . M . , p r i v a t e c o m m u n i c a t i o n . 43. 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Mag, V o l . 1 , 489 (1956). 63. Gilman, J . , Acta Met.., V o l . 1, 357 (1959). 64. Fi s h e r , J . C , Hart, E. Q., and Pry, R, H., Phys. Rev., V o l . 87, 958, (1952). 

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