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The melting behavior of equiaxed grain boundaries Orava, Raimo Norman 1959

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THE MELTING BEHAVIOUR OF EQ.UIAXED GRAIN BOUNDARIES by RAIMO NORMAN ORAVA 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 this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE. Members of the Department Mining' and Metallurgy THE UNIVERSITY OF BRITISH June, 19 59. COLUMBIA i i i ABSTRACT Experiments were performed on b i c r y s t a l s of h i g h - p u r i t y (99.986$ and 99.9987$) t i n to i n v e s t i g a t e the dependence of the m e l t i n g behaviour of g r a i n boundaries, p a r t i c u l a r l y those of the "equiaxed" type, on a p p l i e d s t r e s s , o r i e n t a t i o n d i f f e r e n c e , boundary o r i e n t a t i o n , growth c o n d i t i o n s , and p u r i t y . By a comparison with previous work on columnar boundaries i t was con cluded that there was no s t r u c t u r a l d i f f e r e n c e between equiaxed and columnar boundaries having the same geometry. Any d i f f e r e n c e i n behaviour was a t t r i b u t e d to the b u i l d - u p of i m p u r i t i e s at the equiaxed boundary due to the z o n e - r e f i n i n g e f f e c t on growth. C a l c u l a t i o n s on the d i f f u s i o n of Pb, the major impurity i n Sn, show that the i m p u r i t y content does not decrease a p p r e c i a b l y in the d u r a t i o n of the t e s t , and consequently could be considered constant from specimen to specimen. Thus, the m e l t i n g behaviour i s a p r o p e r t y of the atomic s t r u c t u r e of a g r a i n boundary, q u i t e apart from any e f f e c t due to i m p u r i t i e s . T i l t boundaries e x h i b i t no dependence of m e l t i n g behaviour on o r i e n t a t i o n d i f f e r  ence above 16°, whereas t w i s t boundaries do. A peak of minimum d i s o r d e r appears at 41°. The dependence i s p r e d i c t a b l e from c o i n c i d e n c e p l o t s . < I n 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 o f Mining and Metallurgy The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver 8, Canada. Date July 2, .1959- ACKNOWLEDGEMENT The author is grateful for financial aid in the form of research assistantship granted by the Defence Research Board of Canada. Special thanks are extended to Dr. E. Teghtsoonian for his supervision and patience, and to Mr. R. Richter and Mr. R. Butters for their technical advice and assistance. i v TABLE OF CONTENTS CHAPTER PAGE 1. INTRODUCTION 1 1*1. Object of the I n v e s t i g a t i o n . . . . . . . . 1 1.2. Theories of Grain Boundary S t r u c t u r e . . . . 1 1.3. Previous M e l t i n g Experiments 6 2. EXPERIMENTAL 9 2.1. Specimen P r e p a r a t i o n 9 2.1.1. M a t e r i a l 9 2.1.2. Seed C r y s t a l s 9 2.1.3. Columnar B i c r y s t a l s . . 10 2.1.4. Equiaxed B i c r y s t a l s 12 2.1.5. Test Specimens 14 2.1.6. O r i e n t a t i o n Determination 16 2.2. Experimental Procedure 17 2.2.1. Temperature I n d i c a t i o n 17 2.2.2. M e l t i n g Apparatus 18 2.2.3. Temperature Measurement 19 2.2.4. Q u a l i t y of the Measurements 20 2.3. Observations 22 2.3.1. S t r e s s 24 2.3.2. O r i e n t a t i o n D i f f e r e n c e 28 2.3.3. Boundary O r i e n t a t i o n 31 2.3.4. Growth Conditions 32 2.3.5. P u r i t y . 33 V Table of Contents (Cont'd.) CHAPTER PAGE 2. EXPERIMENTAL (Cont'd.) 2.4. Decantation Experiments . . . 34 2.4.1. Purpose 34 2.4.2. Procedure 34 2.4.3. R e s u l t s 35 2.4.4. D i s c u s s i o n . . . 40 3. DISCUSSION AND CONCLUSIONS 41 3.1. Summary of Experiment Observations 41 3.2. General D i s c u s s i o n 43 3.3. S t r e s s 45 3.4. O r i e n t a t i o n D i f f e r e n c e 45 3.5. Boundary o r i e n t a t i o n 49 3.6. Growth Conditions . 49 3.7. P u r i t y 49 4. SUMMARY 51 5. RECOMMENDATIONS FOR FUTURE INVESTIGATION 52 APPENDICES I . Impurity Segregation to an Equiaxed Boundary 53 I I . D i f f u s i o n of Impurity from an Equiaxed Boundary 57 I I I . Coincidence P l o t s 59 BIBLIOGRAPHY 65 v i LIST OF ILLUSTRATIONS  FIGURE P A G E 1. Simple small-angle t i l t g r a i n boundary showing the a r r a y of edge d i s l o c a t i o n s d e s c r i b i n g the boundary 4 2. Columnar b i c r y s t a l c o n t a i n i n g a symmetrical t i l t boundary of o r i e n t a t i o n d i f f e r e n c e 9° . . . . . . 11 3. Furnace used f o r the growth of equiaxed b i c r y s t a l s 13 4. Equiaxed b i c r y s t a l c o n t a i n i n g a symmetrical t i l t boundary of o r i e n t a t i o n d i f f e r e n c e &° . . . . . . 14 5. Top view of a columnar and equiaxed b i c r y s t a l , showing t y p i c a l t e s t specimens . . . . 15 6a. Schematic r e p r e s e n t a t i o n of the m e l t i n g apparatus . . . . . . . 18 6b. General view of the mel t i n g apparatus 19 7. Heating curves f o r the d u a l thermocouple-block assembly 21 8. The s t r e s s dependence of the time to boundary s e p a r a t i o n 26 9. O r i e n t a t i o n d i f f e r e n c e dependence of the time to boundary s e p a r a t i o n 29 10. Decanted i n t e r f a c e of a Sn c r y s t a l showing pro j e c t i o n s on the hexagonal c e l l s . Growth r a t e : 1 mm./min 38 11. Decanted i n t e r f a c e of a Sn c r y s t a l showing n i p p l e s p r o j e c t i n g from hexagonal c e l l s . Growth . r a t e : 2 mm./min 38 12. Curves f o r normal f r e e z i n g 56 13. Coincidence p l o t f o r a 14° equiaxed t w i s t boundary 60 14. Coincidence p l o t f o r a 33° equiaxed t w i s t boundary 61 l v i i L i s t of I l l u s t r a t i o n s (Cont'd.) FIGURE PAGE 15. Coincidence p l o t f o r a 41° equiaxed t w i s t boundary 62 16. Coincidence p l o t f o r a 46° equiaxed t w i s t boundary 63 v i i i LIST OF TABLES TABLE PAGE 1. X-Ray Traverse Across an Equiaxed B i c r y s t a l of 99.9987$ Sn 16 2. V a r i a t i o n of t* With S t r e s s f o r 45° Columnar T i l t Boundaries of 99.9987$ Sn 25 3. V a r i a t i o n of t* With S t r e s s f o r 45° Equiaxed T i l t Boundaries of 99.9987$ Sn 27 4. V a r i a t i o n of f* With S t r e s s f o r 41° Equiaxed Twist Boundaries of 99.986$ Sn 27 5. V a r i a t i o n of t* With S t r e s s f o r 41° Equiaxed Twist Boundaries of 99.986$ Sn. . . . . . . . . . 27 6. V a r i a t i o n of t* With o r i e n t a t i o n D i f f e r e n c e f o r Equiaxed T i l t Boundaries, of 99.9987$ Sn. . . . . . . . 28 7. V a r i a t i o n of t* With O r i e n t a t i o n D i f f e r e n c e f o r Equiaxed T i l t Boundaries of 99.986$ Sn. . . . . . . 30 8. V a r i a t i o n of t * With O r i e n t a t i o n D i f f e r e n c e f o r Equiaxed Twist Boundaries of 99.9987$ Sn 31 9. E f f e c t of Boat C o n f i g u r a t i o n s on the Time to Boundary S e p a r a t i o n 33 10. Values of the E f f e c t i v e D i s t r i b u t i o n C o e f f i c i e n t Corresponding to the Given Growth Rate, f 54 11. R e l a t i v e Impurity C o n centration C/C D Corresponding to the Given Value of the E f f e c t i v e D i s t r i b u t i o n C o e f f i c i e n t 55 12. C/M f o r Given Annealing Times 58 13. R e l a t i v e Measure of the Disorder of a Twist Boundary 64 1 THE MELTING BEHAVIOUR OF EQUIAXED GRAIN BOUNDARIES 1. INTRODUCTION 1.1 Object of the I n v e s t i g a t i o n The s t r u c t u r e and p r o p e r t i e s of g r a i n boundaries i n metals have been the source of c o n s i d e r a b l e i n t e r e s t i n r e c e n t years. S t u d i e s of measureable i n t r i n s i c p r o p e r t i e s of a g r a i n boundary have l e d to c o n c l u s i o n s concerning i t s s t r u c t u r e . T h i s s t r u c t u r e i s of fundamental importance because g r a i n boundaries have a pronounced e f f e c t on the p r o p e r t i e s of metals. A t t e n t i o n has been c h i e f l y d i r e c t e d towards p r o p e r t i e s such as g r a i n boundary energy, d i f f u s i o n , shear, and m i g r a t i o n . However, o n l y as r e c e n t l y as 1957 have r e s u l t s of c a r e f u l l y performed e x p e r i  ments on the m e l t i n g behaviour of g r a i n boundaries been r e p o r t e d , by Weinberg and T e g h t s o o n i a n 1 . This t h e s i s r e p o r t s f u r t h e r o b s e r v a t i o n s on g r a i n boundary m e l t i n g . 1.2 Th e o r i e s of Grain Boundary S t r u c t u r e A g r a i n boundary i n a pure metal separates r e g i o n s of ordered l a t t i c e d i f f e r i n g i n c r y s t a l l o g r a p h i c o r i e n t a t i o n . The two e a r l i e s t conceptions of the s t r u c t u r e of a c r y s t a l boundary were the amorphous l a y e r theory and the t r a n s i t i o n a l l a t t i c e theory. 2 - Bengoughr and Rosenhain proposed that metal grains were cemented together by a supercooled viscous liquid termed an "amorphous cement" to account for the following facts: (i) deformation by the slip mechanism within the grains gave way to boundary sliding above a certain c r i t i c a l temp erature near the melting point 4. (Recall that an amorphous substance is hard and strong well below the melting point but is capable of softening more rapidly than a crystalline material as the temperature is incr eased.) ( i i ) the transition region between grains was considered to be too thin to allow atoms to bind together as a crystalline substance. ( i i i ) a small stress produced inter crystalline facture a few degrees below the melting point of a polycrystal without producing appreciable distortion to the grain**. The thinness of the boundary was not a valid argument because of the short range of atomic forces. With this realiza tion, Hargreaves and H i l l s 6 proposed a much thinner transitional lattice grain boundary model where the atoms were no longer arranged randomly as implied by the term "amorphous". A definite atomic pattern implied that the boundary in any b i  crystal is reproducible with respect to crystallographic structure if the relative orientation of the two bounding crystals and the orientation of the boundary i t s e l f always remain the same. The - 3 o r i e n t a t i o n d i f f e r e n c e dependence of g r a i n boundary f r e e e n e r g y 1 0 ' 1 5 , d i f f u s i o n 1 2 ' 1 3 * 1 4 , and melting behaviour 1>2 1 , provided the most i n c o n t r o v e r t i b l e evidence for the t r a n s i t i o n a l l a t t i c e theory. At f i r s t , the t r a n s i t i o n a l l a t t i c e could not e x p l a i n the a b i l i t y of one g r a i n to s l i p v i s c o u s l y over another. Mott's theory of i s l a n d s of p e r f e c t l a t t i c e enclosed by regions of m i s f i t attempted to account f o r i n t e r c r y s t a l l i n e deformation. At a c r i t i c a l temperature, the combined e f f e c t pf the thermal energy and the m i s f i t energy was assumed to cause l o c a l i z e d m e l ting. Deformation could then proceed i n t e r g r a n u l a r l y with n e g l i b i b l e s l i p r e s i s t a n c e . From the close argreement found between the a c t i v a t i o n energy for viscous i n t e r c r y s t a l l i n e s l i p and that f o r volume d i f f u s i o n , K$ 8 conclud ed that the l o c a l s t r u c t u r e of the boundary reg i o n r e s p o n s i b l e f o r s l i p was the same as the l o c a l s t r u c t u r e of the i n t e r i o r pf the g r a i n r e s p o n s i b l e for volume d i f f u s i o n . He proposed a boundary which consisted pf disordered groups of atoms or imperfections s i m i l a r to the vacant l a t t i c e s i t e s necessary f o r volume d i f f i s i o n. Between these groups there are regions of r e l a t i v e l y p e r f e c t l a t t i c e . K$ pointed put that any region of disordered l a t t i c e would behave i n a viscous manner. Therefore, the concept of a viscous grain boundary was c o n s i s t e n t w i t h not only the amorphous cement theory but a l s o the t r a n s i t i o n a l l a t t i c e theory. This allows f o r the viscous behaviour of the t r a n s i t i o n boundary du r i n g deformation. 4 A specific model for the transitional l a t t i c e was f i r s t proposed by Burgers 9. He showed that the f i t of two sets of differently oriented lattice planes could be accomplished by an array of dislocations. This is represented diagrammatically in Figure 1 for a t i l t boundary in a simple cubic crystal. Figure 1. Simple small-angle t i l t grain boundary showing the array of edge dislocations describing the bound ary . 5 Read and Shockley u made an extensive study of dislocation models of grain boundaries. They obtained an expression for grain boundary energy as a function of the orientation difference, 0 . Frank 1 1 analyzed dislocation contents as applied to a general grain boundary of arbitrary orientation differeace and arbitrary orientation of the boundary. This form is restricted to small- angle boundaries because, as 8 increases, the dislocations approach so close to each other that they lose their identity. For large differences of orientation, i t would appear that models such as that of Mott or K§ are more plausible descriptions of the boundary. Another large-angle boundary model was proposed by Smoluchowski12 as a result of the orientation dependence of grain boundary d i f f u s i o n 1 3 ' 1 4 . He suggested that a grain boundary consisted of dislocations for small angles merging into rod-like regions of misfit for intermediate orientation d i f f e r  ences. These then coalesce into f l a t slabs of disorder as the condition for maximum misorientation is approached. At this maximum point, the boundary becomes a uniform layer of dis torted material. * Aust and Chalmers^ showed that the specific energy of a crystal boundary in tin was dependent on the orientation d i f f e r  ence at the boundary, when this was less than 6 ° . This furnished very strong support for the transitional l a t t i c e model of the crystal. - 6 - 1.3 Previous M e l t i n g Experiments From experiments i n boundary m e l t i n g , Chalmers concluded i n 1940 that g r a i n boundaries of t i n (Chempur 99.986$) e x h i b i t e d a d e p r e s s i o n i n m e l t i n g p o i n t of 0.14C 0 * 0.0050° from the bulk m e l t i n g p o i n t under the a p p l i c a t i o n of a t e n s i l e s t r e s s between the l i m i t s of 1000 and 3000 gm./cm.'2. Th i s was true f o r angles of o r i e n t a t i o n d i f f e r e n c e i n the range of 14° to 85°. No r e s u l t s were r e p o r t e d f o r & smaller than 14° or greater than 85°. The sharp m e l t i n g poing excluded the p o s s i b i l i t y of an amorphous cement boundary. The change from s o l i d to l i q u i d f o r an amorphous substance i s g r a d u a l . 17 Chaudron, Lacombe, and Y a n n a q u i s A f estimated a boundary melting p o i n t d e p r e s s i o n of 0.25C° i n aluminum by o b s e r v i n g boundaries m e l t i n g ahead of the general i n t e r f a c e . Pumphrey and Lyon 1® conducted t e n s i l e t e s t s , near the m e l t i n g p o i n t , on aluminum. They found that the u l t i m a t e t e n s i l e s t r e n g t h dropped to a small but measureable value at a tempera ture of some 4 or 5 degrees below the m e l t i n g p o i n t . F r a c t u r e was i n t e r c r y s t a l l i n e . I t was concluded that boundaries melt 4 s below the m e l t i n g point of the c r y s t a l . The i n t e r n a l f r i c t i o n measurements of Boulanger^S near t h e m e l t i n g p o i n t of aluminum and some of i t s a l l o y s l e d him to b e l i e v e that no i n c i p i e n t m elting occurs at the g r a i n boundaries unless caused by i m p u r i t i e s or high s t r e s s e s . Shewmon2^ presented a thermodynamic argument showing that any d i f f e r e n c e i n the m e l t i n g p o i n t of a g r a i n boundary and t h a t of the bulk m a t e r i a l would evolve o n l y from n o n e q u i l i b r i u m e f f e c t s such as the n o n e q u i l i b r i u m c o n c e n t r a t i o n of s o l u t e at the boundaries. - 7 - I n c o n t r a s t to t h e above work, W e i n b e r g and T e g h t s o o n i a n d i d n o t d e t e c t any d e p r e s s i o n o f t h e m e l t i n g p o i n t of t h e g r a i n b o u n d a r y i n b i c r y s t a l s of p u r e t i n and p u r e aluminum. R e s u l t s were r e p o r t e d f o r 99.9966$ Sn, 99.999$ Sn, 99.9999$ Sn and 99.995% A l . F o r s m a l l - a n g l e b o u n d a r i e s t h e r e was no t e n d e n c y f o r t h e c r y s t a l s t o p a r t a t t h e b o u n d a r y but p r e f e r e n t i a l b o u n d a r y m e l t i n g d i d o c c u r f o r l a r g e a n g l e s . The t r a n s i t i o n f r o m non- m e l t i n g to m e l t i n g o c c u r r e d a t an o r i e n t a t i o n d i f f e r e n c e o f 12° f o r t i n , and 14° f o r aluminum. Boundary s e p a r a t i o n t o o k p l a c e a f i n i t e t i m e i n t e r v a l , t , a f t e r t h e s p e c i m e n had r e a c h e d t h e m e l t i n g p l a t e a u . The a d d i t i o n of s o l u t e c a u s e d m e l t i n g p o i n t d e p r e s s i o n s w h i c h a g r e e d w i t h t h o s e p r e d i c t e d f r o m e q u i l i b r i u m p h a s e d i a g r a m s . The v a l u e of t * was d e p e n d e n t upon t h e a p p l i e d s t r e s s , t h e h e a t i n g r a t e , t h e p u r i t y o f t h e m a t e r i a l , and t h e o r i e n t a t i o n d i f f e r e n c e i n t h e r a n g e 11°-15 0'. W e i n b e r g 2 ^ has r e c e n t l y i n v e s t i g a t e d t h e b o u n d a r y m e l t i n g b e h a v i o u r o f aluminum and z i n c . The a b s e n c e of a m e l t i n g p o i n t d e p r e s s i o n f o r aluminum was c o n f i r m e d w i t h i n an e x p e r i m e n t a l u n c e r t a i n t y o f 0.05C° and v e r i f i e d i n z i n c w i t h i n 0.020G°. In a d d i t i o n , b o u n d a r i e s i n z i n c d i d n o t s e p a r a t e f o r a n g l e s between 0 ° - 2 6 ° and 1 0 8 ° - 1 8 0 ° . T h e r e i s an i n d i c a t i o n o f a d e p e n d e n c e o f b o u n d a r y m e l t i n g on t h e b o u n d a r y o r i e n t a t i o n i n c l o s e - p a c k e d h e x a g o n a l m e t a l s b e c a u s e b o u n d a r i e s of a n g l e & behave u n l i k e t h o s e of a n g l e ( 1 8 0 - © ) ° . From d i r e c t i o n a l m e l t i n g t e s t s on z o n e - r e f i n e d l e a d and d i l u t e a l l o y s o f t i n , s i l v e r o r g o l d i n l e a d , B o i l i n g and - 8 - 2 2 Winegard concluded t h a t t h e p r e s e n c e of a s m a l l amount, namely 0.005-0.05$, of a second element i n a pure m e t a l enhances or even promotes g r a i n boundary m e l t i n g . C h a l m e r s 1 5 has d i f f e r e n t i a t e d between two types of boundary c l a s s i f i e d a c c o r d i n g to t h e manner i n which they a r e produced, t h a t i s , t h e i r o r i g i n . One i s f a m i l i a r w i t h columnar and equjaxed g r a i n s as t h e y appear i n a c a s t i n g . Columnar b o u n d a r i e s d e l i n e a t e g r a i n s w h i c h grow s i d e - b y - s i d e , normal to the a d v a n c i n g s o l i d - l i q u i d i n t e r f a c e . I n c o n t r a s t , equiaxed b o u n d a r i e s are t h o s e r e s u l t i n g from the impingement of s e p a r a t e l y n u c l e a t e d g r a i n s . Another d i f f e r e n c e between columnar and equiaxed bound a r i e s i s t h e mechanism by which i m p u r i t i e s tend to s e g r e g a t e a t the boundary. Chalmers m a i n t a i n e d t h a t the l a t t e r n e c e s s a r i l y c o n t a i n an e x c e s s i v e amount of i m p u r i t i e s as a r e s u l t of a zone- r e f i n i n g e f f e c t d u r i n g s o l i d i f i c a t i o n . On the o t h e r hand, t h e r e i s no tendency f o r e x c e s s i v e s e g r e g a t i o n at a columnar boundary. To d a t e , no evidence t h a t t h e i n t r i n s i c s t r u c t u r e of a boundary depends on i t s o r i g i n has been p u b l i s h e d . In t h i s t h e s i s , the r e s u l t s of an i n v e s t i g a t i o n of the m e l t i n g b e h a v i o u r of equiaxed g r a i n b o u n d a r i e s are r e p o r t e d . An attempt was made to d e t e r m i n e whether the m e l t i n g b e h a v i o u r i s a f u n c t i o n of c r y s t a l - l o g r a p h i c s t r u c t u r e , q u i t e a p a r t f rom the e f f e c t of i m p u r i t y s e g r e g a t i o n at t h e boundary. 2. EXPERIMENTAL 2.1. Specimen P r e p a r a t i o n 2.1.1, M a t e r i a l The m a t e r i a l used was t i n o b t a i n e d f r o m t h e V u l c a n D e t i n n i n g Co. and was of two g r a d e s : ( i ) V u l c a n e l e c t r o l y t i c : 99.986$ Sn w i t h N i , Sb, Fe and Pb as t h e m a j o r d e t e c t a b l e i m p u r i t e s . ( i i ) V u l c a n e x t r a p u r e : 99.9987$ Sn w i t h Pb as t h e m a j o r d e t e c t a b l e i m p u r i t y . Most o f t h e t e s t s were p e r f o r m e d on t h e e x t r a p u r e t i n . 2.1.2. Seed C r y s t a l s The s t a n d a r d seed was c h o s e n w i t h an o r i e n t a t i o n o f (001) [ l ioj , t h a t i s , t h e (001) p l a n e was i n i t i a l l y h o r i z o n t a l and t h e [lio] d i r e c t i o n p a r a l l e l to t h e g r o w t h d i r e c t i o n . A l l s e e d s were grown by a method commonly r e f e r r e d to as th e m o d i f i e d B r i d g m a n t e c h n i q u e 1 6 . I n d e t a i l , a s i n g l e c r y s t a l , a p p r o x i m a t e l y 5 cm. l o n g was p l a c e d a t one end o f a b o a t w h i c h d i d n o t r e a c t w i t h t i n . G r a p h i t e was u s e d . A t h i n p l a t e o f g r a p h i t e i n t h e b o t t o m o f t h e b o a t f a c i l i t a t e d t h e r e m o v a l o f th e s o l i d i f i e d c r y s t a l . D e v i a t i o n s f r o m t h e s t a n d a r d o r i e n t a t i o n were o b t a i n e d by i n s e r t i n g s u i t a b l e p i e c e s o f g r a p h i t e i n t o t h e b o a t . R o t a t i o n s about t h e [lio] d i r e c t i o n l e d t o s e e d s w h i c h were used to p r o d u c e b i c r y s t a l s w h i c h c o n t a i n e d a columnar t i l t b o u n d a r y . The f o r m a t i o n of an e q u i a x e d t i l t b o u n d a r y r e q u i r e d s e e d s w h i c h were r o t a t e d about t h e [lioj d i r e c t i o n . 10 The boat was allowed to heat up f o r a time before molten t i n was poured i n t o i t . Thereupon the furnace was p u l l e d over the boat and a short l e n g t h of the seed c r y s t a l was melted. To enhance seeding the l i q u i d adjacent to the s o l i d - l i q u i d i n t e r  f a c e was a g i t a t e d with the end of a g l a s s rod. A f t e r the i n t e r f a c e had reached an e q u i l i b r i u m p o s i t i o n the f u r n a c e was removed at the constant r a t e s of e i t h e r 0.3 or 1.0 mm./min. On s o l i d i f i c a t i o n , the c r y s t a l was etched i n a f e r r i c c h l o r i d e reagent (H 20 80; HC1 10; F e C l j l O ) to r e v e a l any spurious changes of o r i e n t a t i o n , and to remove the t h i n oxide l a y e r . A l l c u t t i n g was done wi t h a J e w e l l e r ' s saw using 2/0 blades. The cut f a c e was etched e l e c t r o l y t i c a l l y (H 20 90; HC1 10) to remove any i r o n f i l i n g s that might have come from the b l a d e . A l s o , the deformed s u r f a c e l a y e r r e s u l t e d , on o c c a s i o n , i n r e c r y - s t a l l i z a t i o n when etc h i n g was omitted. Previous work has shown no d e t e c t a b l e d i f f e r e n c e i n r e s u l t s of t e s t s on saw-cut and flame- cut specimens. The h e a t i n g element of the f u r n a c e c o n s i s t e d of nichrome s t r i p wound around f i v e t u b u l a r ceramic i n s u l a t o r s attached to two t r a n s i t s end p i e c e s . This core was encased i n f i r e b r i c k s mounted on a t r o l l e y . The furnace was d r i v e n by a synchronous motor. Two speeds were obtained by u t i l i z i n g two p u l l e y s of d i f f e r e n t diameters on the output of a gear reducer. 2.1.3 Columnar B i c r y s t a l s For ease of n o t a t i o n , b i c r y s t a l s c o n t a i n i n g columnar boundaries are r e f e r r e d to as "columnar b i c r y s t a l s " . S i m i l a r l y , . 11 an "equiaxed b i c r y s t a l " contains an equiaxed boundary. A columnar b i c r y s t a l was grown from two seeds, each, of which differed i n orientation from the standard (001) [lio] by virtue of a rotation, in opposite sense, of ©/2 about the [llOJ d i r e c t i o n . This resulted in a symmetrical t i l t boundary of orientation difference & as i l l u s t r a t e d in Figure 2. The growth procedure was similar to that applied to the seed cr y s t a l s . The same furnace, driven at the slower speed, was used. A slow growth rate provided a boundary which was r e l a t i v e l y straight. A high growth rate sometimes caused the boundary to curve towards the side of the specimen so that i t s geometry ceased to be that o r i g i n a l l y desired. Figure 2. Columnar b i c r y s t a l containing a symmetrical t i l t boundary of orientation difference 9°. - 12 - The b i c r y s t a l s were approximately 20 mm. wide, 5 mm. t h i c k , and anywhere up to 100 mm. l o n g . 2.1.4. Equiaxed B i c r y s t a l s A problem arose here because an equiaxed boundary nec e s s a r i l y forms p a r a l l e l to the f r e e z i n g isotherm. Hence, s o l i d i f i c a t i o n proceeds from a seed at each end of the boat towards the middle. Two b a s i c f u r n a c e requirements had to be met: ( i ) a steep temperature g r a d i e n t which p r o v i d e s f a i r l y s e n s i  t i v e c o n t r o l of the p o s i t i o n s of the two s o l i d - l i q u i d i n t e r f a c e s even though the f u r n a c e remains s t a t i o n a r y . ( i i ) enough heat to melt p a r t of the seeds. To s a t i s f y ( i ) and ( i i ) simultaneously i s d i f f i c u l t because of the maximum heat t h a t can be d e r i v e d from a u n i t l e n g t h of chromel A r i b b o n b e f o r e i t burns out. However, a s a t i s f a c t o r y arrangement was achieved as shown i n F i g u r e 3. The heating element c o n s i s t s of 14 windings spaced about 2 mm. apart f o r a t o t a l width of 5 cm. This core i s encased i n two f i r e  b r i c k s mounted on a t r o l l e y . I t was necessary to make the boat supports, which serve as heat s i n k s , symmetrical about the middle of the boat. These c o n s i s t of two p a i r s of brass p l a t e s , one of which can be swung out to permit the furnace to be moved away when pouring the molten metal. Figure 5. Furnace used for the growth of equiaxed bicrystals. Equiaxed bicrystals were grown from two seeds, each of which differed in orientation from the standard (001) [lio] by virtue of a rotation, in the opposite sense, of d/2 about the [ l loj direction. This resulted in a symmetrical t i l t boundary of orientation difference ft. The [lloj direction was conse quently no longer oriented in the direction of growth. AS a consequence, unwanted changes of orientation occurred because [lid] is a preferred growth direction. A specimen containing an equiaxed boundary is illustrated in Figure 4. 14 tpol] F i g u r e 4. Equiaxed B i c r y s t a l c o n t a i n i n g a symmetrical t i l t boundary of o r i e n t a t i o n d i f f e r e n c e 9. A g r a p h i t e feoat w i t h a g r a p h i t e base p l a t e was used as p r e v i o u s l y . No p a r t i c u l a r c o n s i d e r a t i o n was g i v e n at f i r s t to the heat flow problem i n the boat. I t was assumed that the equiaxed boundary thus produced approached as c l o s e l y as poss i b l e to an i d e a l one as formed i n the equiaxed zone of an i n g o t . However, anomalous observations l e d to the i n v e s t i g a t i o n d i s  cussed i n S e c t i o n 2.4. The b i c r y s t a l s were about 18 mm. wide, 6 mm. t h i c k and 170 mm. l o n g . 2.1.5. Test Specimens Test specimens 10 mm. wide were cut t r a n s v e r s e l y from the o columnar b i c r y s t a l s to g i v e a boundary area of 0.5 cm . - 15 - The equiaxed b i c r y s t a l s had to be sectioned twice t r a n s  v e r s e l y to cut out a 20 mm. l e n g t h of the b i c r y s t a l c o n t a i n i n g the boundary, and l o n g i t u d i n a l l y i n order to o b t a i n two specimens 9 mm. wide. Again the boundary area was about 0.5 cm . Every specimen was notched at both ends for g r i p p i n g pur poses. Chromel wire of gauge 32 proved strong enough. Two notches were a l s o cut f o r the wire h o l d i n g the specimen to the thermocouple bl o c k . Subsequent to the c u t t i n g o p e r a t i o n s , the t e s t specimens were etched e l e c t r o l y t i c a l l y u n t i l the boundary became v i s i b l e on the cut s u r f a c e . A l a r g e s c a t t e r i n experimental v a l u e s on o n l y s l i g h t l y etched b i c r y s t a l s made the above an e s s e n t i a l step i n the p r e p a r a t i o n . F i g u r e 5 shows the two types of b i c r y s t a l s , and the t e s t specimens cut from them. F i g u r e 5. Top view of a columnar and an equiaxed b i c r y s t a l , showing t y p i c a l t e s t specimens. - 16 - 2.1.6. O r i e n t a t i o n Determination The c r y s t a l l o g r a p h i c o r i e n t a t i o n of the s i n g l e and b i c r y s t a l s was determined by the b a c k - r e f l e c t i o n Laue m e t h o d 2 3 ' 2 4 The photographs were i n t e r p r e t e d r e a d i l y by u s i n g a Greninger chart and the standard p r o j e c t i o n of the c r y s t a l . A c o l b a l t t a r g e t X-ray tube was used to which a v o l t a g e of 26 KV and c u r r e n t of 15 ma. were a p p l i e d . The exposure time was 15 minutes. The inherent u n c e r t a i n t y encountered i n the d e t e r m i n a t i o n of o r i e n t a t i o n s by t h i s method was found to be - 0.5°. However, the growth of c r y s t a l s from the melt w i l l r e s u l t i n the d i s o r i e n  t a t i o n of neighbouring s e c t i o n s by r o t a t i o n s of a degree or so about the growth d i r e c t i o n . These s e c t i o n s may extend the e n t i r e l e n g t h of a c r y s t a l but are o n l y of the order of a mm. i n dimen sion i n the t r a n s v e r s e d i r e c t i o n . Consequently, the presence of such a growth i m p e r f e c t i o n , known as l i n e a g e s t r u c t u r e , i n c r e a s e s the e r r o r to approximately -1°, To i l l u s t r a t e t h i s , f i v e Laue photographs were taken across the 20 mm. width of one c r y s t a l of an equiaxed b i c r y s t a l , with the f o l l o w i n g r e s u l t s . (Table 1 ) . Table 1 X-ray Traverse Across an Equiaxed B i c r y s t a l of 99.9987$ Sn. R o t a t i o n About R o t a t i o n About [HQ] [no] 1.5 1.0 2.5, 2.0 0.5 0.5 23.0 23.0 23.0, 23.0 23.0 23.5 17 - The t h i r d exposure was p a r t i c u l a r l y e n l i g h t e n i n g because i t showed d i r e c t l y the e x i s t e n c e of l i n e a g e . Two s e t s of r e  f l e c t i o n s are obtained when the X-ray beam i s i n c i d e n t on a l i n e a g e boundary. Since the e r r o r i n the d e t e r m i n a t i o n of the c r y s t a l - l o g r a p h i c o r i e n t a t i o n of a s i n g l e c r y s t a l i s * 1 0 , the o r i e n t a t i o n d i f f e r e n c e at a columnar g r a i n boundary may be found to w i t h i n -2°, and that of an equiaxed boundary, by i t s geometry, to w i t h i n -0.5°. Note that the e f f e c t of l i n e a g e on the m e l t i n g behaviour of the g r a i n boundaries i s not i n que s t i o n at t h i s time. 2.2. Experimental Procedure 2.2.1* Temperature I n d i c a t i o n A chromel-alumel thermocouple of 28 - gauge wire was cast i n t o a t i n "thermocouple block" of 99.9987$ Sn, s i m i l a r i n s i z e to the specimen. The j u n c t i o n was fused i n an oxygen-gas flame and annealed at 325°C f o r a minimum time of one hour. This temp erature was found to be c r i t i c a l f o r adequate temperature char a c t e r i s t i c s . Subsequent to annealing, 2 cm. of the end was coated with sodium s i l i c a t e to i n s u l a t e the bare wire from the t i n . The thermocouple block had to be r e c a s t a f t e r each t e s t , and the l i f e of the thermocouple i t s e l f was u s u a l l y t h r e e t e s t s . The specimen was wired to the thermocouple b l o c k . Contact between the two was e s t a b l i s h e d with minimum r e s t r i c t i o n to the movement of the upper c r y s t a l of the b i c r y s t a l should f a i l u r e occur at the boundary. 18 - 2.2.2. Melting Apparatus The experimental arrangement that was adopted is shown in Figure 6, Care was taken to suspend the specimen - thermocouple block symmetrically in the cavity and the same distance from the bottom each time. Failure to do this could result in an undetec table variation in the rate at which heat flows into the specimen from test to test. To potentiometer Aluminum stopper Thermocouple Heating element Alundum cement Four layers'of asbestos paper Thermocouple block Bicrystal sp ecimen Aluminum block Transits base plate >/////'/// Figure 6a. Schematic representation of the melting apparatus. Figure 6b. General view of the melting apparatus. 2 .2 .3 . Temperature Measurement A Pye Cambridge potentiometer and a Scalamp galvanometer were used to make the temperature measurements. The apparatus was kept at 190°C between tests to reduce the time of heat ing. After the specimen was i n s e r t e d , the power was increased i n small increments to obtain a constant heating r a t e . The temperature was measured every minute up to 2 2 5 ° C . In the range 225°C to 2 3 1 ° C , the potentiometer readings were s t i l l recorded every minute. However, in a d d i t i o n , the galvano meter was used as a d e f l e c t i o n instrument, with d e f l e c t i o n s being observed 30 seconds af ter potentiometer measurements. The l a t t e r was taken as a zero reference point for the d e f l e c t i o n s . Above 231°C only the galvanometer scale d e f l e c t i o n s were observed at 15 second i n t e r v a l s u n t i l f a i l u r e occurred. When 20' - the plateau was investigated to completion the weight was not allowed to f a l l far enough after f a i l u r e to remove the specimen from the cavity and thereby disturb i t s thermal state. Since this necessarily precluded v i s u a l examination the test was usually stopped immediately after separation of the b i c r y s t a l . The galvanometer scale d e f l e c t i o n was calibrated in y/V./mm. by observing the change i n d e f l e c t i o n when the potentio meter was altered by a d e f i n i t e amount during a period of steady d e f l e c t i o n . 2.2.4. Quality of the Measurements In order that the instant at which the boundary melts be accurately determined, i t was necessary to obtain a heating curve in which the r i s e was constant and f a i r l y steep, the trans i t i o n from r i s e to the plateau sharp, and the plateau f l a t . The heating rate was kept constant to within Q.05 C /min. for 4 or 5 minutes before the t r a n s i t i o n point was reached. No effect of a v a r i a t i o n from the value of 1.0 C /min. was i n  vestigated. The dependence of the time to boundary separation upon heating rate has been previously established 1. The t r a n s i t i o n from the r i s e to the plateau took place within 15 seconds. The plateau was constant within 0.02 C° over a period of approximately 15 minutes at which point the thermo couple block had usually melted completely. Frequently, no deviation from the f l a t portion whatever was detectable on the galvanometer scale. Another important consideration involved the v e r i f i c a t i o n of the i n i t i a l assumption that the thermocouple imbedded i n the block of t i n gave the true temperature of the specimen, and, Figure 7. Heating curves for the dual thermocouple-block assembly. - 22 thereby, of the boundary. Measurements were made on a system i n which the specimen had been r e p l a c e d by a second thermocouple bl o c k . Below the m e l t i n g p o i n t i t was p o s s i b l e to read the poten t i a l of each thermocouple every minute only. on nearing the p l a t e a u s w i t c h i n g back and f o r t h between the two couples d i d not d e f l e c t the galvanometer o f f s c a l e . D e f l e c t i o n s could then be recorded at i n t e r v a l s of 1.5 seconds, and, consequently f o r each couple, at i n t e r v a l s of 30 seconds. The m e l t i n g curves i n F i g u r e 7 show the p a r a l l e l behaviour e x h i b i t e d by the two thermo couple b l o c k s . This i n d i c a t e s that e i t h e r one may be used to measure the temperature of the other r e l a t i v e to the m e l t i n g p l a t e a u . Therefore, replacement of one by a specimen was j u s t i f i e d . U t i l i z i n g the galvanometer as a n u l l - i n d i c a t i n g instrument an experimental u n c e r t a i n t y i n p o t e n t i a l of IJJJ , and i n tempera ture of 0.02C° was p o s s i b l e . By o b s e r v i n g s c a l e d e f l e c t i o n s the u n c e r t a i n t y was reduced to 0.01C°. However, t h i s a p p l i e s o n l y to d e v i a t i o n s from an a b s o l u t e value since the d e f l e c t i o n s are based on a zero determined by n u l l - i n c i a t i o n . The experimental e r r o r i n the d e t e r m i n a t i o n of the time i n t e r v a l , t*, from t r a n s  i t i o n to boundary s e p a r a t i o n was considered to be 0.2 minutes, or l e s s than 15 seconds. 2.3. Observations c The f a i l u r e of a specimen was i n d i c a t e d by the f a l l i n g of the weight. Two modes of f a i l u r e were observed. One was a - 23 - r e s u l t o f s e p a r a t i o n a t t h e b o u n d a r y and t h e o t h e r , e x c e s s i v e m e l t i n g a t t h e s u p p o r t s . B o t h o c c u r r e d a f i n i t e t i m e i n t e r v a l , t , a f t e r t h e o n s e t o f g e n e r a l m e l t i n g as m a n i f e s t e d by t h e p l a t e a u i n t h e h e a t i n g c u r v e . At no t i m e was a d i f f e r e n c e d e t e c t e d between t h e b u l k m e l t i n g p o i n t and t h e t e m p e r a t u r e a t w h i c h b o u n d a r y s e p a r a t i o n t o o k p l a c e , w i t h i n t h e s t a t e d a c c u r a c y o f 0 . 0 2 C ° . From t h e a p p e a r a n c e o f t h o s e b i c r y s t a l s w h i c h s e p  a r a t e d a t t h e b o u n d a r y , i t was e v i d e n t t h a t l i t t l e m e l t i n g of t h e component c r y s t a l s had o c c u r r e d . The s u r f a c e o f s e p a r a t i o n , , at t h e b o u n d a r y of a c o l u m n a r b i c r y s t a l o f 99.9987$ Sn was smooth, s h i n y , and f l a t i n a p p e a r a n c e . T h i s was i n d e p e n d e n t o f s t r e s s , b o u n d a r y o r i e n t a t i o n , and t h e t y p e o f b o u n d a r y , t h a t i s , t i l t o r t w i s t . On o c c a s i o n , a few s u b - b o u n d a r i e s were v i s i b l e , r u n n i n g p a r a l l e l to what was o r i g i n a l l y t h e g r o w t h d i r e c t i o n , ( l i p ] , p a r a l l e l to t h e b o u n d a r y p l a n e . M i c r o s c o p i c e x a m i n a t i o n r e v e a l e d t h e p r e s e n c e , i n a few i n s t a n c e s , of v e r y l o c a l i z e d p o l y c r y s t a l l i n e r e g i o n s on t h e s u r f a c e . A d e c r e a s e i n t h e p u r i t y o f t h e t i n f r o m 99.9987$ t o 99.986$ r e s u l t e d i n a s i g n i f i c a n t change i n t h e c o n d i t i o n o f t h e s u r f a c e at w h i c h f a i l u r e t o o k p l a c e , namely, f r o m smooth to i r r e g u l a r . The i r r e g u l a r i t y c o n s i s t e d o f a f a m i l y of r i d g e s , r u n n i n g p a r a l l e l to t h e [lio] d i r e c t i o n . No d e p e n d e n c e o f t h e s u r f a c e s t r u c t u r e on t h e a p p l i e d s t r e s s or o r i e n t a t i o n d i f f e r e n c e was f o u n d . I n t h e c a s e o f e q u i a x e d b o u n d a r i e s , t h e s u r f a c e o f s e p a r a  t i o n , even f o r t h e e x t r a p u r e m a t e r i a l , was c o v e r e d w i t h s m a l l - 24 - n i p p l e s . They became more pronounced when the im p u r i t y content was increased from 0.0013$ to 0.014$, and resembled somewhat the decanted s o l i d - l i q u i d i n t e r f a c e shown i n F i g u r e 11. However, the sharp boundaries which d e l i n e a t e d the hexagonal c e l l s of a decanted specimen were absent from the surfa c e s of s e p a r a t i o n of a t e s t specimen. The e f f e c t of s t e s s , o r i e n t a t i o n d i f f e r e n c e , boundary o r i e n  t a t i o n , p u r i t y , and growth c o n d i t i o n s , on the m e l t i n g behaviour of equiaxed boundaries i s r e p o r t e d . One set of r e s u l t s on the e f f e c t of s t r e s s on the t values of columnar boundaries i s i n c l u d ed. 2.3.1. S t r e s s The s t r e s s that was app l i e d to the t e s t specimens ranged from 50 to 2000 gm./cm2. I t was b e l i e v e d that by the a p p l i c a t i o n of a s t r e s s i n t h i s range one could d i s p e l the p o s s i b i l i t y of p l a s t i c d e f o rmation. The c r i t i c a l shear s t r e s s f o r ^ 3-Sn, with s l i p plane (110) and s l i p d i r e c t i o n J O O I J i s quoted by B a r r e t t 2 5 as 13,000 gm./cm2. Consequently, a s t r e s s of 2000 gm./cm2. i s not n e a r l y h i g h enough to cause s l i p . For a s e r i e s of t e s t s at a constant s t r e s s l e v e l , 500 gm./cm2. was a p p l i e d . The e f f e c t of s t r e s s on the time, t , to boundary separa t i o n was i n v e s t i g a t e d i n both equiaxed and columnar boundaries. The l a t t e r served as a t i e between the r e s u l t s of e a r l i e r work on columnar boundaries, and t h i s work on equiaxed boundaries. - 25 - The observations in Table 2 were made on 45° columnar t i l t boundaries of 99.9987$ Sn. Table 2 Typ e; Columnar T i l t ; Size; 4 5 ° ; Purity: 99.9987$ Stress (gm./cm2;) t* (min.) 50 4.0 100 3.4 200 2.6 500 1.5 " 2.0 M 1.9 " 1.0 " 1.4 " 1.4 " 1.4 1000 0.9 n 1.2 2000 0.7 The mean t* for 500 gm./cm2. is 1.5 min. and repeated tests f e l l within 30 sec. of this value. Curve I in Figure 8 illustrates the nature of the variation of t with applied stress. The smoothness of the curve, and the closeness of the agreement with the previously determined results plotted in Curve II was con sidered sufficient justification for performing only one or two tests at the other stress levels. Curve II summarizes work1 on 45° columnar t i l t boundaries of 99.999$ Sn, but for a heating rate of 0.75 C°/min. instead of the 1.0 C°/min. utilized here. Tables 3, 4 and 5 l i s t the results of melting tests on 45° equiaxed t i l t (99.9987$ Sn), 4 1 ° equiaxed twist (99.9987$ Sn), and 41° equiaxed twist (99.986$ Sn) boundaries respectively. They are plotted in Curves I I I , IV and v . - 26- Figure 8„ The stress dependence of the time to boundary separation. I - 45° columnar t i l t boundary; purity 99.9987$ Sn II _ ^5° columnar t i l t boundary; purity 99'.999$ Sn (heating rate 0.75C°/min.) III - ^5° equiaxed t i l t boundary! purity 99.9987$ Sn TV „ kl° equiaxed twist boundarytpurity 99.9987$ Sn V - kl° equiaxed twist boundarytpurity 99.986$ Sn 27 Table 3 Type: Equiaxed T i l t ; Size: 45°; Purity: 99.9987$ Sn Stress (gm./cm.) t* (min.) 50 2.6 100 1.5 150 0.8 200 0.8 400 0.7 500 0.6 1000 0.2 2000 0.3 Table 4 Type: Equiaxed Twist; Size: 41°; Purity: 99.9987$ Sn Stress (gm./cm2.) 200 350 500 500 750 1050 1600 t* (min.) 10.5 8.3 7.0 6.1 6.2 3.7 3.4 Table 5 Type; Equiaxed Twist; Size: 41°; Pur i t y : 99.986$ Sn Stress (gm./cm2. ) t (min.) 350 500 750 1000 4.7 2.8 2.2 1.5 28 - 2.3.2. O r i e n t a t i o n D i f f e r e n c e T e s t s were conducted on equiaxed t i l t boundaries of 99. 9987$ Sn of o r i e n t a t i o n d i f f e r e n c e i n a range 8° to 29°, and at approximately 45°. The r e s u l t s of t e s t s on 23 specimens are ta b u l a t e d i n Table 6. A l l specimens which contained an equiaxed boundary of 12° or more separated at the boundary. Those of 11° or l e s s f a i l e d at the g r i p s due to gen e r a l m e l t i n g . On o c c a s i o n , a groove was observed at the 11° boundary upon removal of the b i c r y s t a l from the m e l t i n g apparatus a f t e r a g r i p f a i l u r e . Type: Equiaxed T i l t ; S i z e : V a r i a b l e ; P u r i t y : 99.9987$ Sn Table 6 O r i e n t a t i o n D i f f e r e n c e (d egr ees ) S t r e s s ( gm. / cm 2 . ) (min. ) 9.0 9.0 8.0 8.5 8.0 9.0 10.0 10.0 11.0 11.0 11.0 11.0 12.0 12.0 12.5 13.0 13.0 15.5 17.0 18.0 18.0 20.5 28.5 234 187 183 163 1610 1720 500 500 1180 958 1130 2000 2600 1040 500 500 ( 7 . 3 ) + (11*0) (14.4) (13.4) (0.5) (1.5) (14.4) (15.1) (13.2) (7.4) (8.3) (no r e a d i n g ) no r e a d i n g n 2.8 9.4 8.3 11.1 n 7.0 0.7 0.6 0.3 0.4 0.4 t» n + - Brackets i n d i c a t e absence of boundary s e p a r a t i o n . - 29 - Figure 9. Orientation difference dependence of the time to boundary- separation for (A) an equiaxed t i l t boundary. (B)' an equiaxed twist boundary. - 30 - When the p u r i t y was reduced to 99.986$ Sn, 2 out of 6 b i c r y s t a l s tested i n the range 9° to 10° f a i l e d by s e p a r a t i o n at the boundary (Table 7). The l e n g t h of time that a small-angled specimen remained on the me l t i n g p l a t e a u before s u f f i c i e n t l a t e n t heat had been su p p l i e d to cause a g r i p f a i l u r e was approximately 15 rain. T h i s i n t e r v a l was independent of the a p p l i e d s t r e s s , provided that the grooves f o r the g r i p p i n g wire were cut deeply enough (over 3 wire diameters) and f a r enough from the ,end of the specimen (about 3 mm.) f o r e f f e c t i v e g r i p p i n g . Table 7 Type: Equiaxed T i l t ; S i z e: V a r i a b l e ; P u r i t y ; 99.986$ Sn O r i e n t a t i o n S t r e s s t * D i f f e r e n c e (d egr ees ) (gm./em2.) (min.) 9.5 2230 (15.0) 9.0 1820 10.9 9.5 2090 (9.2) 9.0 1980 8.6 10.0 1090 10.7 9.5 500 15.8 Note that the preceding o b s e r v a t i o n s a l l r e f e r to equiaxed t i l t boundaries. Tests conducted on equiaxed t w i s t boundaries of o r i e n t a t i o n d i f f e r e n c e 15° to 63°, u s i n g 99.9987$ Sn y i e l d e d the r e s u l t s i n Table 8, shown p l o t t e d i n F i g u r e 9. 31 - Table 8 Type: Equiaxed Twist; S i z e : V a r i a b l e ; Pur i t y : 99.9987$ Sn Constant S t r e s s of 500 gm./cm^. Ori entat ion t * D i f f e r ence (min (d agrees ) 15.5 8.4 20.0 6.4 24.5 3.2 35. 5 0.8 41.0 6.1 38.0 1.2 43.0 2.3 45.5 0.7 43. 5 1.3 53.0 0.6 59.0 0.8 63.0 0.7 2.3.3. Boundary O r i e n t a t i o n In t h i s phase of the i n v e s t i g a t i o n the r e f e r e n c e angle 0 = 0 corresponded to a h y p o t h e t i c a l g r a i n boundary where the (001) planes were p a r a l l e l to the plane of the boundary. Thus the standard o r i e n t a t i o n of the seeds was chosen as (110) frloj i n s t e a d of (001) j l io j o r i g i n a l l y s p e c i f i e d i n S e c t i o n 2.1.2. This change 21 was introduced i n order to comply with Weinberg's c h o i c e of a & 8 8 0 i n z i n c b i c r y s t a l s such that the (0001) b a s a l planes were i n i t i a l l y p a r a l l e l to the boundary. Consequently, t e s t s were conducted on columnar t i l t boundaries of o r i e n t a t i o n d i f f e r e n c e i n the range 0° to 90° based on r o t a t i o n s from the (110) [ l ioj standard. The range 90° to 180° has been d e a l t with p r e v i o u s l y 1 using t i n of the same p u r i t y . The t r a n s i t i o n from boundary m e l t i n g to non-melting occurred at 168°. - 32 No boundary s e p a r a t i o n occurred at o r i e n t a t i o n d i f f e r e n c e s l e s s than 12° but d i d so f o r angles g r e a t e r than 13°. The values of t were not measured i n order to determine the p o s s i b l e e x i s t e n c e of an o r i e n t a t i o n d i f f e r e n c e dependence i n the range 13 0 1 to 25°. However, no d e t e c t a b l e dependence was found between 25° and 90°. 2.3.4. Growth Conditions P r e l i m i n a r y experiments showed no a p p r e c i a b l e d i f f e r e n c e i n the m e l t i n g behaviour of equiaxed and columnar boundaries. At t h i s time equiaxed b i c r y s t a l s were being grown i n a g r a p h i t e boat c o n t a i n i n g a g r a p h i t e base p l a t e , as were columnar b i  c r y s t a l s . I t was observed that the boundary t r a c e on the under s i d e of the equiaxed specimen was very i r r e g u l a r . • As a r e s u l t , the boundary no longer met the s p e c i f i c a t i o n of symmetry. In an attempt to produce a s t r a i g h t e r boundary the heat flow c o n d i t i o n s i n the boat were a l t e r e d by the s u b s t i t u t i o n of a pyrex base # p l a t e f o r the g r a p h i t e one. Subsequently measured values of t d i d not agree with those obtained o r i g i n a l l y , Deeantation ex periments were performed to determine a s u i t a b l e boat c o n f i g u r a  t i o n f o r the formation of the most i d e a l equiaxed boundary poss i b l e . This i s d i s c u s s e d i n S e c t i o n 2.4. Table 9 shows the r e s u l t s of m e l t i n g t e s t s on equiaxed specimens grown under the v a r i o u s stated c o n d i t i o n s . - 33 - Table 9 E f f e c t of Boat C o n f i g u r a t i o n s on the Time to Boundary S e p a r a t i o n Type; V a r i a b l e ; S i z e : 45°; P u r i t y : 99.9987$ Sn Type of Boundary Boat C o n f i g u r a t i o n t* (min. ) A. Columnar Graphite boat with 1.5 bottom; g r a p h i t e base p l a t e . B. Equiaxed As above. 1.5 £. Equiaxed Graphite boat with 0.7 bottom; pyrex base p l a t e . P_. Equiaxed Graphite boat with 0.8 bottom removed; pyrex base p l a t e ; g l a s s s i d e - w a l l s . A v a r i a t i o n of the r a t e of growth from 0.5 to 5 mm./min. had no d e t e c t a b l e e f f e c t on the mel t i n g behaviour i n 99.9987$ Sn. Growth d i f f i c u l t i e s precluded the use of a higher growth r a t e than 5 mm./min. 2.3.5. Pur i t y Only one s e r i e s of t e s t s was performed to i n v e s t i g a t e the e f f e c t of p u r i t y on me l t i n g behaviour. Curves IV and v of F i g u r e 8 show the r e l a t i v e e f f e c t of a small decrease i n p u r i t y of the m a t e r i a l used, from 99.9987$ to 99.986$, as re p o r t e d i n Sec t i o n 2.3.1. No d e p r e s s i o n of the me l t i n g point was de t e c t e d at t h i s lower p u r i t y . - 34 - 2.4. Decantation Experiments 2.4.1. Purpose j From the o b s e r v a t i o n s , as c i t e d i n S e c t i o n 2.3.4., i t was c l e a r that the c o n d i t i o n s i n i t i a l l y b e l i e v e d s u i t a b l e f o r the growth of an i d e a l equiaxed boundary led to t values which agreed very w e l l with those f o r columnar boundaries. To account f o r t h i s s i m i l a r i t y i n behaviour, i n view of the d i f f e r e n t r e s u l t s obtained under subsequent c o n d i t i o n s of growth, d e c a n t a t i o n s were performed at v a r i o u s stages of s o l i d i f i c a t i o n f o r s e v e r a l boat conf i g u r a t i o n s . The m i c r o s t r u c t u r e and macroscopic form of the s o l i d - l i q u i d i n t e r f a c e s were examined i n the l i g h t of the a p p l i c a b i l i t y of the term "equiaxed". 2.4.2. Procedure Seeding and s o l i f i c a t i o n of the melt was c a r r i e d out i n the manner s p e c i f i e d p r e v i o u s l y . The g r a p h i t e i n s e r t s and seeds were secured by wire wound around the boat. F i v e boat c o n f i g u r a  t i o n s to give f i v e d i f f e r e n t heat flow c o n d i t i o n s were s t u d i e d : ( i ) g r a p h i t e base p l a t e i n a g r a p h i t e boat, ( i i ) pyrex base p l a t e i n a g r a p h i t e boat, ( i i i ) pyrex base p l a t e i n a bottomless g r a p h i t e boat, ( i v ) g l a s s s i d e - w a l l s with ( i i ) . (v) g l a s s s i d e - w a l l s w i t h ( i i i ) . Growth r a t e s f e l l i n the range of 1 to 5 mm./min. 35 - The molten t i n was poured o f f by t i g h t l y clamping the boat at one end, removing the fu r n a c e , and t i p p i n g the whole boat and support assembly. The time l a g between the removal of the furnace and dumping d i d not exceed 5 seconds. Dec a n t a t i o n was performed at a time when i t was thought that the s o l i d - l i q u i d i n t e r f a c e s were as c l o s e together as p o s s i b l e without a c t u a l l y coming i n t o c ontact, and, a l t e r n a t i v e l y , when the i n t e r f a c e s were 1 to 2 cm. apart. The l a t t e r was done i n order to show the shape of the advancing i n t e r f a c e s at an e a r l i e r stage of growth. The two seeds had been r o t a t e d f o r the fo r m a t i o n of a 28° symmetrical t i l t boundary as di s c u s s e d i n S e c t i o n 2.1.4. The g l a s s w a l l s were made by c u t t i n g a microscope s l i d e i n ha l f l o n g i t u d i n a l l y . These and the pyrex base p l a t e were coated with a f i n e suspension of c o l l o i d a l g r a p h i t e i n water to prevent the s o l i d i f i e d t i n b i c r y s t a l from adhering to them. 2.4.3. R e s u l t s The e f f e c t of each of the f i v e c o n f i g u r a t i o n s i s d i s c u s s e d i n the order i n which they were i n t r o d u c e d . ( i ) S o l i d i f i c a t i o n occurred p r e f e r e n t i a l l y adjacent to the g r a p h i t e base p l a t e . With the s o l i d - l i q u i d i n t e r f a c e s s t i l l 13 mm. apart at the top, a t h i c k n e s s of 1 mm, of t i n j o i n e d the seeds at the bottom. The growth r a t e was 4 mm./min. A r e d u c t i o n of the r a t e of advancement of the i n t e r f a c e s to 1 mm./min. had no e f f e c t on t h i s method of soli d i f i c a t i o n . (The sketches i n each s u b - s e c t i o n i l l u s t r a t e the manner i n which growth proceeded.) - 36 S o l i d 1 i i Liqti id i i i S o l i d s 1 — ! • — ' • S Top View Side View The m i c r o s t r u c t u r e c o n s i s t e d of i r r e g u l a r l y shaped hexa gonal c e l l s over the whole decanted i n t e r f a c e . Upon complete s o l i d i f i c a t i o n , the boundary t r a c e was s t r a i g h t at the top su r f a c e but crooked at the bottom. I t was smooth m i c r o s c o p i c a l l y . ( i i ) When the g r a p h i t e base p l a t e was r e p l a c e d w i t h a pyrex g l a s s one, a p r e f e r e n t i a l heat flow was introduced along the s i d e s of the boat because the thermal c o n d u c t i v i t y of g r a p h i t e i s r o u g h l y s i x times that of pyrex. When the i n t e r f a c e s ad vanced at the r a t e of 1 mm./min. they were s l i g h t l y convex i n t o the l i q u i d . I - 37 - The photomicrographs i n F i g u r e 10 and 11 show the c e l l u l a r s u b s t r u c t u r e that i s t y p i c a l of the s o l i d - l i q u i d i n t e r f a c e s r e v e a l e d by decanting specimens grown at r a t e s i n the s p e c i f i e d range of 1 to 5 mm./min. I n c r e a s i n g the growth r a t e suppressed the p r o j e c t i o n s at the c e l l c e n t r e s , but d i d not d e s t r o y the hexa- g o n a l i t y of the c e l l s although i t reduced them i n s i z e . The r e g u l a r i t y of the c e l l geometry decreased i n t r a v e r s i n g the i n t e r  f a c e from the bottom to the top s u r f a c e of the specimen. Bpundary t r a c e s were s t r a i g h t but saw-toothed. ( i i i ) The removal of the g r a p h i t e bottom decreased the r e l a t i v e heat flow through the pyrex base p l a t e , and r e s u l t e d i n the f o l l o w i n g s u r f a c e contours. A c e l l u l a r s u b s t r u c t u r e was again observed at the s o l i d - l i q u i d i n t e r f a c e . ( i v ) The i n s e r t i o n of g l a s s w a l l s into the g r a p h i t e boat with a pyr ex-graphit e bottom decreased the l a t e r a l heat flow through the edges but s t i l l y i e l d e d s o l i d - l i q u i d i n t e r f a c e s which had a c o n s i d e r a b l e convex curvature towards the l i q u i d . F i g u r e 11. D e c a n t e d i n t e r f a c e of a Sn c r y s t a l showing n i p p l e s p r o j e c t i n g xrom n e z a g o n a l c e l l s . Growth r a t e : 2 mm./min. U n e t c h e d . 100 x 39 - / V  s \ L I s The v e r t i c a l s l o p e and m i c r o s t r u c t u r e remained unchanged from ( i i ) . (v) R e c a l l i n g t h a t the b o t t o m l e s s boat w i t h a g l a s s base p l a t e l e d to p r e f e r e n t i a l s o l i d i f i c a t i o n from t h e edges of the specimen towards t h e c e n t r e , n e a r l y p l a n a r i n t e r f a c e s were ach i e v e d by i n t r o d u c i n g g l a s s s i d e s to t h i s system i n o r d e r to reduce the r e l a t i v e l a t e r a l heat f l o w . s L S S J L s The boundary t r a c e s were s t i l l saw-toothed on t h e m i c r o  s c o p i c s c a l e , but appeared s t r a i g h t to the eye. Hexagonal c e l l s were observed on the decanted s u r f a c e . 40 - 2.4.4. D i s c u s s i o n A p r i s m a t i c c e l l u l a r s u b s t r u c t u r e was f i r s t r e p o r t e d by R u t t e r - and Chalmers a t t h e decanted i n t e r f a c e s of t i n c r y s t a l s f o r growth r a t e s of 1 mm./min. and g r e a t e r . There i s a c l o s e agreement between the m i c r o s t r u c t u r e t h a t they observed and those found i n t h i s work. I t i s i m p o r t a n t t h a t t h e s o l i d - l i q u i d i n t e r f a c e s which are to meet at the equiaxed boundary be as p a r a l l e l as p o s s i b l e . O t h erwise, the term " e q u i a x e d " does not a p p l y because s o l i d i f i c a  t i o n g i v e s a boundary t h a t i s , i n f a c t , grown normal t o t h e ad v a n c i n g i n t e r f a c e , t e c h n i c a l l y a "columnar" boundary. E x p e r i  mental r e s u l t s bear out t h e columnar n a t u r e o f a boundary i n a b i c r y s t a l grown under c o n d i t i o n ( i ) , the f a r t h e s t removed f r o m i d e a l i t y . C o n s equently, a b o t t o m l e s s g r a p h i t e boat, pyrex base p l a t e and g l a s s s i d e - w a l l s were u t i l i z e d to grow the equiaxed b i c r y s t a l s whose behaviour i s to be compared w i t h t h a t of columnar bound ar i es, - 41 - 3. DISCUSSION AND CONCLUSIONS 3.1, Summary of Experimental Observations (1) The t r a n s i t i o n from the r i s e to the p l a t e a u of the heating curve took place w i t h i n a period of 15 seconds. (2) The m e l t i n g p l a t e a u was constant to w i t h i n 0.020°, t h a t i s , a m e l t i n g p o i n t d e p r e s s i o n was d e t e c t a b l e to w i t h i n 0.02C 0. (3) The e r r o r i n the measurement of o r i e n t a t i o n d i f f e r e n c e s was determined to be * 1° f o r columnar boundaries, and - 0.5° f o r equiaxed boundaries. (4) Boundary s e p a r a t i o n occurred a f i n i t e time i n t e r v a l , t * , a f t e r the onset of general m e l t i n g . (5) Boundary s e p a r a t i o n was not accompanied by a p p r e c i a b l e m e l t i n g of the component c r y s t a l s , (6) The s u r f a c e s of s e p a r a t i o n at a columnar boundary of 99.9987$ Sn were smooth, shiny, and f l a t , with the exception of some very l o c a l i z e d p o l y c r y s t a l l i n e r e g i o n s . A decrease of p u r i t y to 99.986$ r e s u l t e d i n the presence of r i d g e s running p a r a l l e l to the growth d i r e c t i o n . (7) N i p p l e s covered the separated s u r f a c e s of equiaxed boun d a r i e s , becoming more pronounced with increased i m p u r i t y content. (8) Generally, the s u r f a c e s t r u c t u r e was independent of s t r e s s , o r i e n t a t i o n d i f f e r e n c e , and type of boundary ( t w i s t or t i l t ) . - 42 - 4 , (9) The t values decreased with an i n c r e a s e i n a p p l i e d s t r e s s fo r a l l boundaries. (10) At a constant s t r e s s l e v e l , the time to boundary separa t i o n i n c reased i n the f o l l o w i n g order, a c c o r d i n g the c h a r a c t e r  i s t i c s of the boundary: Type Equiaxed t i l t Columnar t i l t Columnar t i l t Equiaxed t w i s t Equiaxed t w i s t Si z e 45° 45° 45° 41° 41° P u r i t y 99.9987$ Sn. 99.999$ Sn. (Heating r a t e of 0.75 C°/min. ) 99.9987$ Sn. 99.986$ Sn. 99.9987$ Sn. Refer to F i g u r e 8, page 26. (11) The t r a n s i t i o n from non-separation to boundary s e p a r a t i o n occurred between 11° and 12° f o r both columnar and equiaxed t i l t boundaries of 99.9987$ Sn m a t e r i a l . (12) A decrease i n p u r i t y to 99. to somewhere between 9° and 10°. Sn reduced the t r a n s i t i o n (13) A r a p i d , approximately l i n e a r , decrease i n t was observed from 12° to 17° f o r equiaxed t i l t boundaries. (14) A s i g n i f i c a n t o r i e n t a t i o n d i f f e r e n c e dependence of t* was evident i n l a r g e - a n g l e equiaxed t w i s t boundaries, with a maxi mum t* value o c c u r r i n g at 41°. The value of t* at that p o i n t was approximately ten times that f o r t i l t boundaries under the - 43 same s t r e s s , and of the same o r i e n t a t i o n d i f f e r e n c e . Refer to F i g u r e 9. (15) The t r a n s i t i o n from non-separation to s e p a r a t i o n occurred at ©° and (180°-©)° i n columnar t i l t boundaries, that i s , between 11° and 12°, and 168° and 169°. (16) A g r a p h i t e boat with bottom removed, pyrex base p l a t e and g l a s s s i d e - w a l l s i n s e r t e d , produced the most i d e a l type of equiaxed boundary. (17) A p r i s m a t i c c e l l u l a r s u b s t r u c t u r e was observed at the de canted i n t e r f a c e s of an equiaxed b i c r y s t a l . 3.2. General D i s c u s s i o n I t i s f i r s t n ecessary to e s t a b l i s h whether the occurrence of boundary s e p a r a t i o n i s due to me l t i n g , or to f r a c t u r e , of the boundary r e g i o n . The o b s e r v a t i o n s of Weinberg and Teghtsoonian i n d i c a t e t h at melting was the cause of f a i l u r e at the boundary. They showed t h a t : ( i ) the v i s u a l appearance of the separated i n t e r f a c e s was independent of the a p p l i e d s t r e s s , ( i i ) boundary s e p a r a t i o n occurred at the b u l k - m e l t i n g p o i n t at some c o n s i d e r a b l e time a f t e r the onset of gene r a l m e l t i n g , ( i i i ) specimens of t i n with added i m p u r i t y e x h i b i t e d a melt i n g p o i n t d e p r e s s i o n such that s e p a r a t i o n occurred at a temperature between the solidus and l i q u i d u s tempera tur e s according to the phase diagram of the system. 44 The f i r s t two observations were confirmed. In addition, localized polycrystalline areas were observed on the surfaces of some of the columnar bicrystals exposed by separation during a test. Although such regions are abundant on the exposed boundary surfaces of equiaxed bicrystals they are attributable to the existence of an internal cellular substructure, parallel to the growth direction, that i s , normal to the surface. However, the presence of more than one grain at the surface of a columnar boundary seems to have no explanation other than the rapid hetero geneous solidification of a molten layer at the surface. It now remains to determine the cause of the preferential melting at a grain boundary. Preferential melting w i l l occur in a region whose energy relative to the rest of the l a t t i c e has been changed. The energy difference is a result of either atomic disorder due to a discontinuity in the periodicity of the lattice, or to a segregation of impurites to some region in the l a t t i c e . As i t happens, a grain boundary represents just such a region, namely, having some degree of disorder, and also, at which impur ity atoms tend to concentrate. For this reason, i t is an in teresting problem to try to differentiate between the two effects. Note that a melting point depression was not observed, merely a preference for melting. With this fundamental problem in mind, the effects of stress, orientation difference, boundary orientation, growth conditions, and purity are discussed in turn. - 45 3.3. S t r e s s A s t r e s s was a p p l i e d to the t e s t specimens to f u r t h e r i n c r e a s e the absolute energy of the boundary. The s t r a i n energy thus introduced i n c r e a s e s as the square of the a p p l i e d s t r e s s . S u f f i c i e n t s t r a i n energy i s not added to l e a d to a measureable m e l t i n g - p o i n t d e p r e s s i o n , w i t h i n the experimental accuracy of 0.02 0° . I t i s the presence of d i s o r d e r that i n i t i a l l y promotes the p r e f e r e n t i a l m e l t i n g but the a p p l i c a t i o n of a s t r e s s enhances i t a c o n t r o l l e d amount. Consequently, the shape of the s t r e s s - t * curves r o u g h l y f o l l o w a i i n v e r s e square form. That is,, the gre a t e r i s the a p p l i e d s t r e s s , the l e s s time i t w i l l take to melt the boundary. 3.4. O r i e n t a t i o n D i f f e r e n c e A c r i t i c a l o r i e n t a t i o n d i f f e r e n c e &c i s seen to e x i s t below which no p r e f e r e n t i a l m e l t i n g occurs at a boundary, and above which boundary m e l t i n g i s p r e v a l e n t . T h i s e c i s the same (between 11° and 12°) f o r columnar and equiaxed boundaries of approximately the same p u r i t y (99.996$ Sn and 99.9987$ Sn r e - 2 7 s p e c t i v e l y ) . Read and Shockley's boundary energy equation f o r t i n leads to a maximum at 12° corresponding f a v o u r a b l y with 9 C. Let us assume t h a t the columnar symmetrical t i l t boundary may be represented by an a r r a y of edge d i s l o c a t i o n s which become more numerous as the o r i e n t a t i o n d i f f e r e n c e i n c r e a s e s . Presumably then, the boundary energy, as governed by the d i s l o c a t i o n content of a small-angle boundary, i s s u f f i c i e n t at 0 C to induce pre f e r e n t i a l boundary m e l t i n g . Once t h i s c r i t i c a l energy i s exceeded, the t r a n s i t i o n from non-melting to m e l t i n g i s sudden. 46 As 9 i n c r e a s e s from 9 to 16°, a boundary energy i n c r e a s e i s c f u r t h e r manifested by a lowering of t * v a l u e s . At 16° the over l a p of the d i s l o c a t i o n cores, about f o u r atomic diameters apart, i s so s e r i o u s t h a t the r e s u l t i s a l o s s of i d e n t i t y of i n d i v i d u a l d i s l o c a t i o n s . The values of t* remain constant from 16° to 45° so that l i t t l e may be said about the nature of the t i l t boundary s t r u c t u r e above 16°. The above d i s c u s s i o n d e a l s o n l y with atomic d i s o r d e r . At t h i s stage, an e q u a l l y s a t i s f a c t o r y e x p l a n a t i o n l i e s i n the pres ence of f o r e i g n atoms at the boundary, i f the i m p u r i t y c o n c e n t r a  t i o n i s d i r e c t l y r e l a t e d to the boundary o r i e n t a t i o n . Curves I and I I I i n F i g u r e 8 i n d i c a t e a d i f f e r e n c e i n melt ing behaviour between l a r g e - a n g l e (45°) boundaries of the columnar and equiaxed t i l t o r i e n t a t i o n . The c o n s i s t e n t l y lower values f o r the equiaxed t i l t boundaries may be a t t r i b u t e d to the presence of the impurites b u i l t up at the boundary d u r i n g growth. T h i s i s d i s c u s s e d i n Appendix I. The e q u i l i b r i u m s o l u t e c o n c e n t r a t i o n would be the same f o r both types of boundary provided that t h e i r s t r u c t u r e s were i d e n t i c a l . The method of growth of an equiaxed b i c r y s t a l nec e s s a r i l y f o r c e s an excess amount of impurites to the boundary r e g i o n due to a z o n e - r e f i n i n g e f f e c t . Such a n o n - e q u i l i b r i u m c o n c e n t r a t i o n does not e x i s t at a columnar boundary because i t i s grown along with the bounding c r y s t a l s . However, there i s l i t t l e reason to b e l i e v e that t h i s c o n c e n t r a t i o n of i m p u r i t e s at an equiaxed boundary i n t i n decreases a p p r e c i a b l y i n the course of the time allowed f o r s o l i d s t a t e d i f f u s i o n . Each of - 47 the t e s t specimens remains at a temperature range of 220°C to 232°C f o r a maximum of one hour. Approximate c a l c u l a t i o n s i n Appendix I I show that the amount of Pb, the p r i n c i p a l i m p u r i t y , d i f f u s i n g away from the boundary i s n e g l i g i b l e , even a f t e r 100 hours annealing Just below the m e l t i n g p o i n t . The s i g n i f i c a n c e of the above i s that, f o r a given i n i t i a l p u r i t y of t i n , the impurity content of the boundary i s constant from specimen to specimen, as c l o s e l y as can be c o n t r o l l e d by the growth c o n d i t i o n s . Consequently, the o n l y v a r i a b l e i s o r i e n t a  t i o n d i f f e r e n c e , that i s , atomic s t r u c t u r e . There i s some qu e s t i o n as to whether atomic s t r u c t u r e i s i n f a c t r e p r o d u c i b l e with o r i e n  t a t i o n d i f f e r e n c e once a d i s l o c a t i o n a r r a y no longer d e s c r i b e s the boundary. However, si n c e the t* values remain constant f o r 9 constant, the s t r u c t u r e of a l a r g e - a n g l e t i l t or t w i s t boundary may be considered to be r e p r o d u c i b l e , whatever i t s s t r u c t u r e may be. I t i s concluded that v a r i a t i o n s of m e l t i n g behaviour with v a r i a t i o n s of o r i e n t a t i o n d i f f e r e n c e are a t t r i b u t a b l e to v a r i a  t i o n s of boundary geometry. The d i f f e r e n c e i n t * values i s not great from columnar to equiaxed boundaries. I t i s then not s u r p r i s i n g that the t r a n s  i t i o n from non-melting to m e l t i n g was the same f o r both. The value of t* i s more s e n s i t i v e to changes i n p u r i t y and s t r e s s than the a c t u a l t r a n s i t i o n . For example, a v a r i a t i o n of s t r e s s from 50 to 2000 gm/cm, does not change the t r a n s i t i o n , but a l t e r s the t * c o n s i d e r a b l y . The o n l y evidence of the presence of an excess amount of impurites at an equiaxed boundary as f a r as the t r a n s  i t i o n was concerned was the groove at an 11° boundary t r a c e a f t e r g r i p f a i l u r e . 48 The most i n t e r e s t i n g , and unexpected, r e s u l t of the i n v e s t i g a t i o n was the o r i e n t a t i o n d i f f e r e n c e dependence of the m e l t i n g behaviour of an equiaxed t w i s t boundary. I t was by a c c i d e n t that a 41° boundary was t e s t e d i n the study of l a r g e - angle behaviour. Previous i n v e s t i g a t o r s concluded that l a r g e - angle columnar t w i s t boundaries behave l i k e t i l t boundaries. Their t e s t s i n cluded o n l y 45° boundaries, whereas the peak of the curve i n F i g u r e 9 i s sharp at 41° and t h e r e f o r e easy to miss. I t i s b e l i e v e d that t h i s dependence i s an inherent s t r u c t u r a l prop e r t y of the t w i s t boundary i n t i n and not of i t s equiaxed nature. The v a r i a t i o n of t* with © i s p r e d i c t a b l e from a study of the c r y s t a l l o g r a p h y of the system made i n Appendix I I I . The degree of mismatch, as determined from the c o i n c i d e n c e p l o t s i n Appendix I I I ( F i g u r e 13 to 16) i s shown to vary with o r i e n t a t i o n d i f f e r e n c e i n a s i m i l a r manner to that observed ex p e r i m e n t a l l y . In f a c t , a minimum mismatch i s found, t h e o r e t i c a l l y , at 41°, at the exact o r i e n t a t i o n d i f f e r e n c e where the experimental peak occurred i n F i g u r e 9. A decrease i n the d i s o r d e r r e s u l t s i n a decrease i n boundary energy, and consequently, i n a l o n g e r time i n t e r v a l , t* , to boundary m e l t i n g . The t* value at 41° i s approximately ten times that at 46°, and the measured mismatch at 41° i s o n e - f i f t h that at 46°. The agreement i s considered s u f f i c i e n t l y c l o s e to j u s t i f y the method of a n a l y s i s without implying that t h i s method of e v a l u a t i n g the d i s o r d e r i s unique. - 49 3 * 5 * Boundary O r i e n t a t i o n Since a dependence of m e l t i n g behaviour on boundary o r i e n t a  t i o n was found i n z i n c , a close-packed hexagonal metal with c/a • 1.86, i t was thought that t i n might show a s i m i l a r tendency. The l a t t e r i s t e t r a g o n a l at room temperature up to i t s m e l t i n g p o i n t , with a = b and c/a - 0.55. Contrary to expe c t a t i o n s the r e s u l t s i n d i c a t e that the t r a n s i t i o n from non-melting to m e l t i n g occurred at © and (180-©)°, namely, about 12° and 168" . T h e r e f o r e one may conclude that the atomic d i s o r d e r i s not d e t e c t a b l y d i f f e r e n t at these two boundary angles, and that the m e l t i n g behaviour i s not a f u n c t i o n of the boundary o r i e n t a t i o n i n t i n . 3.6. growth Con d i t i o n s Refer to S e c t i o n 2.4.4. f o r a d i s c u s s i o n on the e f f e c t of boat c o n f i g u r a t i o n on m e l t i n g behaviour. From Appendix I i t i s evident that the growth r a t e s u t i l i z e d to grow a l l of the equiaxed t e s t specimens, that i s , 0.5 to 5 mm./min., l e d to a p p r e c i a b l e s e g r e g a t i o n at the boundary r e g i o n . Not u n t i l a r a t e of approximately 15 mm./min. i s reached would the s o l u t e c o n c e n t r a t i o n at the boundary approach the mean c o n c e n t r a t i o n C Q, exc l u d i n g any tendency f o r e q u i l i b r i u m g r a i n boundary s e g r e g a t i o n . D i f f i c u l t i e s i n producing s a t i s f a c t o r y b i c r y s t a l s i n t e r f e r e d with i n c r e a s i n g the growth r a t e beyond 5 mm./min. 3.7. P u r i t y I t i s to be expected that the c o n c e n t r a t i o n of i m p u r i t i e s at a boundary i n 99.986$ Sn would be more than i n 99.9987$ Sn. - 50 As a consequence, the melting-point of the m a t e r i a l i n the g r a i n boundary w i l l be lowered, according to the phase diagram, by an amount depending on the concentration of the i m p u r i t y . The con c e n t r a t i o n was at no time l a r g e enough to produce a d e t e c t a b l e melting point depression. Nevertheless, the presence of impur i t i e s was manifested by a lowering of the t * values and of the t r a n s i t i o n from non-melting to m e l t i n g . 51 - 4. SUMMARY The fo l lowing are the main conclusions that have been r eached. ( i ) Equiaxed boundaries do not d i f f e r in s t ructure from columnar boundaries. The d i f f e r e n c e in t h e i r behaviour i s due to a presence of impurites b u i l t up during growth as a r e s u l t of a z o n e - r e f i n i n g e f f e c t . ( i i ) The v a r i a t i o n of the melting behaviour of a grain boundary with a v a r i a t i o n i n o r i e n t a t i o n d i f f e r e n c e i s p r i m a r i l y due to a change in the atomic structure of the boundary, with solute atoms being of secondary importance. ( i i i ) Large-angle twist boundaries i n t i n have some degree of order, unl ike t i l t boundaries. ( iv) Boundary melting is established as a measureable i n t r i n s i c property of a boundary, j u s t i f y i n g i t s use to study boundary s t r u c t u r e . 52 - 5. RECOMMENDATIONS FOR FUTURE INVESTIGATION There i s an absence of data on the m e l t i n g behaviour of l a r g e - a n g l e columnar t w i s t boundaries. I t i s suggested that boundary m e l t i n g t e s t s be made, p a r t i c u l a r l y on 41° boundaries, i n order to confirm the f a c t that the o r i e n t a t i o n d i f f e r e n c e dependence i s an inherent p r o p e r t y of a t w i s t boundary and not due to i t s equiaxed nature. I t would be r e v e a l i n g to i n v e s t i g a t e the whole range of 9, that i s , beyond 53°. There i s a suspected t h e o r e t i c a l peak at 81°, but was not confirmed e x p e r i m e n t a l l y . S i n c e the r o l e of impurities n e c e s s a r i l y enters the p i c t u r e , an i n v e s t i g a t i o n of seg r e g a t i o n i n columnar and equiaxed boun d a r i e s of va r y i n g o r i e n t a t i o n d i f f e r e n c e using r a d i o - a c t i v e t r a c e r s would be of c o n s i d e r a b l e i n t e r e s t . 53 - APPENDIX I Impurity Segregation to an Equiaxed Boundary One may c a l c u l a t e the e f f e c t of any growth r a t e on the d i s t r i b u t i o n of the p r i n c i p a l i m p u r i t y Pb i n Sn by u s i n g the e q u a t i o n 2 8 which d e s c r i b e s s e g r e g a t i o n caused hy normal f r e e z i n g : C = k C 0 (1 - g ) k " 1 where C » c o n c e n t r a t i o n i n the s o l i d at the p o i n t where a f r a c t i o n g of the o r i g i n a l l i q u i d has f r o z e n . C Q » mean c o n e n t r a t i o n . k = e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t . The e q u i l i b r i u m d i s t r i b u t i o n c o e f f i c i e n t , k Q , i s d e f i n e d as the r a t i o of the s o l u t e c o n c e n t r a t i o n i n the s o l i d to the s o l u t e c o n c e n t r a t i o n i n the l i q u i d i n e q u i l i b r i u m with the s o l i d . Assume t h a t k 0 i s constant and t h e r e f o r e calculated from the s o l i d s o l u b i l i t y of Pb i n Sn , 2.5 weight per cent, and the e u t e c t i c composition 38.1 weight per cent. Then k Q - 2 * 5 , 0.07 0 38.1 The above equation holds, t h e o r e t i c a l l y , f o r a constant k , and constant d e n s i t y on f r e e z i n g . Since i t i s i m p o s s i b l e f o r k to remain unchanged over the whole range of g , the equation i s o n l y an approximation at best, p a r t i c u l a r l y above g • 0.9 . The e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t k may be found from: - 54 *- r k 0 + (1 - k 0 ) e - t 4 / D where f • growth r a t e , cm../sec. & • t h i c k n e s s of d i f f u s i o n l a y e r at the s o l i d - l i q u i d i n t e r f a c e . D • d i f f u s i o n c o e f f i c i e n t of the l i q u i d . Taking of the order 1 0 2, P f a n n 3 0 shows a p l o t of the above equation f o r s e v e r a l values of k Q . At a growth r a t e of zero cm./sec, k » k Q . I n t e r p o l a t e to f i n d any r e q u i r e d k , given k 0 and f . Table 10 Values of the E f f e c t i v e D i s t r i b u t i o n C o e f f i c i e n t  Corresponding to the Given Growth Rate. f . f (cm./sec.) f (mm./min.) k 0.003 1.8 0.1 0.010 6.0 0.2 0.028 14.8 0.6 The values of C/ C 0 are c a l c u l a t e d f o r each of these three e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t s . The data are p l o t t e d In F i g u r e 12 f o r g ra n g i n g from 0.6 to 0.99. J * 55 - Table 11 R e l a t i v e Impurity C o n c e n t r a t i o n C/C 0 Corresponding to the Given Value of the E f f e c t i v e D i s t r i b u t i o n C o e f f i c i e n t . g C/C 0 (k • 0.1) C/C 0 (k - 0.2) C/C 0 (k » 0.6 0.S28 0.416 0.865 0.7 0.296 0.523 0.971 0.8 0.426 0.724 1.143 0.9 0. 794 1.26 1.507 0.95 1.496 2.20 1.986 0.96 1.811 2.62 2.173 0. 97 2. 350 3.30 2.438 0.96 3.381 5.76 2.871 0.99 6.310 7.94 3.784 Figure 12. Curves for normal freezing. - 57 APPENDIX I I D i f f u s i o n of Impurity from an Equiaxed Boundary Consider the g r a i n boundary as an i n f i n i t e plane at which a t o t a l amount M of s o l u t e i s de p o s i t e d at time t = 0. A f t e r a time t , and at a d i s t a n c e x from the boundary, the c o n c e n t r a t i o n i s given as M -x 2/Dt C « 2 ( t t D t ) 1 / 2 The c o n c e n t r a t i o n at the boundary a f t e r a time t i s , of course, j u s t „ „ M 2 (TTDt) 1/ 2 At time t = 0 , _C = 0 i f x > 0, and at x - 0 , _C i s M. M i n f i n i t e l y l a r g e . M i s the t o t a l amount of d i f f u s i n g m a t e r i a l , and C i s the c o n c e n t r a t i o n of i m p u r i t y per amount of s o l v e n t . In the i n f i n i t e boundary plane there i s assumed to be no s o l v e n t at t = 0, which accounts f o r the value of C/M. This s o l u t i o n i s obtained from the d i f f u s i o n equation by an analogy to the K e l v i n heat-source a f t e r a p p l y i n g the given i n i t i a l and boundary c o n d i t i o n s . The s e l f - d i f f u s i o n c o e f f i c i e n t f o r S n 3 0 p e r p e n d i c u l a r to the c - a x i s (DjJ i s 3.7 x 10-8 e" 5900/RT c m 2 . / s e c . . 58 - and p a r a l l e l to the c - a x i s (Dj| ) i s l o -r ir>-5 a-10,500/HT o /„ „ 1.3 x 10 e ' cm ./sec. Since d i f f u s i o n away from the boundary must proceed, r e l a t i v e l y , p e r p e n d i c u l a r to the c - a x i s , Dj_ i s used. i n a d d i t i o n , Dj. i s b e l i e v e d to be of the c o r r e c t order of magnitude f o r the d i f f u s i o n of Pb i n Sn. A specimen remains at temperature approximately one hour before the completion of a t e s t . Therefore, take t 3600 seconds and x • 0. At 227°C, Dj, • 1.0 x 1 0 ~ 1 0 c m . 2 / s e c , C » 470. In M a d d i t i o n , the C/M values a f t e r 25, 50, and 100 hours are g i v e n i n Table 12. Table 12 C/M For Given Annealing Times Time (hours) C/M 1 470 25 94 50 60 100 47 The l a r g e values of C / M i n d i c a t e that the r e l a t i v e con c e n t r a t i o n of the i m p u r i t y Pb, at the boundary, even a f t e r 100 hours of annealing, i s very high. 59 - APPENDIX I I I Coincidence P l o t s The s t r u c t u r e of t i n at room temperature and above c o n s i s t s of two interwoven body-centered t e t r a g o n a l l a t t i c e s . In f a c t , a u n i t c e l l could be thought of as c o n t a i n i n g a body-centering atom, (1/2, 1/2, 1/2), and the f o l l o w i n g atoms i n the f a c e s : (1/2. 0, 1 / 4 ) -and (0, 1/2, 3/4). As o u t l i n e d i n S e c t i o n 2.1.3. a r o t a t i o n of the p r e s c r i b e d standard o r i e n t a t i o n (001) j l ioj about the |lTo] d i r e c t i o n produced an equiaxed t i l t boundary. From the e x i s t i n g knowledge of t i l t boundaries, as 9 i n c r e a s e s the d i s o r d e r i s expected to i n c r e a s e also without i n t e r r u p t i o n u n t i l 9 becomes 90°. Th i s i s borne out by the experimental r e s u l t s . Now suppose one r o t a t e s each of the c r y s t a l s comprising a b i c r y s t a l by small s u c c e s s i v e r o t a t i o n s 9/2 about [lioj to pro duce an equiaxed t w i s t boundary. A c c o r d i n g l y , the (110) planes r o t a t e but always remain p a r a l l e l to the boundary. This mis match, or d i s o r d e r , i s a r e s u l t of t h i s r o t a t i o n . The t r a n s l a  t i o n of one c r y s t a l with r e s p e c t to the other i n a b i c r y s t a l does not a l t e r the magnitude of the mismatch. It i s necessary f i r s t to i n v e s t i g a t e the q u a l i t a t i v e nature of t h i s d i s o r d e r , and then assess i t q u a n t i t a t i v e l y . Consider the p o s i t i o n s of the atoms i n the two (110) planes adjacent to the boundary. F i g u r e 13, f o r example, gi v e s a p i c t u r e of these planes c o n s i d e r i n g the boundary to l i e i n the plane of the page. The b l a c k dots r e p r e s e n t atoms i n the (110) plane above the boundary, and the c i r c l e s , atoms i n the (110) plane below the - 60 - boundary Figure lh. Coincidence plot for a 33° equiaxed twist boundary. Figure lh. Coincidence plot for a 33° equiaxed twist boundary. - 6 2 - Figure 15. Coincidence plot for a kl° equiaxed twist boundary. - 63 - Figure 16. Coincidence plot for a 46° equiaxed twist boundary. - 64 boundary. I f one atom f a l l s d i r e c t l y above the other, that i s , coin c i d e n c e occurs, then t h i s i s shown as a dot i n s i d e of a c i r c l e . The r e p r e s e n t a t i o n s i n F i g u r e s 13, 14, 15 and 16 are termed c o i n c i d e n c e p l o t s , f o r o r i e n t a t i o n d i f f e r e n c e s of 14°, 33°, 41° and 46°. As ft changes, the i n i t i a l l y p e r f e c t c o i n c i  dence i s destroyed to d i f f e r e n t degrees, depending on the magni tude of ft. At 41° every other atom i s i n coincidence, r e p r e s e n t  ing the minimum l a r g e - a n g l e mismatch. To evaluate t h i s , the t r a c e s of a f a m i l y of p a r a l l e l planes p e r p e n d i c u l a r to the boundary, or page, were drawn. A f a m i l y was chosen such that the d i s t a n c e between planes was a maximum and yet each atom i n the two (110) planes f e l l i n one of the plan e s . This permits one to a s s o c i a t e one black dot wit h one c i r c l e , through out the p l o t thereby accounting f o r a l l of the atoms i n the r e c t a n g u l a r area. Vectors are drawn between the two atoms of a p a i r . The v e c t o r s a c t u a l l y r e p r e s e n t the p r o j e c t e d d i s t a n c e s between the atoms i n the two planes under c o n s i d e r a t i o n . The leng t h s are summed over the r e c t a n g u l a r p l o t and the average l e n g t h i s taken as a r e l a t i v e measure of the mismatch. Table 13 give s the r e l a t i v e mismatch f o r s e v e r a l o r i e n t a t i o n d i f f er enc es. Table 13 R e l a t i v e Measure of the Disorder of a Twist Boundary Or i e n t a t i o n D i f f e r e n c e (d egr ees ) R e l a t i v e Disord er t * (min.) 14 33 41 46 53 1.8 2. 5 0.62 3.1 2.5 9.5 0.7 6.1 0.7 0.7 65 BIBLIOGRAPHY 1. Weinberg, F. and Teghtsoonian, E. ; Acta Met. 5_ (1957 ) 455. 2. Bengough,' G.D. J J . I n s t . Metals 7_ (1912) 123. 3. Rosenhain, W.; J. I n s t . Metals 7_ (1912) 178. 4. Rosenhain, W. and Humphrey, J.C.W.; J. I r o n and S t e e l I n s t . 87 (1913) 219. 5. Rosenhain, W. and Ewen, D.; J. I n s t . Metals 10 (1913) 119. 6. Hargreaves, F. and H i l l s , R.J.; J. I n s t . Metals 41 (1929) 257. .7. Mott, N.F.; Proc. P h y s i c a l S o c i e t y (London) 6_0 (1948) 391. J. Applied Physics 20 (1949) 274. 9. Burgers, J.M.; Proc. P h y s i c a l S o c i e t y 52 (1940) 23. 10. Read, W. T. and Shockley, W„ ; P h y s i c a l Review 78 (1950) 275. 11. Frank, F.C.; Carnegie I n s t i t u t e of Technology Symposium on the P l a s t i c Deformation of C r y s t a l l i n e S o l i d s (1950 ) 150. 12. Smoluchowski, R.; P h y s i c a l Review 87 (1952) 482. 13. AChter, M.R. and Smoluchowski, R.; J . Applied P h y sics 22_ (1951 ) 1260. 14. T u r n b u l l , D. and Hoffman, R.E.J Acta Met. 2 (1954) 419. 15. Aust, K.T. and Chalmers, B.; Proc. Royal S o c i e t y (London) A201 (1950) 210 . 16 . Chalmers, B. ; Proc. Royal S o c i e t y (London) A175 (1940) 100. 17. Chaudron, G., Lacombe, P., and Yannaquis, N.; C R . Acad. S c i . , P a r i s 226 (1948) 1372. 66 - 18. Pumphrey, W.I, and Lyon, J.V. ; J. I n s t . Metals 82 (1953 ) 33. 19. Boulanger, C ; Revue Mfital 5_1 (1954) 210. 20. Shewmon, P.; Acta Met. 5 (1957) 335. 21. Weinberg, F.; Acta Met. 6_ (1958) 53 5. 22. B o i l i n g , G.F. and Winegard, W. C. , Acta Met. 5 (1957) 681. 23. B a r r e t t , C.S.; " S t r u c t u r e of Metals" (1952) 185, McGraw-Hill. 24. C u l l i t y , B.P.; "X-Ray D i f f r a c t i o n " (1956) 215, Addison Wesley. 25. B a r r e t t , C.S.; " S t r u c t u r e of M e t a l s " (1952) 347, McGraw-Hill. 26. R u t t e r , J.W. and Chalmers, B.; Canadian J . P h y s i c s 51 (T953) 15. 27. Read, W.T. J r . , and Shockley, W. ; "Imperfections i n Nearly P e r f e c t C r y s t a l s " (1952) 352, Wiley. 28. Pfann, W. G. ; "Zone M e l t i n g " (1958) 10, Wiley. 29. Crank, J. ; "Mathematics of D i f f u s i o n " (1956) 9, Oxford. 30. S m i t h e l l s , C.J.; "Metals Reference Book", V o l . 2, (1955) 558, Butterworths S c i e n t i f i c P u b l i c a t i o n s . 

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