Annealing twin frequency in lead and lead base alloys
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Annealing Twin Frequency In Lead and Lead Base Alloys C. J. SIMPSON, K. T. AUST, AND W. C. WINEGARD A S pointed out by C. S. Smith, 1 H i b b a r d e t a l . , 2 F u l l m a n and F i s h e r , 3 and B o l l i n g and W i n e g a r d , 4 the r a t i o of the n u m b e r of a n n e a l i n g twins to the n u m b e r of grains remains essentially constant during grain growth in a given m e t a l . A c c o r d i n g to the F u l l m a n - F i s h e r theory of f o r m a tion of a n n e a l i n g twins at g r a i n c o r n e r s , the t w i n n i n g f r e q u e n c y from m e t a l to m e t a l should d e c r e a s e as the r a t i o of twin b o u n d a r y e n e r g y to g r a i n b o u n d a r y e n e r g y i n c r e a s e s . T h i s was c o n f i r m e d by B o l l i n g and W i n e g a r d who m e a s u r e d a n n e a l i n g twin f r e q u e n c i e s in z o n e - r e f i n e d lead and in a P b - 0 . 1 at. pct Ag alloy. O v e r a r a n g e of g r a i n s i z e s , the n u m b e r of twin bounda r i e s per g r a i n was 0.91 for z o n e - r e f i n e d lead and 0.65 for the P b - A g alloy. D u r i n g the c o u r s e of a g r a i n growth i n v e s t i g a t i o n s-7 a Ko > 1 solute, t h a l l i u m , was added to lead and it was o b s e r v e d that the a n n e a l i n g twin f r e q u e n c y was c o n s i d e r a b l y i n c r e a s e d over that of 99.9999 pct P b . The addition of a Ko < 1 s o l u t e , gold, c a u s e d a d e c r e a s e C. J. SIMPSON and K. T. AUST are Graduate Student and Professor, respectively, Department of Metallurgy and Materials Science, University of Toronto, Toronto, Canada. W. C. WINEGARDis President, University of Guelph, Guelph, Ontario, Canada. Manuscript submitted December l, 1969. 1782-VOLUME 1, JUNE 1970
0II n e a r the [110] pole s e e m s o u t s i d e e x p e r i m e n t a l error.
The t h e o r y does r e p r e s e n t the t r e n d of the data for copper and n i c k e l well in the o t h e r c o r n e r s of the s t e r e o g r a p h i c t r i a n g l e , although a d e t a i l e d n u m e r i c a l c o m p a r i s o n r e q u i r e s the t r a n s f o r m a t i o n of the data a s i n d i c a t e d above. It might be p o s s i b l e to make adj u s t m e n t s in the theory to take a c c o u n t of a n o t h e r a s pect of the change of o r i e n t a t i o n d u r i n g glide. As the t e n s i l e axis m o v e s away f r o m the [110] pole, the r e s o l v e d s h e a r s t r e s s e s on the m o r e i m p o r t a n t s e c o n d a r y slip s y s t e m s a r e falling, r e l a t i v e to the s t r e s s on the p r i m a r y s y s t e m in the s e n s e of the a v e r a g e taken by H i r s c h and Mitchell, 4 which is the b a s i s of the theor e t i c a l p r e d i c t i o n of a f a l l i n g 0iI. It is p o s s i b l e that this effect r e s u l t s in s u b s t a n t i a l l y l e s s motion on s e c o n d a r y s y s t e m s , and c o n s e q u e n t l y l e s s h a r d e n i n g of the p r i m a r y s y s t e m , than o c c u r s for c r y s t a l s for w
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