The formation of pb 2 au precipitates at high velocity grain boundaries after quenching
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While the d i s c u s s i o n h e r e was r e s t r i c t e d to s o l i d i fication, s i m i l a r a r g u m e n t s could be a p p l i e d to the m e l t i n g of m e t a l p a r t i c l e s , due to t h e r m a l r a d i a t i o n . P r o b l e m s involving p a r t i c l e s , which a r e not a t t h e i r m e l t i n g t e m p e r a t u r e s i n i t i a l l y , but which would s a t i s f y the c r i t e r i a for a s y m p t o t i c s o l u t i o n s , can be t a c k l e d by c o m b i n i n g the a s y m p t o t i c s o l u t i o n s given h e r e with the r e s u l t s of Ref. 2. 1. H. W.Meyer,F. E. Porter,G. C. Smith,and J. Szekely:J. Metals, vol. 20, p. 35. 2. J. Szekelyand R. J. Fisher:Trans. TMS-AIME, 1968,vol. 242, p. 612.
s e r v e d that p r e c i p i t a t e s ( p r e s u m a b l y Pb2Au, a c c o r d i n g to the P b - A u phase d i a g r a m ) had f o r m e d at the g r a i n b o u n d a r i e s of the s a m p l e s a n n e a l e d at 308~ but not in the s a m p l e s a n n e a l e d at 180~ These precipitates had not b e e n visible i m m e d i a t e l y after etching and hence they had grown in a 24 h r p e r i o d at 23~ To s t u d y this phenomenon in m o r e detail a P b - 0 . 0 1 at. pct Au a l l o y was h o m o g e n e o u s l y solidified 2 and s e c tioned into four groups c o n s i s t i n g of four s a m p l e s each. After r o o m t e m p e r a t u r e d e f o r m a t i o n set A was a n n e a l e d for 120 sec (plus an 8 sec t i m e c o r r e c t i o n ) at 170~ and then quenched into cold w a t e r . Set B was s i m i l a r l y d e f o r m e d and a n n e a l e d for 120 sec (plus a 16 sec t i m e c o r r e c t i o n ) at 310~ and then quenched into cold water. Set C was d e f o r m e d at r o o m t e m p e r a t u r e and a n n e a l e d for 120 sec (plus 16 sec) at 310~ These s a m p l e s w e r e then i m m e d i a t e l y plunged into a n o t h e r salt bath at 215~ for 4.5 hr. A f t e r 4.5 hr at 215~ these s a m p l e s were quenched into cold water. Set D was d e f o r m e d at room t e m p e r a t u r e and a n n e a l e d for 30 m i n at 310~ and then q u e n c h e d into cold water. All s a m p l e s were polished and etched i m m e d i a t e l y a f t e r the cold water quench. P r e c i p i t a t e s at g r a i n b o u n d a r i e s were only o b s e r v e d in set B and these were v i s i b l e 16 h r after the q u e n c h . An example of these Pb2Au p r e c i p i t a t e s i s shown in Fig. I. P r e c i p i t a t e s were not o b s e r v e d in any of the other sets even up to I week after the quench. The equation r e l a t i n g the 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 solute at a g r a i n b o u n d a r y (C B) to that in the bulk (Co) i s : E C B = Co exp ~-~ where E i s a b i n d i n g e n e r g y . F o r gold in lead (Ko = 0.015) the b i n d i n g e n e r g y E is positive and hence the 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 gold at a g r a i n b o u n d a r y would be d e c r e a s e d by r a i s ing the t e m p e r a t u r
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