Measurement of average grain volume and certain topological parameters by serial section analysis
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m e a s u r e of g r a i n s i z e . F o r this r e a s o n , it is the only m e a s u r e of g r a i n size that has the s a m e m e a n i n g for a l l m a t e r i a l s and for all s a m p l e s of the s a m e m a t e r i a l . Although s e r i a l s e c t i o n a n a l y s i s is s i m p l e in p r i n ciple, its execution involves a s e q u e n c e of o p e r a t i o n s which a r e not always obvious and which have not been d i s c u s s e d adequately in the l i t e r a t u r e , bs,4 The p r o c e d u r e d e s c r i b e d in the following r e l a t e s s p e c i f i c a l l y to the e v a l u a t i o n of the topological p a r a m e t e r s of p o l y c r y s t a l l i n e a g g r e g a t e s whose g e o m e t r i c c h a r a c t e r i s t i c s have been dictated by s u r f a c e m i n i m i z a t i o n through the agency of s u r f a c e t e n s i o n . It is c h a r a c t e r i s t i c of such s t r u c t u r e s that t h e i r g r a i n edges a r e t r i p l e l i n e s along which t h r e e g r a i n s meet and t h e i r g r a i n c o r n e r s a r e quadruple points where four g r a i n s come into m u t u a l contact. V i r t u a l l y a l l g r a i n s t r u c t u r e s found in m e t a l s and c e r a m i c s , as well as most of the c e l l u l a r s t r u c t u r e s found in n a t u r e a r e of this kind. T h e t e c h n i q u e s that follow w e r e developed in the c o u r s e of a study of s t e a d y - s t a t e g r a i n growth in a l u m i n u m2 and the data p r e s e n t e d in the r e s u l t i n g p a p e r a r e cited as i l l u s t r a t i o n s of the m e a s u r e m e n t s that can be made by these methods.
F. N. RHINES is DistinguishedService Professor, Department of Materials Science and Engineering,University of Florida, Gainesville, FL K. R. CRAIG, formerly Candidate for the Ph.D at the University of Florida, is currently Supervisor, Materials Application, Bettis Atomic Power Laboratory, West Mifflin, PA. D. A. ROUSSE was formerly Candidate for the MS at the University of Florida. Manuscript submitted November 25, 1974. METALLURGICAL TRANSACTIONS A
SERIAL SECTIONING S e r i a l s e c t i o n s c o n s i s t of consecutive s l i c e s cut through a piece of m a t e r i a l at i n t e r v a l s that a r e so n a r r o w as to expose e v e r y s i g n i f i c a n t d e t a i l of the i n t e r n a l s t r u c t u r e . F o r topological m e a s u r e m e n t s , it is not e s s e n t i a l that the s l i c e s be e i t h e r flat, or exactly p a r a l l e l to one another, but f l a t n e s s and p a r a l l e l i s m c o n t r i b u t e to the p r e c i s i o n of the a l l - i m p o r t a n t d e t e r m i n a t i o n of the total volume of m a t e r i a l that has b e e n sectioned. The use of a m i c r o t o m e for s e r i a l sectioning, as is c o m m o n p r a c t i c e i n the b i o l o g i c a l s c i e n c e s , is not c r i t i c a l , indeed is r a r e l y a d v a n tageous, in m e t a l l o g r a p h i c s e r i a l s e c t i o n i n g . Instead, it is most often
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