Stereological characterization of the interaction between interfaces and its application to the sintering process
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i n t e r a c t i o n between d i f f e r e n t types of i n t e r faces is an i m p o r t a n t f e a t u r e of the m i c r o s t r u c t u r e of many m a t e r i a l s . F o r e x a m p l e , the i n t e r a c t i o n b e tween the s e c o n d - p h a s e m a t r i x i n t e r f a c e and m a t r i x g r a i n b o u n d a r i e s in a t w o - p h a s e m a t e r i a l can have a s t r o n g influence on m a t r i x g r a i n s i z e . I S i n t e r e d m a t e r i a l s a r e a n o t h e r e x a m p l e where two i n t e r f a c e s , the v o i d - s o l i d i n t e r f a c e and g r a i n b o u n d a r i e s in the solid, i n t e r a c t , r e s u l t i n g in a p r o n o u n c e d influence on the g r a i n s t r u c t u r e throughout m o s t of the s i n t e r ing p r o c e s s .2 A m e a s u r e of the i n t e r a c t i o n in c a s e s such as these is r e l a t e d to the length of i n t e r s e c t i o n b e t w e e n the s u r f a c e s p e r unit volume of s t r u c t u r e . F o r a given s t r u c t u r e , where the s u r f a c e a r e a s of the i n t e r f a c e s p e r unit v o l u m e of s t r u c t u r e a r e held constant, the g r e a t e r this length of i n t e r s e c t i o n , the g r e a t e r is the d e g r e e of i n t e r a c t i o n between the i n t e r f a c e s . A q u a n t i t a t i v e m e a s u r e of the d e g r e e of the i n t e r a c t i o n is given by the r a t i o of the a c t u a l length of i n t e r s e c t i o n p e r unit v o l u m e to the length of i n t e r s e c t i o n per unit v o l u m e expected in the case w h e r e both s u r f a c e s have no t e n d e n c y to i n t e r s e c t except on a r a n d o m b a s i s . * This r a t i o can be used to c o m p a r e *Intersectionon a randombasiscan be visualizedas follows:establishtwo surfaces in two separatevolumessuch as a grainstructurein a single-phasematerial and an interphaseinterfacein a two-phasestructure.Then,superimposethese two volumes,allowingno changesin either of the interfaces.In such a structure,the interfacesintersecton a randombasis. the d e g r e e of i n t e r a c t i o n in any s t r u c t u r e with that in any other s t r u c t u r e . F o r example, d u r i n g both O s t wald r i p e n i n g and s i n t e r i n g , the g e o m e t r i c a l s t r u c t u r e can change to a c o n s i d e r a b l e extent. D u r i n g Ostwald r i p e n i n g , changes in the g e o m e t r y of the r i p e n i n g phase, as well as in the m a t r i x g r a i n s t r u c t u r e , take p l a c e . As a r e s u l t , the d e g r e e of i n t e r a c t i o n between the two i n t e r f a c e s may a l s o change. The s a m e is t r u e EDWARD H. AIGELTINGER,formerly with the MetallurgicalDepartment, University of Melbourne, Parkville,Australia, is now with Materials Science Department, University of Florida, Gainesville,FL, and HANS ECKART EXNER is with Max-Planck-Institut fuer Metallforschung, lnstitut fuer Werkstoffwissenschaften,Stuttgart, W. Germany. Manuscript submitted December 23, 1975. METALLUR
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