The classification of binary eutectics
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THE
Hunt and Jackson ~ classification of binary eutectic structures is based upon the Jackson z'3 theory of rough and smooth solid-liquid interfaces, namely, if the solid-liquid interface of a eutectic phase is atomically smooth, then freezing will lead to the formation of observable facets which may markedly influence the eutectic morphology. Thus Hunt and Jackson proposed that: I) binary eutectics in which both phases grew without the formation of facets, i.e. a nonfaceted eutectic, would have lamellar or rod-like eutectics; 2) faceted/nonfaceted eutectics would have complex regular or irregular structures; and 3) faceted-faceted eutectics would have irregular structures. This classification has met with considerable success. 1'4 In Jackson's theory, interface roughness is conveniently expressed in terms of a roughness parameter, a. If the a values of the pure components of a eutectic are used when considering the Hunt and Jackson's classification, correlation of interface roughness with observed eutectic structure is only partial. Following a possible approach by Kerr and Wine,ga.rd, S the effects of the second component on the roughness parameters of phases in binary systems has been demonstrated by the present authors in relation to the Ag-Bi 6 and In-Zn 7 systems. Further eutectic systems have now been examined and the values of the roughness parameters have been computed. These results are reported and discussed in terms of the extent to which they support the Hunt and Jackson e u t e c t i c c l a s s i f i c a t i o n , l Re c en t l y , J a c k s o n a'9 has p r o p o s e d m o r e g e n e r a l t h e o r i e s of the s o l i d - l i q u i d i n t e r f a c e which avoid a s sumpt i o n s r e q u i r e d by his p r e v i o u s theory, z's In the light of t h es e r e c e n t a n a l y s e s , it is i m p o r t a n t to note that the r o u g h n e s s p a r a m e t e r , ~ , is c a l c u l a t e d d i r e c t l y f r o m the entropy of solution which the r e c e n t t h e o r i e s s'9 show to d e t e r m i n e the r a t e of c r y s t a l growth
and its a n i s o t r o p y . Thus growth f e a t u r e s of the i n t e r f a c e can be r e l a t e d to the bulk t h e r m o d y n a m i c quantities calculated here. It has been shown 6 that the r e l a t i v e s u r f a c e f r e e e n e r g y , A F s / N k T , of a l a y e r - p l a n e added to an a t o m i c a l l y s m o o t h s u r f a c e is given by: --~Fs = x' ( 1 - x ' ) c~ + x ' l n x ' + ( 1 - x ' ) NkT where*
in ( 1 - x ' )
*All symbols are defined in the glossary at the end of the paper.
~-,~ n I O~
-
RT
v
When b i n a r y alloys a r e c o n s i d e r e d , L~ is the heat of solution of the solid alloy p h ase in liquid with which it e x i s t s in e q u i l i b r i u m ; i . e . of liquidus c o m p o s i t i o n . Since t h e r e a r e few d i r e c t m e a s u r e m e n t s of b i n a r y h e a t s of solution it is n e c e s s a r y to e s t i m a t e this f r o m o t h e r t h e r m o d y n a m i c data, c o r r e c t e d to the t e
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