Stacking faults in crystals and the model of configurational localization
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FAULTS
CONFIGURATIONAL G. S h .
IN C R Y S T A L S
AND THE
MODEL
OF
LOCALIZATION
Upadkhaya
UDC 539.292:548.4
The energy changes of stacking faults in metals and alloys are discussed in connection with the formation of stable electronic configurations of the fault atoms. The results of the d i s cussions can be used to predict the effect of the admixture of one element on the stackingfault energy for another element. The dislocation concept is frequently used in studying the s t r u c t u r e and mechanical, electric, magnetic, and optical p r o p e r t i e s of real c r y s t a l s [1]. A stacking fault is a s s o c i a t e d with "incomplete" or "partial" dislocations, which o c c u r frequently in c l o s e - p a c k e d s t r u c t u r e s . Noteworthy among attempts which have been made to explain the different stacking-fault energies ~/ for the nontransition metals, on the basis of the c r y s t a l f a c t o r (and, recently, on the basis of tangency of the F e r m i s u r f a c e and the boundary of the B r i l louin zone [2, 3]), as well as for transition metals, on the basis of directional bonds [16, 57], is the attempt to explain the changes in the stacking-fault energies in c r y s t a l s on the basis of the model of configurational localization. According to this model, the valence electrons of isolated atoms s e p a r a t e into a part localized n e a r the atomic c o r e s and an unlocalized part when the atoms f o r m a condensed state [4-6]. This model was developed in [7-10] and has been experimentally checked by x - r a y studies of c e r t a i n transition metals and in a t r e a t m e n t of data on the Hall constant [11]. It has been suggested in the development of this model in [12-15] that the localized part of the valence electrons f o r m s a s p e c t r u m (a statistical set) of c o n f i g u r a tions in which the energetically most stable configurations, c o r r e s p o n d i n g to the minimum f r e e - e n e r g y r e s e r v e , have the g r e a t e s t weight. For present purposes, it is convenient to divide all the c h e m i c a l elements into t h r e e groups on the basis of the configuration of the valence electrons of the isolated atoms: 1) s elements; 2) ds and fds elements; and 3) sp elements. It should be noted that the energetic stability of the c o r r e s p o n d i n g d and f configurations i n c r e a s e s , while that of the s and sp configurations d e c r e a s e s , with i n c r e a s i n g main quantum n u m b e r of the valence e l e c t r o n s . The energetically most stable, or the s o - c a l l e d stable configurations for these groups of elements, a r e s 2, sp 3, s2p 6, d ~ d 5, d 1~ f0, fT, and f14; of these, the most stable a r e the s2p G, d 5, and f7 configurations. Table 1 shows stacking-fault energies T given in the l i t e r a t u r e for c e r t a i n elements. E x t r e m e l y crude methods have been used to estimate these energies. The experimental methods a r e based either on m e a s u r e m e n t of the width of the dislocation split
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