Binary alloys substitutional disorder

Our results demonstrate that the augmented space recursion and the orbital peeling method in conjunction with the LMTO formalism, constitute a viable and computationally feasible approach to the calculation of phase stability in binary substitutionally disordered alloys. ... 

In this section, we consider how to model a bulk (i.e., infinite) substitution-ally disordered binary alloy (DBA), in light of its intrinsic randomness. The fact that the DBA lacks periodicity means that the key tool of Bloch s theorem is inapplicable, so specialized methods (Ehrenreich and Schwartz 1976, Faulkner 1982, Yonezawa 1982, Turek et al 1996) must be used. 

For the case of a binary substitutionally disordered alloy composed of atoms A and B with concentration and Cj = 1 - c, Eq. (6.13) becomes... 

Solid-fluid phase diagrams of binary hard sphere mixtures have been studied quite extensively using MC simulations. Kranendonk and Frenkel [202-205] and Kofke [206] have studied the solid-fluid equilibrium for binary hard sphere mixtures for the case of substitutionally disordered solid solutions. Several interesting features emerge from these studies. Azeotropy and solid-solid immiscibility appear very quickly in the phase diagram as the size ratio is changed from unity. This is primarily a consequence of the nonideality in the solid phase. Another aspect of these results concerns the empirical Hume-Rothery rule, developed in the context of metal alloy phase equilibrium, that mixtures of spherical molecules with diameter ratios below about 0.85 should exhibit only limited solubility in the solid phase [207]. The simulation results for hard sphere tend to be consistent with this rule. However, it should be noted that the Hume-Rothery rule was formulated in terms of the ratio of nearest neighbor distances in the pure metals rather than hard sphere diameters. Thus, this observation should be interpreted as an indication that molecular size effects are important in metal alloy equilibria rather than as a quantitative confirmation of the Hume-Rothery rule. 

Faulkner, Wang and Stocks [2, 3] have analysed the distribution of charges in binary metallic alloys as obtained from LSMS calculations. They have studied large supercells with periodic boundary conditions containing hundreds of atoms and designed to simulate substitutional disorder. LSMS calculations are based on the local density approximation to the density functional theory [4, -5] and the muffin-tin approximation for the crystal potential thus the results of their analysis hold within the same approximations. Below we shall summarize and comment the conclusions obtained in Refs. [2, 3] that are relevant for our present concerns ... 

NiAl can be alloyed with further elements in order to form ternary phases with a B2 structure which is then known as an L2o structure, too, or to obtain additional phases in equilibrium with NiAl. Fe, as well as Co, can substitute for Ni in NiAl completely without affecting the B2 structure, as is expected in view of the binary B2 phases FeAl and CoAl. Correspondingly, the ternary Ni-Fe-Al phase diagram, which is of importance with respect to conventional high temperature alloys, shows the extended B2 phase field and the respective equilibria with NijAl and Al-rich phases on the one hand and with disordered b.c.c. Fe and f.c.c. Fe on the other (Bradley and Taylor, 1938 Dannohl, 1942 Bradley, 1951 Hao et al., 1984). The Ni-Al-Co system behaves in an analogous way (Hao et al., 1984 Ishida et al., 1991 a, 1993). Other ternary systems have been re-... 

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