Disorders binary alloy model

Krumbhaar. Solidification in the one-dimensional model for a disordered binary alloy under diffusion. Eur Phys J. B 5 663, 1998. 

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. 

The heats of formation of equiatomic AB transition-metal alloys may be predicted by generalizing the rectangular d band model for the elements to the case of disordered binary systems, as illustrated in the lower panel of Fig. 7.13. Assuming that the A and transition elements are characterized by bands of width WA and WB, respectively, then they will mix together in the disordered AB alloy to create a common band with some new width, WAB. The alloy bandwidth, WAB may be related to the elemental bond integrals, hAA and , and the atomic energy level mismatch, AE — EB — EAt by evaluating the second moment of the total alloy density of states per atom ab( ), namely... 

As opposed to the binary alloy studied in the above sections, these models involve a pure nondiagonal disorder where the K s (4.26) are all equal and the H m s take random values. 

Eustathopoulos has also summarized some theoretical calculations of a for binary alloys, which are based on lattice models in which the interface layers are treated in the Bragg-Williams approximation, assuming complete atomic disorder in the interface and in the crystal. The calculated surface free energies are related to the surface free energies of the pure components and to the activities in the bulk phases. 

One of us has presented a statistical theory for strong electrolytes according to this point of view. The model of order-disorder is similar to that applied by Bethe in his theory of binary alloys. This model has been applied to adsorption phenomena of gases on surfaces, where it has explained the abnormal cases of isobaric adsorption, and it reproduces the isotherm of Langmuir. It has also been used for condensation phenomena, where we obtain from it the relations between physical quantities at the critical point. 

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