Disordered binary alloys

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

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. ... 

A particular configuration E of a semi-infinite disordered binary alloy Aj,Bi j, is characterized by a set of occupation indices where 7 = 1 if the site R is... 

The order-disorder transition of a binary alloy (e.g. CuZn) provides another instructive example. The body-centred lattice of this material may be described as two interpenetrating lattices, A and B. In the disordered high-temperature phase each of the sub-lattices is equally populated by Zn and Cu atoms, in that each lattice point is equally likely to be occupied by either a Zn or a Cu atom. At zero temperature each of the sub-lattices is entirely occupied by either Zn or Cu atoms. In terms of fractional occupation numbers for A sites, an appropriate order parameter may be defined as... 

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. 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

A more complicated but solvable problem is a definition of the order parameter for antiferromagnetics, binary alloys, superconductors etc. The dimensionless units T/Tc and 77/770 (Fig. 1.4) allow us to present the behaviour of the order parameter rj = r) T) in a form universal for many quite different systems. Moreover, in some cases even quantitative similarities hold which concerns in particular the value of the exponent (3. (The value of 77 = 0 characterizes always disordered phase.)... 

That part of the entropy of a substance that is due to a disordered arrangement of the particles as opposed to a similar but ordered arrangement. The most clear-cut example is the order-disorder transition in binary alloys, in which virtually the whole entropy change is of this kind. The entropy change on fusion of a solid is largely due to entropy of disorder. 

Fusion, as an order-disorder transition, is the concept that fusion of a crystalline solid is essentially a change from the almost perfectly ordered solid state to a disordered liquid slate. The vacant spaces in the crystal lattice correspond lo the other component in the binary alloys, which undergo order-disorder transition in the pure form. Evidence from x-ray diffraction measurements indicates that short-range order is retained during fusion but long-range order is lost. 

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. 

Thus, we study the binary alloy (cf. Section IV.B) with the intermolecular interactions W of Section I. We are in the case of weak disorder A W, e.g. of a virtual crystal with one polariton band, and for A W we have separation into two bands, around vA and vB, each one embodying a polariton broadened by the disorder. 

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... 

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. 

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