Disordered binary alloys occupancies

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... 

A particular configuration T of a semi-infinite disordered binary alloy Aj,Bi j is characterized by a set of occupation indices vr, where 7 = 1 if the site R is occupied by an atom of the type Q, and Tj = 0 o..ierwise. Configurational averaging of occupation indices ( 7r) = yields the local concentrations c. The energy of such a configuration can be expressed in the form of an effective Hamiltonian of Ising type... 

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... 

The magnetic properties of an alloy can be studied as a function of the temperature and concentration of the constituent metals. Order-disorder phenomena can be measured directly and compared with the thermal history and mechanical properties of the alloy. The statistical occupation of the first coordination sphere round the resonant atoms in binary alloys can be derived from magnetic spectra. 

The binary alloy Ac,j Beg, Cyt-I-Ci) = 1, shall be studied by the means of supercells containing N atoms with periodic boundary conditions. Each site of the cell can be occupied by a A or a B atom. If the chemical occupations are not considered, the lattice described by the sites within the supercell and their periodic replicas is a simple lattice, with one atom per unit cell. Below, it shall referred to as the geometrical lattice . In order to have a theory flexible enough to deal on equal footing both with ordered and disordered alloys, in principle, one should consider all the different alloy configurations that belong to the... 

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