A sublattice model of metal alloys and the hypothesis that alloys are described by commensurate phases of the DFK model are put forward. The chemical composition of its grains is predicted for the A_xB_1-x alloy.

A metal alloy is a collection of crystalline grains with an average size R, the space between which is filled with impurities. 

Classical theories of metal alloys are based on the idea of a “random phase”: - atoms in a crystal lattice according to chemistry composition can be arranged randomly.

The DFK model puts forward the idea of a “commensurate phase”, which is realized by the strong interaction of crystal sublattices: for example - an alloy AB of equiatomic composition is considered as a commensurate crystal with AB molecules (N = L). If the main periods of the sublattices are equal, respectively for crystal A - a, for crystal B - b, then the period of the AB alloy crystal is equal to . When heated (T>V₀), the sublattices become independent and return to the original periods (a, b).

Having asked the question about the atomic composition of the grain of the A_xB_1-x alloy, we proceed from the main hypothesis - metal alloys are described by commensurate phases of the DFK structure. Let us project an alloy of cubic symmetry A_xB_1-x (x≥0.5) onto a one-dimensional DFK model. Assuming that the alloy is a commensurate phase of the DFK model with CH(A_x) and CH(B_1-x) sublattices and strong interchain interaction, V₀~1 - we will show that x can only take discretely defined values x=x₀.

To the alloy grain A_xB_1-x (x ≥ 0.5) we associate elastically periodic chains CH(A_x) and CH(B_1-x) of N and L atoms of the same size, respectively, then if the period of the chain CH(A_x) = 1, then the period of the chain CH(B_1-x) is equal to .

Thus, x can only take discrete values x₀:

                                                                                                                              (1)

The chemical composition of the A_xB_1-x alloy grain has the form A_x0B_1-x0. We choose in (1) the first fractional-rational values ≥ 1, with the smallest denominators, because commensurate phases [1-4] with strong interaction can only be realized with them. From (1) we have: x₀ = 0.50; 0.70; 0.89, i.e. very limited number of options depending on V₀.

The dropped atoms, with density Δx=x-x₀, are located between the grains, determining their size R:

                                                              R~1/ Δx.                                                                        (2)

It is interesting to note that the chemical composition of many metal alloys A_xB_1-xC, with high-temperature superconductivity (HTS), lies near the values of x₀ = 0.50; 0.77; 0.89; 0.96.

This suggests that HTS should be described by a model with incommensurate phases [1-3] and a chemical density wave. In this case the variance of R is minimal.