In the framework of the variational method of the spin density functional theory the formation of a monolayer FexNi1-x alloy film on the W, Ag and Au substrates depending on the concentration of the alloy components and coating parameter is described. The temperature effects of the mixing of adsorbate and substrate atoms and ferromagnetic ordering effects are taken into account. The adsorption energy for a close-packed face is minimal for all presented systems. A monolayer film without mixing is formed on Au and W substrate mainly for large values of the coating parameter and the concentration of iron. For the Ag substrate, the difference in the crystal structure leads to an increase in mixing and the formation of a sandwich similar structure with pushing silver atoms onto the surface. The values of the adsorption energy calculated at T = 0 K in the framework of the variational and first-principle approaches are compared. Calculations of the magnetic moments and exchange integrals for FexNi1-x bulk alloy were carried out using the spin-polarized relativistic Korring-Kohn-Rostoker method. The equilibrium lattice constants were obtained by first-principle calculations. The exchange interaction of the nearest neighbors is ferromagnetic and for heterogeneous nearest neighbors J1Ni-Fe increases with increasing nickel concentration, and for the same type neighbors J1Ni - Ni decreases. The next nearest neighbors exchange interaction is carried out only for atoms of the same type, and for iron, atoms have a ferromagnetic character, while for nickel atoms it is weak antiferromagnetic.
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