Quantum mechanical model of interaction of charges of metal atoms during creation of chrome coatings

Purpose. To determine the dependence of the change in chemical bond energy, using a quantum mechanical model of the interaction of dopant ions with a metal substrate in the form of a chain of N-finite centers located along a straight line. Methodology. Numerical calculation of the analytical expressions of a quantum mechanical system consisting of the interaction between metal ions of doping elements and a chain of N-finite centers. Findings. By solving the Schrödinger equation for a charge moving in the field of a chain with N-finite centers, expressions for calculating the energy of chemical bonding of dopant ions with metal substrates were obtained. The analytical expressions for calculating the energies of chemical bonds are obtained. The most probable types of chemical bonds during the formation of protective coatings under non-stationary temperature conditions were determined. Originality. Schrödinger’s equation in ellipsoidal coordinates for the motion of electric charges in a field of N-finite centers located along a straight line was solved and expressions for calculating the energies of chemical bonds were obtained. The solution of the Schrödinger equation is reduced to solving a two-center problem with a perturbation. The model allows us to understand the dynamics of interaction of metal ions with a substrate in the form of chains of atoms. The tendency of change in the energy of chemical bonding of metal ions with substrates depending on the distance between them and the charge value is established. Practical value. The developed method for calculating the energy of chemical bonding between metal ions of alloying elements with a chain of N-finite centers will allow one to qualitatively establish the tendency of formation of certain compounds in the process of obtaining protective coatings under non-stationary temperature conditions. The method can be used to calculate the energies of chemical bonds when selecting alloying elements for other methods of creating protective coatings.