Mathematical modeling of changes in density of near-surface ionic layers in semi-infinite metals. Equations for displacements of ionic layers

: pp. 988–994
Received: June 08, 2023
Revised: September 01, 2023
Accepted: September 07, 2023
Lviv Polytechnic National University
Lviv Polytechnic National University
Lviv Polytechnic National University

In this work, we propose a mathematical model for describing the change in the ion density of the near-surface ionic layers of a semi-infinite metal.  Through averaging over the subsystem of conduction electrons, we obtain in the adiabatic approximation an effective Hamiltonian of the ionic subsystem of a semi-infinite metal, which models the effect of the "metal–vacuum" separation surface on the structure of the near-surface ionic layers.  We calculate the free energy of such a model and, by its minimization, obtain an equation for finding the displacements $\mathbf{\xi}_{m}$ of the ionic layer $m$.  We show that in the absence of an inhomogeneous distribution of the electronic subsystem $\mathbf{\xi}_{m}\equiv 0$.

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Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 988–994 (2023)