On the Self‐Consistent Statistical Theory of Anharmonic Effects in Imperfect Crystals

The improved unsymmetrized self‐consistent field method developed in preceding papers is used to study anharmonic effects in imperfect crystals. Various one‐dimensional models of anharmonic crystals with defects are considered: vacancy, free surface, adsorption with taking into account the influence of adatoms on the adsorbent, and substitutional impurities. The formulae for the lattice relaxation near defects, for the effective amplitudes of the anharmonic vibrations of atoms, and for the Helmholtz free energy are obtained. They are expressed in terms of the nearest‐neighbour interaction potentials and their derivatives of several orders at the equilibrium points. A comparison with known results for some harmonic models is made. The decisive role of the anharmonicity in such effects as the temperature dependence of the lattice relaxation and the influence of the imperfections on thermal properties of crystals is emphasized. The possibility of application of the method to three‐dimensional imperfect crystals, as well as of taking into consideration the interactions with next neighbours is noted. Copyright © 1986 WILEY‐VCH Verlag GmbH & Co. KGaA