Order-Parameter Functional Method

Abstract

It was shown in the previous chapter that the static concentration wave method [1], which is a version of the mean field approximation [2], is effective for describing such complex phenomenon as atomic ordering. Correlations arising as a result of ordering can be taken into account by the cluster variation method [3–9]. However, these methods cannot be used directly for the description of the equilibrium distribution of interstitial atoms and structural vacancies in strongly nonstoichiometric compounds for the following reasons. In the static concentration wave method, energy parameters expressing the free energy are Fourier components of interparticle interaction potentials, which cannot be determined in the framework of this method. In this connection, in order to determine interatomic interaction potentials, it was proposed [1] to use the pseudopotential method, which has been insufficiently developed with respect to transition-metal compounds. As for the cluster variation (CV) method, the correct qualitative and quantitative description of structural order—disorder phase transitions calls for the choice of a basis cluster figure whose minimum size is limited by the unit cell. In complex lattices with unit cells containing a few tens of atoms, the description of order—disorder transformations by such a large cluster encounters insurmountable computational difficulties. Moreover, for quantitative applications of the CV method it is necessary to have a large number of energy parameters.