The correlative method of unsymmetrized self-consistent field is used to study the mean square relative atomic displacements in crystals taking into account the strong anharmonicity and interatomic correlations. General expressions for these quantities in arbitrary crystal lattices are obtained. As an illustration, the mean square relative displacements between nearest, second, and third neighbours in a strongly anharmonic linear chain are calculated. The results are compared with those obtained with more rough approximations (harmonic, quasi-harmonic, etc.). The influence of anharmonic effects is discussed.Es wird eine Korrelationsmethodc des unsymmetrisierten selbstkonsistenten Feldes fur das Studium der relativen quadratischen atomaren Verschiebungen in Kristallen mit Berucksichtigungen starker anharmonischer und interatomarcr Korrelationen verwendet. Man erhalt allgemeine Ausdrucke fur diese GroBe in willkurlichen Kristallgittern. Zur Verdeutlichung werden die relativen quadratischen atomaren Verschiebungen zwischen nachsten, zweiten und dritten Nachbarn in einer stark anharmonischen linearen Kette berechnet. Die Ergebnisse werden mit jenen verglichen, die durch hiihere Naherungen (harmonische, quasi-harmonische, usw.) erhalten wurden. Der EinfluB von anharmonischen Effekten wird diskutiert.
A correlative method of unsymmetrized self-consistent field is utilized to study the interatomic correlations in anharmonic crystals. Using the statistical perturbation theory up to second order the expression for binary correlations is derived. Corresponding diagrams are constructed and classified. As a simple application, the correlation moments are calculated for the one-dimensional model. Es wird eine Korrelationsmethode des unsymmetrisierten, selbstkonsistenten Feldes fur das Studium der interatomaren Korrelationen in anharmonischen Kristallen verwendet. Mittels der statistischen Storungstheorie zweiter Ordnung wird der Ausdruck fur binLre Korrelationen abgeleitet. Die entsprechenden Diagramme werden dargestellt und klassifiziert. Als einfache Anwendung werden die Korrelationsmomente fur ein eindimensionales Modell berechnet.
To study the interatomic correlations in anharmonic crystals we have used the correlative method of unsymmetrized self-consistent field (CUSF). The zeroth-order approximation of this method takes into account the main anharmonic terms but disregards the dynamical interatomic correlations at intermediate and long distances. With the aid of the first- and second-order perturbation theory we have derived the general expressions for quadratic correlations in two-dimensional models of crystals taking into account anharmonic terms up to the fourth order. Herewith we have constructed the corresponding diagrams. Correlations between the nearest, second, and third neighbors in square lattice have been calculated.
Using the correlative method of unsymmetrized self-consistent field we study the dynamical properties of anharmonic crystals, namely, the quadratic correlations between atomic displacements from the equilibrium positions and their mean square relative displacements in anharmonic crystals. In the present paper we calculate these values for a weakly anharmonic crystals with the face-centered cubic lattice in which the nearest neighbors interact. The second order of the method enables one to calculate for this lattice the correlations between the nearest, second, third and fourth neighbors. The results are compared with those obtained previously for simplified models. The dependence on the coordination number and on the dimensionality of the lattice is discussed.
The correlative method of unsymmetrized self-consistent field (CUSF) is used to study the interatomic correlations and mean square displacements in anharmonic crystals. In the first order of CUSF we have derived the formula for the atomic mean square displacement and quadratic correlation between displacements of two nearest neighbors along the line passing through their centers [Formula: see text] where n is the dimensionality of a lattice and Z is the coordinational number. In the second order of CUSF we have calculated the quadratic correlation moments and mean square relative displacements in the two-dimensional model of an anharmonic crystal with hexagonal lattice. The results are compared with those for square lattice obtained previously.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.