Accession Number:

AD0415985

Title:

VIBRATIONAL THERMODYNAMIC PROPERTIES OF LATTICES WITH DEFECTS,

Descriptive Note:

Corporate Author:

MARYLAND UNIV COLLEGE PARK

Personal Author(s):

Report Date:

1959-08-01

Pagination or Media Count:

95.0

Abstract:

Some techniques have been developed for evaluating the changes in the vibrational properties of a lattice due to the presence of defects, and they have been applied to the study of the effect of defects on some lattice models. The techniques are based on the work of Montroll who has given a method for obtaining integral expressions for the change due to defects in an additive function of the normal mode frequencies of a lattice. The integral expressions for the changes in vibrational thermodynamic properties are contour integrals of functions whose poles are distributed in such a way that integration becomes inconvenient. It is shown in this paper that if we restrict ourselves to the evaluation of the change in thermodynamic properties at low and high temperatures, the need for integrating over such singular functions can be avoided by using some special devices. These devices lead to some useful formulae which are employed in the study of the effect of isotope and substitutional impurities in one, two, and three dimensional lattices with nearest neighbour central and noncentral force interactions. Results are given for the low and high temperature values of the change in Helmholtz free energy due to defects in these cases. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE