Abstract
A new phonon-density distribution model was developed. It is composed of five parts corresponding to transverse acoustical, longitudinal acoustical, transverse optical, longitudinal optical, and internal vibrational modes. The model takes account of influence of atomic mass distribution and non-spherical shape of the first Brillouin zone upon the phonon-density distribution. An isometric molar lattice heat-capacity formula was derived on the basis of the new phonon-density distribution model under the harmonic oscillator approximation. Though the formula contains several parameters to be evaluated, a single parameter, θKW, is remained after simple and easy evaluation of the other parameters from chemical and crystallographic data of each particular compound. θKW is similar to the Debye's characteristic temperature in several respects. Three computer codes named LEM-1, -2, and -3 were prepared for its convenient use since the formula requires extremely cumbersome calculation to be evaluated. The new formula as well as the Debye one was compared with experimental low-temperature heat-capacity curves of five scapolite samples to prove its validity.
