Low temperature heat capacity models for substances with diamond-like
structures have been considered on the basis of the Debye model and fr
actal states filling at fixed characteristic temperature. It was shown
that low temperature calorimetry is an efficient tool for scanning th
e distribution of the atomic vibrational states in real substances. Fr
actal dimension and Poisson's ratio in the elastic-isotropic multifrac
tal model are related by a simple interdependence, which enables estim
ation of the fractal dimension from elastic properties of solids.