The universality of energy spectrum of phonon and vacancy excitations in solid helium

摘要

The most careful measurements on the specific heat C(T) and dP/dT (P is the pressure, T is the temperature) are analysed using a model where the thermodynamic properties of He-3 and He-4 crystals are described by a sum of phonon and vacancy contributions. The analysis, in which the Debye model of phonons and the Hetherington model for wide-band vacancies are used, yields a universal molar volume depence for the Debye temperature Theta(D) and the vacancy activation energy Q(V) , and constant values for the Gruneisen parameters in the molar volume range of 14-24 cm(3)/mol. The Theta(D) values are found to be in good agreement with the data obtained from the elastic moduli measurements and with Horner's theoretical calculations. The Q(V) values are in good agreement with the X-ray measurements on the temperature dependences of He-3 and He-4 crystal lattice parameters analysed in terms of the Hetherington model.