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Temperature dependence of Debye frequency and Gruneisen parameter in the low temperature range
Magomedov M. N.
1
1Institute for geothermal problems and renewable energy – branch of the joint Institute of high temperatures of the Russian Academy of Sciences, Makhachkala, Russia
Email: mahmag4@mail.ru
The Debye temperature (Theta) is an important characteristic of a crystal and the Theta values for specific substances are presented in many reference books and monographs. However, for many substances, the experimentally determined Theta value changes with temperature (T). It is shown that in the presence of a functional dependence Theta(T), the expressions for entropy and isochoric heat capacity should include terms with the first and second derivatives of the Theta(T) function with respect to temperature. Therefore, for the fulfillment of the third law of thermodynamics for an n-dimensional crystal, the function Theta(T) and the temperature dependence of the Gruneisen parameter γ(T) at low temperatures must change according to the dependence (T/Theta_0)n+1. At this, the Theta0 value differs from the Theta0s value, which was determined from the experimental temperature dependence of the heat capacity, without taking into account the dependence Theta(T). It is shown that if the Theta(T) function decreases, then the γ(T) function increases with increasing temperature from the values Theta_0>Theta0s and γ_0>γ0s, respectively. At average temperatures, the Theta(T) function has a minimum, and the γ(T) function has a maximum. If the Theta(T) function increases from Theta_0<Theta0s to a maximum, then the γ(T) function decreases from γ_0<γ0s to a minimum. A method for determining the temperature dependence of the Theta(T) function was proposed. Keywords: entropy, isochoric heat capacity, Debye temperature, Gruneisen parameter, graphene.
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