Coupled temperature dependences of volume and compressibility

Abstract

We present a new method for understanding the changes with temperature of the volume and compressibility of solids. These changes depend on five parameters: V ₀, B ₀, Θ, γ _G and δ _T. V ₀ and B ₀ are the atomic volume and bulk modulus at T = 0 K, Θ is the Debye temperature, γ _G is the Grüneisen parameter, and δ _T is the Anderson–Grüneisen parameter. Equations for the temperature-dependent volume, bulk modulus and thermal expansion are given, and examples of the use of these equations are provided, with particular emphasis on the light actinides. For the elements, we examine the relationship between experimental values of γ _G and δ _T, and find no clear correlation. In particular, Swenson's rule, which states that the bulk modulus does not change with temperature if the volume is held constant, is a poor approximation to the data. We reveal a new useful approximate relationship between dB/dP and γ _G. We find that the thermodynamic quantity q, which describes the variation in γ _G with volume, distributes around 2, not around 1, as often assumed. We show that the thermal- expansion behavior of Si and Ge (including negative thermal expansion at low temperatures) are well described with the use of a two-level invar model.

Keywords:

• Grüneisen parameter
• Anderson–Grüneisen parameter
• elasticity
• thermal expansion
• actinides

Acknowledgement

This work was supported in part by the Los Alamos National Laboratory under the auspices of the US Department of Energy.