Proportional correlation between heat capacity and thermal expansion of atomic, molecular crystals and carbon nanostructures

Abstract

Correlation between thermal expansions $\beta (T)$ and heat capacity $C(T)$ of atomic and molecular crystals, amorphous materials with a structural disorder, carbon nanomaterials (fullerite C${}_{60}$, bundles SWCNTs of single-walled carbon nanotubes) was analyzed. The influence of the contribution to the coefficient of linear thermal expansion ${\alpha }_{\text{Xe}}(T)$ of Xe atoms adsorbed on the SWCNTs bundles is considered. The proportional correlation was found between the contribution to the coefficient of linear thermal expansion ${\alpha }_{\text{Xe}}(T)$ and the normalized to the gas constant heat capacity $C_{\text{Xe}}(T)/R$ of Xe atoms adsorbed on the SWCNTs bundles. The proportional correlation $(\beta /{\beta }^{\ast })\sim (C_{\text{V}}/R)$ with the parameter ${\beta }^{\ast }$ for the bulk thermal expansion coefficient for cryocrystals is proposed. In the case of atomic crystals such as Xe and Ar, the proportional correlation $(\beta /{\beta }^{\ast })\sim (C_{\text{V}}/R)$ is observed in the temperature range from the lowest experimental to temperatures where $C_{\text{V}}/R\approx 2.3$. The correlation is not observed in the temperatures where $2.3<C_V/R<3$ (classical Dulong-Petit law). It was found that the universal proportional correlation is also observed for molecular crystals with linear symmetry, such as CO${}_2$, CO, and N${}_2$O if the normalized heat capacity below the values $C_{\text{V}}/R\approx 3÷3.5$.

13 pages, 7 figures, 2 tables