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

Correlation between thermal expansions β(T) and heat capacity C(T) of atomic and molecular crystals, amorphous materials with a structural disorder, carbon nanomaterials (fullerite C60, bundles SWCNTs of single-walled carbon nanotubes) was analyzed. The influence of the contribution to the coefficient of linear thermal expansion αXe(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 αXe(T) and the normalized to the gas constant heat capacity C Xe(T)/R of Xe atoms adsorbed on the SWCNTs bundles. The proportional correlation (β/β*) ∼ (CV/R) with the parameter β* for the bulk thermal expansion coefficient for cryocrystals is proposed. In the case of atomic crystals such as Xe and Ar, the proportional correlation (β/β*) ∼ (CV/R) is observed in the temperature range from the lowest experimental to temperatures where CV/R ≈ 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 CO2, CO, and N2O if the normalized heat capacity below the values CV/R ≈ 3 ÷ 3.5. It indicates that the proportional correlation between thermal expansions (β/β*) and heat capacity (CV/R) is related not only to the translational, but also to the rotational degrees of freedom of the molecule in the crystal. In the case of the C0, molecular crystal with translational and rotational degrees of freedom and intramolecular vibrations, the discussed above correlation occurs below the values of normalized heat capacity CV/R ≈ 7.5. In strongly anisotropic systems, such as systems of compacted bundles of single-walled carbon nanotubes and SWCNTs bundles with adsorbed Xe atoms, this universal dependence appears in a limited temperature range that does not include the lowest temperatures. A qualitative explanation of the observed correlation is proposed.