  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 $\alpha_\textrm{Xe}(T)$ 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
$\alpha_\textrm{Xe}(T)$ and the normalized to the gas constant heat capacity
$C_\textrm{Xe}(T)/R$ of Xe atoms adsorbed on the SWCNTs bundles. The
proportional correlation $(\beta/\beta^*) \sim (C_\textrm{V}/R)$ with the
parameter $\beta^*$ for the bulk thermal expansion coefficient for cryocrystals
is proposed. In the case of atomic crystals such as Xe and Ar, the proportional
correlation $(\beta/\beta^*) \sim (C_\textrm{V}/R)$ is observed in the
temperature range from the lowest experimental to temperatures where
$C_\textrm{V}/R \approx 2.3$. 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 $C_\textrm{V}/R \approx 3 \div 3.5$.
