After the phonon band structures, the thermal properties such as free energy, entropy and heat capacity C v were calculated using the statistical thermodynamic expressions from the phonon frequencies on a high precision sampling mesh in the BZ (cf. the textbook by Dove on 'Lattice Dynamics' ). All three allotropes were found to present similar curves. Fig. shows the temperature change of entropy and heat capacity at constant volume, and he Helmholtz free energy: F = U-TS where U stands for the internal energy and S for entropy. The plots are shown in two panels for diamond and trigonal C 6 as representative of all hexacarbon allotropes.