Constant volume specific heat C_v at temperature T obtained from the integration of the DOS.
        Only positive frequencies will be used.
        Result in J/(K*mol-c). A mol-c is the abbreviation of a mole-cell, that is, the number
        of Avogadro times the atoms in a unit cell. To compare with experimental data the result
        should be divided by the number of unit formulas in the cell. If the structure is provided
        the division is performed internally and the result is in J/(K*mol)

        Args:
            t: a temperature in K
            structure: the structure of the system. If not None it will be used to determine the numer of
                formula units
        Returns:
            Constant volume specific heat C_v

def cv(self, t, structure=None):
        """
        Constant volume specific heat C_v at temperature T obtained from the integration of the DOS.
        Only positive frequencies will be used.
        Result in J/(K*mol-c). A mol-c is the abbreviation of a mole-cell, that is, the number
        of Avogadro times the atoms in a unit cell. To compare with experimental data the result
        should be divided by the number of unit formulas in the cell. If the structure is provided
        the division is performed internally and the result is in J/(K*mol)

        Args:
            t: a temperature in K
            structure: the structure of the system. If not None it will be used to determine the numer of
                formula units
        Returns:
            Constant volume specific heat C_v
        """

        if t == 0:
            return 0

        freqs = self._positive_frequencies
        dens = self._positive_densities

        csch2 = lambda x: 1.0 / (np.sinh(x) ** 2)

        wd2kt = freqs / (2 * BOLTZ_THZ_PER_K * t)
        cv = np.trapz(wd2kt ** 2 * csch2(wd2kt) * dens, x=freqs)
        cv *= const.Boltzmann * const.Avogadro

        if structure:
            formula_units = structure.composition.num_atoms / structure.composition.reduced_composition.num_atoms
            cv /= formula_units

        return cv