It assumes that phonons obey a linear dispersion relation, and that the minimum wavelength is twice the interatomic spacing of the lattice.
This model can be improved by introducing a quantity equal to minus the derivative of the log of the frequency with respect to the log of the volume, a quantity known as the Gruneisen parameter. Calculating the exact solution provided by this model requires integrating e to the x times x to the fourth power divided by the square of the quantity e to the x minus 1, where x is equal to Planck's constant times thermodynamic beta times the maximum frequency. An integral over a cubic volume in phase space taken in this model is replaced with an integral over an octant of a sphere in an approximation named for the same man. It assumes that phonons obey a linear dispersion relation, and that the minimum wavelength is twice the interatomic spacing of the lattice. At low temperatures, the aforementioned (*) heat-capacity integral reduces to a temperature-cubed dependence, and at high temperatures it recapitulates the Dulong-Petit Law. For 10 points, name this model for the heat capacity of a solid named for the Dutch scientist who names a unit of electric dipole moment.
This model can be improved by introducing a quantity equal to minus the derivative of the log of the frequency with respect to the log of the volume, a quantity known as the Gruneisen parameter.
Debye model