  Textbooks introduce the Debye temperature to simplify the integration of the
heat capacity. This approach gives the impression that the Debye temperature is
a parameter which makes the integration more convenient. The Debye frequency
cut occurs when the wavelength of the phonon frequency reaches the size of the
smallest unit of the lattice which is the length of the unit cell. At
frequencies higher than the cut off frequency the 'lattice' unable to 'see' the
vibration because the wavelength of the vibration is smaller than the basic
unit of the atomic arrangement; therefore, the vibration becomes independent
from the lattice. The Debye cut off frequency or temperature separates the
collective thermal lattice vibration from the independent thermal lattice
vibration. The experimental data of highest packing monoatomic arrangements is
used to calculate the wavelength of the Debye cut off frequency. The calculated
values agree well with the unit cell parameters.
