Physics of the Debye temperature

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 temperature separates the independent and the interacting thermal lattice vibration which should be clearly explained to students. An example of such explanation, deriving the Debye temperature from basic quantum and thermodynamic assumptions, is presented. The equations derived from theory are tested by experiments of face-centered cubic structures. Correlation between the minimum acoustic wavelength and the mean acoustic velocity is detected.