The vibration spectra of crystals and the theory of their specific heats

Summary

The enumeration of wave-patterns within an enclosure on a scale of wave-lengths or frequencies presupposes that the waves are perfectly undamped and that the enclosure is perfectly reflecting. In any material medium, however, wave-propagation is necessarily damped and such dam** may be so enormous as altogether to preclude wave-propagation. It follows that it is not permissible to identify the modes of atomic vibration in crystals with wave-patterns. Since the specific heat theories of Debye and of Born-Karman are based on such identification, they cannot be sustained.

For any mechanical model to represent the dynamic behaviour of a crystal, it is necessary that it should satisfy the requirements for dynamic similarity. When these requirements are satisfied, the behaviour of the model does not support the ideas underlying the Debye and Born-Karman theories, but on the other hand agrees with the results of the theory of the dynamics of crystal lattices put forward by the writer in 1943.

The phenomena of light-scattering observed in crystals are also discussed and it is shown that the experimental facts are incompatible with the ideas underlying the Born-Karman theory.