CIX. The zero point energy and Θ crystals

Abstract

The calculations of Montroll of the moments of the frequency spectrum of a number of crystal lattices enable an accurate estimate to be made of the zero point energy of these lattices. It has been customary to use the value 9/8kΘ, based on the Debye approximation, to estimate the zero point energy, and it is shown that this formula is only accurate if Θ _L , the limiting value of Θ for high temperatures is used. It is shown that Θ _L can be simply expressed in terms of the force constants between atoms of the crystal.