Modified Moments for Harmonic Solids

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Abstract
Appropriately defined modified moments of the frequency distribution provide a powerful new tool for studying the properties of solids in the harmonic approximation. They can be calculated much more easily than power moments and stably determine the thermal and dynamic properties of harmonic solids with great accuracy. We define a set of modified moments appropriate for harmonic solids and show how they can be computed directly from the dynamical matrix by algebraic techniques. As an illustration of the method, forty exact modified moments are given for the cubic close-packed solid with nearest-neighbor interactions. The method is stable for the computation of approximate modified moments for models where exact computation is not feasible. In contrast to approximate power moments, approximate modified moments contain sufficient information about the frequency distribution to determine thermal and dynamic properties of harmonic solids.