Comparison of Brillouin-Zone Integration Methods: Combined Linear and Quadratic Interpolation

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Abstract
A combined linear and quadratic interpolation method for Brillouin-zone integration is described. Comparisons of the combined method with previously introduced linear and quadratic approaches indicate that the combined scheme will require the least computer time in most cases. Calculations of the densities of states of phonons in copper and electrons in nickel are given as examples. Problems associated with critical points and the intersection of dispersion curves are also investigated numerically to a limited extent.