Comparison between phenomenological and pseudopotential force constants for the lattice dynamics of Al

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Abstract
In this paper we present a critical comparison of calculations of phonon-dispersion curves for aluminum, based on pseudopotential and empirical force-constant methods. The former method is based on both perturbative and nonperturbative evaluations of the total energy of the crystal. In the perturbative approach the total energy is evaluated to second order in the electron-ion interaction with a local pseudopotential. In the nonperturbative approach the electron-ion interaction is treated exactly using a nonlocal ab initio pseudopotential. In the empirical force-constant method the total energy is represented by a sum of two-body and three-body terms, the latter being restricted to interactions among triplets of nearest neighbors and of nearest and next-nearest neighbors. All models include physical mechanisms for ensuring the breakdown of the Cauchy relation. We show that in each method convergence of the calculated phonon frequencies requires the inclusion of long-range interactions. The radial-force constants obtained by the empirical and perturbative pseudopotential methods are very similar for the first three shells of neighbors. On the other hand, the tangential force constants differ markedly, a reflection of the different physical mechanisms that come into play in the various models in the establishment of equilibrium.

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