Elastic Moduli and Phonons

Abstract

Abstract In this chapter, the calculation of second-order elastic constants and quasiharmonic phonons from quantum-based interatomic potentials (QBIPs) is addressed for nontransition metals at the pair potential level and for transition metals at the level of two-, three- and four-ion potentials. The dynamical matrix establishing the phonon frequencies at constant volume is developed in terms of tangential and radial force-constant functions. Selected QBIP phonon spectra and Debye temperatures thereby obtained for twelve prototype bcc, fcc and hcp metals are compared against experiment. Treatment of the elastic moduli starts from the stress-strain relations of linear elasticity, makes close contact with the long wavelength quasiharmonic phonon limit, and provides local volume corrections where needed to yield accurate values of the shear modulus, bulk modulus and nonshear elastic moduli for bcc, fcc and hcp crystals. Applications to the calculation of thermodynamic properties below the Debye temperature such as the specific heat of bcc Ta and the temperature-induced hcp to bcc phase transition in Mg are discussed.