Anharmonic elastic and phonon properties of Si

A unified framework is suggested for the discussion of anharmonic phonon coupling constants and anharmonic elastic constants in diamond-structure materials. A summary is given, within this framework, of those anharmonic constants which have previously been determined experimentally or theoretically for silicon. New local-density total-energy calculations for X-point phonons in Si are used to add to this database of known anharmonic constants. It is proposed that empirical models for interatomic potentials should be constrained to fit this database. A generalized Keating model which has been fitted in this way, with two- and three-body couplings of third and fourth order, is presented. It can be used to calculate arbitrary anharmonic phonon couplings through fourth order.