Anharmonic phonon quasiparticle theory of zero-point and thermal shifts in insulators: Heat capacity, bulk modulus, and thermal expansion

Abstract

The Quasi-harmonic (QH) approximation uses harmonic vibrational frequencies omega(H,Q,V), computed at volumes V near the volume where the Born-Oppenheimer (BO) energy is minimum. When this is used in the harmonic free energy, QH approximation gives a good zeroth order theory of thermal expansion, and first order theory of bulk modulus. Here, n-th order means smaller than the leading term by n powers of epsilon, where epsilon is the ratio hbar omega(Q)/E(el) or kT/E(el), and E(el) is an electronic energy scale, typically 2 to 10 eV. Experiment often shows evidence for next order corrections. When such corrections are needed, anharmonic interactions must be included. The most accessible measure of anhamonicity is the quasiparticle (QP) energy, omega(Q,V,T), seen experimentally by vibrational spectroscopy. However, this cannot just be inserted into the harmonic free energy F(H). In this paper, a free energy formula is found which corrects the double-counting of anharmonic interactions that is made when F is approximated by F(H,omega(Q,V,T)). The term "QP thermodynamics" is used for this way of treating anharmonicity. It enables (n+1)-order corrections, if QH theory is accurate to order n. This procedure is used to give corrections to specific heat and volume thermal expansion. The QH formulas for isothermal and adiabatic bulk moduli are clarified, and the route to higher order corrections is indicated.