Anharmonic Phonon Quasiparticle Theory of Zero-point and Thermal Shifts in Insulators: Heat Capacity, Bulk Modulus, and Thermal Expansion

摘要

The Quasi-harmonic (QH) approximation uses harmonic vibrational frequenciesomega(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, QHapproximation gives a good zeroth order theory of thermal expansion, and firstorder theory of bulk modulus. Here, n-th order means smaller than the leadingterm by n powers of epsilon, where epsilon is the ratio hbar omega(Q)/E(el) orkT/E(el), and E(el) is an electronic energy scale, typically 2 to 10 eV.Experiment often shows evidence for next order corrections. When suchcorrections are needed, anharmonic interactions must be included. The mostaccessible measure of anhamonicity is the quasiparticle (QP) energy,omega(Q,V,T), seen experimentally by vibrational spectroscopy. However, thiscannot just be inserted into the harmonic free energy F(H). In this paper, afree energy formula is found which corrects the double-counting of anharmonicinteractions 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 isused to give corrections to specific heat and volume thermal expansion. The QHformulas for isothermal and adiabatic bulk moduli are clarified, and the routeto higher order corrections is indicated.