Phonon Quasiparticles and Anharmonic Free Energy in Complex Systems

Abstract

We use a hybrid strategy to obtain anharmonic frequency shifts and lifetimes of phonon quasiparticles from first principles molecular dynamics simulations in modest size supercells. This approach is effective irrespective of crystal structure complexity and facilitates calculation of full anharmonic phonon dispersions, as long as phonon quasiparticles are well defined. We validate this approach to obtain anharmonic effects with calculations in MgSiO3 perovskite, the major Earth forming mineral phase. First, we reproduce irregular thermal frequency shifts of well characterized Raman modes. Second, we combine the phonon gas model (PGM) with quasiparticle frequencies and reproduce free energies obtained using thermodynamic integration. Combining thoroughly sampled quasiparticle dispersions with the PGM we then obtain first-principles anharmonic free energy in the thermodynamic limit (N→∞).

Premelting hcp to bcc Transition in Beryllium

“…Similarly, all other quasiparticle mode frequencies sampled by the 4x4x4 supercell are equally well defined. As previously indicated [30,31], these renormalized phonon frequencies plus the normal modes enable the calculation of the renormalized force constant matrix and complete phonon dispersions. This quantitative characterization of phonon quasiparticles and renormalized phonon dispersion provide a solid foundation for studying thermal properties.…”

“…At P > 11 GPa, bcc Be is dynamically stabilized by pressure and the QHA might, in principle, be applied. However, the hcp/bcc boundary [23][24][25] predicted by the QHA does not agree with experiments [13], suggesting that anharmonic effects still play an important role at higher pressures.In this Letter, we report a new investigation of the phase stability of bcc Be and the associated hcp → bcc phase transition boundary up to 30 GPa and temperatures up to 2,000 K. We have used a recently developed hybrid approach [30,31] that combines first-principles molecular dynamics (MD) and lattice dynamics calculations to address anharmonic effects in the free energy. In this method, the concept of phonon quasiparticles offers a quantitative characterization of the effects of lattice anharmonicity [32,33].…”

“…should have a Lorentzian-type line shape [30,31]. The renormalized phonon frequency ω q,s , and the linewidth, Γ q,s can then be obtained as discussed in more details in the Supplemental Materials.…”

Accurate and precise ab initio anharmonic free-energy calculations for metallic crystals: Application to hcp Fe at high temperature and pressure

“…This includes methods like velocity autocorrelation [21][22][23][24][25] , average force constants [26][27][28][29][30] , variational approaches [31][32][33][34][35] , a semiempirical ansatz [36][37][38] , and the most commonly used method: self-consistent ab initio lattice dynamics (SCAILD) 39 . The general idea in common with these methods is to formulate a temperature-dependent effective harmonic system, defining force constants or the elements of a dynamical matrix, such that some feature of the harmonic system matches that computed in the system being studied, or a formal bound on the target-system FE is minimized.…”

Triggering waves in nonlinear lattices: Quest for anharmonic phonons and corresponding mean-free paths

“…Thus, this MFP is not uniquely given in the sense that various time scales come to mind: namely, the so-termed phonon lifetime (as obtained from Lorentzian fit) in prior phonon quasiparticle studies in the reciprocal lattice space [20][21][22][23][24][25][26][27][28], a phonon collision time, or transport relaxation time (notably being not equivalent with the phonon lifetime) as obtained from a Peierls-Boltzmann approach are just but a few [29,30]. Likewise, the a priori choice for the speed scale taken as the group velocity is also empirical.…”