Phonon Anharmonicity: What Can Grüneisen Parameters Tell Us?*

Phonon anharmonicity is essential for explaining phenomena such as thermal conductivity, thermal expansion, and the change in phonon frequencies with strain. In particular, strain dependence of phonon frequencies can be expressed through Grüneisen parameters, which are often used as a heuristic to quantify anharmonicity in general for a given system. However, the exact nature by which a system departs from anharmonicity is important - third, fourth, and higher order terms in the atomic potential play different roles in different situations. Are the same higher order force constants that contribute to Grüneisen parameters the ones involved in, for example, thermal transport processes, or the ones that cause the quasiharmonic approximation to fail at high temperature? Using both analytic methods and density functional theory to inform and understand the underlying features of anharmonicity for a variety of systems, we find that while Grüneisen parameters provide valuable insight for how phonon modes couple to strain, one must take care in relating this quantity to other anharmonic effects. We further explore the relationship between phonons and strain, and other couplings between periodic eigenfunctions and aperiodic perturbations.