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The microscopic origin of the large negative thermal expansion of cubicscandium trifluorides (ScF3) is investigated by performing a set of anharmonicfree-energy calculations based on density functional theory. We demonstratethat the conventional quasiharmonic approximation (QHA) completely breaks downfor ScF3 and the quartic anharmonicity, treated nonperturbatively by theself-consistent phonon theory, is essential to reproduce the observedtransition from negative to positive thermal expansivity and the hardening ofthe R4+ soft mode with heating. In addition, we show that the contribution fromthe cubic anharmonicity to the vibrational free energy, evaluated by theimproved self-consistent phonon theory, is significant and as important as thatfrom the quartic anharmonicity for robust understandings of the temperaturedependence of the thermal expansion coefficient. The first-principles approachof this study enables us to compute various thermodynamic properties of solidsin the thermodynamic limit with the effects of cubic and quarticanharmonicities. Therefore, it is expected to solve many known issues of theQHA-based predictions particularly noticeable at high temperature and instrongly anharmonic materials.

First-principles study of phonon anharmonicity and negative thermal expansion in ScF3