Thermal Expansion in Insulating Solids From First Principles

Abstract

In this Tutorial, we describe the use of the quasiharmonic approximation and first-principles density functional theory (DFT) to calculate and analyze the thermal expansion of insulating solids. We discuss the theory underlying the quasiharmonic approximation, and demonstrate its practical use within two common frameworks for calculating thermal expansion: the Helmholtz free energy framework and Grüneisen theory. Using the example of silicon, we provide a guide for predicting how the lattice parameter changes as a function of temperature using DFT, including the calculation of phonon modes and phonon density of states, elastic constants, and specific heat. We also describe the calculation and interpretation of Grüneisen parameters, as well as how they relate to coefficients of thermal expansion. The limitations of the quasiharmonic approximation are briefly touched on, as well as the comparison of theoretical results with experimental data. Finally, we use the example of ferroelectric PbTiO${}_3$ to illustrate how the methods used can be adapted to study anisotropic systems.

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Cited by in corpus (13)

• Full optimization of quasiharmonic free energy with anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO
• Anharmonic Grüneisen theory based on self-consistent phonon theory: Impact of phonon-phonon interaction neglected in the quasiharmonic theory
• A First-Principles Explanation of the Luminescent Line Shape of SrLiAl${}_3$N${}_4$:Eu${}^{2+}$ Phosphor for Light-Emitting Diode Applications
• Machine-learning correction to density-functional crystal structure optimization
• Strain game revisited for complex oxide thin-films: Substrate-film thermal expansion mismatch in PbTiO${}_3$
• Metric-driven search for structurally stable inorganic compounds
• Uncertainty quantification in first-principles predictions of phonon properties and lattice thermal conductivity
• Thermal expansion and temperature dependence of Raman modes in epitaxial layers of Ge and Ge${}_{1-x}$Sn${}_x$
• Approximations in first-principles volumetric thermal expansion determination
• Efficient first-principles approach to Gibbs free energy with thermal expansion
• Understanding mechanisms of thermal expansion in PbTiO${}_3$ thin-films from first principles: role of high-order phonon-strain anharmonicity
• Band gap renormalization and indirect optical absorption in MgSiN${}_2$ at finite temperature
• Raman spectroscopy of van der Waals topological magnet GdGaI