We formulate a theory of thermal expansion based on the self-consistent phonon (SCP) theory, which nonperturbatively considers the anharmonic effect. We show that the Grünseisen formula holds within the SCP theory by replacing the phonon frequency by the SCP frequency. By comparing it with the quasiharmonic approximation (QHA), we derive explicit formulas of the correction to the QHA result. We show that the phonon anharmonicity gives a small correction of $O(\langle{\hat{U}_4\rangle}/\langle{\hat{U}_2\rangle})$ to the thermal expansion coefficient $α$, where $\hat{U}_2$ and $\hat{U}_4$ are the harmonic and the quartic terms of the potential energy surface. On the other hand, we show that the phonon anharmonicity gives two correction terms to the temperature ($T$)-dependent phonon frequency shift which are comparable to the original QHA term. In strongly anharmonic materials such as NaCl and MgO, these two correction terms tend to cancel out each other, which explains why the QHA sometimes gives reasonable values for the $T$-dependent phonon frequency shift while it fails for thermal expansion.
Full optimization of quasiharmonic free energy with anharmonic lattice model: Application to thermal expansion and pyroelectricity of wurtzite GaN and ZnO
Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well-understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100-1500K on a single-crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmoni…
All phonons in a single crystal of NaBr were measured by inelastic neutron scattering at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal-optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. Ab initio computations were first performed with the quasiharmonic approximation (QHA), in which the phonon frequencies depend only on $V$, and on $T$ only insofar as it alters $V$ by thermal expansion. This QHA was an unqualified failure for predicting the temperature dependence of phonon frequenci…
We propose a size-consistent Grüneisen-quasiharmonic approach (GQA) to calculate the lattice thermal conductivity $κ_l$ where the Grüneisen parameters that measure the degree of phonon anharmonicity are calculated directly using first-principles calculations. This is achieved by identifying and modifying two existing equations related to the Slack formulae for $κ_l$ that suffer from the size-inconsistency problem when dealing with non-monoatomic primitive cells (where the number of atoms in the primitive cell $n$ is greater than one). In conjunction with other thermal parameters such as the ac…
A first-principles approach called the {\it{self-consistent quasiharmonic approximation}} (SC-QHA) method is formulated to calculate the thermal expansion, thermomechanics, and thermodynamic functions of solids at finite temperatures with both high efficiency and accuracy. The SC-QHA method requires fewer phonon calculations than the conventional QHA method, and also facilitates the convenient analysis of the microscopic origins of macroscopic thermal phenomena. The superior performance of the SC-QHA method is systematically examined by comparing it with the conventional QHA method and experim…
The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. Here we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of t…
The microscopic origin of the large negative thermal expansion of cubic scandium trifluorides (ScF3) is investigated by performing a set of anharmonic free-energy calculations based on density functional theory. We demonstrate that the conventional quasiharmonic approximation (QHA) completely breaks down for ScF3 and the quartic anharmonicity, treated nonperturbatively by the self-consistent phonon theory, is essential to reproduce the observed transition from negative to positive thermal expansivity and the hardening of the R4+ soft mode with heating. In addition, we show that the contributio…
To address the effects of lattice anharmonicity across the perovskite to post-perovskite transition in MgSiO$_3$, we conduct calculations using the phonon quasiparticle (PHQ) approach. The PHQ is based on \textit{ab initio} molecular dynamics and, in principle, captures full anharmonicity. Free energies in the thermodynamic limit ($N \rightarrow \infty$) are computed using temperature-dependent quasiparticle dispersions within the phonon gas model. Systematic results on anharmonic thermodynamic properties and phase boundary are reported. Both the local density approximation (LDA) and the gener…
While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation; at high temperatures, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermal expansion, thermodynamic stability, heat capacity, optical properties, thermal transport and other nonlinear properties…
The thermal properties of materials are critically important to various technologies and are increasingly the target of materials design efforts. However, it is only relatively recent advances in first-principles computational techniques that have enabled researchers to explore the microscopic mechanisms of thermal properties, such as thermal expansion. We use the Grüneisen theory of thermal expansion in combination with density functional calculations and the quasiharmonic approximation to uncover mechanisms of thermal expansion in PbTiO$_3$ thin-films in terms of elastic and vibrational cont…
Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: application to platinum and palladium hydrides
Low temperature and high pressure Raman and x-ray studies of pyrochlore Tb$_2$Ti$_2$O$_7$ : phonon anomalies and possible phase transition
我们对Tb $_2$ Ti $_2$ O $_7$单晶进行了温度和压力相关的拉曼和X射线测量。我们把观察到的声子的反常温度依赖性归因于声子-声子非谐相互作用。准谐波和非谐波贡献的声子频率的温度依赖性的变化定量估计使用模式Grüneisen参数来自压力依赖的拉曼实验和体积模量从高压X射线测量。此外，我们的拉曼和X射线数据表明，在$\sim$ 9 GPa的烧绿石晶格的微妙的结构变形。我们讨论了可能的影响，我们的研究结果上的自旋液体行为的Tb $_2$ Ti $_2$ O $_7$。
We report the development of a forcefield capable of reproducing accurate lattice dynamics of metal-organic frameworks. Phonon spectra, thermodynamic and mechanical properties, such as free energies, heat capacities and bulk moduli, are calculated using the quasi-harmonic approximation to account for anharmonic behaviour due to thermal expansion. Comparison to density functional theory calculations of properties such as Gr$\mathrm{\ddot{u}}$neisen parameters, bulk moduli and thermal expansion supports the accuracy of the derived forcefield model. Material properties are also reported in a full…
Predictions of the anisotropic coefficients of thermal expansion are needed to not only compare to experimental measurement, but also as input for macroscopic modeling of devices which operate over a large temperature range. While most current methods are limited to isotropic systems within the quasiharmonic approximation, our method uses first-principles calculations and includes anharmonic effects to determine the temperature-dependent properties of materials. These include the lattice parameters, anisotropic coefficients of thermal expansion, isothermal bulk modulus, and specific heat at co…
We report an experimental and theoretical investigation of the lattice dynamics and thermal properties of the actinide dioxide NpO$_2$. The energy-wavevector dispersion relation for normal modes of vibration propagating along the $[001]$, $[110]$, and $[111]$ high-symmetry lines in NpO$_2$ at room temperature has been determined by measuring the coherent one-phonon scattering of X-rays from a $\sim$1.2 mg single-crystal specimen, the largest available single crystal for this compound. The results are compared against ab initio phonon dispersions computed within the first-principles density fun…
Negative thermal expansion (NTE) - the phenomenon where some materials shrink rather than expand when heated - is both intriguing and useful, but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, ScF3, from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes - the vibration…
While anomalous diffusion coefficients with non-Arrhenius like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and $β$-Ti by coupling quasiharmonic transition state theory and large displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approac…
