Uneisen Parameter Research Articles

Towards the high-throughput prediction of finite-temperature properties using the quasi-harmonic approximation

Lattice dynamics calculations within the quasi-harmonic approximation (QHA) provide an infrastructure for modelling the finite-temperature properties of periodic solids at a modest computational cost. With the recent widespread interest in materials discovery by data mining, a database of computed finite-temperature properties would be highly desirable. In this work we provide a first step toward this goal with a comparative study of the accuracy of five exchange-correlation functionals, spanning the local density approximation (LDA), generalised-gradient approximation (GGA) and meta-GGA levels of theory, for predicting the properties of ten Group 1, 2 and 12 binary metal oxides. We find that the predictions are bounded by the LDA, which tends to underestimate lattice parameters and cell volumes relative to experiments, but yields the most accurate results for bulk moduli, expansion coefficients and Grüneisen parameters, and the PBE GGA, which shows the opposite behaviour. The PBEsol GGA gives the best overall predictions of the lattice parameters and volumes whilst also giving relatively reliable results for other properties. Our results demonstrate that, given a suitable choice of functional, a variety of finite-temperature properties can be predicted with useful accuracy, and hence that high-throughout QHA calculations are technically feasible.

Phonon instability of a multi-principal element alloy

It is a common wisdom that the emergence of plasticity in crystalline solids is accompanied by the collapse of the softest vibrational mode. However, the recent advance in the multi-principal element alloys (MPEAs) complicates this scenario with essential local chemical inhomogeneity rendered by formation of the chemical short-range order (CSRO) via strong enthalpic interaction between specific atom pairs. Here we develop a set of computational metrics to characterize the features of phonons and the instability pathway in a prototypical ternary CoCrNi MPEA by atomistic simulations. There exists strong anharmonicity in MPEA quantified by a large Gr\"uneisen parameter, which is modulated by the degree of CSRO. Both localized and extended vibrational modes exist at either low- or high-frequency vibrations, whereas extremely high-frequency modes prefer local vibration. Introduction of CSRO increases the phonon density of states at high frequency and reduces the degree of anharmonicity. Therefore, CSRO enhances elastic stability. Upon loading, phonon instability occurs via annihilation of the softest mode, akin to the scenario seen in conventional crystals. However, softening of several low-frequency modes occurs simultaneously in MPEA, and it is the cooperative softening of them that leads to the onset of plasticity. Amid phonon instability, essential variations in the Gr\"ueisen parameter and participation ratio are observed, signifying the correlation between vibrational and configurational space in such compositional complex alloys. The results of unusual phonon features could give insight into how the structure, elasticity, and plasticity interact in generic multi-component high-entropy alloys.

Strong electron-phonon coupling and enhanced phonon Grüneisen parameters in valence-fluctuating metal EuPd2Si2

We study the valence crossover and strong electron-phonon coupling of EuPd$_2$Si$_2$ by polarization-resolved Raman spectroscopy. The fully-symmetric phonon mode shows strongly asymmetric lineshape at low temperature, indicating Fano-type interaction between this mode and a continuum of electron-hole excitations. Moreover, the frequency and linewidth of the phonon modes exhibit anomalies across the valence-crossover temperature, suggesting the coupling between valence fluctuations and lattice vibration. In particular, two phonon modes show significantly enhanced Gr\"uneisen parameter, suggesting proximity to a critical elasticity regime. The relative contribution of the structural change and valence change to the phonon anomalies is evaluated by density functional theory calculations.

First-principles study of the lattice thermal conductivity of the nitride perovskite LaWN3

Recently, ${\mathrm{LaWN}}_{3}$ nitride perovskite with polar symmetry has been synthesized and has shown a large piezoelectric response. In addition to experimentally measured piezoelectricity and theoretically predicted ferroelectricity, the thermal transport properties of ${\mathrm{LaWN}}_{3}$ remains unexplored. In this work, the phonon dispersion, lattice thermal conductivity, group velocity, phonon lifetime, phase space, and Gr\"uneisen parameters of ${\mathrm{LaWN}}_{3}$ are systematically studied using first-principles calculations. The results show that the lattice thermal conductivity of ${\mathrm{LaWN}}_{3}$ is 3.33 and 3.71 W/(mK) along the $a$ and $c$ axes at 300 K, respectively, which is comparable to some typical ferroelectric oxide perovskites such as ${\mathrm{PbTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$. Further analyses imply that over 60% of the lattice thermal conductivity of ${\mathrm{LaWN}}_{3}$ is contributed by the optical phonons. It is found that there exists the coupling effect between the acoustic and low-lying optical phonons which limits the group velocity and the contribution to lattice thermal conductivity of acoustic phonons. Additionally, the four-phonon scattering is found to play an important role in suppressing the lattice thermal conducitivty, which is reduced by \ensuremath{\sim}50% compared to the values where only three-phonon scattering is considered.

High-field quantum spin liquid transitions and angle-field phase diagram of the Kitaev magnet α−RuCl3

The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\alpha$-RuCl$_3$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations, and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K$-$J$-$\Gamma$-$\Gamma'$ model for $\alpha$-RuCl$_3$ [1], we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, and the magnetotropic susceptibility, etc, under a magnetic field with a tilting angle $\theta$ to the $c^*$-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\alpha$-RuCl$_3$ and other candidate Kitaev magnets.

Electric Grüneisen parameters for a biaxial spin-chain system

The electric Gr\"uneisen parameter, which characterizes the electrocaloric effect in the quantum spin system, has been introduced. We have calculated the electric Gr\"uneisen parameter for the biaxial spin-chain system with strong coupling between the spin and the electric subsystems. It is shown that the low-temperature electric field dependence of the electric Gr\"uneisen parameter manifests features at the critical values of the electric field and tends to constant at high temperatures. It is determined by the quantum critical points of the spin system. Such a behavior of the electric Gr\"uneisen parameter can be observed in electrocaloric experiments with spin-chain materials.

Phonon transport in Cu2GeSe3 : Effects of spin-orbit coupling and higher-order phonon-phonon scattering

Much attention has been focused on understanding the mechanism of low lattice thermal conductivity in Cu-based diamondlike thermoelectric compounds. For ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, the underlying origin of low lattice thermal conductivity remains to be clarified. In this work, the first-principles calculations are employed to systematically investigate the effects of spin-orbit coupling, higher-order phonon-phonon scattering, phonon wavelike tunneling, temperature-induced renormalization of phonon and phonon-phonon interaction, and volumetric expanse on the phonon transport of ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$. We show that the spin-orbit coupling results in no detectable change on the phonon frequencies, compared with those obtained without spin-orbit coupling, while it induces slight increase in both Gr\"uneisen parameter and lattice thermal conductivity of ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, and the underlying mechanism is thoroughly analyzed. With the fourth-order phonon scattering and temperature-induced renormalization, the calculated lattice thermal conductivities are well consistent with the experimental results. Due to the enhanced four-phonon scattering process, there are remarkable reductions for the thermal conductivity. In ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, the coherences term ${\ensuremath{\kappa}}_{c}$ contributes increasingly to the total lattice thermal conductivity when temperature arises. And after considering the effects of temperature-induced renormalization and higher-order phonon-phonon interactions, the ${\ensuremath{\kappa}}_{c}$ would provide $\ensuremath{\sim}5%$ and above 25% of total conductivity at 300 and 800 K, respectively. Our finding clarifies the mechanism of low thermal conductivity in ${\mathrm{Cu}}_{2}\mathrm{Ge}{\mathrm{Se}}_{3}$, and benefits the design of similar Cu-based diamondlike materials in thermoelectric applications.

First-principles study of thermoelasticity and structural phase diagram of CaO

We present pressure $(P)$ and temperature $(T)$ variations of elastic and anisotropic properties, solid-solid (rocksalt, B1 to cesium chloride, B2) and solid-liquid structural phase transitions of CaO. We employed first-principles density functional theory supplemented with an anharmonic contribution to phonon dynamics. Good agreement is obtained for all properties up to the pressure and temperature range relevant to the Earth's mantle and outer core. Born elastic criteria are generalized for arbitrary stress to elaborate the structural phase diagram from a thermoelastic viewpoint. We propose a self-consistent computational scheme to incorporate the effect of thermal hysteresis into Lindemann's melting law. This improvised melting law exhibits quantitative agreement with reported findings for the high-$P$ melting curve. We find the triple point (i.e., the coexistence of B1, B2, and liquid phases) at 23 GPa and 4600 K. By examining the pressure-term included elastic properties, we can show that the solid-solid transition is mechanical in a pressure range of 0--200 GPa and temperature up to 3000 K. The softening of shear elastic constant ${C}_{44}$ drives the B1-B2 phase transition. This assertion is corroborated by examining the phonon dispersion curve and mode Gr\"uneisen parameter at different pressures for both B1 and B2 phases. The solid-liquid phase boundary can be treated accurately through the temperature-dependent thermodynamic Gr\"uneisen parameter. Furthermore, in this paper, we predict a negative melting slope $>140\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$ with a peak temperature of 7800 K, suggesting a smaller molar volume on the liquid side than that of the solid phase. This finding is supported by electronic band structure calculation. It is proposed that the hybridization of the empty $3d$ band of the cation with $s$ orbitals lowers the conduction band to cross the Fermi energy at the Brillouin zone center and leads the insulator-to-metal/semimetal phase transition $\ensuremath{\sim}200\phantom{\rule{0.28em}{0ex}}\mathrm{GPa}$. Different electronic states on solid and liquid sides make the liquid phase more compressible than the solid phase, eventually reducing the melting temperature with pressure.

First-principles thermal equation of state of fcc iridium

The thermal equation of states for fcc iridium (Ir) is obtained from first-principles molecular dynamics up to 3000 K and 540 GPa. The equation of state (EoS) is globally fitted to a simplified free-energy model and various parameters are derived. The theoretical principal Hugoniot is compared with shock wave experiments, where discrepancy suggests formation of new Ir phases. A few representative EoS parameters, such as bulk modulus ${K}_{T}$, thermal expansivity $\ensuremath{\alpha}$, Gr\"uneisen parameter $\ensuremath{\gamma}$, constant pressure capacity ${C}_{P}$, and Debye temperature ${\mathrm{\ensuremath{\Theta}}}_{\mathrm{D}}$, are computed to compare with experimental data.

Shock-induced melting of [100] lithium fluoride: Sound speed and Hugoniot measurements to 230 GPa

Although [100] lithium flouride (LiF) is the most widely used optical window material in dynamic compression experiments, its high stress ($>100\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$) shock compression response, including melting, is not well understood. To address this need, we measured wave profiles in plate impact experiments to determine the Hugoniot states and longitudinal sound speeds in [100] LiF crystals shock compressed to 231 GPa. The measured peak states are fitted well by a linear shock velocity--particle velocity relation, providing an accurate determination of the LiF Hugoniot curve to significantly higher stresses than previous experiments. The longitudinal sound speeds show a near linear increase with density compression to 182 GPa. Between 182 GPa and 195 GPa, the sound speed and the longitudinal modulus decrease abruptly, due to shock-induced melting. The increasing sound speeds and moduli at higher stresses suggest that shock compressed LiF is fully liquid at 195 GPa and above, allowing determination of the Gr\"uneisen parameter for liquid LiF. The melt stress determined here differs from that predicted by current multiphase equations of state for LiF. Our results provide important insight into the high stress solid and liquid states of shock compressed LiF and point to the need for an improved multiphase equation of state at high pressures and high temperatures.

Low lattice thermal conductivity in alkali metal based Heusler alloys

On the basis of purely their electronic properties, semiconducting alkali and alkaline earth metal based Heusler alloys have been identified as potentially promising thermoelectrics. Their thermal transport properties are decisive and help to further gauge this potential. This motivates us to systematically investigate lattice properties of three eight valence electron Heusler alloys, namely, ${\mathrm{Li}}_{2}\mathrm{NaSb}, {\mathrm{Na}}_{2}\mathrm{KSb}$, and ${\mathrm{K}}_{2}\mathrm{CsSb}$, using first-principles approaches. On the basis of both qualitative and quantitative descriptors (assessing covalent bonding, the atomic displacement parameter, the phonon density of states, the Gr\"uneisen parameter, the phonon group velocity, and the phonon lifetime) we analyze in detail the lattice degrees of freedom and their contribution to thermal transport. Out of the three materials, ${\mathrm{Na}}_{2}\mathrm{KSb}$ and ${\mathrm{K}}_{2}\mathrm{CsSb}$ exhibit surprisingly low lattice thermal conductivity, which we can attribute to the anharmonic rattling of the loosely bound alkali atom in the crystal lattice. ${\mathrm{K}}_{2}\mathrm{CsSb}$ has a lattice thermal conductivity two times lower than that of SnSe, a material with a record figure of merit.

Comprehensive investigation of the extremely low lattice thermal conductivity and thermoelectric properties of BaIn2Te4

Recently, an extremely low lattice thermal conductivity value has been reported for the alkali-based telluride material ${\mathrm{BaIn}}_{2}{\mathrm{Te}}_{4}$. The value is comparable with low-thermal conductivity metal chalcogenides, and the glass limit is highly intriguing. Therefore, to shed light on this issue, we performed first-principles phonon thermal transport calculations. We predicted highly anisotropic lattice thermal conductivity along different directions via the solution of the linearized phonon Boltzmann transport equation. More importantly, we determined several different factors as the main sources of the predicted ultralow lattice thermal conductivity of this crystal, such as the strong interactions between low-frequency optical phonons and acoustic phonons, small phonon group velocities, and lattice anharmonicity indicated by large negative mode Gr\"uneisen parameters. Along with thermal transport calculations, we also investigated the electronic transport properties by accurately calculating the scattering mechanisms, namely the acoustic deformation potential, ionized impurity, and polar optical scatterings. The inclusion of spin-orbit coupling (SOC) for electronic structure is found to strongly affect the $p$-type Seebeck coefficients. Finally, we calculated the thermoelectric properties accurately, and the optimal $ZT$ value of $p$-type doping, which originated from high Seebeck coefficients, was predicted to exceed unity after 700 K and have a direction averaged value of 1.63 (1.76 in the $y$-direction) at 1000 K around $2\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ hole concentration. For $n$-type doping, a $ZT$ around $3.2\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ concentration was predicted to be a direction-averaged value of 1.40 (1.76 in the $z$-direction) at 1000 K, mostly originating from its high electron mobility. With the experimental evidence of high thermal stability, we showed that the ${\mathrm{BaIn}}_{2}{\mathrm{Te}}_{4}$ compound has the potential to be a promising mid- to high-temperature thermoelectric material for both $p$-type and $n$-type systems with appropriate doping.

Charge density wave transitions, soft phonon, and possible electronic nematicity in BaNi2(As1−xPx)2

A detailed investigation of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ single crystals using high-resolution thermal-expansion, heat-capacity, Young's-modulus, and resistivity measurements is presented. The phase diagram of ${\mathrm{BaNi}}_{\text{2}}{({\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{P}}_{x})}_{\text{2}}$ is shown to be much richer than suggested by the original data of Kudo et al. [Phys. Rev. Lett. 109, 097002 (2012)]. The transition to the commensurate charge density wave (C-CDW) is always preceded by a fourfold symmetry-breaking transition associated with the long-range ordering of a strongly fluctuating unidirectional incommensurate charge density wave (I-CDW). Significant precursors above the I-CDW and C-CDW transitions are seen in the thermal expansion and resistivity and are particularly evident in the temperature dependence of the $c/a$ ratio of the lattice parameters. Heat-capacity measurements of the crystals with a higher P content and a higher critical temperature of 3.2 K uncover a Debye-like behavior of a soft-phonon mode with a very low ${\mathrm{\ensuremath{\Theta}}}_{\text{Debye}}$ of roughly 50 K. Associated with this soft phonon are unusually large thermal-expansion anomalies, resulting in logarithmically diverging uniaxial phonon Gr\"uneisen parameters. Young's-modulus data of these higher-${T}_{c}$ crystals exhibit a significant softening in both ${B}_{1g}$ and ${B}_{2g}$ channels, which is argued to be incompatible with nematic criticality and is rather associated with a broad phase transition to an hitherto unknown structure. Possible origins of the increase in the superconducting critical temperature with P substitution are discussed.

Zero-point lattice expansion and band gap renormalization: Grüneisen approach versus free energy minimization

The zero-point lattice expansion (ZPLE) is a small variation of the lattice parameters induced by the presence of phonons in a material compared to the static lattice picture. It contributes significantly to the zero-point renormalization (ZPR) of the band gap energy, but its consequences have not been investigated as thoroughly as those stemming from electron-phonon interactions. In the usual first-principles approach, one evaluates the ZPLE by minimizing the $T=0$ K Helmholtz free energy. In this work, we show that the formalism based on the Gr\"uneisen parameters, which commonly neglects zero-point effects, can be efficiently used to compute the ZPLE for both isotropic and anisotropic materials at a much lower computational cost. We systematically test this formalism on 22 cubic and wurtzite materials, and we obtain excellent agreement with free energy minimization results for both the ZPLE and the resulting band gap ZPR. We use our results to validate an empirical expression estimating the ZPLE-induced ZPR, and we unveil its sensitivity to the temperature range involved in estimating the ZPLE from experimental data. Our findings finally reveal that the ZPLE contribution to the band gap ZPR can reach from 20% to more than 80% of the electron-phonon interaction contribution for heavier or more ionic materials, including materials containing light atoms. Considering both contributions on an equal footing is thus essential should one attempt to compare theoretical ZPR results with experimental data.

Structural stability of orthorhombic DyScO3 under extreme conditions of pressure and temperature

In the present work, the effect of elevated pressure and lowered temperature on the structural and vibrational stability of dysprosium scandate (${\mathrm{DyScO}}_{3}$) is studied via high-pressure synchrotron x-ray diffraction (HPXRD) and high-pressure (HP) and low-temperature Raman spectroscopy. A solid-state reaction route is employed to synthesize the material with a crystallite size of 92 nm, which at ambient conditions exhibits an orthorhombic phase with the space group $Pbnm$ (62). HPXRD results reveal excellent phase stability of the material, with the ratio of the polyhedral volumes and the compressibility for the ${\mathrm{DyO}}_{12}$ and ${\mathrm{ScO}}_{6}$ polyhedra to be around 4.26 and 1 for the entire applied pressure range of up to 40 GPa. Interestingly, the combination of HPXRD and HP Raman measurements signals a change in the preferred orientations in the crystalline structure with the increased pressure, while keeping the structure stable. The bulk modulus of the material is estimated to be 189.4 GPa from the HPXRD data and is further used to estimate the mode Gr\"uneisen parameter (\ensuremath{\gamma}) for various Raman modes. The behavior of phonon frequency with varying temperature is explained by considering the anharmonic effects, i.e., lattice expansion and perturbation in the Hamiltonian, with an increase in temperature. Furthermore, the implicit and explicit anharmonicity contributions were calculated to elucidate the phonon decay mechanisms. Our results offer valuable insights relating to the behavior of this intriguing class of materials under extreme conditions and lays the foundation for further exploration.

Lattice Anharmonicity in BiS2-Based Layered Superconductor RE(O,F)BiS2 (RE = La, Ce, Pr, Nd)

We studied Gr\"uneisen parameter ({\gamma}G) to investigate lattice anharmonicity in a layered BiS2-based superconductor system REO1-xFxBiS2 (RE = La, Ce, Pr, Nd), where in-plane chemical pressure was tuned by substituting the RE elements. With increasing in-plane chemical pressure, bulk modulus remarkably increases, and a high {\gamma}G is observed for RE = Nd. The dependence of {\gamma}G on in-plane chemical pressure exhibits a good correlation with Tc, and a higher Tc is achieved when {\gamma}G is large for RE = Nd. In addition, {\gamma}G shows a slight decrease by a decrease of F concentration (x) in REO1-xFxBiS2. Our results show that the anharmonic vibration of Bi along the c-axis is present in REO1-xFxBiS2, and the enhancement of the anharmonicity is positively linked to superconducting Tc and pairing mechanisms.

Magnetovolume Effect on the First-Order Metamagnetic Transition in UTe2

The link between the metamagnetic transition and novel spin-triplet superconductivity of UTe$_2$ was discussed thermodynamically through magnetostriction measurements in a pulsed-magnetic field. We revealed a discontinuous magnetostriction across the metamagnetic transition at $\mu_0H_{\rm m}\approx 35$~T for the applied magnetic fields along the crystallographic $b$ axis in the orthorhombic structure. The resultanting volume magnetostriction of $\Delta V/V \approx-5.9\times 10^{-4}$ gives the initial pressure dependence of $H_{\rm m}$ by employing the Clausius-Clapeyron's equation, which agrees with previous pressure experiments. Further, significant anisotropic magnetostriction (AMS), derived by subtracting the averaged linear magnetostriction, was revealed. Contrary to the weakly field-dependent AMS along the $a$ axis, those along the $b$ and $c$ axes show strong field dependences with a similar magnitude but with opposite signs, indicating its lattice instability. The relationship between characteristic energy scales of magnetic fields and temperatures was discussed in terms of the Gr\"uneisen parameters compared to the other $f$-electron systems. The volume shrinkage in UTe$_2$ at $H_{\rm m}$, contrary to the volume expansion in typical heavy fermion metamagnets, pushes to invoke the link with the valence instability related to the itinerant-localized dual nature of the U magnetism.

Uniaxial strain tuning of Raman spectra of a ReS2 monolayer

In contrast to the intensively investigated transition metal dichalcogenides like ${\mathrm{MoS}}_{2}$, ${\mathrm{ReS}}_{2}$ crystals possess a reduced in-plane symmetry, leading to anisotropic optical properties. Here, we report on the impact of strain on the Raman response of a ${\mathrm{ReS}}_{2}$ monolayer. Since mechanical strain can be used to shift the Raman-active phonon frequencies, we apply uniaxial tensile strain of up to 0.74% along the Re-chain direction ($x$ axis) of the atomically thin crystal and measure the Raman response with the scattered light polarized parallel and perpendicular to the strain direction along the $x$ axis. Complementarily, we carry out ab initio calculations to determine the phonon energies and Raman intensities under strain. We find a shift to lower energies for all phonon modes when tensile strain is applied to the monolayer. The determined gauge factors/Gr\"uneisen parameters are in good agreement between experiment and theory. Our study demonstrates that the optomechanical properties of ${\mathrm{ReS}}_{2}$ can be tuned by external straining, which is of importance for potential future strain-sensor applications, e.g., in the biomedical sector.

Effect of low-frequency optical phonons on the thermal conductivity of 2H molybdenum disulfide

Phonon engineering is a novel and effective approach to tailor the thermal conductivity for the thermoelectric performance and heat dissipation. In general, the acoustic phonons rather than the optical phonons are dominant in heating carriers. Here we report an unprecedented large contribution, 47% overall, from the low-frequency optical phonons to the in-plane thermal conductivity in 2H molybdenum disulfide, revealed by low-wave-number high-pressure Raman technology assisted with first-principles calculations. The analysis of phonon dispersion curves and Gr\"uneisen parameters of individual phonon modes reveals that the large contribution originates in a joint effect of the large group velocity of low-frequency optical phonons and their strong anharmonic effects. The joint effect is continuously maintained when pressure increases, up to 20 GPa. Our work provides new insights into the optical phonon transport, paving the way for the phonon engineering and thermal management.

Enhancing efficiency and scope of first-principles quasiharmonic approximation methods through the calculation of third-order elastic constants

A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Gr\"uneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.