Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calculations cannot be overly emphasized.Phonopy is an open source code for such calculations launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calculations are applied in materials science.

The tetragonal to orthorhombic ferroelastic phase transition between rutile-and CaCl 2 -type SiO 2 at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with B 1g and A g symmetries, shear moduli, transverse-acoustic mode, rotation angle of the SiO 6 octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.

Lattice thermal conductivities of zincblende-and wurtzite-type compounds with 33 combinations of elements are calculated with the single-mode relaxation-time approximation and linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calculations. In 9 zincblende-type compounds, distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary non-smoothly with respect to wave vector, which is explained from the imaginary parts of the self energies. It is presented that detailed combination of phonon-phonon interaction strength and three phonon selection rule is critically important to determine phonon lifetime for these compounds. This indicates difficulty to predict phonon lifetime quantitatively without anharmonic force constants. However it is shown that joint density of states weighted by phonon numbers, which is calculated only from harmonic force constants, can be potentially used for a screening of the lattice thermal conductivity of materials.

First-principles calculations based on hybrid Hartree-Fock density functionals provide a clear picture of the defect energetics and electronic structure in ZnO. Among the donorlike defects, the oxygen vacancy and hydrogen impurity, which are deep and shallow donors, respectively, are likely to form with a substantial concentration in n-type ZnO. The zinc interstitial and zinc antisite, which are both shallow donors, are energetically much less favorable. A strong preference for the oxygen vacancy and hydrogen impurity over the acceptorlike zinc vacancy is found under oxygen-poor conditions, suggesting that the oxygen vacancy contributes to nonstoichiometry and that hydrogen acts as a donor, both of which are without significant compensation by the zinc vacancy. The present results show consistency with the relevant experimental observations.

The formation energies and electronic structure of native defects in tin monoxide are investigated by first-principles calculations. Equilibrium defect concentrations, which are obtained using the calculated formation energies and charge neutrality, indicate that the tin vacancy is the dominant defect under oxygen-rich conditions. It forms shallow acceptor states, suggesting that the p-type conductivity of tin monoxide originates from the tin vacancy. The equilibrium concentration of the oxygen interstitial is comparable with the tin vacancy at elevated temperatures. However, it is hardly ionized and therefore not expected to contribute to the conductivity. The concentrations of donorlike defects such as the tin interstitial and the oxygen vacancy are low enough not to compensate holes generated by the tin vacancy.

Compounds of low lattice thermal conductivity (LTC) are essential for seeking thermoelectric materials with high conversion efficiency. Some strategies have been used to decrease LTC. However, such trials have yielded successes only within a limited exploration space. Here we report the virtual screening of a library containing 54,779 compounds. Our strategy is to search the library through Bayesian optimization using for the initial data the LTC obtained from first-principles anharmonic lattice dynamics calculations for a set of 101 compounds. We discovered 221 materials with very low LTC. Two of them have even an electronic band gap < 1 eV, what makes them exceptional candidates for thermoelectric applications. In addition to those newly discovered thermoelectric materials, the present strategy is believed to be powerful for many other applications in which chemistry of materials are required to be optimized.Thermoelectric generators are essential for utilizing otherwise waste heat. Because of the technological importance, researchers have been seeking materials with high conversion efficiency for decades [1][2][3][4]. Compounds of low lattice thermal conductivity (LTC) are essential for this purpose. Different strategies have been used to decrease LTC. Recently, high throughput screening (HTS) of materials using materials database constructed by first principles calculations has been recognized as an efficient tool for accelerated materials discovery [5][6][7][8][9]. Thanks to the recent progress of computational power and techniques, a large set of first principles calculations can be performed with the accuracy comparable to experiments. This is a straightforward strategy when both of the following conditions are satisfied: 1) the target physical property can be accurately computed by first principles methods. 2) The exploration space is well defined and not too large to compute the target physical property exhaustively in the space.In order to evaluate LTC with the accuracy comparable to experimental data, however, we need to develop a method that is far beyond the ordinary density functional theory (DFT) calculations. Since we need to treat multiple interactions among phonons, or anharmonic lattice dynamics, the computational cost is many orders of magnitudes higher than the ordinary DFT calculations. Such expensive calculations are practically possible only for a small number of simple compounds. HTS of a large DFT database of LTC is not a realistic approach unless the exploration space is narrowly confined. In the year 2014, Carrete and coworkers concentrated their efforts to search low LTC materials within half-Heusler compounds [10]. They made HTS of wide variety of halfHeusler compounds by examination of thermodynamical stability via DFT results. Then LTC was estimated either by full first principles calculations or by a machinelearning algorithm for a selected small number of compounds. HTS of low LTC using a quasiharmonic Debye model was also reported in 2014 [11]. Efficient prediction of LTC throu...

The pressure-induced transitions from molecular to nonmolecular CO 2 crystals are systematically investigated by using first-principles lattice dynamics calculations. Geometrically, likely transition pathways are derived from the dynamical instability of the molecular crystals under high pressures. Layered CO 2 crystals composed of a two-dimensional network of corner-sharing CO 4 tetrahedra are proposed as metastable products of high-pressure phases obtained through the transition pathways. The layered crystals are similar to phase VI in geometry and Raman spectrum.

The layered semiconductor SnSe is one of the highest-performing thermoelectric materials known. We demonstrate, through a first-principles lattice-dynamics study, that the high-temperature Cmcm phase is a dynamic average over lower-symmetry minima separated by very small energetic barriers. Compared to the low-temperature Pnma phase, the Cmcm phase displays a phonon softening and enhanced three-phonon scattering, leading to an anharmonic damping of the low-frequency modes and hence the thermal transport. We develop a renormalization scheme to quantify the effect of the soft modes on the calculated properties, and confirm that the anharmonicity is an inherent feature of the Cmcm phase. These results suggest a design concept for thermal insulators and thermoelectric materials, based on displacive instabilities, and highlight the power of lattice-dynamics calculations for materials characterization.