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At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic structure. At low temperature, SnTe undergoes a ferroelectric transition with a critical temperature strongly dependent on the hole concentration, while PbTe is an incipient ferroelectric. By using the stochastic self-consistent harmonic approximation, we investigate the anharmonic phonon spectra and the occurrence of a ferroelectric transition in both systems. We find that vibrational spectra strongly depend on the approximation used for the exchange-correlation kernel in density-functional theory. If gradient corrections and the theoretical volume are employed, then the calculation of the phonon frequencies as obtained from the diagonalization of the free-energy Hessian leads to phonon spectra in good agreement with experimental data for both systems. In PbTe we evaluate the linear thermal expansion coefficient $\ensuremath{\gamma}=2.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$, finding it to be in good agreement with experimental value of $\ensuremath{\gamma}=2.04\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{4.pt}{0ex}}{\text{K}}^{\ensuremath{-}1}$. Furthermore, we study the phonon spectrum and we do reproduce the transverse optical mode phonon satellite detected in inelastic neutron scattering and the crossing between the transverse optical and the longitudinal acoustic modes along the $\mathrm{\ensuremath{\Gamma}}\mathrm{X}$ direction. The phonon satellite becomes broader at high temperatures but its energy is essentially temperature independent, in agreement with experiments. We decompose the self-consistent harmonic free energy in second-, third-, and fourth-order anharmonic terms. We find that the third- and fourth-order terms are small. However, treating the third-order term perturbatively on top of the second-order self-consistent harmonic free energy overestimates the energy of the satellite associated with the transverse optical mode. On the contrary, a perturbative treatment on top of the harmonic Hamiltonian breaks down and leads to imaginary phonon frequencies already at 300 K. In the case of SnTe, we describe the occurrence of a ferroelectric transition from the high-temperature $Fm\overline{3}m$ structure to the low-temperature $R3m$ one. The transition temperature is, however, underestimated with respect to the experimental one. No satellites are present in the SnTe phonon spectra despite a not negligible anharmonic broadening of the zone-center TO mode.

X-ray method to test the material properties and to obtain elastic constants is commonly based on the Reuss model and Kroner model. Y parameter has been turned out to be an effective method to estimate elastic properties of polycrystalline material. Since Y-parameters of cubic polycrystalline material based on the certain uniform stress (Reuss model) has not been given, our work aims to complete this part of the theoretical analysis, which can effectively compare elastic constants measured by the X-ray diffraction method. The structural and the elastic properties of cubic structures (CaO and MgO) and hexagonal structures (CH and Calcite CaCO3) are investigated by the density functional theory method. And then the credibility of Y parameters for determing elastic moduli of cubic structures is proved and elastic properties in typical crystallographic planes of [100], [110] and [111] are also calculated. Meanwhile, Young’s moduli of CH and Calcite structure are 58.08 GPa and 84.549 GPa, which are all close to references. Elastic properties of cubic and hexagonal structures under various pressures are calculated and the surface constructions of elastic moduli are drawn, showing the anisotropy at various directions. The crystal structure investigated in this work are typical of some primary or secondary components of Hardened Cements Pastes and their homogenized elastic properties are needed in a hierarchical multi-scale modeling, such as the one developed by some of the authors of this paper.

Focusing on isotropic elastic networks we propose a novel simple-average expression $G(t) = \mu_A - h(t)$ for the computational determination of the shear-stress relaxation modulus $G(t)$ of a classical elastic solid or fluid and its equilibrium modulus $\G_{eq} = \lim_{t \to \infty} G(t)$. Here, $\mu_A = G(0)$ characterizes the shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear stress $\hat{\tau}(t)$ as a function of time $t$. While investigating sampling time effects we also discuss the related expressions in terms of shear-stress autocorrelation functions. We argue finally that our key relation may be readily adapted for more general linear response functions., Comment: 6 pages, 4 figures

International audience; Comparing isotropic solids and fluids at either imposed volume or pressure, we investigate various correlations of the instantaneous pressure and its ideal and excess contributions. Focusing on the compression modulus K, it is emphasized that the stress fluctuation representation of the elastic moduli may be obtained directly (without a microscopic displacement field) by comparing the stress fluctuations in conjugated ensembles. This is made manifest by computing the Rowlinson stress fluctuation expression K-row of the compression modulus for NPT-ensembles. It is shown theoretically and numerically that K-row vertical bar P = P-id(2 - P-id/K) with P-id being the ideal pressure contribution.

The shear modulus G of two glass-forming colloidal model systems in d=3 and d=2 dimensions is investigated by means of, respectively, molecular dynamics and Monte Carlo simulations. Comparing ensembles where either the shear strain gamma or the conjugated (mean) shear stress tau are imposed, we compute G from the respective stress and strain fluctuations as a function of temperature T while keeping a constant normal pressure P. The choice of the ensemble is seen to be highly relevant for the shear stress fluctuations mu_F(T) which at constant tau decay monotonously with T following the affine shear elasticity mu_A(T), i.e. a simple two-point correlation function. At variance, non-monotonous behavior with a maximum at the glass transition temperature T_g is demonstrated for mu_F(T) at constant gamma. The increase of G below T_g is reasonably fitted for both models by a continuous cusp singularity, G(T) is proportional to (1-T/T_g)^(1/2), in qualitative agreement with some recent replica calculations. It is argued, however, that longer sampling times may lead to a sharper transition. The additive jump discontinuity predicted by mode-coupling theory and other replica calculations thus cannot ultimately be ruled out.

In subduction zones, the anisotropic fast shear-wave component is generally observed to be orientated parallel to the strike of the trench. The interpretation of this shear-wave splitting above subduction zones has, however, been controversial and none of the inferred models appears to be explain the whole range of anisotropic patterns observed worldwide. Manuele Faccenda and colleagues now show that the amount and geometry of seismic anisotropy measured in the forearc regions of subduction zones strongly depend on the preferred orientation of hydrated faults in the subducting oceanic plate. The anisotropy originates from the crystallographic preferred orientation of highly anisotropic hydrous minerals formed along steeply dipping faults and from the larger scale vertical layering consisting of dry and hydrated crust-mantle sections whose spacing is several times smaller than teleseismic wavelengths. Faults orientations and estimated delay times are consistent with the observed shear-wave splitting patterns in most subduction zones. It is shown that the amount and geometry of seismic anisotropy measured in the forearc regions of subduction zones strongly depend on the preferred orientation of hydrated faults in the subducting oceanic plate. The anisotropy originates from the crystallographic preferred orientation of highly anisotropic hydrous minerals formed along steeply dipping faults and from the larger-scale vertical layering consisting of dry and hydrated crust–mantle sections, the spacing of which is several times smaller than teleseismic wavelengths. The variation of elastic-wave velocities as a function of the direction of propagation through the Earth’s interior is a widely documented phenomenon called seismic anisotropy. The geometry and amount of seismic anisotropy is generally estimated by measuring shear-wave splitting, which consists of determining the polarization direction of the fast shear-wave component and the time delay between the fast and slow, orthogonally polarized, waves. In subduction zones, the teleseismic fast shear-wave component is oriented generally parallel to the strike of the trench1, although a few exceptions have been reported (Cascadia2 and restricted areas of South America3,4). The interpretation of shear-wave splitting above subduction zones has been controversial and none of the inferred models seems to be sufficiently complete to explain the entire range of anisotropic patterns registered worldwide1. Here we show that the amount and the geometry of seismic anisotropies measured in the forearc regions of subduction zones strongly depend on the preferred orientation of hydrated faults in the subducting oceanic plate. The anisotropy originates from the crystallographic preferred orientation of highly anisotropic hydrous minerals (serpentine and talc) formed along steeply dipping faults and from the larger-scale vertical layering consisting of dry and hydrated crust–mantle sections whose spacing is several times smaller than teleseismic wavelengths. Fault orientations and estimated delay times are consistent with the observed shear-wave splitting patterns in most subduction zones.