Finite-temperature atomic relaxations: Effect on the temperature-dependent C elastic constants of Si and BAs.

The effect of atomic relaxations on the temperature-dependent elastic constants (TDECs) is usually taken into account at zero temperature by the minimization of the total energy at each strain. In this paper, we investigate the order of magnitude of this approximation on a paradigmatic example: the C elastic constant of diamond and zincblende materials. We estimate the effect of finite-temperature atomic relaxations within the quasi-harmonic approximation by computing ab initio the internal strain tensor from the second derivatives of the Helmholtz free-energy with respect to strain and atomic displacements.

Quasi-harmonic thermoelasticity of palladium, platinum, copper, and gold from first principles.

We calculate the temperature-dependent elastic constants (ECs) of palladium, platinum, copper and gold within the quasi-harmonic approximation using a first-principles approach and evaluating numerically the second derivatives of the Helmholtz free-energy with respect to strain at the minimum of the free-energy itself. We find an overall good agreement with the experimental data although the anomalies of palladium and platinum reported at room temperature are not reproduced. The contribution of electronic excitations is also investigated: we find that it is non-negligible for theECs of palladium and platinum while it is irrelevant in the other cases.

Quasi-harmonic temperature dependent elastic constants: applications to silicon, aluminum, and silver.

We presentcalculations of the quasi-harmonic temperature dependent elastic constants. The isothermal elastic constants are calculated at each temperature as second derivatives of the Helmholtz free energy with respect to strain and corrected for finite pressure effects. This calculation is repeated for a grid of geometries and the results interpolated at the minimum of the Helmholtz free energy.

Temperature-dependent atomic B factor: an ab initio calculation.

The Debye-Waller factor explains the temperature dependence of the intensities of X-ray or neutron diffraction peaks. It is defined in terms of the B matrix whose elements B are mean-square atomic displacements in different directions. These quantities, introduced in several contexts, account for the effects of temperature and quantum fluctuations on the lattice dynamics.