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

Ab initio quasi-harmonic thermoelasticity of molybdenum at high temperature and pressure

We present the ab initio thermoelastic properties of body-centered cubic molybdenum under extreme conditions obtained within the quasi-harmonic approximation including both the vibrational and electronic thermal excitation contributions to the free energy. The quasi-harmonic temperature-dependent elastic constants are calculated and compared with existing experiments and with the quasi-static approximation. We find that the quasi-harmonic approximation allows for a much better interpretation of the experimental data, confirming the trend found previously in other metals. Using the Voigt-Reuss-Hill average, we predict the compressional and shear sound velocities of polycrystalline molybdenum as a function of pressure for several temperatures, which might be accessible in experiments.

Pressure and temperature dependentab-initioquasi-harmonic thermoelastic properties of tungsten

We present theab-initiotemperature and pressure dependent thermoelastic properties of body-centered cubic tungsten. The temperature dependent quasi-harmonic elastic constants (ECs) are computed at several reference volumes including both the phonon and the electronic excitations contribution to the free energy and interpolated at different temperatures and pressures. Good agreement with the experimental ECs on a single crystal at ambient pressure is found. The pressure and temperature dependence of the shear sound velocity measured on polycrystalline tungsten by Qiet alis also in agreement with theory. Some discrepancies are found instead for the compressional velocity at high temperature and this is attributed to the temperature derivative of the bulk modulus, higher in theory than in experiment. These conclusions are reached both by PBE and by PBEsol functionals. The two give elastic properties with a similar pressure and temperature dependence although the latter is closer to experiment at 0 K.

Finite-temperature atomic relaxations: Effect on the temperature-dependent C44 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 C₄₄ 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. We apply our approach to Si and BAs and find a visible difference between the softening of the TDECs computed with the zero-temperature and finite-temperature atomic relaxations. In Si, the softening of C₄₄ passes from 8.6% to 4.5%, between T = 0 K and T = 1200 K. In BAs, it passes from 8% to 7%, in the same range of temperatures. Finally, from the computed elastic constant corrections, we derive the temperature-dependent Kleinman parameter, which is usually measured in experiments.

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 theC₄₄ECs of palladium and platinum while it is irrelevant in the other cases. Its effect is not sufficient to explain the details of the anomalies found by experiments, not even when, in the case of platinum, we take into account the electron-phonon interaction. Lastly, the effect of the exchange and correlation functional is addressed and it is found that it is important atT= 0 K, while all functionals give similar temperature dependencies.

Effects of Geometric and Crystallographic Factors on the Reliability of Al/Si Vertically Cracked Nanofilm/Substrate Systems

In this study, tensile tests on aluminum/silicon vertically cracked nanofilm/substrate systems were performed using atomistic simulations. Various crystallographic orientations and thicknesses of the aluminum nanofilms were considered to analyze the effects of these factors on the reliability of the nanofilm/substrate systems. The results show that systems with some specific crystallographic orientations have lower reliability compared to the other orientations because of the penetration of the vertical crack into the silicon substrate. This penetration phenomenon occurring in a specific model is related to a high coincidence of atomic matching between the interfaces in the model. This high coincidence leads to a tendency of the interface to maintain a coherent form in which the outermost silicon atoms of the substrate that are bonded to the aluminum nanofilm tend to stick with the aluminum atoms under tensile loads. This phenomenon was verified by interface energy calculations in the simulation models.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.