Ab Initio Thermodynamic and Thermophysical Properties of Sodium Metasilicate, Na₂SiO₃, and Their Electron-Density and Electron-Pair-Density Counterparts

Abstract

Thermodynamic and thermophysical properties of NaSiO in the Cmc2 structural state are computed ab initio using the hybrid B3LYP density functional method. The static properties at the athermal limit are first evaluated through a symmetry-preserving relaxation procedure. The thermodynamic properties that depend on vibrational frequencies, viz., heat capacities, thermal expansion, thermal derivative of the bulk modulus, thermal correction to internal energy, enthalpy, and Gibbs free energy, are then computed in the framework of quasi-harmonic approximation. Acoustic branches are computed by solving the Christoffel determinant and are assumed to follow sine wave dispersion when traveling within the Brillouin zone. The procedure generates several thermo-physical properties of interest in materials science and geophysics (transverse and longitudinal wave velocities, shear modulus, Young modulus, Poisson ratio) all consistent with experimentally determined properties. A representative cluster is then abstracted from the cell and a detailed electron localization/delocalization analysis is performed on it, in the ground state geometry, and on deformed states imposed by two peculiar mixed asymmetric stretching/bending modes affecting the silicate chain that, according to literature data, have anomalous mode Grüneisen parameters. A Bader analysis reveals an intriguing feature associated with these deformations: an increase in the covalence of the Si-O bond that strengthens the linkage opposing the weakening induced by thermal stress. Finally, on the same cluster, the Ramsey contributions to the J coupling are evaluated by the gauge-independent atomic orbital method. The calculated isotropic chemical shifts of both Na andSi are again in substantial agreement with observations.

Thermodynamic, elastic, and vibrational (IR/Raman) behavior of mixed type-AB carbonated hydroxylapatite by density functional theory

“…Figure 8 reports the entropy (Figure 8a) and the isobaric heat capacity (Figure 8c), which were plotted as a function of temperature at different pressures between 0 GPa and 30 GPa. It is worth stressing that the entropy term lacks the so-called anharmonic term, as described by Belmonte et al (2016). In addition, these quantities were also reported as bidimensional contour at different P-T settings (Figures 8b,d).…”

“…While the size of the unit cell of type-AB carbonated apatite (43 atoms) is sufficiently large for an accurate description of the thermoelastic and thermodynamic properties obtained from the optical contributions (Prencipe et al, 2011;Ulian and Valdrè, 2019), the lack of phonon dispersion relations can not provide the thermodynamics arising from the acoustic branch. To improve the overall quality of the data, particularly at low temperatures, we considered the approach proposed by Kieffer (1979), which was discussed and adopted in recent literature within the quasi-harmonic approximation framework (Belmonte et al, 2016;De La Pierre and Belmonte, 2016). However, since no elastic This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.…”

Czochralski growth of mixed cubic sesquioxide crystals in the ternary system Lu2O3–Sc2O3–Y2O3

“…After the measurement of each sample, the composition was altered by additional weighing of one component into the crucible. To account for the known change of the characteristic function of the tungsten-rhenium thermocouples due to the preferred evaporation of rhenium at such high temperatures (Burns & Scroger, 1989), they were regularly recalibrated against pure Al 2 O 3 with a melting point of 2054 C (Belmonte et al, 2013). In the first cycle, each composition was heated to temperatures above the melting point, which was found to be below 2250 C for all compositions under investigation, and held at the maximum temperature for about 10 min for homogenization.…”

Thermomechanical, electronic and thermodynamic properties of ZnS cubic polymorphs: anab initioinvestigation on the zinc-blende–rock-salt phase transition

“…From the elastic constants, it is also possible to calculate the velocities of acoustic (seismic) waves in the zinc sulfide polymorphs by solving the Christoffel's equation (Musgrave, 1970, Belmonte et al, 2016, Jaeken & Cottenier, 2016. For the sake of an example, they were calculated at zero pressure and reported in Fig.…”