Giulio Ottonello

Thermodynamic and thermophysical properties of Na₂SiO₃ in the Cmc2₁ 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_NM coupling are evaluated by the gauge-independent atomic orbital method. The calculated isotropic chemical shifts of both ²³Na and ²⁹Si are again in substantial agreement with observations.

Throughout geological history, partial melting of mantle rocks and magma ascent and crystallization have played key roles in shaping the Earth. The importance of magmas stems from their liquid nature, that is, from their high atomic mobility and lack of long-range order. Compared to crystals, magmas thus have peculiar thermodynamic properties. A few examples illustrate how solid–liquid and liquid–volatile equilibria can be predicted. Given the almost infinite diversity of conditions of chemical composition, temperature and pressure in nature, thermodynamic modelling has become a necessary tool for understanding magmatic processes.

We present the results of a computational investigation with ab initio procedures of the structure-energy and vibrational properties of silica clusters in a dielectric continuum with dielectric constant ε=3.8, through density functional theory/B3LYP gas phase calculations coupled with a polarized continuum model approach [integral equation formalism applied to a polarized continuum (IEFPCM)] and those of the periodical structure D6h which leads to the α-cristobalite polymorph of silica when subjected to symmetry operations with the same functional within the linear combination of atomic orbitals (LCAO) approximation and in the framework of Bloch’s theorem. Based on the computed energies and vibrational features, an aggregate of the D6h network and the monomer locally ordered in the short-medium range and both present in the glass in a mutual arrangement lacking of spatial continuity reproduces satisfactorily the experimentally observed low T heat capacity and the deviation from the Debye T3 law. Above Tg, the experimental heat capacity of the liquid is perfectly reproduced summing to the internal modes the translational and rotational contributions to the bulk heat capacity and subtracting the (acoustic) terms arising from coherent motion (no longer existent).

Ab-initio thermophysical properties and isotopic separative effects in MgCr₂O₄ were computed with the CRYSTAL03 code. All calculations were carried out within the LCAO approach (Linear Combination of Atomic Orbitals) by using the Hartree-Fock and the hybrid B3LYP density functional methods. Vibrational frequencies have been computed at the long-wavelength limit corresponding to the center of the Brillouin zone (k → 0). Since thermodynamic functions depend on the phonon dispersion relation, the ab-initio based vibrational analysis of the optical modes has been coupled with the semiempirical Kieffer model for the acoustic modes, which is based on a sine wave dispersion equation. All computed magnitudes (zero point energy, internal energy, Helmholtz free energy, optical vibrational modes, thermal corrections to internal energy, enthalpy and Gibbs free energy, thermal pressure, bulk modulus and its P and T derivatives, entropy, isochoric and isobaric heat capacity, and isotopic separative effects) are consistent with direct observations and/or reasonable estimates, within the accuracy of the method. The computed separative effects are similar to those observed in other Cr³⁺-bearing substances. The crystal field seems to have no influence on the separative effect for an isotopomeric couple with respect to an isolated gaseous couple with Cr³⁺ as central cation.