M. S. T. Bukowinski

Polymorphs of Alumina Predicted by First Principles: Putting Pressure on the Ruby Pressure Scale

Fully optimized quantum mechanical calculations indicate that Al2O3 transforms from the corundum structure to the as yet unobserved Rh2O3 (II) structure at about 78 gigapascals, and it further transforms to Pbnm-perovskite structure at 223 gigapascals. The predicted x-ray spectrum of the Rh2O3 (II) structure is similar to that of the corundum structure, suggesting that the Rh2O3 (II) structure could go undetected in high-pressure x-ray measurements. It is therefore possible that the ruby (Cr3+-doped corundum) fluorescence pressure scale is sensitive to the thermal history of the ruby chips in a given experiment.

Variational stabilization of the ionic charge densities in the electron-gas theory of crystals: applications to MgO and CaO

The electron-gas theory of crystals is extended to include the effects of many-body forces that arise from both electrostatic and overlap interactions. These effects are incorporated through a self-consistent spherical relaxation of the ionic charge distributions such that the crystal binding energy is minimized. This variational model is used to compute the elastic constants and equations of state of MgO and CaO, and we compare its results to those derived from earlier electron-gas models. In the variational model, the anion charge distributions are markedly more sensitive to the local crystal environment than they are in the PIB or other electron-gas models. We find that for these oxides the variational model gives the best overall agreement with experiment for lattice constants, equations of state, dissociation energies, and elastic moduli.

Framework silica structures generated using simulated annealing with a potential energy function based on an H6Si2O7 molecule

AbstractA simulated annealing technique was used to search for global and local minimum energy structures of a potential energy model for silica. The model is based on ab initio SCF MO calculations on the disilicic acid molecule, H6Si2O7. Starting with 4 SiO2 units, with the atoms randomly distributed in the unit cell, 23 distinct silica tetrahedral framework structures were found, with a variety of space group symmetries and cell dimensions. Despite the assumption of P 1 space group symmetry for the starting structure, only 7 of the local minimum energy structures were found to possess triclinic symmetry with the remainder exhibiting symmetries ranging from P c to

The energetics of aluminum solubility into MgSiO3 perovskite at lower mantle conditions

I\bar 42d

Stability of (Mg,Fe)SiO3 perovskite and the structure of the lowermost mantle

to within 0.001 Å. Although the interaction potential for the disilicic acid molecule has a single minimum energy SiO bond length and SiOSi angle, the local minimum energy structures exhibit angles that range between 105° and 180° and bond lengths that range between 1.55 and 1.68 Å. The correlation observed for coesite and the other silica polymorphs between SiO bond length and fs(O) is reproduced. The generated structures show a wide variety of coordination sequences, ring sizes and framework densities, the later ranging from 19.8 to 35.5 Si/1000 Å3. The energies of these structures correlate with their framework densities, particularly for higher energy structures.

Equation of State and Possible Critical Phase Transitions in MgSiO3 Perovskite at Lower-Mantle Conditions

We present a covalent potential model of tetrahedrally coordinated SiO2. The interactions include covalent effects in the form of a Si-O bond-stretching potential, O-Si-O and Si-O-Si angle-bending potentials, and oxygen-oxygen repulsion. Calculated equations of state of α-quartz and coesite agree well with experiment (calculated densities within 1 percent of experiment up to 6 GPa). The calculated α-quartz-coesite transition pressure agrees with the experimental value of ≈2 GPa. Furthermore, the compression mechanisms predicted by the model (i.e. pressure induced changes in Si-O bond lengths and O-Si-O and Si-O-Si angles) are accurate.

Variationally induced breathing equations of state of pyrope, grossular, and majorite garnets

Experiments [T. Irifune (1994) Nature 370, 131–133; E. Ito et al. (1998) Geophys. Res. Lett. 25, 821–824; A. Kubo, M. Akaogi (2000) Phys. Earth Planet. Int. 121, 85–102] indicate that (Mg,Fe)SiO3 perovskite, commonly believed to be the most abundant mineral in the Earth, is the preferred host phase of Al2O3 in the Earth’s lower mantle. Aiming to better understand the effects of Al2O3 on the thermoelastic properties of the lower mantle, we use atomistic models to examine the chemistry and elasticity of solid solutions within the MgSiO3(perovskite)–Al2O3(corundum)–MgO(periclase) mineral assemblage under conditions pertinent to the lower mantle: low Al cation concentrations, P=25–100 GPa, and T=1000–2000 K. We assess the relative stabilities of two likely substitution mechanisms of Al into MgSiO3 perovskite in terms of reactions involving MgSiO3, MgO, and Al2O3, in a manner similar to the 0 Kelvin calculations of Brodholt [J.P. Brodholt (2000) Nature 407, 620–622] and Yamamoto et al. [T. Yamamoto et al. (2003) Earth Planet. Sci. Lett. 206, 617–625]. We determine the equilibrium composition of the assemblage by examining the chemical potentials of the Al2O3 and MgO components in solid solution with MgSiO3, as functions of concentration. We find that charge coupled substitution dominates at lower mantle pressures and temperatures. Oxygen vacancy-forming substitution accounts for 3–4% of Al substitution at shallow lower mantle conditions, and less than 1% in the deep mantle. For these two pressure regimes, the corresponding adiabatic bulk moduli of aluminous perovskite are 2% and 1% lower than that of pure MgSiO3 perovskite.

The role of theoretical mineral physics in modeling the earth's interior

Monte Carlo simulations of tetrahedrally bonded SiO2 liquid show that pressure induces large changes in the topology of its four-coordinated framework structure but leaves the average properties of local coordination environments virtually unchanged. Ring statistics are used to describe the liquids topology; the observed changes paradoxically indicate that the liquid compresses primarily by increasing the size of its rings. A theory for the effects of ring formation on density, which also explains the density of crystalline tectosilicates, accounts for the compression of the liquid.