Periodic pseudopotential Hartree–Fock calculations have been performed on the quartz structure of silica and germanium dioxide. It is shown that the tilt angle is the most important structural parameter. This parameter emphasizes the role of the oxygen polarization function which appear to be necessary to recover the correct geometry of low quartz. The structure of β-quartz is rationalized on the basis of the energy dependence upon the tilt angle and the absence of β-structure in GeO2 is explained. Finally the behavior of both oxides under pressure is discussed.
Grossular and andradite are garnet end-members stable under upper mantle conditions. We perform ab initio simulations to investigate the dependence of the bulk modulus on chemical composition of the grossular-andradite solid solution, Ca3Fe(2-2x)Al(2x)(SiO4)3. All-electron local basis sets of Gaussian-type orbitals and the hybrid B3LYP density functional are used. Our calculations predict a linear modulus-composition trend, in contrast to previous conjectures based on "heterogeneous" experimental measurements. We estimate the largest deviation from linearity to be about 0.5 GPa under ambient conditions, and to progressively reduce to less than 0.2 GPa at pressure P = 20 GPa. The bulk modulus is computed over the whole composition range 0 ≤x≤ 1 following two independent approaches: fitting energy-volume data to an equation-of-state and calculating elastic tensors. Results from the two methods are in perfect agreement, assuring consistency and high numerical accuracy of the adopted algorithms.
Abstract The change in chemical composition trend of magmatic nepheline through magma evolution has been characterized from the alkaline series of the Messum complex in which nepheline occurs in a succession of different mineral parageneses from mafic-rich (theralites) to strongly evolved felsic-rich rock types (nepheline syenites). The nepheline compositions are dependent on those of coexisting feldspar(s). They record an evolution parallel to that of the melt schematized according to experimental phase diagrams, from initially Ca-rich compositions in equilibrium with calcic plagioclase towards increasingly Ca-poor, Na-rich and Si-rich compositions. The K contents show a maximum that corresponds to the appearance of alkali feldspar in the parageneses. This evolution is qualitatively preserved in spite of the low- T Na/K re-equilibration typical of plutonic nephelines. Although a slight increase in the silica content of nepheline is consistent with the experimentally defined magmatic trend, several high-silica nephelines from the Messum rocks as well as from other reported occurrences, cannot be reconciled with the experimental data. The nepheline solid-solution model available suggests that such ‘abnormal’ compositions might be related to different crystallization mechanisms between natural nephelines and some synthetic analogues.
The geometries of Mg 2 SiO 4 , Mg 2 GeO 4 , Al 2 MgO 4 , and Ga 2 MgO 4 spinels have been correctly calculated using the periodic Hartree‐Fock method at core pseudopotential level. The bonding properties are studied on the basis of electron population analysis and electron density. The band structure and density of states have been computed and are discussed. The bulk modulus and its pressure derivative of each compound have been derived. The structures yielded by our calculations are a little bit too stiff. Different compression mechanisms are proposed for, on the one hand, Mg 2 SiO 4 and Mg 2 GeO 4 and, on the other hand, Al 2 MgO 4 and Ga 2 MgO 4 .
Abstract. Understanding the geochemical behaviour of trace and minor elements in mineral assemblages is of primary importance to study small- and large-scale geological processes. Partition coefficients are frequently used to model the chemical evolution of minerals and fluids during melting and in metamorphic rocks of all grades. However, kinetic effects hampering equilibrium partitioning may invalidate the modelling. This study aims at calculating partition coefficients and testing their applicability in natural mineral assemblages, choosing Cr in garnet and clinopyroxene via exchange with Al as a case study. First-principle modelling has been combined with measurements and element mapping to estimate partition coefficients for Cr and the deviation from equilibrium. Results highlight the role of crystal chemistry over the strain field around point defects, controlling the dynamics of the Cr3+ = Al3+ exchange between clinopyroxene and garnet. Ab initio calculations allowed estimation of Cr partition coefficients between garnet and clinopyroxene, using a thermodynamic approach based on endmembers and mixing models simplified for trace element behaviour. The Cr3+ = Al3+ exchange reaction between garnet and the jadeite component of clinopyroxene depends on the grossular and pyrope content, with Cr preferentially incorporated into grossular over jadeite but preferentially incorporated into jadeite over pyrope. Comparison of predicted partition coefficients to measured concentrations in natural samples, together with element mapping, shows large disequilibrium. Cr-rich and Cr-poor sectors exhibit disequilibrium attributed to slow diffusivity of Cr during crystal growth and interface-coupled dissolution–precipitation, even for garnet–clinopyroxene assemblages crystallized around 850 ∘C.
