Calorimetric study of high-pressure polymorphs of MnSiO3

With increasing pressure, MnSiO₃ rhodonite stable at atmospheric pressure transforms to pyroxmangite, then to clinopyroxene and further to tetragonal garnet, which finally decomposes into MnO (rocksalt) plus SiO₂ (stishovite). High temperature solution calorimetry of synthetic rhodonite, clinopyroxene and garnet forms of MnSiO₃ was used to measure the enthalpies of these transitions. ΔH ₉₇₄ ⁰ for the rhodonite-clinopyroxene and ΔH ₂₉₈ ⁰ for the clinopyroxene-garnet transition are 520±490 and 8,270±590 cal/mol, respectively. The published data on the enthalpy of the rhodonite-pyroxmangite transition, phase equilibrium boundaries, compressibility and thermal expansion data are used to calculate entropy changes for the transitions. The enthalpy, entropy and volume changes are very small for all the transitions among rhodonite, pyroxmangite and clinopyroxene. The calculated boundary for the clinopyroxene-garnet transition is consistent with the published experimental results. The pyroxene-garnet transition in several materials, including MnSiO₃, is characterized by a relatively small negative entropy change and large volume decrease, resulting in a small positiveP – T slope. The disproportionation of MnSiO₃ garnet to MnO plus stishovite and of Mn₂SiO₄ olivine to garnet plus MnO are calculated to occur at about 17–18 and 14–15 GPa, respectively, at 1,000–1,500 K.     

Raman scattering and lattice vibrations of Ni2SiO4 spinel at elevated temperature

Raman spectra of Ni₂SiO₄ spinel (O _h ⁷ Z=8) have been measured in the temperature range from 20 to 600 °C and the Raman active vibrations (A _1g +E _g +3F _2g ) have been assigned. A calculation of the optically active lattice vibrations of this spinel has been made, assuming a potential function which combines general valence and short range force constants. The values of the force constants at 20 and 500 °C have been calculated from the vibrational frequencies of the observed Raman spectra and infrared (IR) spectral data. The Ni spinel at 20 °C has a prominently small Si-O bond stretching force constant of K(SiO)=2.356 ～ 2.680 md/Å and a large Ni-O bond stretching constant of K(NiO)=0.843 ～ 1.062 md/Å and these force constants at 500 °C decrease to K(SiO)=2.327 ～ 2.494 md/Å and K(NiO)=0.861 ～ 0.990 md/Å. The Si-O bond is noticeably weakened at high temperatures, despite the small thermal expantion from 1.657 Å (20 °C) to 1.660 Å (500 °C). These changes of the interatomic force constants of the spinel at high temperatures are in accord with the thermal structure changes observed by X-ray diffraction study. The weakened Si-O bond is consistent with the fact that Si atoms in the spinel lattice can diffuse at significant rates at elevated temperature.     

Magnetic structure and cation distribution in (Fe,Mn)2SiO4 (olivine) by neutron diffraction

The cation distribution in the synthetic samples of olivine-type structure with composition (Fe _x Mn_1?x )₂SiO₄ was determined at room temperature and confirms previous Mössbauer results. At low temperature an antiferromagnetic ordering is observed. The magnetic structures can be described in the crystallographic cell (i.e. k=0). They are interpreted on the basis of the irreducible representations (modes) of the symmetry groups which are compatible with Pnma. The dominant modes observed for all compounds, including Fe₂SiO₄ and Mn₂SiO₄, only differ in their direction. The main direction of magnetization is dominated by the Fe²⁺ single-ion anisotropy. At 4.2K, for x=0.29, it is parallel to the c-axis, whereas for x=0.76 the direction is parallel to the b-axis. The anisotropy of the M1-sites dominates in the first case, whereas M2-anisotropy dominates in the second case. The influence of temperature is demonstrated for x=0.50 where c is the main direction at 4.2K, when it is b at 38K.     

Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry

Using a Fizeau interferometry technique, we have measured the coefficients of linear thermal expansion of single-crystal forsterite (Mg₂SiO₄) along three axial directions to 1023 K during heating and cooling cycles. Overall, the present data are consistent in magnitude (within 1 to 2%) with those previously reported but have less scatter. We used the Grüneisen statistical mechanical approach in analzying the data. The least-squares method was applied to evaluate thermal parameters (?, Q ₀, k and a) in two cases. The expansion coefficients in wider temperature ranges were extrapolated by using the parameters of solution 2 (i.e., solution by fixing ? and k). In contrast to earlier findings, our results show that for forsterite the Grüneisen parameter decreases with temperature, implying that it does not behave too differently from fayalite (Fe₂SiO₄) and periclase (MgO).     

Crystal structures of Ni2SiO4 and Fe2SiO4 as a function of temperature and heating duration

X-ray structure refinements of Ni₂SiO₄ and Fe₂SiO₄ spinels have been made as a function of temperature and heating duration by intensity measurements at high temperatures and room pressure. The lattice parameters of Ni₂SiO₄ spinel linearly increased with temperature up to 1,000° C. However, Fe₂SiO₄ spinel exhibited a nonlinear thermal expansion and was converted to a polycrystalline mixture of spinel and olivine by heating of less than one-hour at 800° C. The ratios between the octahedral and tetrahedral bond lengths D _oct/D _tetr and between the shared and unshared edge distances (O-O)_sh/(O-O)_unsh in Fe₂SiO₄ spinel were both much larger than those in Ni₂SiO₄. These ratios increase with temperature. The Fe₂SiO₄ spinel more readily approached a activation state which facilitated the transition to the olivine structure than the Ni₂SiO₄ spinel. The lattice parameter of Ni₂SiO₄ spinel decreased with heating period at constant temperatures of 700° C and 800° C. The parameter of the quenched sample after heating for 52 h at 700° C was smaller than that of the nonheated sample. The refinements of the site occupancies at each heating duration indicated an increase in the cation deficiency in both tetrahedral and octahedral sites. Electron microprobe analysis, however, proved no significant difference in the chemical compositions between the quenched and nonheated samples. Si and Ni atoms displaced from normally occupied spinel lattice sites are assumed to settle in vacant sites defined by the cubic close packed oxygen sublattice in a manner which preserves the electric neutrality of the bulk crystal.     

Exploration of structure and bonding in stishovite with fourier and pseudoatom refinement methods using single crystal and powder X-ray diffraction data

The structure and bonding in stishovite, SiO₂, is explored with Fourier summation and pseudoatom refinement of merged x-ray single crystal and powder diffraction data. Replacement of the 25 lowest-angle, highly extinction-affected, single crystal reflections with structure factors obtained from low-extinction powder diffraction data has resulted in a significant improvement in the analysis compared with earlier studies. The deformation electron density, total electrostatic potential and total and valence electron densities are mapped. Accumulations of electron density are observed in both SiO bonds, together with non-bonding features displayed about the oxygen on both sides of a plane formed by three bonds with Si. Deficits of electron density between O atoms across the shared-edges are rationalized in terms of the Pauli exclusion principle. There is no evidence for strong repulsion of Si atoms across the same ring. The total electrostatic potential has a continuous low value for the vacant channels in the structure along c with localized minima between O atoms on opposite sides of the channel. The sizes of Si and O are related to the electron density and to the electrostatic potential.     

Ab initio calculated geometries and charge distributions for H4SiO4 and H6Si2O7 compared with experimental values for silicates and siloxanes

Ab initio STO-3G molecular orbital theory has been used to calculate energy-optimized Si-O bond lengths and angles for molecular orthosilicic and pyrosilicic acids. The resulting bond length for orthosilicic acid and the nonbridging bonds for pyrosilicic acid compare well with Si-OH bonds observed for a number of hydrated silicate minerals. Minimum energy Si-O bond lengths to the bridging oxygen of the pyrosilicic molecule show a close correspondence with bridging bond length data observed for the silica polymorphs and for gas phase and molecular crystal siloxanes when plotted against the SiOSi angle. In addition, the calculations show that the mean Si-O bond length of a silicate tetrahedron increases slightly as the SiOSi angle narrows. The close correspondence between the Si-O bond length and angle variations calculated for pyrosilicic acid and those observed for the silica polymorphs and siloxanes substantiates the suggestion that local bonding forces in solids are not very different from those in molecules and clusters consisting of the same atoms with the same coordination numbers. An extended basis calculation for H₄SiO₄ implies that there are about 0.6 electrons in the 3d-orbitals on Si. An analysis of bond overlap populations obtained from STO-3G* calculations for H₆Si₂O₇ indicates that Si-O bond length and SiOSi angle correlations may be ascribed to changes in the hybridization state of the bridging oxygen and (d – p) π-bonding involving all five of the 3d AO's of Si and the lone-pair AO's of the oxygen. Theoretical density difference maps calculated for H₆Si₂O₇ show a build-up of charge density between Si and O, with the peak-height charge densities of the nonbridging bonds exceeding those of the bridging bonds by about 0.05 e Å^?3. In addition, atomic charges (+1.3 and ?0.65) calculated for Si and O in a SiO₂ moiety of the low quartz structure conform reasonably well with the electroneutrality postulate and with experimental charges obtained from monopole and radial refinements of diffraction data recorded for low quartz and coesite.     

GeO2 vs SiO2: Glass transitions and thermodynamic properties of polymorphs

Relative-enthalpy measurements have been made on the hexagonal, tetragonal, glass and liquid phases of GeO₂. The glass transition is very sensitive to the impurity content, with a T _g ranging from 980 K for a pure product to 780 K for a Li-doped sample with 0.06 mol % Li. The relative C _p change at T _g of about 5% increases with the impurity content as a result of lower glass transition temperatures. Above 298 K the derived heat capacities are similar for all forms, with slightly higher values for the amorphous phases and two C _p cross-overs at 400 and 1000 K between the hexagonal and tetragonal modifications. For both GeO₂ and SiO₂ the coordination state markedly affects C _p and the entropy below 300 K, where the properties are much lower for the tetragonal than for the hexagonal modifications, i.e., S ₂₉₈ = 39.7 vs 55.3 J/mole K and 27.8 vs 41.4 J/ mole K for GeO₂ and SiO₂, respectively. The high-temperature C _p's of coesite and stishovite are likely similar to those of the low-pressure SiO₂ forms. Finally, these results, low-temperature C _p data and enthalpy-of-solution measurements have been used to derive a consistent set of thermodynamic properties for the GeO₂ modifications.     

Upper temperature tolerance of spot,Leiostomus xanthurus,from the cape Fear River estuary,North Carolina

The temperature tolerance and resistance times of postlarval (<25 mm SL) and small juvenile spot,Leiostomus xanthurus, from the Cape Fear Estuary, North Carolina were tested in the laboratory. Critical thermal maximum techniques were used to determine first equilibrium loss (FEL) and critical thermal maximum (CTM) end points and thermal shock methods were used to determine 96-h upper incipient lethal temperatures (LT₅₀). Acclimation temperatures ranged from 10 to 35°C and acclimation salinities were 10, 20 and 30‰. A quadratics model was fit to the CTM and FEL data; r² values were 0.924 and 0.928 respectively. Acclimation salinity, estimated weight, acclimation salinity by acclimation temperature interaction and acclimation temperature by estimated weight interaction were the significant components of the CTM model. Predicted CTM values ranged from 30°C at 10 °C and 30‰ acclimation to just over 40°C at 30 °C and 30‰ acclimation. Acclimation temperature, acclimation temperature squared, estimated weight and acclimation temperatures by estimated weight interaction were the significant components of the FEL model. Predicted FEL values ranged from around 28°C at 10°C and 10‰ acclimation to about 39°C at 30°C and 30‰ acclimation. The 96-h LT₅₀ values of spot acclimated to 20‰ increased linearly with acclimation temperature to 25°C. From about 25 to 35°C, LT₅₀ values increased very little with acclimation temperature. The ultimate upper incipient lethal temperature of postlarval and small juvenile spot was estimated at 35.2°C. Increased salinity increased resistance time but decreased LT₅₀ estimates. Thermal shock tests were better for predicting the effects of thermal addition than were CTM tests.     

The effect of crystal field stabilization on the olivine→spinel transition in the system Mg2SiO4 - Fe2SiO4

Crystal field stabilization (CFS) plays a significant role in determining equilibrium phase boundaries in olivine→spinel transformations involving transition-metal cations, including Fe²⁺ which is a major constituent of the upper mantle. Previous calculations for Fe₂SiO₄ ignored pressure and temperature dependencies of crystal field stabilization enthalpies (CFSE) and the electronic configurational entropy (S _CFS). We have calculated free energy changes (ΔG _CFS) due to differences of crystal field splittings between Fe₂SiO₄ spinel and fayalite from: ΔG _CFS=?ΔCFSE?TΔS _CFS, as functions of P and T, for different energy splittings of t _2g orbital levels of Fe²⁺ in spinel. The results indicate that ΔG _CFS is always negative, suggesting that CFS always promotes the olivine→spinel transition in Fe₂SiO₄, and expands the stability field of spinel at the expense of olivine. Because of crystal field effects, transition pressures for olivine→spinel transformations in compositions (Mg_1?x Fe _x )₂SiO₄ are lowered by approximately 50x kbar, which is equivalent to having raised the olivine→spinel boundary in the upper mantle by about 15 km.     

X-ray and HRTEM study of sursassite: Crystal structure,stacking disorder,and sursassite-pumpellyite intergrowth

Sursassite is monoclinic, space group P2 ₁/m, a=8.70, b=5.79, c=9.78 Å, β=108.9°. The crystal structure was determined with X-rays and refined to R=0.065, obtaining Mn₂Al₃[(OH)₃(SiO₄)(Si₂O₇)] as ideal crystal chemical formula. Sursassite, isostructural with macfallite Ca₂Mn₃[(OH)₃(SiO₄)(Si₂O₇)], is closely related to pumpellyite Ca₂Al₃[(OH)₃(SiO₄)(Si₂O₇)]. In fact both sursassite and pumpellyite, apart from the different chemical composition, are built up by common structural layers, which are repeated by different stacking vectors. As a result, faulted stacking sequences are energetically possible. Examination by high resolution transmission electron microscopy (HRTEM) shows that frequent (001) pumpellyite-like lamellae are intergrown with thicker (001) sursassite lamellae. Usually, the guest lamellae are a few unit cells thick along [001] and continuous along the (001) plane, although also rare interrupted lamellae are found.     

On the relationship between refractive index and density for SiO2 polymorphs

The Gladstone-Dale law (specific refraction) and the Drude law (molecular refraction) for silica polymorphs, at “sodium light” (λ _D =0.5893 μm), are derived from simple atomic properties of SiO₂ complex (atomic weight, first ionization potential). The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) v ₀ of elementary electron oscillators (in energy units, hv) is identified with the band gap E _G of a solid; on the other hand, this E _G -gap is identified with the single ionization potential \(\tilde U\) of non-free atoms. For \(\tilde U\) =E _G =10.2 eV (energy gap of quartz, see Nitsan and Shankland 1976b) the Gladstone-Dale law, or specific refraction, is (n?1)/ρ=0.208 cm³/g, where n and ρ are the refractive index and the density of medium, respectively. According to empirical data, the average value of the specific refraction of pure SiO₂ polymorphs (except stishovite-high density phase of silica) is (〈n〉?1)/ρ=0.207±0.001 (〈n〉 denotes the mean refractive index of crystal). For stishovite the Drude law (n ²?1)/ρ=0.542 cm³/g is valid under an assumption that the first ionization potential \(\tilde U\) =E _G ≈9 eV; this result is good agreement with the empirical value (〈n〉²?1)/ρ=0.536 cm³/g.     

The tetrahedral framework in glasses and melts — inferences from molecular orbital calculations and implications for structure,thermodynamics, and physical properties

Results of ab initio molecular orbital (MO) calculations provide a basis for the interpretation of structural and thermodynamic properties of crystals, glasses, and melts containing tetrahedrally coordinated Si, Al, and B. Calculated and experimental tetrahedral atom-oxygen (TO) bond lengths are in good agreement and the observed average SiO and AlO bond lengths remain relatively constant in crystalline, glassy, and molten materials. The TOT framework geometry, which determines the major structural features, is governed largely by the local constraints of the strong TO bonds and its major features are modeled well by ab initio calculations on small clusters. Observed bond lengths for non-framework cations are not always in agreement with calculated values, and reasons for this are discussed in the text. The flexibility of SiOSi, SiOAl, and AlOAl angles is in accord with easy glass formation in silicates and aluminosilicates. The stronger constraints on tetrahedral BOB and BOSi angles, as evidenced by much deeper and steeper calculated potential energy versus angle curves, suggest much greater difficulty in substituting tetrahedral B than Al for Si. This is supported by the pattern of immiscibility in borosilicate glasses, although the occurrence of boron in trigonal coordination is an added complication. The limitations on glass formation in oxysulfide and oxynitride systems may be related to the angular requirements of SiSSi and Si(NH)Si groups. Although the SiO and AlO bonds are the strongest ones in silicates and aluminosilicates, they are perturbed by other cations. Increasing perturbation and weakening of the framework occurs with increasing ability of the other atom to compete with Si or Al for bonding to oxygen, that is, with increasing cation field strength. The perturbation of TOT groups, as evidenced by TO bond lengthening predicted by MO calculations and observed in ordered crystalline aluminosilicates, increases in the series Ca, Mg and K, Na, Li. This perturbation correlates strongly with thermochemical mixing properties of glasses in the systems SiO₂-M ₁ ^n/n+ AlO₂ and SiO₂-M ⁿ⁺O _n/2 (M=Li, Na, K, Rb, Cs, and Mg, Ca, Sr, Ba, Pb), with tendencies toward immiscibility in these systems, and with systematics in vibrational spectra. Trends in physical properties, including viscosity at atmospheric and high pressure, can also be correlated.     

Compressional behavior of omphacite to 47 GPa

Omphacite is an important mineral component of eclogite. Single-crystal synchrotron X-ray diffraction data on natural (Ca, Na) (Mg, Fe, Al)Si₂O₆ omphacite have been collected at the Advanced Photon Source beamlines 13-BM-C and 13-ID-D up to 47 GPa at ambient temperature. Unit cell parameter and crystal structure refinements were carried out to constrain the isothermal equation of state and compression mechanism. The third-order Birch–Murnaghan equation of state (BM3) fit of all data gives V ₀ = 423.9(3) Å³, K _T0 = 116(2) GPa and K _T0′ = 4.3(2). These elastic parameters are consistent with the general trend of the diopside–jadeite join. The eight-coordinated polyhedra (M2 and M21) are the most compressible and contribute to majority of the unit cell compression, while the SiO₄ tetrahedra (Si1 and Si2) behave as rigid structural units and are the most incompressible. Axial compressibilities are determined by fitting linearized BM3 equation of state to pressure dependences of unit cell parameters. Throughout the investigated pressure range, the b-axis is more compressible than the c-axis. The axial compressibility of the a-axis is the largest among the three axes at 0 GPa, yet it quickly drops to the smallest at pressures above 5 GPa, which is explained by the rotation of the stiffest major compression axis toward the a-axis with the increase in pressure.     

Energy gap and density in SiO2 polymorphs

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.     

A molecular orbital study of bond length and angle variations in framework structures

Molecular orbital calculations on a variety of silicate and aluminosilicate molecules have been used to explore the bonding forces that govern tetrahedral bond length variations, r(TO), in framework silicates and aluminosilicates. Not only do the calculations provide insight into the variety of structural types and the substitution limits of one tetrahedral atom for another, but they also provide an understanding of the interrelationships among r(TO) and linkage factors, bond strength sum, coordination number, and angles within and between tetrahedra. A study of these interrelationships for a theoretical data set shows that r(SiO) and r(AlO) are linearly correlated with (1) p _o, the bond strength sum to a bridging oxygen, (2) f _s(O), the fractional s-character of a bridging oxygen, and (3) f _s (T), the fractional s-character of the T atom. In a multiple linear regression analysis of the data, 92% of the variation of r(SiO) and 99% of the variation of r(AlO) can be explained in terms of a linear dependence on p _o, f _s (O), and f _s (T). Analogous regression analyses completed for observed r(Al, SiO) bond length data from a number of silica polymorphs and ordered aluminosilicates account for more than 75% of the bond length variation. The lower percentage of bond length variation explained is ascribed in part to the random and systematic errors in the experimental data which have a negligible effect on the theoretical data. The modeling of more than 75% of the variation of r(Al, SiO) in the framework silicates using the same model used for silicate and aluminosilicate molecules strengthens the viewpoint that the bonding forces that govern the shapes of such molecules are quite similar to the forces that govern the shapes of chemically similar groups in solids. The different regression coefficients calculated for f _s (T) indicate that SiO and AlO bond length variations in framework structures should not be treated as a single population in estimating the average Al, Si content of a tetrahedral site.     

Lattice dynamics and inelastic neutron scattering from forsterite,Mg2SiO4: Phonon dispersion relation,density of states and specific heat

Magnesium-rich olivine (Mg_0.9Fe_0.1)₂SiO₄ is considered to be a major constituent of the Earth's upper mantle. Because of its major geophysical importance, the temperature and pressure dependence of its crystal structure, elastic and dielectric constants, long-wavelength phonon modes and specific heat have been measured using a variety of experimental techniques. Theoretical study of lattice dynamics provides a means of analyzing and understanding a host of such experimental data in a unified manner. A detailed study of the lattice dynamics of forsterite, Mg₂SiO₄, has been made using a crystal potential function consisting of Coulombic and short-range terms. Quasiharmonic lattice dynamical calculations based on a rigid molecular-ion model have provided theoretical estimates of elastic constants, long-wavelength modes, phonon dispersion relation for external modes along the three high symmetry directions in the Brillouin zone, total and partial density of states and inelastic neutron scattering cross-sections. The neutron cross-sections were used as guides for the coherent inelastic neutron scattering experiment on a large single crystal using a triple axis spectrometer in the constant Q mode. The observed and predicted phonon dispersion relation show excellent agreement. The inelastically scattered neutron spectra from a powder sample have been analyzed on the basis of a phonon density of states calculated from a rigid-ion model, which includes both external and internal modes. The experimental data from a powder sample show good agreement with the calculated spectra, which include a multiphonon contribution in the incoherent approximation. The computed phonon densities of states are used to calculate the specific heat as a function of temperature using both the rigid molecular-ion and rigid ion models. These results are in very good agreement with the calorimetric measurement of the specific heat. The interatomic potential developed here can be used with some confidence to study physical properties of forsterite as a function of pressure and temperature.     

Polymorphism of wollastonite

Different superstructures of wollastonite from the regional metamorphic Lepontine zone (Southern Alps) and other localities (e.g., Sierra Nevada, California) have been found. Besides well ordered normal 1T, 2M (2T ?), 4T-wollastonite, all disordered intermediate states exist. The various polymorphs were studied with the precession method. The superstructure is observed in reflections hkl k=odd. 4T-wollastonite is described with a ₀=31.659 Å and is shown to be a common polymorph. The superstructure seems to be independent of metamorphic grade (in the well-zoned Lepontine area it does not follow any mineralogical isograds) and occurs only in strained rocks with well developed lineation and strong preferred orientation. Thus the formation of the superstructure is explained as a deformation effect. Contrary to temperature and pressure, both stress and strain show large local variations and inhomogeneities. Experimental deformation of a 2T-wollastonite at 4 kb and 700° C produced complete disorder. It is suggested that consecutive annealing of strained disordered wollastonite causes periodic stacking sequences of [SiO₃]-chains along the a^*-axis. It appears from these studies that superstructures in chainsilicates are more common than presently known and that they might be useful petrogenetic indicators for the deformation and cooling history of a rock.     

Theoretical studies of charge relaxation effects on the statics and dynamics of oxides

Inclusion of spherical charge relaxation in response to the long-range electrostatic potential (potential induced breathing, or PIB) gives improved results for the static and dynamic properties of oxides. PIB is a Gordon-Kim type model, in which the crystal charge density is estimated by overlapping ionic charge densities. No experimental data are used, except for the values of universal constants, and in this sense the results are from first principles. In contrast to earlier models which include some form of charge relaxation, we explicitly include the breathing effects on the self-energy and pair potentials in the model Hamiltonian. PIB is a many-body effect that couples the long-and short-range forces in a way that is not present in any other first principles or empirical models. It leads to the observed violations of the Cauchy relations for the elastic constants whereas central force rigid ion models cannot violate the Cauchy relations. PIB also reduces the predicted LO-TO splitting because the breathing effect introduces dynamical effective charges that are lower in magnitude than the ionic charges. Some results are shown and discussed for MgO (periclase), BeO (bromellite), Al₂O₃ (corundum), TiO₂ (rutile) and SiO₂ (quartz and stishovite).     

Thermal equation of state of natural tourmaline at high pressure and temperature

Synchrotron-based in situ angle-dispersive X-ray diffraction experiments were conducted on a natural uvite-dominated tourmaline sample by using an external-heating diamond anvil cell at simultaneously high pressures and temperatures up to 18 GPa and 723 K, respectively. The angle-dispersive X-ray diffraction data reveal no indication of a structural phase transition over the P–T range of the current experiment in this study. The pressure–volume–temperature data were fitted by the high-temperature Birch–Murnaghan equation of state. Isothermal bulk modulus of K ₀ = 96.6 (9) GPa, pressure derivative of the bulk modulus of \(K_{0}^{\prime } = 12.5 \;(4)\), thermal expansion coefficient of α ₀ = 4.39 (27) × 10^?5 K^?1 and temperature derivative of the bulk modulus (?K/?T) _P  = ?0.009 (6) GPa K^?1 were obtained. The axial thermoelastic properties were also obtained with K _a0 = 139 (2) GPa, \(K_{a0}^{\prime }\) = 11.5 (7) and α _a0 = 1.00 (11) × 10^?5 K^?1 for the a-axis, and K _c0 = 59 (1) GPa, \(K_{c0}^{\prime }\) = 11.4 (5) and α _c0 = 2.41 (24) × 10^?5 K^?1 for the c-axis. Both of axial compression and thermal expansion exhibit large anisotropic behavior. Thermoelastic parameters of tourmaline in this study were also compared with that of the other two ring silicates of beryl and cordierite.