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1.
A central interatomic potential model is presented for compounds in the binary system MgO-SiO2. The potential, of a simple form which consists of a Coulombic term, a Born repulsive term, and a Van der Walls term for oxygen-oxygen interactions, is designed to predict the properties of magnesium silicates containing Si in octahedral and tetrahedral coordination. This is achieved by fitting simultaneously to forsterite and MgSiO3 ilmenite crystal structure data, and fixing the partial ionic charges using elastic data for forsterite. The potential is found to transfer successfully to γ-Mg2SiO4 and MgSiO3 perovskite. The potential results in local structural errors around the bridging oxygen ions in clinoenstatite and β-Mg2SiO4. The predicted structure for MgSiO3 garnet is similar to the experimentally measured structure of the MnSiO3 analogue. Calculated elastic constants average to K=2.41 Mbar and μ=1.44 Mbar for the bulk and shear moduli of MgSiO3 perovskite, and K=1.87 Mbar and μ=1.10 Mbar for the bulk and shear moduli of MgSiO3 garnet.  相似文献   

2.
The structures of MgSiO3 and NaMgF3 are described in terms of the angle ø by which the SiO6 (MgF6) octahedra are rotated from the ideal cubic perovskite structure. The expected effects of temperature and pressure on ø (and hence on the atomic coordinates and volume) are discussed. It is predicted that the effect of pressure will be to decrease the coordination of Mg in MgSiO3.  相似文献   

3.
The electric field gradient (EFG) in Mg2SiO4 is calculated on the basis of the extended point ion model, including the local term of the overlap contribution. The agreement with experimental data deduced from the quadrupole coupling constants and principal axes at the Mg sites is quite good. The results of the present calculation exhibit a small overlap contribution to the EFG at M1 and a clearly bigger one at M2, whereas the lattice contribution to the EFG at M1 and M2 is reversed. The distinct overlap effects are assumed to be due to the particular Mg2SiO4 crystal structure and the different point symmetry at M1 and M2. The oxygen polarizability and charge used to calculate the EFG tensor were found to be smaller than the theoretical polarizability and formal charge, respectively. The sign of the Mg quadrupole coupling constants at M1 and M2, which has not been determined experimentally, results from the EFG calculation as positive.  相似文献   

4.
Reversal experiments at 1,150–1,300°C on the reaction forsterite+cordierite=aluminous orthopyroxene+spinel in the system MgO-Al2O3-SiO2 show the equilibrium to have a negativedT/dP. The slope andT-P location of this equilibrium have been modelled using available heat capacity data and various structural models which explore the configurational entropy contributions to the totalΔS. The experimental data are consistent with the aluminous orthopyroxene model of Ganguly and Ghose (1979) where limited Al disorder occurs between theM1 andM2 sites, Al-Si mixing occurs on the tetrahedralB site with the ‘aluminum avoidance’ principle maintained, and Mg-Al disorder occurs in spinel with an interchange enthalpy of 9–12 kcal mol?1. Additionally, Al-Si disordering which occurs in the indialite structure of cordierite is inconsistent with the experimental data and all pyroxene and spinel mixing models; consequently, Si and Al in anhydrous cordierites to 1,300°C in the system MgO-Al2O3-SiO2 must be largely ordered.  相似文献   

5.
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6.
Variations of Raman spectra of MgSiO3·10% Al2O3-perovskite were investigated up to about 270 kbar at room temperature and in the range 108–425 °K at atmospheric pressure. Like MgSiO3-perovskite, the Raman frequencies of MgSiO3·10% Al2O3-perovskite increase nonlinearly with increasing pressure and decrease linearly with increasing temperature within the experimental uncertainties and the range investigated. A comparison of these data with those of MgSiO3-perovskite suggests that MgSiO3·10% Al2O3-perovskite is slightly more compressible than MgSiO3-perovskite, and that the volume thermal expansion for MgSiO3·10% Al2O3-perovskite is also slightly greater than that for MgSiO3-perovskite.  相似文献   

7.
The crystal structure of perovskite-type MgSiO3 has been studied up to 96 kbar, using a miniature diamondanvil pressure cell and by means of single-crystal four-circle diffractometry. The observed unit cell compression gives a bulk modulus of K o=2.47 Mbar, assuming K′o=4. The unit cell compression is controlled mainly by the tilting of SiO6 octahedra. The effect of pressure is to change Mg polyhedron towards 8-fold coordination rather than 12-fold coordination. The polyhedral bulk moduli of SiO6 and MgO8 are 3.8 Mbar and 1.9 Mbar, respectively.  相似文献   

8.
Synthetic clinoenstatite (MgSiO3) has been converted to a single phase with the perovskite structure in complete reactions at approx. 300 kbar in experiments that utilize the laser-heated diamond-anvil pressure apparatus. The structure of this phase after quenching was determined by powder X-ray diffraction intensity measurement to be similar to that of the distorted rare-earth, orthoferrite-type, orthorhombic perovskites, but it is suggested that such distortion from ideal cubic perovskite would diminish at high pressure. The unit cell dimensions and density of perovskite-type MgSiO3 at ambient conditions (1 bar, 25°C) are a=4.780(1) Å, b=4.933(1) Å, c=6.902(1) Å, V=162.75 Å3, and ρ=4.098(1) g/cm3. This phase is 3.1% denser than the isochemical oxide mixture [periclase (MgO)+stishovite (SiO2)]. The small crystal-field stabilization energy of the cation site in the perovskite structure may play an important role in limiting the high-pressure stability field of perovskites that contain transition metal cations. Approximate calculations of the crystal-field effects indicate that perovskite of pure FeSiO3 composition may become stable at 400–600 kbar; pressures greater than 800 kbar would be required to stabilize CoSiO3 or NiSiO3 perovskite.  相似文献   

9.
Calcium-olivine, γ-Ca2SiO4, larnite, β-Ca2SiO4, merwinite, Ca3Mg(SiO4)2, and monticellite, CaMgSiO4, are considered. According to a rigid oxyanion scheme, eulerian orientation angles of the SiO4 tetrahedra and translation coordinates of Ca and Si atoms are specified as structural variables τk. All derivatives of the static energy (Born model) contain atomic charges and repulsive parameters as unknowns; the minimum energy conditions ?E L/?τk=0 yield 34 equations which are solved by a least-squares method. The set of energy parameters fitting structural properties of all four phases together is: z Ca=1.50, z o=?1.10 e, r Ca=1.05, ρ=0.25 Å; the Mg charge was fixed at 1.38 e, from a previous study on forsterite. An average shift of 0.04 Å is observed between experimental and least-energy calculated atomic positions. Results are compared with those of Mg2SiO4, where the fit was based both on thermoelastic and on structural properties. If no charge values were fixed “a priori”, just ratios between charges could be determined by fitting them to structural data only.  相似文献   

10.
The crystal structure and site preference of Co2+ in a synthetic Co1.10Mg0.90SiO4 olivine have been determined from single crystal X-ray diffraction data collected on an automatic diffractometer. The R factor is 0.044 for 612 reflections. The site occupancies are: Ml site: Co 0.730±0.006; Mg 0.270; M2 site: Co 0.370, Mg 0.630. The Gibbs free energy change, ΔG° for the ion-exchange reaction between M1 and M2 sites is ?4.06 kcals/mole, assuming ideal mixing at each set of sites. This energy may be called ‘site preference energy’ of Co2+ in olivine. The strong preference of Co2+ for the M1 site can be quantitatively explained by two competing forces: preference of ions larger than Mg2+ for the M2 site and stronger covalent bonding of transition metal ions at the M1 site. For Fe2+, Mg2+, these two effects nearly neutralize each other, explaining the lack of considerable cation-ordering in Fe-Mg olivines.  相似文献   

11.
Magnetization and neutron diffraction measurements have been made on grunerite, Fe7Si8O22(OH)2, a monoclinic double-chain silicate with Fe2+ octahedral bands. The mineral orders antiferromagnetically at 47K into a collinear structure with a second transition at 8K to a canted arrangement. The magnetic susceptibility follows a Curie-Weiss Law above 120K, with a paramagnetic Curie temeprature ?p=67K. Magnetization measurements below 47K indicate a spin-flop or metamagnetic transition in an applied field of about 12KOe. Powder neutron diffraction measurements between 8–45K reveal that all the Fe2+ spins within an octahedral band are ferromagnetically coupled parallel to the b axis, with each band antiferromagnetically coupled to neighboring bands. Below 8K Fe2+ spins at the M1 and M4 sites are canted away from the b axis, whereas those at the M2 and M3 sites are not significantly affected. The ordered Fe2+ moment on the M4 site is substantially lower than those on the other sites, most likely indicating strong covalency effects, i.e. considerable spin transfer to neighboring oxygen atoms.  相似文献   

12.
We calculated the forsterite Mg K-edge and the fayalite Fe K-edge X-ray absorption spectra both for the M 1 and M 2 sites and for the overall edge by using the one-electron multiple-scattering theory. The validity of the theoretical model is well illustrated by comparison of calculations with experimental data at the Mg K-edge of MgO (periclase) and at the Mg and Fe K-edges spectra of forsterite and fayalite. Starting from these results at room conditions, we calculated the Mg and Fe K-edges X-ray absorption spectra of forsterite and fayalite at low and high temperatures and at high pressures as well. Variations of fine structures occur mostly in the intermediate multiple scattering (IMS) regions and as a result of the applied pressure. In order to demonstrate the capability of XAS to lead to deeper knowledge of structure relevant to Earth's upper mantle we also attempted calcuating the high-P edge for Fe 2+ in low-spin using a different occupation of valence electrons. If a change in spin state really occurs in fayalite, our simple model shows that XAS would evidence it easily even with low resolution.  相似文献   

13.
The maxima of the electron difference densities of Fe2+ atM(1) andM(2) positions of fayalite, Fe2SiO4, determined by x-ray diffraction are considered to correspond to atomic dipoles. Provided the selection rules of dipole radiation are satisfied and the energy of the incident radiation lies within the appropriate range, the interaction of incident radiation with these atomic dipoles should lead to three absorption bands of which two originate from Fe2+ atM(1), one from Fe2+ atM(2). The relative intensities of the three bands, dependent on the polarization direction, are estimated. The result ist in excellent agreement with the interpretation of olivine spectra given by Burns (1970).  相似文献   

14.
Synthetic (Mg0.51, Mn0.49)2SiO4 olivine samples are heat-treated at three different pressures; 0, 8 and 12 GPa, all at the same temperature (～500° C). X-ray structure analyses on these single crystals are made in order to see the pressure effect on cation distribution. The intersite distribution coefficient of Mg and Mn in M1 and M2 sites, K D = (Mn/Mg) M1/(Mn/Mg) M2, of these samples are 0.192 (0 GPa), 0.246 (8 GPa) and 0.281 (12 GPa), indicating cationic disordering with pressure. The small differences of cell dimensions between these samples are determined by powder X-ray diffraction. Cell dimensions b and c decrease, whereas a increases with pressure of equilibration. Cell volume decreases with pressure as a result of a large contraction of the b cell dimension. The effect of pressure on the free energy of the cation exchange reaction is evaluated by the observed relation between the cell volume and the site occupancy numbers. The magnitude of the pressure effect on cation distribution is only a fifth of that predicted from the observed change in volume combined with thermodynamic theory. This phenomenon is attributed to nonideality in this solid solution, and nonideal parameters are required to describe cation distribution determined in the present and previous experiments. We use a five-parameter equation to specify the cationic equilibrium on the basic of thermodynamic theory. It includes one energy parameter of ideal mixing, two parameters for nonideal effects, one volume parameter, and one thermal parameter originated from the lattice vibrational energy. The present data combined with some of the existing data are used to determine the five parameters, and the cation distribution in Mg-Mn olivine is described as a function of temperature, pressure, and composition. The basic framework of describing the cationic behavior in olivine-type mineral is worked out, although the result is preliminary: each of the determined parameters is not accurate enough to enable us to make a reliable prediction.  相似文献   

15.
The thermodynamic properties of 25 substances (elements, compounds, modifications) are calculated on the basis of an extrapolation of their caloric values and compressibilities into the region of pressures up to 2mbar and temperatures up to 4,000K. The extrapolation methods are described. The ratio of molar volumes is used to predict the thermodynamic properties of the high pressure modifications. It is inferred that water vapour and oxides of Mg, Fe, and Si ought to be stable in the entire mantle. In the lower mantle garnet should be more stable than the perovskite-type phase of MgSiO3 (in presence of Al2O3 or Fe2O3). ‘Perovskite’ phase plus MgO are more stable here than forsterite, Mg2SiO4. Pyrrhotite, FeS, reveals astonishing stability in the entire mantle and in the outer core as well. Carbon dioxide, CO2, may exist only in the upper mantle, whereas methane, CH4, remains stable in the entire mantle.  相似文献   

16.
Isotope fractionation during the evaporation of silicate melt and condensation of vapor has been widely used to explain various isotope signals observed in lunar soils, cosmic spherules, calcium–aluminum-rich inclusions, and bulk compositions of planetary materials. During evaporation and condensation, the equilibrium isotope fractionation factor (α) between high-temperature silicate melt and vapor is a fundamental parameter that can constrain the melt’s isotopic compositions. However, equilibrium α is difficult to calibrate experimentally. Here we used Mg as an example and calculated equilibrium Mg isotope fractionation in MgSiO3 and Mg2SiO4 melt–vapor systems based on first-principles molecular dynamics and the high-temperature approximation of the Bigeleisen–Mayer equation. We found that, at 2500 K, δ25Mg values in the MgSiO3 and Mg2SiO4 melts were 0.141?±?0.004 and 0.143?±?0.003‰ more positive than in their respective vapors. The corresponding δ26Mg values were 0.270?±?0.008 and 0.274?±?0.006‰ more positive than in vapors, respectively. The general \(\alpha - T\) equations describing the equilibrium Mg α in MgSiO3 and Mg2SiO4 melt–vapor systems were: \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.264 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\) and \(\alpha_{{{\text{Mg}}\left( {\text{l}} \right) - {\text{Mg}}\left( {\text{g}} \right)}} = 1 + \frac{{5.340 \times 10^{5} }}{{T^{2} }}\left( {\frac{1}{m} - \frac{1}{{m^{\prime}}}} \right)\), respectively, where m is the mass of light isotope 24Mg and m′ is the mass of the heavier isotope, 25Mg or 26Mg. These results offer a necessary parameter for mechanistic understanding of Mg isotope fractionation during evaporation and condensation that commonly occurs during the early stages of planetary formation and evolution.  相似文献   

17.
X-ray Absorption Near-Edge Structure (XANES) analysis of the calcium K-edge of a series of natural pyroxenes is reported. The samples belong to the solid solution series diopside (CaMgSi2O6) — jadeite (NaAlSi2O6). In diopside, the M2 site is occupied by Ca only, but along the join Na substitutes Ca in this position. From XANES analysis of different samples we found a distortion of the polyhedron around the M2 site varying as a function of Ca content. This is probably due to compression of the site in a selected direction with an unchanged average distance, so that the coordination around the Ca atom changes from the 4-2-2 configuration typical of the diopside structure to the 6-2 configuration typical of Na in the jadeite structure. Intermediate pyroxenes exhibit both configurations, and acquire therefrom the structural order as already detected by X-ray diffraction techniques.  相似文献   

18.
The relative stability of MgSiO3-ilmenite, MgSiO3-perovskite and (periclase+stishovite) assemblage phases as a function of the pressure is investigated with the periodic quantum mechanical ab initio HartreeFock program CRYSTAL. For the first time, the structure of MgSiO3-ilmenite is fully optimized. Basis set effects are explored. It turns out that relatively small basis sets reproduce correctly experimental geometries. However, larger basis sets (triple zeta quality, plus polarization d functions) are needed to yield significant thermochemical results. All contributions to the 0 K enthalpy are discussed. On the basis of the present highest level calculations, it appears that in the explored range of pressure (0P< 60=" gpa)=" the=" mineralogical=" assemblage=" periclase+stishovite=" has=" higher=" enthalpy=" than=">3-ilmenite or perovskite, and that ilmenite transforms to orthorhombic perovskite around to 29.4 GPa in good agreement with experimental data extrapolated down to 0 K.  相似文献   

19.
Polarized single-crystal absorption and reflection spectra of fundamental modes in both the mid- and far-infrared are presented for microscopic crystals of forsterite and fayalite. All modes predicted by symmetry were observed for forsterite, but two B3u modes were not observed for fayalite. Consideration of previously determined frequency shifts for isotopically and chemically substituted olivines, along with symmetry analysis, produced a complete set of band assignments satisfying all constraints for forsterite. A plausible assingment was derived for fayalite by analogy. The frequency shifts from forsterite to fayalite are consistently small for bands assigned to SiO4 stretching and bending, moderate for rotations, and large for translations of M-site ions, suggesting that in olivine, SiO4 groups vibrate separately from the lattice. Allocating the bending and external modes among multiple continua in Kieffer's (1979c) model considerably improves prediction of quasiharmonic heat capacityC v and entropy for forsterite (～1% discrepancy from 200–1000 K). The experimental entropy of fayalite is closely accounted for (1.8 to 0.1%) by summing lattice, electronic (from Burns' (1985) optical band assignment), and constant magnetic contributions above 200 K.S magnetic determined from the difference of the experimental and model lattice entropies shows inflection points at the two magnetic transition temperatures (23 and 66 K) and indicates that complete spin disorder is not achieved below 680 K.  相似文献   

20.
A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al2O3-Na2O-SiO2 is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO3, Fe = FeSiO3, Ca = CaSiO3, Al = (Al2O3-Na2O)] K D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe2++Fe3+.  相似文献   

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