首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
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.
We use an approach based upon the Born model of solids, in which potential functions represent the interactions between atoms in a structure, to calculate the phonon dispersion of forsterite and the lattice dynamical behaviour of the beta-phase and spinel polymorphs of Mg2SiO4. The potential used (THB1) was derived largely empirically using data from simple binary oxides, and has previously been successfully used to model the infrared and Raman behaviour of forsterite. It includes ‘bond bending’ terms, that model the directionality of the Si-O bond, in addition to the pair-wise additive Coulombic and short range terms. The phonon dispersion relationships of the Mg2SiO4 polymorphs predicted by THB1 were used to calculate the heat capacities, entropies, thermal expansion coefficients and Gruneisen parameters of these phases. The predicted heat capacities and entropies are in outstandingly good agreement with those determined experimentally. The predicted thermodynamic data of these phases were used to construct a phase diagram for this system, which has Clausius-Clapeyron slopes in very close agreement with those found by experiment, but which has predicted transformation pressures that show less close agreement with those inferred from experiment. The overall success, however, that we have in predicting the lattice dynamical and thermodynamic properties of the Mg2SiO4 polymorphs shows that our potential THB1 represents a significant step towards finding the elusive quantitative link between the microscopic or atomistic behaviour of minerals and their macroscopic properties.  相似文献   

3.
Magnesium-rich olivine (Mg0.9Fe0.1)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.  相似文献   

4.
  相似文献   

5.
The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe2SiO4, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: Vp = 6.67 km/s; Vs = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)T = 5.2; (?μ/?P)T=1.5;(?K/?T)P= ?0.030 GPa/K;and,(?/?T)P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg2SiO4, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C ij for which i=j) values, and generally higher for the off-diagonal (C ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.  相似文献   

6.
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   

7.
  相似文献   

8.
The powder XRD analysis of ringwoodite(γ-Fe2SiO4),which was synthesized in a II-stage anvil high-pressure capsule,was made,Its unit-cell parameter was calculated:a=8.219A,After the refinements,for several cycles,of the oxygen parameter x and the occupancy rate of Si in octahedron site,i.e.,the iversion degree u,the final result is R=0.077,when x=0.379A and u=27.5%,with the structural formula (Fe1.725 Si0.275)VI(Si0.725Fe0.275)IV O4 and atomic distances(Fe,Si)VI-O=2.022 A and (Si,Fe)IV-O=1.836A,Meanwhile,the Moessbauer spectroscopic analysis of the sample was conducted and the results obtained are in good agreement with those of X-ray structural analysis ,This paper focuses on the phase transformation and the properties of bonds of α－Fe2SiO4→γ-Fe2SiO4.  相似文献   

9.
  相似文献   

10.
Ni, Co, and Zn are widely distributed in the Earth’s mantle as significant minor elements that may offer insights into the chemistry of melting in the mantle. To better understand the distribution of Ni2+, Co2+, and Zn2+ in the most abundant silicate phases in the transition zone and the upper mantle, we have analyzed the crystal chemistry of wadsleyite (Mg2SiO4), ringwoodite (Mg2SiO4), forsterite (Mg2SiO4), and clinoenstatite (Mg2Si2O6) synthesized at 12–20 GPa and 1200–1400 °C with 1.5–3 wt% of either NiO, CoO, or ZnO in starting materials. Single-crystal X-ray diffraction analyses demonstrate that significant amounts of Ni, Co, and Zn are incorporated in octahedral sites in wadsleyite (up to 7.1 at%), ringwoodite (up to 11.3 at%), olivine (up to 2.0 at%), and clinoenstatite (up to 3.2 at%). Crystal structure refinements indicate that crystal field stabilization energy (CFSE) controls both cation ordering and transition metal partitioning in coexisting minerals. According to electron microprobe analyses, Ni and Co partition preferentially into forsterite and wadsleyite relative to coexisting clinoenstatite. Ni strongly prefers ringwoodite over coexisting wadsleyite with \({D}_{\text{Ni}}^{\text{Rw}/\text{Wd}}\)?=?4.13. Due to decreasing metal–oxygen distances with rising pressure, crystal field effect on distribution of divalent metal ions in magnesium silicates is more critical in the transition zone relative to the upper mantle. Analyses of Ni partitioning between the major upper-mantle phases implies that Ni-rich olivine in ultramafic rocks can be indicative of near-primary magmas.  相似文献   

11.
The effect of Cr on the silicate system has been studied in air at 1 atm by adding a small amount of MgCr2O4 (0.2–0.5 wt.%) to the join Mg2SiO4 (forsterite) — CaAl2Si2O8 (anorthite) — CaMgSi2O6 (diopside), which has been considered to form a thermal divide in the system CaO-MgO-Al2O3-SiO2. The spinel primary field is enlarged compared with that in the Cr-free join at the expense of the anorthite primary field. The piercing points forsterite+anorthite+diopside+liquid and forsterite+anorthite+spinel+liquid approach each other with increasing MgCr2O4, meet at the join with 0.25 wt.% MgCr2O4 (0.20 wt.% Cr2O3) to form the ‘isobaric quaternary invariant point’ forsterite+anorthite+diopside+spinel+liquid, and then separate again as new ‘piercing points’ of diopside+spinel+anorthite+liquid and forsterite+diopside+ spinel+liquid. This process indicates that the join Mg2SiO4-CaAl2Si2O8-CaMgSi2O6 containing more than 0.2 wt.% Cr2O3 cannot be a thermal divide in the basalt tetrahedron. The results of the present study show that the presence of a minor amount of Cr causes a significant effect on the phase relations and therefore, the role of Cr must be taken into account in the formulation of a petrologic model.  相似文献   

12.
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   

13.
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).  相似文献   

14.
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   

15.
In the lattice energy expression of forsterite, based on a Born-Mayer (electrostatic+repulsive+dispersive) potential, the oxygen charge z o, the hardness parameter ρ and the repulsive radii r Mg and r Si appear as unknown parameters. These were determined by calculating the first and second partial derivatives of the energy with respect to the cell edges, and equalizing them to quantities related to the crystal elastic constants; the overdetermined system of equations was solved numerically, minimizing the root-mean-square deviation. To test the results obtained, the SiO 4 4? ion was assumed to move in the unit-cell, and the least-energy configuration was sought and compared with the experimental one. By combining the two methods, the optimum set of parameters was: z o=?1.34, ρ=0.27 Å, r Mg=0.72 Å, r Si=0.64 Å. The values ?8565.12 and ?8927.28 kJ mol?1 were obtained, respectively, for the lattice energy E Land for its ionic component E L 0 ,which accounts for interactions between Mg2+ and SiO 4 4? ions only. The charge distribution calculated on the SiO 4 4? ion was discussed and compared with other results. Using appropriate thermochemical cycles, the formation enthalpy and the binding energy of SiO 4 4? were estimated to be: ΔH f(SiO 4 4? )=2117.6 and E(SiO 4 4? )=708.6 kJ mol?1, respectively.  相似文献   

16.
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   

17.
The relative stabilities of spinelloid polytypic modifications are analysed in terms of the relative magnitudes of the interaction energies between first, second and third neighbour structural modules. Structures which exhibit minimum interaction energies are deduced, and it is found that of all the possible polytypic modifications considered, only five spinelloid structures can possess a minimum value for the interaction energy between modules. It is shown that the spinelloid structures adopted in the system Ni2SiO4-NiAl2O4 can be satisfactorily analysed in terms of these interaction energies, and it is suggested that the dominant factors influencing the energy of interaction between structural units in this system are electrostatic charge imbalance effects. Strain energy effects, associated with cation size mismatch, however, appear to play a significant role in determining the behaviour of the analogous iron and cobalt systems.  相似文献   

18.
Stoichiometric mixtures of tremolite and dolomite were heated to 50° C above equilibrium temperatures to form forsterite and calcite. The pressure of the CO2-H2O fluid was 5 Kb and \(X_{{\text{CO}}_{\text{2}} }\) varied from 0.1 to 0.6. The extent of the conversion was determined by the amount of CO2 produced. The resulting mixtures of unreacted tremolite and dolomite and of newly-formed forsterite and calcite were examined with a scanning electron microscope. All tremolite and dolomite grains showed obvious signs of dissolution. At fluid compositions with \(X_{{\text{CO}}_{\text{2}} }\) less than about 0.4, the forsterite and calcite crystals are randomly distributed throughout the charges, indicating that surfaces of the reactants are not a controlling factor with respect to the sites of nucleation of the products. A change is observed when \(X_{{\text{CO}}_{\text{2}} }\) is greater than about 0.4; the forsterite and calcite crystals now nucleate and grow at the surface of the dolomite grains, thus indicating a change in mechanism at medium CO2 concentrations. As the reaction progresses, the dolomite grains become more and more surrounded by forsterite and calcite, finally forming armoured relics of dolomite. Under experimental conditions this characteristic texture can only be formed if the CO2-concentration is greater than about 40 mole %. These findings make it possible to estimate the CO2-concentration from the texture of the dolomite+tremolite+forsterite+calcite assemblage. The results suggest a dissolution-precipitation mechanism for the reaction investigated. In a simplified form it consists of the following 4 steps:
  1. Dissolution of the reactants tremolite and dolomite.
  2. Diffusion of the dissolved constituents in the fluid.
  3. Heterogeneous nucleation of the product minerals.
  4. Growth of forsterite and calcite from the fluid.
Two possible explanations are discussed for the development of the amoured texture at \(X_{{\text{CO}}_{\text{2}} }\) above 0.4. The first is based upon the assumption that dolomite has a lower rate of dissolution than tremolite at high \(X_{{\text{CO}}_{\text{2}} }\) values resulting in preferential calcite and forsterite nucleation and growth on the dolomite surface. An alternative explanation is the formation of a raised CO2 concentration around the dolomite grains at high \(X_{{\text{CO}}_{\text{2}} }\) values, leading to product precipitation on the dolomite crystals.  相似文献   

19.
A high temperature calorimetric solution method involving the use of a sodium and lithium metaborate (NaBO2+LiBO2) molten bath at 1,180 K, has been developed in order to measure the enthalpy of formation of the forsterite-fayalite (Mg2SiO4-Fe2SiO4) system. The samples used for these measurements have been obtained by synthesis. They have been carefully controlled by chemical and X-ray analysis and Mössbauer spectroscopy. The results obtained for forsterite and fayalite agree closely with the data commonly found in the literature. Owing to the uncertainty of the experimental results, it is not possible to determine conclusively whether an enthalpy of mixing exists in this system.  相似文献   

20.
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.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号