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1.
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   

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.
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4.
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5.
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   

6.
The aim of the work presented is to develop a computer simulation technique which will predict the structure and physical properties of forsterite and ringwoodite, the major mantle-forming polymorphs of Mg2SiO4. The technique is based upon energy minimization, in which all structural parameters are varied until the configuration with the lowest energy is achieved. The lattice energy and physical properties (e.g. elasticity and dielectric constants) are calculated from interatomic potentials, which generally include electrostatic and short-range terms. We investigate several types of traditional potential models, and present a new type of model which includes partial ionic charges and a Morse potential to describe the effect of covalency on the Si-O bond. This new form of potential model is highly successful, and not only reproduces the zero-pressure structural, elastic and dielectric properties of forsterite and ringwoodite, but also accurately describes their pressure dependence.  相似文献   

7.
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   

8.
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.  相似文献   

9.
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   

10.
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   

11.
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   

12.
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   

13.
Ab initio force constants calculated for Si-O stretch and Si...Si non-bonded interactions in H6Si2O7 are found comparable with experimental values derived from the lattice dynamics of α quartz. The bulk moduli of α quartz and α cristobalite are calculated using the molecular Si...Si force constant and assuming rigid regular SiO4 tetrahedra. In the case (α quartz) where data are available the calculation agrees well with experiment.  相似文献   

14.
Infrared absorption spectra of the high-pressure polymorphs β-Mg2SiO4 and β-Co2SiO4 have been measured between 0 and 27 GPa at room temperature. Grüneisen parameters determined for 11 modes of β-Mg2SiO4 (frequencies of 300 to 1,050 cm?1) and 5 modes of β-Co2SiO4 (490 to 1,050 cm?1) range between 0.8 and 1.9. Averaging the mid-infrared spectroscopic data for β-Mg2SiO4 yields an average Grüneisen parameter of 1.3 (±0.1), in good agreement with the high-temperature thermodynamic value of 1.35. Similarly, we find a value of 1.05 (±0.2) for the average spectroscopic Grüneisen parameter of β-Co2SiO4.  相似文献   

15.
We applied molecular dynamics (MD) simulations to finding likely paths of atomic migration of the Mg ion in forsterite (Mg2SiO4) and the oxygen ion in MgSiO3-perovskite to better understand atomic diffusion in minerals. Our simulations show that there exist two routes of Mg migration in the forsterite structure, that is, paths between the M1 and M2 sites and between the M1 and M1 sites. In the MgSiO3-perovskite structure, some oxygen ions migrate to the next sites all together through the O1 vacant site showing co-operative movements. The O ions are relatively mobile mainly along the b axis in the perovskite structure. Meta-stable sites are often present between a stable site and another stable site on atomic migration. In spite of many assumptions, our MD simulations may show likely paths of atomic migration in crystal.  相似文献   

16.
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   

17.
Experiments on the join Al2SiO5-“Mn2SiO5” of the system Al2O3-SiO2-MnO-MnO2 in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn2O3, and high purity SiO2 as starting materials and using /O2-buffer techniques to preserve the Mn3+ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al1.88Mn 0.12 3+ )SiO5 and, thus, equals approximately that on the join Al2SiO5-“Fe2SiO5” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn3+ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a o, b o, c o, and V o to increase by 0.015, 0.009, 0.014 Å, and 1.6 Å3, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn3+-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusitess (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al1.86Mn 0.14 3+ )SiO5-(Al1.56Mn 0,44 3+ )SiO5. Thus, Al→Mn3+ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn3+ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a o, b o, c o, and V o to increase by 0.118, 0.029, 0.047 Å and 9.4 Å3, resp. At “Mn2SiO5”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn2SiO5”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn2+Mn3+[O8/Si04]), pyrolusite and SiO2 were found to coexist with the Mn3+-saturated ky ss or and ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn3+). Pure synthetic braunites had the lattice constants a o 9.425, c o, 18.700 Å, V o 1661.1 Å3 (ideal compn.) and a o 9.374, c o 18.593 Å3, V o 1633.6 Å3 (1 Al for 1 Mn3+). Stable coexistence of the Mn2+-bearing phase braunite with the Mn4+-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO2-SiO2.  相似文献   

18.
Enstatites (Mg2Si2O6) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO6 octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg2+ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg2SiO4 and fayalite, Fe2-SiO4) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)0.6Mg1.4Si2O6 stable at room temperature using the 488 nm or 514.5 nm lines of an Ar+ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.  相似文献   

19.
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.  相似文献   

20.
Electrical conductivities of Ni2SiO4, Fe2SiO4, and MgSiO3 were measured on synthetic powders in the temperature range 340° to 1,100° C and at pressures up to 20 kbars. For ternary compounds such as olivines and pyroxenes the control of two further variables, like the chemical activities of two components are needed, besides temperature and pressure. The activities of the corresponding binary oxides were controlled by equilibrating the samples with their neighbour-phases. Control of the oxygen partial pressure was achieved by buffer techniques. From the slopes of the lg σ vs. 1/T lines the activation energies were calculated for 10 kbar: 0.56 eV and 2.7 eV for Ni2SiO4 in equilibrium with SiO2 and Ni/NiO-buffer for the temperature range 500°–800°C and 800°–1,000°C resp. 0.52 eV for Fe2SiO4 in equilibrium with SiO2 and metallic iron, and 0.38 eV in equilibrium with SiO2 and magnetite; 1.11 eV for MgSiO3 in equilibrium with SiO2, and 1.25 eV in equilibrium with Mg2SiO4.  相似文献   

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