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).     

Thermal expansion of fayalite,Fe2SiO4

Thermal expansion of single-crystal fayalite has been measured by a dilatometric method at temperatures between 25 °C and 850 °C. The results show the presence of anomalous expansion in the b axis, which is correlated to the anomalous variation of elastic moduli with temperature. Grüneisen's parameter is 1.10 and the thermal Debye temperature is 565 K, which is close to the acoustic Debye temperature of 511 K.     

Infrared vibrational spectra of Beta-Phase Mg2SiO4 and Co2SiO4 to Pressures of 27 GPa

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.     

Decomposition of fayalite (Fe2SiO4) in an oxygen potential gradient at 1,418 K

The decomposition of fayalite (Fe₂SiO₄) in oxygen potential gradients is studied at T=1,418 K. The compound will be decomposed into its component oxides wüstite, Fe_1?δO, and silica, SiO₂, by the simultaneous action of two different oxygen partial pressures, exceeding a critical ratio, despite the fact that fayalite is stable at both the lower and the higher oxygen potential. A quantitative analysis of the decomposition process caused by defect fluxes within the bulk Fe₂SiO₄ is given.     

Compressibility of strontium orthophosphate Sr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>2</Subscript> at high pressure

High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr₃(PO₄)₂ has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V ₀ = 498.0 ± 0.1 Å³, an isothermal bulk modulus of K _T  = 89.5 ± 1.7 GPa, and first pressure derivative of K _T ′ = 6.57 ± 0.34. If K _T ′ is fixed at 4, K _T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K _a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K _c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO₄ vibrations of Sr₃(PO₄)₂ is calculated to be 0.30(2).     

High-pressure X-ray diffraction and Raman spectroscopy of CaFe<Subscript>2</Subscript>O<Subscript>4</Subscript>-type β-CaCr<Subscript>2</Subscript>O<Subscript>4</Subscript>

In situ high-pressure synchrotron X-ray diffraction and Raman spectroscopic studies of orthorhombic CaFe₂O₄-type β-CaCr₂O₄ chromite were carried out up to 16.2 and 32.0 GPa at room temperature using multi-anvil apparatus and diamond anvil cell, respectively. No phase transition was observed in this study. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a zero-pressure volume of V ₀ = 286.8(1) ų, an isothermal bulk modulus of K ₀ = 183(5) GPa and the first pressure derivative of isothermal bulk modulus K ₀′ = 4.1(8). Analyses of axial compressibilities show anisotropic elasticity for β-CaCr₂O₄ since the a-axis is more compressible than the b- and c-axis. Based on the obtained and previous results, the compressibility of several CaFe₂O₄-type phases was compared. The high-pressure Raman spectra of β-CaCr₂O₄ were analyzed to determine the pressure dependences and mode Grüneisen parameters of Raman-active bands. The thermal Grüneisen parameter of β-CaCr₂O₄ is determined to be 0.93(2), which is smaller than those of CaFe₂O₄-type CaAl₂O₄ and MgAl₂O₄.     

Electron microscopy of high-pressure phases synthesized from natural olivine in diamond anvil cell

The products of the transformation of natural (Mg_0.83Fe_0.17)₂SiO₄ olivine have been prepared at various high pressures (between 25 GPa and 90 GPa), and high temperature in a laser-heated diamond-anvil cell (DAC). Studies of the high-pressure phases have been made by transmission electron microscopy (TEM), and X-ray microanalysis. The olivine/spinel boundaries exhibit all the characteristics of a diffusionless shear transition, having a finely sheared structure and a constant orientation relationship between the close-packed planes of the two structures ((100)_ol∥(111)_sp). The TEM observations of zones where olivine (or spinel) transforms into post-spinel phases show that the transformation possesses the features of an eutectoïdal decomposition, leading to a lamellar intergrowth of magnesiowüstite (Mg,Fe)O and perovskite (Mg,Fe)SiO₃. With increasing temperature and/or decreasing pressure, the grain size of the high-pressure phases increases and obeys an Arrhenius law with an activation volume equal to zero. (Mg,Fe)O grains exhibit a very high density of dislocations (higher than 10¹¹cm^?2), whereas (Mg,Fe)SiO₃ grains exhibit no dislocations but systematic twinning. The composition plane of the twins is (112) of the GdFeO₃-type perovskite, corresponding to the {110} plane of the cubic lattice of ideal perovskite.     

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.     

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2

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 (Al_1.88Mn _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 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _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 ų, 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 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (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.     

Charge distribution from least-energy structure in Ca - Mg orthosilicates

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/?τ_k=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.     

The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO 4 4− ion

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.     

Chemistry of peralkaline phonolite dykes from the Grønnedal-Íka area,South Greenland

The chemical variation observed in a suite of fifteen aphyric peralkaline phonolite dykes of mid-Gardar age from the vicinity of the Grønnedal-Íka alkaline complex in south-west Greenland is discussed. From relationships in the system Na₂O-K₂O-Al₂O₃-SiO₂ it is argued that the members of the series are related by the fractionation of feldspar approximating to Ab₅₅Or₄₀An₅ in composition, along with augite and lesser amounts of other ferromagnesian minerals. The bearing of these rocks on phase equilibria in the analogous natural system is discussed, and consideration is given to the possible origins of the initial peralkaline phonolite magma.     

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.     

Exoelectron spectroscopy of traps in surface layers of phenakite and quartz

The possibilities of exoelectron spectroscopy to investigate defects in dielectrics are demonstrated for phenakite Be₂SiO₄, its structural analogs Zn₂ SiO₄, Be₂GeO₄, solid solutions Be₂Si_1?x Ge _x O₄ (x=0÷1) and α-quartz. Emission maxima at 330 and 670 K in phenakite have been found to be due to [GeO₄]^5? andE' centers, respectively. Structural disturbances in the silicon and oxygen positions have been shown to control the exoemission activity of the crystals. Radiation induced decrease of exoemission activity connected with generation ofE' centers by neutron irradiation has been discovered. The energy level scheme of active centers in the subsurface region of Be₂SiO₄ has been established.     

Thermoelastic properties of chromium oxide Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> (eskolaite) at high pressures and temperatures

A new synchrotron X-ray diffraction study of chromium oxide Cr₂O₃ (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K _0,T0), 206 ± 4 GPa; its pressure derivative K′_0,T , 4.4 ± 0.8; (?K _0,T /?T) = ?0.037 ± 0.006 GPa K^?1; a = 2.98 ± 0.14 × 10^?5 K^?1 and b = 0.47 ± 0.28 × 10^?8 K^?2, where α _0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr₂O₃ was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α _0,T0 was determined to be 2.95 × 10^?5 K^?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α ₀ value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K _0,T0 = 205 ± 3 GPa, K′_0,T  = 4.0, Grüneisen parameter (γ ₀) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr₂O₃ undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr₂O₃ is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.     

High temperature solvent growth of anorthite on the join CaAl2Si2O8-SiO2

Stoichiometric anorthite, CaAl₂Si₂O₈, Pˉ1, with sharp a, b, c, and d diffractions was grown, using a CaV₂O₆ solvent, by cooling at 2 ° C per hour from 1450 to 750 ° C in air. Euhedral crystals up to 5 × 3× 0.5 mm, with prominent {010} and well-developed {110} and {001}, were obtained by spontaneous nucleation. Nonstoichiometric anorthite with excess SiO₂ (CaAl₂Si₂O₈+Si₂Si₂O₈) was grown on the join CaAl₂Si₂O₈-SiO₂. Chemical analysis of the synthetic anorthite, having the highest SiO₂ content, with maximum vacancies on M-site gave □_0.110 Na_0.006Ca_0.884Al_1.80Si_2.20O₈, and X-ray diffraction showed a trend from stoichiometric Pˉ1 through diffuse Pˉ1 to body-centered Iˉ1 probably reflecting increasing disorder caused by a higher Si/Al ratio in the T-sites and the positional disorder accompanied by M-site vancancies. Annealing of the nonstoichiometric diffuse Iˉ1 anorthite in air at 1050 ° C for 14 days resulted in exsolution of minute SiO₂ inclusions due to probable ordering in the T-sites and filling of M-sites by Ca. Stoichiometric Pˉ1 anorthite was not obtained by annealing at 1050 ° due to appreciable solubility of SiO₂ in CaAl₂Si₂O₈. Metastable hexagonal CaAl₂Si₂O₈ was found to be a twinned monoclinic crystal with cell dimensions: a = 10.24 (2), b = 17.74 (3), c= 14.99 (5) ?, β = 92.05 (5) °, space group C2.     

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.     

High-pressure behavior of natural single-crystal epidote and clinozoisite up to 40 GPa

The comparative compressibility and high-pressure stability of a natural epidote (0.79 Fe-total per formula unit, Fe_tot pfu) and clinozoisite (0.40 Fe_tot pfu) were investigated by single-crystal X-ray diffraction and Raman spectroscopy. The lattice parameters of both phases exhibit continuous compression behavior up to 30 GPa without evidence of phase transformation. Pressure–volume data for both phases were fitted to a third-order Birch–Murnaghan equation of state with V ₀ = 461.1(1) ų, K ₀ = 115(2) GPa, and \(K_{0}^{'}\) = 3.7(2) for epidote and V ₀ = 457.8(1) ų, K ₀ = 142(3) GPa, and \(K_{0}^{'}\) = 5.2(4) for clinozoisite. In both epidote and clinozoisite, the b-axis is the stiffest direction, and the ratios of axial compressibility are 1.19:1.00:1.15 for epidote and 1.82:1.00:1.19 for clinozoisite. Whereas the compressibility of the a-axis is nearly the same for both phases, the b- and c-axes of the epidote are about 1.5 times more compressible than in clinozoisite, consistent with epidote having a lower bulk modulus. Raman spectra collected up to 40.4 GPa also show no indication of phase transformation and were used to obtain mode Grüneisen parameters (γ _i) for Si–O vibrations, which were found to be 0.5–0.8, typical for hydrous silicate minerals. The average pressure coefficient of Raman frequency shifts for M–O modes in epidote, 2.61(6) cm^?1/GPa, is larger than found for clinozoisite, 2.40(6) cm^?1/GPa, mainly due to the different compressibility of FeO₆ and AlO₆ octahedra in M3 sites. Epidote and clinozoisite contain about 2 wt% H₂O are thus potentially important carriers of water in subducted slabs.     

A Stucture—mineralogical Study of Ringwoodite

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.     

High pressure Ca2SiO4, the silicate K2NiF4-isotype with crystalchemical and geophysical implications

The first silicate possessing a K₂NiF₄-type structure (Ca₂SiO₄) has been synthesized at loading pressures between 220 and 260 kbar and a temperature of about 1000° C in a diamond-anvil press coupled with a YAG laser heater. The lattice parameters for Ca₂SiO₄ (K₂NiF₄-type) area=3.564±0.002 andc=11.66±0.01 Å at room temperature and 1 bar pressure, and the molar volume is 44.57±0.05 cm³. The lattice parameter for the non-quenchable high-pressure perovskite modification of CaSiO₃ is estimated to be 3.56±0.03 Å at STP conditions. To date, A₂BX₄ compounds possessing the K₂NiF₄-type structure arein all cases less dense than their corresponding mixtures of ABX₃ and AX compounds possessing, respectively, the perovskite (or related structures) and rocksalt structures. Hence the K₂NiF₄ structure is unstable relative to the mixture perovskite plus rocksalt at high pressures. For example, in a preliminary experimental study Ca₂GeO₄ in the K₂NiF₄-type structure has been found to transform to an as-yet-undetermined phase or assemblage at pressures between 200 and 250 kbar and at about 1000° C. It is concluded that a similar phase transformation might also occur in Ca₂SiO₄ (K₂NiF₄ type) but that the K₂NiF₄-type structure would not be adopted by Mg₂SiO₄ in the earth's mantle.