Calorimetric study of olivine solid solutions in the system Mg2SiO4-Fe2SiO4

Solution enthalpies of synthetic olivine solid solutions in the system Mg₂SiO₄-Fe₂SiO₄ have been measured in molten 2PbO·B₂O₃ at 979 K. The enthalpy data show that olivine solid solutions have a positive enthalpy of mixing and the deviation from ideality is approximated as symmetric with respect to composition, in contrast to the previous study. Applying the symmetric regular solution model to the present enthalpy data, the interaction parameter of ethalpy (W_H) is estimated to be 5.3±1.7 kJ/mol (one cation site basis). Using this W_h and the published data on excess free energy of mixing, the nonideal parameter of entropy (W_s) of olivine solid solutions is estimated as 0.6±1.5 J/mol·K.     

Elasticity of the olivine and spinel polymorphs of Ni2SiO4

The single-crystal elastic moduli, c _ij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni₂SiO₄ olivine: c ₁₁=3.40(2), c ₂₂=2.38(2), c ₃₃=2.53(2), c ₄₄=0.71(1), c ₅₅=0.87(1), c ₆₆=0.78(1), c ₁₂=1.09(2), c ₁₃=1.10(4), c ₂₃=1.13(3), Ni₂SiO₄ spinel: c ₁₁=3.66(3), c ₄₄=1.06(1), c ₁₂=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c ₁₁>c ₃₃>c ₂₂, regardless of composition. The moduli c ₅₅ and c ₆₆ are approximately equal, and greater than c ₄₄. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO₄ tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\) . When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\) , and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\) . The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni₂SiO₄ (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni₂SiO₄ are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c _ij's and shear modulus of a spinel-structure silicate to be estimated from c ₁₁ of the corresponding α phase and the bulk modulus of the γ phase.     

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.     

Computer simulations of the structural and physical properties of the olivine and spinel polymorphs of Mg2SiO4

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.     

Comparison of the raman microprobe spectra of (Mg,Fe)2SiO4 and Mg2GeO4 with olivine and spinel structures

Raman microprobe (RMP) spectra were produced for each of the olivine and spinel structured phases of Mg₂GeO₄ and (Mg, Fe)₂SiO₄. The assembled data show that bands due to the tetrahedra in silicate and germanate olivines shift in a way that indicates a dominant mass effect. This correspondence is difficult to make in spinels due to differences in structural type. Differences in Fe/Mg content of olivine shift the tetrahedral vibration bands only slightly, but their linear shifts could be used to indicate the composition of the phase.     

Pseudopotential periodic Hartree-Fock study of Mg2SiO4 polymorphs: Olivine,modified spinel and spinel

Pseudopotential periodic Hartree-Fock calculations have been performed on the three polymorphs of Mg₂SiO₄ with a polarized split valence basis set. The energy differences between polymorphs at their experimental geometries are correctly predicted. The olivine to modified spinel and olivine to spinel phase transition pressures have been estimated and agree within a few GPa with their experimental values. The bonding in Mg₂SiO₄ is discussed from the point of view of the, band structures, projected density of states, electron density and electron localization function (ELF) curves. It is concluded that both Mg-O and Si-O bonds are highly ionic.     

Single-crystal infrared reflectivity of pure Mg2SiO2 forsterite and (Mg0.86,Fe0.14)2SiO4 olivine

New polarized infrared reflectance spectra of pure synthetic forsterite and natural Fo₈₆-olivine have been recorded from 5000 to 100cm^-1. Out of the 35 expected infrared active modes, 33 have been observed (8 B_1u, 12 B_2u, 13 B_3u). The observed frequency shift from pure forsterite to Fo₈₆-olivine is consistent with the higher mass of the substituted iron. The substitution of only 14% of iron also reduces the overal far-infrared reflectivity of olivine as compared to pure forsterite. Several discrepancies associated with previous studies of forsterite are explained by our investigation. We suggest that some of the previous investigations were complicated by polarization mixing.     

The rheology of olivine and spinel magnesium germanate (Mg2GeO4): TEM study of the defect microstructures

Synthetic polycrystals of α-Mg₂GeO₄ (with the olivine structure) and γ-Mg₂GeO₄ (with the spinel structure) deformed at high temperature and pressure in their respective stability fields were investigated by analytical transmission electron microscopy. Specimens with a mean grain size of 20–30 µm deform by dislocation glide and/or climb. The predominance of glide versus climb depends on stress and grain orientation. The defect microstructures of both polymorphs are very similar to those observed in their respective silicate analogues, α- and γ-(Mg,Fe)₂SiO₄, and, in the case of the spinel phase, very similar to those observed in magnesium aluminate spinels. These observations suggest that Mg₂GeO₄ is a good rheological analogue for the Earth’s upper mantle. A spinel specimen deformed under the same conditions of temperature and strain rate as an olivine specimen was approximately three times stronger than olivine. In specimens of both phases deformed at or above 1400 K, a thin amorphous film composed of Mg, Ge, and O was detected along some grain boundaries. Grains ≤10 µm diameter surrounded by a film of amorphous phase (>10 nm thick) exhibited low dislocation densities, and deformation appeared to have occurred by grain boundary sliding.     

A computer simulation study of OH defects in Mg2SiO4 and Mg2GeO4 spinels

Classical atomistic simulation techniques have been used to investigate the energies of hydrogen defects in Mg₂SiO₄ and Mg₂GeO₄ spinels. Ringwoodite (γ-Mg₂SiO₄) is considered to be the most abundant mineral in the lower part of the transition zone and can incorporate large amounts of water in the form of hydroxyls, whereas the germanate spinel (γ-Mg₂GeO₄) corresponds to a low-pressure structural analogue for ringwoodite. The calculated defect energies indicate that the most favourable mechanisms for hydrogen incorporation are coupled either with the reduction of ferric iron or with the creation of tetrahedral vacancies. Hydrogen will go preferentially into tetrahedral vacancies, eventually leading to the formation of the hydrogarnet defect, before associating with other negatively charged point defects. The presence of isolated hydroxyls is not expected. The same trend is observed for germanate, and thus γ-Mg₂GeO₄ could be used as a low-pressure analogue for ringwoodite in studies of water-related defects and their effect on physical properties.     

Strong site preference of Co2+ in olivine,Co1.10Mg0.90SiO4

The crystal structure and site preference of Co²⁺ in a synthetic Co_1.10Mg_0.90SiO₄ 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.     

Tracerdiffusion of the Fe-cations in olivine (Fe x Mg1−x )2SiO4 (III)

Tracerdiffusion coefficients D _Fe* (and D _Mg*) are presented for olivines of composition (Fe _x Mg_1?x )₂SiO₄ at T=1,130° C as a function of x, and oxygen activity, a _{O 2}. Since the oxygen activity dependence of D _Fe* (D _Mg*) and that of the cation vacancy concentration are almost identical, it is concluded that a vacancy diffusion mechanism is operative in the octahedrally coordinated cation sublattices. From D _Fe* and D _Mg*, the chemical diffusion coefficient \(\bar D\) can be calculated. The calculated \(\bar D\) is in agreement with \(\bar D\) -values obtained by Boltzmann-Matano analysis of interdiffusion experiments. In addition, correlation factors are evaluated from the tracerdiffusion data in order to calculate selfdiffusion coefficients.     

Olivine flotation and settling experiments on the join Mg2SiO4-Fe2SiO2

Some unusual density relations between olivine and coexisting liquid in the system fosterite-fayalite are reported. At 1 atmosphere pressure olivine floats on its coexisting liquid for intermediate compositions on this binary because of extreme partitioning of Fe into the melt phase. At 20 kilobars the usual behavior of olivine settling occurs because the partitioning of Fe in the melt is reduced, aided possibly by the dissolution of CO₂ in the melt from use of a graphite container. Olivine flotation and settling are rapid in a time period of only a few hours because viscosities are a little greater than that of paraffin oil at room temperature. Some adcumulate textures with good triple junction grain boundaries are developed. General observations of differentiated magmatic systems on a number of scales and experimental data indicate that the mechanisms by which magmas can differentiate vary considerably in the ultramafic to tholeiitic compositional range.     

High pressure phase transformations in the joins Mg2SiO4-Ca2SiO4 and MgO-CaSiO3

High pressure phase transformations for all the mineral phases along the joins Mg₂SiO₄-Ca₂-SiO₄ and MgO-CaSiO₃ in the system MgO-CaO-SiO₂ were investigated in the pressure range between 100 and 300 kbar at about 1,000 °C, by means of the technique involving a diamond-anvil press coupled with laser heating. In addition to the four end-members, there are three stable intermediate mineral components in these two joins. Phase behaviour of all the end-member components at high pressure have been reported earlier and are reviewed here. Results of this study reveal that the three intermediate components are all unstable relative to the end-members at pressures greater than 200 kbar. Ultimately, monticellite (CaMgSiO₄) decomposes into CaSiO₃ (perovskite-type)+MgO; merwinite (Ca₃MgSi₂O₈) decomposes into Ca₂SiO₄(K₂NiF₄-type)+CaSiO₃ (perovskite-type)+MgO; and akermanite (Ca₂MgSi₂O₇) decomposes into CaSiO₃ (perovskite-type)+MgO. Note that the decomposition reactions of all phases studied here result in the formation of MgO. Intermediate Ca-Mg silicates transform to pure Ca-silicates plus MgO, while pure Mg₂SiO₄ transforms to MgSiO₃+MgO.     

Temperature-dependent magnetic susceptibility behaviour of spinelloid and spinel solid solutions in the systems Fe2SiO4–Fe3O4 and (Fe,Mg)2SiO4–Fe3O4

The magnetic behaviour and Curie temperatures (T _C ) of spinelloids and spinels in the Fe₃O₄–Fe₂SiO₄ and Fe₃O₄–(Mg,Fe)₂SiO₄ systems have been determined from magnetic susceptibility (k) measurements in the temperature range –192 to 700 °C. Spinelloid II is ferrimagnetic at room temperature and the k measurements display a characteristic asymmetric hump before reaching a T _C at 190 °C. Spinelloid V from the Mg-free system is paramagnetic at room temperature and hysteresis loops at various low temperatures indicate a ferri- to superparamagnetic transition before reaching the T _{C .} The T _C shows a non-linear variation with composition between –50 and –183 °C with decreasing magnetite component (X _Fe3O₄). The substitution of Mg in spinelloid V further decreases T _C . Spinelloid III is paramagnetic over nearly the total temperature range. Ferrimagnetic models for spinelloid II and spinelloid V are proposed. The T _C of Fe₃O₄–Fe₂SiO₄ spinel solid solutions gradually decrease with increasing Si content. Spinel is ferrimagnetic at least to a composition of X _Fe3O₄=0.20, constraining a ferrimagnetic to antiferromagnetic transition to occur at a composition of X _Fe3O₄<0.20. A contribution of the studied ferrimagnetic phases for crustal anomalies on the Earth can be excluded because they lose their magnetization at relatively low temperatures. However, their relevance for magnetic anomalies on other planets (Mars?), where these high-pressure Fe-rich minerals could survive their exhumation or were formed by impacts, has to be considered.     

New orthorhombic phases on the join NiAl2O4 (spinel analog)-Ni2SiO4 (olivine analog): Stability and implications to mantle mineralogy

Three new crystalline phases differing in Si/Al ratio have been synthesized from compositions along the join NiAl₂O₄-Ni₂SiO₄. Four reversible univariant equilibria involving these new phases plus Ni₂SiO₄ (olivine) have been located within the P-T region studied (1 atm–40 kb, 1000–1700° C); an invariant point occurs near 22 kb, 1150°C.All three new phases are orthorhombic. Precession photographs and electron microprobe analyses yield the following information:Phase I: 5NiO·3Al₂O₃·SiO₂ = 3NiAl₂O₄·Ni₂SiO₄, Pmma, a=5.67, b=11.51, c=8.10 (Å)Phase II: 7NiO·3Al₂O₃·2SiO₂ = 3NiAl₂O₄· 2Ni₂SiO₄, Imma, a=5.66, b=17.32, c=8.11Phase III: 3NiO· Al₂O₃· SiO₂ = NiAl₂O₄·Ni₂SiO₄, Imma, a=5.68, b=11.49, c=8.12Comparison with known structures suggests that these three phases plus NiAl₂O₄ spinel and high pressure Ni₂SiO₄ spinel belong to a homologous series based on a cubic close oxygen packing of the formula: M_2n O _n}-1 (T _n O_3n+1) where M and T are octahedrally and tetrahedrally coordinated cations, respectively. When n=1 the formula for spinel is obtained; n = 2 for phase I and phase III, both similar to the beta-phase of orthosilicates; and n = 3 for phase II which is related to the manganostibite structure.Similar phase equilibria and structural relations may occur on other joins of the aluminateorthosilicate type. Furthermore, the occurrence of such structural modifications between the spinel (aluminate) and olivine (orthosilicate) compositions suggests that there could be a corresponding polymorphic series between the olivine and spinel forms of orthosilicates.     

Single crystal growth of the modified spinel (β) and spinel (γ) phases of (Mg,Fe)2SiO4 and some geophysical implications

Single crystals of ferromagnesian orthosilicates with modified spinel (β) and spinel (γ) structure as large as 500 μm have been grown by solid state crystallization at high temperature and high pressure using an MA8-type apparatus driven in a 2,000-ton uniaxial press. This system is capable of generating pressures of 24.0 (±0.3) GPa at 2,400 (±50)°C for one hour in a sample assembly volume of 0.14 cm³. Crystals larger than 100 μm were observed to grow only at pressures within 5 percent of the phase boundary between the stability fields of the β and γ phases. Experimental determination of the phase boundaries between β or β+γ and γ phases for (Mg,Fe)₂SiO₄ has been extended to 22 GPa and 2,400°C. The effect of configurational entropy due to disordering is evaluated to be minimal on the basis of the cationic distribution in the synthesized samples; thus, we conclude that the phase boundary between β or β+γ and γ phases remains essentially linear to 2,400°C. In (Mg,Fe)₂SiO₄ solid solutions, the stability field of the γ phase shifts towards the lower pressures with increasing iron content at a rate of a 1 GPa for each 10 mole percent Fe. Assignment of the β→β+γ→γ transition to the seismic 550 km discontinuity is rejected by the present phase diagram results for (Mg_0.9Fe_0.1)₂SiO₄ and measurement of acoustic velocities for β and γ Mg₂SiO₄, but the discontinuity may be caused by a phase transition of pyroxene to a garnet-like structure.     

Magnetic properties of the Fe2SiO4-Fe3O4 spinel solid solutions

 Magnetic measurement of Fe_{3− x} Si _x O₄ spinel solid solutions indicates that their Curie temperatures decrease gradually, but not linearly, from 851 to 12 K with increasing content of nonmagnetic ions Si⁴⁺. Magnetic hysteresis becomes more noticeable in solid solutions having a larger content of Fe₂SiO₄. Saturation magnetizations of Fe_{3− x} Si _x O₄ samples increase up to x=0.357 and they are easily saturated in the field of H=0.1 T. However, magnetization of the sample of x=0.794 does not approach saturation even at high field of H=7.0 T and has a large coercive force. The Si⁴⁺ disordered distribution is confirmed to be ^tetr[Fe³⁺ _{1− x + x t} Si⁴⁺ _{x (1− t )}] ^octa[Fe²⁺ _{1+ x} Fe³⁺ _{1− x − x t} Si⁴⁺ _{x t} ] O₄ by the spin moment, which is consistent with site occupancy obtained from X-ray crystal structure refinement. Their molecular magnetizations would be expressed as M _B={4(1+x)+10xt}μ_B as functions of composition parameter x and Si⁴⁺ ordering parameter t of the solid solution. The sample of x=0.794 is antiferromagnetic below the Néel temperature, mainly due to the octahedral cation interaction M _O–M _O, while both M _T–M _O and M _O–M _O interactions induce a ferrimagnetic property. Concerning magnetic spin configuration, in the case of x>0.42, the lowest dɛ level becomes a singlet, resulting in no orbital angular momentum. Received: 20 April 2000 / Accepted: 11 September 2000     

The lattice dynamics and thermodynamics of the Mg2SiO4 polymorphs

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.