Calorimetric study of the stability of spinelloids in the system NiAl2O4-Ni2SiO4

Enthalpies of solution in molten 2 PbO · B₂O₃ at 974 K were measured for four spinelloids, phases I (0.75 NiAl₂O₄ · 0.25 Ni₂SiO₄), II (0.60 NiAl₂O₄ · 0.40 Ni₂SiO₄), III and IV (0.50 NiAl₂O₄ · 0.50 Ni₂SiO₄) in the system NiAl₂O₄ · Ni₂SiO₄. The enthalpies (in cal per 4-oxygen mol) of formation from NiAl₂O₄ and Ni₂SiO₄ spinels are: phase I, 945±366; phase II, 1072±360; phase III, 2253±390; phase IV, 3565±544. Using these enthalpy data in combination with phase relations at high pressure at 1373 K, positive entropies of formation of the spinelloids from NiAl₂O₄ and Ni₂SiO₄ spinels were estimated (in cal mol^?1 K^?1): phase I, 1.2; phase II, 1.5; phase III, 2.0–2.3; phase IV, 3.0–3.1. The thermochemical data obtained above suggest that the spinelloids are “entropy-stabilized” phases with partially disordered cation distributions. The configurational entropies of the spinelloids were calculated based on the observed cation distribution in each spinelloid phase. The positive entropies of formation of the spinelloids from the spinel endmembers are due primarily to the configurational entropies although small positive vibrational entropy changes may also exist.     

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.     

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.     

A MEG study of the olivine and spinel forms of Mg2SiO4

In this paper we present a theoretical investigation of the structures and relative stability of the olivine and spinel phases of Mg₂SiO₄. We use both a purely ionic model, based on the Modified Electron Gas (MEG) model of intermolecular forces, and a bond polarization model, developed for low pressure silica phases, to investigate the role of covalency in these compounds. The standard MEG ionic model gives adequate structural results for the two phases but incorrectly predicts the spinel phase to be more stable at zero pressure. This is mainly because the ionic modeling of Mg₂SiO₄ only accounts for 95 percent of the lattice energy. The remainder can be attributed to covalency and many-body effects. An extension of the MEG ionic model using “many-body” pair potentials corrects the phase stability error, but predicts structures which are in poorer agreement with experiment than the standard ionic approach. In addition, calculations using these many-body pair potentials can only account for 10 percent of the missing lattice energy. This model predicts an olivine-spinel phase transition of 8 GPa, below the experimental value of 20 GPa. Therefore, in order to understand more fully the stability of these structures we must consider polarization. A two-shell bond polarization model enhances the stability of both structures, with the olivine structure being stabilized more. This model predicts a phase transition at about 80 GPa, well above the observed value. Also, the olivine and spinel structures calculated with this approach are in poorer agreement with experiment than the ionic model. Therefore, based on our investigations, to properly model covalency in Mg₂SiO₄, a treatment more sophisticated than the two-shell model is needed.     

Magnetite activities across the MgAl2O4-Fe3O4 spinel join,with application to thermobarometric estimates of upper mantle oxygen fugacity

The activity of Fe₃O₄ component in MgAl₂O₄-Fe₃O₄ spinels has been measured at 900° and 1000° C and 1 atm total pressure using a zirconia oxygen electrolyte. As previously reported for the dilute Fe₃O₄ concentration region (Mattioli and Wood 1986a), magnetite activity at 1000° C is greater than at 900° C at constant Fe₃O₄ mole fraction, for compositions across the MgAl₂O₄-Fe₃O₄ join between 20 and 80 mol% Fe₃O₄ component. The 1-atm solvus crest lies between 900° and 1000° C and, at 900° C the limbs are at Fe₃O₄ mole fractions of 0.2 and 0.6 approximately.Application of the O'Neill and Navrotsky (1983, 1984) cation distribution model indicates that the unusual activity — composition behavior of Fe₃O₄ is caused by changes in the equilibrium state of disorder of mixed MgAl₂O₄-Fe₃O₄ spinels relative to the disordered Fe₃O₄ standard state. In addition, both stoichiometric volumes (Mattioli et al. 1987) and activities across the MgAl₂O₄-Fe₃O₄ join suggest that short range order is significant for this binary. Excess free energy terms must be added to ideal Fe₃O₄ activities formulated from equilibrium cation distributions in complex MgAl₂O₄-Fe₃O₄ spinels in order to increase Fe₃O₄ activities to values consistent with observation and to generate the apparent region of immiscibility at 900° C.We have applied our activity data to the estimation of upper mantle spinel-lherzolite oxygen fugacities. We calculated that minimum 's are about 2 log units below the synthetic QFM buffer at 15 kbar total pressure for Fe₃O₄ concentration of 2 mol%, in a Cr-free spinel phase. If a preliminary calibration of an additional 25 mol% Fe²⁺-substitution as FeCr₂O₄ or FeAl₂O₄ component is incorporated into Fe₃O₄ activity, then olivine-orthopyroxene-spinel assemblages of depleted-Type 1-spinel-lherzolite xenoliths indicate 's close to QFM at 15 kbar. This is in good agreement with previous thermobarometric estimates and in sharp contrast to 1 atm intrinsic measurements near IW.     

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.     

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.     

Stability of wadeite (Zr2K4Si6O18) under upper mantle conditions: Petrological implications

Wadeite of composition Zr₂K₄Si₆O₁₈, synthesized at 1 atm, is stable between 12–25 kb at 800 °–1,250 ° C; conditions appropriate to those of partial melting of an anomalous K-enriched upper mantle. If published hypotheses for the generation of high potash mafic to ultramafic lavas based on partial melting of such an anomalous mantle are correct, wadeite is a possible K-bearing mineral, in addition to phlogopide and K-richterite, stable under mantle conditions. The restricted occurrence of wadeite to rocks of West Kimberley, Australia and Leucite Hills, Wyoming is believed to be due to their high K/Al and Zr contents relative to other high potash rocks. The cell constants of wadeite of Zr₂K₄Si₆O₁₈ composition are in agreement with those of natural Zr-rich wadeite and with the values predicted from synthetic wadeites with smaller tetravalents ions in the Zr site.     

Temperature dependence of the cation distribution in nickel aluminate (NiAl2O4) spinel: a powder XRD study

NiAl₂O₄ is a largely inverse spinel, which in detail shows increasing randomisation with temperature of Ni and Al between the octahedral and tetrahedral cation sites of the spinel structure. We have used powder XRD to determine this cation distribution in various samples of NiAl₂O₄ quenched after annealing between 700 and 1400° C. The inversion parameter (x) can be measured with a precision of ± 0.004 (one standard deviation), and a comparison of different methods of synthesis, X-ray diffraction and refinement techniques, suggests a probable accuracy of better than 0.01. The results are supported by some preliminary single crystal refinements on flux-grown samples.Below 800° C the rate of cation ordering becomes very slow, and, despite reaching an apparently steady state, it is doubtful if our samples attained complete internal equilibrium. Above 1250° C the cation redistribution becomes so fast that the quenching method becomes unreliable. Between 800 and 1250° C inclusive, the degree of inversion changes smoothly from 0.87 at 800° C to 0.79 at 1250° C, and is accompanied by linear changes in u, the oxygen parameter, from 0.2555 to 0.2563 (±0.0002), and a₀, the lattice parameter, from 8.0462 to 8.0522 Å (±0.0002 Å).     

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.     

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.     

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.     

Infrared spectroscopic investigation of hydroxyl in β-(Mg,Fe)2SiO4 and coexisting olivine: Implications for mantle evolution and dynamics

Wadsleyite (β-(Mg,Fe)₂SiO₄) is a major constituent of the Earth's transition zone and is known to accommodate OH. The portion of the transition zone between 400–550 km could be an important source or sink for hydroxyl in plumes and slabs intersecting this region. Micro-infrared spectroscopy has been carried out on the β-phase and coexisting metastable olivine synthesized in a multianvil apparatus at 14 GPa and 1550–1650 K under hydrous conditions. Single-crystal and polycrystal specimens of both phases were analyzed in the 1800–8500 cm^?1 frequency region to determine the speciation, abundances, and partitioning behavior of the hydrous components in coexisting β-phase and olivine. β-phase spectra consistently show three distinct OH bands at 3329, 3580, and 3615 cm^?1. OH concentrations range from 10000–65000 H/10⁶ Si. A strong positive correlation of grain size and extent of transformation with OH concentration in the β-phase indicates that grain-growth and transformation rates are enhanced in a hydrous environment. Olivine spectra are variable, but consistently show a prominent broad-band absorbance representing molecular H₂O, consistent with the infrared signature of the starting material. OH concentrations in olivine range from <300–1400 H/10⁶ Si. The highest OH concentrations measured for olivine and the β-phase may represent solubility limits, in which case the OH solubility ratio between these two phases is approximately 1∶40. Where both phases coexist and are undersaturated with OH, the partitioning ratio of OH between them is about 1∶100. The large solubility contrast between olivine and the β-phase suggests a mechanism for hydrating the transition zone via olivine carried down in subducting slabs. Plumes impinging on an OH-rich upper transition region could cause H₂ or H₂O to be released upon transformation of the β-phase to olivine, resulting in initiation of secondary upwellings. If dissolution of OH weakens the β-phase, and if OH is present in the mantle, the region between 400–550 km could be a zone of low viscosity.     

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.     

Stability of dense hydrous magnesium silicate phases in the systems Mg2SiO4-H2O and MgSiO3-H2O at pressures up to 27 GPa

We conducted high-pressure phase equilibrium experiments in the systems MgSiO₃ with 15 wt% H₂O and Mg₂SiO₄ with 5 wt% and 11 wt% H₂O at 20 ∼ 27 GPa. Based on the phase relations in these systems, together with the previous works on the related systems, we have clarified the stability relations of dense hydrous magnesium silicates in the system MgO-SiO₂-H₂O in the pressure range from 10 to 27 GPa. The results show that the stability field of phase G, which is identical to phase D and phase F, expands with increasing water contents. Water stored in serpentine in the descending cold slabs is transported into depths greater than 200 km, where serpentine decomposes to a mixture of phase A, enstatite, and fluid. Reaction sequences of the hydrous phases which appear at higher pressures vary with water content. In the slabs with a water content less than about 2 wt%, phase A carries water to a depth of 450 km. Hydrous wadsleyite, hydrous ringwoodite, and ilmenite are the main water reservoirs in the transition zone from 450 to 660 km. Superhydrous phase B is the water reservoir in the uppermost part of the lower mantle from 670 to 800 km, whereas phase G appears in the lower mantle only at depths greater than 800 km. In cold slabs with local water enrichment greater than 2 wt%, the following hydrous phases appear with increasing depths; phase A to 450 km, phase A and phase G from 450 km to 550 km, brucite, superhydrous phase B, and phase G from 550 km to 800 km, and phase G at depths greater than 800 km. Received: 4 August 1999 / Accepted: 1 March 2000     

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.     

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.     

High-Pressure crystal chemistry of spinel (MgAl2O4) and magnetite (Fe3O4): Comparisons with silicate spinels

High-pressure crystal structures and compressibilities have been determined by x-ray methods for MgAl₂O₄ spinel and its isomorph magnetite, Fe₃O₄. The measured bulk moduli, K, of spinel and magnetite (assuming K′=4) are 1.94±0.06 and 1.86±0.05 Mbar, respectively, in accord with previous ultrasonic determinations. The oxygen u parameter, the only variable atomic position coordinate in the spinel structure (Fd3m, Z=8), decreases with pressure in MgAl₂O₄, thus indicating that the magnesium tetrahedron is more compressible than the aluminum octahedron. In magnetite the u parameter is unchanged, and both tetrahedron and octahedron display the 1.9 Mbar bulk modulus characteristic of the entire crystal. This behavior contrasts with that of nickel silicate spinel (γ-Ni₂SiO₄), in which the u parameter increases with pressure because the silicon tetrahedron is relatively incompressible compared to the nickel octahedron.     

Magnetic structure and cation distribution in (Fe,Mn)2SiO4 (olivine) by neutron diffraction

The cation distribution in the synthetic samples of olivine-type structure with composition (Fe _x Mn_1?x )₂SiO₄ was determined at room temperature and confirms previous Mössbauer results. At low temperature an antiferromagnetic ordering is observed. The magnetic structures can be described in the crystallographic cell (i.e. k=0). They are interpreted on the basis of the irreducible representations (modes) of the symmetry groups which are compatible with Pnma. The dominant modes observed for all compounds, including Fe₂SiO₄ and Mn₂SiO₄, only differ in their direction. The main direction of magnetization is dominated by the Fe²⁺ single-ion anisotropy. At 4.2K, for x=0.29, it is parallel to the c-axis, whereas for x=0.76 the direction is parallel to the b-axis. The anisotropy of the M1-sites dominates in the first case, whereas M2-anisotropy dominates in the second case. The influence of temperature is demonstrated for x=0.50 where c is the main direction at 4.2K, when it is b at 38K.