High-temperature creep in a Ni2GeO4: a contribution to creep systematics in spinel

 High-temperature creep behavior in Ni₂GeO₄ spinel was investigated using synthetic polycrystalline aggregates with average grain sizes ranging from submicron to 7.4 microns. Cylindrical samples were deformed at constant load in a gas-medium apparatus at temperatures ranging from 1223 to 1523 K and stresses ranging from 40 to 320 MPa. Two deformation mechanisms were identified, characterized by the following flow laws: where σ is in MPa, d is in μm and T is in Kelvin. These flow laws suggest that deformation was accommodated by dislocation creep and grain-boundary diffusion (Coble) creep, respectively. A comparison with other spinels shows that an isomechanical group can be defined for spinels although some differences between normal and inverse spinels can be identified. When creep data for olivine and spinel are normalized and extrapolated to Earth-like conditions, spinel (ringwoodite) has a strength similar to olivine in the dislocation creep regime and is considerably stronger than olivine in the diffusion creep regime at coarse grain size. However, when grain-size reduction occurs, spinel can become weaker than olivine due to its high grain-size sensitivity (Coble creep behavior). Analysis of normalized diffusion creep data for olivine and spinel indicate that spinel is weaker than olivine at grain sizes less than 2 μm. Received: 18 June 2000 / Accepted: 3 April 2001     

Crystal structures of Ni2SiO4 and Fe2SiO4 as a function of temperature and heating duration

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Electrical conduction of Co2SiO4

This paper reports measurements of electrical conductivity in Co₂SiO₄ as a function of temperature in the range from 780 to 1540 K and oxygen fugacity in the range from 5 × 10^–8 to 2.6 × 10^–5 MPa at 1540 K. From the present data and available literature data on defect concentrations in Co₂SiO₄, the mobility of the defect responsible for conduction is determined to be 8.6 × 10^–7 m²/V-s at 1373 K. On the basis of these data and the observed dependence of conduction on oxygen fugacity, it is concluded that small polarons associated with oxidized cobalt ions is the likely mechanism controlling conduction. The mobility of small polarons in iron-bearing olivine under similar conditions is likely to be of the same order of magnitude.     

Electrical conductivity measurements on olivines Mg2SiO4-Fe2SiO4 under defined thermodynamic conditions

The isobaric (P=10 kb) temperature dependence of the electrical conductivities of forsterite, fayalite and forsterite-fayalite mixed crystals was measured with special regard to the thermodynamics of point defects in these minerals. Measurements, taken at increasing and decreasing temperature, were performed on synthetic powders of the following compositions: Fo 100/Fa 0, Fo 90/Fa 10, Fo 80/Fa 20, Fo 60/Fa 40, and Fo 0/Fa100. Control of oxygen partial pressure was achieved with solid state buffers (Fa/Q/M, Fa/Q/I, and Fe/FeO). Activities of the binary components were controlled by equilibrating the sample with its neighbouring phases. All values for σ, obtained with controlled pO₂ and fixed activities of the binary components, agree well upon either heating or cooling. From the gradient of lg σ vs. 1/T plots, the following activation energies were estimated: 2,461 eV (970°–1075°C) and 0.984 eV (522°–970°C) for Fo 100/Fa 0 equilibrated with MgO; 0.777 eV and 0.683 eV for Fo 90/Fa 10 and Fo 80/Fa 20 equilibrated with enstatite and pO₂ controlled by Fe/FeO buffer; 0.622 eV, 0.528 eV, and 0.479 eV for Fo 90/Fa 10, Fo 80/Fa 20, and Fo 60/Fa 40 equilibrated with enstatite and pO₂ controlled by Fa/Q/M buffer; and 0.524 eV and 0.383 eV for Fo 0/Fa 100 equilibrated with Q/I and Q/M respectively.     

Thermodynamics and behavior of γ-Mg2SiO4 at high pressure: Implications for Mg2SiO4 phase equilibrium

Raman spectra of γ-Mg₂SiO₄ taken to 200 kbar were used to calculate entropy and heat capacity at various P-T conditions. These new thermodynamic data on γ-MgSiO₄, similar data on MgSiO₃ perovskite (pv), previous data on β-MgSiO₄ and MgO (mw), and previous volumetric data of all phases were used to calculate the phase boundaries in the Mg₂SiO₄ phase diagram. Our resulting slope for the β→γ transition (50±4 bar K^-1) is in excellent agreement with recent multi-anvil studies. The slopes for the β→pv+MgO and γ→pv+MgO are-7±3 and -25±4 bar K^-1, respectively, and are consistent with our CO₂ laser heated diamond anvil studies. These slopes result in a β-γ-MgO+pv triple point at approximately 229 kbar and 2260 K for the iron free system.     

The system Mg2SiO4-Ca2SiO4-CaAl2O4-NaAlSiO4-SiO2: one atmosphere liquidus equilibria of analogs of alkaline mafic lavas

One atmosphere liquidus relationships in the system Mg₂SiO₄ (Fo)–Ca₂SiO₄ (La)–NaAlSiO₄ (Ne)–CaAl₂O₄ (CA)–SiO₂ (Sil) are presented as analogs for alkaline mafic lavas. Liquidus diagrams are constructed from electron microprobe analyses of quenched liquids and coexisting mineral phases produced in melting experiments and they are depicted in terms of sub-projections within the pseudo-quaternary system Fo–La–[Ne,CA]–Sil. The Ne and CA components are combined to create a normative feldspathoid component defined as Ne#=Ne/[Ne+CA]. Liquidus relations at Ne#=0.5 from this study are compared to relations at Ne#=0.0 and 1.0 from previous studies. In general, liquidus temperatures decrease and positions of liquidus boundaries involving feldspathic phases shift toward the [Ne, CA] component as Ne# increases. The pseudoinvariant points fo+di+pl+mel+l and fo+pl+mel+sp+l exist at Ne#=0.5. These equilibria between forsterite-plagioclase-melilite-liquid are not present in the system when Ne#=1.0 because a boundary curve (fo+di+ne+l) separates the plagioclase and melilite liquidus fields. The liquidus diagrams provide useful analogs for the crystallization sequences of natural primary alkali olivine basalts, basanitoids, basanites, olivine nephelinites, olivine-melilite nephelinites and olivine melilitites.     

Determination of cation distribution in (Co,Ni,Zn)2SiO4 olivine by synchrotron X-ray diffraction

 The cation distribution of Co, Ni, and Zn between the M1 and M2 sites of a synthetic olivine was determined with a single-crystal diffraction method. The crystal data are (Co_0.377Ni_0.396Zn_0.227)₂SiO₄, M _r  = 212.692, orthorhombic, Pbnm, a = 475.64(3), b = 1022.83(8), and c = 596.96(6) pm, V = 0.2904(1) nm³, Z = 4, D _x  = 4.864 g cm⁻³, and F(0 0 0) = 408.62. Lattice, positional, and thermal parameters were determined with MoKα radiation; R = 0.025 for 1487 symmetry-independent reflections with F > 4σ(F). The site occupancies of Co, Ni, and Zn were determined with synchrotron radiation employing the anomalous dispersion effect of Co and Ni. The synchrotron radiation data include two sets of intensity data collected at 161.57 and 149.81 pm, which are about 1 pm longer than Co and Ni absorption edges, respectively. The R value was 0.022 for Co K edge data with 174 independent reflections, and 0.034 for Ni K edge data with 169 reflections. The occupancies are 0.334Co + 0.539Ni + 0.127Zn in the M1 sites, and 0.420Co + 0.253Ni + 0.327Zn in the M2 sites. The compilation of the cation distributions in olivines shows that the distributions depend on ionic radii and electronegativities of constituent cations, and that the partition coefficient can be estimated from the equation: ln [(A/B)_M1/(A/B)_M2] = −0.272 (IR _A -IR _B ) + 3.65 (EN _A −EN _B ), where IR (pm) and EN are ionic radius and electronegativity, respectively. Received: 8 April 1999 / Revised, accepted: 7 September 1999     

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.     

Thermodynamic properties of the forsterite-fayalite (Mg2SiO4-Fe2SiO4) solid solution. determination of heat of formation

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.     

Experimental study of the effect of SiO2 on Ni solubility in silicate melts

The solubility of Ni in silicate melts with variable SiO₂ content was studied at a total pressure of 1 atm within a wide range of temperature and oxygen fugacity. The maximum solubility of Ni (minimum activity coefficient of NiO) was observed in melts with ～55–57 wt % SiO₂, regardless of temperature and oxygen fugacity. Melts beyond this range showed significantly lower Ni solubility and, correspondingly, higher NiO activity coefficients. The analysis of our results and literature data led us to the conclusion that the NBO/T (number of nonbridging oxygen atoms per tetrahedrally coordinated atom) is inadequate to describe the effect of melt composition on Ni solubility.     

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.     

Mechanism of the olivine-spinel transformation in Co2SiO4

An experiment conducted in a 2000-ton uniaxial split-sphere apparatus (USSA-2000) utilizes large sample volume and a substantial temperature gradient to synthesize intergrowths of the olivine and spinel polymorphs of Co₂SiO₄. The olivine starting material consists of a finegrained fraction (<20μm) which records the stable polymorphs along the length of the sample plus large olivine grains (100–500 μm) which help decipher the mechanism of the phase transformation. At conditions near equilibrium, the olivine-spinel transformation in the large grains occurs by inward growth of a few large single crystals of spinel nucleated on the surfaces of the olivine. The overall rate of transformation is governed by the mobility of the interphase boundary, whose morphology is crystallographically controlled by the spinel. No renucleation of spinel is observed in the host olivine crystal, even in the region immediately adjacent to the olivine/spinel interface; analysis of this region with transmission electron microscopy reveals an extremely high density of dislocations induced by plastic flow accommodating the volume change associated with the phase transformation.     

Oxidation kinetics of fayalite (Fe2SiO4)

Single crystals of fayalite (Fe₂SiO₄) have been oxidized either in the hematite or the magnetite stability field to investigate the kinetics and mechanisms of oxidation. For samples heated in air at 770° C, a two-phase region composed of fine-grained iron oxide and silica phases formed as the reaction front moved into the sample, and an iron oxide layer formed external to this two-phase region. The presence of the single-phase oxide layer coating the specimens indicates that oxidation occurs by the migration of iron from the fayalite to the gas-solid interface rather than by the movement of oxygen in the opposite direction. For oxidation in air, the kinetics followed a parabolic growth law, with the rate of oxidation limited by the diffusion of iron from the internal reaction front to the gas-solid interface through the iron oxide. When fayalite was oxidized in the magnetite stability field, using a CO/CO₂ gas mixture at 1030° C, oxidation was controlled by the reaction at the gas-solid interface, yielding an oxidation rate considerably slower than that predicted for diffusion-controlled growth of the oxide layer.