Temperature dependence of intersite distribution of Mg and Fe in olivine and the associated change of lattice parameters

The cation distribution of natural and heated ferromagnesian olivine with chemical composition, Fo₆₇Fa₃₃, from metagabbro was examined by X-ray diffraction. Heating and quenching experiments were made by a newly devised apparatus which enables us to obtain very fast quenching speed in comparison with the usual technique. The distribution constants, K _D=(Fe⁺²/Mg) _M1/(Fe⁺²/Mg) _M2, of the natural samples were less than 1.07, and those of heat-treated samples were more than 1.15, indicating that cation ordering takes place with temperature. The distribution of Fe⁺² and Mg is nearly random at low temperatures, whereas Fe⁺² shows a slight but significant preference for a smaller M1 site at high temperatures. The change of the distribution constant was observed on specimens which were heated for a short period of time (6–1,060 s) and quenched within 10 ms. Thus the rate of the cation reordering reaction is a very fast process. The lattice parameters b and c decrease whereas a increases with the increase of distribution constant. The overall effect on unit cell volume is a decrease with the increasing distribution constant, suggesting the presence of significant pressure dependence of the cation distribution towards the ordering of Fe at M1 site in ferromagnesian olivine.     

Pressure effect on the divalent cation distribution in nonideal solid solution of forsterite and fayalite

The divalent cation distribution in olivine (Mg, Fe)₂SiO₄ under high pressure and temperature was studied to clarify the detailed state of olivine in the mantle. Single crystal samples were heated for a sufficient period of time for the cations to migrate and quenched fast enough to preserve the equilibrated state under high pressures, and the crystal structure was determined with X-ray method. The pressure effect on the distribution coefficient K _D[= (Fe/Mg) _M1/(Fe/Mg) _M2] was determined for the first time; dK _D/dP?0.02 GPa^?1. A set of five thermodynamic parameters required to describe the regular solution model was determined from data concerning the pressure dependence and the known temperature and compositional effects. As a result we have shown how K _D depends on pressure, temperature, and composition. The notable feature clarified is the very large contribution of nonideality in the olivine solid solution. The K _D of olivine crystals in the mantle is predicted; K _D increases to ～ 2.2 at the depth of 400 km, in contrast to 0.9 ～ 1.2 of natural samples available at the surface of the Earth.     

Kinetics of intracrystalline cation redistribution in olivine and its implication

The rate of cation redistribution between M 1 and M 2 sites in olivine is theoretically studied on the basis of elementary processes of cationic migration. Cationic migration in olivine structure is assumed to be the superposition of a unit exchange of cations between closely spaced couple of sites. Such a process gives rise to both cation redistribution and also cationic interdiffusion in olivine crystal. The time constant of cationic equilibration in the redistribution reaction is related to the interdiffusion coefficient along b-axis, and its numerical value is given as a function of temperature and composition in Mg-Fe olivine. This time constant is very short, e.g., in the order of 10^?2～10^?4 s at 1000 ° C. The temperature dependence of cation distribution in Mg-Fe olivine could not be detected by heating and quenching experiments in some previous works, because of insufficient cooling rate. A skepticism is presented for the utility of cation distribution as a geothermometer or rate meter of cooling. Cation redistribution in olivine in the deep upper mantle is sufficiently fast to take place almost in phase with the seismic waves of long periods.     

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.     

High-pressure transformations in silicates,germanates, and titanates with ABO3 stoichiometry

High-pressure phase transformations were investigated for two silicates, MgSiO₃ and ZnSiO₃; six germanates, MGeO₃ and six titanates, MTiO₃ (M=Ni, Mg, Co, Zn, Fe, and Mn) at about 1,000°C and pressures up to ca. 30 GPa. CoGeO₃ was found to assume the ilmenite form. The ilmenite phases were confirmed to transform in the following schemes: to perovskite in MgSiO₃ and MnGeO₃, to corundum in MgGeO₃ and ZnGeO₃, to rocksalt plus rutile in ZnSiO₃ and CoGeO₃ and to rocksalt plus TiO₂ (possibly of some denser structure) in NiTiO₃, MgTiO₃, CoTiO₃, ZnTiO₃ and FeTiO₃. In the case of FeTiO₃, the corundum form appeared as an intermediate phase. The possibility that the corundum type MnTiO₃ might transform to some denser modification could not be excluded. The compound NiGeO₃ was nonexistent throughout the pressure range studied. High-pressure phases of ABO₃ (A=Ni, Mg, Co, Zn, Fe, and Mn; B=Si, Ge and Ti) are summarized, and those stabilized at pressures higher than 20 GPa are discussed.     

Effects of non-stoichiometry on the spinel structure at high pressure: Implications for Earth’s mantle mineralogy

A non-stoichiometric sample of spinel with composition ^T(Mg_0.4Al_0.6)^M(Al_1.8□_0.2)O₄ was investigated by single-crystal X-ray diffraction in situ up to about 8.7 GPa using a diamond anvil cell. The P(V) data were fitted using a third-order Birch-Murnaghan equation of state and the unit-cell volume V₀, the bulk modulus K_T0 and its first pressure derivative K′ were refined simultaneously providing the following coefficients: V₀ = 510.34(6) Å³, K_T0 = 171(2) GPa, K′ = 7.3(6). This K_T0 value represents the lowest ever found for spinel crystal structures. Comparing our data with a stoichiometric and natural MgAl₂O₄ (pure composition) we observe a decrease in K_T0 by about 11.5% and a strong increase in K′ by about 33%. These results demonstrate how an excess of Al accompanied by the formation of significant cation vacancies at octahedral site strongly affects the thermodynamic properties of spinel structure. If we consider that the estimated mantle composition is characterized by 3-5% of Al₂O₃ this could imply an Mg/Al substitution with possible formation of cation vacancies. The results of our study indicate that geodynamic models should take into account the potential effect of Mg/Al substitution on the incompressibility of the main mantle-forming minerals (olivine, wadsleyite, ringwoodite, Mg-perovskite).     

A thermochemical data base for phase equilibria in the system Fe-Mg-Si-O at high pressure and temperature

A thermochemical data base for phases in the system Fe-Mg-Si-O at high pressures up to 300 kbar is established by supplementing the available calorimetric data with data calculated from experimental high pressure synthesis studies. Phases included in the data base are the SiO₂ polymorphs, rock salt solid solutions (Fe-Mg-O), Fe₂O₃, Fe₃O₄, (Mg, Fe)₂SiO₄ olivine, spinel, modified spinel and (Mg, Fe)SiO₃ perovskite and pyroxene. Phases not included are the MgSiO₃-ilmenite and -garnet. Fe-Mg solution properties of olivine, spinel, perovskite and wustite (rock salt) are estimated. The wüstite solid solution has been modeled as a nonideal solution of three end members; FeO, FeO_1.5 and MgO. The new data base is made consistent with most of the available information on high pressure phase studies. The data base is useful in generating phase diagrams of various different compositions for the purpose of planning new experiments and analysing existing phase synthesis data.     

The genesis of mid-ocean ridge basalt

The tholeiitic volcanics erupted at mid-ocean ridges (mid-ocean ridge basalts or MORB) constitute the dominant volcanic lithology on Earth. Analyses of tachylites from Atlantic, Pacific and Indian Ocean spreading centres range widely in 100 Mg/(Mg + Fe²⁺) ratios (= M) and M varies from 70 to 30. Glasses with M = 55?65 are the most common variants and only a small percentage of glass analyses has M approaching 70. The latter defines the M -value of basaltic melts in equilibrium with residual upper-mantle source peridotites with M ～ 88. The frequency histogram of the M -values of average compositions of MORB glasses at 88 ocean floor localities is similar in analysis distribution to the frequency histograms depicting variation in the M -values of glasses from the various spreading centres.M -values and nickel contents of MORB and the nature and compositions of the near-liquidus phases crystallized experimentally from MORB melts at elevated pressures have been applied to identify primary (unfractionated) melts erupted in a mid-ocean ridge environment. However, Ni abundances and high-pressure phase relationships are not necessarily unique or definitive parameters of primary melts. The latter are generally linked genetically with Mg-rich lherzolitic source rocks of ‘pyrolite’ type (M ～ 90. The spectrum of M -values displayed by MORB glasses, with a definite bias towards relatively Fe-rich compositions (average M of approximately 600 MORB glasses is 58.6), suggests that the melts may have evolved either via ferromagnesian fractionation of relatively Mg-rich parental melts (M = 70?80), or by partial melting of a heterogeneous upper mantle with variable M values, or as a result of magma mixing of already fractionated melts and primitive magma batches.For a number of reasons fractonation models based on the extraction of olivine or one or more of olivine, plagioclase and clinopyroxene, either from picritic melts (M > 75 or ‘primitive’ basaltic melts with M ～ 70, are questionable as prime controls of MORB chemistry. These include: (1) the extreme rarity of ‘quenched’ picritic or Mg-basaltic melts in ocean ridge environments; (2) the lack of adequate evidence of the appropriate (of necessity voluminous) complementary cumulates (dunites, allivalites, troctolites, anorthosites) demanded by olivine, plagioclase, or olivine + plagioclase fractionation models; and (3) the aberrent frequencies of glass M -values whereby the assumed derivatives (M = 55?65 are much more abundant (and presumably much more voluminous) than the alleged parents or transitional derivatives (65 < M < 75). The nature of the trends of Na₂O, CaO and Al₂O₃ in Galapagos Spreading Centre tachylites of extended composition (M = 65?30) indicates the ‘gabbroic’ fractionation is also unlikely to exert important controls on MORB chemistry.As their M -values increase, mid-ocean ridge basalts increase in Al, Ca, Ni, Co, Cr and decrease in Ti, Mn, Na, K and P. Except for Al and Ca, these trends are similar to those displayed by upper-mantle peridotites increasing in M, i.e., becoming more refractory following one or more partial melting episodes. It is suggested that at least a majority of mid-ocean ridge basalts is intrinsically primary and generated by variable degrees of partial melting of heterogeneous lherzolitic upper mantle (80 < M < 90) with variable abundances of elements such as Ti, Al, Ca and Na and also depleted in large ion lithophile (LIL) elements. Negative europium anomalies in the rare-earth patterns of some oceanridge basalts (ferrobasalts with low M) are ascribed mainly to the persistence of residual plagioclase in relatively Fe-rich plagioclase lherzolite source rocks, following low degrees of partial melting. The partial melting events leading to the generation of mid-ocean ridge basalts took place over a relatively modes pressure range (approximately 8–15 kb) which encompassed the transition of plagioclase lherzolite to spinel lherzolite. This proposal appears consistent with the nature and occurrence of megacrysts (xenocrysts) of tschermakitic Cr-diopside (Ca₄₃Mg₅₂Fe₅), olivine (mg 89–91), plagioclase (An_92-85) and spinel (Fe₂Al₆₀Cr₃₈) in some MORB. The megacryst compositions suggest that these phases represent disaggregated plagioclase peridotite or spinel lherzolite acquired by melts during their passage through the oceanic upper mantle.     

Pressure dependence on partition coefficients for trace elements between olivine and the coexisting melts

Partition coefficients between olivine and melt at upper mantle conditions, 3 to 14 GPa, have been determined for 27 trace elements (Li, Be, B, Na, Mg, Al, Si, P, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Rb, Sr, Y, Zr, Cs, Ba, La and Ce) using secondary-ion mass-spectrometry (SIMS) and electron-probe microanalysis (EPMA). The general pattern of olivine/melt partitioning on Onuma diagrams resembles those reported previously for natural systems. This agreement strongly supports the argument that partitioning is under structural control of olivine even at high pressure. The partition coefficients for mono- and tri-valent cations show significant pressure dependence, both becoming larger with pressure, and are strongly correlated with coupled substitution into cation sites in the olivine structure. The dominant type of trace element substitution for mono- and tri-valent cations into olivine changes gradually from (Si, Mg)↔(Al, Cr) at low pressure to (Si, Mg)↔(Al, Al) and (Mg, Mg)↔(Na, Al) at high pressure. The change in substitution type results in an increase in partition coefficients of Al and Na with pressure. An inverse correlation between the partition coefficients for divalent cations and pressure has been observed, especially for Ni, Co and Fe. The order of decreasing rate of partition coefficient with pressure correlates to strength of crystal field effect of the cation. The pressure dependence of olivine/melt partitioning can be attributed to the compression of cation polyhedra induced by pressure and the compensation of electrostatic valence by cation substitution. Received: March 6, 1997 / Revised, accepted: March 12, 1998     

High-pressure Raman spectroscopic study of Mn2GeO4, Ca2GeO4, Ca2SiO4, and CaMgGeO4 olivines

We present a Raman spectroscopic study of the structural modifications of several olivines at high pressures and ambient temperature. At high pressures, the following modifications in the Raman spectra are observed: 1)?in Mn₂GeO₄, between 6.7 and 8.6?GPa the appearance of weak bands at 560 and 860?cm^?1; between 10.6 and 23?GPa, the progressive replacement of the olivine spectrum by the spectrum of a crystalline high pressure phase; upon decompression, the inverse sequence of transformations is observed with some hysteresis in the transformation pressures; this sequence may be interpreted as the progressive transformation of the olivine to a spinelloid where Ge tetrahedra are polymerized, and then to a partially inverse spinel; 2)?in Ca₂SiO₄, the olivine transforms to larnite between 1.9 and 2.1?GPa; larnite is observed up to the maximum pressure of 24?GPa and it can partially back-transform to olivine during decompression; 3)?in Ca₂GeO₄, the olivine transforms to a new structure between 6.8 and 8?GPa; the vibrational frequencies of the new phase suggest that the phase transition involves an increase of the Ca coordination number and that Ge tetrahedra are isolated; this high pressure phase is observed up to the maximum pressure of 11?GPa; during decompression, it transforms to a disordered phase below 5?GPa; 4)?in CaMgGeO₄, no significant modification of the olivine spectrum is observed up to 15?GPa; between 16 and 26?GPa, broadening of some peaks and the appearance of a weak broad feature at 700–900?cm^?1 suggests a progressive amorphization of the structure; near 27?GPa, amorphization is complete and an amorphous phase is quenched down to ambient pressure; this unique behaviour is interpreted as the result of the incompatibilities in the high pressure behaviour of the Ca and Mg sublattices in the olivine structure.     

Single-crystal x-ray diffraction of brucite to 14 GPa

Single-crystal brucite, Mg(OH)₂, was studied to 14 GPa in a quasi-hydrostatic pressure medium using a diamond anvil cell and energy-dispersive synchrotron x-ray diffraction. The parameters of a third-order Birch-Murnaghan equation of state fit to the data are: K _OT=42(2) GPa, and (?K _OT/?P)_T= 5.7(5). The bulk modulus is significantly lower than that obtained in recent shock compression and powder x-ray diffraction experiments under non-hydrostatic conditions. No evidence was found for a transition involving the Mg -O sub-structure over the pressure range of these experiments. This implies that the structural change previously identified at high pressure by Raman spectroscopy probably involves rearrangement of hydrogen atoms, leaving the Mg — O substructure largely unaffected.     

Double carbonate breakdown reactions at high pressures: an experimental study in the system CaO–MgO–FeO–MnO–CO2

The pressure–temperature conditions of the reactions of the double carbonates CaM(CO₃)₂, where M = Mg (dolomite), Fe (ankerite) and Mn (kutnohorite), to MCO₃ plus CaCO₃ (aragonite) have been investigated at 5–8 GPa, 600–1,100°C, using multi-anvil apparatus. The reaction dolomite = magnesite + aragonite is in good agreement with the results of Sato and Katsura (Earth Planet Sci 184:529–534, 2001), but in poor agreement with the results of Luth (Contrib Mineral Petrol 141:222–232, 2001). The dolomite is partially disordered at 620°C, and fully disordered at 1,100°C. All ankerite and kutnohorite samples, including the synthetic starting materials, are disordered. The P–T slopes of the three reactions increase in the order M = Mg, Fe, Mn. The shallower slope for the reaction involving magnesite is due partly to its having a higher compressibility than expected from unit-cell volume considerations. At low pressures there is a preference for partitioning into the double carbonate of Mg > Fe > Mn. At high pressures the partitioning preference is reversed. Using the measured reaction positions, the P–T conditions at which dolomite solid solutions will break down on increasing P and T in subduction zones can be estimated.     

Partitioning of iron and magnesium between crystals and partial melts in peridotite upper mantle

The iron-magnesium distribution coefficient, $$K'_D = (X_{\Sigma {\text{FeO}}} /X_{{\text{MgO}}} )^{{\text{olivine}}} (X_{{\text{MgO}}} /X_{\Sigma {\text{FeO}}} )^{{\text{liquid}}} ,$$ has frequently been used as a means of testing whether experimental and natural silicate liquids could have been in equilibrium with olivine of mantle composition. It is shown here that this K′ _D decreases with increasing oxygen fugacity (xxx) for a hydrous partial melt in equilibrium with a natural spinel peridotite assemblage under pressure and temperature conditions corresponding to those of the upper mantle (from 0.52 at the xxx of the iron-wüstite buffer to 0.04 at the xxx of the magnetite-hematite buffer). K′ _D also increases with increasing pressure, with decreasing temperature, and probably with increasing Mg/(Mg+∑ Fe) of the parental peridotite, suggesting that $$K_D = (X_{{\text{FeO}}} /X_{{\text{MgO}}} )^{{\text{olivine}}} (X_{{\text{MgO}}} /X_{{\text{FeO}}} )^{{\text{liquid}}}$$ also increases with increasing pressure and decreasing temperature. Thus, unless these four variables (P, T, xxx, silicate composition) are known for a natural magma, K′ _D and probably K _D are variables, and the Mg/(Mg+∑ Fe) of such a magma cannot be correlated to that of the parent. The K _D determined at 1 atm pressure by Roeder and Emslie has frequently been used to test whether the Mg/(Mg+∑ Fe) ratios of experimentally formed liquids at high pressure in equilibrium with olivine of known Fo content represent the equilibrium Mg/(Mg+Fe²⁺) of this liquid, assuming that ∑Fe=Fe²⁺ and that K′ _D does not vary with P, T, and composition of the system. Published data demonstrate that the oxygen fugacities of the experimental designs employed by different laboratories vary between those of the magnetite-hematite and magnetite-wüstite buffers (6 orders of magnitude), resulting in K′ _D between 0.04 and 0.31 at 1050° C and 15 kbar, for example. Thus, published arguments as to whether the quenched liquids represent equilibrium compositions based on iron-magnesium partitioning are inadequate. The effects of P, T, xxx, and the composition of the starting material must also be considered.     

Experimental determination of Mn-Mg mixing properties in garnet,olivine and oxide

We have measured the mixing properties of Mn-Mg olivine and Mn-Mg garnet at 1300° C from a combination of interphase partitioning experiments involving these phases, Pt-Mn alloys and Mn-Mg oxide solid solutions. Activity coefficients of Mn dilute in Pt-Mn alloys at 1300° C/1 atm were measured by equilibrating the alloy with MnO at known f _{O 2}. Assuming that the log f _{O 2} of the Mn-MnO equilibrium under these conditions is-17.80 (Robie et al. 1978), we obtain for _Mn: log_Mn = –5.25 + 3.67 X_Mn + 11.41X² _Mn Mixing properties of (Mn,Mg)O were determined by reversing the Mn contents of the alloys in equilibrium with oxide at known f _{O 2}. Additional constraints were obtained by measuring the maximum extent of immiscibility in (Mn,Mg)O at 800 and 750° C. The data are adequately described by an asymmetric (Mn,Mg)O solution with the following upper and lower limits on nonideality: (a) W_Mn = 19.9kj/Mol; W_Mg = 13.7kj/Mol; (b) W_Mn = 19.9kj/Mol; W_Mg = 8.2kj/Mol; Olivine-oxide partitioning was tightly bracketed at 1300° C and oxide properties used to obtain activity-composition relations for Mn-Mg olivine. Despite strong M2 ordering of Mn in olivine, the macroscopic properties are adequately described by a symmetric model with: W^ol = 5.5 ± 2.5 kj/mol (1-site basis) Using these values for olivine, garnet-olivine partitioning at 27 kbar/1300° C leads to an Mn-Mg interaction parameter in garnet given by: W^gt = 1.5 ± 2.5kJ/mol (1-site basis) Garnet-olivine partitioning at 9 kbar/1000° C is consistent with the same extent of garnet nonideality and the apparent absence of excess volume on the pyrope-spessartine join indicates that any pressure-dependence of W^Gt must be small. If olivine and garnet properties are both treated as unknown and the garnet-olivine partitioning data alone used to derive W^Ol and W^Gt, by multiple linear regression, best-fit values of 6.16 and 1.44 kJ/mol. are obtained. These are in excellent agreement with the values derived from metal-oxide, oxide-olivine and olivine-garnet equilibria.     

Formation of a solid solution in the MgSiO3–MnSiO3 perovskite system

Experiments using laser-heated diamond anvil cells combined with synchrotron X-ray diffraction and SEM–EDS chemical analyses have confirmed the existence of a complete solid solution in the MgSiO₃–MnSiO₃ perovskite system at high pressure and high temperature. The (Mg, Mn)SiO₃ perovskite produced is orthorhombic, and a linear relationship between the unit cell parameters of this perovskite and the proportion of MnSiO₃ components incorporated seems to obey Vegard’s rule at about 50 GPa. The orthorhombic distortion, judged from the axial ratios of a/b and \( \sqrt{2}\,a/c, \) monotonically decreases from MgSiO₃ to MnSiO₃ perovskite at about 50 GPa. The orthorhombic distortion in (Mg_0.5, Mn_0.5)SiO₃ perovskite is almost unchanged with increasing pressure from 30 to 50 GPa. On the other hand, that distortion in (Mg_0.9, Mn_0.1)SiO₃ perovskite increases with pressure. (Mg, Mn)SiO₃ perovskite incorporating less than 10 mol% of MnSiO₃ component is quenchable. A value of the bulk modulus of 256(2) GPa with a fixed first pressure derivative of four is obtained for (Mg_0.9, Mn_0.1)SiO₃. MnSiO₃ is the first chemical component confirmed to form a complete solid solution with MgSiO₃ perovskite at the P–T conditions present in the lower mantle.     

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.     

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.     

Influence of oxygen partial pressure on the Mg/Fe distribution in olivines

The dependence of Mg/Fe ordering on oxygen partial pressure in natural olivine crystals of volcanic origin has been studied by X-ray diffraction. Two natural crystals with 10% and 12% fayalite have been investigated and the atomic positions, anisotropic temperature factors, extinction coefficients and site occupancies have been refined, reaching R-values of 2.2%. After subjecting the crystals to oxygen partial pressures of 10^?16 bar and 10^?21 bar the crystals were studied again. In total six crystals were studied and the distribution coefficients K _D determined. The natural untreated crystals had K _D=1.09 and 1.06, e.g., a slight preference of Fe in (M1). p(O₂) of 10^?16 bar increased the ordering of Fe in (M1) to K _D=1.2, while p(O₂)=10^?21 bar reversed K _D to 0.8 with ordering of Fe in (M2). These experiments suggest that Mg/Fe ordering in olivines is primarily determined by the prevailing oxygen partial pressure.     

Cation diffusion in olivine—II. Ni-Mg,Mn-Mg,Mg and Ca

Diffusivities of bivalent cations. Mg, Ni. Mn and Ca, in olivine were determined experimentally. The diffusivities of Ni and Mn in forsterite were determined by couple annealing between Ni₂SiO₄ and Mg₂SiO₄, and Mn₂SiO₄ and Mg₂SiO₄, respectively. The diffusivities of Mg and Ca in forsterite were determined by the use of ²⁶Mg and Ca tracers, respectively. Combined with other published results, the diffusion coefficients for bivalent cation diffusion in pure forsterite along the c crystallographic axis range from 2.45 × 10^?11 to 1.4 × 10^?13 cm² sec^?1 at 1200°C, in the order of Fe > Mn > Co > Ni > Mg > Ca. The results suggest that the diffusivity is governed by at least two factors, i.e. the size of the diffusing ionic species and the change of defect density in the crystal structure which is induced by substitution of diffusing ion for Mg ion.     

Mg-Fe partitioning between olivine and ultramafic melts at high pressures

Precise determination of the partitioning of Mg and Fe²⁺ between olivine and ultramafic melt has been made at pressures from 5 to 13 GPa using a MA-8 type multi-anvil high-pressure apparatus (PREM) installed at Earthquake Research Institute, University of Tokyo. A very short rhenium capsule (<100 μm sample thickness) was adopted to minimize temperature variation within the sample container. Synthetic gels with the composition of the upper mantle peridotite were used as starting materials to promote the homogeneity. Analyses of quenched melts and coexisting olivines were made with an electron probe microanalyzer. The obtained partition coefficient, K_D [=(FeO/MgO)^ol/(FeO/MgO)^melt], decreases from 0.35 to 0.25 with increasing pressure from 5 to 13 GPa, suggesting a negative correlation between pressure and K_D above 5 GPa. Our result is consistent with a parabolic relationship between K_D and degree of polymerization (NBO/T) of melts reported by previous studies at lower pressures. The negative correlation between pressure and K_D suggests that olivine crystallizing in a magma ocean becomes more Mg-rich with depth and that primary magmas generated in the upper mantle become more Fe-rich with depth than previously estimated.