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.     

Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines

Existing data on the temperature and composition dependence of the Fe²⁺-Mg²⁺ distribution between Fe-Mg olivine and orthopyroxene, the intra-crystalline distribution of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxene, and macroscopic activity-composition relations in olivine and orthopyroxene are shown to be inconsistent with generally accepted thermodynamic formulations which assume that the non-configurational Gibbs energy of orthopyroxene is independent of the degree of long-range ordering of Fe²⁺ and Mg⁺ between M1 and M2 sites. These data are interpreted in terms of the constraints they provide on the size of Bragg-Williams type energy, entropy, and volume terms for olivine and orthopyroxene. The apparent equilibrium constant for Fe-Mg exchange between olivine and orthopyroxene is shown to be a potentially useful ‘geothermometer’ for olivine-orthopyroxene assemblages with olivines with mole fraction of Fe₂SiO₄ component less than 0.2 or greater than 0.6. A provisional calibration of this ‘geothermometer’ is presented.     

Interdiffusion of Mg–Fe in olivine at 1,400–1,600 °C and 1 atm total pressure

The interdiffusion coefficient of Mg–Fe in olivine (D _Mg–Fe) was obtained at 1,400–1,600 °C at the atmospheric pressure with the oxygen fugacity of 10^?3.5–10^?2 Pa using a diffusion couple technique. The D _Mg–Fe shows the anisotropy (largest along the [001] direction and smallest along the [100] direction), and its activation energy (280–320 kJ/mol) is ~80–120 kJ/mol higher than that estimated at lower temperatures. The D _Mg–Fe at temperatures of >1,400 °C can be explained by the cation-vacancy chemistry determined both by the Fe³⁺/Fe²⁺ equilibrium and by the intrinsic point defect formation with the formation enthalpy of 220–270 kJ/mol depending on the thermodynamical model for the Fe³⁺/Fe²⁺ equilibrium in olivine. The formation enthalpy of 220–270 kJ/mol for the point defect (cation vacancy) in olivine is consistent with that estimated from the Mg self-diffusion in Fe-free forsterite. The increase in the activation energy of D _Mg–Fe at >1,400 °C is thus interpreted as the result of the transition of diffusion mechanism from the transition metal extrinsic domain to the intrinsic domain at the atmospheric pressure.     

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.     

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 order in olivines: Evidence from vibrational spectra

A simple theory is developed which relates cation ordering in the olivine structure to compositional trends in the vibrational spectra of olivines. Quantitative results for (Mg, Mn) and (Fe, Mn) olivines indicate that Mn²⁺ favors the M2 site relative to both Mg²⁺ and Fe²⁺.     

Fe-Ti oxide geothermometry: thermodynamic formulation and the estimation of intensive variables in silicic magmas

A new thermodynamic formulation of the Fe–Ti oxide geothermometer/oxygen barometer is developed. The method is based upon recently calibrated models for spinel solid solutions in the quinary system (Fe²⁺, Mg)(Al,Fe³⁺,Cr)₂O₄–(Fe²⁺, Mg)₂TiO₄ by Sack and Ghiorso, and rhombohedral oxides in the quaternary system (Fe²⁺,Mg,Mn)TiO₃–Fe₂O₃ (this paper). The formulation is internally consistent with thermodynamic models for (Fe²⁺,Mg)-olivine and -orthopyroxene solid solutions and end-member thermodynamic properties tabulated by Berman. The constituent expressions account for compositional and temperature dependent cation ordering and reproduce miscibility gap features in all of the component binaries. The calibration does not account for the excess Gibbs energy resulting from compositional and temperature dependent magnetic ordering in either phase. This limits application of the method to assemblages that equilibrated at temperatures above 600° C. Practical implementation of the proposed geothermometer/oxygen barometer requires minimal use of projection algorthms in accommodating compositions of naturally occurring phases. The new formulation is applied to the estimation of temperature and oxygen fugacity in a wide variety of intermediate to silicic volcanic rocks. In combination with previous work on olivine and orthopyroxene thermodynamics, equilibration pressures are computed for a subset of these volcanics that contain the assemblage quartz, oxides and either ferromagnesian silicate. The calculated log₁₀ f _{O 2}-T relations are reflected in coexisting ferromagnesian mineral assemblages. Volcanics with the lowest relative oxygen fugacity (log₁₀ f _{O 2}) are characterized by the assemblage olivine-quartz, those with slightly higher log₁₀ f _{O 2} s, by the assemblage orthopyroxene-quartz. The sequence proceeds with the necessary phases biotite-feldspar, then hornblende-quartz-clinopyroxene, and finally at the highest log₁₀ f _{O 2} s, sphene-quartz-clinopyroxene. Quantitative analysis of these trends, utilizing thermodynamic data for the constituent phases, establishes that, in most cases, the T-log₁₀ f _{O 2}value computed from the oxides is consistent with the compositions of coexisting silicate phases, indicating that phenocryst equilibrium was achieved prior to eruption. There is, however, considerable evidence of oxide-silicate disequilibrium in samples collected from more slowly cooled domes and obsidians. In addition, T-log₁₀ f _{O 2}trends from volcanic rocks that contain biotite and orthopyroxene are interpreted to imply a condition of Fe²⁺–Mg exchange disequilibrium between orthopyroxene and coexisting ferromagnesian silicates and melt. It is suspected that many biotite-feldspar-quartz-orthopyroxene bearing low temperature volcanic rocks inherit orthopyroxene xenocrysts which crystallized earlier in the cooling history of the magma body.The problem is probably at least as complex as that of the feldspars... A.F. Buddington (1956)     

An experimental investigation into the metastable formation of phosphoran olivine and pyroxene

The formation of phosphoran olivine by crystallization from a melt was investigated experimentally using a one atmosphere furnace, using San Carlos olivine [(Mg,Fe)₂SiO₄] mixed with either iron phosphide (FeP) or magnesium pyrophosphate (Mg₂P₂O₇). Both dynamic crystallization and isothermal experiments produced phosphoran olivine as zoned single crystals and as overgrowths surrounding normal, phosphorus-free olivine grains. The crystallization pathways that form phosphoran olivine were traced and confirm that it is a metastable phase that can crystallize from a phosphorus-rich melt over timescales of hours to days. Removal of the P and equilibration of the olivine however requires weeks to months in the presence of silicate melt. Phosphoran olivine with up to 27 wt% P₂O₅ was generated and up to 69% of the Si tetrahedral sites were replaced by P. The substitution of Si by P into olivine was confirmed as 4^VIM⁺² + 2^IVSi⁺⁴ ↔ 3^VIM⁺² + 2^IVP⁺⁵ + ^VI[]. Phosphoran olivine compositions that vary from (Mg,Fe)₂SiO₄ to (Mg,Fe)_1.65[]_0.35Si_0.3P_0.7O₄ have been produced in these experiments.Phosphoran pyroxene was also generated in a few experiments and forms when phosphoran olivine reacts with either tridymite or melt. It has compositions compatible with protopyroxene, orthopyroxene, pigeonite and sub-calcic augite, and can contain up to 31.5 wt% P₂O₅. Like phosphoran olivine, it is also a metastable phase. Phosphorus replaces Si in pyroxene by the following substitution methods: 8^IVSi⁺⁴ ↔ 3^IVSi⁺⁴ + 4^IVP⁺⁵ + ^IV[] with Al entering the structure by the exchange 2^IVSi⁺⁴ ↔ ^IVAl⁺³ + ^IVP⁺⁵. Phosphoran pyroxene compositions vary from (Mg,Fe)₈Si₈O₂₄ to (Mg,Fe)₈Si₃P₄[]O₂₄.     

Reequilibration of chromite within Kilauea Iki lava lake,Hawaii

Chromite mainly occurs as tiny inclusions within or at the edges of olivine phenocrysts in the 1959 Kilauea Iki lava lake. Liquilus chromite compositions are only preserved in scoria that was rapidly quenched from eruption temperatures. Analyses of drill core taken from the lava lake in 1960, 1961, 1975, 1979, and 1981 show that chromite becomes richer in Fe⁺², Fe⁺³, Ti and poorer in Mg, Al, Cr than the liquidus chromite. The amount of compositional change depends on the time elapsed since eruption, the cooling history of the sample, the extent of differentiation of the interstitial melt, and the position of the chromite inclusion within the olivine phenocryst. Compositional changes of the chromite inclusions are thought to be a result of reequilibration with the residual melt by cationic diffusion (Mg, Al, Cr outwards and Fe⁺², Fe⁺³, Ti inwards) through olivine. The changing chemical potential gradients produced as the residual melt cools, crystallizes and differentiates drives the reequilibration process. Major and minor element zoning profiles in olivine phenocrysts suggest that volume diffusion through olivine may have been the major mechanism of cationic transport through olivine. The dramatic compositional changes observed in chromite over the 22 years between eruption and 1981 has major implications for othe molten bodies.     

Kinetics of Fe<Superscript>2+</Superscript>–Mg order–disorder in orthopyroxene: experimental studies and applications to cooling rates of rocks

We determined the forward rate constant (K⁺) for the Fe²⁺–Mg order–disorder between the M2 and M1 sites of orthopyroxene (OPx), which is described by the homogeneous reaction Fe²⁺ (M2) + Mg(M1) ↔ Mg(M2) + Fe²⁺ (M1), by both ordering and disordering experiments at isothermal condition and also by continuous cooling experiments. The rate constant was determined as a function of temperature in the range of 550–750°C, oxygen fugacity between quartz–fayalite–iron and Ni–NiO buffers, and at compositions of 16 and 50 mol% ferrosilite component. The K⁺ value derived from disordering experiment was found to be larger than that derived from ordering experiment at 550°C, while at T>580°C, these two values are essentially the same. The fO₂ dependence of the rate constant can be described by the relation K⁺ α (fO₂) ⁿ with n=5.5–6.5, which is compatible with the theoretically expected relation. The Arrhenius relation at the WI buffer condition is given by

Extended planar defects and the rapid incorporation of Ti4+ into olivine

The formation of extended planar defects in minerals such as olivine is related to high point defect concentration and can be driven by large gradients in chemical potential, where the energy of the system is lowered by the ordering of defects along specific planes in the crystal. The presence of extended defects has the potential to create the (apparently) anomalous ionic diffusion in olivine as reported recently (Spandler and O’Neill in Contrib Mineral Petrol 159(6):791–818, 2010). High-resolution transmission electron microscopy and energy-filtered imaging were done using experimental samples designed to examine the impact of a _TiO2 and f _O2 on the potential to form such defects in ferromagnesian olivine. Doped basalt (5 wt% TiO₂)–olivine reaction couple experiments were run at 1 atm and 1,310 and 1,410 °C for 50 h at various f _O2, ranging from 10² below to 10² above the quartz–fayalite–magnetite buffer. Our results show that extended planar defects in olivine, parallel to {101}_ol and occurring in ordered “clusters” with a prolate spheroid geometry ~5–25 nm across and extending up to 150 nm into the olivine, are present near the olivine–glass interfaces in all of our experimental high-TiO₂ basalt–olivine samples. Increased Ti content in the olivine is associated with the defects; ordering of Ti⁴⁺ and octahedral site vacancies leads to a two- or three-layer superstructure in the olivine. Defect nucleation and growth is driven by the large TiO₂ chemical potential gradient across the phase boundary at the start of the experiments, which provides access to microstructures not otherwise present.     

Pressure and temperature dependence of cation distribution in Mg-Mn olivine

Synthetic (Mg_0.51, Mn_0.49)₂SiO₄ olivine samples are heat-treated at three different pressures; 0, 8 and 12 GPa, all at the same temperature (～500° C). X-ray structure analyses on these single crystals are made in order to see the pressure effect on cation distribution. The intersite distribution coefficient of Mg and Mn in M1 and M2 sites, K _D = (Mn/Mg) _M1/(Mn/Mg) _M2, of these samples are 0.192 (0 GPa), 0.246 (8 GPa) and 0.281 (12 GPa), indicating cationic disordering with pressure. The small differences of cell dimensions between these samples are determined by powder X-ray diffraction. Cell dimensions b and c decrease, whereas a increases with pressure of equilibration. Cell volume decreases with pressure as a result of a large contraction of the b cell dimension. The effect of pressure on the free energy of the cation exchange reaction is evaluated by the observed relation between the cell volume and the site occupancy numbers. The magnitude of the pressure effect on cation distribution is only a fifth of that predicted from the observed change in volume combined with thermodynamic theory. This phenomenon is attributed to nonideality in this solid solution, and nonideal parameters are required to describe cation distribution determined in the present and previous experiments. We use a five-parameter equation to specify the cationic equilibrium on the basic of thermodynamic theory. It includes one energy parameter of ideal mixing, two parameters for nonideal effects, one volume parameter, and one thermal parameter originated from the lattice vibrational energy. The present data combined with some of the existing data are used to determine the five parameters, and the cation distribution in Mg-Mn olivine is described as a function of temperature, pressure, and composition. The basic framework of describing the cationic behavior in olivine-type mineral is worked out, although the result is preliminary: each of the determined parameters is not accurate enough to enable us to make a reliable prediction.     

Intracrystalline relationships in olivine,orthopyroxene, clinopyroxene and spinel from a suite of spinel lherzolite xenoliths from Mt. Noorat,Victoria, Australia

A detailed crystal chemical study of coexisting olivine, orthopyroxene, clinopyroxene and spinel from selected Victorian (Australia) lherzolite suites was carried out by means of single crystal x-ray diffraction and electron probe microanalysis to obtain actual site occupancies. The aim of this study was primarily to characterise the intracrystalline configurations and related cation ordering on sites in major mantle constituents. The results demonstrate that cation ordering on sites is subject to distinctive crystallographic controls which depend on the petrological evolution of the suite. Mg-Fe²⁺ ordering in M1–M2 pyroxene sites depends on variations of the smaller cations, mainly Al^vi, Ti⁴⁺, Fe³⁺, and related configurations of M 1. Pressuresensitive Al^vi is crucial to Fe²⁺, the more ordered clinopyroxene showing high Al^vi configurations which tend to exclude the larger bivalent cations and yield small polyhedral volumes for M 1, M 2, T sites and the unit cell. Conversely, the coexisting orthopyroxene, characterised by lower Al^vi configuration and higher M 1 and unit cell volumes, is relatively more disordered. Olivine is consistent with the coexisting clinopyroxene, the more disordered crystals coexisting with more disordered clinopyroxene, while Al-Mg order in the coexisting spinel shows the reverse relationship. Estimated temperatures of apparent equilibration based on current geothermometers are not considered realistic. Assumptions of ideal cation mixing on sites in pyroxene and spinel are not supported.     

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.     

57Fe Mössbauer spectroscopy and magnetization of cation deficient Fe2TiO4 and FeCr2O4. Part II: Magnetization data

Magnetic properties are reported for synthetic cation deficient Fe₂TiO₄ and FeCr₂O₄ particles (<1 μm). Cation deficiency, achieved by oxidation, is characterized by the oxidation parameter z which represents the fraction of Fe²⁺ ions converted to Fe³⁺ in the spinel lattice (0≤z≤1). Fe₂TiO₄ (z=0.85) has a Curie temperature T _c that can only approximately be given with a value in the range 400–700 K and it has a magnetic moment per formula unit M≈0.50 μ_B (μ_B=Bohr's magneton) at 4.2 K, for FeCr₂O₄ it is T _c≥520 K and M (4.2 K) ≈0.16 μ_B. Magnetic hysteresis parameters at various temperatures show in part characteristic features due to relaxation phenomena. In the Ti-spinel, the latter are caused by a superposition of superparamagnetism and spin relaxation and in the Cr-spinel by superparamagnetism, in agreement with Mössbauer data (part I of this paper). The cation and vacancy distribution and magnetic coupling are discussed in both compositions with respect to magnetic moment data considering magnetic dilution by incorporated vacancies, and in the Ti-spinel also by non magnetic Ti⁴⁺.     

Iron in silicate glasses of granitic composition: a Mössbauer spectroscopic study

⁵⁷Fe Mössbauer spectra of natural glasses (pumices and obsidians) and of synthetic glasses of granitic composition have been analyzed. — Ferric iron is found in tetrahedral coordination if enough M⁺-cations are available to balance the charge of both M⁺Fe³⁺O₂ and M⁺AlO₂ complexes. In other compositions the ratio of tetrahedrally to octahedrally coordinated Fe³⁺ depends on the ratio of mono-to divalent cations. — Ferrous iron occurs in two distinctly different octahedral sites. The existence of these sites can be attributed to different anionic units adjacent to Fe²⁺. The degree of polymerization of these units is reflected in the quadrupole splitting. The anionic units adjacent to Fe²⁺ are depolymerized for increasing mean Z/r ² of the network modifiers, which do not stabilize M³⁺ in the tetrahedra by local charge balance. — Increasing pressure diminishes the geometric differences between these types of ferrous iron-oxygen-octahedra, which gives rise to a more even distribution of Fe²⁺ among these sites and thereby to an ordering in the network of melts.     

Electron density and polarized absorption spectra of fayalite

The maxima of the electron difference densities of Fe²⁺ atM(1) andM(2) positions of fayalite, Fe₂SiO₄, determined by x-ray diffraction are considered to correspond to atomic dipoles. Provided the selection rules of dipole radiation are satisfied and the energy of the incident radiation lies within the appropriate range, the interaction of incident radiation with these atomic dipoles should lead to three absorption bands of which two originate from Fe²⁺ atM(1), one from Fe²⁺ atM(2). The relative intensities of the three bands, dependent on the polarization direction, are estimated. The result ist in excellent agreement with the interpretation of olivine spectra given by Burns (1970).     

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe²⁺)(Al, Cr, Fe³⁺)₂O₄ ? (Mg, Fe²⁺)₂TiO₄. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg²⁺, Al³⁺, and Fe³⁺ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.     

The crystal chemistry of lithium and Fe3+ in synthetic orthopyroxene

Lithian ferrian enstatite with Li₂O = 1.39 wt% and Fe₂O₃ 7.54 wt% was synthesised in the (MgO–Li₂O–FeO–SiO₂–H₂O) system at P = 0.3 GPa, T = 1,000°C, fO₂ = +2 Pbca, and a = 18.2113(7), b = 8.8172(3), c = 5.2050(2) Å, V = 835.79(9) Å³. The composition of the orthopyroxene was determined combining EMP, LA-ICP-MS and single-crystal XRD analysis, yielding the unit formula ^M2(Mg_0.59Fe _0.21 ²⁺ Li_0.20) ^M1(Mg_0.74Fe _0.20 ³⁺ Fe _0.06 ²⁺ ) Si₂O₆. Structure refinements done on crystals obtained from synthesis runs with variable Mg-content show that the orthopyroxene is virtually constant in composition and hence in structure, whereas coexisting clinopyroxenes occurring both as individual grains or thin rims around the orthopyroxene crystals have variable amounts of Li, Fe³⁺ and Mg contents. Structure refinement shows that Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site of the orthopyroxene, whereas Mg (and Fe²⁺) distributes over both octahedral sites. The main geometrical variations observed for Li-rich samples are actually due to the presence of Fe³⁺, which affects significantly the geometry of the M1 site; changes in the geometry of the M2 site due to the lower coordination of Li are likely to affect both the degree and the kinetics of the non-convergent Fe²⁺-Mg ordering process in octahedral sites.     

A possible effect of melt structure on the Mg-Fe partitioning between olivine and melt

Partitioning of Mg and Fe²⁺ between olivine and mafic melts has been determined experimentally for eight different synthetic compositions in the temperature range between 1335 and 1425°C at 0.1 MPa pressure and at fo₂ ∼1 log unit below the quartz-fayalite-magnetite buffer. The partition coefficient [K_D = (Fe²⁺/Mg)^ol/(Fe²⁺/Mg)^melt] increases from 0.25 to 0.34 with increasing depolymerization of melt (NBO/T of melt from 0.25-1.2), and then decreases with further depolymerization of melt (NBO/T from 1.2-2.8). These variations are similar to those observed in natural basalt-peridotite systems. In particular, the variation in NBO/T ranges for basaltic-picritic melts (0.4-1.5) is nearly identical to that obtained in the present experiments. Because the present experiments were carried out at constant pressure (0.1 MPa) and in a relatively small temperature range (90°C), the observed variations of Mg and Fe²⁺ partitioning between olivine and melt must depend primarily on the composition or structure of melt. Such variations of K_D may depend on the relative proportions of four-, five-, and six-coordinated Mg²⁺ and Fe²⁺ in melt as a function of degree of NBO/T.