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.     

Cation diffusion in olivine—I. Cobalt and magnesium

Cobalt and magnesium interdiffusion coefficients in synthetic crystals of olivine have been determined by a method of couple annealing. These coefficients increase with temperature and Co concentration. The coefficients in forsterite along the c crystallographic axis range from 1.13 × 10^?12 to 6.85 × 10^{?11 cm2sec?1} at temperatures ranging from 1150 to 1400°C. The calculated activation energies for Co-Mg interdiffusion in forsterite are 526 kJmol^?1 above approximately 1300°C and 196 kJmol^?1 at lower temperatures. These results indicate that the Co-Mg mobility in olivine is relatively low compared to published results for Fe-Mg interdiffusion.     

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.     

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.     

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.     

Distribution of Mg and Fe in cummingtonite-hornblende and cummingtonite-actinolite pairs from metamorphic assemblages

The atomic fractions Mg/(Mg + Fe) and the Mg-Fe distribution coefficient $$K_{{\text{D}}{\text{.Mg - Fe}}}^{{\text{Ca - am - Cum}}} \left( { = \tfrac{{[{\text{Mg/Fe]}}_{{\text{Ca - am}}} }}{{{\text{[Mg/Fe]}}_{{\text{Cum}}} }}} \right)$$ are calculated for 31 metamorphic cummingtonite-hornblende pairs. Data on 21 pairs are taken from the litterature, and new electron microprobe analyses and structural formulae are presented of nine pairs from Tydal, Sör-Tröndelag, Norway, and of one pair from Cooma, N.S.W., Australia (cf. Kisch, 1969). The electron microprobe methods used are described, particularly the use of mineral standards, and the variation of the mass absorption in substitution series. The hornblendes from the Tydal pairs are markedly pargasitic in composition, and contain minor proportions of the cummingtonite “molecule”. The Mg-Fe distributions in the cummingtonite-hornblende pairs — as plotted on a [Mg/(Mg + Fe)]_Ca-am vs. [Mg/(Mg + Fe)]_Cum diagram (Fig. 3) — differ significantly from the Mg-Fe distribution curve for cummingtonite-actinolite pairs from Quebec (Mueller, 1961). Whereas the actinolites have markedly higher Mg/Fe ratios than the co-existing cummingtonites (K _D.Mg-Fe ^Ca-am-Cum ≈ 1.5–2.0), the cummingtonite-hornblende pairs diverge towards lower values from the distribution coefficient. In most of the metamorphic cummingtonite-hornblende pairs — including the nine pairs from Tydal — the Mg/Fe ratio of the hornblende is lower than in the co-existing cummingtonite, i.e K _D.Mg-Fe ^Ca-am-Cum <1. A relation appears to exist between the Mg-Fe distribution and the Al content of the calcic amphibole phase. This is believed to be due to the non-random distribution of Al^Y among the octahedral lattice sites: in hornblende Al^VI enters the M ₁+M₃ positions, in which Mg is preferred over Fe, rather than M ₂, in which Fe is preferred (Ghose, 1965). Since the cummingtonites remain Al-poor, the over-all Mg/Fe ratio in the hornblende is reduced relative to the co-existing cummingtonite as a result. The variations of the Mg-Fe distribution in the cummingtonite-hornblende pairs can also be related directly to the presence and composition of the plagioclase and other Al-rich phases in the metamorphic mineral assemblage. In any range of Mg/Fe ratios, the cummingtonite-hornblende pairs associated with oligoclase have lower distribution coefficients (0.61–0.81; 12 pairs) than those associated with calcic plagioclase or plagioclase-free assemblages (0.97 to 1.89; 6 pairs); the pairs associated with andesine have intermediate Mg-Fe distributions (0.74–1.15; 6 pairs).     

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.     

Olivine-spinel geospeedometry: Analysis of diffusion-controlled Mg-Fe2+ exchange

Subsolidus Mg-Fe²⁺ exchange between olivine and spinel is governed by Mg-Fe²⁺ interdiffusion. Incomplete exchange results in Mg-Fe²⁺ heterogeneity in both olivine and spinel, which provides information on the thermal histories of the host rocks. A composite sphere model has been developed to obtain quantitative cooling rates or heating duration from the Mg-Fe²⁺ heterogeneity. The model assumes that a spherical core of spinel and a surrounding semi-infinite spherical shell of olivine interact by diffusion-controlled exchange of Mg and Fe²⁺. The differential equations describing the model are solved numerically by finite difference approximations. The numerical solution reveals that cooling rates or heating duration can be estimated from the relationship between the grain size of spinel and temperature calculated from the chemical compositions of the core of a spinel grain and of olivine far away from it. The calculated temperature is employed in place of $\text{Mg}\text{(Mg + Fe}{}^{\mathrm{2+}}\text{)}$ at the center of spinel to obtain the absolute temperature of thermal events.This olivine-spinel geospeedometer has been applied to peridotites. gabbro, and picrites from some ophiolite complexes in Japan to estimate their cooling rates. The estimated cooling rates for the peridotites range from 10^?4 to 10^?1 °C/yr, and those for the picrites from 10³ to 10⁴ °C/yr. The geospeedometer has been extended to estimate the heating duration of lherzolite xenoliths in basalt from the Ichinomegata crater, northeast Japan. The estimated heating duration of the xenoliths is less than one day.     

Fe–Mg Interdiffusion in (Mg,Fe)O

We have performed a series of interdiffusion experiments on magnesiowüstite samples at room pressure, temperatures from 1,320° to 1,400°C, and oxygen fugacities from 10^?1.0 Pa to 10^?4.3 Pa, using mixed CO/CO₂ or H₂/CO₂ gases. The interdiffusion couples were composed of a single-crystal of MgO lightly pressed against a single-crystal of (Mg_1-x Fe _x )_1-δO with 0.07<x<0.27. The interdiffusion coefficient was calculated using the Boltzmann–Matano analysis as a function of iron content, oxygen fugacity, temperature, and water fugacity. For the entire range of conditions tested and for compositions with 0.01<x<0.27, the interdiffusion coefficient varies as $$\tilde D\, =\,2.9\times10^{ - 6}\,f_{{\text{O}}_2 }^{0.19}\,x^{0.73}\,{\text{e}}^{ - (209,000\, -\,96,000\,x)/RT}\,\,{\text{m}}^{\text{2}} {\text{s}}^{ -1} $$ These dependencies on oxygen fugacity and composition are reasonably consistent with interdiffusion mediated by unassociated cation vacancies. For the limited range of water activity that could be investigated using mixed gases at room pressure, no effect of water on interdiffusion could be observed. The dependence of the interdiffusion coefficient on iron content decreased with increasing iron concentration at constant oxygen fugacity and temperature. There is a close agreement between our activation energy for interdiffusion extrapolated to zero iron content (x=0) and that of previous researchers who used electrical conductivity experiments to determine vacancy diffusivities in lightly doped MgO.     

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.     

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.     

Diffusion compensation in natural silicates

The temperature dependence of diffusion is usually found to follow the Arrhenius law: D = D₀e^?E/RT Winchell (1969) showed that there is commonly an inter-dependence between D₀ and E (for diffusion in silicate glasses), such that diffusion of different species show a positive correlation on a log D₀ vs E plot. A similar effect was noted by Hofmann (1980) for cation diffusion in basalt. This implies that diffusion rates of different species tend to converge at a particular temperature; this effect is known as the ‘compensation effect’. I will show that this effect is also present for diffusion in feldspars and olivines. The equations for the compensation lines (with E given in kcal/mol) are: basalt—E = 50 + 7.5 log D₀ feldspar—E = 50.7 + 3.4 log D₀ olivine—E = 78.0 + 7.5 log D₀ The convergence, or crossover, temperatures for diffusion in various materials are: obsidian—3400°C basalt—1370°C olivine—1360°C feldspar—460°C Compensation plots are useful for evaluating and comparing experimental diffusion data (though of limited usefulness in a predictive sense) and for understanding ‘closure temperatures’ for diffusion in petrogenetic processes (since closure temperature, the temperature at which natural diffusion processes are frozen in, is dependent on E, log d₀, and cooling rate). I show that most diffusing species in feldspar have a closure-temperature close to the crossover or convergence temperature, implying that all species in feldspars can be expected to ‘freeze-in’ simultaneously at temperatures in the range 400–600°C (for cooling rates in the range 10¹–10⁵°C/myr). Closure temperatures of various species in olivine, on the other hand, span a much larger range (800°C) for a similar range in cooling rates, implying that different elements in olivine will record different time-temperature stages in petrogenetic processes.     

Determination of quantitative cation distribution in orthopyroxenes from electronic absorption spectra

Electronic and Mössbauer absorption spectra and electron microprobe data are correlated for iron-bearing orthopyroxenes. The correlation provides a means of quantitatively determining the distribution of Fe²⁺ between the M(1) and M(2) sites of orthopyroxene crystals from electronic spectra and electron microprobe analysis. The electronic spectra are used to analyze the changes in the Fe²⁺ distribution produced during heating experiments and confirm earlier results from Mössbauer spectra. Two components of the spin-allowed transition of Fe²⁺ in the M(1) site are identified at about 13,000 cm^?1 and 8,500 cm^?1 in γ. Molar absorptivity (?) values for all spin-allowed Fe²⁺ absorption bands in the near-infrared region are determined. The M(2) Fe²⁺ band at ～5,000 cm^?1 in β is the analytically most useful for site occupancy determinations. It remains linear with concentration (?=9.65) over the entire compositional range. The band at ～10,500 cm^?1 in α is the most sensitive to M(2) Fe²⁺ concentration (?=40.8), but deviates from linearity at high iron concentrations. The origins of spin-forbidden transitions in the visible region are examined.     

The dust envelope of R Cas

The spectral energy distribution in the far infrared and the shape of a broad emission band in the spectrum of R Cas at 9–13 µm can be reproduced in a model with a dust envelope consisting of approximately half amorphous olivine (Mg_0.8Fe_1.2SiO₄) and half amorphous aluminum-oxide grains (Al₂O₃), with a small admixture of spinel grains (MgAl₂O₄). The dust envelope’s optical depth τ(50 µm) is ≈5×10^?3 [τ(1.25 µm)≈0.07 for a _gr≈0.05 µm], and its mass within r≤0.025 pc M _dust is ≈8×10^?6 M _⊙. The index α in the power-law radial dust distribution, n _d ∝(R ₊/r)^α, is ≈1.8. Over the last several thousand years, the mass-loss rate of R Cas has been decreasing as $\dot M(t) \propto t^{0.2} $ (where time is measured backward from the present). This probably implies that R Cas experienced a thermal helium flare several thousand years ago. If M _gas/M _dust≈200 (where M _gas is the gas mass), the mean mass-loss rate of the star is $\dot M \approx 6 \times 10^{ - 7} M_ \odot /yr$ .     

Kinetics of intracrystalline order-disorder reactions in tremolite

The temperature dependent Fe-Mg distribution in tremolite from Zillertal, Austria was investigated using Mössbauer spectroscopy. The standard free energy change for the exchange reaction Fe²⁺(M4)+Mg(M2)=Mg(M4)+Fe²⁺(M2) decreases with increasing temperature, corresponding to an enthalpy term of 9.2±1.5 kcal/mole and an entropy term of 1.9±1.7 cal/mole K. Kinetic experiments performed as hydrothermal runs, yield an activation energy of 70±7 kcal/mole for the disordering reaction. Difficulties in analysing the very small amount of Mg(M4) in the natural sample introduce large errors in the calculation of cooling rates for the natural rock. The estimated error in the Mg(M4) site occupancy results in a shift of the obtained cooling rate of about three orders of magnitude, making tremolite less useful for estimations of rock cooling rates.     

A model of the OH positions in olivine,derived from infrared-spectroscopic investigations

Polarized infrared (IR) spectroscopy of olivine crystals from Zabargad, Red Sea shows the existence of four pleochroic absorption bands at 3,590, 3,570, 3,520 and 3,230 cm^?1, and of one non pleochroic band at 3,400 cm^?1. The bands are assigned to OH stretching frequencies. Transmission electron microscopy (TEM) shows no oriented intergrowths in this olivine; it is concluded that OH is structural. On the basis of the pleochroic scheme of the absorption spectra it is proposed that [□O(OH)₃] and [□O₂(OH)₂] tetrahedra occur as structural elements, assuming that the vacancies are on Si sites. If M2 site vacancies were assumed [SiO₃(OH)] and [SiO₂(OH)₂] tetrahedra occur as structural elements.     

OH point defects in olivine from Pakistan

The infrared (IR) spectra of gem-quality olivine crystals from Pakistan, formed in serpentinised dunitic rocks, are characterised by strongly pleochroic absorption bands at 3,613, 3,597, 3,580 and 3,566 cm^?1. These bands are assigned to O-H stretching vibrations of OH point defects corresponding to H₂O concentrations of about 35 wt ppm. Unlike other olivine spectra, the dominating bands are strongly polarised parallel to the b-axis. The unusual spectra type, excludes the presence of planar defects. This finding is supported by transmission electron microscopy. The 3,613 cm^?1 band is related to vacant Si sites, the slightly lower energetic bands preferentially to vacant M2 sites. The exclusive presence of these bands is not only a characteristic feature of olivines treated under high P,T conditions equivalent to mantle environment, the presence of these bands in untreated natural olivine also indicates formation conditions equivalent to crustal rocks.     

Extrinsic and intrinsic mode of hydrogen occurrence in natural olivines: FTIR and TEM investigation

Olivine crystals from two mantle nodules in kimberlites (pipe Udachnaya and pipe Obnazennaya, Yakutiya, Siberia) were investigated using EMP, TEM, AEM and FTIR techniques to determine the mode of hydrogen occurrence in olivine. Olivine contains three types of nanometer-sized inclusions: “large” inclusions of hexagonal-like shape up to several hundred nm in size (1), lamellar defects (2) and small inclusions of hexagon-like shape up to several 10?nm in size (3). Lamellar defects and small inclusions are considered to be a “hydrous” olivine. All three types of inclusions contain OH^? or water, but they are different with respect to their phase composition. In “large” inclusions (1) hydrous magnesium silicates, such as serpentine?+?talc (“kerolite”?) and 10-Å phase?+?talc were identified. Lamellar defects (2) and small inclusions (3) are depleted in Mg and Fe compared to the olivine matrix, while the silica content is the same as that of olivine. Modulations in the periodicity of the olivine structure are observed in SAED patterns and HREM images of (2) and (3). The superperiodicity can be referred to OH^?-bearing point defect ordering in the olivine structure. If this is the case, the material of both lamellar defects and small inclusions can be assumed to be a “hydrous olivine” Mg_{2– x} v _x SiO₄H_{2 x} with a cation-deficient olivine crystal structure. Thus, both an extrinsic mode of hydrogen occurrence in olivine, such as nanometer-sized inclusions of OH^?-bearing magnesium silicates, and an intrinsic mode of hydrogen incorporation into the olivine structure, such as “hydrous olivine” in itself, were found. The data obtained here show that the OH absorption bands observed in olivine spectra at 3704(3717) and 3683(3688) cm^?1 can be unambiguously identified with serpentine; the band at 3677(3676) cm^?1 can be associated with talc. The absorption bands observed at 3591 and 3660?cm^?1 in olivine match those of the 10-Å phase at 3594, 3662 and 3666?cm^?1.     

Distribution of titanium atoms in oxy-kaersutite

The distribution of Ti atoms in oxy-kaersutite has been studied by the neutron diffraction method. The cation distribution over the three octahedral sites determined by the x-ray method (Kitamura and Tokonami, 1971) is as follows; M1∶0.40MG+0.60 FE, M2∶0.75 MG+0.25 FE, M3∶0.50 MG+0.50 FE, where MG and FE represent (Mg+Al) and (Fe+Ti), respectively. The neutron diffraction study indicates that Ti atoms are enriched in the M1 site more than M2 and M3 sites as follows; M1∶0.40 MG+0.33 Fe+0.27 Ti, M2∶ 0.75 MG+0.23 Fe+0.02 Ti, M3∶0.50 MG+0.46 Fe+0.04 Ti. This distribution agrees with the result based on the Madelung energy of oxy-kaersutite by Whittaker (1972).     

Prediction of Gibbs free energies of formation of minerals of the alunite supergroup

A method for the prediction of Gibbs free energies of formation for minerals belonging to the alunite family is proposed, based on an empirical parameter Δ_GO⁼ M^z+(c) characterizing the oxygen affinity of the cation M^z+. The Gibbs free energy of formation from constituent oxides is considered as the sum of the products of the molar fraction of an oxygen atom bound to any two cations, multiplied by the difference of oxygen affinity Δ_GO⁼ M^z+(c) between any two consecutive cations. The Δ_GO⁼ M^z+(c) value, using a weighing scheme involving the electronegativity of a cation in a specific site (12-fold coordination site, octahedral and tetrahedral) is assumed to be constant. It can be calculated by minimizing the difference between experimental Gibbs free energies (determined from solubility measurements) and calculated Gibbs free energies of formation from constituent oxides. Results indicate that this prediction method gives values within 0.5% of the experimentally measured values. The relationships between Δ_GO⁼ M^z+(alunite) corresponding to the electronegativity of a cation in either dodecahedral sites, octahedral sites or tetrahedral sites and known as Δ_GO⁼ M^z+(aq) were determined, thereby allowing the prediction of the electronegativity of rare earth metal ions and trivalent ions in dodecahedral sites and highly charged ions in tetrahedral sites. This allows the prediction of Gibbs free energies of formation of any minerals of the alunite supergroup (bearing various ions located in the dodecahedral and tetrahedral sites). Examples are given for hydronium jarosite and hindsalite, and the results appear excellent when compared to experimental values.