Enthalpy of formation of Fe3Al2Si3O12 (almandine) by high temperature alkali borate solution calorimetry

A high-temperature solution calorimetric method suitable for thermochemical studies of anhydrous minerals containing Fe²⁺ ions has been developed. The method is based on an oxide melt solvent with 52 wt% LiBO₂ and 48 wt% NaBO₂ maintained at a temperature of 750°C. In a first application of this method the enthalpies of solution of synthetic almandine, fayalite, a mixture of fayalite plus quartz on FeSiO₃ composition, and natural quartz were measured. For the reaction:

the enthalpy change at 1023 K is ?3.82 ± 0.87 kcal, based on fayalite, quartz, corundum and almandine, and ?5.96 ± 0.90 kcal based on the fayalite plus quartz mixture, corundum, and almandine. These values lead to standard molar enthalpies of formation of almandine from the oxides at 1023 K of ?14.10 ± 1.22 kcal and ?16.24 ± 1.74 kcal, respectively. The measured enthalpy of formation of almandine is less negative by several kilocalories than values derived from analysis of the phase equilibrium work of Hsu (1968), but in closer agreement with the phase equilibrium study of O'Neill and Wood (1979) and similar to the phase equilibrium deduction of Froese (1973).The agreement of the present almandine enthalpy of formation with O'Neill and Wood (1979) and Froese (1973) suggests that almandine entropies at 298 K to be obtained from their studies, in the range 79–81 cal/K, are more nearly correct than the several estimates based on oxide sum and volume-entropy systematics, most of which are much lower.     

The Mg2GeO4 olivine-spinel phase transition

Enthalpies and entropies of transition for the Mg₂GeO₄ olivine-spinel transformation have been determined from self-consistency analyses of Dachille and Roy's (1960), Hensen's (1977) and Shiota et al.'s (1981) phase boundary studies. When all three data sets are analyzed simultaneously,ΔH ₉₇₃ andΔS ₉₇₃ are constrained between ?14000 to ?15300 J mol^?1 and ?13.0 to ?14.1·J mol^?1 K^?1, respectively. High-temperature solution calorimetric experiments completed on both polymorpha yield a value of ?14046±1366 J mol^?1 forΔH ₉₇₃. Kieffer-type lattice vibrational models of Mg₂GeO₄ olivine and spinel based on newly-measured infrared and Raman spectra predict a value of ?13.3±0.6 J mol^?1 K^?1 forΔS ₁₀₀₀. The excellent agreement between these three independent determinations ofΔH andΔS suggests that the synthesis runs of Shiota et al. (1981) at high pressures and temperatures bracket equilibrium conditions. In addition, no configurational disorder of Mg and Ge was needed to obtain the consistent parameters quoted. The Raman spectrum and X-ray diffractogram show that little disorder, if any, is present in Mg₂GeO₄ spinel synthesized at 0.2 GPa and 973–1048 K.     

The effect of crystal field stabilization on the olivine→spinel transition in the system Mg2SiO4 - Fe2SiO4

Crystal field stabilization (CFS) plays a significant role in determining equilibrium phase boundaries in olivine→spinel transformations involving transition-metal cations, including Fe²⁺ which is a major constituent of the upper mantle. Previous calculations for Fe₂SiO₄ ignored pressure and temperature dependencies of crystal field stabilization enthalpies (CFSE) and the electronic configurational entropy (S _CFS). We have calculated free energy changes (ΔG _CFS) due to differences of crystal field splittings between Fe₂SiO₄ spinel and fayalite from: ΔG _CFS=?ΔCFSE?TΔS _CFS, as functions of P and T, for different energy splittings of t _2g orbital levels of Fe²⁺ in spinel. The results indicate that ΔG _CFS is always negative, suggesting that CFS always promotes the olivine→spinel transition in Fe₂SiO₄, and expands the stability field of spinel at the expense of olivine. Because of crystal field effects, transition pressures for olivine→spinel transformations in compositions (Mg_1?x Fe _x )₂SiO₄ are lowered by approximately 50x kbar, which is equivalent to having raised the olivine→spinel boundary in the upper mantle by about 15 km.     

Application of the cBΩ model to the calculation of diffusion parameters of He in olivine

The validity of the thermodynamic cBΩ model is tested in terms of the experimentally determined diffusion coefficients of He in a natural Fe-bearing olivine (Fo₉₀) and a synthetic end-member forsterite (Mg₂SiO₄) over a broad temperature range (250–950 °C), as reported recently by Cherniak and Watson (Geochem Cosmochim Acta 84:269–279, 2012). The calculated activation enthalpies for each of the three crystallographic axes were found to be (134 ± 5), (137 ± 13) and (158 ± 4) kJ mol^?1 for the [100], [010] and [001] directions in forsterite, and (141 ± 9) kJ mol^?1 for the [010] direction in olivine, exhibiting a deviation of <1 % with the corresponding reported experimental values. Additional point defect parameters such as activation volume, activation entropy and activation Gibbs free energy were calculated as a function of temperature. The estimated activation volumes (3.2–3.9 ± 0.3 cm³ mol^?1) of He diffusion in olivine are comparable with other reported results for hydrogen and tracer diffusion of Mg cations in olivine. The pressure dependence of He diffusion coefficients was also determined, based on single experimental diffusion measurements at 2.6 and 2.7 GPa along the [001] direction in forsterite at 400 and 650 °C.     

Thermodynamic data for phases in the FeO-MgO-SiO2 system and phase relations in the mantle transition zone

Based on the available experimental data on phase equilibria in the FeO -MgO -SiO₂ system the mixing properties of the solid solutions (olivine, β- and γ-spinel, pyroxene, majorite, ilmenite and perovskite and magnesiowustite), the enthalpies of FeO and fictive FeSiO₃ phases with ilmenite and majorite structures have been assessed. The entropies, temperature dependance of heat capacities for fictive FeSiO₃ end-members were estimated from structural analogies. The calculated phase diagrams for Mg₂SiO₄-Fe₂SiO₄ and MgSiO₃ — FeSiO₃ systems at pressures up to 30 GPa and temperatures between 1000 and 2100 K are quite consistent with the available experimental determinations except for the fine features of the phase diagram at 2073 K.     

Dielectric constants of tephroite,fayalite and olivine and the oxide additivity rule

The dielectric constants and dissipation factors of synthetic tephroite (Mn₂SiO₄), fayalite (Fe₃SiO₄) and a forsteritic olivine (Mg_1.80Fe_0.22SiO₄) were measured at 1 MHz using a two-terminal method and empirically determined edge corrections. The results are: tephroite, κ′_a= 8.79 tan δ_a = 0.0006 κ′_b = 10.20 tan δ_b = 0.0006 κ′_c= 8.94 tan δ_c= 0.0008 fayalite, gk′_a = 8.80 tan δ_a = 0.0004 gk′_b= 8.92 tan δ_b = 0.0018 gk′_c = 8.58 tan δ_c = 0.0010 olivine, gk′_a = 7.16 tan δ_a = 0.0006 gk′_b = 7.61 tan δ_b = 0.0008 gk′_c = 7.03 tan δ_c = 0.0006 The low dielectric constant and loss of the fayalite indicate an exceptionally low Fe³⁺ content. An FeO polarizability of 4.18 ų, determined from α_D(FeO) = [α_D (Fe₂SiO₄)-α_D(SiO₂)]/2, is probably a more reliable value for stoichiometric FeO than could be obtained from Fe_xO where x = 0.90–0.95. The agreement between measured dielectric polarizabilities as determined from the Clausius-Mosotti equation and those calculated from the sum of oxide polarizabilities according to α_D(M₂M′X₂) = 2α_D(MX) + α_D(M′X₂) is ～+2.8% for tephroite and +0.2% for olivine. The deviation from additivity in tephroite is discussed.     

The solubility of olivine in basaltic liquids: an ionic model

A simple ionic model which describes the solution of the forsterite component of olivine in silicate liquids is reported. The melting relation is represented: (Mg₂SiO₄)_ol = 2(Mg²⁺)_L + (SiO₄^4?_L and is extended to all silicate liquids by normalizing their compositions to 4 oxygens. At 1 bar, the temperature at which olivine is in equilibrium with any alkali-depleted basaltic composition can be calculated to within ±30°C. This error is increased considerably when applied to terrestrial basalts which contain several weight percent alkalis. Alkalis interfere with the equilibrium by generating strongly repulsive interionic forces which can be crudely modelled in a manner consistent with constraints imposed by regular solution theory.The model quantifies the reduced activity of SiO₄^4? monomers due to increasing SiO₂ concentrations in the melt. This is a consequence of polymerization which does not appear to operate gradually over the entire spectrum of mafic and ultramafic compositions. The coordination of alumina in melts which precipitate olivine only appears to be dominantly octahedral. Titanium acts as a polymerizing agent by interconnecting previously isolated SiO₄^4? monomers. Calcium associated with normative diopside tends to exhibit small but perceptible repulsive forces involving Mg²⁺.     

Thermodynamics and crystal chemistry of the hematite–corundum solid solution and the FeAlO3 phase

High-temperature oxide-melt calorimetry and Rietveld refinement of powder X-ray diffraction patterns were used to investigate the energetics and structure of the hematite–corundum solid solution and ternary phase FeAlO₃ (with FeGaO₃ structure). The mixing enthalpies in the solid solution can be described by a polynomial ΔH_mix=WX _hem(1?X _hem) with W=116 ± 10 kJ mol^?1. The excess mixing enthalpies are too positive to reproduce the experimental phase diagram, and excess entropies in the solid solution should be considered. The hematite–corundum solvus can be approximately reproduced by a symmetric, regular-like solution model with ΔG _excess=(W _H ?TW _S )X _hem X _cor, where W _H= 116 ± 10 kJ mol^?1 and W _S =32 ± 4 J mol^?1 K^?1. In this model, short-range order (SRO) of Fe/Al is neglected because SRO probably becomes important only at intermediate compositions close to Fe:Al=1:1 but these compositions cannot be synthesized. The volume of mixing is positive for Al-hematite but almost ideal for Fe-corundum. Moreover, the degree of deviation from Vegard's law for Al-hematite depends on the history of the samples. Introduction of Al into the hematite structure causes varying distortion of the hexagonal network of oxygen ions while the position of the metal ions remains intact. Distortion of the hexagonal network of oxygen ions attains a minimum at the composition (Fe_0.95Al_0.05)₂O₃. The enthalpy of formation of FeAlO₃ from oxides at 298 K is 27.9 ± 1.8 kJ mol^?1. Its estimated standard entropy (including configurational entropy due to disorder of Fe/Al) is 98.9 J mol^?1 K^?1, giving the standard free energy of formation at 298 K from oxides and elements as +19.1 ± 1.8 and ?1144.2 ± 2.0 kJ mol^?1, respectively. The heat capacity of FeAlO₃ is approximated as C _p (T in K)= 175.8 ? 0.002472T ? (1.958 × 10⁶)/T ²? 917.3/T ^0.5+(7.546 × 10^?6) T ² between 298 and 1550 K, based on differential scanning calorimetric measurements. No ferrous iron was detected in FeAlO₃ by Mössbauer spectroscopy. The ternary phase is entropy stabilized and is predicted to be stable above about 1730 ± 70 K, in good agreement with the experiment. Static lattice calculations show that the LiNbO₃-, FeGaO₃-, FeTiO₃-, and disordered corundum-like FeAlO₃ structures are less stable (in the order in which they are listed) than a mechanical mixture of corundum and hematite. At high temperatures, the FeGaO₃-like structure is favored by its entropy, and its stability field appears on the phase diagram.     

Enthalpy of formation of forsterite,enstatite, akermanite,monticellite and merwinite at 1073 K determined by alkali borate solution calorimetry

Enthalpies of solution of synthetic enstatite (Mg₂Si₂O₆), forsterite (Mg₂SiO₄), akermanite (Ca₂MgSi₂O₇), monticellite (CaMgSiO₄), and merwinite (Ca₃MgSi₂O₈) and their component oxides were determined in eutectic (Li, Na)BO₂ at 1073 K. Resulting enthalpies of formation at 1073 are enstatite: $\text{?8.10 ± 0.42}\text{kcal}$; forsterite: $\text{?14.23 ± 0.45}\text{kcal}$; akermanite: $\text{?42.60 ± 0.39}\text{kcal}$; monticellite: $\text{?25.05 ± 0.41}\text{kcal}$; and merwinite: $\text{?51.10 ± 0.49}\text{kcal}$. The value for the synthetic monticellite of composition Mo_.965Fo_.035 was corrected slightly for non-stoichiometry based on experimental monticellite-forsterite phase equilibrium relations.The enthalpies of formation of enstatite and forsterite are somewhat less negative than yielded by several other solution calorimetric studies but are in good agreement with the recent Pb₂B₂O₅ solution calorimetry of Kiselevaet al. (1979), and are in good agreement with values to be derived from reliable phase equilibrium data in the system MgO-Al₂O₃-SiO₂. The enthalpies of formation of akermanite, monticellite and merwinite are all much less negative than values tabulated by robieet al. (1978) and helgesonet al. (1978) but are shown to be compatible with reliable phase equilibrium data for the system CaO-MgO-SiO₂, whereas the tabulated values are not. Several methods of analysis yield an entropy of monticellite at 1000 K of $\text{69.9 ± 0.2 cal/K}$.     

X-ray diffraction study of Fe2+-Mg order-disorder in orthopyroxene. Some kinetic results

Kinetic rates of Fe²⁺-Mg disordering in three orthopyroxenes (mean value of X_Fe = Fe²⁺/(Fe²⁺+Mg) = 0.175,0.482,0.770 respectively) have been determined employing heating experiments and single crystal X-ray structural refinements. Disordering rate constants \((\vec K)\) (550800° C) for two pyroxenes are given by: ln \((\vec K)\) = 27.107(±5.177)?32062(±783)T^?1(X_Fe = 0.175) ln \((\vec K)\) = 16.142(±0.057)?18227(±423)T^?1(X_Fe = 0.770) The distribution coefficients K_D (representing a steady state of disordering Fe_M2 + Mg_M1 ? Fe_M1 + Mg_M2) are given by: ln K_D = 5.016(±0.223)-7033(±1473) T^?1(X_Fe = 0.175) ln K_D = 1.988(±0.122)-3809(±913)T^?1(X_Fe = 0.770) These distribution coefficients provide the constraint of the disordering reaction on the value of the equilibrium constant for Fe²⁺-Mg order-disorder. Until the low temperature dependence of K_D is well constrained, the calculation of cooling rates of pyroxenes and host rocks cannot be done reliably.     

High temperature calorimetry of sulfide systems

Enthalpies of solution of synthetic pentlandite Fe_4.5Ni_4.5S₈, natural violarite (Fe_0.2941Ni_0.7059)₃S₄ from Vermillion mine, Sudbury, Ontario, synthetic pyrrhotite, FeS, synthetic high temperature NiS, synthetic vaesite, NiS₂, synthetic pyrite, FeS₂, Ni and Fe have been measured in a Ni_0.6S_0.4 melt at 1,100 K. Using these data and the standard enthalpies of formation of binary sulfides, given in literature, standard enthalpies of formation of pentlandite and violarite were calculated. The following values are reported: ΔH _f ^{o, Pent} =?837.37±14.59 kJ mol^?1 and ΔH _f ^{o, Viol} =?378.02±11.81 kJ mol^?1. While there are no thermo-chemical data for pentlandite with which our new value can be compared, an equilibrium investigation of stoichiometric violarite by Craig (1971) gives a significantly less negative enthalpy of formation. It is suggested that the difference may be due to the higher degree of order in the natural sample.     

Thermochemistry of glasses along joins of pyroxene stoichiometry in the system Ca2Si2O6-Mg2Si2O6-Al4O6

Enthalpies of solution in 2PbO · B₂O₃ at 974 K have been measured for glasses along the joins Ca₂Si₂O₆ (Wo)-Mg₂Si₂O₆ (En) and Mg₂Si₂O₆-MgAl₂SiO₆ (MgTs). Heats of mixing are symmetric and negative for Wo-En with W_H = ?31.0 ± 3.6 kJ mol^?. Negative heats of mixing were also found for the En-MgTs glasses (W_H = ?33.4 ± 3.7 kJ mol^?).Enthalpies of vitrification of pyroxenes and pyroxenoids generally increase with decreasing alumina content and with decreasing basicity of the divalent cation.Heats of mixing along several glassy joins show systematic trends. When only non-tetrahedral cations mix (outside the aluminosilicate framework), small exothermic heats of mixing are seen. When both nontetrahedral and framework cations mix (on separate sublattices, presumably), the enthalpies of mixing are substantially more negative. Maximum enthalpy stabilization near compositions with Al/Si ≈ 1 is suggested.     

Enthalpies of formation at 970 K of compounds in the system MgO-Al2O3-SiO2 from high temperature solution calorimetry

The enthalpies of solution of petrologically important phases in the system MgO-Al₂O₃-SiO ₂ were measured in a melt of composition 2PbO · B₂O₃ at 970 ± 2K. The substances investigated included synthetic and natural (meteoritic) enstatite (MgSiO₃), synthetic aluminous enstatite (MgSiO_30.9Al₂O_30.1), synthetic and natural cordierite (Mg₂Al₄Si₅O₁₈), synthetic and natural sapphirine (approx. 7MgO·9Al₂O₃ · 3SiO₂), synthetic spinel (MgAl₂O₄), natural sillimanite (Al₂SiO₅), synthetic forsterite (Mg₂SiO₄), synthetic pyrope (Mg₃Al₂Si₃O₁₂), natural quartz (SiO₂), synthetic periclase (MgO) and corundum (Al₂O₃). Improvement in standardization of the calorimeter solvent made possible greater precision in this study than obtainable in former work in this laboratory on some of the same substances.The enthalpies of formation of enstatite, synthetic cordierite, forsterite and spinel are in reasonable agreement with values previously determined by solution calorimetry. The enthalpy of formation of enstatite is about 0.7 kcal less negative than the value for clinoenstatite resulting from the HF calorimetry of Torgesen and Sahama (J. Amer. Chem. Soc.70. 2156–2160, 1948), and is in accord with predictions based on analysis of published pyroxene equilibrium work. Aluminous enstatite with 10 wt.% Al₂O₃ shows an enthalpy of solution markedly lower than pure MgSiO₃: the measurements lead to an estimate of the enthalpy of formation at 970 K for MgAl₂SiO₆ (Mg-Tschermak) orthopyroxene of + 9.4 ± 1.5 kcal/mole from MgSiO₃ and Al₂O₃.Comparison of the enthalpies of formation of synthetic cordierite and anhydrous natural low-iron cordierite shows that they are energetically quite similar and that the synthetic cordierite is not likely to have large amounts of (Al, Si) tetrahedral disorder. Comparison of the enthalpies of formation of synthetic sapphirine and natural low-iron sapphirine shows, on the other hand, that the former is not a good stability model for the latter. The lower enthalpy of formation of the high-temperature synthetic sample is undoubtedly a consequence of cation disordering.The enthalpy of formation of natural sillimanite is considerably less negative than given by the tables of Robie andWaldbaum (U.S. Geol. Surv. Bull.1259 1968).The measured enthalpy of formation of synthetic pyrope is consistent with that deduced from published equilibrium diagrams in conjunction with the present measured enthalpy of formation of aluminous enstatite. Calculation of the entropy of synthetic pyrope from the present data yields surprisingly high values and suggests that synthetic pyrope is not a good stability model for natural pyrope-rich garnets. Hence, considerable doubt exists about the direct quantitative application of experimental diagrams involving pyropic garnet to discussions of the garnet stability field in the Earth's outer regions.     

The effect of silica activity on the diffusion of Ni and Co in olivine

The diffusion of Ni and Co was measured at atmospheric pressure in synthetic monocrystalline forsterite (Mg₂SiO₄) from 1,200 to 1,500 °C at the oxygen fugacity of air, along [100], with the activities of SiO₂ and MgO defined by either forsterite + periclase (fo + per buffer) or forsterite + protoenstatite (fo + en buffer). Diffusion profiles were measured by three methods: laser-ablation inductively-coupled-plasma mass-spectrometry, nano-scale secondary ion mass spectrometry and electron microprobe, with good agreement between the methods. For both Ni and Co, the diffusion rates in protoenstatite-buffered experiments are an order of magnitude faster than in the periclase-buffered experiments at a given temperature. The diffusion coefficients D _M (M = Ni or Co) for the combined data set can be fitted to the equation:

$$\log \,D_{\text{M}} \,\left( {{\text{in}}\,{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right) = - 6.77( \pm 0.33) + \Delta E_{\text{a}} (M)/RT + 2/3\log a_{{SiO_{2} }}$$

with E_a(Ni) = ? 284.3 kJ mol^?1 and E_a(Co) = ? 275.9 kJ mol^?1, with an uncertainty of ±10.2 kJ mol^?1. This equation fits the data (24 experiments) to ±0.1 in log D _M. The dependence of diffusion on \(a_{{{\text{SiO}}_{2} }}\) is in agreement with a point-defect model in which Mg-site vacancies are charge-balanced by Si interstitials. Comparative experiments with San Carlos olivine of composition Mg_1.8Fe_0.2SiO₄ at 1,300 °C give a slightly small dependence on \(a_{{{\text{SiO}}_{2} }}\), with D \(\propto\) (\(a_{{{\text{SiO}}_{2} }}^{0.5}\)), presumably because the Mg-site vacancies increase with incorporation of Fe³⁺ in the Fe-bearing olivines. However, the dependence on fO₂ is small, with D \(\propto\) (fO₂)^0.12±0.12. These results show the necessity of constraining the chemical potentials of all the stoichiometric components of a phase when designing diffusion experiments. Similarly, the chemical potentials of the major-element components must be taken into account when applying experimental data to natural minerals to constrain the rates of geological processes. For example, the diffusion of divalent elements in olivine from low SiO₂ magmas, such as kimberlites or carbonatites, will be an order of magnitude slower than in olivine from high SiO₂ magmas, such as tholeiitic basalts, at equal temperatures and fO₂.

     

The importance of defining chemical potentials,substitution mechanisms and solubility in trace element diffusion studies: the case of Zr and Hf in olivine

The diffusion, substitution mechanism and solubility limits of Zr and Hf in synthetic forsterite (Mg₂SiO₄) and San Carlos olivine (Mg_0.9Fe_0.1)₂SiO₄ have been investigated between 1,200 and 1,500 °C as a function of the chemical potentials of the components in the system MgO(FeO)–SiO₂–ZrO₂(HfO₂). The effect of oxygen fugacity and crystallographic orientation were also investigated. The solubilities of Zr in forsterite are highest and diffusion fastest when the coexisting three-phase source assemblage includes ZrSiO₄ (zircon) or HfSiO₄ (hafnon), and lower and slower, respectively, when the source assemblage includes MgO (periclase). This indicates that Zr and Hf substitute on the octahedral sites in olivine, charge balanced by magnesium vacancies. Diffusion is anisotropic, with rates along the crystal axes increasing in the order a < b < c. The generalized diffusion relationship as a function of chemical activity (as \(a_{{{\text{SiO}}_{2} }}\)), orientation and temperature is: \(logD_{\text{Zr}} = \frac{1}{4}loga_{{{\text{SiO}}_{2} }} + logD_{0} - \left( {\frac{{368 \pm 17\;{\text{kJ}}\;{\text{mol}}^{ - 1} }}{{2.303\;{\text{RT}}}}} \right)\) where the values of log D ₀ are ?3.8(±0.5), ?3.4(±0.5) and ?3.1(±0.5) along the a, b and c axes, respectively. Most experiments were conducted in air (fO₂ = 10^?0.68 bars), but one at fO₂ = 10^?11.2 bars at 1,400 °C shows no resolvable effect of oxygen fugacity on Zr diffusion. Hf is slightly more soluble in olivine than Zr, but diffuses slightly slower. Diffusivities of Zr in experiments in San Carlos olivine at 1,400 °C, fO₂ = 10^?6.6 bars are similar to those in forsterite at the same conditions, showing that the controls on diffusivities are adequately captured by the simple system (nominally iron-free) experiments. Diffusivities are in good agreement with those measured by Spandler and O’Neill (Contrib Miner Petrol 159:791–818, 2010) in San Carlos olivine using silicate melt as the source at 1,300 °C, and fall within the range of most measurements of Fe–Mg inter-diffusion in olivine at this temperature. Forsterite–melt partitioning experiments in the CaO–MgO–Al₂O₃–SiO₂–ZrO₂/HfO₂ show that the interface concentrations from the diffusion experiments represent true equilibrium solubilities. Another test of internal consistency is that the ratios of the interface concentrations between experiments buffered by Mg₂SiO₄ + Mg₂Si₂O₆ + ZrSiO₄ or Mg₂SiO₄ + ZrSiO₄ + ZrO₂ (high silica activity) to those buffered by Mg₂SiO₄ + MgO + ZrO₂ (low silica activity) agree well with the ratios calculated from thermodynamic data. This study highlights the importance of buffering chemical potentials in diffusion experiments to provide constraints on the interface diffusant concentrations and hence validate the assumption of interface equilibrium.     

Thermodynamic properties of copper carbonates — malachite Cu2(OH)2CO3 and azurite Cu3(OH)2(CO3)2

The thermodynamic properties of the copper carbonates malachite and azurite have been studied by adiabatic calorimetry, by heat-flux Calvet Calorimetry, by differential thermal analysis (DTA) and by thermogravimetrie (TGA) analysis. The heat capacities, C _p ⁰ of natural malachite and azurite have been measured between 3.8 and 300 K by low-temperature adiabatic calorimetry. The heat capacity of azurite exhibits anomalous behavior at low temperatures. At 298.15 K the molar heat capacities C _p ⁰ and the third law entropies S _298.15 ⁰ are 228.5±1.4 and 254.4±3.8 J mol^?1 K^?1 for azurite and 154.3±0.93 and 166.3±2.5 J mol^?1 K^?1 for malachite. Enthalpies of solution at 973 K in lead borate 2PbO·B₂O₃ have been measured for heat treated malachite and azurite. The enthalpies of decomposition are 105.1±5.8 for azurite and 66.1±5.0 kJ mol^? for malachite. The enthalpies of formation from oxides of azurite and malachite determined by oxide melt solution calorimetry, are ?84.7±7.4 and ?52.5±5.9 kJ mol^?1, respectively. On the basis of the thermodynamic data obtained, phase relations of azurite and malachite in the system Cu²⁺-H₂O-CO₂ at 25 and 75 °C have been studied.     

Experimental determination of activity-composition relations in Ni2SiO4− Mg2SiO4 and Co2SiO4-Mg2SiO4 olivine solid solutions at 1200 K and 0.1 MPa and 1573 K and 0.5 GPa

Activity-composition relations in the olivine solid solutions Ni₂SiO₄⁻ -Mg₂SiO₄ and Co₂SiO₄-Mg₂SiO₄ have been determined at 1200 K and 0.1 MPa and at 1573 K and 0.5 GPa by equilibration with the corresponding oxide solutions. Both olivine solutions show small positive deviations from ideal (two site) mixing, which, within the limits of accuracy of the method, may be described by the simple regular solution model with parameters W_Ni+Mg^ol= 0.35 ± 1.0 kJ/g-atom and W_Co-Mg^ol = 1.37 ± 0.9 kJ/g-atom. The requirements of internal consistency between the two systems also show that the recent determination by Brousse et al. (1984) of the enthalpy of formation of Mg₂SiO₄is to be preferred over earlier work, and that their value is also probably more accurate than the uncertainty in their own measurements indicates; activities in the NiO-MgO system are close to ideal.     

Modification of olivine surface morphology and reactivity by microbial activity during chemical weathering

Prior transmission electron microscope studies showed that the surface geometry of olivine changes dramatically during natural chemical weathering. However, similar morphological evolution has not been reported in laboratory studies of olivine dissolution. In this study, we examined the development of fayalite (Fe₂SiO₄) surface morphology during both abiotic and biotic (using Acidithiobacillus ferrooxidans) laboratory dissolution experiments at an initial pH of 2.0. The fayalite came from Cheyenne Canyon, Colorado (Smithsonian # R 3516) and contains a few percent laihunite (olivine structure with ordered ferric iron and vacancies, ∼Fe_0.8²⁺Fe_0.8³⁺SiO₄). High-resolution field emission low voltage scanning electron microscope (SEM) characterization of all reacted samples showed etch patterns consistent with those reported from naturally reacted olivine. High-resolution transmission electron microscope (HRTEM) data demonstrated pervasive channeling on (001), with channel spacings that range down to < 10 nm. Formation of channels on (001) is probably initiated by preferential removal of cations from olivine M1 sites. Channeling confers at least an order of magnitude increase in surface area. Relict strips of olivine between channels contain laihunite layers that are oriented parallel to channel margins. X-ray diffraction analyses indicated that the relative abundance of laihunite is higher in reacted compared to unreacted samples. This result is consistent with prior studies of naturally weathered olivine that suggest that laihunite is far less readily dissolved than olivine.Samples reacted in the presence of A. ferrooxidans cells that enzymatically oxidized iron, or in solutions where ferric iron was added to simulate biological activity, dissolve at a much slower rate than samples reacted abiotically. We attribute suppression of the olivine dissolution rate to surface adsorption of Fe³⁺. It is probable that ferric iron adsorption is controlled by M2 sites in the underlying olivine structure. If this is coupled with removal of M1 cations during channel formation, then a modified laihunite-like surface will develop (vacancies in laihunite are on M1 sites). Although surface modification might only penetrate a few atomic layers, an inherently unreactive laihunite-like surface structure could explain both the pervasive channeling and the dramatic suppression of the measured dissolution rate.     

Partitioning of Fe and Mn between ilmenite and olivine at 1100 °C: constraints on the thermodynamic mixing properties of (Fe, Mn)TiO3 ilmenite solid solutions

The partitioning of Fe²⁺ and Mn²⁺ between (Fe, Mn)TiO₃ and (Fe, Mn)₂SiO₄ solid solutions in the system FeO-MnO-TiO₂-SiO₂ has been experimentally investigated at 1100 ^∘C and pressures of 1 bar and 25 kbar, over a wide range of Fe/Mn ratios, using electron microprobe analysis of quenched run products. The ilmenite solid solution in this system is within analytical uncertainty a simple binary between FeTiO₃ and MnTiO₃, but the olivine solid solution appears to contain up to 2.5 wt% TiO₂. The Fe-Mn partitioning results constrain precisely the difference in the thermodynamic mixing properties of the two solid solutions. If the mixing properties of (Fe, Mn)₂SiO₄ solid solutions are assumed to be ideal, as experimentally determined by Schwerdtfeger and Muan (1966), then the ilmenite is a regular, symmetric solution with W ^ilm _Fe-Mn=1.8±0.1 kJ mol⁻¹. The quoted uncertainty does not include the contribution from the uncertainty in the mixing properties of the olivine solution, which is estimated to be ±1.8 kJ mol⁻¹, and which therefore dominates the uncertainty in the present results. Nevertheless, this result is in good agreement with the previous experimental study of O'Neill et al. (1989), who obtained W ^ilm _Fe-Mn=2.2±0.3 kJ mol⁻¹ from an independent method. The results provide another item of empirical evidence supporting the proposition that solid solutions between isostructural end-members, in which order-disorder effects are not important, generally have simple thermodynamic mixing properties, with little asymmetry, modest excess entropies, and excess enthalpies approximately proportional to the difference in the molar volumes of the end-members. Received: 11 February 1998 / Accepted: 29 June 1998