A clinopyroxene geobarometer for basaltic systems based on crystal-structure modeling

 The crystal chemical response of basalt clinopyroxene to increasing pressure was investigated by means of crystal-structure simulation (a procedure that enables modeling of the structural parameters of a clinopyroxene of known chemistry without requiring direct X-ray diffraction analysis) using available experimental chemical data. Pressure proved the main physical variable governing clinopyroxene behavior in a magmatic environment. The general internal consistency of the simulation data permitted construction of an empirical geobarometer based on the relationship of cell volume (Vc) vs M1-site volume (VM1). The straightforward geobarometric formulation in the absence of direct X-ray analysis is: P(kbar)=698.443+4.985⋅Al_T−26.826⋅Fe²⁺ _M1−3.764⋅Fe³⁺ +53.989⋅Al_M1+3.948⋅Ti+14.651⋅Cr −700.431⋅Ca−666.629⋅Na−682.848⋅Mg_M2−691.138⋅Fe²⁺ _M2−688.384⋅Mn−6.267⋅(Mg_M2)²−4.144⋅(Fe²⁺ _M2 where: (Fe²⁺ _M1⋅Mg_M2)/(Fe²⁺ _M2⋅Mg_M1)=e^**(0.238⋅R³⁺+0.289⋅CNM−2.315), CNM=Ca+Na+Mn, and R³⁺=Al_M1+Fe³⁺+Ti+Cr, with cations in atoms per formula unit. The geobarometer reproduces experimental pressures within ±2 kbar (=1σ; max. dev. ≤5 kbar; N=29) in the range 0–24 kbar and is applicable to near-liquidus C2/c clinopyroxenes crystallized from basaltic melts in the absence of garnet (excepting high-Al₂O₃ basalts). It is therefore suitable for many natural clinopyroxenes occurring as mega- or phenocrysts or forming well-preserved cumulate pyroxenites. If the above restrictions are not wholly satisfied, the Vc vs VM1 plot can also be used qualitatively to deduce the relative pressure conditions of clinopyroxenes forming from similar batches of magma. The structural simulation of experimental data also provided insight into the influence of minor chemical changes of the parental magma on the crystal chemistry of clinopyroxene at high pressure. Within the considered compositional space at given P-T, a _CaO and a _SiO2 in the melt have opposite effects on M2- and T-site cation populations. As a result, under similar physical conditions, clinopyroxenes from higher-CaO or more undersaturated basalts have higher VM2, VT and Vc and lower VM1. For basalts with normal contents of Al₂O₃ (<18 wt %), variations of major elements in the melt do not reduce the accuracy of the geobarometer. Received: 3 April 1994 / Accepted: 23 December 1995     

The low-pressure stability of phase A,Mg7Si2O8(OH)6

 Phase A, Mg₇Si₂O₈(OH)₆, is a dense hydrous magnesium silicate whose importance as a host of H₂O in the Earth’s mantle is a subject of debate. We have investigated the low-pressure stability of phase A in experiments on the reaction phase A=brucite+forsterite. Experiments were conducted in piston-cylinder and multi-anvil apparatus, using mixtures of synthetic phase A, brucite and forsterite. The reaction was bracketed between 2.60 and 2.75 GPa at 500° C, between 3.25 and 3.48 GPa at 600° C and between 3.75 and 3.95 GPa at 650^° C. These pressures are much lower than observed in the synthesis experiments of Yamamoto and Akimoto (1977). At 750^° C the stability field of brucite + chondrodite was entered. The enthalpy of formation and entropy of phase A at 1 bar (10⁵ Pa), 298 K, were derived from the experimental brackets on the reaction phase A=brucite+forsterite using a modified version of the thermodynamic dataset THERMOCALC of Holland and Powell (1990), which includes a new equation of state of H₂O derived from the molecular dynamics simulations of Brodholt and Wood (1993). The data for phase A are: ΔH ^o _f =−7126±8 kJ mol^-1, S ^o=351 J K^-1 mol^-1. Incorporating these data into THERMOCALC allows the positions of other reactions involving phase A to be calculated, for example the reaction phase A + enstatite=forsterite+vapour, which limits the stability of phase A in equilibrium with enstatite. The calculated position of this reaction (753° C at 7 GPa to 937° C at 10 GPa) is in excellent agreement with the experimental brackets of Luth (1995) between 7 and 10 GPa, supporting the choice of equation of state of H₂O used in THERMOCALC. Comparison of our results with calculated P-T paths of subducting slabs (Peacock et al. 1994) suggests that, in the system MgO–SiO₂–H₂O, phase A could crystallise in compositions with Mg/Si>2 at pressures as low as 3 GPa. In less Mg rich compositions phase A could crystallise at pressures above approximately 6 GPa. Received: 3 July 1995/Accepted: 14 December 1995     

Mössbauer study of synthetic Mg0.22Fe0.78SiO3 clinopyroxene

Summary  Transmission M?ssbauer spectra of synthetic Ca-free P2₁/c Mg_0.22Fe_0.78SiO₃ clinopyroxene were collected at temperatures in the range 4.2 to 745 K and in an external magnetic field of 60 kOe at 180 K. The magnetic order-disorder transition temperature was determined by M?ssbauer thermoscanning to be 21 ± 3 K. Above this temperature, all M?ssbauer spectra consist of a superposition of two doublets, respectively produced by Fe²⁺ ions at an almost regular octahedral M1 site and at a more distorted octahedral M2 site. The temperature variation of the Fe²⁺ center shifts were analyzed using the Debye model for the lattice vibrations. The characteristic M?ssbauer temperatures were found to be 356 K ± 35 K for M1 and 333 K ± 25 K for M2. From the external field (60 kOe) M?ssbauer spectrum recorded at 180 K, the principal component V _zz of the electric field gradient (EFG) was determined to be positive for both sites but precise values for the magnitudes of the asymmetry parameters η of the EFG could not be determined. The temperature variations of the M1 and M2 quadrupole splittings ΔE _Q(T ) are consistent with the higher distortion of the M2 octahedra. Using the crystal-field model to interpret ΔE _Q(T ), the energy gaps δ₁ and δ₂ of the first excited electronic states within the ⁵D orbital term were estimated to be 410 ± 50 cm⁻¹ and 730 ± 50 cm⁻¹ for M1, and δ₁ = 1050 ± 75 cm⁻¹ for M2. Received May 29, 2000;/revised version accepted July 13, 2001     

Thermal Expansion of Periclase (MgO) and Tungsten (W) to Melting Temperatures

 In situ x-ray data on molar volumes of periclase and tungsten have been collected over the temperature range from 300 K to melting. We determine the temperature by combining the technique of spectroradiometry and electrical resistance wire heating. The thermal expansion (α) of periclase between 300 and 3100 K is given by α=2.6025 10⁻⁵+1.3535 10⁻⁸ T+6.5687 10⁻³ T⁻¹−1.8281 T⁻². For tungsten, we have (300 to 3600 K) α=7.862 10⁻⁶+6.392 10⁻⁹ T. The data at 298 K for periclase is: molar volume 11.246 (0.031) cm³, α=3.15 (0.07) 10⁻⁵ K⁻¹, and for tungsten: molar volume 9.55 cm³, α=9.77 (10.08) 10⁻⁶ K⁻¹. Received: July 18, 1996 / Revised, accepted: February 14, 1997     

Potential protonation sites in the Al<Subscript>2</Subscript>SiO<Subscript>5</Subscript> polymorphs based on polarized FTIR spectroscopy and properties of the electron density distribution

Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a mapping of the (3, −3) critical points displayed by their L(r) = −∇²ρ(r) distributions, are compared with polarized single-crystal FTIR spectra of kyanite and sillimanite determined earlier and with andalusite measured in this study. For andalusite, seven peaks were observed when the electric vector, E, is parallel to [100]: four intense ones at 3,440, 3,460, 3,526, and 3,597 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹. Six peaks, three intense ones at 3,440, 3,460, and 3,526 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹ when E parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of water in andalusite varies between 110 and 168 ppm by weight % H₂O. Polarized FTIR spectra indicate that the OH vector is parallel to (001) in andalusite and sillimanite and in kyanite. Examination of the L(r) (3, −3) critical points in comparison with the polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and O2 in andalusite and O2 and O4 in sillimanite which correspond to the underbonded oxygen atoms and those with the largest L(r) maxima. In kyanite, comparison of the FTIR spectrum and the critical points indicates that H will preferentially bond to the two 4-coordinated O2 and O6 atoms.     

The reaction MgCr2O4 + SiO2 = Cr2O3 + MgSiO3 and the free energy of formation of magnesiochromite (MgCr2O4)

Low-temperature heat capacity measurements for MgCr₂O₄ have only been performed down to 52 K, and the commonly quoted third-law entropy at 298 K (106 J K⁻¹ mol⁻¹) was obtained by empirical extrapolation of these measurements to 0 K without considering the magnetic or electronic ordering contributions to the entropy. Subsequent magnetic measurements at low temperature reveal that the Néel temperature, at which magnetic ordering of the Cr³⁺ ions in MgCr₂O₄ occurs, is at ∼15 K. Hence a substantial contribution to the entropy of MgCr₂O₄ has been missed. We have determined the position of the near-univariant reaction MgCr₂O₄+SiO₂=MgSiO₃+Cr₂O₃. The reaction, which has a small positive slope in P-T space, has been bracketed at 100 K intervals between 1273 and 1773 K by reversal experiments. The reaction is extremely sluggish, and lengthy run times with a flux (H₂O, BaO-B₂O₃ or K₂O-B₂O₃) are needed to produce tight reversal brackets. The results, combined with assessed thermodynamic data for Cr₂O₃, MgSiO₃ and SiO₂, give the entropy and enthalpy of formation of MgCr₂O₄ spinel. As expected, our experimental results are not in good agreement with the presently available thermodynamic data. We obtain Δ _f H ^∘ ₂₉₈=−1759.2±1.5 kJ mol⁻¹ and S ^∘ ₂₉₈=122.1±1.0 J K⁻¹ mol⁻¹ for MgCr₂O₄. This entropy is some 16 J K⁻¹ mol⁻¹ more than the calorimetrically determined value, and implies a value for the magnetic entropy of MgCr₂O₄ consistent with an effective spin quantum number (S') for Cr³⁺ of 1/2 rather than the theoretical 3/2, indicating, as in other spinels, spin quenching. Received: 9 May 1997 / Accepted: 28 July 1997     

An empirical model for the calculation of spinel-melt equilibria in mafic igneous systems at atmospheric pressure: 1. Chromian spinels

 In order to develop a model for simulating naturally occurring chromian spinel compositions, we have processed published experimental data on chromian spinel-melt equilibrium. Out of 259 co-existing spinel-melt experiments reported in the literature, we have selected 118 compositions on the basis of run time, melt composition and experimental technique. These data cover a range of temperatures 1150–1500° C, oxygen fugacities of −13<log f _O2< −0.7, and bulk compositions ranging from basalt and norite, to komatiite. Six major spinel components with Cr³⁺, Al³⁺, Ti⁴⁺, Mg²⁺, Fe³⁺ and Fe²⁺-bearing end-members were considered for the purpose of describing chromite saturation as a function of melt composition, temperature and oxygen fugacity at 1 atmosphere pressure (0.101 MPa). The empirically calibrated mineral-melt expression based on multiple linear regressions is: K ^Sp _i =A/T(K)+B log f _O2+C ln (Fe³⁺/Fe²⁺)_L+D ln R _L +E, where K ^Sp _i is an equilibrium constant and R _L is a melt structure-chemical parameter (MSCP). Twenty-eight forms of equilibrium constants were considered, including single distribution coefficients, exchange equilibrium constants, formation constants for AB₂O₄ components, as well as simple “spinel cation ratios”. For each form of the equilibrium constants, a set of 16 combinations of the MSCPs have been investigated. The MSCP is present in the form of composite ratios [e.g., Si/O, NBO/T,(Al+Si)/Si, or (Na+K)/Al] or as simple cation ratios (e.g., Mg/Fe²⁺). For the calculation of Fe³⁺ and Fe²⁺ species in silicate melts, we used existing equations, whereas the Fe³⁺/Fe²⁺ ratio of spinels was calculated from the spinel stoichiometry. The regression parameters that best repoduce the experimental data were for the following constants: (Fe³⁺/Fe²⁺) _Sp , (Mg/Fe²⁺) _Sp /(Mg/Fe²⁺) _L , (Cr/Al) _Sp / (Cr/Al) _L , K _FeCr2O4, and Ti _Sp /Ti _L . These expressions have been combined into a single program called SPINMELT, which calculates chromite crystallization temperature and composition at a given f _O2 with an average accuracy of ∼10° C and 1–2 mol%. An example of the use of SPINMELT is presented for a magma parental to the Bushveld Complex. Received: 30 May 1995/Accepted: 1 November 1995     

X-ray diffraction study of magnesite at high pressure and high temperature

 P–V–T measurements on magnesite MgCO₃ have been carried out at high pressure and high temperature up to 8.6 GPa and 1285 K, using a DIA-type, cubic-anvil apparatus (SAM-85) in conjunction with in situ synchrotron X-ray powder diffraction. Precise volumes are obtained by the use of data collected above 873 K on heating and in the entire cooling cycle to minimize non-hydrostatic stress. From these data, the equation-of-state parameters are derived from various approaches based on the Birch-Murnaghan equation of state and on the relevant thermodynamic relations. With K′₀ fixed at 4, we obtain K₀=103(1) GPa, α(K⁻¹)=3.15(17)×10⁻⁵ +2.32(28)×10⁻⁸ T, (∂K_T/∂T)_P=−0.021(2) GPaK⁻¹, (dα/∂P)_T=−1.81×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V= −0.007(1) GPaK⁻¹; whereas the third-order Birch-Murnaghan equation of state with K′₀ as an adjustable parameter yields the following values: K₀=108(3) GPa, K′₀=2.33(94), α(K⁻¹)=3.08(16)×10⁻⁵+2.05(27) ×10⁻⁸ T, (∂K_T/∂T)_P=−0.017(1) GPaK⁻¹, (dα/∂P)_T= −1.41×10⁻⁶ GPa⁻¹K⁻¹ and (∂K_T/∂T)_V=−0.008(1) GPaK⁻¹. Within the investigated P–T range, thermal pressure for magnesite increases linearly with temperature and is pressure (or volume) dependent. The present measurements of room-temperature bulk modulus, of its pressure derivative, and of the extrapolated zero-pressure volumes at high temperatures, are in agreement with previous single-crystal study and ultrasonic measurements, whereas (∂K_T/∂T)_P, (∂α/∂P)_T and (∂K_T/∂T)_V are determined for the first time in this compound. Using this new equation of state, thermodynamic calculations for the reactions (1) magnesite=periclase+CO₂ and (2) magnesite+enstatite=forsterite+CO₂ are consistent with existing experimental phase equilibrium data. Received September 28, 1995/Revised, accepted May 22, 1996     

Computer modelling of a pressure induced phase change in clinoenstatite pyroxenes

 Using lattice dynamic modelling of pure MgSiO₃ clinopyroxenes, we have be able to simulate the properties of both the low-clino (P2₁/c) and a high-density-clino (C2/c) phases and our results are comparable with the high pressure (HP) X-ray study of these phases (Angel et al. 1992). The transition between the two phases is predicted to occur at 6GPa. The volume variation with pressure for both phases is described by a third-order Birch-Murnaghan equation of state with the parameters V _{0  low}=31.122 cm³·mol⁻¹, K _{T0  low}= 107.42 GPa, K′ _{T0  low}=5.96, V _{0  high}=30.142 cm³·mol^–1, K _{T0  high}102.54 GPa and K′ _{T0  high}=8.21. The change in entropy between the two modelled phases at 6GPa is ΔS _{6 Gpa}=−1.335 J·mol⁻¹·K⁻¹ and the equivalent change in volume is ΔV _{6 GPa}=−0.92 cm³·mol⁻¹, from which the gradient of the phase boundary δP/δT is 0.0014 GPa·K⁻¹. The variation of the bulk modulus with pressure was also determined from the modelled elastic constants and compares very well with the EOS data. The reported Lehmann discontinuity, ∼220 km depth and pressure of 7.11Gpa, has an increase in the seismic compressional wave velocity, v _p , of 7.14% using the data given for PREM (Anderson 1989). At a pressure of 7GPa any phase transition of MgSiO₃ pyroxene would be between ortho (Pbca) and high-clino. We find the value of v _p at 7GPa, for modelled orthoenstatite (Pbca), is 8.41 km·sec⁻¹ and that for the modelled high-clino phase at 7GPa is 8.93 km·sec⁻¹, giving a dv _p /v _p of 6.18%. Received: July 26, 1996 / Revised, accepted: September 27, 1996     

Experimentally derived thermochemical data for pargasite and reinvestigation of its stability with quartz in the system Na2O–CaO–>MgO–Al2O3–SiO2–H2O

 The stability of pargasite in the presence of excess quartz has been determined in the range of 0.5–6.0 kbar and 500–950 °C in the system Na₂O– CaO–MgO–Al₂O₃–SiO₂–H₂O, using synthetic minerals. The experimental results from this study indicate the presence of two distinct mineral assemblage regions: (1) a high temperature supersolidus region containing tremolitic amphibole+melt+quartz; (b) a low temperature subsolidus region consisting of Al-rich amphibole+plagioclase+enstatite+quartz. Compositional reversals have been determined for the following three equilibria: (a) 2 pargasite+9 quartz=tremolite+4 plagioclase (An₅₀)+1.5 enstatite+H₂O, (b) 2 pargasite+10 quartz=tremolite+4 plagioclase (An₅₀)+talc, and (c) pargasite+diopside+5 quartz=tremolite+2 plagioclase (An₅₀). These experiments indicate a continuous change of amphibole composition from pargasite to tremolite with increasing temperature, and an opposite effect with increasing pressure. The third equilibria is used to constrain a site-mixing model for the pargasitic amphiboles, which favor a single-coupled Na^A-Al^T1 site mixing. The thermochemical data for pargasite estimated from the reversal data of the three equilibrium reactions is estimated as for ΔG ⁰ _f ,Pg=−12022.11±5.2 kJ mole^-1, and S ⁰ _Pg=591.7 ±7.9 JK^-1 mole^-1. Received: 31 July 1995/Accepted: 3 June 1996     

Single-crystal electronic absorption spectroscopy of synthetic chromium-, cobalt-, and vanadium-bearing pyropes at different temperatures and pressures

 Single crystals of synthetic vanadium-, chromium- and cobalt-bearing garnets, Pyr:V0.06, Pyr:V0.13, Pyr:Cr0.04, Pyr:Co0.10, and Gt:Co3.00, and a natural vanadium-bearing grossular, Gross:V0.07 (Cr³⁺ < 0.005), were studied by electronic absorption spectroscopy in the wavenumber range 35 000–5000 cm⁻¹ under ambient conditions and at temperatures up to 600 K and pressures up to 8 GPa. The T and P behavior of the absorption band energies and intensities shows the following for the different transition metal-bearing garnets: Cr: The thermal expansion of chromium octahedra are similar to and the Racah parameter the same in synthetic Cr-doped pyrope, α_poly≅ 1.3 × 10⁻⁵ K⁻¹, and in natural pyrope, α_poly≅ 1.5 × 10⁻⁵ K⁻¹, and B=655 cm⁻¹, respectively. Ca^2+[8]-free garnets have a slightly stronger crystal field at the Y^[6] site and, therefore, the energies of the two spin-allowed Cr³⁺ dd bands are ca. 300 cm⁻¹ higher in Mg-pyrope than in natural Ca-bearing pyrope. Co: Increasing temperature causes only a small thermal expansion of the cobalt dodecahedra. Increasing pressure gives rise to appreciable compression, which is similar to that of the Fe²⁺-dodecahedra in almandine, where k=125 ± 25 GPa. T and P dependence of the Co band intensities may be caused by strong spin-orbit coupling. V: Occurs in at least two valence states and structural sites: (1) V³⁺ in octahedral sites gives rise to two spin-allowed bands, at 17 220 cm⁻¹ and 24 600 cm⁻¹, whose temperature dependence is typical for spin-allowed dd transitions in centrosymmetric sites. (2) V⁴⁺, which causes a set of dd absorption bands similar to those observed in the spectrum of V⁴⁺-doped Zr[SiO₄]. The P behavior of the V absorption bands indicates an interaction between V³⁺ and V⁴⁺ species. Received: 27 June 2001 / Accepted: 19 December 2001     

A theoretical study of the absorption spectra of Pb+ and Pb3+ in site K+ of microcline: application to the color of amazonite

The blue-green color of amazonite has been assigned by various authors to ions Pb⁺ (6 s)² (6 p) and/or Pb³⁺ (6 s) in site of K⁺ of microcline. Owing to the complex which forms between the ion Pb³⁺ and the lone pairs of the oxygen atoms surrounding it, the peripheral electron of Pb³⁺ passes on the levels (6 p) of the latter, which results in a great similarity of the spectra of Pb⁺ and Pb³⁺ in amazonite (the transition energies are multiplied by a factor greater than 1), whereas, in the isolated state, these spectra are completely different from one another. An analytical development of the crystal field around a site K⁺ is established. Under the effect of the crystal field, the transition ² P _1/2→² P _3/2 (6 p) is split into two double transitions. The lower transition only falls in the visible domain (1.6–1.8 eV for Pb⁺), the second in U−V. The green color would arise from the ion Pb⁺, whereas the blue one would be attributed to the ion Pb³⁺. Received: 23 January 1997 / Revised, accepted: 10 September 1997     

Ca–Mn exchange between grossular and MnCl2 solutions at 2 kbar and 600°°C: reaction mechanism and evidence for non-ideal mixing in spessartine-grossular garnets

 The hydrothermal reaction between grossular and 1 molar manganese chloride solution was studied at 2 kbar and 600 °C at various bulk Ca/(Ca+Mn) compositions: Ca₃Al₂Si₃O₁₂+3Mn²⁺(aq) ⇔ Mn₃Al₂Si₃O₁₂+3Ca²⁺(aq) The reaction products are garnets of the spessartine-grossular solid-solution series which discontinuously armour the dissolving grossular grains. The first garnet to crystallize is spessartine rich (X ^gt _Mn≥0.95), reflecting the high Mn content of the solution, but as the reaction proceeds more calcium-rich garnets progressively overgrow the initial products. The armouring product layer is detached from the dissolving grossular, which allows the progressive overgrowth to occur on both its external and internal surfaces and results in the development of a two directional Ca/(Ca+Mn) zoning pattern in the product grains. The compositional changes in the run products are consistent with attainment of heterogeneous equilibrium between the external rims of the spessartine-grossular garnets and the bulk solutions in runs of duration ≥24 hours. Plots of ln K_D versus X ^gt _Ca maxima show linear variations that are not consistent with the ideal mixing that has been proposed for spessartine-grossular garnets at temperatures of 900 to 1200 °C. The data rather fit a regular solution model with the parameters ΔG° (600 °C, 2 kbar)=−8.0±0.8 kJ/mol and w ^gt _CaMn=2.6±2.0 kJ/mol. Existing solubility measurements and thermodynamic data from other Ca and Mn silicates support the calculated data. Grossular activities calculated using the w ^gt _CaMn parameter indicate that even in manganese-rich metapelites pressure estimates calculated using the garnet-plagioclase-Al₂SiO₅-quartz barometer will not be increased by more than 0.2 kbar. Received: 18 January 1995/Accepted: 4 June 1996     

Crystal field transitions in Co2[Al4Si5]O18 cordierite and CoAl2O4 spinel determined by neutron spectroscopy

Inelastic magnetic neutron scattering has been used to determine the energy of the ⁴ A ₂→⁴ T ₂ transition in CoAl₂O₄ spinel and the δ₁ transition in Co₂[Al₄Si₅]O₁₈ cordierite. The observed crystal field splitting in Co-spinel is 485 meV (3900 cm⁻¹), which corresponds to a crystal field stabilization energy of 56.2 kJmol⁻¹. The transition energy of the δ₁ transition in Co-cordierite has been determined to be 21 meV (170 cm⁻¹). The present data demonstrate that magnetic neutron scattering can be used to measure crystal field transitions at energies of interest in the study of 3d-containing silicates. It may be used to measure transition energies when the use of optical spectroscopy is inappropriate. Received: 30 January 1997 / Accepted: 5 July 1997     

Calorimetric study of perovskite solid solutions in the CaSiO3–CaGeO3 system

 Enthalpies of drop solution (ΔH _drop-sol) of CaGeO₃, Ca(Si_0.1Ge_0.9)O₃, Ca(Si_0.2Ge_0.8)O₃, Ca(Si_0.3Ge_0.7)O₃ perovskite solid solutions and CaSiO₃ wollastonite were measured by high-temperature calorimetry using molten 2PbO · B₂O₃ solvent at 974 K. The obtained values were extrapolated linearly to the CaSiO₃ end member to give ΔH _drop-sol of CaSiO₃ perovskite of 0.2 ± 4.4 kJ mol⁻¹. The difference in ΔH _drop-sol between CaSiO₃, wollastonite, and perovskite gives a transformation enthalpy (wo → pv) of 104.4 ± 4.4 kJ mol⁻¹. The formation enthalpy of CaSiO₃ perovskite was determined as 14.8 ± 4.4 kJ mol⁻¹ from lime + quartz or −22.2 ± 4.5 kJ mol⁻¹ from lime + stishovite. A comparison of lattice energies among A²⁺B⁴⁺O₃ perovskites suggests that amorphization during decompression may be due to the destabilizing effect on CaSiO₃ perovskite from a large nonelectrostatic energy (repulsion energy) at atmospheric pressure. By using the formation enthalpy for CaSiO₃ perovskite, phase boundaries between β-Ca₂SiO₄ + CaSi₂O₅ and CaSiO₃ perovskite were calculated thermodynamically utilizing two different reference points [where ΔG(P,T )=0] as the measured phase boundary. The calculations suggest that the phase equilibrium boundary occurs between 11.5 and 12.5 GPa around 1500 K. Its slope is still not well constrained. Received: 20 September 2000 / Accepted: 17 January 2001     

Thermobarometry of mafic igneous rocks based on clinopyroxene-liquid equilibria, 0–30 kbar

 Models for estimating the pressure and temperature of igneous rocks from co-existing clino-pyroxene and liquid compositions are calibrated from existing data and from new data obtained from experiments performed on several mafic bulk compositions (from 8–30 kbar and 1100–1475° C). The resulting geothermobarometers involve thermodynamic expressions that relate temperature and pressure to equilibrium constants. Specifically, the jadeite (Jd; NaAlSi₂O₆)–diopside/hedenbergite (DiHd; Ca(Mg, Fe) Si₂O₆) exchange equilibrium between clinopyroxene and liquid is temperature sensitive. When compositional corrections are made to the calibrated equilibrium constant the resulting geothermometer is (i) 10⁴ T=6.73−0.26^* ln [Jd^px*Ca^liq*Fm^liqDiHd^px*Na^liq*Al^liq] −0.86^* ln [Mg^liqMg^liq+Fe^liq]+0.52^*ln [Ca^liq] an expression which estimates temperature to ±27 K. Compared to (i), the equilibrium constant for jadeite formation is more sensitive to pressure resulting in a thermobarometer (ii) P=−54.3+299^* T10⁴+36.4^* T10⁴ ln [Jd^px[Si^liq]^2*Na^liq*Al^liq] +367^*[Na^liq*Al^liq] which estimates pressure to ± 1.4 kbar. Pressure is in kbar, T is in Kelvin. Quantities such as Na^liq represent the cation fraction of the given oxide (NaO_0.5) in the liquid and Fm=MgO+FeO. The mole fractions of Jd and diopside+hedenbergite (DiHd) components are calculated from a normative scheme which assigns the lesser of Na or octahedral Al to form Jd; any excess Al^VI forms Calcium Tschermak’s component (CaTs; CaAlAlSiO₆); Ca remaining after forming CaTs and CaTiAl₂O₆ is taken as DiHd. Experimental data not included in the regressions were used to test models (i) and (ii). Error on predictions of T using model (i) is ±40 K. A pressure-dependent form of (i) reduces this error to ±30 K. Using model (ii) to predict pressures, the error on mean values of 10 isobaric data sets (0–25 kbar, 118 data) is ±0.3 kbar. Calculating thermodynamic properties from regression coefficients in (ii) gives V^Jd _f of 23.4 ±1.3 cm³/mol, close to the value anticipated from bar molar volume data (23.5 cm³/mol). Applied to clinopyroxene phenocrysts from Mauna Kea, Hawaii lavas, the expressions estimate equilibration depths as great as 40 km. This result indicates that transport was sufficiently rapid that at least some phenocrysts had insufficient time to re-equilibrate at lower pressures. Received: 16 May 1994/Accepted: 15 June 1995     

On the Stability of the <Emphasis Type="Italic">AlOSi</Emphasis>(<Emphasis Type="Italic">OH</Emphasis>)<Stack><Subscript>3</Subscript><Superscript>2+</Superscript></Stack> Complex in Aqueous Solution

Summary The complexation of aluminium(III) and silicon(IV) was studied in a simplified seawater medium (0.6 M Na(Cl)) at 25 °C. The measurements were performed as potentiometric titrations using a hydrogen electrode with OH ⁻ ions being generated coulometrically. The total concentrations of Si(IV) and Al(III) respectively [Si _tot ] and [Al _t ot], and −log[H ⁺] were varied within the limits 0.3 < [Si _tot ] < 2.5 mM, 0.5 < [Al _tot ] < 2.6 mM, and 2 ≤ -log[H ⁺] ≤ 4.2. Within these ranges of concentration, evidence is given for the formation of an AlSiO(OH) ₃ ²⁺ complex with a formation constant log β_1,1-1 = −2.75 ± 0.1 defined by the reaction Al ³⁺+Si (OH)₄ ↔ AlOSi(OH) ₃ ²⁺ +H ⁺ An extrapolation of this value to I=0 gives log β_1,1-1 = −2.30. The calculated value of log K (Al ³⁺+SiO(OH) ₃ ⁻ ↔ AlOSi(OH) ₃ ²⁺ ) = 6.72 (I=0.6 M) can be compared with corresponding constants for the formation of AlF ²⁺ and AlOH ²⁺ , which are equal to 6.16 and 8.20. Obviously, the stability of these Al(III) complexes decreases within the series OH ⁻>SiO(OH) ₃ ⁻  > F ⁻     

Structural thermal behavior of paragonite and its dehydroxylate: a high-temperature single-crystal study

 The lattice constants of paragonite-2M₁, NaAl₂(AlSi₃)O₁₀(OH)₂, were determined to 800 °C by the single-crystal diffraction method. Mean thermal expansion coefficients, in the range 25–600 °C, were: α_a = 1.51(8) × 10⁻⁵, α_b = 1.94(6) × 10⁻⁵, α_c = 2.15(7) ×  10⁻⁵ °C⁻¹, and α_V = 5.9(2) × 10⁻⁵ °C⁻¹. At T higher than 600 °C, cell parameters showed a change in expansion rate due to a dehydroxylation process. The structural refinements of natural paragonite, carried out at 25, 210, 450 and 600 °C, before dehydroxylation, showed that the larger thermal expansion along the c parameter was mainly due to interlayer thickness dilatation. In the 25–600 °C range, Si,Al tetrahedra remained quite unchanged, whereas the other polyhedra expanded linearly with expansion rate proportional to their volume. The polyhedron around the interlayer cation Na became more regular with temperature. Tetrahedral rotation angle α changed from 16.2 to 12.9°. The structure of the new phase, nominally NaAl₂ (AlSi₃)O₁₁, obtained as a consequence of dehydroxylation, had a cell volume 4.2% larger than that of paragonite. It was refined at room temperature and its expansion coefficients determined in the range 25–800 °C. The most significant structural difference from paragonite was the presence of Al in fivefold coordination, according to a distorted trigonal bipyramid. Results confirm the structural effects of the dehydration mechanism of micas and dioctahedral 2:1 layer silicates. By combining thermal expansion and compressibility data, the following approximate equation of state in the PTV space was obtained for paragonite: V/V ₀ = 1 + 5.9(2) × 10⁻⁵ T(°C) − 0.00153(4) P(kbar). Received: 12 July 1999 / Revised, accepted: 7 December 1999     

High-temperature heat capacity and thermodynamic properties for end-member titanite (CaTiSiO5)

 The heat capacity of end-member titanite and (CaTiSiO₅) glass has been measured in the range 328–938 K using differential scanning calorimetry. The data show a weak λ-shaped anomaly at 483 ± 5 K, presumably associated with the well-known low-pressure P2₁/a ⇆ A2/a transition, in good agreement with previous studies. A value of 0.196 ± 0.007 kJ mol⁻¹ for the enthalpy of the P2₁/a ⇆ A2/a transition was determined by integration of the area under the curve for a temperature interval of 438–528 K, bracketing the anomaly. The heat capacity data for end-member titanite and (CaTiSiO₅) glass can be reproduced within <1% using the derived empirical equations (temperature in K, pressure in bars):

The high-pressure stability of zoisite and phase relationships of zoisite-bearing assemblages

The fluid-absent reaction 12 zoisite = 3 lawsonite + 7 grossular + 8 kyanite + 1 coesite was experimentally reversed in the model system CaO-Al₂O₃-SiO₂-H₂O (CASH) using a multi-anvil apparatus. The upper pressure stability limit for zoisite was found to extend to 5.0 GPa at 700 °C and to 6.6 GPa at 950 °C. Additional experiments both in the H₂O-SiO₂-saturated and in the H₂O-Al₂O₃-saturated portions of CASH provide further constraints on high pressure phase relationships of lawsonite, zoisite, grossular, kyanite, coesite, and an aqueous fluid. Consistency of the present experiments with the H₂O-saturated breakdown of lawsonite is demonstrated by thermodynamic analysis using linear programming techniques. Two sets of data consistent with databases of Berman (1988) and Holland and Powell (1990) were retrieved combining experimental phase relationships, calorimetric constraints, and recently measured elastic properties of solid phases. The best fits result in G _{f ,1,298} ^∘,zoisite=−6,499,400 J and S _1,298 ^∘,zoisite=302 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,514,600 J and S _1,298 ^{∘,lawsonite}=220 J/K for the dataset of Holland and Powell, and G _{f ,1,298} ^∘,zoisite=−6,492,120 J and S _1,298 ^∘,zoisite=304 J/K, and G _{f ,1,298} ^{∘,lawsonite}=−4,513,000 J and S _1,298 ^{∘,lawsonite}= 218 J/K for the dataset of Berman. Examples of the usage of zoisite as a geohygrometer and as a geobarometer in rocks metamorphosed at eclogite facies conditions are worked, profiting from the thermodynamic properties retrieved here. Received: 23 December 1996 / Accepted: 29 August 1997