O.J. Kleppa

Thermochemistry of the high structural state plagioclases

Abstract The enthalpies of solution of a suite of 19 high-structural state synthetic plagioclases were measured in a Pb2B2O5 melt at 970 K. The samples were crystallized from analyzed glasses at 1200°C and 20 kbar pressure in a piston-cylinder apparatus. A number of runs were also made on Amelia albite and Amelia albite synthetically disordered at 1050–1080°C and one bar for one month and at 1200°C and 20 kbar for 10 hr. The component oxides of anorthite, CaO, Al2O3 and SiO2, were remeasured. The ΔH of disorder of albite inferred in the present study from albite crystallized from glass is 3.23 kcal, which agrees with the 3.4 found by Holm and Kleppa (1968). It is not certain whether this value includes the ΔH of a reversible displacive transition to monoclinic symmetry, as suggested by Helgeson et al. (1978) for the Holm-Kleppa results. The enthalpy of solution value for albite accepted for the solid solution series is based on the heat-treated Amelia albite and is 2.86 kcal less than for untreated Amelia albite. The enthalpy of formation from the oxides at 970 K of synthetic anorthite is −24.06 ± 0.31 kcal, significantly higher than the −23.16 kcal found by Charlu et al. (1978), and in good agreement with the value of −23.89 ± 0.82 given by Robie et al. (1979), based on acid calorimetry. The excess enthalpy of mixing in high plagioclase can be represented by the expression, valid at 970 K: ΔHex(±0.16 kcal) = 6.7461 XabX2An + 2.0247 XAnX2Ab where XAb and XAn are, respectively, the mole fractions of NaAlSi3O8 and CaAl2Si2O8. This ΔHex, together with the mixing entropy of Kerrick and Darkens (1975) Al-avoidance model, reproduces almost perfectly the free energy of mixing found by Orville (1972) in aqueous cation-exchange experiments at 700°C. It is likely that Al-avoidance is the significant stabilizing factor in the high plagioclase series, at least for XAn≥ 0.3. At high temperatures the plagioclases have nearly the free energies of ideal one-site solid solutions. The Al-avoidance model leads to the following Gibbs energy of mixing for the high plagioclase series: ΔG mix = ΔH ex + RT X Ab ln[X 2 Ab (2 − X Ab )]+ X An ln [X An (1+X An ) 2 ] 4 . The entropy and enthalpy of mixing should be very nearly independent of temperature because of the unlikelihood of excess heat capacity in the albite-anorthite join.

Thermochemistry of high pressure garnets and clinopyroxenes in the system CaO-MgO-Al2O3-SiO2

Abstract The enthalpies of solution of several synthetic garnets on the join Mg 3 Al 2 Si 3 O 12 -Ca 3 Al 2 Si 3 O 12 (pyrope-grossular) and of several synthetic clinopyroxenes on the join CaMgSi 2 O 6 -CaAl 2 SiO 6 (diopside-Ca-Tschermaks molecule) were measured in a melt of composition 2PbO · B 2 O 3 at 970 K. The determinations were made with sufficient precision so that thermochemical characterizations of the solid solutions could be achieved. The pyrope-grossular solutions show positive enthalpies of mixing. The non-ideality in the range 0–30 mole % grossular is relatively the largest and is in good agreement with the predictions of Ganguly and Kennedy (1974) based largely on cation partitioning of natural high grade metamorphic garnets with biotite, and with the deductions of Hensen et al. (1975) based on measurement of the compositions of synthetic pyrope-rich garnets equilibrated with anorthite, Al 2 SiO 5 and quartz. However, the garnets show smaller excess enthalpies at higher grossular contents. This would lead to an asymmetric solvus with a critical temperature lower than predicted by the symmetrical regular solution model of Ganguly and Kennedy (1974). The composition-dependent non-ideality can be understood by simple ionic size considerations in solid substitution and is analogous to the situations for the calcite-dolomite and enstatite-diopside solvi. The heats of solution of pyropes crystallized in the range 1000–1500°C were all the same, within the precision of measurement, and thus we have found no evidence for temperature-dependent cation disordering as a possible explanation of the high entropy of pyrope, as suggested by Charlu et al. (1975). Positional disorder of dodecahedral Mg is a more probable reason. The diopside-CaTs join is also non-ideal, with the larger positive enthalpy deviations near the diopside end. The calorimetric data in the magnesian range are consistemt with the model for completely disordered tetrahedral Si and Al which results from the free energy derivations of wood (1975) based on syntheses of diopside-rich aluminous pyroxenes in the presence of anorthite and quartz. At higher Al concentrations the calorimetric data seem more consistent with the ‘local charge-balance’ model of Wood (1975). No evidence for temperature-dependent disorder was found for either the diopside or CaTs end-members.

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

Abstract 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 (MgSiO30.9Al2O30.1), 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 and Waldbaum (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 Earths outer regions.

Thermodynamics of polymorphic transformations in silica. Thermal properties from 5 to 1070° K and pressure-temperature stability fields for coesite and stishovite☆

Abstract Cryogenic heat-capacity measurements on coesite and stishovite provide thermo-dynamic properties from 5 to 350°K. The heat capacities (Cp), entropies (S°), and Gibbs energy functions [ -(G° − H° 0 ) T ] are 10.85, 9.65, 4.124, and 10.27, 6.64, 2.362 at 298.15°K for coesite and stishovite, respectively, in cal/(mole °K). Enthalpies of transition for phase changes were determined by solution calorimetry in a lead-cadmium-borate solvent at 697°C. The following values (in kcal/mole) were obtained upon adjustment to 298.15°K: quartz → coesite (1.21 ± 0.15), quartz → cristobalite (0.64 ± 0.15), quartz → silica glass (2.15 ± 0.15), and cristobalite → silica glass (1.51 ± 0.15). The enthalpy of coesite to 1070°K and the enthalpy of transformation for stishovite-silica glass were provided by means of a novel technique, “transposed-temperature” drop calorimetry. These data permit the delineation of P-T field phase boundaries for the stable equilibria coesite-quartz and coesite—stishovite, as well as for the metastable quartz-stishovite boundary, which are in reasonable agreement with the results of recent equilibrium and formation studies.

Thermochemistry of forsterite-fayalite olivine solutions

Abstract The enthalpies of solution of synthetic Mg2SiO4-Fe2SiO4 olivine solid solutions have been measured in Pb2B2O5 melt at 970 K. The heat of solution of forsterite was found to be 15.62 ± 0.3 kcal mol−1 and that of fayalite 9.39 ± 0.14 kcal mol−1. Solid solutions between these end-members exhibit small positive deviations from mixing ideality, asymmetric towards the Fe end-member. In terms of the sub-regular solution model, excess enthalpies of intermediate olivine are adequately represented by the equation Hxs = 2(1000 + 1000XFe) XFeXMg The enthalpies of solution at 970 K are consistent with high temperature phase equilibrium measurements of activity-composition relationships in the olivine series. Excess entropy terms are not needed to relate the phase equilibrium data to the calorimetric data presented here. The enthalpy of solution of FeSiO3 ferrosilite at 970 K was found to be 4.36 ± 0.10 kcal mol−1. This value, when taken together with calorimetric measurements on fayalite and quartz, is consistent with phase equilibrium investigations of the reaction: 2FeSiO3 = Fe2SiO4 + SiO2 Ferrosilite Fayalite Quartz These provide a check on the internal consistency of the calorimetric data presented here.

Enthalpy of mixing of synthetic almandine-grossular and almandine-pyrope garnets from high-temperature solution calorimetry

Abstract Enthalpy of solution measurements of synthetic garnet solid solutions on the joins Fe3Al2Si3O12 (almandine)-Ca3Al2Si3O12 (grossular) and Fe3Al2Si3O12-Mg3Al2Si3O12 (pyrope) have been made in eutectic (Li, Na)BO2 at 760°C. Garnets were prepared by high pressure, high temperature crystallization of homogeneous glasses and mechanical mixtures of end-member glasses and characterized by X-ray diffraction, microprobe analysis and Mossbauer resonance spectroscopy. Less than one percent of the total iron is ferric. The calorimetry shows that Ca, Fe2+ enthalpy of mixing in garnet is virtually zero and that Mg, Fe2+ mixing is substantially non-ideal, with largest positive deviations near the almandine composition. Leastsquares fits to the midpoints of the experimental brackets, including the end-members, give, for (Fe, Ca)3Al2Si3O12 and (Fe, Mg)3Al2Si3O12 solid solutions: W H G r = −9.08 KJ , W H A 1 = 13.68 KJ , W H P y = 36.17 KJ , W H A 1 = −15.76 KJ where ΔH ex = X 2 Gr X A 1 W H A 1 + X 2 A 1 X Gr W H Gr and similarly for the almandine-pyrope excess enthalpy. These calorimetric results are not predictable from ionic size considerations, which would suggest ideality for Mg, Fe2+ mixing and considerable non-ideality for Ca, Fe2+ mixing. They are, however, consistent with predictions based on analysis of natural garnet occurrences. Apparently, subtle effects of X-site volume and distortion in garnet solid solutions produce important energetic effects not currently predictable from crystal chemistry. The present calorimetry, in conjunction with experimental phase equilibrium work, indicates that excess entropy in both solid solutions is very small.

Enthalpy of formation of some lime silicates by high-temperature solution calorimetry, with discussion of high pressure phase equilibria

The enthalpies of solution of anorthite, grossular, the three CaSiO3 polymorphs and CaO were measured at 970 K in a lead borate melt. These data, combined with previously published work, determine the enthalpies of formation (kcal/gfw) of the above silicates and diopside and CaAl2SiO6 pyroxene from the oxides at 970 K: n• nCaAl2Si2O8-anorthite (synthetic) −23.14 ± 0.45 n n• nCaAl2Si2O8-anorthite (natural) −23.93 ± 0.48 n n• nCa3Al2Si3O12-grossular (synthetic) −77.91 ± 0.67 n n• nCaMgSi2O6-diopside (synthetic and natural) −34.99 ± 0.41 n n• nCaAl2SiO6-pyroxene (synthetic) −18.23 ± 0.39 n n• nCaSiO3-wollastonite (synthetic and natural) −21.48 ± 0.36 n n• nCaSiO3-pseudowollastonite (synthetic) −19.92 ± 0.31 n n• nCaSiO3-high pressure polymorph (synthetic) −19.84 ± 0.34 n n n n nNatural high temperature anorthite has a significantly more negative enthalpy of formation than synthetic anorthite. The enthalpy of formation of synthetic anorthite agrees with that given by the acid calorimetry of Barany (1962, U.S. Bur. Mines Kept. Inv.5900). n nSynthetic grossulars prepared both hydrothermally at 1000°C and 28 kbar and in the dry way at 1250°C and 35 kbar have the same enthalpy of solution. The enthalpy of formation of grossular from the oxides is more positive by 2–4 kcal/gfw than estimated by other workers from high pressure equilibrium diagrams. n nThe enthalpy of formation of diopside agrees with that reported by Navtrosky and Coons (1976, Geochim. Cosmochim. Acta40, 1281–1288) and is about two kcal less negative than given by Robie and Waldbaum (1968, U.S. Geol. Surv. Bull.1259). n nThe enthalpy of formation and entropy of CaAl2SiO6 pyroxene agree well with the parameters derived from high temperature, high pressure phase equilibria by Robie and Waldbaum (1968). n nThe enthalpies of formation of wollastonite and pseudowollastonite agree very well with those resulting from HF solution calorimetry. The dense high pressure CaSiO3 polymorph has an anomalously high entropy. The dP/dT slope of the stability boundary relative to wollastonite is indeed negative, as found by Essene (1974, Contrib. Mineral. Petrol.45, 247–250) and Huang and Wyllie (1975, Am. Mineralogist60, 213–217).

Thermochemistry of synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6

Abstract Enthalpies of solution of synthetic clinopyroxenes on the join CaMgSi2O6-Mg2Si2O6 have been measured in a melt of composition Pb2B2O5 at 970 K. Most of the measurements were made on samples crystallized at 1600°–1700°C and 30 kbar pressure, which covered the range 0–78 mole per cent Mg2Si2O6, and whose X-ray patterns could be satisfactorily indexed on the diopside (C2/c) structure. For the reaction: Mg2Si2O6→-Mg2Si2O6 enstatite diopside the present data, in conjunction with previous and new measurements on Mg2Si2O6 enstatite, determine ΔH° ~ 2 kcal and WH (regular solution parameter) ~ 7 kcal. These values are in good agreement with those deduced by Saxena and Nehru (1975) from a study of high temperature, high pressure phase equilibrium data under the assumption that the excess entropy of mixing is small, but, in light of the recent theoretical treatment of Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), the meanings of these parameters may be ambiguous. Heat of solution measurements on Ca-rich binary diopsides made by annealing glasses at 1358°C in air gave slighter higher values than the higher temperature high pressure samples. This may be evidence for some (Ca, Mg) disorder of the sort postulated by Navrotsky and Loucks (1977, Phys. Chem. Min.1, 109–127), although no differences in heat of solution dependent on synthesis temperature in the range 1350°–1700°C could be found in stoichiometric CaMgSi2O6.

A Calorimetric Investigation of the Stability of Anhydrous Magnesium Cordierite with Application to Granulite Facies Metamorphism

The heats of solution of synthetic anhydrous Mg-cordierite and of its high-pressure breakdown assemblage sapphirine + quartz (+ enstatite?) have been measured in a lead borate melt at 694°C. The ΔH of this reaction at this temperature and one atmosphere is 6.1±1 kilocalorie per mole of cordierite.A P-T stability diagram of cordierite relative to other synthetic phases in the system MgO-Al2O3-SiO2 was constructed which satisfies the heat of reaction data and all other reliable observations pertaining to the stability of anhydrous cordierite. The stability field of cordierite is limited by boundaries of very small dP/dT slopes. The maximum pressure of cordierite stability is about 8 kilobars. Above an invariant point near 950°C the sapphirine-bearing assemblage is the stable breakdown product of cordierite. Below 950°C the stable breakdown assemblage is enstatite + sillimanite + quartz. New heat of solution data for orthorhombic enstatite are presented which allow a calculation of the lower-temperature breakdown boundary. This calculation is in good agreement with the boundary deduced above. The calculated breakdown pressure of cordierite at 700°C is 5.6±1.5 kilobars. This is much lower than estimates of earlier workers and shows that cordierite stability is greatly restricted under very dry conditions.Heat of solution data of natural low-iron cordierite and sapphirine samples are presented. These indicate that synthetic cordierite is energetically close to natural cordierite and is therefore an adequate stability model to apply to natural occurrences but that the synthetic sapphirine prepared by the breakdown of cordierite is quite different from natural sapphirine. An estimate of the breakdown relations of cordierite relative to natural sapphirine is presented, which looks quite like the diagram of the synthetic system except that the invariant point is shifted to considerably lower temperatures.A consequence of the present work is that if conditions of metamorphism were very dry, pressures of only six to eight kilobars would have been necessary to produce the dense anhydrous assemblages equivalent to natural cordierite which are found in some ancient granulites. The subcrustal pressures considered necessary by some workers should not be regarded as established by presently available evidence.

Thermochemistry of jadeite—diopside pyroxenes

The enthalpies of solution of seven synthetic clinopyroxenes on the join CaMg2Si2O6 (diopside)-NaAlSi2O6 (jadeite), of two natural low-Fe ordered omphacites near the 1:1 composition, and of a nearly pure natural jadeite, were measured in molten Pb2B2O5 at 970 K. Enthalpies of solution of the natural omphacites experimentally disordered at 1350°C and 30 kbar were also measured. n nThe synthetic clinopyroxenes have positive excess enthalpies of mixing, which can be expressed by a symmetrical function ΔHmix = WHXJdXDi, with WH = 7250 ±950 calories. The enthalpy of disordering of the two natural omphacites averages 1.8 kcal, which is nearly the same as the excess enthalpy of mixing of a 1:1 disordered pyroxene. n nThe interaction parameter, WH, can be shown to be essentially equivalent to ΔG° of the reciprocal reaction: CaMgSi2O6 + NaAlSi2O6 = CaAlSi2O+6 + NaMgSi2O−6 M-site cation distribution data of natural omphacites heat-treated at 1000°C (Aldridgeet al., 1978) lead to ΔG° = 7200 cal for the above reaction, in good agreement with the calorimetric WH. The reciprocal solution theory with ΔG° = 7200 cal predicts closely the activities of NaAlSi2OP6 in jadeite-diopsides found from phase equilibrium measurements at 600°C (Holland, 1979a) and is nearly equivalent to an entropically ideal two site mixing model with a (fictive) WH of 5800 cal. n nJadeite-diopside solid solutions near the 1:1 composition at temperatures of 1000–1500 K are ‘pseudoideal’; that is, they have nearly the free energies of ideal one-site mixtures (Ganguly, 1973). If the order-disorder transition is nearly first-order at about 1000 K, as suggested by Fleetet al. (1978), the pseudo-ideality holds also for ordered omphacites at least somewhat below 1000 K.