The compositions of coexisting pyroxenes and garnet in the system CaO-MgO-Al2O3-SiO2 at 900°–1,100°C and high pressures

The compositions of coexisting orthopyroxene, clinopyroxene and garnet in the CaO-MgO-Al₂O₃-SiO₂ system are fixed at any givenP andT. Reversed hydrothermal experiments over theP/T range 15–40 kb/900°–l,100° C indicate that the garnet composition is nearly constant at Py₈₆Gr₁₄; the Alcontent and Ca/Ca+Mg values of the pyroxenes vary significantly, however:

Synthesis and physical properties of piemontite Ca2Al3-pMn p 3+ (Si2O7/SiO4/O/OH)

Mn³⁺-bearing piemontites and orthozoisites, Ca₂(Al_3-pMn³⁺ _p)-(Si₂O₇/SiO₄/O/OH), have been synthesized on the join Cz (p = 0.0)-Pm (p = 3.0) of the system CaO-Al₂O₃-(MnO·MnO₂)-SiO₂-H₂O atP = 15 kb,T= 800 °C, and \(f_{O_2 } \) of the Mn₂O₃/MnO₂ buffer. Pure Al-Mn³⁺-piemontites were obtained with 0.5≦p≦1.75, whereas atp=0.25 Mn³⁺-bearing orthozoisite (thulite) formed as single phase product. The limit of piemontite solid solubility is found near p=1.9 at the above conditions. Withp>1.9, the maximum piemontite coexisted with a new high pressure phase CMS-X1, a Ca-bearing braunite (Mn _0.2 ²⁺ Ca_0.8)Mn ₆ ³⁺ O₈(SiO₄), and quartz. Al-Mn³⁺-piemontite lattice constants (LC),b ₀,c ₀,V ₀, increase with increasingp:

Garnet-orthopyroxene-plagioclase-quartz barometry: refinement and application to the English River subprovince and the Minnesota River valley

Recent experimental, theoretical, and thermodynamic studies permit better calibration of two reactions for geobarometry: grossular+pyrope+quartz=anorthite+enstatite grossular+almandine+quartz=anorthite+ferrosilite If both reactions are applied using the same thermodynamic data and activity models they should yield the same pressure for a given garnet-pyroxene-plagioclase-quartz assemblage. Application to a variety of high-grade terrains generally yielded excellent results. However, poor results have been obtained for high-Fe rocks which can be traced to errors in activity models for garnet and/or pyroxene. Either a two-site ideal mixing model for orthopyroxene (cf. Wood and Banno 1973) underestimates enstatite activity for high-Fe orthopyroxenes or the Ganguly and Saxena (1984) model overestimates pyrope activity in low-Mg garnets. Application of both barometers to a variety of high-grade terrains gives the following average pressures:

Partitioning of Hf,Lu, Ti,and Mn between olivine,clinopyroxene and basaltic liquid

The crystal/liquid partition coefficients of Lu, Hf, Ti, Mn and Ca have been measured between olivine, clinopyroxene and basaltic melt. The Ti, Mn, and Ca partition coefficients were determined at natural abundance levels. The Lu and Hf partition coefficients were determined at doping levels ranging from 0.5 to 1.5 wt% “trace element” as oxide in order to allow analysis by electron microprobe. Olivine/liquid partition coefficients for Lu, Hf, Ti, Mn, and Ca were determined at 1 bar and temperatures from 1150 to 1177° C. Clinopyroxene/liquid partition coefficients were determined for Lu, Hf, Ti, and Mn at pressures of 10, 15, and 20 kbars and temperatures from 1250 to 1290° C. The olivine/liquid partition coefficients of Hf, Lu, Ti, and Ca are small. D(Hf-ol) is zero within the analytical uncertainty. Both D(Lu-ol) and D(Mn-ol) decrease with increasing temperature, but D(Ti-ol) and D(Ca-ol) are constant over the narrow temperature range studied. The partition coefficient results are summarized below.

A high pressure experimental study on a magnesian-rich leucite-lamproite from the West Kimberley area,Australia: petrogenetic implications

Liquidus and subliquidus phase relations of a leucite-lamproite (wolgidite) from the West Kimberley area, Australia have been studied experimentally under the volatile conditions of 3.22 wt.% H₂O ( \(X_{CO_2 }\) =0.11) and 13.0 wt.% H₂O ( \(X_{CO_2 }\) =0.03) between 10 to 40 kbar. Under these conditions, liquids are vapour undersaturated. In experiments with 13.0 wt.% H₂O, olivine is the liquidus phase up to 24 kbar and orthopyroxene above 24 kbar. Phlogopite and rutile occur close to the liquidus above 16 kbar. Crystallization temperatures of clinopyroxenes are 50–120° C below the liquidus. Based on these results, wolgidite magma is unlikely to be a partial melt of a garnet- or spinel-lherzolite mantle but could be derived from phlogopite+rutile±olivine±or-thopyroxene assemblages occurring as metasomatized mantle.     

The role of water in the 1944 Vesuvius eruption

The P-T path of magma associated with the 1944 Vesuvius eruption has been outlined on the basis of probe mineralogy and the relationships between the crystallising phases. Equilibrium P-T values, obtained from the reactions:

1. CaMgSi₂O_6(liq) = CaMgSi₂O_6(cpx)
2. NaAlSi₃O_{8 (liq)} = NaAlSi₃O_{8 (plag)}
3. CaAl₂Si₂O_{8 (plag)}=CaAl₂SiO_6(cpx)+SiO_2(liq) have been established for three intracrustal crystallisation stages: I) 8.0 kbar and 1255 °C; II) 4.0 kbar and 1178 °C; III) 0.5 kbar and 1105 °C.

The H₂O content in the magma has been estimated from an experimental calibration of \(a_{^{CaMgSi_2 O_6 } }^{liq}\) as a function of \(X_{H_2 O}^{liq}\) at P _tot = 2 kbar. The estimated water contents of the magma for the three stages, I) 0.7%; II) 0.9%; III) 1.1%, are consistent with the pattern of activity of the 1944 Vesuvius eruption and with the relationship between the lavas. The shallow depth of H₂O-saturation of the magma, 0.24 kbar at 1100 °C, is consistent with the eruption sequence of lava flows followed by lava fountain activity.     

Experimental calibration of Forsterite–Anorthite–Ca-Tschermak–Enstatite (FACE) geobarometer for mantle peridotites

The crystallization of plagioclase-bearing assemblages in mantle rocks is witness of mantle exhumation at shallow depth. Previous experimental works on peridotites have found systematic compositional variations in coexisting minerals at decreasing pressure within the plagioclase stability field. In this experimental study we present new constraints on the stability of plagioclase as a function of different Na₂O/CaO bulk ratios, and we present a new geobarometer for mantle rocks. Experiments have been performed in a single-stage piston cylinder at 5–10 kbar, 1050–1150?°C at nominally anhydrous conditions using seeded gels of peridotite compositions (Na₂O/CaO?=?0.08–0.13; X _Cr = Cr/(Cr?+?Al)?=?0.07–0.10) as starting materials. As expected, the increase of the bulk Na₂O/CaO ratio extends the plagioclase stability to higher pressure; in the studied high-Na fertile lherzolite (HNa-FLZ), the plagioclase-spinel transition occurs at 1100?°C between 9 and 10 kbar; in a fertile lherzolite (FLZ) with Na₂O/CaO?=?0.08, it occurs between 8 and 9 kbar at 1100?°C. This study provides, together with previous experimental results, a consistent database, covering a wide range of P–T conditions (3–9 kbar, 1000–1150?°C) and variable bulk compositions to be used to define and calibrate a geobarometer for plagioclase-bearing mantle rocks. The pressure sensitive equilibrium:

$$\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{4}}}^{{\text{Ol}}}}\limits_{{\text{Forsterite}}} +\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{8}}}^{{\text{Pl}}}}\limits_{{\text{Anorthite}}~} =\mathop {{\text{CaA}}{{\text{l}}_{\text{2}}}{\text{Si}}{{\text{O}}_{\text{6}}}^{{\text{Cpx}}}}\limits_{{\text{Ca-Tschermak}}} +{\text{ }}\mathop {{\text{M}}{{\text{g}}_{\text{2}}}{\text{S}}{{\text{i}}_{\text{2}}}{{\text{O}}_{\text{6}}}^{{\text{Opx}}}}\limits_{{\text{Enstatite}}} ,$$

has been empirically calibrated by least squares regression analysis of experimental data combined with Monte Carlo simulation. The result of the fit gives the following equation:

$$P=7.2( \pm 2.9)+0.0078( \pm 0.0021)T{\text{ }}+0.0022( \pm 0.0001)T{\text{ }}\ln K,$$

$${R^2}=0.93,$$

where P is expressed in kbar and T in kelvin. K is the equilibrium constant K?=?a _CaTs × a _en/a _an × a _fo, where a _CaTs, a _en, a _an and a _fo are the activities of Ca-Tschermak in clinopyroxene, enstatite in orthopyroxene, anorthite in plagioclase and forsterite in olivine. The proposed geobarometer for plagioclase peridotites, coupled to detailed microstructural and mineral chemistry investigations, represents a valuable tool to track the exhumation of the lithospheric mantle at extensional environments.

     

Experimental study of subsolidus phase relations and mixing properties of pyroxene and plagioclase in the system Na2O-CaO-Al2O3-SiO2

In the system Na₂O-CaO-Al₂O₃-SiO₂ (NCAS), the equilibrium compositions of pyroxene coexisting with grossular and corundum were experimentally determined at 40 different P-T conditions (1,100–1,400° C and 20.5–38 kbar). Mixing properties of the Ca-Tschermak — Jadeite pyroxene inferred from the data are (J, K): $$\begin{gathered} G_{Px}^{xs} = X_{{\text{CaTs}}} X_{{\text{Jd}}} [14,810 - 7.15T - 5,070(X_{{\text{CaTs}}} - X_{{\text{Jd}}} ) \hfill \\ {\text{ }} - 3,350(X_{{\text{CaTs}}} - X_{{\text{Jd}}} )^2 ] \hfill \\ \end{gathered} $$ The excess entropy is consistent with a complete disorder of cations in the M2 and the T site. Compositions of coexisting pyroxene and plagioclase were obtained in 11 experiments at 1,190–1,300° C/25 kbar. The data were used to infer an entropy difference between low and high anorthite at 1,200° C, corresponding to the enthalpy difference of 9.6 kJ/mol associated with the C \(\bar 1\) =I \(\bar 1\) transition in anorthite as given by Carpenter and McConnell (1984). The resulting entropy difference of 5.0 J/ mol · K places the transition at 1,647° C. Plagioclase is modeled as ideal solutions, C \(\bar 1\) and I \(\bar 1\) , with a non-first order transition between them approximated by an empirical expression (J, bar, K): $$\Delta G_T = \Delta G_{1,473} \left[ {1 - 3X_{Ab} \tfrac{{T^4 - 1,473^4 }}{{\left( {1,920 - 0.004P} \right)^4 - 1,473^4 }}} \right],$$ where $$\Delta G_{1,473} = 9,600 - 5.0T - 0.02P$$ The derived mixing properties of the pyroxene and plagioclase solutions, combined with the thermodynamic properties of other phases, were used to calculate phase relations in the NCAS system. Equilibria involving pyroxene+plagioclase +grossular+corundum and pyroxene+plagioclase +grossular+kyani te are suitable for thermobarometry. Albite is the most stable plagioclase.     

Precision,accuracy and meaning of fission track ages

The precision, meaning, and accuracy of the fission track (ft) dating method are reviewed from an examination of the recent literature as well as previously unpublished data from the author's laboratory. It is concluded that forapparent ft ages (i.e. ages derived from the canonical age equation) a precision (2σ level) of the order of ±4% to ±5% can be reached provided that (i) uranium is sufficiently homogeneously distributed in the dated samples, at least locally; and (ii) a large enough number of tracks can be counted. Model ft ages,i.e. ages for which partial geological track annealing is taken into account, have variable degrees of precision. While model ages obtained with the track-size method seem, as evaluated from the literature, to have usually a limited precision of the order of ±30% (2σ), plateau ages usually have a precision better than ±5% at a 2σ confidence level. Because it provides an objective test on the accuracy of track identification, as well as some insight of the variability of closing temperatures between various samples of a given mineral phase, the Isochronal Plateau (icp) method, when applicable, will be preferred (Poupeauet al 1980a). However, for phases which could be damaged by heating at relatively high temperatures, as for example hydrated glass shards from tephra, an Isothermal Plateau (itp) approach is to be preferred. Due to uncertainties about the value of the²³⁸U spontaneous fission decay constant λ _f as well as difficulties inherent in the dosimetry of thermal neutrons in nuclear reactors, theft method of dating is not an independent one. Presently, it relies on the existence of geological standards (volcanic rocks) of known age, allowing to determine anoperational ‘λ _f ’ value (Naeseret al 1980). Accordingly, the accuracy of anft age is limited by the accuracy on the age of the standard. It should be better than ～5%. For volcanic, hypovolcanic rocks, and shallow intrusives, theft method dates the time of formation, provided they were not further reheated. More generally, the track method providescooling ages. Closing temperatures calculated from laboratory experiments vary from ?300°C to 100°C, according to minerals, for slow cooling rates (～1°C/m.y.). For apatites, recent geological calibrations (Naeseret al 1980; Gleadow and Duddy 1980) confirmed laboratory extrapolations. The association of theft method with other geochronometers is therefore critical to the study of the cooling history of old cratons as well as to the evaluation of uplift/erosion rates in recent belts.     

Ephesite,Na(LiAl2) [Al2Si2O10] (OH)2: I. thermal stability and standard state thermodynamic properties

Ephesite, Na(LiAl₂) [Al₂Si₂O₁₀] (OH)₂, has been synthesized for the first time by hydrothermal treatment of a gel of requisite composition at 300≦T(° C)≦700 and \(P_{H_2 O}\) upto 35 kbar. At \(P_{H_2 O}\) between 7 and 35 kbar and above 500° C, only the 2M₁ polytype is obtained. At lower temperatures and pressures, the 1M polytype crystallizes first, which then inverts to the 2M₁ polytype with increasing run duration. The X-ray diffraction patterns of the 1M and 2M₁ poly types can be indexed unambiguously on the basis of the space groups C2 and Cc, respectively. At its upper thermal stability limit, 2M₁ ephesite decomposes according to the reaction (1) $$\begin{gathered} {\text{Na(LiAl}}_{\text{2}} {\text{) [Al}}_{\text{2}} {\text{Si}}_{\text{2}} {\text{O}}_{{\text{10}}} {\text{] (OH)}}_{\text{2}} \hfill \\ {\text{ephesite}} \hfill \\ {\text{ = Na[AlSiO}}_{\text{4}} {\text{] + LiAl[SiO}}_{\text{4}} {\text{] + }}\alpha {\text{ - Al}}_{\text{2}} {\text{O}}_{\text{3}} {\text{ + H}}_{\text{2}} {\text{O}} \hfill \\ {\text{nepheline }}\alpha {\text{ - eucryptite corundum}} \hfill \\ \end{gathered}$$ Five reversal brackets for (1) have been established experimentally in the temperature range 590–750° C, at \(P_{H_2 O}\) between 400 and 2500 bars. The equilibrium constant, K, for this reaction may be expressed as (2) $$log K{\text{ = }}log f_{{\text{H}}_{\text{2}} O}^* = 7.5217 - 4388/T + 0.0234 (P - 1)T$$ where \(f_{H_2 O}^* = f_{H_2 O} (P,T)/f_{H_2 O}^0\) (1,T), with T given in degrees K, and P in bars. Combining these experimental data with known thermodynamic properties of the decomposition products in (1), the following standard state (1 bar, 298.15 K) thermodynamic data for ephesite were calculated: H _f,298.15 ⁰ =-6237372 J/mol, S _298.15 ⁰ =300.455 J/K·mol, G _298.15 ⁰ =-5851994 J/mol, and V _298.15 ⁰ =13.1468 J/bar·mol.     

Carbon Dioxide in igneous petrogenesis: I

A number of experimental CO₂ solubility data for silicate and aluminosilicate melts at a variety of P- T conditions are consistent with solution of CO₂ in the melt by polymer condensation reactions such as SiO _4(m ^4? +CO_2(v)+Si _n O _3n+1(m) ⁽²ⁿ⁺¹⁾ ?Si _n+1O _3n+4(m) ^(2n+4)? +CO _3(m ^)2? . For various metalsilicate systems the relative solubility of CO₂ should depend markedly on the relative Gibbs free change of reaction. Experimental solubility data for the systems Li₂O-SiO₂, Na₂O-SiO₂, K₂O-SiO₂, CaO-SiO₂, MgO-SiO₂ and other aluminosilicate melts are in complete accord with predictions based on Gibbs Free energies of model polycondesation reactions. A rigorous thermodynamic treatment of published P- T-wt.% CO₂ solubility data for a number of mineral and natural melts suggests that for the reaction CO_2(m) ? CO_2(v)

1. CO₂-melt mixing may be considered ideal (i.e., { \(a_{{\text{CO}}_{\text{2}} }^m = X_{{\text{CO}}_{\text{2}} }^m \) );
2. \(\bar V_{{\text{CO}}_{\text{2}} }^m \) , the partial molal volume of CO₂ in the melt, is approximately equal to 30 cm³ mole^?1 and independent of P and T;
3. Δ C _p ⁰ is approximately equal to zero in the T range 1,400° to 1,650 °C and
4. enthalpies and entropies of the dissolution reaction depend on the ratio of network modifiers to network builders in the melt. Analytic expressions which relate the CO₂ content of a melt to P, T, and \(f_{{\text{CO}}_{\text{2}} } \) for andesite, tholeiite and olivine melilite melts of the form

$$\ln X_{{\text{CO}}_{\text{2}} }^m = \ln f_{{\text{CO}}_{\text{2}} } - \frac{A}{T} - B - \frac{C}{T}(P - 1)$$ have been determined. Regression parameters are (A, B, C): andesite (3.419, 11.164, 0.408), tholeiite (14.040, 5.440,0.393), melilite (9.226, 7.860, 0.352). The solubility equations are believed to be accurate in the range 3<P<30 kbar and 1,100°<T<1,650 °C. A series of CO₂ isopleth diagrams for a wide range of T and P are drawn for andesitic, tholeiitic and alkalic melts.     

Alpha-radioactivity-related upper age limit for thermoluminescence dating?

A systematic underestimation of the age of mineralisation by the thermoluminescence (tl) technique has been observed in a variety of samples older than Quaternary although their naturaltl was not saturated. The samples included calcites, oozes, lime stones, shales, gypsum, basalts and dolerites. It is shown that thetl build-up in nature reaches a dynamic equilibrium level much ahead of the lifetime of thetl trap concerned and is solely determined by the alpha radioactivity of the sample; the validity fortl dating does not exist once such an equilibrium is reached. For the samples considered, the limiting Paleo-alpha dose fortl dating validity works out to be about 150 kilorads; beyond this dose, thetl age and the geological age bears a ratio given by \(t'/t = a\left[ {\smallint _0^t \dot D_\alpha dt} \right]^{ - b} \) wherea andb are constants and \(\dot D_\alpha \) is the annual alpha irradiation rate in the sample. For a suite of samples withb≠1, relative dating seems possible by thetl technique. It may be generalised that samples with 1ppm level of U, Th content cannot betl dated if they are older than about 500 kiloyears even though theirntl trap lifetimes may be 100 myrs; conversely, a 1000 myr-old sample can betl dated only if its U, Th content is much less than ppb levels and itstl trap lifetime greater than 10¹⁰ years.     

Thermodynamic calculation of peridotite phase relations in the system MgO-Al2O3-SiO2-Cr2O3, with some geological applications

The system MgO-Al₂O₃-SiO₂(MAS) comprises 88–90% of the bulk composition of an average peridotite. The MAS ternary is thus a suitable starting point for exploring peridotite phase relations in multicomponent natural systems. The basic MAS phase relations may be treated in terms of the reactions (see list of symbols etc).

1. py (in Gt)=en (in Opx)+mats (in Opx),
2. en (in Opx)+sp (in Sp)=mats (in Opx)+fo (in Ol), and
3. py (in Gt)+fo (in Ol)=en (in Opx)+sp (in Sp).

Extensive reversed phase equilibria data on these three reactions by Danckwerth and Newton (1978), Perkins et al. (1981), and Gasparik and Newton (1984) employing identical experimental methods in the same laboratory have been used by us to deduce the following internally consistent thermodynamic data applying the technique of linear programming:ΔH ₂₉₈₍₁₎ ⁰ = 2536 J, ΔS ₂₉₈₍₁₎ ⁰ =? 6.064 J/K;ΔH ₂₉₈₍₂₎ ⁰ = 29435 J, ΔS ₂₉₈₍₂₎ ⁰ = 8.323 J/K; andΔH ₂₉₈₍₃₎ ⁰ =?26899 J, ΔS ₂₉₈₍₃₎ ⁰ =?14.388 J/K.These data are also found to be consistent with results of calorimetry. Figure 2 shows the calculated phase relations based on our thermodynamic data; they are consistent with the phase equilibria experiments. Successful extension of the MAS phase relations to multicomponent peridotites pivots on the extent to which the effects of the “non-ternary” (i.e. other than MAS) components can be quantitatively handled. Particularly hazardous in this context is Cr₂O₃, although it barely makes up 0.2 to 0.5 wt% of such rocks. This is because Cr⁺³ fractionates extremely strongly into Sp. This study focuses on the peridotite phase relations in the MgO-Al₂O₃-SiO₂-Cr₂O₃ (MASCr) quaternary. Thermodynamic calculations of the MASCr phase relations have been accomplished by using ΔH ₂₉₈ ⁰ and ΔS ₂₉₈ ⁰ values for the reactions (1) through (3) indicated above, in conjunction with data on thermodynamic mixing properties of

1. binary Sp (sp-pc) crystalline solution (Oka et al. 1984),
2. ternary Opx (en-mats-mcts) crystalline solution (this study), and
3. binary Gt (py-kn) crystalline solution (this study).

The results are shown in P-T projections (Figs. 3a and b) and isobaric-isothermal sections of MASCr in a projection through the component fo onto the SiO₂-Al₂O₃-Cr₂O₃ ternary (Figs. 4a and b). The most important results of this work may be summarized as follows:

1. With increasing incorporation of Cr⁺³ into Sp and Gt, the X _mats isopleths of the reactions (1) and (2) are shifted to higher temperatures (Fig. 3a); simultaneously, the spinel-peridotite to garnet-peridotite phase transition is moved to higher pressures (Fig. 3b).
2. At identical P and T, the X _mats values of Opx coexisting in equilibrium with Ol and Sp is strongly dependent upon the X _pc value in the latter phase (Figs. 4a and b). Accurate correction for the composition of Sp is, therefore, a necessary precondition for geothermometry of the spinelperidotites.
3. The discrepant temperatures reported by Sachtleben und Seck (1981, Fig. 5) from the spinel-peridotites of the Eifel area (systematically too high temperatures as a function of X _pc in Sp) are demonstrated to be the result of ignoring the nonideality in the chromian spinels.

     

An experimental study of the partitioning of Fe and Mg between garnet and orthopyroxene

The partitioning of Fe and Mg between garnet and aluminous orthopyroxene has been experimentally investigated in the pressure-temperature range 5–30 kbar and 800–1,200° C in the FeO-MgO-Al₂O₃-SiO₂ (FMAS) and CaO-FeO-MgO-Al₂O₃-SiO₂ (CFMAS) systems. Within the errors of the experimental data, orthopyroxene can be regarded as macroscopically ideal. The effects of Calcium on Fe-Mg partitioning between garnet and orthopyroxene can be attributed to non-ideal Ca-Mg interactions in the garnet, described by the interaction term:W _CaMg ^ga -W _CaFe ^ga =1,400±500 cal/mol site. Reduction of the experimental data, combined with molar volume data for the end-member phases, permits the calibration of a geothermometer which is applicable to garnet peridotites and granulites: $$T(^\circ C) = \left\{ {\frac{{3,740 + 1,400X_{gr}^{ga} + 22.86P(kb)}}{{R\ln K_D + 1.96}}} \right\} - 273$$ with $$K_D = {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } \mathord{\left/ {\vphantom {{\left\{ {\frac{{Fe}}{{Mg}}} \right\}^{ga} } {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}} \right. \kern-\nulldelimiterspace} {\left\{ {\frac{{Fe}}{{Mg}}} \right\}}}$$ and $$X_{gr}^{ga} = (Ca/Ca + Mg + Fe)^{ga} .$$ The accuracy and precision of this geothermometer are limited by largerelative errors in the experimental and natural-rock data and by the modest absolute variation inK _D with temperature. Nevertheless, the geothermometer is shown to yield reasonable temperature estimates for a variety of natural samples.     

An empirical Redlich-Kwong-type equation of state for water to 1,000 °C and 200 Kbar

An empirically derived Redlich-Kwong type of equation of state (ERK) is proposed for H₂O, expressing a, the term related to the attraction between the molecules, as a pressure-independent function of temperature, and b, the covolume, as a temperature-independent function of pressure. The coefficients of a(T) and b(P) were derived by least squares non-linear regression, using P-V-T data given by Burnham et al. (1969b) and Rice and Walsh (1957) in conjunction with more precise recent data obtained by Tanishita et al. (1976), Hilbert (1979) and Schmidt (1979): $$a(T) = 1.616 x 10^8 - 4.989 x 10^4 T - 7.358 x 10^9 T^{ - 1} $$ and $$ = \frac{{1 + 3.4505x 10^{--- 4} P + 3.8980x 10^{--- 9} P^2 - 2.7756x 10^{--- 15} P^3 }}{{6.3944x 10^{--- 2} + 2.3776x 10^{--- 5} + 4.5717x 10^{--- 10} P^2 }}$$ , where T is expressed in Kelvin and P in bars. The ERK works very well at upper mantle conditions, at least up to 200 kbar and 1,000 °C. At subcritical conditions and those somewhat above the critical point, it still reproduces the molar Gibbs energy, \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) , with a maximum deviation of 400 joules. Thus, for the purpose of calculation of geologically interesting heterogeneous equilibria, it predicts the thermodynamic properties of H₂O well enough. The values of molar volume, \(\tilde V_{{\text{H}}_{\text{2}} {\text{O}}} \) , and \(\tilde G_{{\text{H}}_{\text{2}} {\text{O}}} \) are tabulated in the appendix over a considerable P-T range. A FORTRAN program generating these functions as well as a FORTRAN subroutine for calculating the fugacity values, \(f_{{\text{H}}_{\text{2}} {\text{O}}} \) for incorporation into existing programs, are available upon request.     

On the nonstoichiometry and point defects of olivine

This paper presents the point-defect thermodynamics for fayalite and olivine solid solutions (Fe _x Mg_1?x )₂SiO₄. By means of thermogravimetry, the metal-to-oxygen ratio of these silicates has been determined as a function of oxygen potential, compositionx and temperature. Experiments were performed in the range of 1,000° C≦T≦1,280° C and 0.2≦x≦1.0. It is found that V _Me ^″ , Fe _Me ^· and the associate {Fe′ _Si ^′ Fe _Me ^· } are the majority defects. With this knowledge it is possible to calculate the nonstoichiometry at given temperature as a function of \(p_{O_2 } \) and \(a_{SiO_2 } \) . The cation vacancy concentration shows a \(p_{O_2 }^{1/5} \) -dependence (forx≧0.2) and increases at givenT and \(p_{O_2 } \) almost exponentially with compositionx. In the composition range studied here, the silicates show an oxygen excess, and FeO is more soluble in the olivine than SiO₂.     

High-pressure phase transition in MnTiO3 from the ilmenite to the LiNbO3 structure

Crystals of a high-pressure phase of MnTiO₃ have been synthesized at pressures of 60 kbar using the SAM-85 cubic-anvil high pressure apparatus. Although all crystals examined were twinned on (10 \(\bar 1\) \(\bar 2\) ), a set of diffraction intensities that are essentially unaffected by the twinning were obtained. Three possible structure models were considered: (1) the corundum (completely disordered Mn and Ti), (2) the partially-disordered ilmenite, and (3) the LiNbO₃ structures. The R factors of the corundum and the disordered ilmenite models were much larger than that of LiNbO₃. Using structure factors unaffected by twinning, the final LiNbO₃-type refinement gave R _w=0.037 and R=0.034. The averaged bond lengths for Mn-O and Ti-O were consistent with ones calculated using Shannon and Prewitt's (1969) radii. The study concludes that MnTiO₃ II actually has an ordered LiNbO₃-type structure rather than the disordered one as reported previously. From the analysis of the two MnTiO₃ structures, the transition can be related to a cation reordering process, in which half of the cations participate, accompanied by the rotation of oxygens to accommodate the cations.     

Experimental study of the physico-chemical conditions of skarn formation

Experimental results show that skarns can—800°C and 500–1,000 bars. Starting materials include intermediate-acidic igneous rocks, volcanic rocks, metamorphic rocks, carbonates of various purities and chemical reagents of analytical purity-grade. Experimental media are: NaCl, NaCl+CaCl₂, NaCl+CaCl₂+MgCl₂, Na₂CO₃ and Na₂SiO₃ solutions. Experimental results show that skarns can be formed under wide physico-chemical conditions:T=400°–800°C,P=500–1,000 bars,pH=4–11, and \(f_{O_2 } = 10^{ - 23} - 10^{ - 11} \) bar. The mineralogy of skarns and the chemical compositions of skarn minerals are generally controlled by the combined factors: the chemical composition of the original rocks, pH values, redox conditions, temperatures and pressures. Isomorphous substitution may have agreat effect on the temperature of formation andfo ₂ of some major skarn minerals. It is found that skarnization occurs preferentially in NaCl and NaCl+CaCl₂ solutions and subortinately in MaCO₃ and Na₂SiO₃ soiutions.     

Mica-feldspar equilibria in supercritical alkali chloride solutions

The equilibrium position of the reaction $$\begin{gathered} 1.5 KAlSi_3 O_8 + HCl = 0.5 KAl_3 Si_3 O_{10} (OH)_2 \hfill \\ + 3SiO_2 + KCl \hfill \\ \end{gathered} $$ has been located at 1 and 2 kb pressure and temperatures between 600° and 670° C using the Ag-AgCl buffer. These data can be combined with information on the dissociation of KC1, HC1 and H₂O to determine species abundances in supercritical aqueous fluids in equilibrium with muscovite — K-feldspar — quartz assemblages. Chloride species become increasingly associated with increasingT, increasing total molality, (m _tot or \(m_{Cl_{tot} } \) ), and decreasing \(P_{H_2 O} \) . Master variable diagrams indicate that the pH of the solutions may vary from near neutral to quite acid. Published data on the paragonite-albite-quartz reaction and exchange reactions involving feldspars and micas were included to calculate speciation in mica-feldspar-NaCl-KCl-HCl-H₂O fluids at 2kb pressure and temperatures between 300° and 600° C. The data are not accurate enough to distinguish different feldspar structural states. Concentration gradients were calculated for individual species between K-feldspar+quartz, muscovite+quartz and andalusite+quartz assemblages at 500° C, 2 kb. Assuming that the proton diffuses most rapidly and that there are no [H⁺] gradients, the molality of the solution must vary 30-fold, with feldspar+quartz at the more concentrated side. The data on mica-feldspar-chloride equilibria are used to interpret the spacial distribution of micas, feldspar and quartz in microfolds. This distribution can be accounted for by pressure solution, due to the fact that non-hydrostatic pressure affects congruently dissolving minerals, auch as quartz, differently from minerals which dissolve incongruently, such as micas and feldspars. We postulate, that during folding at constant \(P_{H_2 O} \) ,T and \(m_{Cl - } \) , gradients in KC1 and SiO₂ are created by stress differences between hinge and limb of a microfold, such that both migrate to the hinge area where quartz precipitates and muscovite is converted to K-felspar, thus accounting for the observed mineral distribution.     

High-pressure phengite decomposition in the Weissenstein eclogite,Münchberger Gneiss Massif,Germany

The petrography, mineral chemistry and petrogenesis of a sample from the Weissenstein eclogite, Bavaria, Germany, has been investigated. The total mineral assemblage comprises garnet, clinopyroxene_I+II, quartz, amphibole_I+II, rutile, phengite, epidote/allanite, plagioclase, biotite, apatite, pumpellyite, titanite (sphene), zircon, alkali feldspar and calcite. Textural observations combined with geothermobarometry (Fe/Mg distribution between clinopyroxene/garnet and phengite/garnet; jadeite-content of omphacite, Si-content of phengite, and An-content of plagioclase) provide indications of two different stages in the metamorphic evolution of the rock. The main phengitequartz-eclogite mineral equilibration occurred at minimum P=13–17kbar, minimum T=620±50° C; the retrograde symplectite stage (clinopyroxene_II, amphibole_II, biotite, plagioclase) occurred at P _total between 12 and 8.5 kbar. Reactions of the symplectite stage are:

1. phengite (core) + Na₂O_aq + CaO_aq=phengite (rim) + biotite + plagioclase + K₂O_aq + H₂O
2. phengite (core) + clinopyroxene_I + Na₂O_aq=phengite (rim + biotite + plagioclase + amphibole_II + SiO₂ + K₂O_aq + CaO_aq + H₂O
3. clinopyroxene_I + SiO₂ + K₂O_aq + H₂O=clinopyroxene_II + plagioclase+amphibole_II + Na₂O_aq + CaO_aq

The phengite decomposition produces H₂O, whereas the clinopyroxene decomposition consumes H₂O. The estimated P-T-conditions for the Weissenstein eclogite are in the same order of magnitude as those for other eclogite bodies from the Alps and Caledonides believed to be related to subduction processes.