A re-evaluation of the olivine-spinel geothermometer: Discussion

The recent contribution on the olivine-spinel geothermometer by Roeder, Campbell, and Jamieson (1979) contains several noteworthy inconsistencies that result in what we consider misleading conclusions. The paper fails to present an up-to-date reevaluation of the geothermometer. We note the following points: (1) The criteria of geological reasonableness used by Roeder et al. to evaluate previously proposed versions of the geothermometer are not applied to their own revised model. (2) The experimental results presented are (a) of questionable quality as equilibrium data, and (b) if anything, more supportive of other published calibrations than of the revised thermometer put forward by the authors. (3) Despite the repeated acknowledgment by Roeder et al. of the problems inherent in formulating a thermodynamic model of the geothermometer based on a set of (independently gathered) free-energy data for the spinel end-members, the authors do just that.We conclude that the thermometric Eq. (3) derived by Roeder et al. does not give meaningful temperatures. Reconciliation of their isotherms with those inferred from suites of natural samples would suggest kinetic problems in interpreting the latter, for which there is no evidence. We do not dispute the likelihood that olivine and spinel undergo exchange re-equilibration at subsolidus temperatures in slowly-cooled intrusions. However, we believe that the suggested closure temperatures (in the range 500°–800° C) are inaccurate, since their proposed geothermometer yields temperature-composition relations that are entirely at odds with those indicated by metamorphic assemblages in that temperature range.     

An Improved Experimental Calibration of the Olivine-Spinel Geothermometer

The calibration of the olivine-spinel geothermometer by Fabries(1979) is commonly adopted by a number of petrologists.But the temperatures calculated in this way for ultramafic focks are significantly lower than those obtained by the pyroxene geothermometers.These O1-Sp temperatures are also lower than those measured experi-mentally in the natural system (four-phase lherzolite).Different rates of cation diffusion cannot fully account for these differences.The temperature deviation is actually related to the inconsistencies between natural and experimental data which support the calibration .A re-evaluation of the calibration is proposed on the basis of a set of new experimental data.     

A nepheline-alkali feldspar geothermometer

A nepheline-alkali feldspar geothermometer has been developed which is based on the thermodynamics of an Na—K exchange reaction between nepheline and alkali feldspar. The activities are formulated in terms of site occupancies, and the regular solution model is used to represent non-ideal mixing of the cations on each site. The distribution of Na and K on the alkali sites in nepheline is calculated from published nepheline-brine ion-exchange data. The standard Gibbs energy of the geothermometer reaction is calculated from experimental data on coexisting nephelines and alkali feldspars (Hamilton and MacKenzie, 1960, 1965). The geothermometer is applied to nepheline syenites from the Precambrian Igdlerfigssalik intrusion, S.W. Greenland, and gives temperatures which suggest that nepheline and alkali feldspar continue to equilibrate with cooling after they crystallise from the magma.     

A precise olivine-augite Mg-Fe-exchange geothermometer

 Olivine and augite that were experimentally equilibrated in the temperature interval 1175–1080°C at 1 bar in natural basaltic and andesitic bulk compositions are used to calibrate an Mg-Fe²⁺ cation-exchange geothermometer. Within its temperature interval of experimental calibration, and over a broad range in olivine Mg/Fe ratio, the geothermometer has a standard error of ±6°C. In compositionally simpler synthetic systems, the same calibration retrieves appropriate experimental temperatures up to at least 1250°C. In application to intermediate and felsic volcanic rocks erupted at ∼1080 –800°C (below the range of experimental calibration), calculated olivine-augite temperatures are in good agreement with Fe-Ti oxide thermometry in the same samples. These results encourage confidence in the olivine-augite geothermometer over at least the 800–1250°C interval at low pressures. Sparse experimental data up to 1250°C at higher pressures for olivine + augite in the assemblage olivine + plagioclase + augite ± pigeonite or orthopyroxene suggest that the low-pressure calibration recovers experimental temperatures without systematic bias to pressures of 10 kbar. Examples illustrate applications to determining igneous equilibration temperatures in holocrystalline extrusive and intrusive rocks, and to estimating intratelluric H₂O content dissolved in magmas. Received: 24 February 1995 / Accepted: 1 March 1996     

Garnet-clinopyroxene geothermometer

A garnet-clinopyroxene geothermometer based on the available experimental data on compositions of coexisting phases in the system MgO-FeO-MnO-Al₂O₃-Na₂O-SiO₂ is as follows: $$T({\text{}}K) = \frac{{8288 + 0.0276 P {\text{(bar)}} + Q1 - Q2}}{{1.987 \ln K_{\text{D}} + 2.4083}}$$ where P is pressure, and Q1, Q2, and K _D are given by the following equations $$Q1 = 2,710{\text{(}}X_{{\text{Fe}}} - X_{{\text{Mg}}} {\text{)}} + 3,150{\text{ }}X_{{\text{Ca}}} + 2,600{\text{ }}X_{{\text{Mn}}} $$ (mole fractions in garnet) $$\begin{gathered}Q2 = - 6,594[X_{{\text{Fe}}} {\text{(}}X_{{\text{Fe}}} - 2X_{{\text{Mg}}} {\text{)]}} \hfill \\{\text{ }} - 12762{\text{ [}}X_{{\text{Fe}}} - X_{{\text{Mg}}} (1 - X_{{\text{Fe}}} {\text{)]}} \hfill \\{\text{ }} - 11,281[X_{{\text{Ca}}} (1 - X_{{\text{Al}}} ) - 2X_{{\text{Mg}}} 2X_{{\text{Ca}}} ] \hfill \\{\text{ + 6137[}}X_{{\text{Ca}}} (2X_{{\text{Mg}}} + X_{{\text{Al}}} )] \hfill \\{\text{ + 35,791[}}X_{{\text{Al}}} (1 - 2X_{{\text{Mg}}} )] \hfill \\{\text{ + 25,409[(}}X_{{\text{Ca}}} )^2 ] - 55,137[X_{{\text{Ca}}} (X_{{\text{Mg}}} - X_{{\text{Fe}}} )] \hfill \\{\text{ }} - 11,338[X_{{\text{Al}}} (X_{{\text{Fe}}} - X_{{\text{Mg}}} )] \hfill \\\end{gathered} $$ [mole fractions in clinopyroxene Mg = MgSiO₃, Fe = FeSiO₃, Ca = CaSiO₃, Al = (Al₂O₃-Na₂O)] K _D = (Fe/Mg) in garnet/(Fe/Mg) in clinopyroxene. Mn and Cr in clinopyroxene, when present in small concentrations are added to Fe and Al respectively. Fe is total Fe²⁺+Fe³⁺.     

A note on the calibration of the garnet-cordierite geothermometer and geobarometer

Experimental and theoretical considerations indicate that the distribution coefficient for iron and magnesium between coexisting garnet and cordierite increases with temperature in the assemblage cordierite-garnet-sillimanite-quartz. This conclusion is confirmed by distribution coefficients from natural garnet and cordierite from geologically well defined settings. The only published calibration which incorporates this feature is that of Currie (1971), and this is the only calibration which can be qualitatively correct although it may be wrong in detail. Other calibrations encounter catastrophes, particularly in andalusite-bearing assemblages.     

An olivine-clinopyroxene geothermometer

The iron-magnesium exchange reaction between olivine and calcium-rich clinopyroxene is formulated as a geothermometer. It is shown that the clinopyroxene M1 site must be nonideal and it is expressed as a regular solution. The appropriate mixing parameters are calculated from a set of groundmass olivine-clinopyroxene pairs from lavas for which there are groundmass iron-titanium oxide temperatures. The pressure dependence of the geothermometer is calculated from abailable experimental work, and is approximately 5°C per kilobar. Layered gabbros from the Kap Edvard Holm Complex, East Greenland, show no significant variation of temperature with structural height in the intrusion, while those of Skaergaard give temperatures which do not have a consistent variation with height. Continued equilibration during post-crystallisation cooling is a possibility in slowly cooled intrusions. Inclusions in diamond give a pressure-temperature line consistent with formation at 1300°C at 55 kb, 1400°C 72 kb and 1500°C 90 kb. Ultrabasic xenoliths in Basutoland kimberlites have similar pressure-temperature lines. Lavas, including alkali basalts, basanites, andesites and rhyolites give temperatures from 1025°C to 890° C.     

A revision of the garnet-clinopyroxene Fe2+-Mg exchange geothermometer

A comprehensive experimental dataset was used to analyse the compositional dependence of the garnet-clinopyroxene Fe²⁺/Mg partition coefficient (K _d). The Mg no. of garnet was found to have a significant effect on the K _d, in addition to calcium content of garnet. An empirical model was developed to relate these effects with equilibrium temperature and pressure in the form of a conventional geothermometer, T(K) = { – 1629[X^Gt _Ca]² + 3648.55[X^Gt _Ca] – 6.59[Mg no. (Gt)] + 1987.98 + 17.66P (kbar)}/(In k_d + 1.076). Application of this thermometer produced reasonable temperature estimates for rocks from the lower crust (garnet amphibolites, granulites and eclogites) and the upper mantle (eclogite and lherzolite xenoliths in kimberlites, mineral inclusions in diamonds).     

Regression diagnostics and robust regression in geothermometer/geobarometer calibration: the garnet-clinopyroxene geothermometer revisited

Abstract The calibration of geothermometers and geobarometers should involve not only the determination of the parameters in the equation used, but also the uncertainties on, and the correlations between, these parameters. This necessitates the use of a technique such as least squares. Given the poor performance of least squares in the presence of outliers in the data, techniques for identifying outliers for exclusion—regression diagnostics, and techniques for handling data which include outliers—robust regression and jackknifing, are essential. These techniques are summarized and their importance is emphasized, and they are applied to the calibration of the garnet-clinopyroxene Fe-Mg exchange geothermometer.
The experimental data of Raheim & Green (1974) and Ellis & Green (1979) are explored using regression diagnostics to discover outliers in the data. After exclusion of the two influential outliers found, a new geothermometer equation for garnet-clinopyroxene Fe-Mg exchange is derived using robust regression and based on all the data: thus, T (K) = 2790 + 10 P + 3140x_ca,g/1.735 + In K _D where T is in Kelvin and P is in kbar. This equation, as might be hoped, is essentially identical to that of Ellis & Green (1979). Equations for calculating the uncertainty in a calculated temperature, contributed by uncertainties in the calibration, are also derived.     

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.     

黑云母—斜方辉石温度计的重新标度及其应用

黑云母 斜方辉石是较为常见的共生矿物对, 它们之间 Ｆｅ Ｍｇ 交换模式反应的标准熵变与标准体积变化量之比很大, 具备了构成温度计的必要条件。根据 Ｆｏｎａｒｅｖ ａｎｄ Ｋｏｎｉｌｏｖ 的平衡实验数据, 考虑了黑云母、斜方辉石中 Ｆｅ Ｍｇ 的非理想混合效应, 得出了合理的黑云母、斜方辉石中 Ｆｅ Ｍｇ 的交换能数据。此外还采纳了 Ｄａｓｇｕｐｔａ 等关于黑云母活度的数据、ｖｏｎ Ｓｅｃｋｅｎｄｏｒｆｆ ａｎｄ Ｏ＇ Ｎｅｉｌｌ关于斜方辉石活度的数据和 Ｐａｔｔｉｎｏ Ｄｏｕｃｅ 等关于黑云母中 ＡｌⅥ、 Ｔｉ对黑云母活度效应的数据, 重新标度了黑云母 斜方辉石温度计。该温度计重现实验温度的误差为±６０℃, 应用于天然岩石的温度计算误差一般小于±７０℃, 适用于绿帘角闪岩相至麻粒岩相的变质岩变质温度的估算。     

锗橄榄石-尖晶石扭转大变形实验研究

对(Mg,Ni)2GeO4尖晶石一橄榄石集合体进行了高温高压扭转大变形实验研究。试验在一台高分辨率的气体介质试验机上进行,试验温度为1473K,围压为300MPa,应变率为10^-4～10^-5S^-1,剪切应力为80～250MPa,剪切应变为30％～700％。将变形后试件沿轴向切开进行了显微结构分析,确定了两相成分的比值。利用EBSD方法分别对变形前后试件中的橄榄石和尖晶石中的晶格最优取向(LPO)进行了测定,由微结构的差异确定了变形机制及两相材料的相对强度。     

Mechanism of the olivine-spinel transformation in Co2SiO4

An experiment conducted in a 2000-ton uniaxial split-sphere apparatus (USSA-2000) utilizes large sample volume and a substantial temperature gradient to synthesize intergrowths of the olivine and spinel polymorphs of Co₂SiO₄. The olivine starting material consists of a finegrained fraction (<20μm) which records the stable polymorphs along the length of the sample plus large olivine grains (100–500 μm) which help decipher the mechanism of the phase transformation. At conditions near equilibrium, the olivine-spinel transformation in the large grains occurs by inward growth of a few large single crystals of spinel nucleated on the surfaces of the olivine. The overall rate of transformation is governed by the mobility of the interphase boundary, whose morphology is crystallographically controlled by the spinel. No renucleation of spinel is observed in the host olivine crystal, even in the region immediately adjacent to the olivine/spinel interface; analysis of this region with transmission electron microscopy reveals an extremely high density of dislocations induced by plastic flow accommodating the volume change associated with the phase transformation.     

TitaniQ: a titanium-in-quartz geothermometer

Titanium is one of many trace elements to substitute for silicon in the mineral quartz. Here, we describe the temperature dependence of that substitution, in the form of a new geothermometer. To calibrate the “TitaniQ” thermometer, we synthesized quartz in the presence of rutile and either aqueous fluid or hydrous silicate melt, at temperatures ranging from 600 to 1,000°C, at 1.0 GPa. The Ti contents of quartz (in ppm by weight) from 13 experiments increase exponentially with reciprocal T as described by:

A new chlorite geothermometer for diagenetic to low-grade metamorphic conditions

The evolution of chlorite composition with temperature (and pressure) serves as basis to a number of chlorite chemical thermometers, for which the oxidation state of iron has been recognised as a recurrent issue, especially at low temperature (T). A new chlorite geothermometer that does not require prior Fe³⁺ knowledge is formulated, calibrated on 161 analyses with well-constrained T data covering a wide range of geological contexts and tested here for low-T chlorites (T < 350 °C and pressures below 4 kbar). The new solid-solution model used involves six end-member components (the Mg and Fe end-members of ‘Al-free chlorite S’, sudoite and amesite) and so accounts for all low-T chlorite compositions; ideal mixing on site is assumed, with an ordered cationic distribution in tetrahedral and octahedral sites. Applied to chlorite analyses from three distinct low-T environments for which independent T data are available (Gulf Coast, Texas; Saint Martin, Lesser Antilles; Toyoha, Hokkaido), the new pure-Fe²⁺ thermometer performs at least as well as the recent models, which require an estimate of Fe³⁺ content. This relief from the ferric iron issue, combined with the simple formulation of the semi-empirical approach, makes the present thermometer a very practical tool, well suited for, for example, the handling of large analytical datasets—provided it is used in the calibration range (T < 350 °C, P < 4 kbar).     

A chlorite solid solution geothermometer the Los Azufres (Mexico) geothermal system

Chlorite constitutes a major hydrothermal alteration product of metamorphism of andesites, in the active geothermal system of Los Azufres (Mexico). Electron microprobe analyses performed on a set of crystals from each sample show wide variations in composition. Correlation coefficients among chemical constituents were calculated. It is shown that the tetrahedral charge is positively correlated with the octahedral vacancy and negatively with the iron content, and there is almost no correlation with the octahedral aluminium and magnesium content. A procedure is proposed to select end-members and substitution vectors, and to give a general formula for these chlorites.Their formation temperatures are estimated with great accuracy, combining results of microthermometric data on fluid inclusions from gangue minerals of chlorites (quartz, calcite), direct measurements in wells (Kuster equipment), and chemical geothermometers. Correlations between chlorite compositions, range and nature of site occupancy, and temperature are good. Formation temperatures of chlorites range from 130° C to 300° C. As no other thermodynamic parameter varies significantly in the studied field (composition of the host rocks, nature of the geothermal fluids, pressure, ...), these variations of site occupancy (mainly Al(IV) and the octahedral occupancy (6-Al(VI)-(Mg+Fe(2+)) = VAC) are considered mainly as temperature dependent.Molar fractions of each end-member show very different variations with increasing temperature: X-kaolinite decreases, and X-chamosite increases, while X-talc-3 brucite does not show significant change. From these data, activity coefficients and standard state chemical potential of major components, and molar free energy formation of chlorite have been calculated for each temperature of crystallisation.     

Towards a more practical two-feldspar geothermometer

The thermodynamic basis of several recent attempts to formulate a simple two-feldspar geothermometer is discussed, together with a review of earlier empirical geothermometers and ones based on experimental studies in the ternary feldspar system. It is shown that double-binary thermometers which involve the combination of regular solution mixing models for the binary alkali feldspar system with ideal mixing in plagioclases do not give a satisfactory representation of two-feldspar relations, especially for albite-rich compositions where a critical point exists. Thermometers based on mixing parameters for ordered alkali feldspar frameworks are even more unjustified both because low-plagioclases are certainly non-ideal, and because of uncertainty in knowing the degree of Al-Si order in the alkali feldspar when exchange equilibrium was achieved. A thermodynamic thermometer requires knowledge of ternary activities which are at present unknown.Experimental determinations of relationships in the ternary feldspar system are reviewed and the correct general form of the thermometer constructed using mainly the experimental data of Seck (1971a) and Smith and Parsons (1974). Chemographic tests for equilibrium between feldspar pairs are suggested and petrographie features discussed.In an appendix new values are given of Margules parameters calculated for binary disordered alkali feldspars from recent solvus data up to 15 kbars, and their physico-chemical basis examined. We suggest that accurate representations of the mixing properties of disordered alkali feldspars using Margules parameters are at present premature.