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 re-evaluation of the olivine-spinel geothermometer

The Irvine olivine-spinel geothermometer, as formulated by Jackson (1969), appears to yield magmatic temperatures when applied to plutonic rocks such as the Stillwater Complex but Evans and Wright (1972) have demonstrated that it gives temperatures in excess of 2,000 ° C when applied to volcanic assemblages. A re-evaluation of the geothermometer has shown that more realistic temperatures can be obtained for volcanic rocks by using a different free energy value of FeCr₂O₄ in the formulation. The revised geothermometer gives temperatures in the range 1,100–1,300 ° C for samples from Kilauea and 500–800 ° C for basic plutonic rocks from layered intrusions, indicating that Mg and Fe²⁺ have re-equilibrated at subsolidus temperatures in these intrusions as suggested by Irvine (1965). This theory was tested by heating uncrushed natural samples from layered intrusions to magmatic temperatures for periods ranging from two days to four weeks. The result was a marked increase in the Mg/Fe²⁺ ratio in the spinels and a decrease in the Mg/Fe²⁺ ratio in the olivines, confirming that considerable subsolidus re-equilibration had taken place in the unheated samples.     

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⁺.     

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 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.     

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).     

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.     

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.     

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).     

Fluorine-hydroxyl exchange in apatite and biotite: A potential igneous geothermometer

The free energy data for the simple fluorides, chlorides and hydroxides have been used to predict the distribution of these anions in hydrous minerals. The calculated partition of fluorine in phlogopite agrees well with published results; the distribution of fluorine and hydroxyl between apatite and phlogopite is temperature dependent and has been calculated. The temperatures deduced from analyses of natural apatite-biotite pairs frequently show discrepancies as compared with independent temperature estimates; these probably arise from late-stage exchange of the fluorine in phlogopite with an aqueous fluid, for which independent evidence is available.The fugacity of phosphorus in equilibrium with apatite, a ubiquitous hydrous mineral, has been calculated for various mineral assemblages. The estimates, which are subject to considerable error, are lower for basanites and alkali-basalts than for tholeiites and range from approximately 10^–14 at 1000° C to 10^–16 bars at 750° C for fayalitic rhyolites.     

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.     

Aluminum in quartz as a geothermometer

Quartz forming in aluminum-saturated environments has a trace aluminum content which varies linearly and directly with its temperature of crystallization. The aluminum content varies at a rate of approximately 1 ppm Al per 3.6° C change in temperature. Use of this geothermometer gives temperatures which are consistent with those expected by geologic reasoning or through the use of other geothermometers.     

Zircon and sphene as fission track geochronometer and geothermometer: A reappraisal

The data published earlier on zircon and sphene fission track ages and annealing are discussed in the light of different etching conditions used for age determination and annealing experiments in order to explain the age discordances of some zircon and sphene pairs, as well as numerous closing temperatures obtained for individual minerals. Using the new set of simple etching conditions, zircon (KOH melt) and sphene (HF+HCl), the annealing experiments indicate that tracks in sphene are annealed more easily than in zircon. The closing temperature of zircon and sphene have been calculated at 300° and 250° C respectively. The study reveals that both the fission track age and the closing temperature of a mineral can vary considerably if different etchants are used. For different etching conditions the closing temperatures (T) of sphene have the following order: ^T NaOH> ^T HF+HCl+HNO₃+H₂O> ^THF+HCl>^THCl. An alternative method can be used to obtain thermal histories of rocks by selectively applying various etchants on the same mineral.     

The Ni-in-garnet geothermometer: calibration at natural abundances

Experiments to study the partitioning of Ni between olivine and garnet at natural abundances were performed at 1200 °C – 3 GPa, 1300 °C – 3, 5 and 7 GPa and 1500 °C – 5 GPa using piston-cylinder and multi-anvil apparatus. The experiments were intended to provide a further test of the Ni-in-garnet geothermometer calibrated previously using enhanced Ni levels. The run products were analysed by electron microprobe using special operating conditions to enhance counting statistics. Ni-Mg and Fe-Mg exchange between olivine and garnet was tightly reversed. Results of the experiments suggest that Ni substitution in garnet behaves according to Henry's Law up to levels of ∼3000 ppm. The Ni-in-garnet geothermometer derived from reversed experiments in this study is consistent (within error) with that derived from previous experiments at enhanced levels of Ni; neither of these experimental calibrations is consistent with any empirically derived Ni-in-garnet geothermometer. Sources of the discrepancy between the empirical and experimental calibrations of the Ni-in-garnet geothermometer are examined in detail and it is concluded that the main reason for the differences involves errors in the calculation of temperatures in the empirical version. These errors are clearly demonstrated using a recently published data set for garnet peridotite xenoliths in which both Ni-in-garnet and more conventional multi-equilibrium thermobarometry was employed. Received: 25 August 1998 / Accepted: 10 March 1999     

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。     

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.