Fluid-mineral equilibria and thermodynamic mixing properties of fluid systems

The paper presents a review of an experimental method to quantitatively constrain thermodynamic mixing properties of fluid systems at high temperature T and pressure P. The method is based on bracketing equilibrium parameters of simple fluid-mineral reactions. Experimental data obtained with this technique for the H₂O-CO₂, H₂O-N₂, and H₂O-H₂ binary systems were utilized to calculate mixing parameters corresponding to the simplified van Laar model W ₁₂ ^VL , according to which the equation for the integral excess Gibbs free energy of a binary mixture G ^ex is G ^ex =X ₁ X ₂ W ₁₂ ^VL /(X ₁ V ₁ ⁰ + X ₂ V ₂ ⁰ ), where X _i is the mole fractions of the components, and V _i ⁰ are pure species molar volumes at given P and T (in cm³). The W ₁₂ ^VL for the three mixtures correspond to 202, 219, and 331 kJ cm³/mol. The empirical correlation $W_{H_2 O - X}^{VL}$ (kJ cm³/mol) = 887.012 Q _X ? 16.674, where Q = P _c (critical pressure, bar)/T _c (critical temperature, K) for gas X (where X = CH₄, CO, H₂S, O₂, Ar, and NH₃) is used to evaluate the van Laar parameters for a number of petrologically important water-gas mixtures. The H₂O-H₂ system is characterized by the greatest positive deviation from the ideal mixing and can thus decompose into two immiscible fluid phases under the P-T parameters typical of deep lithospheric zones. The exsolution of the H₂O-CO₂ and H₂O-N₂ systems is expected to occur only under high pressure and low temperature. This combination of parameters may be expected only in the environments of cold subduction. Salts (highly soluble simple salts and/or silicates) should significantly expand the exsolution regions in petrologically important fluids.     

Calculation of thermodynamic properties of hydrated borates by group contribution method

 General equations to correlate and predict the thermodynamic properties of hydrated borates were developed based on the experimental results according to their structural types. The thermodynamic properties (ΔH _f ⁰ and ΔG _f ⁰) of a hydrated borate phase are the sum of the contributions of the cations in aqueous solution, the borate polyanions, and the structural water to the corresponding thermodynamic properties. This method is called the group contribution method, and it is extensively used to calculate the thermodynamic properties of many kinds of inorganic compounds, such as silicates and clay minerals. Received: 23 November 1998 / Accepted: 11 October 1999     

The thermodynamic properties of radium

The enthalpy, Gibbs free energy, and entropies of aqueous radium species and radium solids have been evaluated from empirical data, or estimated when necessary for 25°C and 1 bar. Estimates were based on such approaches as extrapolation of the thermodynamic properties of Ca, Sr, and Ba complexes and solids plotted against cationic radii and charge to radius functions, and the use of the Fuoss or electrostatic mathematical models of ion pair formation (Langmuir, 1979). Resultant log K (assoc) and ΔH⁰ (assoc) (kcal/mol) values are: for RaOH⁺ 0.5 and 1.1; RaCl⁺ ?0.10 and 0.50; RaCO⁰₃ 2.5 and 1.07; and RaSO⁰₄ 2.75 and 1.3. Log Ksp and ΔH⁰ (dissoc) (kcal/mol) values for RaCO₃(c) and RaSO₄(c) are ?8.3 and ?2.8, and ?10.26 and ?9.4, respectively.Trace Ra solid solution in salts of Pb and of the lighter alkaline earths, has been appraised based on published distribution coefficient (D) data, where D ～- (mM²⁺)(N_RaX)/(mRa²⁺)(N_MX) (m and N are the aqueous molality and mole fraction of Ra and cation M in salt X, respectively. The empirical solid solution data have been used to derive both enthalpies and Gibbs free energies of solid solution of trace Ra in sulfate and carbonate minerals up to 100°C. Results show that in every case D values decrease with increasing temperature. Among the sulfate and carbonate minerals, D values decrease for the following minerals in the order: anhydrite > celestite > anglesite > barite > aragonite > strontianite > witherite > cerussite.     

Calculated thermodynamic properties of silica polymorphs

Accurate interatomic potentials have been employed to compute the phonon density of states of αquartz, stishovite and coesite polymorphs of silica. The temperature variation of several thermodynamic properties is calculated by using the phonon density of states to describe the vibrational entropy contribution to the free energy. Results for these polymorphs are in surprisingly good agreement with available experimental data. Moreover, the microscopic origin of quantitative differences in the heat capacity behavior of low and high density polymorphs is established.     

GC-MS法测定地下水中28种半挥发性有机物

本文针对地下水监测网运行维护规范(DZ/T 0307-2017)中的半挥发性有机物,建立了一种液/液萃取-气相色谱质谱联用法,可同时测定28种半挥发性有机物(SVOCs),涵盖规范中除多氯联苯外全部的27个SVOCs.方法 采用二氯甲烷萃取,SIM模式经气相色谱质谱联用仪(GC-MS)对样品进行测定,内标法定量,可实现...     

Constraints on the thermodynamic mixing properties of plagioclase feldspars

Taking account of the Cˉ1/Iˉ1 (Al/Si order/disorder) transformation at high temperatures in the albite-anorthite solid solution leads to a simple model for the mixing properties of the high structural state plagioclase feldspars. The disordered (Cˉ1) solid solution can be treated as ideal (constant activity coefficient) and, for anorthite-rich compositions, deviations from ideality can be ascribed to cation ordering. Values of the activity coefficient for anorthite in the Cˉ1 solid solution (γ _An ^Cˉ1 ) are then controlled by the free energy difference between Cˉ1 and Iˉ1 anorthite at the temperature (T) of interest according to the relation: ΔˉG _ord ^Iˉ1 ⇌Cˉ1 =RT ln γ _An ^Cˉ1 . If the Iˉ1⇌Cˉ1 transformation in pure anorthite is treated, to a first approximation, as first order and the enthalpy and entropy of ordering are taken as 3.7±0.6 kcal/mole (extrapolated from calorimetric data) and 1.4–2.2 cal/mole (using an equilibrium order/disorder temperature for An₁₀₀ of 2,000–2,250 K), a crude estimate of γ _An ^Cˉ1 for all temperatures can be made. The activity coefficient of albite in the Cˉ1 solid solution (γ _Ab ^Cˉ1 ) can be taken as 1.0. The possible importance of this model lies in its identification of the principal constraints on the mixing properties rather than in the actual values of γ _An ^Cˉ1 and γ _Ab ^Cˉ1 obtained. In particular it is recognised that γ _An ^Cˉ1 depends critically on ordering in anorthite as well as, at lower temperatures, any ordering in the Cˉ1 solid solution. A brief review of activity-composition data, from published experiments involving ranges of plagioclase compositions and from the combined heats of mixing plus Al-avoidance entropy model (Newton et al. 1980), reveals some inconsistencies. The values of γ _An ^Cˉ1 calculated using the approach of Newton et al. (1980), although consistent with Orville's (1972) ion exchange data, are slightly lower than values derived from experiments by Windom and Boettcher (1976) and Goldsmith (1982) or from ion-exchange experiments of Kotel'nikov et al. (1981). Based on the Cˉ1/Iˉ1 transformation model, values of γ _An ^Cˉ1 <1.0 are unlikely. Discrepancies between the experimental data sets are attributed to incomplete (non-equilibrium) Al/Si order attained during the experiments. It is suggested that the choice of activity coefficients remains somewhat subjective. The development of accurate mixing models would be greatly assisted by better thermodynamic data for ordering in pure anorthite and by more thorough characterisation of the state of order in plagioclase crystals used for phase equilibrium experiments.     

The thermodynamic properties of reciprocal solid solutions

A multisite solid solution of the type (A, B) (X, Y) has the four possible components AX, AY, BX, BY. Taking the standard state to be the pure phase at the pressure and temperature of interest, the mixing of these components is shown not to be ideal unless the condition: $$\Delta G^0 = (\mu _{AX}^0 + \mu _{BY}^0 - \mu _{AY}^0 - \mu _{BX}^0 = 0$$ applies. Even for the case in which mixing on each of the individual sublattices is ideal, ΔG ⁰ contributes terms of the following form to the activity coefficients of the constituent components: $$RT\ln \gamma _{AX} = - X_{B_1 } X_{Y_2 } \Delta G^0$$ (X _Ji refers to the atomic fraction of J on sublattice i). The above equation, which assumes complete disorder on (A, B) sites and on (X, Y) sites is extended to the general n-component case. Methods of combining the “cross-site” or reciprocal terms with non-ideal terms for each of the individual sites are also described. The reciprocal terms appear to be significant in many geologically important solid solutions, and clinopyroxene, garnet and spinel solid solutions are all used as examples. Finally, it is shown that the assumption of complete disorder only applies under the condition: $$\Delta G^0 \ll zn_1 RT$$ where z is the number of nearest-neighbour (X, Y) sites around A and n ₁ is the number of (A, B) sites in the formula unit. If ΔG ⁰ is relatively large, then substantial short range oder must occur and the activity coefficient is given by (ignoring individual site terms): $$\gamma _{AX} = \left( {\frac{{1 - X'_{Y_2 } }}{{1 - X_{Y_2 } }}} \right)^{zn_1 }$$ where X′_Y2 is the equilibrium atomic fraction of Y atoms surrounding A atoms in the structure. The ordered model may be developed for multicomponent solutions and individual site interactions added, but numerical methods are needed to solve the simultaneous equations involved.     

Scaling of thermodynamic mixing properties in garnet solid solutions

 The volumes and enthalpies of mixing, ΔV ^Mix and ΔH ^Mix, of binary solid-solution aluminosilicate garnets have been studied by computer simulation. The use of “average atoms” to simulate solid solution was found to give results that are considerably different from those obtained by calculating and averaging over many configurations of cations at a given composition. Although we expect mineral properties calculated from model calculations to be correct only on a qualitative rather than a quantitative scale, fair agreement with experiment was obtained where carefully tested potential parameters were used. The results show that mixing behaviour in these materials is controlled by local strain and relaxation effects resulting from the atomic size mismatch of the mixing divalent cations. In particular, ΔV ^Mix and ΔH ^Mix are shown to scale quadratically with the volume difference between the end members, and to vary essentially symmetrically with composition, with a moderate dependence on the degree and nature of cation order. We conclude that computer modelling should be useful in providing detailed qualitative information about the mixing properties of solid solutions, which can help to better constrain and interpret experimental results. Received: 8 March 2000 / Accepted: 1 October 2000     

Determination of uranium and thorium in meteorites by the delayed neutron method

Delayed neutron measurements of U and Th in three meteorites yield the following values:

     

14.

Structural and thermodynamic properties of water related defects in α-quartz     

A. L. Rosa  A. A. El-Barbary  M. I. Heggie  P. R. Briddon 《Physics and Chemistry of Minerals》2005,32(5-6):323-331

We have investigated the atomic geometries and thermodynamic properties of water related defects in α-quartz using first-principles calculation. We confirm that the (OH)₄ group is thermodynamically most stable and aggregates to form platelets in the form of microcracks with hydrolysed surfaces. We also examine other forms of defects which can be accessible out of equilibrium at high temperature. Finally, we discuss the consequences of our results for the hydrolytic weakening of α-quartz.     

15.

Low-temperature heat capacity and thermodynamic properties of natural polylithionite     

I. E. Paukov  Yu. A. Kovalevskaya  I. A. Kiseleva  T. N. Shuriga  V. N. Ikorskii 《Geochemistry International》2007,45(9):926-930

     

16.

容量法测定植物中氮     

李艳梅  张跃春  王忠伟  毛荐 《吉林地质》2009,28(2):120-122

介绍了容量法测定植物中氮.方法检出限2×10-3,经国家级标准物质检验,结果与标准值相符,精密度RSD(n=8)0.8%～4.4%.     

17.

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group     

I. E. Paukov  N. K. Moroz  Yu. A. Kovalevskaya  I. A. Belitsky 《Physics and Chemistry of Minerals》2002,29(4):300-306

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

18.

Effects of layer-charge distribution on the thermodynamic and microscopic properties of Cs-smectite     

Xiandong Liu  Rucheng Wang  Huiqun Zhou 《Geochimica et cosmochimica acta》2008,72(7):1837-1847

To explore the effects of layer-charge distribution on the thermodynamic and microscopic properties of Cs-smectites, classical molecular dynamic simulations are performed to derive the swelling curves, distributions and mobility of interlayer species, and Cs binding structures. Three representative smectites with distinct layer-charge distributions are used as model clay frameworks and interlayer water content is set within a wide range from 0 to 380 mg_water/g_clay. All the three smectites swell in a similar way, presenting the characteristic swelling plateaus and similar trends of swelling energetic profiles. The full-monolayer hydrate, corresponding to the global minima of the immersion energy, is the most stable hydrated state of Cs-smectites. The calculated diffusion coefficients of interlayer species disclose the confining effects in all smectites: both water molecules and ions diffuse slower than corresponding bulk cases and they are much more mobile in the direction parallel to the clay surfaces than perpendicular to them. The formed inner-sphere complex structures are very similar in different smectites: ions bind on the H-sites or T-sites and water molecules form cage-like caps covering the ions. Layer-charge distribution is found to have significant influences on the mobility of interlayer species and preference of ion binding sites. A general sequence is proposed to elucidate the preferences of various hexagonal sites (H-sites) and triangular sites (T-sites), that is, tetrahedrally substituted H-sites > nonsubstituted H-sites > tetrahedrally substituted T-sites > nonsubstituted T-sites, but the influence of octahedral substitutions on the preference of the neighboring sites is not obvious. Analysis of mobility indicates that H-sites are more stable Cs-fixation positions than T-sites and smectite with higher fraction of octahedral charges seems to be the most effective barrier material no matter how water content varies although all smectites can immobilize Cs ions in relatively dry conditions. These findings will not only facilitate basic research in geochemistry and material sciences, but also promote the barrier material designing.     

19.

Biomolecules in hydrothermal systems: Calculation of the standard molal thermodynamic properties of nucleic-acid bases, nucleosides, and nucleotides at elevated temperatures and pressures     

Douglas E. LaRowe  Harold C. Helgeson 《Geochimica et cosmochimica acta》2006,70(18):4680-4724

Calculation of the thermodynamic properties of biomolecules at high temperatures and pressures is fundamental to understanding the biogeochemistry of hydrothermal systems. Ample evidence indicates that hyperthermophilic microbes interact chemically with their mineralogical environment in these systems. Nevertheless, little is known about the thermodynamic properties of the biomolecules involved in such processes. Recent advances in theoretical biogeochemistry make it possible to calculate these properties using the limited experimental data available in the literature, together with correlation and group additivity algorithms, reference model compounds, and the revised HKF equations of state. This approach permits calculation of the standard molal thermodynamic properties of the 120 common protonated and deprotonated nucleotides and their constituent nucleic-acid bases and nucleosides as a function of temperature and pressure. The requisite equations of state parameters can be calculated from experimental standard molal heat capacities, volumes, and compressibilities reported in the literature for nucleic-acid bases and nucleosides. Because no calorimetric or densimetric data are available for the nucleotides, experimental heats of reaction taken from the literature were used together with correlation and group additivity algorithms to generate provisional values of the corresponding equations of state parameters for the nucleotides. The thermodynamic properties and revised HKF equations of state parameters generated in the present study can be used to carry out comprehensive mass transfer and Gibbs energy calculations to describe and quantify the chemical interaction of minerals and microbes in hydrothermal systems.     

20.

Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines     

Richard O. Sack 《Contributions to Mineralogy and Petrology》1980,71(3):257-269

Existing data on the temperature and composition dependence of the Fe²⁺-Mg²⁺ distribution between Fe-Mg olivine and orthopyroxene, the intra-crystalline distribution of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxene, and macroscopic activity-composition relations in olivine and orthopyroxene are shown to be inconsistent with generally accepted thermodynamic formulations which assume that the non-configurational Gibbs energy of orthopyroxene is independent of the degree of long-range ordering of Fe²⁺ and Mg⁺ between M1 and M2 sites. These data are interpreted in terms of the constraints they provide on the size of Bragg-Williams type energy, entropy, and volume terms for olivine and orthopyroxene. The apparent equilibrium constant for Fe-Mg exchange between olivine and orthopyroxene is shown to be a potentially useful ‘geothermometer’ for olivine-orthopyroxene assemblages with olivines with mole fraction of Fe₂SiO₄ component less than 0.2 or greater than 0.6. A provisional calibration of this ‘geothermometer’ is presented.     

Bruderheim	U (ppb)	Th(ppb)
Bruderheim	$\text{14.5 ± 1.0}$	$\text{171 ± 65}$
Peace River	$\text{11.8 ± 0.7}$	$\text{96 ± 46}$
Stannern	$\text{220 ± 6}$	$\text{563 ± 190}$

Structural and thermodynamic properties of water related defects in α-quartz

We have investigated the atomic geometries and thermodynamic properties of water related defects in α-quartz using first-principles calculation. We confirm that the (OH)₄ group is thermodynamically most stable and aggregates to form platelets in the form of microcracks with hydrolysed surfaces. We also examine other forms of defects which can be accessible out of equilibrium at high temperature. Finally, we discuss the consequences of our results for the hydrolytic weakening of α-quartz.     

容量法测定植物中氮

介绍了容量法测定植物中氮.方法检出限2×10-3,经国家级标准物质检验,结果与标准值相符,精密度RSD(n=8)0.8%～4.4%.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Effects of layer-charge distribution on the thermodynamic and microscopic properties of Cs-smectite

To explore the effects of layer-charge distribution on the thermodynamic and microscopic properties of Cs-smectites, classical molecular dynamic simulations are performed to derive the swelling curves, distributions and mobility of interlayer species, and Cs binding structures. Three representative smectites with distinct layer-charge distributions are used as model clay frameworks and interlayer water content is set within a wide range from 0 to 380 mg_water/g_clay. All the three smectites swell in a similar way, presenting the characteristic swelling plateaus and similar trends of swelling energetic profiles. The full-monolayer hydrate, corresponding to the global minima of the immersion energy, is the most stable hydrated state of Cs-smectites. The calculated diffusion coefficients of interlayer species disclose the confining effects in all smectites: both water molecules and ions diffuse slower than corresponding bulk cases and they are much more mobile in the direction parallel to the clay surfaces than perpendicular to them. The formed inner-sphere complex structures are very similar in different smectites: ions bind on the H-sites or T-sites and water molecules form cage-like caps covering the ions. Layer-charge distribution is found to have significant influences on the mobility of interlayer species and preference of ion binding sites. A general sequence is proposed to elucidate the preferences of various hexagonal sites (H-sites) and triangular sites (T-sites), that is, tetrahedrally substituted H-sites > nonsubstituted H-sites > tetrahedrally substituted T-sites > nonsubstituted T-sites, but the influence of octahedral substitutions on the preference of the neighboring sites is not obvious. Analysis of mobility indicates that H-sites are more stable Cs-fixation positions than T-sites and smectite with higher fraction of octahedral charges seems to be the most effective barrier material no matter how water content varies although all smectites can immobilize Cs ions in relatively dry conditions. These findings will not only facilitate basic research in geochemistry and material sciences, but also promote the barrier material designing.     

Biomolecules in hydrothermal systems: Calculation of the standard molal thermodynamic properties of nucleic-acid bases, nucleosides, and nucleotides at elevated temperatures and pressures

Calculation of the thermodynamic properties of biomolecules at high temperatures and pressures is fundamental to understanding the biogeochemistry of hydrothermal systems. Ample evidence indicates that hyperthermophilic microbes interact chemically with their mineralogical environment in these systems. Nevertheless, little is known about the thermodynamic properties of the biomolecules involved in such processes. Recent advances in theoretical biogeochemistry make it possible to calculate these properties using the limited experimental data available in the literature, together with correlation and group additivity algorithms, reference model compounds, and the revised HKF equations of state. This approach permits calculation of the standard molal thermodynamic properties of the 120 common protonated and deprotonated nucleotides and their constituent nucleic-acid bases and nucleosides as a function of temperature and pressure. The requisite equations of state parameters can be calculated from experimental standard molal heat capacities, volumes, and compressibilities reported in the literature for nucleic-acid bases and nucleosides. Because no calorimetric or densimetric data are available for the nucleotides, experimental heats of reaction taken from the literature were used together with correlation and group additivity algorithms to generate provisional values of the corresponding equations of state parameters for the nucleotides. The thermodynamic properties and revised HKF equations of state parameters generated in the present study can be used to carry out comprehensive mass transfer and Gibbs energy calculations to describe and quantify the chemical interaction of minerals and microbes in hydrothermal systems.     

Some constraints on the thermodynamic mixing properties of Fe-Mg orthopyroxenes and olivines

Existing data on the temperature and composition dependence of the Fe²⁺-Mg²⁺ distribution between Fe-Mg olivine and orthopyroxene, the intra-crystalline distribution of Fe²⁺ and Mg²⁺ between M1 and M2 sites in orthopyroxene, and macroscopic activity-composition relations in olivine and orthopyroxene are shown to be inconsistent with generally accepted thermodynamic formulations which assume that the non-configurational Gibbs energy of orthopyroxene is independent of the degree of long-range ordering of Fe²⁺ and Mg⁺ between M1 and M2 sites. These data are interpreted in terms of the constraints they provide on the size of Bragg-Williams type energy, entropy, and volume terms for olivine and orthopyroxene. The apparent equilibrium constant for Fe-Mg exchange between olivine and orthopyroxene is shown to be a potentially useful ‘geothermometer’ for olivine-orthopyroxene assemblages with olivines with mole fraction of Fe₂SiO₄ component less than 0.2 or greater than 0.6. A provisional calibration of this ‘geothermometer’ is presented.