An Evaluation of Garnet – Clinopyroxene Geothermometer

Abstract

The garnet-clinopyroxene pair commonly found in upper amphibolite, granulite, and eclogite facies assemblage, as well as in garnet peridotites serves as a basic tool to estimate the equilibrium temperature for these metamorphic rocks. Several empirical and experimental calibrations for garnet-clinopyroxene thermometers have been proposed in the last four decades. Due to several calibrations for this pair, scholars often find difficulty in choosing the most optimum and valid thermometer. In the present study, eleven garnet-clinopyroxene thermometers formulated since 1972 have been evaluated to find the most valid thermometer checked on 89 sample data collated from the published global literature and processed through Gt-Cpx.Exe software. The authors used the relationship of LnKD versus the inverse of temperature and regression values. Out of the eleven geothermometer models, five models showing highest regression values with clustering of data at smaller ranges and less deviation for the collated data have been considered the best one: Raheim and Green (Contributions to Mineralogy and Petrology 48: 179–203, 1974); Mysen and Heier (Contributions to Mineralogy and Petrology 36: 73–94, 1972); Jun Lui (International Geology Review 40: 579–608, 1998); Ganguly and Saxena (Minerals Rocks 19: 1–291, 1987) and Ganguly (Geochimica et Cosmochimica Acta, 43: 1021–1029, 1979).

1. Introduction

Since the advent of thermodynamics in petrological studies, geothermobarometry has played a vital role in deciphering metamorphic conditions and understanding the evolution of the crust. In the last fifty years, several geothermobarometers have been proposed for rocks ranging from greenschist to eclogite facies, such as garnet biotite and garnet cordierite thermometer by Thompson 1976, garnet hornblende thermometer by Ravna 2000, and many more.

Valid geothermobarometry is a fundamentally important tool in deciphering metamorphic conditions and understanding the evolution of the crust as it provides information about the pressure-temperature conditions at which the rocks have formed, serving as a window into the lower continental crust. To determine the metamorphic conditions of rocks from greenschist to eclogite facies, and at a range of pressures, several geothermometers and geobarometers have been proposed in the last few decades that serve as pressure-temperature sensors helpful in decoding the chemical evolution of the rocks.

Several thermobarometric studies have been undertaken over the years, which led to the development of a range of thermometers and barometers, such as garnet-clinopyroxene thermometry [1, 2], garnet-orthopyroxene thermometry [3], garnet-biotite thermometry [4, 5], garnet-hornblende thermometry [6], garnet cordierite thermometry [7], and two pyroxene thermometry [8].

The study of garnet-clinopyroxene geothermometry has a long history, and we now have several versions of the geothermometer. As the assemblage of garnet-clinopyroxene occurs in an array of rock types ranging from eclogites to albite-epidote amphibolites and amphibolites to granulites to garnet peridotites, this potential underscores the need to carefully evaluate the accuracy and precision of the thermometer. The Fe-Mg substitution in the garnet-clinopyroxene system along with the effect of X_Ca garnet and X_Na clinopyroxene are not fully understood. Although few models have tried to understand the effect of these substitutions, still there has been less work done on the assessment of these thermometers. To recommend the best calibration for geologists, the authors have compared eleven garnet-clinopyroxene thermometer models proposed since 1972, the first equation proposed by Mysen and Heier [9]. Quantification of garnet-clinopyroxene Fe-Mg equilibrium is a widely applied thermometer for high-grade upper amphibolite, granulite, and eclogite facies assemblages, as well as garnet peridotite, where the distribution of the Fe⁺² and Mg between coexisting garnet and clinopyroxene is expressed by the exchange reaction:

$$1/3{\mathrm{Mg}}_3{\mathrm{Al}}_2{\mathrm{Si}}_3{\mathrm{O}}_{12}+{\text{CaFeSi}}_2{\mathrm{O}}_6=1/3{\mathrm{Fe}}_3{\mathrm{Al}}_2{\mathrm{Si}}_3{\mathrm{O}}_{12}+{\text{CaMgSi}}_2{\mathrm{O}}_6$$E1

$$\text{Pyrope}+\text{Hedenbergite}=\text{Almandine}+\text{Diopside}$$E2

The partitioning of Fe⁺² and Mg, expressed by the distribution coefficient between coexisting garnet and clinopyroxene, has clearly shown that this distribution is a function of both physical conditions, as well as compositional variations of the phases involved [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]:

$${\mathrm{K}}_{\mathrm{D}}=\frac{{\left({\mathrm{Fe}}^{2+/}\mathrm{Mg}\right)}^{\mathrm{Gt}}}{{\left({\mathrm{Fe}}^{2+/}\mathrm{Mg}\right)}^{\mathrm{Cpx}}}$$E3

A brief description of various models of garnet-clinopyroxene geothermometers considered for this comparative study is summarized as follows:

2. Mysen and Heier (1972)

Mysen and Heier [9], studied the Hariedland eclogites of Western Norway and justified K = f (T) as a basis for the genetic classification of eclogites. They used the equation proposed by Banno [21] to calculate the distribution coefficient K_D^Fe2+−Mg for the calculation of temperature. Banno [21] also suggested that the effect of pressure and variable chemical composition on the distribution coefficient was found to be negligible. The pressure range used for calculation is large enough (6–36 kbar) so that the effect of pressure on the distribution coefficient K_D^Fe2+−Mg for the calculation of temperature is found to be negligible. Their formulation is:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{2475}{{\mathrm{lnK}}_{\mathrm{D}}+0.781}$$E4

3. Raheim and Green (1974)

Raheim and Green [15] conducted an experimental study of eclogites using (a) a mineral mix, (b) a glass of typical tholeiitic composition, and (c) a series of glasses of tholeiitic composition. They calculated the distribution coefficient keeping Fe²⁺and Mg in consideration while assuming other variables Na/Ca and Ca/Al values constant. Also, the effect of Fe₂O₃ values was found to be negligible. They formulated the equation as:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left(3686+{28.35}^{\ast }\mathrm{P}\right)}{\left({\mathrm{lnK}}_{\mathrm{D}}+2.33\right)}$$E5

4. Ellis and Green (1979)

Ellis and Green [11] carried out an experimental study on a series of basaltic compositions and compositions within the simple system CaO-MgO-FeO-Al₂O₃-SiO₂ on the effect of Ca on garnet-clinopyroxene Fe-Mg exchange equilibrium in the range of 24–30 kb pressure and 750°-1300°C temperature. Their formulation is as follows:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{{3104}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}+3030+{0.01086}^{\ast }\left(\mathrm{P}–1\right)}{\text{In}{\mathrm{K}}_{\mathrm{D}}+1.9034}$$E6

X_Ca^Gt has been used as a parameter in the equation. The authors opined that the Ca effect is believed to be the nonideal mixing of Ca and Mg in garnet and clinopyroxene. The previous inconsistencies of temperature dependence on K_D are proposed to be reconciled and resolved in this model. To check the effect, the graph of lnK_D versus X_Ca^Gt has been plotted as shown in Figure 1, showing a very gentle positive slope and X_Ca^Gt values scattered for a range less than 0.3, which means as the value of lnK_D increases_, X_Ca^Gt values increases very gently.

Figure 1.

Graph of lnK_D versus X_Ca^Gt.

5. Ganguly (1979)

Ganguly [12] critically evaluated all the available thermodynamic mixing data of garnet and clinopyroxene proposed till 1979 and integrated these with the thermochemical and selected experimental data to express the Fe-Mg in distribution coefficient giving the equation as:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left(4801+{11.07}^{\ast }\mathrm{P}\left(\mathrm{kb}\right)+{1586}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}+{1308}^{\ast }{{\mathrm{X}}_{\mathrm{Mn}}}^{\mathrm{Gt}}\right)}{\text{In}{\mathrm{K}}_{\mathrm{D}}+1.9034}$$E7

The application of the proposed model is said to be restricted to Na-poor bulk compositions due to a lack of sufficient data on the mixing properties of jadeite with hedenbergite and diopside. The error estimation of this model is said to be ±25°C. X_Ca and X_Mn of garnet have been used as a factor in the formulation. The graph of lnK_D versus X_Mn^Gt has been plotted as shown in Figure 2 where X_Mn values are clustered at a very low range less than 0.02. Both X_Ca (Figure 1) and X_Mn of garnet show the same behavior concerning lnK_D.

Figure 2.

Graph of lnK_D versus X_Mn^Gt.

6. Wells (1979)

Wells [16] tried to explain the formation of granulite facies rocks in Southern West Greenland using thermometers calibrated against the result of phase equilibrium experiments. Assuming that the departures from the ideal mixing in the pyroxene and garnet phases are mutually canceled out, Wells gave the following equation:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left(\left(24440+{0.06524}^{\ast }\left(\mathrm{P}-1\right)\right)\right.}{13.41-3^{\ast }{\mathrm{R}}^{\ast }\text{In}{\mathrm{K}}_{\mathrm{D}}}$$E8

7. Dahl (1980)

Dahl [10] showed estimates of the analysis of thirteen mineral pairs, stating that the regressed parameters for Ca and Mn agree well with those calculated by Ganguly [12] and his formulation is as follows:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{170+{0.01107}^{\ast }\left(\mathrm{P}–1\right)+{759.44}^{\ast }\left({{\mathrm{X}}_{\mathrm{Fe}}}^{\mathrm{Gt}}-{{\mathrm{X}}_{\mathrm{Mg}}}^{\mathrm{Gt}}\right)+{1414}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}+{1437}^{\ast }{{\mathrm{X}}_{\mathrm{Mn}}}^{\mathrm{Gt}}}{\text{In}{\mathrm{K}}_{\mathrm{D}}}$$E9

The graph of lnK_D versus X_Fe^Gt shown in Figure 3 shows a positive correlation with lnK_D as the values of X_Fe^Gt increase with the increase in lnK_D. The graph of lnK_D versus X_Mg^Gt, Figure 4 shows a negative correlation with lnK_D as the values of X_Mg^Gt increase with a decrease in lnK_D.

Figure 3.

Graph of lnK_D versus X_Fe^Gt.

Figure 4.

Graph of lnK_D versus X_Mg^Gt.

8. Ganguly and Saxena (1987)

Ganguly and Saxena [13] modified the equation given by Ganguly [12], providing an updated calibration on composition and the Fe-Mg distribution between garnet and clinopyroxene with the modified equation as follows:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{4100+{0.01107}^{\ast }\left(\mathrm{P}–1\right)+{1510}^{\ast }\left({{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}+{{\mathrm{X}}_{\mathrm{Mn}}}^{\mathrm{Gt}}\right)}{\text{In}{\mathrm{K}}_{\mathrm{D}}}$$E10

9. Krogh (1988)

Krogh [14] reinterpreted the existing experimental data on the partitioning of Fe⁺² and Mg between garnet and clinopyroxene [11, 15, 22] to construct a new expression including a curvilinear relationship between lnK_D and X_Ca^GT giving expression as:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left(\left(-{6173}^{\ast }{\left({{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}\right)}^2+{6731}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}+1879+{10}^{\ast }\mathrm{P}\left(\mathrm{kb}\right)\right)\right.}{\text{In}{\mathrm{K}}_{\mathrm{D}}+1.393}$$E11

The proposed model shows that the grossular content of garnet have the major compositional effect on Fe-Mg partitioning of garnet and clinopyroxene. This model is expected to give optimum results for X_Ca values ranging between 0.1 and 0.5.

10. Yang (1994)

Yang [18] carried out an experimental study of the compositional dependence of the garnet-clinopyroxene Fe⁺²/Mg partition coefficient. The Mg number of garnet was found to have a significant effect on the K_D and his formulation is as follows:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left[1987.98+\left({0.01766}^{\ast }\mathrm{P}\right)–\left({1629}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\ast }{\mathrm{X}}_{\mathrm{Ca}}\right)+\left({3648.55}^{\ast }{\mathrm{X}}_{\mathrm{Ca}}\right)–\left({6.59}^{\ast }\text{MgNo}\right)\right]}{\left(\text{In}{\mathrm{K}}_{\mathrm{D}}+1.076\right)}$$E12

11. Jun Lui (1998)

Jun Lui [19] gave a new formulation using new experimental data measured at 600 to 950°C, 0.8–3.0 GPa, and f(O₂) defined by the fayalite-quartz-magnetite buffer in the basalt-H₂O system as:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{3820}{\left(\left(1.828+\text{In}{\mathrm{K}}_{\mathrm{D}}\left(1+\mathrm{a}\left(2.2-\mathrm{P}\right)\right)\right.\right.}$$E13

The model is opined to be in excellent agreement with the low-temperature end amphibolite to high-temperature end granulites of crustal P-T conditions.

12. Krogh Ravna (2000)

Krogh Ravna [20] gave an updated calibration through multiple regression analysis on an extended dataset to refine the relationship between temperature, pressure, composition, and the Fe-Mg distribution between garnet and clinopyroxene. The formulation is as follows:

$$\mathrm{T}\left(\mathrm{K}\right)=\frac{\left(\left(\begin{array}{l}1939.9+{3270}^{\ast }{{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}–1396{\left({{\mathrm{X}}_{\mathrm{Ca}}}^{\mathrm{Gt}}\right)}^2+{3319}^{\ast }{{\mathrm{X}}_{\mathrm{Mn}}}^{\mathrm{Gt}}-3535{\left({{\mathrm{X}}_{\mathrm{Mn}}}^{\mathrm{Gt}}\right)}^2+{1105}^{\ast }{{\mathrm{X}}_{\mathrm{Mg}\#}}^{\mathrm{Gt}}–\\ {3561}^{\ast }{\left({{\mathrm{X}}_{\mathrm{Mg}\#}}^{\mathrm{Gt}}\right)}^2+{2324}^{\ast }{\left({{\mathrm{X}}_{\mathrm{Mg}\#}}^{\mathrm{Gt}}\right)}^3+{169.4}^{\ast }\mathrm{P}\left(\mathrm{GPa}\right)\end{array}\right)\right.}{\left(\text{In}{\mathrm{K}}_{\mathrm{D}}+1.223\right)}$$E14

This calibration is said to be unaffected by the sodic variations of clinopyroxenes in the range of X_Na=0.051 giving optimum results for variegated rock types.

13. Valid garnet-clinopyroxene geothermometry in granulites

Granulites are typical rocks of the Earth’s middle to lower crust formed under high-temperature conditions. They are found as xenoliths in basaltic volcanic rocks, mainly within continental rifts, but most granulites occur as complexes or terranes in orogenic settings that have suffered significant erosion and exhumation where we can access directly the deep crustal assemblages. Orogenic granulites display a wide compositional range [23] and are known from a variety of collisional belts such as Aldan Shield, Adirondack highlands, Southern granulite terrain, and Rajasthan, India, Ruby Range, Montana, USA, Antarctica, and many more that formed during different episodes, including the Archean, since granulites are very common here. Determination of bulk rock and mineral compositions, calculation of peak equilibration conditions, and dating of orogenic granulites are known to have important constraints on the thermal and chemical structure of the Earth’s continental crust throughout Earth's history. Harley [23] showed that equilibration conditions deduced from orogenic granulites cover a wide range. In particular, pressures are highly variable, and the granulite field may be divided into low-pressure, medium-pressure, and a high-pressure facies [24]. Peak temperatures for many granulites scatter around 800°C [25], but an increasing number of ultra-high temperature granulite complexes (900–1100°C and 0.7–1.3 GPa) are being recognized [26, 27].

To test the validity and applicability of garnet-clinopyroxene thermometry, we have collated 89 samples from the literature all over the world (supplementary sheet attached). Samples were selected to fit the following criteria [3, 4]:

1. There is a clear description of textural equilibrium between garnet and clinopyroxene.

2. There are detailed and high-quality electron microprobe analyses of the minerals involved at least SiO₂, TiO₂, Al₂O₃, FeO, MnO, MgO, CaO, Na₂O, and K₂O, and the stoichiometry of the analyzed minerals was confirmed.

3. The core composition of garnet and rim composition of clinopyroxene have mostly been used. If there is growth zoning in garnet, only the rim composition was used, and accordingly, only the rim composition of matrix clinopyroxene has been used.

4. Data are used where elemental oxide totals for the minerals analyzed were 100$\pm$1.5%.

5. The effect of Fe₂O₃ on garnet and clinopyroxene has been considered negligible for the calculation of temperature.

14. Effect of Fe³⁺, Na in clinopyroxene and Ca, Mn in garnet

While proposing several experimental and empirical calibrations of garnet-clinopyroxene thermometer, various assumptions have been made regarding Fe³⁺, Na, and Ca content of pyroxenes, such as Raheim and Green [15] Na/Ca and Ca/Al content and [11] effect of Ca. In this contribution, the authors have considered quaternary parameters Fe²⁺, Mg, Ca, and Mn of garnet and Fe²⁺, Mg of clinopyroxene. Fe³⁺ content of garnet and clinopyroxene has been considered negligible. The collected samples are of granulitic terrain having high Fe, Mg content and low Mn content in garnet due to which the effect of Mn has been reduced profoundly. A very less amount of Na-Cpx is present in the collected samples, mostly falling in the range of 0–0.2. The 89 samples listed in the table (See supplementary data) fall in the mineral composition range: X_Fe= 0.06–0.61 (mostly between 0.2 and 0.4); X_Mg = 0.32–0.95 (mostly between 0.6 and 0.9) in clinopyroxene; X_Fe = 0.07–0.79 (mostly between 0.45 and 0.60); X_Mg = 0.009–0.70 (mostly between 0.1 and 0.3); X_Mn = 0.004–0.13 (mostly between 0.01 and 0.03) and X_Ca = 0.01–0.89 (mostly between 0.10 and 0.20) in garnet.

15. Results and discussion

The total of 89 pairs of data have been processed for the different models of garnet-clinopyroxene pair by the software Gt-Cpx.EXE [28, 29]. A comparison of the calculated lnK_D and 1/T for different geothermometric models has been undertaken. The plots of lnK_D vs 1/T are shown in Figures 5–15. The data selected in this way were used to check the temperature dependence of the distribution coefficient:

Figure 5.

Reciprocal relation of temperature (1/T) versus lnK_D for Raheim and Green [15] model.

Figure 6.

Reciprocal relation of temperature (1/T) versus lnK_D for Mysen and Heier [9] model.

Figure 7.

Reciprocal relation of temperature (1/T) versus lnK_D for Jun Lui [19] model.

Figure 8.

Reciprocal relation of temperature (1/T) versus lnK_D for Ganguly and Saxena [13] model.

Figure 9.

Reciprocal relation of temperature (1/T) versus lnK_D for Ganguly [12] model.

Figure 10.

Reciprocal relation of temperature (1/T) versus lnK_D for Krogh [20] model.

Figure 11.

Reciprocal relation of temperature (1/T) versus lnK_D for Wells [16] model.

Figure 12.

Reciprocal relation of temperature (1/T) versus lnK_D for Ellis and Green [11] model.

Figure 13.

Reciprocal relation of temperature (1/T) versus lnK_D for Krogh [14] model.

Figure 14.

Reciprocal relation of temperature (1/T) versus lnK_D for Dahl [10] model.

Figure 15.

Reciprocal relation of temperature (1/T) versus lnK_D for Yang [18] model.

The Raheim and Green [15] Figure 5 graph of lnK_D vs 1/T has been plotted as lnK_D = 1870/ T(°C) - 1.024 with R² = 0.995.

Mysen and Heier [9] Figure 6 lnK_D = 1165/ T (°C) + 0.068 with R² = 0.988.

Jun Lui [19] Figure 7, as lnK_D = 1435/ T (°C) - 0.380 with R² =0.988.

Ganguly and Saxena [13] Figure 8, as lnKD = 2395 / T (°C) -1.145 with R² = 0.847.

Ganguly [12] Figure 9, as lnK_D =2825/ T (°C) -1.551 with R² = 0.843.

Krogh [20] Figure 10, as lnK_D = 1007/ T (°C) + 0.256 with R² = 0.601.

Wells [16] Figure 11, as lnK_D = 1760 / T (°C) - 0.468 with R² = 0.582.

Ellis and Green [11] Figure 12, as lnK_D =1397/ T (°C) –0.025with R² = 0.562.

Krogh [14] Figure 13, as lnK_D = 966.7 / T (°C) +0.415 with R² = 0.546.

Dahl [10] Figure 14, as lnK_D = 730.7 / T (°C) +0.774with R² = 0.525 and

Yang [18] Figure 15, as lnK_D = 852.7 / T (°C) + 0.476with R² = 0.458.

From the very beginning, proper evaluation of metamorphic temperatures has been a matter of discussion. Various methods are applied for determining precise temperatures. Some researchers determine temperature by averaging the results from all applicable thermometers. Few also use consensus peak temperature in which a temperature is chosen where the spread in temperatures from each thermometer overlap. The averaging of results from different thermometers can be unjustified yielding an approximate estimation of temperature. Although, the use of consensus temperature can be found fissible for evaluation of temperature variation within a terrane. With the above considerations in mind, we have attempted to evaluate the accuracy of eleven models taking each separately and checking the regression and scattering of temperature values. In eleven models used despite the use of the compositional effect of X_Fe, X_Mg, X_Ca, and X_Mn of garnet on lnK_D in various models, the accuracy of models has not been resolved to a large extent. Raheim and Green [15], as well as Mysen and Heier [9], have given the best precision, followed by Jun Lui [19] which used an iteration method giving a confined range of temperature and less scattering. Ganguly [12] and Ganguly and Saxena [13] have used the compositional effect of X_Ca and X_Mn of garnet in their equation, although the scattering of temperature is a little more as compared to Raheim and Green [15], Mysen and Heier [9] and Jun Lui [19] leading to less regression values. The box plot in Figure 16 shows the temperature range of the best five models. The model of Raheim and Green [15] has shown the clustering of temperature at a shorter range leading to the highest regression followed by Mysen and Heier [9] model giving the widest range of temperature as compared to other best models. Ganguly [12] and Ganguly and Saxena [13] models have yielded high-temperature values as compared to other best models, still clustering for a short range resulting in high regression values. The rest of the models have given a wide spread in the data leading to fewer regression values.

Figure 16.

Box plot showing the best five models with their calculated temperature range.

To observe the effect of X_Fe and X_Mg of clinopyroxene and X_Fe, X_Mg, X_Ca, and X_Mn of garnet on K_D, we have plotted the graphs between X_Fe and X_Mg of clinopyroxene vs K_D and X_Fe, X_Mg, X_Ca,and X_Mn of garnet on K_D (supplementary figures associated with this article can be obtained from the journal), respectively.

In the case of X_Fe and X_Mg of clinopyroxene, it is observed that X_Fe(CPX) is showing a horizontal trend as X_Fe(CPX) =2E–5/K_D + 0.275 with R² = 2E–07, having a compositional range of 0.0692–0.6183 (mostly between 0.2 and 0.4) showing a scattering of values of X_Fe(CPX); while X_Mg(CPX) = –0.00/K_D + 0.724 with R² = 6E–05, is showing gentle negative slope having a compositional range of 0.324–0.9591 (mostly between 0.6 and 0.9) showing clustering of X_Mg(CPX) at higher range.

Despite the spread in the data of X_Mg(GT), it shows a negative slope as X_Mg(GT) = –0.018/K_D + 0.39 with R² = 0.21, having a compositional range of 0.0099–0.7058 (mostly between 0.10-0.30) shows clustering of data at intermediate range, inferred as to be a tendency for more magnesium bulk composition to yield lower K_D [2].

Based on the regression values and clustering of temperature ranges calculated for each model, it is evident that Raheim and Green [15], Mysen and Heier [9], Jun Lui [19], Ganguly and Saxena [13], and Ganguly [12] model show very good relation between lnK_D vs 1/T with the maximum number of points (values of temperature) providing best fit lines with high regression values and shorter range of temperature variation.

16. Conclusion

We emphasize that our testing of eleven versions of the GCPX thermometers to the empirical data collected from the literature for this comparative study applies only to rocks containing garnet and clinopyroxene whose compositions can be well described by (Fe-Mg-Ca)₃Al₂Si₃O₁₂ and (Ca-Fe-Mg)Si₂O_6, respectively. The result of this study may not apply to rocks of greatly different thermal regimes and/or mineral chemistry.

We conclude that the following five GCPX thermometers [9, 12, 13, 15, 19] are almost equally valid. These models show the highest regression values and maximum numbers of points (values of temperature) are providing the best fit lines Figures 5–9. Therefore, these models can be considered as the most appropriate ones to be used for the calculation of temperature. The other calibrations gave highly erratic results, and hence are not recommended.

However, Raheim and Green [15] are the best among them as the regression correlation coefficient value; R² is close to 1, which indicates that the maximum number of points defines the best fit line. Therefore, the temperature value obtained by Raheim and Green [15] model is more precise compared to the others.

Although it is always necessary to do further experimental work to refine the calibration of the GCPX thermometer using garnet and clinopyroxene with chemical compositions comparable to natural minerals, it is equally important to improve our knowledge of the various chemical interactions within minerals, such as garnet and clinopyroxene, so that we can improve the activity models for these minerals.

Acknowledgments

The authors thank the Head, Department of Applied Geology, Doctor Harisingh Gour Vishwavidyalaya, Sagar (M.P.), and the Department of Science and Technology, New Delhi, India for providing facilities as including PURSE- Phase-II for conducting present research work.

Supporting information

Additional supporting information may be found in the supporting information tab for this chapter: https://bit.ly/3tL7FKI

Supporting information description:

1. Table S1: Data of KD, lnKD, XFeCpx, XMgCpx, XFeGt, XMg Gt, XCaGt and XMnGt of different rocks samples by different authors

2. Table S2: Data of the Calculated Temperature (ºC) of different rock samples by different authors.

3. Supplementary data:

   1. Figures S(1a-h): Graph of KD versus XFE, XMG, XCA, XMN of garnet and XFE, XMG of Clinopyroxene respectively.

   2. Appendix S1: Reference list of published journals whose data have been used.

Figure S1a.

KD vs X_Fe^Cpx.

Figure S1b.

KD vs X_Mg^Cpx.

Figure S1c.

KD vs X_Fe^Gt.

Figure S1d.

KD vs X_Mg^Gt.

Figure S1e.

KD vs X_Mn^Gt.

Figure S1f.

KD vs X_Ca^Gt.