Instructions

Instructions are given on this sheet in the program. Note: if users encounter an Excel-Circular Reference problem, they need to go to File > Options > Formulas, and select the ‘Enable iterative calculation’ check box in the Calculation options section. After clicking on the check boxes in the ‘Data Input’ spreadsheet, the output of formula proportions in atoms per formula unit (apfu) and thermobarometry results can take a few seconds due to iterative equations.

Data Input

‘Data Input’ contains access to the spreadsheets for user data (i.e. major oxides-wt.% of mineral and glass/whole-rock compositions). First, to enable data entry the check boxes on the ‘Data Input’ spreadsheet must be clicked in the order: (1) select ‘Data input’; (2) select the appropriate ‘Mineral’ and enter compositions in the appropriate panel on the right; (3) select ‘Calculation’ to enable the calculation of cation formula and P–T results – presented in the subsequent sheets (Fig. 2). In the majority of the ‘Data Input’ sheets, the upper right panel is for mineral compositions, the lower right panel is for ‘glass’ or ‘whole-rock compositions’ – the latter should be used if users want to make P–T calculations based on mineral–liquid geothermobarometry.

Fig. 2. The control panel for data entry which must be in the order of each mineral: 1) Data input, 2) Minerals, and 3) Calculation.

Olivine

Olivine is a ferromagnesian mineral represented by the two end-members of forsterite (Mg₂SiO₄) and fayalite (Fe₂SiO₄). Olivine compositions are recalculated on the basis of four oxygens and typically shown as molar percentages of forsterite (Fo) and fayalite (Fa) in the literature and also in MagMin_PT.

MagMin_PT calculates T (°C) from EPMA data using liquid thermometers (Helz and Thornber, Reference Helz and Thornber1987; Beattie, Reference Beattie1993; Sisson and Grove, Reference Sisson and Grove1993; Putirka et al., Reference Putirka, Perfit, Ryerson and Jacksond2007; Putirka, Reference Putirka, Putirka and Tepley2008). For the olivine–liquid thermometer, the composition of ‘whole rock’ or ‘glass’ needs to be entered in the ‘Data Input’ sheet. Then, the program calculates the Fe–Mg exchange coefficient or K_D(Fe–Mg)^ol–liq using equations 1 and 2 to test for equilibrium between olivine and liquid. If the entered liquid is under equilibrium with the olivine composition, this value is expected to be in the range of K_D = 0.30 ± 0.03 (Roeder and Emslie, Reference Roeder and Emslie1970; Toplis, Reference Toplis2005), which means that the thermometer can be applicable to the volcanic system. The results are presented in the ‘Olivine’ sheet.

Pyroxene

This sheet designed for pyroxenes whose general chemical formula is M2M1T2O6. They are classified according to the occupancy of the M2 site, though Morimoto et al. (Reference Morimoto, Fabries, Ferguson, Ginzburg, Ross, Seifert, Zussman, Aoki and Gottardi1988) assumed the M1 and M2 sites were a single M site, because T, M1 and M2 sites are a function of temperature in pyroxenes (Yavuz, Reference Yavuz2013). In MagMin_PT, a pyroxene formula is recalculated on the basis of six oxygens according to the scheme of allocation of cations by Morimoto et al. (Reference Morimoto, Fabries, Ferguson, Ginzburg, Ross, Seifert, Zussman, Aoki and Gottardi1988) and the estimation of Fe³⁺ is made using the following equation given by Droop (Reference Droop1987):

(3)$${\it F\ } = 2{\it X}( {1 \ndash {\it T}/{\it S}} ) $$

where T is the ideal number of cations per formula unit, and S is the observed cation total per X oxygens calculated assuming all iron to be Fe²⁺.

In the ‘Data Input’ sheet in MagMin_PT, three different options exist for pyroxene data entry. One option is ‘Two pyroxene’ data under the heading ‘Minerals’, with results appearing in the ‘Pyroxene’ sheet. In this sheet, many classification diagrams (Morimoto and Kitamura, Reference Morimoto and Kitamura1983; Morimoto et al., Reference Morimoto, Fabries, Ferguson, Ginzburg, Ross, Seifert, Zussman, Aoki and Gottardi1988) and several two pyroxene geothermobarometers (Wood and Banno, Reference Wood and Banno1973; Wells, Reference Wells1977; Lindsley and Andersen, Reference Lindsley and Andersen1983; Brey and Köhler, Reference Brey and Köhler1990; Putirka, Reference Putirka, Putirka and Tepley2008) are produced (Fig. 3). Another option for data input is to enter ortho- and clinopyroxene data independently. This is especially useful for mineral–liquid geothermobarometry that requires calculations of the Fe–Mg exchange coefficient for orthopyroxene (K_D(Fe–Mg)^opx–liq) and clinopyroxene (K_D(Fe–Mg)^cpx–liq) to test for equilibrium between mineral–liquid pairs according to equation 2. K_D values are expected to be in the range of 0.29 ± 0.06 for opx and 0.27 ± 0.03 for cpx to meet equilibrium conditions. The equilibrium tests are also graphically portrayed in a ‘Rhodes Diagram’ (Rhodes et al., Reference Rhodes, Dungan, Blanchard and Long1979) in the ‘Pyroxene’ sheet, resulting in a binary plot of 100×Mg# Liquid vs. 100×Mg# orthopyroxene or clinopyroxene. On such a plot, the equilibrated mineral–liquid pairs lie between two dashed lines marking error bounds.

Fig. 3. Plot of ortho- and clinopyroxene compositions (Deer et al., Reference Deer, Howie and Zussman1992) on the pyroxene isotherm curves (Lindsley and Andersen, Reference Lindsley and Andersen1983).

MagMin_PT also includes an equilibrium test for clinopyroxene in the ‘Pyroxene’ sheet, which is a comparison between predicted and observed values for the clinopyroxene components on a binary plot. Under equilibrium conditions, the predicted and observed values plot on, or close to, the one-to-one regression line.

Amphibole

Amphiboles are one of the most complex rock-forming double-chain inosilicates with a wide range of compositions, and are represented by a general formula of AB₂C₅T₈O₂₂W₂. Amphibole classification has not been satisfactory since Leake (Reference Leake1968) presented the first classification for calcic amphiboles. New discoveries of amphibole compositions has led to many classification attempts in parallel with ongoing development in analytical techniques in the intervening years (e.g. IMA reports of Leake, Reference Leake1978; Leake et al., Reference Leake, Woolley, Arps, Birch, Gilbert, Grice, Hawthorne, Kato, Kisch, Krivovichev, Linthout, Laird, Mandarino, Maresch, Nickel, Rock, Schumacher, Smith, Stephenson, Ungaretti, Whittaker and Guo1997; Leake et al., Reference Leake, Woolley, Birch, Burke, Ferraris, Grice, Hawthorne, Kisch, Krivovichev, Schumacher, Stephenson and Whittaker2003; and Hawthorne et al., Reference Hawthorne, Oberti, Harlow, Maresch, Martin, Schumacher and Welch2012). These attempts have also been accompanied by the addition of new computer programs and spreadsheets to overcome classification problems resulting from the compositional complexity of amphiboles (e.g. Currie, Reference Currie1997; Yavuz, Reference Yavuz1999; Mogessie et al., Reference Mogessie, Ettinger, Leake and Tessadri2001; Esawi, Reference Esawi2004; Yavuz, Reference Yavuz2007; Locock, Reference Locock2014).

MagMin_PT converts the entered amphibole microprobe analysis in ‘Data Input’ to formula proportions in atoms per formula unit (apfu) in the ‘Amphibole’ sheet according to the IMA 2012 recommendations (Hawthorne et al., Reference Hawthorne, Oberti, Harlow, Maresch, Martin, Schumacher and Welch2012), which results in eight different binary classification diagrams (Fig. 4). MagMin_PT includes an alternative formula calculation scheme based on the machine learning method for Li-free and Li-bearing amphiboles by Li et al. (Reference Li, Zhang, Behrens and Holtz2020a). The users can compare their formula calculations between this new approach and IMA 2012. The Fe³⁺/Fe²⁺ ratio cannot be determined routinely by electron microprobe techniques therefore in MagMin_PT Fe³⁺ it is estimated empirically on the basis of the electroneutrality and stoichiometry rule. Further details on the Fe³⁺ calculations for IMA 2012 classification are given in Appendix III of Hawthorne et al. (Reference Hawthorne, Oberti, Harlow, Maresch, Martin, Schumacher and Welch2012).

Fig. 4. Classification diagram of calcic-amphibole according to IMA 2012 (Hawthorne et al., Reference Hawthorne, Oberti, Harlow, Maresch, Martin, Schumacher and Welch2012). Data set from Deer et al. (Reference Deer, Howie and Zussman1992).

MagMin_PT includes mineral–mineral (e.g. amphibole–plagioclase), mineral–liquid (e.g. amphibole–liquid) and single-phase amphibole (e.g. Al-in-hornblende) geothermobarometers proposed by different authors in the ‘Amphibole’ sheet. Al-in-hornblende calibrations are the most commonly used barometers based on EPMA-derived data. Several Al-in-hornblende barometers (Hammerstrom and Zen, Reference Hammerstrom and Zen1986; Hollister et al., Reference Hollister, Grissom, Peters, Stowell and Sisson1987; Johnson and Rutherford, Reference Johnson and Rutherford1989; Blundy and Holland, Reference Blundy and Holland1990; Schmidt, Reference Schmidt1992; Anderson and Smith, Reference Anderson and Smith1995) are included in the program. However, these barometers should be used with caution because they are valid only under restricted conditions, and so not generally applicable to igneous systems (Erdmann et al., Reference Erdmann, Martel, Pichavant and Kushnir2014; Putirka, Reference Putirka2016). Amphibole–plagioclase (Blundy and Holland, Reference Blundy and Holland1990; Holland and Blundy, Reference Holland and Blundy1994; Molina et al., Reference Molina, Moreno, Castro, Rodríguez and Fershtater2015; Molina et al., Reference Molina, Cambeses, Moreno, Morales, Montero and Bea2021) and amphibole–liquid (Molina et al., Reference Molina, Moreno, Castro, Rodríguez and Fershtater2015; Putirka, Reference Putirka2016) geothermobarometers require plagioclase and glass or whole-rock compositions to be entered into the program (lower right panel on Data Input sheet). The Fe–Mg exchange coefficient (K_D(Fe–Mg)^amp–liq) is expected to be in the range of 0.28 ± 0.11 for the amphibole–liquid thermobarometer.

The program also presents oxygen buffers constraining oxygen fugacity ($f_{\rm{O_2}}$) as a function of temperature (Fegley, Reference Fegley2012), and water content (%) of melt (Ridolfi et al., Reference Ridolfi, Renzulli and Puerini2010; Ridolfi, Reference Ridolfi2021) calculated from amphibole compositions.

Biotite

Biotites are trioctahedral micas characterised by end-members of KFe₃AlSi₃O₁₀(OH)₂ (annite), KMg₃AlSi₃O₁₀(OH)₂ (phlogopite), KFe₂AlAl₂Si₂O₁₀(OH)₂ (siderophyllite) and KMg₂AlAl₂Si₂O₁₀(OH)₂ (eastonite) (Rieder et al., Reference Rieder, Cavazzini, D'yakonov, Frank-Kamenetskii, Gottardi, Guggenheim, Koval’, Müller, Neiva, Radoslovich, Robert, Sassi, Takeda, Weiss and Wones1999). In MagMin_PT, the biotite formula is calculated on the basis of 11, 22 or 24 oxygens depending on user data (e.g. available of H₂O analysis) and oxidation state of biotite, etc. Therefore, this can be done traditionally using Rieder et al. (Reference Rieder, Cavazzini, D'yakonov, Frank-Kamenetskii, Gottardi, Guggenheim, Koval’, Müller, Neiva, Radoslovich, Robert, Sassi, Takeda, Weiss and Wones1999), and Fe³⁺ can be calculated on the basis of the equations given by Dymek (Reference Dymek1983), though this may result in large errors in the estimations of Fe³⁺/ΣFe. The concentration of Li₂O in biotites, if essential but not known, can be estimated using the empirical equations in the program (Tindle and Webb, Reference Tindle and Webb1990; Tischendorf et al., Reference Tischendorf, Gottesmann, Förster and Trumbull1997; Tischendorf et al., Reference Tischendorf, Förster and Gottesmann1999). Alternatively, MagMin_PT includes a new scheme for the biotite formula calculation and Fe³⁺ estimation based on a machine learning method by Li et al. (Reference Li, Zhang, Behrens and Holtz2020b). The program includes basic classification diagrams for biotites, and for micas to some extent. MagMin_PT also has options for P–T (Luhr et al., Reference Luhr, Carmichael and Varekamp1984; Uchida et al., Reference Uchida, Endo and Makino2007) calculations and oxygen buffers (Wones and Eugster, Reference Wones and Eugster1965; Wones, Reference Wones1989). Pressure–temperature calculations for biotites do not require whole-rock or glass analysis data because these are not liquid-based thermobarometers.

Feldspars

Feldspars are classified according to the end-members of the NaAlSi₃O₈ (albite, Ab) – CaAl₂Si₂O₈ (anorthite, An) – KAlSi₃O₈ (orthoclase, Or) solid solution (after Deer et al., Reference Deer, Howie and Zussman1992). Compositions between Ab and An are referred to as plagioclases and those between Ab and Or as alkali feldspars (Fig. 5).

Fig. 5. Classification of feldspars according to the end-members of the Ab–An–Or ternary diagram. Data set from Deer et al. (Reference Deer, Howie and Zussman1992).

In MagMin_PT, the feldspar formula is recalculated on the basis of 8, 16 or 32 oxygens depending on user choice, allowing Ab–An–Or components to be calculated and plotted in the feldspar ternary diagram. The program includes several thermobarometers (e.g. plagioclase–liquid, alkali feldspar–liquid, two feldspar etc). For mineral–liquid thermobarometers, users should enter their whole-rock or glass composition into the ‘Data Input’ sheet, and then test for equilibrium between pairs on the basis of the Ab–An exchange coefficient (K_D) using equation 4. The plagioclase–liquid equilibrium can also be used for a hygrometer, if the temperature is well-defined (Putirka, Reference Putirka2005, Reference Putirka, Putirka and Tepley2008). Thus, the program calculates H₂O (wt.%) content of the liquid using results from the aforementioned hygrometer. MagMin_PT includes another water content (H₂O wt.%) calculation procedure using the Al₂O₃ content of the melt as a hygrometer (P < 4 kbar) (Pichavant and Macdonald, Reference Pichavant and Macdonald2007), so that users can compare H₂O results from two different calculations.

(4)$$K_D( {\rm An-Ab} ) ^{\,pl-liq\;} = \displaystyle{{X_{Ab}^{\,pl} X_{AlO_{1.5}}^{liq} X_{CaO}^{liq} } \over {X_{An}^{\,pl} X_{NaO_{0.5}}^{liq} X_{SiO_2}^{liq} }}$$

Magnetite–Ilmenite

Ilmenite and magnetite are generally termed as Fe–Ti oxides with the idealised formula of FeTiO₃ and Fe₃O₄, respectively. Two major solid-solution series occur as ‘ulvöspinel–magnetite’ and ‘ilmenite–hematite’ in the FeO–Fe₂O₃–TiO₂ system. The compositions of coexisting ilmenite and magnetite have been used extensively as a thermobarometer because their compositions are strongly dependent on ${f_{\rm{O_2}}}$ (oxygen fugacity) and the T at which they equilibrated.

In natural magmatic systems, there are several buffer reactions that magnetite is involved in that can be used to characterise the oxidation state of magmas, such as the hematite–magnetite (HM), the quartz–fayalite–magnetite (QFM), and the magnetite–wüstite (MW) reactions. The Nickel-Nickel Oxide (NNO) buffer reaction does not occur in natural magmas though is commonly used for reference. Log oxygen fugacity, an index of the redox state in a magma for each buffer assemblage was compiled by Frost (Reference Frost and Lindsley1991) and calculated from:

(5)$${\rm log}\;{f_{\rm{O_2}}} = \displaystyle{{\rm A} \over {\it T}} + {\rm B} + \displaystyle{{{\rm C}( {{\it P}-1} ) } \over {\it T}}$$

where T is temperature in Kelvin (K), P is pressure (bar), and A, B and C are buffers from equilibrium expressions according to Frost (Reference Frost and Lindsley1991).

Magnetite and ilmenite formulae are calculated on the basis of 4 and 3 oxygens, respectively in MagMin_PT. The calculation results are shown on ternary diagrams (e.g. FeO–Fe₂O₃–TiO₂ or R²⁺–R³⁺–Ti⁴⁺). Fe³⁺ separation is according to the equation of Droop (Reference Droop1987). MagMin_PT calculates T (°C) and $f_{\rm{O_2}}$ values, calibrated by different researchers (Powell and Powell, Reference Powell and Powell1977; Spencer and Lindsley, Reference Spencer and Lindsley1981; Andersen and Lindsley, Reference Andersen and Lindsley1985; Sauerzapf et al., Reference Sauerzapf, Lattard, Burchard and Engelmann2008), and their results are plotted on a binary diagram with several buffer curves (e.g. MW, QFM, NNO and HM). Users can adjust the buffer curves of the HM and QFM as ‘low T’, ‘medium T’ or ‘high T’ according to their systems. The program presents another binary diagram of T (°C) vs. ΔNNO, which is the relative oxygen fugacity at given T for NNO.

A revised Fe–Ti oxide geothermometer and oxygen-barometer has been published by Ghiorso and Evans (Reference Ghiorso and Evans2008). This is based on a thermodynamic model that produces different results than older calibrations, most notably in the estimation of oxidation state under relatively oxidised conditions (>NNO + 1). This thermobarometry is not included in MagMin_PT, however users can find an icon in the ‘Magnetite-Ilmenite’ sheet redirecting them to a web-based application designed by these authors for the T (°C) and NNO calculations.

Apatite

Apatite, Ca₅(PO₄)₃(F,Cl,OH), is a member of the group of phosphate minerals, and it is very common as an accessory phase in igneous rocks. MagMin_PT includes apatite formula (e.g. 25 or 26 oxygens) and saturation temperature calculations. Apatite saturation temperature (Piccoli et al., Reference Piccoli, Candela and Williams1999; Piccoli and Candela, Reference Piccoli, Candela, Kohn, Rakovan and Hughes2002) is calculated from whole-rock geochemical data that must be entered into the ‘Data Input’ sheet in the program.

Zircon

Zircon is an accessory orthosilicate with the formula of ZrSiO₄. It is commonly found as early-formed small crystals enclosed in later minerals in magmatic rocks. When enclosed, especially in biotite or amphibole, pleochroic haloes resulting from radioactive element content (Th,U) can be observed optically around zircon (Deer et al., Reference Deer, Howie and Zussman1992).

MagMin_PT calculates zircon formulae on the basis of 4 oxygens. The program includes options for ‘zircon saturation temperature’ and ‘Ti-in-zircon thermometry’. Therefore, the saturation temperature of zircon (Hanchar and Watson, Reference Hanchar, Watson, Hanchar and Hoskin2003; Boehnke et al., Reference Boehnke, Watson, Trail, Harrison and Schmitt2013) can be calculated from the whole-rock chemistry with the parameters M [(Na + K + 2Ca)/(Al × Si)] of Watson and Harrison (Reference Watson and Harrison1983) and FM [(Na + K + (2Ca + Fe + Mg))/(Al × Si)] of Ryerson and Watson (Reference Ryerson and Watson1987). Additionally, Ti-in-zircon thermometry T (°C) of Watson et al. (Reference Watson, Wark and Thomas2006) can be calculated by the program and is included in the ‘Zircon’ spreadsheet.