Heat capacity and third-law entropy of kaersutite, pargasite, fluoropargasite, tremolite and fluorotremolite

The heat capacities ( C p) of natural kaersutite, tremolite and fluoropargasite, as well as of synthetic pargasite were measured in the temperature range from 5 to 764 K and were used to calculate the standard entropy ( S °) of the pure end-members. The data between 5 and 300 K were obtained by relaxation calorimetry, the high-temperature data (282–764 K) by differential scanning calorimetry (DSC). Natural kaersutite was characterized by electron microprobe analysis and Mossbauer spectroscopy, the other samples had been characterized previously. Assuming ideal OH–F mixing, the C p data of natural fluoropargasite ( X F = 0.605) were used to estimate the heat capacity and standard entropy difference between OH and F end-members of pargasite and tremolite. Fits to the DSC data yielded the following polynomials for the corrected pure end-members (valid above 298 K, T [K], C p [J/mol·K]): \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{eqnarray*}&&Kaersutite\ {-}\ NaCa\_{2}(Mg\_{4}\ Ti^{4+})\ (Si\_{6}Al\_{2})O\_{22}(OH)O\\&&\mathit{C}\_{p}\ =\ 1145.3014\ {-}\ 3356.9700\mathit{T}^{{-}0.5}\ {-}\ 4.3995\ {\times}\ 10^{7}\mathit{T}^{{-}2}\ +\ 5.8164\ {\times}\ 10^{9}\mathit{T}^{{-}3}\end{eqnarray*} \end{document} \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{eqnarray*}&&Pargasite\ {-}\ NaCa\_{2}(Mg\_{4}Al)(Si\_{6}Al\_{2})O\_{22}(OH)\_{2}\\&&\mathit{C}_{p}\ =\ 1251.9495\ {-}\ 5934.2927\mathit{T}^{{-}0.5}\ {-}\ 3.6235\ {\times}\ 10^{7}\mathit{T}^{{-}2}\ +\ 4.8999\ {\times}\ 10^{9}\mathit{T}^{{-}3}\end{eqnarray*} \end{document} \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{eqnarray*}&&Fluoropargasite\ {-}\ NaCa\_{2}(Mg\_{4}Al)(Si\_{6}Al\_{2})O\_{22}F\_{2}\\&&\mathit{C}_{p}\ =\ 1218.8568\ {-}\ 5923.9772\mathit{T}^{{-}0.5}\ {-}\ 2.9302\ {\times}\ 10^{7}\mathit{T}^{{-}2}\ +\ 3.4496\ {\times}\ 10^{9}\mathit{T}^{{-}3}\end{eqnarray*} \end{document} \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{eqnarray*}&&Tremolite\ {-}\ Ca\_{2}Mg\_{5}Si\_{8}O\_{22}(OH)\_{2}\\&&\mathit{C}\_{p}\ =\ 1278.1996\ {-}\ 8114.5798\mathit{T}^{{-}0.5}\ {-}\ 2.3199\ {\times}\ 10^{7}\mathit{T}^{{-}2}\ +\ 2.8845\ {\times}\ 10^{9}\mathit{T}^{{-}3}\end{eqnarray*} \end{document} \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{eqnarray*}&&Fluorotremolite\ {-}\ Ca\_{2}Mg\_{5}Si\_{8}O\_{22}F\_{2}\\&&\mathit{C}\_{p}\ =\ 1145.1069\ {-}\ 8104.2643\mathit{T}^{{-}0.5}\ {-}\ 1.6266\ {\times}\ 10^{7}\mathit{T}^{{-}2}\ +\ 1.4342\ {\times}\ 10^{9}\mathit{T}^{{-}3.}\end{eqnarray*} \end{document} A comparison with the various C p- T polynomials and additive estimation techniques suggested in the literature for T > 300 K indicates that most of these lie in a corridor within ±1 % of the values derived here. However, none of these individual alternatives works equally well over the whole temperature range 300–1000 K. Fits of the low-temperature C p’s to a combination of Debye, Einstein and Schottky functions yielded a standard entropy of 599.7 ± 0.8 J/mol·K for kaersutite, 591.0 ± 4.7 J/mol·K for pargasite and 550.1 ± 0.8 J/mol·K for tremolite (no site-configurational entropy contributions added). These S ° values of pargasite and tremolite are in excellent agreement with previous determinations from phase equilibrium experiments and low-temperature adiabatic calorimetry. The entropy difference between OH and F pargasite was found to be 5.3 J/mol·K and S ° of fluoropargasite is 585.7 ± 1.2 J/mol·K. Assuming the same difference for tremolite, S ° of fluorotremolite amounts to 544.8 ± 0.8 J/mol·K. Similar to F-phlogopite and F-apatite, fluoropargasite has a larger heat capacity at low temperatures compared to its OH analogue with a cross-over around 50 K and a possible reason for this behaviour is discussed. Based on the S ° values of pargasite, tremolite and their F analogues from this study, and on the results of OH–F partitioning experiments from the literature, a standard reaction enthalpy Δ H Ro = −5.5 ± 1.0 kJ/mol for the pargasite-phlogopite F–OH exchange, and a Δ H Ro = − 14.8 ± 2.5 kJ/mol for the tremolite-phlogopite F–OH exchange were calculated. Standard enthalpy of formation values for fluoropargasite and fluorotremolite can then be derived.