Abstract
Calculations using the density-functional theory (DFT) in combination with the single defect method were carried out to determine the heat of mixing behaviour of mineral solid solution phases. The accuracy of this method was tested on the halite–sylvite (NaCl–KCl) binary, pyrope–grossular garnets (Mg3Al2Si3O12–Ca3Al2Si3O12), MgO–CaO (halite structure) binary, and on Al/Si ordered alkali feldspars (NaAlSi3O8–KAlSi3O8); as members for coupled substitutions, the diopside–jadeite pyroxenes (CaMgSi2O6–NaAlSi2O6) and diopside–CaTs pyroxenes (CaMgSi2O6–CaAlAlSiO6) were chosen for testing and, as an application, the heat of mixing of the tremolite–glaucophane amphiboles (Ca2Mg5Si8O22(OH)2–Na2Mg3Al2Si8O22(OH)2) was computed. Six of these binaries were selected because of their experimentally well-known thermodynamic mixing behaviours. The comparison of the calculated heat of mixing data with calorimetric data showed good agreement for halite–sylvite, pyrope–grossular, and diopside–jadeite binaries and small differences for the Al/Si ordered alkali feldspar solid solution. In the case of the diopside–CaTs binary, the situation is more complex because CaTs is an endmember with disordered cation distributions. Good agreement with the experimental data could be, however, achieved assuming a reasonable disordered state. The calculated data for the Al/Si ordered alkali feldspars were applied to phase equilibrium calculations, i.e. calculating the Al/Si ordered alkali feldspar solvus. This solvus was then compared to the experimentally determined solvus finding good agreement. The solvus of the MgO–CaO binary was also constructed from DFT-based data and compared to the experimentally determined solvus, and the two were also in good agreement. Another application was the determination of the solvus in tremolite–glaucophane amphiboles (Ca2Mg5Si8O22(OH)2–Na2Mg3Al2Si8O22(OH)2). It was compared to solvi based on coexisting amphiboles found in eclogites and phase equilibrium experiments.
Highlights
Introduction∆Hmix is a substantial thermodynamic property describing the behaviour of solid solutions
This contribution is a continuation of our former study (Benisek and Dachs 2018), where we calculated internal energies and entropies of 21 well-known endmembers using the density-functional theory (DFT) and transformed them into standard enthalpies of formation from the elements and Electronic supplementary material The online version of this article contains supplementary material, which is available to authorized users.The enthalpy of a solid solution at a particular composition (H(X)) may deviate from the behaviour of a mechanical mixture, i.e. from the linear combination of the enthalpies of the endmembers A and B (Hmechmix): Hmechmix = XAHA + XBHB . (1)HA, HB, XA, and XB are the enthalpies and the mole fractions of the A and B components, respectively
Physics and Chemistry of Minerals (2020) 47:15 deviation is called the excess enthalpy of mixing or the heat of mixing (∆Hmix): ΔHmix = H(X)− 1 − XB HA + XBHB
Summary
∆Hmix is a substantial thermodynamic property describing the behaviour of solid solutions This property is responsible for ordering and exsolution phenomena, e.g. exsolution lamellae in feldspars (perthite), in calcite–dolomite and in pyroxene solid solutions; ordering in omphacite. Navrotsky 1997; Hovis 2017; Benisek et al 2003; Carpenter et al 1985; Newton et al 1977), which is a rather time-consuming technique These data are described by a mixing model using so-called interaction parameters (WAB and WBA), e.g. the Margules mixing model: ΔHmix = 1 − XB XB2 WAB + 1 − XB 2XBWBA. Such a description is necessary to define the activity–composition relations, which are needed for petrological investigations (e.g. geothermometry, calculations of equilibrium phase diagrams)
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