Dachs Edgar, Benisek Artur
Department of Chemistry and Physics of Materials, Division Mineralogy, University of Salzburg, Jakob-Haringerstrasse 2a, 5020 Salzburg, Austria.
Contrib Mineral Petrol. 2024;179(10):93. doi: 10.1007/s00410-024-02173-6. Epub 2024 Sep 30.
A new activity model for biotite is formulated in the system KO-FeO-MgO-AlO-SiO-HO-TiO-O (KFMASHTO), which extends that for the KFMASH system by introducing a titanium-biotite and a ferric-biotite end-member (: K(TiMg)[(O)(AlSi)O] and : K(FeMg)[(OH)(AlSi)O]), as well as a pyrophyllite end-member (: Al[(OH)SiO]) that accounts for the presence of octahedral excess-Al in natural biotites. Phonon calculations applying density functional theory (DFT) using the software yielded the standard entropies of and as = 328.06 J/(mol·K) and = 301.69 J/(mol·K), and their heat capacity functions. From experimental phase-equilibrium data, the enthalpy of formation value of was constrained as = -6124.68 ± 3.33 kJ/mol. Natural data were used to derive = -5935.3 ± 6.6 kJ/mol. The single-defect DFT method was applied to parameterize important macroscopic mixing properties (macro-'s) involving and end-members in the model ( was treated ideal). -derived microscopic interaction energies (micro-'s) are presented herein for KFMASH-biotite. The octahedral same-site (M1) Mg-Al mixing micro- ( ), the same-site tetrahedral Si-Al mixing parameter ( ) and the related cross-site term are: = 82.5 kJ/mol, = 95.6 kJ/mol (two T1-sites) and 175.1 kJ/mol. The linear combination of these micro-'s gives a macroscopic = 18.8 kJ/mol, that is not transferable to other mineral groups. Micro 's for Mg-Fe mixing in biotite ( , ), are all close to ideality. The biotite activity model of this study is thus a first example of next-generation activity models that use DFT- and thus physically based micro-'s and reassembled macro-'s for petrological calculations. Test calculations on 5 samples from low- to high-grade metamorphic environments covering metapelite to greywacke bulk-compositions using suite of programs illustrate the performance of the new biotite activity model. Computed mineral-chemistries are in all cases in better agreement with measured compositions than resulting from published activity models of biotite.
The online version contains supplementary material available at 10.1007/s00410-024-02173-6.
在KO-FeO-MgO-AlO-SiO-HO-TiO-O（KFMASHTO）体系中建立了一种新的黑云母活度模型，该模型通过引入钛黑云母和铁黑云母端元（：K(TiMg)[(O)(AlSi)O]和：K(FeMg)[(OH)(AlSi)O]）以及叶蜡石端元（：Al[(OH)SiO]）扩展了KFMASH体系的模型，叶蜡石端元解释了天然黑云母中八面体过剩铝的存在。使用该软件应用密度泛函理论（DFT）进行的声子计算得出了 和 的标准熵，分别为 = 328.06 J/(mol·K)和 = 301.69 J/(mol·K)，以及它们的热容函数。根据实验相平衡数据， 的生成焓值被约束为 = -6124.68 ± 3.33 kJ/mol。利用天然数据得出 = -5935.3 ± 6.6 kJ/mol。应用单缺陷DFT方法对模型中涉及 和 端元的重要宏观混合性质（宏观‘ ）进行参数化（ 被视为理想状态）。本文给出了KFMASH - 黑云母基于DFT推导的微观相互作用能（微观‘ ）。八面体同位点（M1）Mg - Al混合微观 （ ）、同位点四面体Si - Al混合参数（ ）以及相关的交叉位点项分别为： = 82.5 kJ/mol， = 95.6 kJ/mol（两个T1位点）和 175.1 kJ/mol。这些微观‘ 的线性组合给出宏观 = 18.8 kJ/mol，该值不可转移到其他矿物组。黑云母中Mg - Fe混合的微观 （ ， ）均接近理想状态。因此，本研究的黑云母活度模型是下一代活度模型的首个实例，该模型使用DFT——从而基于物理的微观‘ 和重新组合的宏观‘ 进行岩石学计算。使用 程序套件对5个从低级到高级变质环境的样品进行测试计算，这些样品涵盖了变质泥质岩到杂砂岩的整体成分，说明了新的黑云母活度模型的性能。在所有情况下，计算得到的矿物化学组成与实测组成的一致性都比已发表的黑云母活度模型更好。
在线版本包含可在10.1007/s00410 - 024 - 02173 - 6获取的补充材料。
