ISSN 2360-7963
Abstract
This study presents a comprehensive mathematical framework to model the crystallization processes of mafic magma, integrating Goldschmidt and Bowen’s theories within a thermodynamic context. By employing advanced mathematical tools such as metrical matrices, set notation, and complex analysis, the research aims to elucidate the distribution and substitution of chemical elements during mineral formation from magma. The model addresses the gap between Bowen’s reaction series and Goldschmidt’s elemental substitution rules, establishing a coordinate geometric relationship between continuous and discontinuous reaction series. The approach facilitates the calculation of mineral compositions and their evolution throughout the crystallization process, with applications to basaltic rocks and associated mineralogy. The methodology incorporates thermodynamic principles, ionic radii, electronegativity, and complex lattice interactions, enabling a holistic understanding of mineral formation and elemental distribution. The findings offer valuable insights for mineral exploration, petrology, and geochemical modeling, advancing the quantitative understanding of igneous rock genesis.
Keywords: Mathematical modeling, Mafic magma, Crystallization processes, Elemental substitution Goldschmidt