Application of Metrical Matrix and set Notation to Rock Formining Minerals using Combined Goldschmidt and Bowen’s Concept with Respect to Thermodynamic Principles

Abstract

Using mathematical context such as Metrical matrix and Set notation methods, the formation of rock forming minerals from magma, depends on the numerical value of each mineral under thermodynamic conditions. Any stable mineral depends on the numerical value for that mineral to exist at certain control condition of temperature, especially at room temperature of 25⁰C (298k) and 1atm pressure. The problem involving the distribution of chemical elements and elemental substitutions in rocks during crystallization of magma, from the beginning of crystallization to the end of crystallization was mathematically formulated using Bowen’s and Goldschmidt combined concept and models and analyzed using Metrical matrix and Set notion methods. This research was focused on bridging the gap between Bowen’s and Goldschmidt concepts concerning the problem of elemental substitution and distribution of chemical elements in rocks throughout the time of crystallization from the beginning to the end of crystallization with mathematical foundation such as Metrical matrix and Set notion methods under thermodynamic change. Finally the “mathematical connection” between Bowen’s and Goldschmidt concepts was used in this research for complete explanation of rock forming minerals from the beginning to the end of crystallization and would help the ‘beginners’ especially students of Earth sciences such as Geology, Mineralogy, Petrology and other chemical science such as Geochemistry and Petroleum Geology to have clear understanding of rock forming minerals from the Magma.