Effect of Tantalum on Coltan in Cassiterite Using Mathematical Modeling Approach with Respect to Gibbs Energy

Abstract

The objectives of this study were to evaluate the effect of tantalum on COLTAN in Cassiterite using mathematical modeling approach and how it controls the strength, cell size, magnetization, and density (grade), as well as electrical conductivity of COLTAN in Cassiterite. The effectiveness of COLTAN in Cassiterite in Extractive Industry depends on the ratio of tantalum to niobium in the solid solution during crystallization of magma with respect to Gibbs free energy and can be mathematically expressed as Z[X_n-xY_x]O₆ as n ranges from 0 to 5 where x depends on' n'. Mathematically, cassiterite consists of small ion lithophile elements, large ionic charge, with intermediate to greater ionic potential and these elements are partitioned along the aqueous phase, if both the aqueous phase and silicate phase coexist together during crystallization of magma. These trace elements include tin, iron; niobium, tantalum, and zircon are incompatible trace elements because of their inability to achieve a charge balance with silicate structure (SiO₄) in the silicate magma phase. These elements do not exist as free ions in the magma but form complexes with oxygen in the magma during crystallization. Methodologically, 20kg of cassiterite was crushed and pulverized in the laboratory mill machine for an hour, and was taken and sized by sieving into number of size fractions using the automatic sieve shaker for 15 minutes, after processing using high intensity magnetic separator and with the help of ordinary hand magnet of about 0.01Tesla, relative density measure, triaxial testing machine to measure the strength, the relationship between columbite and tantalite can be mathematically established using a COLTAN model. Findings have shown that, with increasing amount of tantalum atom on COLTAN, the COLTAN becomes more tantalized, and both are strong when subjected to shear modulus ,electrical conductivity of COLATN also increases with increasing tantalum, but with its greater density, small cell size because of lanthanide contraction than the niobium, increasing the number of tantalum on COLTAN in cassiterite increases the quality of COLTAN in cassiterite, therefore we haveniobate type cassiterite, tantalized type cassiterite and coltan type cassiterite. In conclusion, the presence or absence of tantalum on COLTAN determines their genetic rock origin, in which the amount of tantalum on COLTAN increased from alkali rock with ∆G ≥ 0, e.g., nephelinesyenite to more silicic, with ∆G > 0, e.g., granite pegmatite which gives the account that cassiterite rich in niobium is less dense than the cassiterite rich in tantalum.After comparative analyses between columbite and tantalite in cassiterite, concise valuable substantive empirical novel model was developed and can be employed to study COLTAN in cassiterite. This concise empirical novel model was, "COLTAN model designed with the aid of: Matrix equation, Oxidation and the Tantalization process, and can be recommended to study the effect of tantalum on COLTAN and the application can improve mineral processing in extractive Industry.