Mathematical Modeling of Cassiterite Using Certain High Field Strength Elements (HFSE) with Respect to Thermodynamics Principle

Abstract

The main purpose of this study was to evaluate Cassiterite ore mathematically, using certain selected minerals of high field strength elements (HFSE) with respect to thermodynamic principle and how they control the formation of cassiterite during crystallization of magma. The effectiveness of Cassiterite ore in Extractive Industry depends on the properties of these minerals of HFSE that composed the Cassiterite during crystallization of magma and can be mathematically expressed as Z[X_n-xY_x]O_{6 ,} [X_n-xY_x]O₄ and, _[X_n-xY_x]O₃  as n ranges from 0 to 5 where x depends on' n'. These minerals contain HFSE and are those that essentially partitioned along the aqueous phase during cratallization magma. 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, the relationship between minerals of HFSE can be mathematically established using a Cassiterite model. Mathematically, findings have shown that, the minerals obtained from cassiterite during processing are mainly minerals of HFSE such as tin, ilmenite, columbite, tantalite, zircon, monazite and sand, and as such classified as, Ferri/Ferrous-Columbte, Ilmeno-Columbite Cassiterite type, and Ilmeno-tantalite types and chemical analysis using XRF revealed the following chemical compositions of cassiterite; SnO_2, TiO₂, Fe₂O₃/Fe₃O₄, Nb₂O₆, Ta₂O_6, ZrO₂. At a given chemical equilibrium under standard condition of temperature and pressure, these HFSE are partitioned along the aqueous phase and they set in matrices to form an Ore of these HFSE that is stable with minimum Gibbs free energy and is highly resistance to weathering during weathering breakdown, such as Cassiterite. In conclusion after the comparative analysis among the minerals of HFSE in cassiterite using matrix equations and certain measures such as density, magnetic susceptibility, and their electrical conductivity, it is observed that, the type of reactions that take place during the formation of Cassiterite are oxidized and isomorphous which include complex, isovalent and heterovalent reactions. This means that there was an oxidation of these complexes from one form to the other and substitution of one element to the other according to size and charge during the formation of cassiterite ore from magma. Presumably, if the reactions occur throughout the time of crystallization from the dry melt to an aqueous state with increasing particular trace elements over the others, then at a given chemical equilibrium with minimum Gibbs free energy, cassiterite can be processed in terms of ferrous/ferric – colubite cassiterite type Ilmeno-Columbite Cassiterite type and Ilmeno – tantalite cassiterite type. Finally, the presence or absence of  HFSE over the other in cassiterite ore determine their genetic rock origin, in which the amount of titanium - tantalum in Cassiterite increased from alkali rock (magmatic) with ∆G ≥ 0, e.g. nepheline syenite to more silicic, with ∆G > 0, e.g. granite pegmatite (hydrothermal) which gives the account that cassiterite rich in ferrous/ferric -niobium is less dense than the cassiterite rich in titanium-tantalum,  therefore as result of this, concise valuable substantive empirical novel model was developed and can be employed to study cassiterite ore. This concise empirical novel model was, ‘Cassiterite' model designed with the aid of: Matrix equation, Oxidation and the isomorphic process, and can be recommended to study the Cassiterite and the application can improve mineral processing in extractive Industry.