Using Mathematical Methods Finding Physical Properties of Magnetite

The present work is based on group theoretic analysis of crystal structures. Group theory can be employed to a variety of problems in physics and chemistry. It plays a major role in the solution of solid state physics problems. The concept of symmetry plays an important role in our physical environment. The symmetry of a molecule can be used to determine various physical properties of a crystal using group theoretical methods. The applications of magneto-electric devices lie in the regions of millimeter and sub-millimeter wavelengths and in the areas of reducing electrical conductivity, improving dielectric magnetic or magneto-electric properties by solid solutions improving optical quality and obtaining larger crystals. Ferro-electric, Ferro-elastic and magneto-electric polarized domain pairs and tensor pairs are calculated using coset decomposition and double coset decomposition respectively for the crystal magnetite (Fe3O4). While considering Ferro-electric and Ferro-elastic properties only ordinary point group m3m is considered as prototypic point group since they are non-magnetic properties.