Crystalline Accommodation Law Explains The Crystalline Structure of Materials
Keywords:Fermi sphere, Brillouin zone, Valence electron concentration, Crystal Systems, Primitive Cell, Hume-Rothery rules, crystalline accommodation law, OEQS notation
All crystalline materials crystallize in one of seven crystalline systems which have different shapes and sizes. Why crystalline materials take particular forms of crystals and what make the atoms arrange themselves in these forms. Actually, until now there is no well defined law can account for the crystalline structure of materials. Here we show that the crystalline accommodation law, which is theoretically derived and experimentally verified, can explain the crystalline structure of all types of phases. This law is derived directly from the quantum conditions on the free electrons Fermi gas inside the crystal. The new law relates both the volume of Fermi sphere VF and volume of Brillouin zone VB to the valence electron concentration VEC as, for all crystalline systems and phases, where n is the number of atoms per lattice point or primitive cell. Also because of this law, we introduce the occupied electronic quantum states notation (OEQS), which determine the number of occupied zones in the valence band.
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