Abstract
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.
Highlights
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
A very important note is that this law gives the number of occupied electronic quantum states (OEQS)
Summary
All crystalline materials crystallize in one of seven crystalline systems which have different shapes and sizes. The first attempt to answer this question was initiated by Hume Rothery rules and his coworkers [1] formulated in 1926. These rules include solid solubility rules and electron concentration rule. Electron concentration rule states that at particular value of valence electron concentration ratio (VEC), intermetallic compounds are formed and have the same crystal structure. These compounds are termed electron compounds or Hume-Rothery compounds and do not obey the valency laws of chemistry.
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