We extend the weak crystallization theory, commonly used to describe liquid-crystal phase transitions, to the case of metallic alloys. T which are absent in the generic theory with only local interactions. In particular, the condition for stability of iQC that we find, very closely corresponds to the Hume-Rothery rules known empirically for majority of stable iQC; namely, the length of the primary Bragg peak wavevector is approximately equal to the diameter of the Fermi surface. \cite{smth}
he additional ingredient – itinerant electrons – generates non-trivial dependence of free energy on the angles between ordering wave vectors of ionic density. That leads to stabilization of FCC, Rhombohedral, and icosahedral quasicrystalline (iQC) phases,
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