The nearly free electron model has been applied to investigate the origin of structural stability in quasi-crystalline alloys containing s, p and d elements, through an analysis of X-ray or neutron diffraction patterns. The existence of a Hume-Rothery relation and the presence of a pseudogap in the density of states near the Fermi level is discussed making reference to recent measurements of electronic properties of quasi-crystals. On the basis of the agreement between model predictions and experimental data, a specific electron phase, associated with the quasi-crystalline state, is defined. © 1992.
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