Abstract
Stable icosahedral quaicrystals (i-QC) have been identified in a large number alloys. Stability of the i-QCs has been understood in terms of Hume-Rothery rules i.e., atomic size factor and valency electron concentration (e/a) . The stable i-QCs are electron compounds which have strict e/a, and hence most stable i-QCs were discovered along the criterion of e/a. According to the structures of icosahedral clusters derived from the corresponding approximants, the stable i-QCs are classified into three classes ; Al-Mn-Si, Zn-Mg-Al and Cd-Yb. All the i-QCs commonly have their corresponding e/a, but the dependence of stability on the atomic size factor is different among the three classes. Qualitatively, the most relevant criterion for the formation of the stable i-QC is that the alloys should have a definite e/a. On top of this, a higher stability of the i-QC is expected when the atomic size factor is favored.
