準結晶の合成とヒュームロザーリ則 [in Japanese] Formation of Quasicrystals and Hume-Rothery Rules [in Japanese]
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Stable icosahedral quaicrystals (<I>i-QC</I>) have been identified in a large number alloys. Stability of the <I>i-QCs</I> has been understood in terms of Hume-Rothery rules <I>i.e</I>., atomic size factor and valency electron concentration (<I>e/a</I>) . The stable <I>i-QCs</I> are electron compounds which have strict <I>e/a</I>, and hence most stable <I>i-QCs</I> were discovered along the criterion of <I>e/a</I>. According to the structures of icosahedral clusters derived from the corresponding approximants, the stable <I>i-QCs</I> are classified into three classes ; Al-Mn-Si, Zn-Mg-Al and Cd-Yb. All the <I>i-QCs</I> commonly have their corresponding <I>e/a</I>, 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>i-QC</I> is that the alloys should have a definite <I>e/a</I>. On top of this, a higher stability of the <I>i-QC</I> is expected when the atomic size factor is favored.
X-RAYS 49(1), 12-17, 2007-02-27
The Crystallographic Society of Japan