Microscopic Theory of Quasicrystal-Crxrstal Transformation

本文采用蒙特卡罗计算方法研究了十方Al-Ni-Co准晶体的结构模型，其中考虑了准周期平铺中相邻不同种类原子的交换和胖薄六边形中三个菱形的重新洗牌。我们对瓷砖和原子装饰作为原子组成的函数进行了系统的研究。我们发现顶点上有Al原子的HBS平铺的框架在Al成分变化的合理范围内没有变化。这里的HBS瓷砖是由六边形(H)，船形(B)和星形(S)瓷砖组成的图案，并带有适当的原子装饰。在Co含量较高的情况下，得到了具有十角形瓦片的结构。Al和Co之间的相互作用比Al和Ni之间的相互作用更有吸引力，从而稳定了这种十角形图案。除了研究准晶体的结构模型外，我们还对最近发现的镉基和锌基准晶体的近似晶体的电子结构进行了第一性原理研究。发现来自元素形成的Cd和Zn化合物的低空d态对态电子密度赝隙的形成很重要。虽然准晶体和近似物中赝隙的起源已经在近乎自由电子模型（休谟-罗瑟利机制）的框架下进行了讨论，但目前的结果表明，化学物质的选择不仅对控制价电子密度而且对赝隙的形成至关重要。利用“晶体轨道汉密尔顿居布数”，我们发现波函数的成键性质在赝隙处由成键变为反键。这一观察结果表明，cd和zn基化合物的电子结构与普通合金非常不同，而更类似于半导体。

Structural models for decagonal Al-Ni-Co quasicrystals have been studied by Monte-Carlo calculations, in which a swap of nearby atoms of different species and reshuffling of the three rhombi in a fat and thin hexagons in quasiperiodic tiling are considered. We have done systematic studies of the tiling and the atomic decoration as a function of the atomic composition. We find that a framework of the HBS tiling with Al atoms on vertices does not change within a reasonable range of the Al composition change. Here the HBS tiling is a pattern consisting of hexagon (H), boat (B) and star (S) tiles with appropriate atomic decoration. For higher Co composition, a structure with a decagonal tile is obtained. Such a decagonal pattern is stabilized by the more attractive interaction between Al and Co than that between Al and Ni.Besides the studies of structural models of quasicrystals, we have done first-principles studies of electronic structures of approximant crystals for recently discovered Cd-and Zn-based quasicrystals. It is found that low-lying unoccupied d-states coming from an element forming compounds with Cd and Zn are important for formation of pseudogap in the electronic density of states. Although origin of the pseudogap in quasicrystals and approximants has been discussed in a framework of a nearly-free electron model (the Hume-Rothery mechanism), the present results show that choice of chemical species is essential not only for controlling the valence electron density but for the pseudogap formation. Using quantity called "crystal orbital Hamilton population", we find that the bonding nature of wavefunctions is changed from bonding to antibonding at the pseudogap. This observation suggests that the electronic structures of Cd-and Zn-based compounds are very different from ordinary alloys and more similar to semiconductors.