由正方形-三角形十二边形镶嵌导出的准周期Frank-Kasper相位
Quasiperiodic Frank-Kasper phases derived from the square-triangle dodecagonal tiling
摘要：
Frank-Kasper（F-K）相形成描述许多金属间合金的一组重要的大晶胞晶体结构。它们通常用原子环境来描述，原子有$12, 14, 15$和$16$邻居，编码成规范的$Z_p$单元（$p$是配位数），$p=12$对应于局部二十面体环境。此外，长程结构由仅连接非二十面体位点（具有$p\ne 12$）的网络（称为“主骨架”或“向错网络”）的几何结构捕获。另一个有趣的描述，有效的所谓的“分层的F-K相位”，相当于给出简单的规则来装饰特定的周期性的2d平铺三角形和正方形，并最终得到3d周期性的F-K相位。准晶相有时可以在相图中F-K晶体合金的附近找到;因此，理解标准F-K结构规则是否以及如何在基础准周期结构之上推广是很有意义的。特别自然的是，研究由正方形和（等边）三角形组成的具有十二角对称性的正方形-三角形准周期镶嵌如何可以用作生成某些F-K类准晶结构的构建框架。我们在这里展示了如何产生两种类型的这样的结构，这是准周期性的平面和周期性的第三方向，并包含（或不包含）$Z_{16}$网站。
英文摘要：
Frank-Kasper (F-K) phases form an important set of large-cell crystalline structures describing many inter-metallic alloys. They are usually described in term of their atomic environments, with atoms having $12, 14, 15$ and $16$ neighbours, coded into the canonical $Z_p$ cells (with $p$ the coordination number), the case $p=12$ corresponding to a local icosahedral environment. In addition, the long range structure is captured by the geometry of a network (called either "major skeleton" or "disclination network") connecting only the non-icosahedral sites (with $p\ne 12$). Another interesting description, valid for the so-called "layered F-K phases", amounts to give simple rules to decorate specific periodic 2d tilings made of triangles and squares and eventually get the 3d periodic F-K phases. Quasicrystalline phases can sometime be found in the vicinity, in the phase diagram, of the F-K crystalline alloys; it is therefore of interest to understand if and how the standard F-K construction rules can be generalized on top of an underlying quasiperiodic structure. It is in particular natural to investigate how well square-triangle quasiperiodic tilings with dodecagonal symmetry, made of square and (equilateral) triangles, can be used as building frames to generate some F-K-like quasicrystalline structures. We show here how to produce two types of such structures, which are quasiperiodic in a plane and periodic in the third direction, and containing (or not) $Z_{16}$ sites.
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