An algebraic approach to cooperative rotations in networks of interconnected rigid units
An algebraic approach to cooperative rotations in networks of interconnected rigid units
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DOI：
10.1107/s2053273318009713
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发表时间：
2018-09-01
影响因子：
1.8
通讯作者：
Stokes, Harold T.
中科院分区：
文献类型：
--
作者：
Campbell, Branton;Howard, Christopher J.;Stokes, Harold T.
由相互连接的刚性单元组成的三维网络组成的结晶固体在功能材料中普遍存在。在许多情况下，应用关键性能对低温、高压或特定化学计量下的刚性单元旋转很敏感。连接刚性单元的共享原子对任何旋转自由度都施加了严格的约束，因此必须在整个网络中保持协作。在晶体中识别协同旋转刚性单元模式（rum）的成功努力已经采用了原子分裂调和势，对群表示理论允许的旋转对称模式的详尽测试，甚至简单的几何考虑。本文提出了一种纯代数方法来识别RUM，其中连通性的条件是用来构建一个线性方程组的旋转对称模振幅。
Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.