We review a set of ideas concerning the flexibility of network materials, broadly defined as structures in which atoms form small polyhedral units that are connected at corners. One clear example is represented by the family of silica polymorphs, with structures composed of corner-linked SiO₄ tetrahedra. The rigid unit mode (RUM) is defined as any normal mode in which the structural polyhedra can translate and/or rotate without distortion, and since forces associated with changing the size and shape of the polyhedra are much stronger than those associated with rotations of two polyhedra around a shared vertex, the RUMs might be expected to have low frequencies compared to all other phonon modes. In this paper we discuss the flexibility of network structures, and how RUMs can arise in such structures, both in principle and in a number of specific examples of real systems. We also discuss applications of the RUM model, particularly for our understanding of phenomena such as displacive phase transitions and negative thermal expansion in network materials.

中文翻译：

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刚体单元模式模型：思想和应用回顾


我们回顾了一组关于网络材料柔韧性的想法，广义上定义为原子形成在角落连接的小多面体单元的结构。一个明显的例子是二氧化硅多晶型物家族，其结构由角连接的 SiO₄ 四面体组成。刚体模式（RUM）被定义为结构多面体可以平移和/或旋转而不失真的任何法向模式，并且由于与改变多面体的大小和形状相关的力比与两个多面体围绕共享顶点旋转相关的力强得多，因此与所有其他声子模式相比，RUM可能预期具有低频率。在本文中，我们讨论了网络结构的灵活性，以及 RUM 如何在这种结构中出现，包括原则上和实际系统的一些具体示例。我们还讨论了 RUM 模型的应用，特别是对于我们理解网络材料中的位移相变和负热膨胀等现象。