Topological Order and Hyperorder in Oxide Glasses and Liquids

The advent of quantum beam sources, which can generate high-flux high-energy neutrons and X-rays, and the development of advanced instruments make it feasible to probe atomic arrangement in disordered materials with high real space resolution [1–5]. A combination of quantum-beam (X-ray and neutron) diffraction (see Chap. 4 ), theoretical simulations such as density functional theory (DFT) (see Chap. 8 ) and molecular dynamics (MD) (see Chap. 9 ), and data-driven structural modeling such as reverse Monte Carlo (RMC, see Chap. 10 ) modeling [6–8] enables us to study topological order in disordered materials. In this chapter, recent research topics on probing the topological order in oxide glasses (see Chap. 15 ) and liquids are introduced. Moreover, the application of topological analyses (see Chap. 11 ) to uncover the hidden topological ordering in the pair correlation is addressed. Finally, we introduce hyperordered glasses and liquids that have been recently discovered to discuss the relationships among diffraction peaks, topological order, and hyperorder in disordered materials.