Similarity Between Amorphous and Crystalline Phases: The Case of TiO2

Amorphous and crystalline materials differ in their long-range structural order. On the other hand, short-range order in amorphous and crystalline materials often appears similar. Here, we use a recently introduced method for obtaining quantitative measures for structural similarity to compare crystalline and amorphous materials. We compare seven common crystalline polymorphs of TiO 2 , all assembled out of TiO 6 or TiO 7 polyhedral building blocks, to liquid and amorphous TiO 2 in a quantitative two-dimensional similarity plot. We find high structural similarity between a model of amorphous TiO 2 , obtained by ab initio molecular-dynamics, and the B-TiO 2 crystalline polymorph. The general approach presented here sheds new light on a long-standing controversy in the structural theory of amorphous solids.