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 TiO2, all assembled out of TiO6 or TiO7 polyhedral building blocks, to liquid and amorphous TiO2 in a quantitative two-dimensional similarity plot. We find high structural similarity between a model of amorphous TiO2, obtained by ab initio molecular-dynamics, and the B-TiO2 crystalline polymorph. The general approach presented here sheds new light on a long-standing controversy in the structural theory of amorphous solids.