Abstract
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.
Highlights
The major difference between amorphous and crystalline materials lies in the long-range structural order
Progress has been made with the advance of reliable computational techniques, and it is possible to simulate the amorphous−crystalline phase transition in PC materials at experimental time scales using density functional theory (DFT).[9−11] On the other hand, while structural data on particular amorphous systems is collected, little progress has been made on a fundamental understanding of the structure of the amorphous state itself
What is the extent of intermediate and long-range order in the amorphous structure, i.e., the amount of randomness in the system? how close is the relationship between the fundamental building blocks in amorphous materials and the corresponding crystals?
Summary
Figure 1. 216-atom models of (a) liquid (2250 K, 3.21 g cm−3) and (b) solid (300 K, 3.57 g cm−3) a-TiO2, as obtained from AIMD simulations. The proportion of octahedral TiO6 units is larger in the amorphous phase (49.8%) than in the liquid (29.0%) This trend is in accordance with previous findings, considering the different densities of the phases.[15−17] What about the crystalline polymorphs? Another important feature of the similarity map is that a distinction between liquid and solid phases is clearly visible, an indication of their fundamental structural differences. The vertex/edge sharing ratio between polyhedral units explains the similarity of the amorphous phase to brookite, but no analogous simple argument can be made for the similarity to B-TiO2. It can be readily extended to other systems (e.g., the Si/Ge systems, where the liquid structure is very different from those of the normal crystalline/ amorphous phases) to find analogous similarities, to discriminate between amorphous phases of the same material (e.g., prepared in different ways), or even to facilitate the search for structure−property relationships for amorphous materials, e.g., by searching for correlations of a structure-map, as presented in this paper, with properties of interest
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