A New Methodology for Evaluating the Structural Similarity between Different Phases Using a Dimensionality Reduction Technique

[Image: see text] A new methodology for definitively evaluating the structural similarity between different phases in an impartial manner is proposed. This methodology utilizes a dimensionality reduction (DR) technique that was developed in the fields of machine learning and statistics. The basis of the proposed methodology is that the structural similarity between different phases can be evaluated by the geometrical similarity of pair and/or angular distribution functions that reflect the atomic-scale structure of each phase. The DR technique is used for the analysis of this geometrical similarity. In this study, the proposed methodology is applied to evaluate the similarity in the atomic-scale structure, as obtained from molecular dynamics simulations, between amorphous CaCO(3) and CaCO(3) crystal phases in the presence or absence of additives, namely, Mg(2+) ions, Sr(2+) ions, and water molecules. The results indicate that in the absence of additives, the structure of the amorphous phase is closer to that of vaterite than to those of calcite or aragonite. However, the degree of structural similarity between the amorphous phase and vaterite decreases if Mg(2+) ions are present. This tendency is also evident when Sr(2+) ions are present, although these ions do not influence the structure of the amorphous phase as strongly as Mg(2+) ions. In addition, the results indicate that at a high water concentration, the amorphous phase is separated into small particles by hydrogen-bonded networks of water molecules and the structure of the amorphous phase more closely approaches that of vaterite. The proposed methodology is widely applicable to the evaluation of the structural similarity between different phases for complex multicomponent systems.