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

Abstract

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.

Melt crystallization mechanism analyzed with dimensional reduction of high-dimensional data representing distribution function geometries

“…The structural similarity among different periods was evaluated by the distance between the 2D data points on the sheet; the shorter the distance was, the higher the similarity. In a previous study 16 , it was confirmed that the transformation of the PDF and ADF geometries into 2D data points with PCA provided qualitatively the same results as the transformation of them into three-dimensional data points with PCA. This result of the previous study suggests that the exactness of the features of the PDF and ADF geometries represented by 2D data points with PCA is sufficiently high.…”

“…So far, DR has been used to evaluate geometrical similarities or dissimilarities between different objects, such as surface recognition 22 , face recognition 23 , and surface matching 24 , in which DR was performed for high-dimensional data representing the geometry of each object. Recently, DR was used to evaluate the geometrical similarity of the PDF and ADF between different phases of calcium carbonate, and the results represented the structural similarity among those phases in real systems 16 .…”

“…A method of visualizing high-dimensional data using DR, which was recently proposed for evaluating the structural similarity between different phases 16 , was used to investigate the mechanism of melt crystallization. The time sequence of the 2D data points created by the DR of the geometry of the PDF or ADF, which were obtained with an MD simulation of a supercooled LJ melt, was mapped onto a 2D sheet.…”

“…Recently, a method for evaluating the structural similarity between different phases using a dimensional reduction (DR) technique, which was developed for machine learning and statistics, has been proposed 16 . In this method, high-dimensional data representing the geometry of the PDF or ADF for each phase is transformed into a two-dimensional (2D) data point by DR.…”

“…The structural similarity between different phases is evaluated by the distance between 2D data points for those phases assuming that the structural similarity can be regarded as the geometrical similarity of the PDF or ADF. This method provided a reasonable description of the structural similarity for different crystal polymorphs and the amorphous phase of calcium carbonate 16 . Thus, we expect that the time evolution of the long- and short-range orders during crystallization can be evaluated quantitatively by applying this method to the geometry of the PDF or ADF at each moment during crystallization.…”