Feature Space of XRD Patterns Constructed by an Autoencoder

X-ray diffraction (XRD) is commonly used to analyze systematic variations occurring in compounds to tune their material properties. Machine learning can be used to extract such significant systematics among a series of observed peak patterns. The feature space concept, in the context of autoencoders, can be the platform for performing such extractions, where each peak pattern is projected into a space to extract the systematics. Herein, an autoencoder is trained to learn to detect the systematics driven by atomic substitutions within a single phase without structural transitions. The feature space constructed by the trained autoencoder classifies the substitution compositions of XRD patterns satisfactorily. The compositions interpolated in the feature space are in good agreement with those of an XRD pattern projected to a point. Subsequently, the autoencoder generates a virtual XRD pattern from an interpolated point in the feature space. When the feature space is effectively optimized by enough training data, the autoencoder predicts an XRD pattern with a concentration, which is difficult to be described using the possible resolution of the supercell method of ab initio calculations.