Phase Relations in the Pseudo-Binary BiFeO3–EuFeO3 System in the Subsolidus Region Derived from X-Ray Diffraction Data—A Machine Learning Approach

BiFeO3 and EuFeO3 are some of the most studied ferrites and part of the larger category of multiferroic and magnetic compounds. The instabilities reported for BiFeO3 that hinder its use in practical applications can be overcome by substitution with rare-earth ions, such as Eu3+, on the Bi3+ site. This paper reports on the phase relations in the BiFeO3-EuFeO3 pseudo-binary system, which were not established previously. Solid-state reactions were employed to prepare different compositions according to the nominal formula Bi1−xEuxFeO3 (where x = 0, 0.05, 0.10, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1). Phase equilibria were studied at different temperatures between 800 and 1200 °C from X-ray diffraction (XRD) data. The analysis of the XRD patterns by machine learning approaches revealed eight defined clusters and four unclustered points. The validation test showed that most of the points could belong to several clusters and thus, traditional identification was employed. Phase identification and quantification by traditional approaches revealed six crystallization zones on the diagram. Although the machine learning approach offers speed in the process of classification of XRD patterns, validation by the traditional method was necessary for the construction of the phase diagram with high accuracy.