Ruddlesden-Popper tolerance factor: An indicator predicting stability of 2D Ruddlesden-Popper phases

Abstract

Two-dimensional Ruddlesden-Popper (RP) phases receive the focus of extensive research because of their unique optical and electrical properties. Accurate prediction of stable RP phases can expedite finding new RP compositions with improved properties for practical applications. However, most attempts are limited to finding new RP phases by employing time-consuming computational approaches. Although descriptors such as cationic radius ratio or Goldschmidt tolerance factor can be used alternatively, they have shown limitation in predicting stable RP phases. In this study, thus we develop a novel RP tolerance factor ($t_{RP}$) derived through machine learning based process, which exhibits high accuracy in classifying RP and non-RP phases. The $t_{RP}$ is a simple form based solely on ionic radii and incorporates two meaningful parameters: inverse cationic radius ratio and inverse octahedral factor. Additionally, $t_{RP}$ shows a linear correlation with first-principles density functional theory formation energies, allowing us to determine the relative stability of RP phases beyond mere classification. By utilizing $t_{RP}$ as a descriptor, we propose the new compounds that showing potential for RP phases, and we expect it will pave the way for the discovery of novel RP phases for future optoelectronic applications.