Insights into Cation Ordering of Double Perovskite Oxides from Machine Learning and Causal Relations

摘要

This work investigates origins of cation ordering in double perovskites using first-principles theory computations combined with machine learning(ML) and causal relations.We have considered various oxidation states of A,A',B,and B'from the family of transition metal ions to construct a diverse compositional space.A conventional framework employing traditional ML classification algorithms such as Random Forest(RF) coupled with appropriate features including geometry-driven and key structural modes leads to accurate prediction(~98) of A-site cation ordering.We have evaluated the accuracy of ML models by employing analyses of decision paths,assignments of probabilistic confidence bound,and finally a direct non-Gaussian acyclic structural equation model to investigate causality.Our study suggests that structural modes are crucial for classifying layered,columnar,and rock-salt ordering.The charge difference between A and A'is the most important feature for predicting clear layered ordering,which in turn depends on the B and B'charge separation.We have also designed mathematical relationships with these features to derive energy differences to form clear layered ordering.The trilinear coupling between tilt,in-phase rotation,and A-site antiferroelectric displacement in the Landau free-energy expansion becomes the necessary condition behind formation of A-site cation ordering.