Causality Analysis of Physical Parameters Derived from Atomic-Resolution STEM*

Atomic scale Scanning Transmission Electron Microscopy data can be parameterized to infer local physical parameters such as structure (e.g. unit cell volume), chemistry, and electrical polarization. In the absence of tunable independent variables it is challenging to ascertain not just the correlation but the causal direction between such parameters, especially in the presence of noise. In this work we implement a workflow and evaluate causal analysis methods for parameterized HRSTEM from the natural experiment of inherent parameter variation in large datasets. Our system is a Sm_xBi_1-xFeO₃ perovskite for 0≦x≦20% which traverses a ferroelectric phase boundary. Descriptors are defined from local (unit-cell) atomic HAADF STEM corresponding to structural, compositional, and polarization parameters. These are subject to information-geometric causal inference (IGCI), additive noise models (ANM), and a linear non-gaussian acyclic models (LiNGAM) to determine pairwise causality, causal chains, and in the latter estimates of linear connection coefficients.  Generally, chemical effects including local composition and molar volume are found to be higher on the causal chain, polarization effects being secondary, and tetragonality and differential chemical contrast the weakest.