Robust Surface Structure Analysis With Reliable Uncertainty Estimation Using The Exchange Monte Carlo Method (Vol 53, Pg 387, 2020)

The exchange Monte Carlo (MC) method is implemented in a surface structure refinement software using Bayesian inference. The MC calculation successfully reproduces crystal truncation rod intensity profiles from perovskite oxide ultrathin films, which involves about 60 structure parameters, starting from a simple model structure in which the ultrathin film and substrate surface have an atomic arrangement identical to the substrate bulk crystal. This shows great tolerance of the initial model in the surface structure search. The MC software is provided on the web. One of the advantages of using the MC method is the precise estimation of uncertainty of the obtained parameters. However, the parameter uncertainty is largely underestimated when one assumes that the diffraction measurements at each scattering vector are independent. The underestimation is caused by the correlation of experimental error. A means of estimation of uncertainty based on the effective number of observations is demonstrated.