Abstract
Monte Carlo (MC)-based refinement software to analyze the atomic arrangements of perovskite oxide ultrathin films from the crystal truncation rod intensity is developed on the basis of Bayesian inference. The advantages of the MC approach are (i) it is applicable to multi-domain structures, (ii) it provides the posterior probability of structures through Bayes' theorem, which allows one to evaluate the uncertainty of estimated structural parameters, and (iii) one can involve any information provided by other experiments and theories. The simulated annealing procedure efficiently searches for the optimum model owing to its stochastic updates, regardless of the initial values, without being trapped by local optima. The performance of the software is examined with a five-unit-cell-thick LaAlO3 film fabricated on top of SrTiO3. The software successfully found the global optima from an initial model prepared by a small grid search calculation. The standard deviations of the atomic positions derived from a dataset taken at a second-generation synchrotron are ±0.02 Å for metal sites and ±0.03 Å for oxygen sites.
Highlights
Perovskite oxides have been studied for a long time and still attract much attention because of their variety of conductive, electronic and magnetic properties, as well as their practical applications (Tokura & Nagaosa, 2000; Goodenough, 2001; Dagotto, 2005)
The interfacial structure is often examined by using scanning transmission electron microscopy, which is sometimes combined with electron energy loss spectroscopy (Perna et al, 2010; Cantoni et al, 2012)
To evaluate the performance of the Monte Carlo (MC) refinement, the software developed for this purpose was applied to artificial crystal truncation rods (CTRs) intensity profiles calculated from the reported structure parameters of a five-unit-cell-thick LaAlO3 film on a TiO2terminated SrTiO3(001) substrate (Yamamoto et al, 2011); we will refer to the structure as HVM
Summary
Perovskite oxides have been studied for a long time and still attract much attention because of their variety of conductive, electronic and magnetic properties, as well as their practical applications (Tokura & Nagaosa, 2000; Goodenough, 2001; Dagotto, 2005). Such resolution can be achieved by using surface X-ray diffraction to measure the crystal truncation rods (CTRs) arising from a sudden change in electron density at a specific plane (Robinson, 1986; Feidenhans’l, 1989) This method does not require slicing of the samples, allows tuning of the sample environment and has a resolution better than 0.1 A. Holographic phase retrieval methods (Takahashi et al, 2001; Yacoby et al, 2002) are often used to generate the initial models for the refinements (Fong et al, 2005; Willmott et al, 2007; Yamamoto et al, 2011; Fister et al, 2014) Such techniques to find a good initial model are indispensable for the interfacial structure analysis of perovskite oxides (Willmott et al, 2007). We refined the structure of a ten-unit-cell-thick region from the surface
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