Pristine and hydrated fluoroapatite (0001)

The surface structure of fluoroapatite (0001) (FAp0001) under quasi-dry and humid conditions has been probed with surface X-ray diffraction (SXRD). Lateral and perpendicular atomic relaxations corresponding to the FAp0001 termination before and after H2O exposure and the location of the adsorbed water molecules have been determined from experimental analysis of the crystal truncation rod (CTR) intensities. The surface under dry conditions exhibits a bulk termination with relaxations in the outermost atomic layers. The hydrated surface is formed by a disordered partially occupied H2O layer containing one water molecule (33% surface coverage) adsorbed at each of the three surface Ca atoms, and is coupled with one OH group randomly bonded to each of the three topmost P atoms with a 33% surface coverage.

Direct determination of one-dimensional interphase structures using normalized crystal truncation rod analysis

A one-dimensional non-iterative direct method was employed for normalized crystal truncation rod analysis. The non-iterative approach, utilizing the Kramers–Kronig relation, avoids the ambiguities due to an improper initial model or incomplete convergence in the conventional iterative methods. The validity and limitations of the present method are demonstrated through both numerical simulations and experiments with Pt(111) in a 0.1 M CsF aqueous solution. The present method is compared with conventional iterative phase-retrieval methods.

Bayesian inference of metal oxide ultrathin film structure based on crystal truncation rod measurements

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 LaAlO3film 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.