Focus issue on studies of structural disorder using reverse Monte Carlo methods

Extended x-ray absorption fine structure (EXAFS) spectroscopy combined with reverse Monte Carlo (RMC) and evolutionary algorithm (EA) modelling is used to advance the understanding of the local structure and lattice dynamics of copper nitride (Cu₃N). The RMC/EA-EXAFS method provides a possibility to probe correlations in the motion of neighboring atoms and allows us to analyze the influence of anisotropic motion of copper atoms in Cu₃N.

Neutron- and high-energy synchrotron x-ray diffraction experiments have been performed on the (75−x)SiO₂–xB₂O₃–25Na₂O x = 5, 10, 15 and 20 mol% glasses. The structure factor has been measured over a broad momentum transfer range, between 0.4 and 22 Å⁻¹. For data analyses and modelling the Fourier transformation and the reverse Monte Carlo simulation techniques have been applied. The partial atomic pair correlation functions, the nearest neighbour distances, coordination number distributions and average coordination number values and three-particle bond angle distributions have been revealed. The Si–O network proved to be highly stable consisting of SiO₄ tetrahedral units with characteristic distances at r_Si–O = 1.60 Å and r_Si–Si = 3.0(5) Å. The behaviour of network forming boron atoms proved to be more complex. The first neighbour B–O distances show two distinct values at 1.30 Å and a characteristic peak at 1.5(5) Å and, both trigonal BO₃ and tetrahedral BO₄ units are present. The relative abundance of BO₄ and BO₃ units depend on the boron content, and with increasing boron content the number of BO₄ is decreasing, while BO₃ is increasing.

Atomistic simulations of the experimental Fe K-edge extended x-ray absorption fine structure (EXAFS) of rhombohedral (space group $R\bar{3}c$) FeF₃ at T = 300 K were performed using classical molecular dynamics and reverse Monte Carlo (RMC) methods. The use of two complementary theoretical approaches allowed us to account accurately for thermal disorder effects in EXAFS and to validate the developed force-field model, which was constructed as a sum of two-body Buckingham-type (Fe–F and F–F), three-body harmonic (Fe–F–Fe) and Coulomb potentials. We found that the shape of the Fe K-edge EXAFS spectrum of FeF₃ is a more sensitive probe for the determination of potential parameters than the values of structural parameters (a, c, x(F)) available from diffraction studies. The best overall agreement between the experimental and theoretical EXAFS spectra calculated using ab initio multiple-scattering approach was obtained for the iron effective charge q(Fe) = 1.71. The RMC method coupled with the evolutionary algorithm was used for more elaborate analysis of the EXAFS data. The obtained results suggest that our force-field model slightly underestimates the amplitude of thermal vibrations of fluorine atoms in the direction perpendicular to the Fe–F bonds.

Pd₈₁Ge₁₉ metallic glass was investigated by neutron diffraction, x-ray diffraction and extended x-ray absorption fine structure spectroscopy at the Ge K-edge. Large scale structural models were obtained by fitting the three measurements simultaneously in the framework of the reverse Monte Carlo simulation technique. It was found that the experimental data sets can be adequately fitted without Ge–Ge nearest neighbours. Mean Pd–Pd and Pd–Ge distances are 2.80 ± 0.02 Å and 2.50 ± 0.02 Å, respectively. The total average coordination number of Pd is 12.1 ± 0.5 while Ge is surrounded by 10.6 ± 1.1 Pd atoms. The coordination numbers calculated from partial pair correlation functions were compared to those obtained by Voronoi tessellation method. It was found that the latter technique overestimates the number of nearest neighbours by about 20% due to the significant contribution of distant pairs.

Classical molecular dynamics (MD) and reverse Monte Carlo methods coupled with ab initio multiple-scattering extended x-ray absorption fine structure (EXAFS) calculations were used for modeling of scheelite-type AWO₄ (A = Ca, Sr, Ba) W L₃-edge EXAFS spectra. The two theoretical approaches are complementary and allowed us to perform analysis of full EXAFS spectra. Both methods reproduce well the structure and dynamics of tungstates in the outer coordination shells, however the classical MD simulations underestimate the W–O bond MSRD due to a neglect of quantum zero-point-motion. The thermal vibration amplitudes, correlation effects and anisotropy of the tungstate structure were also estimated.

The atomic and magnetic structures of CoO and NiO have been probed using reverse Monte Carlo (RMC) refinements of neutron total scattering data. The results obtained show that the known magnetic structure for NiO can be recovered by the RMC process starting from random spin configurations, but it is insensitive to the spin direction in the {111} ferromagnetic planes. Refinements of the magnetic structure of CoO starting from random spin configurations result in collinear or non-collinear magnetic structures, consistent with those reported by other techniques. Starting from an ordered collinear spin structure for CoO and NiO leads to different results than when starting from a random arrangement of spins, which is evidence for configurational bias that highlights the need to take care when selecting a starting model for RMC refinements of magnetic structures.

Neutron- and x-ray weighted total structure factors of liquid water have been calculated on the basis of the intermolecular parts of partial radial distribution functions resulting from various computer simulations. The approach includes reverse Monte Carlo (RMC) modelling of these partials, using realistic flexible molecules, and the calculation of experimental diffraction data, including the intramolecular contributions, from the RMC particle configurations. The procedure has been applied to ten sets of intermolecular partial radial distribution functions obtained from various computer simulations, including one set from an ab initio molecular dynamics, of water. It is found that modern polarizable water potentials, such as SWM4-DP and BK3 are the most successful in reproducing measured diffraction data.

A reverse Monte Carlo analysis method was employed to extract the structure of CeO₂ from Neutron total scattering (comprising both neutron diffraction (ND) and pair-distribution functions (PDF) and Ce L₃- and K-edge EXAFS data. Here it is shown that there is a noticeable difference between using short ranged x-ray absorption spectroscopy data and using medium-long range PDF and ND data in regards to the disorder of the cerium atoms. This illustrates the importance of considering multiple length scales and radiation sources.