RMC: modelling neutron diffraction, X-ray diffraction and EXAFS data simultaneously for amorphous materials

This special issue contains a collection of papers reflecting the content of the fifth workshop on reverse Monte Carlo (RMC) methods, held in a hotel on the banks of the Danube in the Budapest suburbs in the autumn of 2012. Over fifty participants gathered to hear talks and discuss a broad range of science based on the RMC technique in very convivial surroundings.Reverse Monte Carlo modelling is a method for producing three-dimensional disordered structural models in quantitative agreement with experimental data. The method was developed in the late 1980s and has since achieved wide acceptance within the scientific community [1], producing an average of over 90 papers and 1200 citations per year over the last five years. It is particularly suitable for the study of the structures of liquid and amorphous materials, as well as the structural analysis of disordered crystalline systems. The principal experimental data that are modelled are obtained from total x-ray or neutron scattering experiments, using the reciprocal space structure factor and/or the real space pair distribution function (PDF). Additional data might be included from extended x-ray absorption fine structure spectroscopy (EXAFS), Bragg peak intensities or indeed any measured data that can be calculated from a three-dimensional atomistic model. It is this use of total scattering (diffuse and Bragg), rather than just the Bragg peak intensities more commonly used for crystalline structure analysis, which enables RMC modelling to probe the often important deviations from the average crystal structure, to probe the structures of poorly crystalline or nanocrystalline materials, and the local structures of non-crystalline materials where only diffuse scattering is observed. This flexibility across various condensed matter structure-types has made the RMC method very attractive in a wide range of disciplines, as borne out in the contents of this special issue. It is however important to point out that since the method is akin to a structural refinement method (albeit with some inbuilt Monte Carlo ‘randomness’), high-quality data are needed to yield the best structural models. In this regard it is particularly pleasing to see the continued (planned and actual) growth in diffractometers at neutron and synchrotron x-ray facilities that have been designed with total scattering in mind.Since the previous RMC workshop in 2009 [2] (and indeed the earlier workshops in 2006 [3] and 2003 [4]) there have been several developments in the technique and in the range of its application. It is good to see that the program RMCProfile [5] is now being used as a refinement tool in a wide range of crystalline materials spanning molecular crystals, proton conductors and spinels. This is one of the growth areas in recent years; crystalline supercell models are constructed by replicating the average unit cell contents and the atoms are then relaxed using the RMC method to fit the data, while maintaining appropriate atom connectivity. This refined supercell is then investigated to determine how the average structure has changed to accommodate defects, local distortions, molecular rotations etc. There have also been technical developments to enhance the total scattering and RMC method as seen in the papers on new ways to process x-ray total scattering data, on the analysis of molecular liquid structures using a new version of RMC_POT [6], the program SPINVERT for determining disordered magnetic structures from magnetic diffuse scattering and papers concerned with other algorithmic improvements. These are all in addition to some excellent papers on the structures of amorphous materials, liquids and solutions using more established RMC methods.Many of the papers have been written by RMC workshop participants. We are pleased that the workshop enabled students and other young researchers to gain a deeper understanding of the RMC method at the start of their scientific careers. It is our hope that the collection of research papers within this special issue will communicate the vibrancy of this field to the wider scientific community by showing the current ‘state of the art’ research opportunities using the RMC method. Furthermore, by including a small number of papers from colleagues working on similar disordered problems with complementary analysis techniques, we hope that the RMC method may be placed in a broader scientific context.AcknowledgmentsWe are very grateful to IOP Publishing for their willingness to publish this collection of papers which celebrates the 24th anniversary of the first RMC publication in a special issue of Journal of Physics: Condensed Matter and for their co-ordination during the refereeing process.

We present a detailed and comprehensive structural study of molecular models of liquid methanol, ethanol, and 1-propanol that originate from a series of reverse Monte Carlo (RMC), molecular dynamics (MD), and united-atom Monte Carlo (UA:MC) simulations. We compare several modeling approaches: RMC simulations that employ experimental neutron and X-ray diffraction data as sole constraints, RMC with diffraction data complemented with partial radial distribution functions (PRDFs) from MD or UA:MC, and conventional MD and UA:MC simulations. The assessment is done in view of the structural parameters of the hydrogen bond and resulting morphological characteristics of molecular aggregates. To achieve these tasks, a computer program for structural analysis of molecular configurations together with the appropriate aggregate classification scheme has been developed. We have analyzed the morphology of clusters, their probability, and size distributions. Any cyclic structures that appeared in the configurations were extracted and characterized in the same manner. We found that MD and UA:MC simulations resulted in configurations with bulkier, more threadlike aggregates that were not entirely consistent with the experimental evidence from diffraction experiments. A combination of neutron and X-ray diffraction data with PRDFs from MD simulations, simultaneously applied as constraints in the RMC procedure, proved to be a modeling approach with the most conclusive results.

Atomistic simulations of the experimental W L3-edge extended x-ray absorption fine structure (EXAFS) of bcc tungsten at T = 300 K were performed using classical molecular dynamics (MD) and reverse Monte Carlo (RMC) methods. The MD-EXAFS method based on the results of MD simulations allowed us to access the structural information, encoded in EXAFS, beyond the first coordination shell and to validate the accuracy of two interaction potential models—the embedded atom model potential and the second nearest-neighbor modified embedded atom method potential. The RMC-EXAFS method was used for more elaborate analysis of the EXAFS data giving access to thermal disorder effects. The results of both methods suggest that the correlation in atomic motion in bcc tungsten becomes negligible above 8 Å. This fact allowed us to use the EXAFS data to determine not only mean-square relative displacements of atomic W–W pair motion but also mean-square displacements of individual tungsten atoms, which are usually accessible from diffraction data only.

The mixed glass former systems 0.35Na(2)O + 0.65[xB(2)O(3) + (1 - x)P2O5] and 0.5Na(2)O + 0.5[xB(2)O(3) + (1 - x)P2O5] with x = 0-1 were investigated with neutron diffraction (ND) together with reverse Monte Carlo (RMC) modeling of 0.35Na(2)O + 0.65[xB(2)O(3) + (1 - x)P2O5]. The results show that the structure of both systems is reflected by an intermediate-range ordering, with a characteristic x-dependent length scale of about 4-6 angstrom and which contracts slightly with the increase of the Na concentration. Results obtained from RMC modeling of the 0.35Na(2)O + 0.65[xB(2)O(3) + (1 - x)P2O5] system, using both previously reported X-ray diffraction (XRD) data as well as the here obtained ND data as independent constraints in the modeling, show that the intermediate-range structural features, notably the Na coordination and volume fraction of the conducting pathways, are only weakly dependent on the choice of the constraints used. In particular, we observe that the volume fraction of the conducting pathways and the activation energy for ionic conduction are only weakly correlated to each other, as opposed to what is found for binary alkali borate and phosphate glasses.

To make an estimation of the internal charging effect caused by the high energy electrons, a high-efficient 3-D transportation simulation code for satellite has been developed based on a reverse Monte Carlo (RMC) method implemented in Geant4. Charge production distribution, dose distribution in the sensitive volume has been simulated via forward Monte Carlo (FMC) and RMC, respectively, for the same geometry construction. Simulation results show that the computing time is significantly reduced in this RMC electron transportation simulation, especially when the sensitive volume is much smaller than the entire geometry. As an example, the computing time of RMC for a sensitive volume accounting for 0.0001% in the entire structure is only 1/500 of that of FMC. Difference of the results between RMC simulation and traditional Monte Carlo simulation is less than 10%.

For the first time neutron diffraction, X-ray diffraction and EXAFS data have been combined simultaneously using the RMC method to model the fast-ion conducting glass, (AgI)x(AgPO3)1−x. This material is of considerable technological and scientific interest due to its high ionic conductivity at ambient temperature. We present some details of the RMC technique and highlight some of the structural information obtained from our models. The origin of the “first sharp diffraction peak” in the neutron diffraction data is explained, about which there has been considerable speculation. Diffusion pathways for ionic conduction are observed. A simple analysis of available free volume shows that a percolation transition in the ionic conductivity occurs between x=0.2 and 0.3, in agreement with a prediction based on conductivity measurements. This study highlights the considerable power that these developments of the RMC method have for the structural modelling of complex amorphous materials.

We report on new neutron and x-ray diffraction data on D2O:D3PO4 solutions at two concentrations, 1:1 and 3:1. The experimental datasets were modelled simultaneously by the reverse Monte Carlo (RMC) method. From the resulting models, partial radial distribution functions (prdf) and coordination numbers were obtained. The acidity was found to decrease with increasing D3PO4 concentration. The ratio of dissociated acidic protons was estimated by dedicated simulation runs using average coordination number constraints. It was found that in the saturated solution the ratio of dissociated protons cannot exceed 20%.

The local atomic structure of the glassyAl92U8 alloy was modelled by the reverse Monte Carlo (RMC) method, fitting x-ray diffraction (XRD)and extended x-ray absorption fine structure (EXAFS) signals. The final structuralmodel was analysed by means of partial pair correlation functions, coordinationnumber distributions and Voronoi tessellation. In our study we found that themost probable atomic separations between Al–Al and U–Al pairs in the glassyAl92U8 alloy are 2.7 Å and 3.1 Å with coordination numbers 11.7 and 17.1, respectively. The Voronoianalysis did not support evidence of the existence of well-defined building blocks directlyembedded in the amorphous matrix. The dense-random-packing model seems tobe adequate for describing the connection between solvent and solute atoms.

An implementation of the reverse Monte Carlo (RMC) method for the study of crystalline materials from polycrystalline neutron total scattering data is presented. The new feature is that explicit account is taken of the intensities of Bragg peaks, which are extracted from the data using the Pawley method. The use of Bragg peaks ensures that the RMC models reproduce both the long-range and the short-range order reflected in the experimental data. The relative effects of different contributions to the data sets in the RMC method are assessed and successful applications are illustrated using the quartz and cristobalite polymorphs of silica as examples.

The structure of liquid Si2Cl6, CBr3D and CD3I has been studied by the method of neutron diffraction. The structure factors have been analysed by means of the Reverse Monte Carlo (RMC) method and, therefore, partial pair-correlation functions have also been obtained from the particle coordinates. It seems that reliability of models set up by the RMC method is strongly connected to simple steric considerations.

Structural analysis for crystalline and amorphous RFe 2D x (R: Ho, Tb) by X-ray/neutron diffraction and reverse Monte Carlo modeling

Diffraction data play an important role in the structural characterizations of solids. While reverse Monte Carlo (RMC) and similar methods provide an elegant approach to (re)construct a three-dimensional model of noncrystalline solids, a satisfactory solution to the RMC problem is still not available. Following our earlier efforts, we present here an accurate structural solution of the inverse problem by developing an information-driven inverse approach (INDIA). The efficacy of the approach is illustrated by choosing amorphous silicon as an example, which is particularly difficult to model using total-energy-based relaxation methods. We demonstrate that, by introducing a subspace optimization technique that sequentially optimizes two objective functions (involving experimental diffraction data, a total-energy functional, and a few geometric constraints), it is possible to produce models of amorphous silicon with very little or no coordination defects and a pristine gap around the Fermi level in the electronic spectrum. The structural, electronic, and vibrational properties of the resulting INDIA models are shown to be fully compliant with experimental data from x-ray diffraction, Raman spectroscopy, differential scanning calorimetry, and inelastic neutron scattering measurements. A direct comparison of the models with those obtained from the Wooten-Winer-Weaire approach and from recent high-quality molecular-dynamics simulations is also presented.

The structure of aqueous lithium chloride solutions at high concentrations as revealed by a comparison of classical interatomic potential models

New quaternary chalcogenide GexSb40−xS50Te10 and GexSb40−xSe50Te10 (x=20 and 27at%) glasses have been synthesized and studied by neutron and high-energy X-ray diffraction. Both the traditional Fourier transformation technique and the Reverse Monte Carlo (RMC) modeling of the experimental data have been applied to model the 3-dimensional atomic configurations. From the analysis of the partial atomic correlation functions and structure factors the first and second neighbor distances, coordination numbers and bond-angle distributions are calculated. The influence of S(Se) content on the atomic environment in the glassy structure is considered and discussed in a function of glass composition. In addition, the packing density, average atomic volume and compactness for each composition are determined.

Enhancing the reliability of Reverse Monte Carlo simulations of metallic glass structure by imposing strict constraints from partial pair correlation functions