Information-driven inverse approach to disordered solids: Applications to amorphous silicon

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.

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.

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%.

The choice of appropriate interaction models is among the major disadvantages of conventional methods such as molecular dynamics and Monte Carlo simulations. On the other hand, the so-called reverse Monte Carlo (RMC) method, based on experimental data, can be applied without any interatomic and/or intermolecular interactions. The RMC results are accompanied by artificial satellite peaks. To remedy this problem, we use an extension of the RMC algorithm, which introduces an energy penalty term into the acceptance criteria. This method is referred to as the hybrid reverse Monte Carlo (HRMC) method. The idea of this paper is to test the validity of a combined potential model of coulomb and Lennard-Jones in a fluoride glass system BaMnMF_{7} (M=Fe,V) using HRMC method. The results show a good agreement between experimental and calculated characteristics, as well as a meaningful improvement in partial pair distribution functions. We suggest that this model should be used in calculating the structural properties and in describing the average correlations between components of fluoride glass or a similar system. We also suggest that HRMC could be useful as a tool for testing the interaction potential models, as well as for conventional applications.

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

The analysis of the short-range-order atomic structure of liquid metals by the Voronoi polyhedron method and a check of the adequacy of the results gained by the RMC method

(Received 30 January 2012; Accepted 2 July 2012; Published 25 August 2012)A reverse Monte Carlo (RMC) method is developed in this work to study the energy-loss process of signalelectrons in surface electron spectroscopy. This method derives the effective energy-loss function (EELF) froma measured reflection electron energy loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC)simulation procedure other than deconvolution procedure, in accordance with the complicated electron transportprocess. The method combines the Markov chain Monte Carlo (MCMC) sampling (i.e. Metropolis importantsampling) of oscillator parameters with a usual MC simulation of electron interaction with solids, which acts as asingle step of MCMC sampling. To examine the reliability of this method, we have performed a test which leadsto derive the same EELF with different trial inputs of initial oscillator parameters. Calculation results show thatEELF can be pretty well derived by the RMC method even without a proper choice of initial trial parameters. Asan example the EELFs for Ag at different electron energies are derived from the measured REELS spectra by thisRMS method.[DOI: 10.1380/ejssnt.2012.441]

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.

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.

A new reverse Monte Carlo (RMC) method has been developed for creating three-dimensionalstructures in agreement with small angle scattering data. Extensive tests, using computergenerated quasi-experimental data for aggregation processes via constrained RMC andLangevin molecular dynamics, were performed. The software is capable of fitting severalconsecutive time frames of scattering data, and movie-like visualization of thestructure (and its evolution) either during or after the simulation is also possible.

The structure of liquid gallium has been studied along the melting curve from 0.64 to 5.6 GPa by the energy dispersive x-ray diffraction technique, followed by modeling of the experimental data by the reverse Monte Carlo (RMC) method. The RMC models were constrained by the experimentally obtained equation of states of liquid Ga and in good accordance with experimental data. Analysis of the structure factor $S(Q)$ and the radial distribution function $g(r)$ shows that the anisotropic local structure of liquid Ga deviates from that of a simple hard-sphere-like liquid metal structure. Whereas the third and fourth coordination shell positions and position of the first maximum of $S(Q)$ demonstrate pressure dependencies close to a uniform compression scaled by the ${(V/{V}_{0})}^{1/3}$ volume relation, the positions of the first (especially) and second coordination spheres have more flat pressure dependencies. At the same time, the first and second coordination numbers increase: The first coordination number starts from 10 to 10.5 and increases by $\ensuremath{\sim}$5$%$ in the studied pressure interval. This indicates that liquid gallium contraction is nonuniform, and the local structure changes with increasing pressure. Analysis of the radial distribution function $g(r)$ by a distorted-crystalline model shows that at lower pressures liquid consists of two species similar to the solid Ga I and Ga II structures. The fraction of the Ga I-like part is about $0.2\ifmmode\pm\else\textpm\fi{}0.05$ at 0.64 GPa, and it gradually decreases under pressure to zero at approximately $7.5\ifmmode\pm\else\textpm\fi{}0.5$ GPa.

Non-collinear local configurations with null total moment are expected to be a hallmark of geometrically frustrated antiferromagnets. We attempt an experimental verification of such ideas in SrCr9xGa12-9xO19 (SCGO), using the reverse Monte Carlo (RMC) analysis, recently adapted to the investigation of the magnetic correlations starting from total scattering powder data. The microscopic spin configurations obtained by RMC were used to calculate the spin nematic correlation function proposed to be of importance for classical spins on the kagome lattice. In the low-temperature range our analysis shows a strong deviation from the behaviour of classical spins on the SCGO lattice obtained with our standard Monte Carlo simulations.

The reverse Monte Carlo (RMC) method has been widely used to gain 3D structural ordering information from experimental scattering data. Recently, we have introduced a novel application of RMC, viz., calculating thermodynamic properties of crystalline materials, construction of phase diagram and rapid estimation of the local structural order [Agrahari and Chatterjee, Physical Review E, 104, 044129 (2021).]. The method has been shown to be accurate and orders-of-magnitude faster than standard Monte Carlo simulations – this makes the approach quite promising. However, the error in RMC has never been systematically quantified. The goal here is to perform a thorough investigation into the types of error in RMC-based thermodynamic calculations, assess the relative magnitude of these errors, and develop strategies to improve the accuracy. Some of the conclusions presented are also relevant to previous experiment-based RMC implementations.

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

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.