Thermodynamic calculations using reverse Monte Carlo: Simultaneously tuning multiple short-range order parameters for 2D lattice adsorption problem

Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice thermodynamic calculations that is based on the use of the reverse Monte Carlo (RMC) technique and multiple short-range order (SRO) parameters. The approach is comparable in accuracy to the Metropolis Monte Carlo (MC) method. The equilibrium configuration is determined in 5-10 Newton-Raphson iterations by solving a system of coupled nonlinear algebraic SRO growth rate equations. This makes the RMC-based method computationally more efficient than MC, given that MC typically requires sampling of millions of configurations. The technique is applied to the interacting 2D adsorption problem. Unlike grand canonical MC, RMC is found to be adept at tackling geometric frustration, as it is able to quickly and correctly provide the ordered c(2 × 2) adlayer configuration for Cl adsorbed on a Cu (100) surface.

A probabilistic microkinetic modeling framework for catalytic surface reactions

We present a probabilistic microkinetic modeling (MKM) framework that incorporates the short-ranged order (SRO) evolution for adsorbed species (adspecies) on a catalyst surface. The resulting model consists of a system of ordinary differential equations. Adsorbate-adsorbate interactions, surface diffusion, adsorption, desorption, and catalytic reaction processes are included. Assuming that the adspecies ordering/arrangement is accurately described by the SRO parameters, we employ the reverse Monte Carlo (RMC) method to extract the relevant local environment probability distributions and pass them to the MKM. The reaction kinetics is faithfully captured as accurately as the kinetic Monte Carlo (KMC) method but with a computational time requirement of few seconds on a standard desktop computer. KMC, on the other hand, can require several days for the examples discussed. The framework presented here is expected to provide the basis for wider application of the RMC-MKM approach to problems in computational catalysis, electrocatalysis, and material science.

A Brief Guide to the Structure of High-Temperature Molten Salts and Key Aspects Making Them Different from Their Low-Temperature Relatives, the Ionic Liquids

High-temperature molten salt research is undergoing somewhat of a renaissance these days due to the apparent advantage of these systems in areas related to clean and sustainable energy harvesting and transfer. In many ways, this is a mature field with decades if not already a century of outstanding work devoted to it. Yet, much of this work was done with pioneering experimental and computational setups that lack the current day capabilities of synchrotrons and high-performance-computing systems resulting in deeply entrenched results in the literature that when carefully inspected may require revision. Yet, in other cases, access to isotopically substituted ions make those pioneering studies very unique and prohibitively expensive to carry out nowadays. There are many review articles on molten salts, some of them cited in this perspective, that are simply outstanding and we dare not try to outdo those. Instead, having worked for almost a couple of decades already on their low-temperature relatives, the ionic liquids, this is the perspective article that some of the authors would have wanted to read when embarking on their research journey on high-temperature molten salts. We hope that this will serve as a simple guide to those expanding from research on ionic liquids to molten salts and vice versa, particularly, when looking into their bulk structural features. The article does not aim at being comprehensive but instead focuses on selected topics such as short- and intermediate-range order, the constraints on force field requirements, and other details that make the high- and low-temperature ionic melts in some ways similar but in others diametrically opposite.

Unraveling Local Structure of Molten Salts via X-ray Scattering, Raman Spectroscopy, and Ab Initio Molecular Dynamics

In this work, we resolve a long-standing issue concerning the local structure of molten MgCl₂ by employing a multimodal approach, including X-ray scattering and Raman spectroscopy, along with the theoretical modeling of the experimental spectra based on ab initio molecular dynamics (AIMD) simulations utilizing several density functional theory (DFT) methods. We demonstrate the reliability of AIMD simulations in achieving excellent agreement between the experimental and simulated spectra for MgCl₂ and 50 mol % MgCl₂ + 50 mol % KCl, and ZnCl₂, thus allowing structural insights not directly available from experiment alone. A thorough computational analysis using five DFT methods provides a convergent view that octahedrally coordinated magnesium in pure MgCl₂ upon melting preferentially coordinates with five chloride anions to form distorted square pyramidal polyhedra that are connected via corners and to a lesser degree via edges. This is contrasted with the results for ZnCl₂, which does not change its tetrahedral coordination on melting. Although the five-coordinate MgCl₅^3- complex was not considered in the early literature, together with an increasing tendency to form a tetrahedrally coordinated complex with decreasing the MgCl₂ content in the mixture with alkali metal chloride systems, current work reconciles the results of most previous seemingly contradictory experimental studies.

Automated Development of Molten Salt Machine Learning Potentials: Application to LiCl

The in silico modeling of molten salts is critical for emerging "carbon-free" energy applications but is inhibited by the cost of quantum mechanically treating the high polarizabilities of molten salts. Here, we integrate configurational sampling using classical force fields with active learning to automate and accelerate the generation of Gaussian approximation potentials (GAP) for molten salts. This methodology reduces the number of expensive ab initio evaluations required for training set generation to O(100), enabling the facile parametrization of a molten LiCl GAP model that exhibits a 19 000-fold speedup relative to AIMD. The developed molten LiCl GAP model is applied to sample extended spatiotemporal scales, permitting new physical insights into molten LiCl's coordination structure as well as experimentally validated predictions of structures, densities, self-diffusion constants, and ionic conductivities. The developed methodology significantly lowers the barrier to the in silico understanding and design of molten salts across the periodic table.

The Use of Scattering Data in the Study of the Molecular Organisation of Polymers in the Non-Crystalline State

Scattering data for polymers in the non-crystalline state, i.e., the glassy state or the molten state, may appear to contain little information. In this work, we review recent developments in the use of scattering data to evaluate in a quantitative manner the molecular organization of such polymer systems. The focus is on the local structure of chain segments, on the details of the chain conformation and on the imprint the inherent chemical connectivity has on this structure. We show the value of tightly coupling the scattering data to atomistic-level computer models. We show how quantitative information about the details of the chain conformation can be obtained directly using a model built from definitions of relatively few parameters. We show how scattering data may be supplemented with data from specific deuteration sites and used to obtain information hidden in the data. Finally, we show how we can exploit the reverse Monte Carlo approach to use the data to drive the convergence of the scattering calculated from a 3d atomistic-level model with the experimental data. We highlight the importance of the quality of the scattering data and the value in using broad Q scattering data obtained using neutrons. We illustrate these various methods with results drawn from a diverse range of polymers.

Elucidating Ionic Correlations Beyond Simple Charge Alternation in Molten MgCl2-KCl Mixtures

The development of technologies for nuclear reactors based on molten salts has seen a big resurgence. The success of thermodynamic models for these hinges in part on our ability to predict at the atomistic level the behavior of pure salts and their mixtures under a range of conditions. In this letter, we present high-energy X-ray scattering experiments and molecular dynamics simulations that describe the molten structure of mixtures of MgCl₂ and KCl. As one would expect, KCl is a prototypical salt in which structure is governed by simple charge alternation. In contrast, MgCl₂ and its mixtures with KCl display more complex correlations including intermediate-range order and the formation of Cl^--decorated Mg²⁺ chains. A thorough computational analysis suggests that intermediate-range order beyond charge alternation may be traced to correlations between these chains. An analysis of the coordination structure for Mg²⁺ ions paints a more complex picture than previously understood, with multiple accessible states of distinct geometries.

Pressure promoted low-temperature melting of metal-organic frameworks

Metal-organic frameworks (MOFs) are microporous materials with huge potential for chemical processes. Structural collapse at high pressure, and transitions to liquid states at high temperature, have recently been observed in the zeolitic imidazolate framework (ZIF) family of MOFs. Here, we show that simultaneous high-pressure and high-temperature conditions result in complex behaviour in ZIF-62 and ZIF-4, with distinct high- and low-density amorphous phases occurring over different regions of the pressure-temperature phase diagram. In situ powder X-ray diffraction, Raman spectroscopy and optical microscopy reveal that the stability of the liquid MOF state expands substantially towards lower temperatures at intermediate, industrially achievable pressures and first-principles molecular dynamics show that softening of the framework coordination with pressure makes melting thermodynamically easier. Furthermore, the MOF glass formed by melt quenching the high-temperature liquid possesses permanent, accessible porosity. Our results thus imply a route to the synthesis of functional MOF glasses at low temperatures, avoiding decomposition on heating at ambient pressure.

Molten alkali halides – temperature dependence of structure, dynamics and thermodynamics

Temperature-induced structural, dynamical and thermodynamic changes reveal novel insights into the mechanism and dynamics of ion transport in molten salts.

Aggregate Formation of Surface-Modified Nanoparticles in Solvents and Polymer Nanocomposites

A new method based on the combination of small-angle scattering, reverse Monte Carlo simulations, and an aggregate recognition algorithm is proposed to characterize the structure of nanoparticle suspensions in solvents and polymer nanocomposites, allowing detailed studies of the impact of different nanoparticle surface modifications. Experimental small-angle scattering is reproduced using simulated annealing of configurations of polydisperse particles in a simulation box compatible with the lowest experimental q-vector. Then, properties of interest like aggregation states are extracted from these configurations and averaged. This approach has been applied to silane surface-modified silica nanoparticles with different grafting groups, in solvents and after casting into polymer matrices. It is shown that the chemistry of the silane function, in particular mono- or trifunctionality possibly related to patch formation, affects the dispersion state in a given medium, in spite of an unchanged alkyl-chain length. Our approach may be applied to study any dispersion or aggregation state of nanoparticles. Concerning nanocomposites, the method has potential impact on the design of new formulations allowing controlled tuning of nanoparticle dispersion.

On reverse Monte Carlo constraints and model reproduction

Reverse Monte Carlo (RMC) simulations were performed to investigate the effectiveness of any combination of five experimentally motivated constraints on the reproduction of a test case, a ternary ab initio model. It was found that low energy structures fitting a variety of constraints commonly used in the RMC methodology could still provide an incorrect description of the chemical structural unit populations in multi-elemental systems. It is shown that the use of an elemental bond type constraint is an effective way to avoid this. © 2017 Wiley Periodicals, Inc.

Uniqueness of rotationally invariant polyhedra classification

In the past, algorithms have been proposed that yield a classification of coordination polyhedra (coordination stars) in terms of an infinite set of rotationally invariant coefficients. It is shown that this set provides a unique characterization of the polyhedra, in the sense that two polyhedra with the same set of coefficients can always be transformed into each other by a rotation or a rotation combined with an inversion.

The structure of molten CuCl, CuI and their mixtures as investigated by using neutron diffraction

The structure of molten CuCl, CuI and their mixtures (CuCl)(x)(CuI)(1-x) with x = 0.294, 0.576, 0.801 was studied by using neutron diffraction. The results are discussed by reference to the information that is available on the structure of CuCl and CuI from experiment, theory and computer simulation. The comparison points to a need for more realistic models for the CuCl-CuI system which should take into account the presence of chemical bonds that have been found in CuI by the application of ab initio molecular dynamics methods.

The structure of liquid water by polarized neutron diffraction and reverse Monte Carlo modelling

The coherent static structure factor of water has been investigated by polarized neutron diffraction. Polarization analysis allows us to separate the huge incoherent scattering background from hydrogen and to obtain high quality data of the coherent scattering from four different mixtures of liquid H(2)O and D(2)O. The information obtained by the variation of the scattering contrast confines the configurational space of water and is used by the reverse Monte Carlo technique to model the total structure factors. Structural characteristics have been calculated directly from the resulting sets of particle coordinates. Consistency with existing partial pair correlation functions, derived without the application of polarized neutrons, was checked by incorporating them into our reverse Monte Carlo calculations. We also performed Monte Carlo simulations of a hard sphere system, which provides an accurate estimate of the information content of the measured data. It is shown that the present combination of polarized neutron scattering and reverse Monte Carlo structural modelling is a promising approach towards a detailed understanding of the microscopic structure of water.

Comparison of partial structures of melts of superionic AgI and CuI and non-superionic AgCl

Neutron and high-energy x-ray diffraction analyses of molten AgI have been performed and the partial structures are discussed in detail with the aid of the structural modelling procedure of the reverse Monte Carlo (RMC) technique by comparison with those of molten CuI and AgCl. It is well known that AgI and CuI have a superionic solid phase below the melting point, in which the cations favour a tetrahedral configuration, while solid AgCl has a rock-salt structure with an octahedral environment around both Ag and Cl atoms. Even in the molten states, there is a significant difference between superionic and non-superionic melts. The cation is located on the triangular plain formed by three iodine ions in molten AgCl and CuI, while molten AgCl favours a 90° Cl-Ag-Cl bond angle, which is understood to maintain a similar local environment to that in the solid state. The atomic configurations of the RMC model suggest that the cation distributions in superionic melts of CuI and AgI exhibit large fluctuations, while Ag ions in the non-superionic melts of AgCl are distributed much more uniformly.

Analysis of Liquid Structure without Construction of Any Structure Models by the X-Ray Scattering Method

A simple approach for determining a liquid structure using X-ray scattering data, in which a liquid structure is uniquely evaluated without construction of any plausible structure models, has been applied to liquid acetonitrile, acetone and cyclohexane. For a pair of molecules, a given point within a molecule is located at the origin with a given molecular orientation. The site of the given point of another molecule is defined by the polar coordinates and the molecular orientation is treated by three Eulerian angles. These parameters are optimized by a non-linear least-squares calculation applied to X-ray scattering data. The reliability of the method was examined by determining the liquid structure of polar acetonitrile and the obtained intermolecular interatomic distances are in good agreement with the previously reported values. The method was then successfully applied to the determination of the liquid structure of acetone and cyclohexane. Especially for nonpolar cyclohexane, the construction of a variety of plausible structural models is very difficult. It was revealed that acetone has an ordered liquid arrangement similar to that found in its crystal, although the intermolecular distances in liquid acetone are different from those in the crystal. On the other hand, the liquid structure of cyclohexane is disordered.

On the structure of simple molecular liquids SbCl5 and WCl6

Neutron diffraction measurements on liquid antimony pentachloride and tungsten hexachloride have been carried out using the Studsvik liquids and amorphous diffractometer (SLAD) at the Studsvik Neutron Research Laboratory. The corrected structure factors have been interpreted by means of reverse Monte Carlo modeling which provides large structural models, containing thousands of atoms, that are consistent with the experimental data within their uncertainties. From these models, partial structure factors and pair correlation functions can be calculated. It is demonstrated that the intramolecular structure can be determined on the basis of data extending up to 10 Angstrom (-1). SbCl(5) is found to have a trigonal bipyramidal shape in the liquid, while liquid WCl(6) consists of octahedral molecules. The intermolecular structure of liquid SbCl(5) and WCl(6) seems to be determined largely by steric effects (excluded volume and molecular shape).

Reverse Monte Carlo modeling of the structure of colloidal aggregates

In this work we present results for the structure of aerogels coming from the diffusion-limited cluster aggregation simulation method. Pair distribution functions and structure factors, resulting from simulation, were considered as experimental input for reverse Monte Carlo modeling. The modeling yielded structural models with pair distribution functions and structure factors nearly identical to the results of the simulations. Particle configurations from both the simulations and reverse Monte Carlo modeling have been analyzed in terms of the distribution of the number of neighbors. It is suggested that the reverse Monte Carlo method, when applied to the structure factor, may be a suitable technique for the interpretation of experimental scattering data on colloidal aerogels.

Local Structure Evolution in Particle Network Formation Studied by Brownian Dynamics Simulation

The effect of solid content and colloidal interactions on the structure of forming networks of colloidal particles is studied by Brownian dynamics simulation. The different situations are compared in terms of the pair distribution function and the distribution of nearest neighbors around each particle. The results indicate that, in fast coagulation, the higher solid contents lead to a freezing-in of the liquid structure. Nevertheless, this effect can be reduced substantially by the introduction of a shallow secondary minimum and an energy barrier in the interaction potential. However, the structures resulting from such slow coagulation show a substantial degree of porosity, larger than those produced at the same solid content but by fast coagulation. It is also shown how the porosity (defined on a few particle diameters) is reflected in the distribution of nearest neighbors around the center particle, i.e., the very local conformation in the particle network. Fractal analysis shows that, at the relatively high volume fractions considered in this study, no intermediate fractal regime exists. Copyright 2000 Academic Press.

Modeling glasses using the reverse Monte Carlo algorithm: addition of nuclear magnetic resonance and expanded coordination number constraints

In simple oxide glasses the coordination number and oxidation state of the glass-forming element can be predicted directly from the "8--n" rule. Tellurite glasses, however, are unusual in that the coordination number of oxygen around tellurium varies without a corresponding change in the oxidation state of tellurium. To model sodium tellurite glasses successfully using the reverse Monte Carlo algorithm several new constraints have been added. Changes include extending the original coordination constraint to allow multiple coordination numbers, and the addition of a new coordination constraint to keep the oxidation state of tellurium constant by limiting the number of bridging and nonbridging oxygens bonded to each tellurium atom. In addition, the second moment of the distribution of dipolar couplings for sodium atoms obtained from a spin-echo NMR experiment was added as a new constraint. The resulting real-space models are presented and the effectiveness of the new constraints is discussed.

Identification, display, and use of symmetry elements in atomic and electronic structure models

Crystallographic symmetry plays an important role in structure determination from diffraction or scattering data, in spectroscopy and in simulations. It is convenient and insightful to integrate the display and use of such symmetry data with data analysis and modeling methods. We outline the integration of a suite of crystallographic algorithms, closely coupled with interactive graphical displays. These include techniques for identifying the unit cell of a solid, for automatically determining space and point group symmetries, for generalized displays of symmetry elements overlaid on structural models, and for construction, editing, and transformation of models subject to symmetry constraints. In addition, electron densities derived from periodic density functional calculations can be symmetrized and displayed with the corresponding symmetry elements. Applications of these various capabilities in crystallographic research are illustrated by topical examples.

The structure of molten and glassy 2:1 binary systems: an approach using the Bhatia—Thornton formalism

A systematic analysis of those liquid binary 2:1 systems (denoted MX 2 ), for which experimental partial structure factors are available from the isotopic substitution method in neutron diffraction, is made using the Bhatia-Thornton (BT) formalism.Particular attention is paid to the origin of the first sharp diffraction peak (FSDP ), which occurs in the measured diffraction patterns for some of the MX 2 systems, since it appears, from recent studies, that this feature is a signature of directional bonding. It is found that FSDPS can occur in all three BT partial structure factors S xB (k). A FSDP feature in the concentration-concentration partial structure factor S cc (k) is not, however, pronounced except in the case of MgCl 2 and the glass forming network melts ZnCl 2 and GeSe 2 . To the extent that these systems can be regarded as ionic melts a FSDP in S cc (k) implies a non-uniformity in the charge distribution on the scale of the intermediate-range order (IRO). The structure of molten GeSe 2 is compared with the structures of molten ZnCl 2 , glassy GeS 2 and glassy Si0 2 . Although the GeSe 2 and ZnCl 2 melts have different short-range order, there are similarities in the observed IRO which can be attributed to the arrangement of the electropositive species M. The essential features of the measured total structure factor for glassy GeS 2 can be reproduced by using the molten GeSe 2 S zB (k). This result lends support to the notion that the S zB (k) for liquid GeSe 2 (and ZnCl 2 ) are characteristic of both the liquid and glassy states of other network glass forming systems. The structures of molten GeSe 2 (or ZnCl 2 ) and glassy Si0 2 are, however, found to be different. The observed discrepancies are largest in the region of the FSDP which signifies pronounced differences in the nature of the IRO for these systems.

Real space manifestation of the first sharp diffraction peak in the structure factor of liquid and glassy materials

The problem of those discernible features of the intermediate range order (IRO) which can be attributed to the first sharp diffraction peak (FSDP) observed in the structure factor of many liquid and glassy materials is approached by treating this peak as a distinct feature. It is found, by considering the measured partial structure factors, S αβ ( k ), for molten ZnCl 2 , GeSe 2 , MgCl 2 , NiBr 2 and Nil 2 and the measured total structure factors, F ( k ), for glassy SiO 2 , PS 4 and liquid CCl 4 , that the propensity of the FSDP to have a prominent effect on the underlying features of the IRO depends noticeably on the system type. Specifically, the FSDP confers a marked oscillatory character of periodicity 2π/ k 1 (where k 1 is the FSDP position) on the IRO when the local structural units, which give rise to the density fluctuations on the IRO scale, exist as stable entities for a timescale τ ≫ 5 × 10 -12 s. The FSDP therefore accounts for the discernible features of the underlying IRO for the viscous glass forming liquids ZnCl 2 and GeSe 2 , for the glasses SiO 2 and PS 4 , and for the molecular liquid CCl 4 . The influence of the FSDP on the IRO is less pronounced for molten MgCl 2 and is negligible for molten NiBr 2 and Nil 2 , both of which have a high cation mobility which leads to a relative instability of the Ni 2+ centred structural units. The effect on the FSDP of temperature and pressure are briefly considered as are the development of the FSDP in molten ZnX 2 (when X is changed from Cl to I to Br) and the minimum size of r -space model which is required if the FSDP is to be accurately predicted.

Correlations between entropy and volume of melting in halide salts

Melting parameters and transport coefficients in the melt are collated for halides of monovalent, divalent and trivalent metals. A number of systems show a deficit of entropy of melting relative to the linear relations between entropy change and relative volume change on melting that are found to be approximately obeyed by most halides. These behaviours are discussed on the basis of structural and transport data. The deviating systems are classified into three main classes, namely (i) fast-ion conductors in the high-temperature crystal phase such as AgI, (ii) strongly structured network-like systems such as ZnCl 2 , and (iii) molecular systems melting into associated molecular liquids such as SbCl 3 .