Rigid Ion Potential Research Articles

Binary salt structure classification with convolutional neural networks: Application to crystal nucleation and melting point calculations

Convolutional neural networks are constructed and validated for the crystal structure classification of simple binary salts such as the alkali halides. The inputs of the neural network classifiers are the local bond orientational order parameters of Steinhardt, Nelson, and Ronchetti [Phys. Rev. B 28, 784 (1983)], which are derived solely from the relative positions of atoms surrounding a central reference atom. This choice of input gives classifiers that are invariant to density, increasing their transferability. The neural networks are trained and validated on millions of data points generated from a large set of molecular dynamics (MD) simulations of model alkali halides in nine bulk phases (liquid, rock salt, wurtzite, CsCl, 5-5, sphalerite, NiAs, AntiNiAs, and β-BeO) across a range of temperatures. One-dimensional time convolution is employed to filter out short-lived structural fluctuations. The trained neural networks perform extremely well, with accuracy up to 99.99% on a balanced validation dataset constructed from millions of labeled bulk phase structures. A typical analysis using the neural networks, including neighbor list generation, order parameter calculation, and class inference, is computationally inexpensive compared to MD simulations. As a demonstration of their accuracy and utility, the neural network classifiers are employed to follow the nucleation and crystal growth of two model alkali halide systems, crystallizing into distinct structures from the melt. We further demonstrate the classifiers by implementing them in automated MD melting point calculations. Melting points for model alkali halides using the most commonly employed rigid-ion interaction potentials are reported and discussed.

Electrostatic treatment of charged interfaces in classical atomistic simulations

Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for model systems of increasing complexity, both neutral and charged, and with either open or periodic boundary conditions. This allows to correctly interpret results of classical atomistic simulations which are directly affected by the appearance of these potentials. We demonstrate our approach at the example of a strontium titanite supercell containing an asymmetric tilt grain boundary. The formation energies of charged oxygen vacancies and the relaxed interface structure are calculated based on an interatomic rigid-ion potential, and the results are analyzed in consideration of the electrostatic effects.

Investigation of the effect of local atomic polarization on field-enhanced ion transport in insulating binary oxides: The case of CeO2

Over the course of more than 70 years, several theoretical models for electric field-enhanced ion diffusion in crystalline insulators have been presented. However, there is no assessment of the validity of these models despite the urge to have a correct description of field-enhanced ion diffusion in several emerging technologies. Herein, an assessment of five models was carried out by computing the field-dependent migration enthalpy $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$ for the oxide ion in ${\mathrm{CeO}}_{2}$. The input to these models is the zero-field and zero-temperature migration pathway and/or the activation barrier obtained from an interatomic potential. $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$ from these models was compared with reference values obtained from a set of classical molecular-dynamics simulations in the temperature range of $1000\phantom{\rule{4pt}{0ex}}\ensuremath{\le}T\ensuremath{\le}1600\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and the electric field range of $0\phantom{\rule{4pt}{0ex}}\ensuremath{\le}E\ensuremath{\le}30\phantom{\rule{4pt}{0ex}}\mathrm{MV}/\mathrm{cm}$. It is revealed that the most successful theoretical models are those that consider local polarization effects induced in the diffusing ion itself and its vicinity. However, all the models did not account for the effect of the electric field and finite temperature on the local polarization, leading to discrepancies between the predicted and the reference $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$, particularly at high fields. By comparing results from a rigid-ion potential and a polarizable core-shell potential, it is concluded that an intraionic polarization degree of freedom in the polarizable potential is an important factor in predicting $\mathrm{\ensuremath{\Delta}}{H}_{\mathrm{mig}}(E)$, regardless of the field-enhanced diffusion model particularly for low to moderate field. Future more accurate treatments should consider the field- and temperature-dependent interionic and intraionic local polarization effects.

A critical assessment of interatomic potentials for modelling lattice defects in forsterite Mg_2SiO_4 from 0 to 12\xa0GPa

Five different interatomic potentials designed for modelling forsterite Mg_2SiO_4 are compared to ab initio and experimental data. The set of tested properties include lattice constants, material density, elastic wave velocity, elastic stiffness tensor, free surface energies, generalized stacking faults, neutral Frenkel and Schottky defects, in the pressure range 0-12 GPa relevant to the Earth’s upper mantle. We conclude that all interatomic potentials are reliable and applicable to the study of point defects. Stacking faults are correctly described by the THB1 potential, and qualitatively by the Pedone2006 potential. Other rigid-ion potentials give a poor account of stacking fault energies, and should not be used to model planar defects or dislocations. These results constitute a database on the transferability of rigid-ion potentials, and provide strong physical ground for simulating diffusion, dislocations, or grain boundaries.

Modeling Superionic Behavior of Plutonium Dioxide

AbstractThe Bredig transition to the superionic phase indicated with the $$\lambda $$-peak in $${C_p}$$ was highly expected for plutonium dioxide ($${\rm{Pu}}{{\rm{O}}_2}$$) as other actinide dioxides. However, least-square fit and local smoothing techniques applied to the experimental enthalpy data of PuO2 in 1980s could not detect a $$\lambda $$-peak in specific heat that might be due to too scattered and insufficient experimental data. Therefore, this issue has not been yet put beyond the doubts. In the current article, a superionic model of $${\rm{Pu}}{{\rm{O}}_2}$$ is developed with partially ionic model of a rigid ion potential. Thermophysical properties were calculated in constant pressure–temperature ensemble using molecular dynamics simulation. The Bredig transition with vicinity of a $$\lambda $$-peak in specific heat was successfully observed for the model system at about 2,100 K. Moreover, the experimental enthalpy change was well reproduced before and after the estimated transition temperature.

Modeling Superionic Behavior of Plutonium Dioxide

The Bredig transition to the superionic phase indicated with the lambda-peak in Cp was highly expected for PuO2 as other actinide dioxides. However, least-square fit and local smoothing techniques applied to the experimental enthalpy data of plutonium dioxide in 80's could not detect a lambda-peak in specific heat that might be due to too scattered and insufficient experimental data. Therefore, this issue has not been yet put beyond the doubts. In the current article, a superionic model of PuO2 is developed with partially ionic model of a rigid ion potential. Thermophysical properties were calculated in constant pressure-temperature ensemble using molecular dynamics simulation. The Bredig transition with vicinity of a lambda-peak in specific heat was a successfully observed for the model system at about 2100K. Moreover, the experimental enthalpy change was well reproduced before and after the estimated transition temperature.

A charge-optimized many-body potential for the U–UO2–O2 system

Building on previous charge-optimized many-body (COMB) potentials for metallic α-U and gaseous O2, we have developed a new potential for UO2, which also allows the simulation of U–UO2–O2 systems. The UO2 lattice parameter, elastic constants and formation energies of stoichiometric and non-stoichiometric intrinsic defects are well reproduced. Moreover, this is the first rigid-ion potential that produces the correct deviation of the Cauchy relation, as well as the first classical interatomic potential that is able to determine the defect energies of non-stoichiometric intrinsic point defects in UO2 with an appropriate reference state. The oxygen molecule interstitial in the α-U structure is shown to decompose, with some U–O bonds approaching the natural bond length of perfect UO2. Finally, we demonstrate the capability of this COMB potential to simulate a complex system by performing a simulation of the α-U + O2 → UO2 phase transformation. We also identify a possible mechanism for uranium oxidation and the orientation of the resulting fluorite UO2 structure relative to the coordinate system of orthorhombic α-U.

Accelerated molecular dynamics force evaluation on graphics processing units for thermal conductivity calculations

Thermal conductivity is a very important property of a material both for testing theoretical models and for designing better practical devices such as more efficient thermoelectrics, and accurate and efficient calculations of thermal conductivity are very desirable. In this paper, we develop a highly efficient molecular dynamics code fully implemented on graphics processing units for thermal conductivity calculations using the Green–Kubo formula. We compare two different schemes for force evaluation, a previously used thread-scheme, where a single thread is used for one particle and each thread calculates the total force for the corresponding particle, and a new block-scheme, where a whole block is used for one particle and each thread in the block calculates one or several pair forces between the particle associated with the given block and its neighbor particle(s) associated with the given thread. For both schemes, two different classical potentials, namely, the Lennard-Jones potential and the rigid-ion potential are implemented. While the thread-scheme performs a little better for relatively large systems, the block-scheme performs much better for relatively small systems. The relative performance of the block-scheme over the thread-scheme also increases with the increasing cutoff radius. We validate the implementation by calculating lattice thermal conductivities of solid argon and lead telluride. The efficiency of our code makes it very promising to study thermal conductivity properties of more complicated materials, especially, materials with interesting nanostructures.

Molecular dynamics simulation of surface energy of low miller index surfaces in UO2

Molecular dynamics simulation based on the rigid-ion potential is carried out to investigate the surface energies of low miller index crystallographic faces such as (100), (110) and (111) in UO2 in a temperature range of 300 K-1500 K. The results indicate that the surface energies of the three low miller index crystallographic faces decline gradually with temperature rising, and the variation of the surface energy with temperature is confirmed to be consistent with the experimental data. The (111) crystallographic face which is the closest surface has the lowest surface energy; the (100) crystallographic face has the biggest surface energy; the (100) crystallographic face has a surface energy in between them. The surface atoms have compressed towards the vertical line of surface with respect to the inside atoms layer obviously. The symmetry of surface atoms declines. Surface phenomena such as relaxation and reconstruction occur on the surface atoms and the relaxation effect extends to the five layers. The results presented in the study are useful for understanding the behaviors of fission gas bubbles growing up and cracking up due to the swelling in fuels under the irradiation.

Modelling the structural evolution of ternary phosphate glasses from melts to solid amorphous materials.

The local and medium-range structural properties of phosphate-based melts and glasses have been characterized by means of first principles (density functional theory) and classical (shell-model) molecular dynamics simulations. The structure of glasses with biomedically active molecular compositions, (P2O5)0.45(CaO)x(Na2O)0.55-x (x = 0.30, 0.35 and 0.40), have been generated using first principles molecular dynamics simulations for the full melt-and-quench procedure and the changes in the structural properties as the 3000 K melt is cooled down to room temperature have been compared extensively with those of the final glasses. The melts are characterized by a significant fraction of threefold (P3c) and fivefold (P5c) phosphorus atoms, but structural defects rapidly decrease during the cooling phase and for temperatures lower than 1800 K the system is free of under- and over-coordinated species. The analysis of the structures of the glasses at 300 K shows a prevalence of the metaphosphate Q2 and pyrophosphate Q1 species, whereas the number of Q3 units, which constitute the three-dimensional phosphate network, significantly decreases with the increase of calcium content in the glass. The radial and angular distribution functions indicate that higher calcium concentration in the glass leads to an increase of the rigidity of the phosphate tetrahedral network, which has been explained in terms of the calcium's higher field strength compared to that of sodium. The structural characterization of the melts and glasses obtained from first principles simulations was used to assess and validate a recently developed interatomic shell-model forcefield for phosphate-based materials. For all three compositions, our potential model is in good agreement with the first principles data. In the glass network, the forcefield provides a very good description of the split between the shorter distances of phosphorus to non-bonded oxygen and the longer distances of the phosphorus to bonded oxygen; the phosphorus-phosphorus medium-range distribution; and the coordination environment around the Na and Ca glass modifiers. Moreover, the distribution of the Qn species in the melts and glasses is in excellent agreement with the values extracted from the first principles simulations. In contrast, simulations using standard rigid ion potentials do not provide a satisfactory description of the local short-range structure of phosphate-based glasses and are therefore less suitable to model this class of multicomponent amorphous system.

Hypernetted chain calculations of molten uranium dioxide: Comparison of rigid ion potentials

The first liquid state calculations within the hypernetted chain approximation for molten uranium dioxide using six different rigid ion model potentials are presented and discussed. Applicability of the existing rigid ion potentials to the molten phase of uranium dioxide is examined. Despite the minor differences, the radial distribution functions and static structure factors of all potentials are typical of a system which melted from a fast ion conducting phase. Only in one case, the breakdown in the local structure of oxygen ions in the solid state is reflected in the calculated coordination numbers. The behavior of static dielectric function is related to the onset of freezing and found to mimic that of the classical one component plasma at low values of plasma parameter. Finally, the enthalpy change is calculated and compared with molecular dynamic simulation results and experimental data.

Structure and transport properties of LiF–BeF2 mixtures: Comparison of rigid and polarizable ion potentials#

Molecular dynamics simulations are performed to study the structure and dynamics of the LiF–BeF2 system over a range of compositions using the transferable rigid-ion model (TRIM). The densities obtained with the TRIM potential are approximately 17–20% lower than the experimental values while polarizable ion models (PIM) give densities within 5% of the experimental value. The TRIM and PIM potentials give essentially identical radial distribution functions (RDFs) for Li–F and Be–F ion pairs though the Be–Be pair correlation differ significantly and reflect the corresponding density differences. The variation in the radial distribution functions with concentration, particularly the anion–anion pair correlation function, reflects the reorganization of the fluoride ions as the addition of BeF2 in the mixture promotes the formation of the tetrahedral fluoroberyllate network. Along the 67 mole% LiF isopleth, diffusivities and Nernst–Einstein ionic conductivities from simulations using the PIM and TRIM potentials are in good agreement for temperatures up to 925 K. The viscosity data using the PIM model is also found to be in good agreement with the TRIM results presented here along the 873 K isotherm for compositions ranging from 0 to 50 mole% BeF2. The main conclusion from this study is that the non-polarizable, TRIM provides reasonable results for the structural correlations and transport properties of the LiF–BeF2 system in comparison with first-principles-based, PIM. Behaviour of ionic conductivity as a function of temperature, calculated using a rigid ion model is compared with experiment and with a polarizable ion model for the LiF–BeF2 system at 33 mole% BeF2. Simulation snapshots of the LiF–BeF2 melt at concentrations of 10 and 70 mole% BeF2 along the 1500K isotherm are shown on the right. The green, blue and red coloured spheres represent the lithium, beryllium and fluorine, respectively.

The influence of dipole polarisation on threshold displacement energies in UO2

Molecular dynamics simulations of radiation damage in nuclear materials have traditionally been performed using rigid ion empirical potential models. The inclusion of dipole polarisability via the shell model offers the possibility to incorporate more of the underlying physics into simulations of radiation damage via cascade simulations. Here we assess the impact of dipole polarisability on the evolution of radiation damage in UO2 by performing molecular dynamics simulations to determine the threshold displacement energies using both a standard rigid ion potential and the equivalent model including dipole polarisability. The inclusion of dipole polarisability reduces the threshold displacement energies by 20–30% relative to the rigid ion model, suggesting a significant increase in the number of defects created during the collisional phase of the cascade. However, a reduction in the activation energies for migration due to inclusion of polarisability may increase the rate of subsequent interstitial–vacancy recombination. The overall level of radiation damage will, therefore, be determined by the relative effectiveness of these two opposing processes.

THERMOPHYSICAL PROPERTIES OF URANIUM DIOXIDE: A MOLECULAR DYNAMICS STUDY OF SOLID AND LIQUID PHASES OF STOICHIOMETRIC UO2

Thermodynamic and transport properties of solid and liquid uranium dioxide were studied using classical molecular dynamics simulation, with a newly parametrized interionic model potential. In addition to the static and transport properties which have been previously reported by the authors, this study further confirms that temperature dependence of the calculated thermophysical properties of uranium dioxide are in agreement with the available experimental data at both solid and liquid phases in providing an alternative rigid ion potential to the other model potentials in literature. Although lattice parameter and density have been underestimated, overall results give a fairly good description of the UO 2 system for wide range of temperature (0–4000 K). The transition to the superionic phase, Bredig transition, was successfully observed as a distinct λ-peak in specific heats at about 400 K below the experimental value. The results presented in our previous article and here show that the introduced alternative model potential for uranium dioxide is very promising and we are confident in the success of its use in future studies.

MOLECULAR DYNAMICS SIMULATION OF UO2: AN ALTERNATIVE RIGID ION MODEL POTENTIAL

A semi-empirical effective interionic potential model has been parameterized to investigate UO 2 by molecular dynamics simulation technique. The simulations were performed in the constant pressure–temperature ensemble between 300 K–3200 K at 100 K intervals. The pair distribution functions and coordination numbers signal the onset of structural changes at temperatures in accord with the Bredig transition and melting. The oxygen ion diffusion coefficients calculated from the mean square displacements markedly increase the liquid like value at T > 2100 K . The transition to the superionic state and melting are well reproduced within the limitations of a rigid ion potential.

A polarizable ion model for the structure of molten CuI

The results are reported of the molecular dynamics simulations of the coherent static structure factor of molten CuI at 938 K using a polarizable ion model. This model is based on a rigid ion potential to which the many body interactions due to the anions induced polarization are added. The calculated structure factor reproduces the clear sharp prepeak observed in neutron diffraction data. The corresponding partial structure factors and the related radial distribution functions calculated by molecular dynamics are compared with those found in the literature derived from a combination of neutron and x-ray diffraction data with the aid of the reverse Monte Carlo simulation technique, as well as those calculated by ab initio MD simulations.

Ab initioconstruction of interatomic potentials for uranium dioxide across all interatomic distances

We provide a methodology for generating interatomic potentials for use in classical molecular-dynamics simulations of atomistic phenomena occurring at energy scales ranging from lattice vibrations to crystal defects to high-energy collisions. A rigorous method to objectively determine the shape of an interatomic potential over all length scales is introduced by building upon a charged-ion generalization of the well-known Ziegler-Biersack-Littmark universal potential that provides the short- and long-range limiting behavior of the potential. At intermediate ranges the potential is smoothly adjusted by fitting to ab initio data. Our formalism provides a complete description of the interatomic potentials that can be used at any energy scale, and thus, eliminates the inherent ambiguity of splining different potentials generated to study different kinds of atomic-materials behavior. We exemplify the method by developing rigid-ion potentials for uranium dioxide interactions under conditions ranging from thermodynamic equilibrium to very high atomic-energy collisions relevant for fission events.

Energetic recoils in UO2 simulated using five different potentials

This report presents the results of classical molecular dynamics simulations of the diffuse premelting transition, melting, and defect production by 1 keV U recoils in UO(2) using five different rigid ion potentials. The experimentally observed premelting transition occurred for all five cases. For all the potentials studied, dynamic defect annealing is highly effective and is accompanied by replacement events on the anion sublattice. The primary damage state after approximately 15 ps consists of isolated Frenkel pairs and interstitial and vacancy clusters of various sizes. The average displacement energy varies from approximately 28 to approximately 83 eV and the number of Frenkel pairs is different by a factor of 3 depending on the choice of potential. The size and spatial distribution of vacancy and interstitial clusters is drastically different for the potentials studied. The results provide statistics of defect production. They point to a pressing need to determine defect formation, migration, and binding energies in UO(2) from first principles and to develop reliable potentials based on this data for simulating microstructural evolution in nuclear fuel under operating conditions.

Short- and medium-range structure of multicomponent bioactive glasses and melts: An assessment of the performances of shell-model and rigid-ion potentials

Classical and ab initio molecular dynamics (MD) simulations have been carried out to investigate the effect of a different treatment of interatomic forces in modeling the structural properties of multicomponent glasses and melts. The simulated system is a soda-lime phosphosilicate composition with bioactive properties. Because the bioactivity of these materials depends on their medium-range structural features, such as the network connectivity and the Q(n) distribution (where Q(n) is a tetrahedral species bonded to n bridging oxygens) of silicon and phosphorus network formers, it is essential to assess whether, and up to what extent, classical potentials can reproduce these properties. The results indicate that the inclusion of the oxide ion polarization through a shell-model (SM) approach provides a more accurate representation of the medium-range structure compared to rigid-ion (RI) potentials. Insight into the causes of these improvements has been obtained by comparing the melt-and-quench transformation of a small sample of the same system, modeled using Car-Parrinello MD (CPMD), to the classical MD runs with SM and RI potentials. Both classical potentials show some limitations in reproducing the highly distorted structure of the melt denoted by the CPMD runs; however, the inclusion of polarization in the SM potential results in a better and qualitatively correct dynamical balance between the interconversion of Q(n) species during the cooling of the melt. This effect seems to reflect the slower decay of the fraction of structural defects during the cooling with the SM potential. Because these transient defects have a central role in mediating the Q(n) transformations, as previously proposed and confirmed by the current simulations, their presence in the melt is essential to produce an accurate final distribution of Q(n) species in the glass.

Molecular dynamics study of polarizable point dipole models for molten sodium iodide

The structure, the ionic transport properties, and the dynamics of long-wavelength charge-density fluctuations, for two polarizable point dipole models of molten NaI, have been studied by molecular dynamics simulations. These models are based on a rigid ion potential to which the induced dipole polarization of the anions is added. The polarization is added in such a way that point dipoles are induced on the anions by both local electric field and short-range damping interactions that oppose the electrically induced dipole moments. The two polarizable ion models differ only in the range of the damping polarization interactions. The influence of the induced anion polarization on the different properties of simulated molten NaI is discussed.