Superionic UO2: A model anharmonic crystalline material

Stringlet excitation model of the boson peak

The boson peak (BP), a low-energy excess in the vibrational density of states over the Debye contribution, is often identified as a characteristic of amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes involving one-dimensional (1D) string-like excitations ("stringlets"). We build on a theory originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in simulations. We provide an analytical prediction for the BP frequency ωBP in the temperature regime well below the observed glass transition temperature Tg. The prediction involves no free parameters and accords quantitatively with prior simulation observations in 2D and 3D model glasses based on inverse power law potentials. The comparison of the string model to observations is more uncertain when compared to simulations of an Al-Sm metallic glass material at temperatures well above Tg. Nonetheless, our stringlet model of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in simulations of glass-forming liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes above Tg, which leads to a large low-frequency contribution to the 3D vibrational density of states, observed in both experiments and simulations.

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Decoupling Ion Transport and Matrix Dynamics to Make High Performance Solid Polymer Electrolytes

Transport of ions through solid polymeric electrolytes (SPEs) involves a complicated interplay of ion solvation, ion-ion interactions, ion-polymer interactions, and free volume. Nonetheless, prevailing viewpoints on the subject promote a significantly simplified picture, likening ion transport in a polymer to that in an unstructured fluid at low solute concentrations. Although this idealized liquid transport model has been successful in guiding the design of homogeneous electrolytes, structured electrolytes provide a promising alternate route to achieve high ionic conductivity and selectivity. In this perspective, we begin by describing the physical origins of the idealized liquid transport mechanism and then proceed to examine known cases of decoupling between the matrix dynamics and ionic transport in SPEs. Specifically we discuss conditions for "decoupled" mobility that include a highly polar electrolyte environment, a percolated path of free volume elements (either through structured or unstructured channels), high ion concentrations, and labile ion-electrolyte interactions. Finally, we proceed to reflect on the potential of these mechanisms to promote multivalent ion conductivity and the need for research into the interfacial properties of solid polymer electrolytes as well as their performance at elevated potentials.

Machine learning molecular dynamics simulations toward exploration of high-temperature properties of nuclear fuel materials: case study of thorium dioxide

Predicting materials properties of nuclear fuel compounds is a challenging task in materials science. Their thermodynamical behaviors around and above the operational temperature are essential for the design of nuclear reactors. However, they are not easy to measure, because the target temperature range is too high to perform various standard experiments safely and accurately. Moreover, theoretical methods such as first-principles calculations also suffer from the computational limitations in calculating thermodynamical properties due to their high calculation-costs and complicated electronic structures stemming from f-orbital occupations of valence electrons in actinide elements. Here, we demonstrate, for the first time, machine-learning molecular-dynamics to theoretically explore high-temperature thermodynamical properties of a nuclear fuel material, thorium dioxide. The target compound satisfies first-principles calculation accuracy because f-electron occupation coincidentally diminishes and the scheme meets sampling sufficiency because it works at the computational cost of classical molecular-dynamics levels. We prepare a set of training data using first-principles molecular dynamics with small number of atoms, which cannot directly evaluate thermodynamical properties but captures essential atomistic dynamics at the high temperature range. Then, we construct a machine-learning molecular-dynamics potential and carry out large-scale molecular-dynamics calculations. Consequently, we successfully access two kinds of thermodynamic phase transitions, namely the melting and the anomalous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}λ transition induced by large diffusions of oxygen atoms. Furthermore, we quantitatively reproduce various experimental data in the best agreement manner by selecting a density functional scheme known as SCAN. Our results suggest that the present scale-up simulation-scheme using machine-learning techniques opens up a new pathway on theoretical studies of not only nuclear fuel compounds, but also a variety of similar materials that contain both heavy and light elements, like thorium dioxide.

Role of Optical Phonons and Anharmonicity in the Appearance of the Heat Capacity Boson Peak-like Anomaly in Fully Ordered Molecular Crystals

We demonstrate that the heat capacity Boson peak (BP)-like anomaly appearing in fully ordered anharmonic molecular crystals emerges as a result of the strong interactions between propagating (acoustic) and low-energy quasi-localized (optical) phonons. In particular, we experimentally determine the low-temperature (<30 K) specific heat of the molecular crystal benzophenone and those of several of its fully ordered bromine derivatives. Subsequently, by means of theoretical first-principles methods based on density functional theory, we estimate the corresponding phonon dispersions and vibrational density of states. Our results reveal two possible mechanisms for the emergence of the BP-like anomaly: (i) acoustic-optic phonon avoided crossing, which gives rise to a pseudo-van Hove singularity in the acoustic phonon branches, and (ii) piling up of low-frequency optical phonons, which are quasi degenerate with longitudinal acoustic modes and lead to a surge in the vibrational density of states at low energies.

Understanding fast-ion conduction in solid electrolytes

The ability of some solid materials to exhibit exceptionally high ionic conductivities has been known since the observations of Michael Faraday in the nineteenth century (Faraday M. 1838 Phil. Trans. R. Soc. 90), yet a detailed understanding of the atomic-scale physics that gives rise to this behaviour remains an open scientific question. This theme issue collects articles from researchers working on this question of understanding fast-ion conduction in solid electrolytes. The issue opens with two perspectives, both of which discuss concepts that have been proposed as schema for understanding fast-ion conduction. The first perspective presents an overview of a series of experimental NMR studies, and uses this to frame discussion of the roles of ion-ion interactions, crystallographic disorder, low-dimensionality of crystal structures, and fast interfacial diffusion in nanocomposite materials. The second perspective reviews computational studies of halides, oxides, sulfides and hydroborates, focussing on the concept of frustration and how this can manifest in different forms in various fast-ion conductors. The issue also includes five primary research articles, each of which presents a detailed analysis of the factors that affect microscopic ion-diffusion in specific fast-ion conducting solid electrolytes, including oxide-ion conductors [Formula: see text] and [Formula: see text], lithium-ion conductors [Formula: see text] and [Formula: see text], and the prototypical fluoride-ion conductor [Formula: see text]-[Formula: see text]. This article is part of the Theo Murphy meeting issue 'Understanding fast-ion conduction in solid electrolytes'.

Structural Aspects of the Superionic Transition in AX2 Compounds With the Fluorite Structure

Some AX₂ binary compounds with the fluorite structure (space group Fm3¯m) are well-known examples of materials exhibiting transitions to ionic superconducting phases at high temperatures below their melting points. Such superionic states have been described as either highly defective crystals or part-crystal, part-liquid states where the A ions retain their crystalline order whilst the X ions undergo partial melting. However, no detailed description of the structure of these phases exists. We present here the results of our investigation of the structural changes that occur during these transitions and the structural characteristics of the resulting superionic materials. This work is based on atomic-scale molecular dynamics modelling methods as well as computational diffraction techniques. We employed a set of empirical potentials representing several compounds with the fluorite structure to investigate any potential-dependent effect. We show the importance of small-scale structure changes, with some local environments showing a hexagonal symmetry similar to what is seen in the scrutinyite structure that has been documented for example in UO₂.

Spatial Dimensionality Dependence of Heterogeneity, Breakdown of the Stokes-Einstein Relation, and Fragility of a Model Glass-Forming Liquid

We investigate the heterogeneity of dynamics, the breakdown of the Stokes-Einstein relation and fragility in a model glass forming liquid, a binary mixture of soft spheres with a harmonic interaction potential for spatial dimensions from 3 to 8. The dynamical heterogeneity is quantified through the dynamical susceptibility χ₄ and the non-Gaussian parameter α₂. We find that the fragility, the degree of breakdown of the Stokes-Einstein relation, and the heterogeneity of the dynamics decrease with increasing spatial dimensionality. We briefly describe the dependence of fragility on the density and use it to resolve an apparent inconsistency with previous results.

Relations Between Dynamic Localization and Solute Diffusion in Polymers

Various public health concerns can arise from the unintended leaching of additives and impurities from polymeric medical devices or food packaging, which is directly related to each solute's diffusivity D. Both experimental and simulation methods can be used to quantify D, but slow diffusion at physiologic temperature in glassy polymers can render these approaches impractical. Here, we investigate a simulation approach with the potential to more rapidly calculate D. Specifically, we examine links between dynamic localization, characterized by the Debye-Waller factor, ⟨u²⟩, and D in a variety of polymer/solute systems using atomistic molecular dynamics (MD) simulations. Using short, high-temperature MD simulations to estimate D at physiologic temperature, we find that the relation ln D ∝ 1/⟨u²⟩ quantitatively predicts D for small solutes and produces an upper-bound estimate of D for larger solutes. Upper-bound estimates are useful in certain contexts, and we compare our results with another approach for determining upper bounds, the Piringer model, to show where each method may be useful. Then, we examine a modified relation where the Debye-Waller factor is rescaled by the mode coupling temperature T_c, which can produce better estimates of D if T_c is carefully chosen. Last, we compare our approach with several other models that relate temperature or localized dynamics with diffusivity. Although each of these approaches can be used to model D across wide temperature ranges using one or more adjustable parameters, none of them are truly predictive in glassy polymers. Further developments are needed to predict the optimal values of the adjustable parameters a priori.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

Mechanistic Origin of Superionic Lithium Diffusion in Anion-Disordered Li6PS5 X Argyrodites

The rational development of fast-ion-conducting solid electrolytes for all-solid-state lithium-ion batteries requires understanding the key structural and chemical principles that give some materials their exceptional ionic conductivities. For the lithium argyrodites Li6PS5X (X = Cl, Br, or I), the choice of the halide, X, strongly affects the ionic conductivity, giving room-temperature ionic conductivities for X = {Cl,Br} that are ×103 higher than for X = I. This variation has been attributed to differing degrees of S/X anion disorder. For X = {Cl,Br}, the S/X anions are substitutionally disordered, while for X = I, the anion substructure is fully ordered. To better understand the role of substitutional anion disorder in enabling fast lithium-ion transport, we have performed a first-principles molecular dynamics study of Li6PS5I and Li6PS5Cl with varying amounts of S/X anion-site disorder. By considering the S/X anions as a tetrahedrally close-packed substructure, we identify three partially occupied lithium sites that define a contiguous three-dimensional network of face-sharing tetrahedra. The active lithium-ion diffusion pathways within this network are found to depend on the S/X anion configuration. For anion-disordered systems, the active site-site pathways give a percolating three-dimensional diffusion network; whereas for anion-ordered systems, critical site-site pathways are inactive, giving a disconnected diffusion network with lithium motion restricted to local orbits around S positions. Analysis of the lithium substructure and dynamics in terms of the lithium coordination around each sulfur site highlights a mechanistic link between substitutional anion disorder and lithium disorder. In anion-ordered systems, the lithium ions are pseudo-ordered, with preferential 6-fold coordination of sulfur sites. Long-ranged lithium diffusion would disrupt this SLi6 pseudo-ordering, and is, therefore, disfavored. In anion-disordered systems, the pseudo-ordered 6-fold S-Li coordination is frustrated because of Li-Li Coulombic repulsion. Lithium positions become disordered, giving a range of S-Li coordination environments. Long-ranged lithium diffusion is now possible with no net change in S-Li coordination numbers. This gives rise to superionic lithium transport in the anion-disordered systems, effected by a concerted string-like diffusion mechanism.

Localization model description of the interfacial dynamics of crystalline Cu and [Formula: see text] metallic glass nanoparticles

Many of the special properties of nanoparticles (NPs) and nanomaterials broadly derive from the significant fraction of particles (atoms, molecules or segments of polymeric molecules) in the NP interfacial region in which the interparticle interactions are characteristically highly anharmonic in comparison to the bulk material. This leads to relatively large mean square particle displacements relative to the material interior, often resulting in a strong increase interfacial mobility and reactivity in both crystalline and glass NPs. The 'Debye-Waller factor', or the mean square particle displacement [Formula: see text] on a ps 'caging' timescale relative to the square of the average interparticle distance [Formula: see text], provides an often experimentally accessible measure of the strength of this anharmonic interaction. The Localization Model (LM) of the dynamics of condensed materials relates this thermodynamic property to the structural relaxation time [Formula: see text], determined from the intermediate scattering function, without any free parameters. Moreover, the LM allows for the prediction of the diffusion coefficient D when combined with the 'decoupling' or Fractional Stokes-Einstein relation linking [Formula: see text] to D. In the current study, we employed classical molecular dynamics simulation to investigate the structural relaxation and diffusion of model [Formula: see text] metallic glass and Cu crystalline NPs with different sizes. As with previous studies validating the LM on model bulk and crystalline materials, and for the interfacial dynamics of thin crystalline and metallic glass films, we find the LM model also describes the interfacial dynamics of model crystalline metal (Cu) and metallic glass ([Formula: see text] NPs to a good approximation, further confirming the generality of the model.

Localization model description of the interfacial dynamics of crystalline Cu and Cu64Zr36 metallic glass films

Recent studies of structural relaxation in Cu-Zr metallic glass materials having a range of compositions and over a wide range of temperatures and in crystalline UO₂ under superionic conditions have indicated that the localization model (LM) can predict the structural relaxation time τ_α of these materials from the intermediate scattering function without any free parameters from the particle mean square displacement ⟨r²⟩ at a caging time on the order of ps, i.e., the "Debye-Waller factor" (DWF). In the present work, we test whether this remarkable relation between the "fast" picosecond dynamics and the rate of structural relaxation τ_α in these model amorphous and crystalline materials can be extended to the prediction of the local interfacial dynamics of model amorphous and crystalline films. Specifically, we simulate the free-standing amorphous Cu₆₄Zr₃₆ and crystalline Cu films and find that the LM provides an excellent parameter-free prediction for τ_α of the interfacial region. We also show that the Tammann temperature, defining the initial formation of a mobile interfacial layer, can be estimated precisely for both crystalline and glass-forming solid materials from the condition that the DWFs of the interfacial region and the material interior coincide.

Structure and dynamics of the Lennard-Jones fcc-solid focusing on melting precursors

The Lennard-Jones potential is taken as a basis to study the structure and dynamics of the face centered cubic (fcc) solid along an isochore from low temperatures up to the solid/fluid transition. The Z method is applied to estimate the melting point. Molecular dynamics simulations are used to calculate the pair distribution function, numbers of nearest neighbors, and the translational order parameter, analyzing the weakening of the fcc-symmetry due to emerging premelting effects. A range of dynamic properties, such as the mean-squared displacement, non-Gaussian parameter, Debye-Waller factor, and vibrational density of states, is considered for the analysis of the solid state. All of these parameters clearly show that bulk mobility is activated at about 2/3 of the melting temperature, known as the Tammann temperature. This indicates that vibrational motion of atoms is not maintained exclusively in the entire stable solid state and that collective atomic motion constitutes a precursor of the melting process.

Optimization of a new interatomic potential to investigate the thermodynamic properties of hypo-stoichiometric mixed oxide fuel U1-yPuyO2-x

The behaviour of stoichiometric U1-yPuyO2compounds used as nuclear fuel is relatively well understood. Conversely, the effects of stoichiometry deviation on fuel performance and fuel stability are intricate and poorly studied. In order to investigate what affect these have on the thermophysical properties of hypo-stoichiometric U1-yPuyO2-xmixed oxide fuel, new interaction parameters based on the many-body CRG (Cooper-Rushton-Grimes) potential formalism were optimized. The new potential has been fitted to match experimental lattice parameters of U0.7Pu0.3O1.99(O/M = 1.99) and U0.7Pu0.3O1.97(O/M = 1.97), where M represents the total amount of metallic cations, through a rigorous procedure combining classical molecular dynamic and classical molecular Monte Carlo simulation methods. This new potential provides an excellent description of the U1-yPuyO2-x system. Concerning lattice parameter, although fitted on only one Pu content (30%) and two stoichiometries (1.99 and 1.97), our potential allows good predictions compared to available experimental results as well as to available recommendations in wide ranges of O/M ratio, Pu content and temperature. For the U0.7Pu0.3O2-xhypo-stoichiometric system (30% Pu content and O/M ratio ranging from 1.94 to 2.00), some direct properties (lattice parameter and enthalpy) and some derivative properties (linear thermal expansion coefficient and specific heat) were systematically investigated from room temperature up to the expected melting temperatures and a good agreement with experiments is found. Moreover, our potential shows a good transferability to the plutonium sesquioxide Pu2O3system.

Universal nature of dynamic heterogeneity in glass-forming liquids: A comparative study of metallic and polymeric glass-forming liquids

Glass-formation is a ubiquitous phenomenon that is often observed in a broad class of materials ranging from biological matter to commonly encountered synthetic polymer, as well as metallic and inorganic glass-forming (GF) materials. Despite the many regularities in the dynamical properties of GF materials, the structural origin of the universal dynamical properties of these materials has not yet been identified. Recent simulations of coarse-grained polymeric GF liquids have indicated the coexistence of clusters of mobile and immobile particles that appear to be directly linked, respectively, to the rate of molecular diffusion and structural relaxation. The present work examines the extent to which these distinct types of "dynamic heterogeneity" (DH) arise in metallic GF liquids (Cu-Zr, Ni-Nb, and Pd-Si alloys) having a vastly different molecular structure and chemistry. We first identified mobile and immobile particles and their transient clusters and found the DH in the metallic alloys to be remarkably similar in form to polymeric GF liquids, confirming the "universality" of the DH phenomenon. Furthermore, the lifetime of the mobile particle clusters was found to be directly related to the rate of diffusion in these materials, while the lifetime of immobile particles was found to be proportional to the structural relaxation time, providing some insight into the origin of decoupling in GF liquids. An examination of particles having a locally preferred atomic packing, and clusters of such particles, suggests that there is no one-to-one relation between these populations of particles so that an understanding of the origin of DH in terms of static fluid structure remains elusive.

Localization model description of diffusion and structural relaxation in superionic crystalline UO2

We test the Localization Model (LM) prediction of a parameter-free relationship between the α-structural relaxation time τ_α and the oxygen ion diffusion coefficient D_O with the Debye-Waller factor ⟨u²⟩ for crystalline UO₂ under superionic conditions where large anharmonic interactions lead to non-Arrhenius relaxation and high ion mobility. As in a previous study of structural relaxation in Cu-Zr metallic glass materials having a range of compositions, we find that the LM relationship between the picosecond atomic dynamics ("fast" beta relaxation) and the long-time structural relaxation time and oxygen ion diffusion coefficient holds to an excellent approximation without any free parameters over the full range of temperatures and pressures investigated in our simulations.