[en] Defect reactions involving charged species are commonplace in nuclear fuels fabrication and burn-up. Even the simplest of these fuels, uranium dioxide (UO2), typically involves the nominal charge states of +3, +4, and +5 or +6 in U and -1 and -2 states in O. Simulations that attempt to model evolutionary processes in the fuels require tracking changes among these charge states. At the atomistic level, modeling defect reactions poses a particularly vexing problem. Typical potential energy surfaces do not have this type of physical phenomena built into them. Those models that do attempt to model charge-defect reactions do not have especially strong physical bases for the models. For instance, most do not obey established limits of charge behavior at dissociation or lack internal consistency. This work presents substantial generalizations to earlier work of Perdew et al. No matter the size of the system, total system hamiltonians can be decomposed into subsystem or site hamiltonians and coulombic interactions. Site hamiltonians can be evaluated in a spectral representation, once an integer number of electrons are assigned. For both pair and individual site hamiltonians a dilemma emerges in that many sites are better understood as possessing a fractional charge. The dilemma is how to weight the site integer-charge states in a physically consistent manner. One approach to solving the dilemma results in two distinct charge-dependent energy contributions emerge, arising from intra- and inter-subsystem charge transfer. Further analysis results in a model of the intra-subsystem charge-transfer that can accommodate the mixed valence states of either U or O in nuclear fuels. Mixed valence properties add complications to the model that originate in the phenomenological fact that it typically requires different amounts of energy to increase or decrease charge. As a result of the inherent complexity one has the option of using multiple charges, a concept with strong ties to shell models, or modeling parameters not directly related to charge as functions of charge. This later approach is illustrated by invoking a minimization principle that does preserve the important dissociation limits of Perdew et al., in order to complete the model.

[en] Charge flow in materials is controlled at the atomistic level through some model of the chemical potential, such as the Iczkowski-Margrave (IM) model. This model is built largely on heuristic arguments. Here a model Hamiltonian is constructed at the atomistic level commensurate with the IM model. Essential properties of the model Hamiltonian are presented, including a possible revision of the charge dependence in the IM model. Transitional properties of the model are shown to be central to regulating charge flow.

[en] Highlights: • A novel first principles approach towards the fragment ionicity. • Constrained DFT and valance charge density decomposition were employed. • Correct dissociation limit achieved for diatomics. • Ionicity is an input parameter for a new class of atomistic potentials. - Abstract: We develop a first principles approach towards the ionicity of fragments. In contrast to the bond ionicity, the fragment ionicity refers to an electronic property of the constituents of a larger system, which may vary from a single atom to a functional group or a unit cell to a crystal. The fragment ionicity is quantitatively defined in terms of the coefficients of contributing charge states in a superposition of valence configurations of the system. Utilizing the constrained density functional theory-based computations, a practical method to compute the fragment ionicity from valence electron charge densities, suitably decomposed according to the Fragment Hamiltonian (FH) model prescription for those electron densities, is presented for the first time. The adopted approach is illustrated using BeO, MgO and CaO diatomic molecules as simple examples. The results are compared and discussed with respect to the bond ionicity scales of Phillips and Pauling

[en] Nuclear fuels and materials present special problems to atomistic-scale modeling. At a metal-metal-oxide interface, the metal centers are charged on the oxide side, but neutral on the metallic side. The intimate contact necessitates that atomistic models for these materials be both compatible and consistent with one another at some level. A new “fragment” Hamiltonian (FH) model, at the atomistic level, is presented that reduces qualitatively to existing, successful models for metals, such as the embedded atom method, and ceramics, such as the charge equilibration models. Moreover, the FH model possesses both electron hopping and fundamental gaps that appear as separate terms in a generalized embedding function. The electron hopping contributions come from both one-electron and two-electron sources. These contributions appear as a result of the FH point of view, rather than being postulated. The model obeys certain well known theoretical limits that come from the nonlinearity of electron hopping processes as the volume of a crystal is changed. The generalized notion of embedding entails two variables instead of one. The ability to account for multiple charge states in the cations leads to the capability within the model to distinguish the qualitative differences among metallic, ionic, and covalent bonding environments. The details of all of these energies, among with fragment interactions, combine to determine the state of the atom in the material. (author)

[en] Recently progress has been achieved with a modified embedded atom method (MEAM) potential for pure Pu. The MEAM potential is able to capture the most salient features of atomic volume and enthalpy of solid and liquid Pu metal as a function of temperature at zero pressure. The atomic volume difference between monoclinic (α-phase) and fcc (δ-phase) was captured nearly quantitatively. From molecular dynamics (MD) simulations, we find that Pu, under these conditions, has an approximately 10 eV minimum displacement threshold energy, very low compared to most other fcc metals, and shows less crystallographic anisotropy in this minimum. At 0 K, the constant volume cell relaxes to a rhombohedrally distorted structure, which is connected to the low minimum displacement threshold energy. Split interstitials orient themselves in a <1 0 0> direction and migrate over a 0.056 eV barrier. Mono-vacancies migrate over a 0.84-1.00 eV barrier

[en] Using rates for vacancy diffusion in plutonium (Pu) found with parallel-replica dynamics, we develop a kinetic Monte Carlo (KMC) model of void growth and mobility. We compare and contrast the behavior of voids in Pu as predicted using vacancy mobilities from two different modified embedded atom method (MEAM) descriptions of Pu. We find that void behavior depends sensitively on the values used for vacancy mobility. In particular, we find that voids are very mobile in one model of Pu, but are essentially immobile in another, leading to very different void structures over time. This second model also predicts lifetimes for voids that are extremely long, and seemingly unphysical, suggesting that the first model is more representative of real Pu

[en] A phase-field model was developed to simulate the accumulation and transport of fission products and the evolution of gas bubble microstructures in nuclear fuels. The model takes into account the generation of gas atoms and vacancies, and the elastic interaction between diffusive species and defects as well as the inhomogeneity of elasticity and diffusivity. The simulations show that gas bubble nucleation is much easier at grain boundaries than inside grains due to the trapping of gas atoms and the high mobility of vacancies and gas atoms in grain boundaries. Helium bubble formation at unstable vacancy clusters generated by irradiation depends on the mobilities of the vacancies and He, and the continuing supply of vacancies and He. The formation volume of the vacancy and He has a strong effect on the gas bubble nucleation at dislocations. The effective thermal conductivity strongly depends on the bubble volume fraction, but weakly on the morphology of the bubbles.

[en] The Fragment Hamiltonian (FH) model is introduced as the basis for a new class of atomistic potentials that may be viewed as generalizations of the embedded atom method (EAM) and related atomistic potentials. Many metals and alloys have been successfully modeled by this method and other related methods, but the nature of the metallic character in the models has been lost. Here we attempt to recover this character, at a qualitative level, by defining an embedding energy as a function of two variables through the FH model. One of these variables, called the ionicity, is associated with the established concept of background density in EAM models. The FH embedding energy is composed of two types of energies, one for energies of different states of an atom and the other for hopping energies that transform an atom from one state to another. A combination of the energies for the states of an atom yield a local gap energy that conforms to a generalized definition of the ‘Hubbard-U’ energy. The hopping energies compete with the gap energy to provide a notion of metallic behavior in an atomic-scale model. Lattices of nickel with different coordinations and spatial dimensions, elastic constants, energies for several types of defects in three-dimensional lattices and two surface energies are calculated to show the strengths and limitations of the current implementation and to explore their metallic character. (paper)

[en] We develop two new modified embedded-atom method (MEAM) potentials for elemental iron, intended to reproduce the experimental phase stability with respect to both temperature and pressure. These simple interatomic potentials are fitted to a wide variety of material properties of bcc iron in close agreement with experiments. Numerous defect properties of bcc iron and bulk properties of the two close-packed structures calculated with these models are in reasonable agreement with the available first-principles calculations and experiments. Performance at finite temperatures of these models has also been examined using Monte Carlo simulations. We attempt to reproduce the experimental iron polymorphism at finite temperature by means of free energy computations, similar to the procedure previously pursued by Müller et al (2007 J. Phys.: Condens. Matter 19 326220), and re-examine the adequacy of the conclusion drawn in the study by addressing two critical aspects missing in their analysis: (i) the stability of the hcp structure relative to the bcc and fcc structures and (ii) the compatibility between the temperature and pressure dependences of the phase stability. Using two MEAM potentials, we are able to represent all of the observed structural phase transitions in iron. We discuss that the correct reproductions of the phase stability among three crystal structures of iron with respect to both temperature and pressure are incompatible with each other due to the lack of magnetic effects in this class of empirical interatomic potential models. The MEAM potentials developed in this study correctly predict, in the bcc structure, the self-interstitial in the 〈110〉 orientation to be the most stable configuration, and the screw dislocation to have a non-degenerate core structure, in contrast to many embedded-atom method potentials for bcc iron in the literature. (paper)

[en] Using parallel-replica dynamics and temperature accelerated dynamics, we extract the rates for mono- and di-vacancy diffusion in δ-plutonium (Pu) using two parameterizations of the modified embedded atom method (MEAM). We find that mono-vacancy diffusion is faster in 'pure' Pu than in δ-stabilized Pu. Also, at higher temperatures, the rate of double jumps is nearly the same as single jumps in pure Pu. Since these double jumps contribute four times as much as single jumps to the diffusion constant, models incorporating mono-vacancy diffusion must account for this mechanism to predict mass transport in Pu. While di-vacancies are energetically only slightly preferred compared to mono-vacancies, they are significantly more mobile. Surprisingly, this enhanced mobility is due to the prefactor; the migration barrier is essentially identical. The di-vacancy dissociates at a rate similar to the mono-vacancy hop rate