Radiation-Induced Patterning at the Nanometric Scale: A Phase Field Approach.

The phase field approach was developed in the last 20 years to handle radiation damage in materials. This approach bridges the gap between atomistic simulations extensively used to model first step of radiation damage at short time and continuum approach at large time. The main advantage of such an approach lies in its ability to compute not only the microstructure at the nanometric scale but also to calculate generalized susceptibilities such as elastic constants under irradiation. After a brief description of the rate theory, used to model the microstructure induced by irradiation, we briefly discuss the foundation of the phase field method, highlighting not only its advantages, but also its limitations in comparison with the rate theory. We conclude this presentation by proposing future orientations for computing the microstructure in irradiated materials.

Insight Into Disorder, Stress and Strain of Radiation Damaged Pyrochlores: A Possible Mechanism for the Appearance of Defect Fluorite.

We have examined the irradiation response of a titanate and zirconate pyrochlore-both of which are well studied in the literature individually-in an attempt to define the appearance of defect fluorite in zirconate pyrochlores. To our knowledge this study is unique in that it attempts to discover the mechanism of formation by a comparison of the different systems exposed to the same conditions and then examined via a range of techniques that cover a wide length scale. The conditions of approximately 1 displacement per atom via He2+ ions were used to simulate long term waste storage conditions as outlined by previous results from Ewing in a large enough sample volume to allow for neutron diffraction, as not attempted previously. The titanate sample, used as a baseline comparison since it readily becomes amorphous under these conditions behaved as expected. In contrast, the zirconate sample accumulates tensile stress in the absence of detectable strain. We propose this is analogous to the lanthanide zirconate pyrochlores examined by Simeone et al. where they reported the appearance of defect fluorite diffraction patterns due to a reduction in grain size. Radiation damage and stress results in the grains breaking into even smaller crystallites, thus creating even smaller coherent diffraction domains. An (ErNd)2(ZrTi)2O7 pyrochlore was synthesized to examine which mechanism might dominate, amorphization or stress/strain build up. Although strain was detected in the pristine sample via Synchrotron X-ray diffraction it was not of sufficient quality to perform a full analysis on.

Nano-Structured Materials under Irradiation: Oxide Dispersion-Strengthened Steels.

Oxide dispersion-strengthened materials are reinforced by a (Y, Ti, O) nano-oxide dispersion and thus can be considered as nanostructured materials. In this alloy, most of the nanoprecipitates are (Y, Ti, O) nano-oxides exhibiting a Y2Ti2O7 pyrochlore-like structure. However, the lattice structure of the smallest oxides is difficult to determine, but it is likely to be close to the atomic structure of the host matrix. Designed to serve in extreme environments-i.e., a nuclear power plant-the challenge for ODS steels is to preserve the nano-oxide dispersion under irradiation in order to maintain the excellent creep properties of the alloy in the reactor. Under irradiation, the nano-oxides exhibit different behaviour as a function of the temperature. At low temperature, the nano-oxides tend to dissolve owing to the frequent ballistic ejection of the solute atoms. At medium temperature, the thermal diffusion balances the ballistic dissolution, and the nano-oxides display an apparent stability. At high temperature, the nano-oxides start to coarsen, resulting in an increase in their size and a decrease in their number density. If the small nano-oxides coarsen through a radiation-enhanced Ostwald ripening mechanism, some large oxides disappear to the benefit of the small ones through a radiation-induced inverse Ostwald ripening. In conclusion, it is suggested that, under irradiation, the nano-oxide dispersion prevails over dislocations, grain boundaries and free surfaces to remove the point defects created by irradiation.

Phase Separation in Fluorite-Related U1-yCeyO2-x: A Re-Examination by X-ray and Neutron Diffraction.

The phase separation observed at low temperature (below circa 600 K) in the U1-yCeyO2-x system and for values of y between roughly 0.34 and 0.5 purportedly involves fluorite structures only. However, for y values above 0.5, an oxygen-deficient C-type bixbyite is also reported. In this work, the phase separation in U0.54Ce0.46O2-x has been reexamined using X-ray and neutron diffraction. Below a critical temperature, the existence of two fluorite related structures in the miscibility gap is confirmed: a stoichiometric U0.54Ce0.46O2 phase and an oxygen-deficient U0.54Ce0.46O2-x phase. Although the former is indeed a fluorite, we show that the other end-member phase has a C-type bixbyite structure. This would suggest that the oxygen-deficient phase can be described as a bixbyite over the entire cerium composition range.

Irradiation-based design of mechanically resistant microstructures tuned via multiscale phase-field modeling.

We present a multi-scale phase field modeling of stationary microstructures produced under 1 MeV krypton ion irradiation in a phase separating concentrated solid solution of silver and copper. We show that the mixture reaches ultimately a stationary micro-structural state made of phase domains with composition and size distribution mapped to the values of the incident flux of particles and of the temperature, variables that help defining a non equilibrium phase-diagram for the irradiated alloy. The modeling predicts the formation of diverse microstructures likely connected to spinodal hardening, thus opening the perspective of the on-purpose tuning of mechanically resistant microstructures and the preparation of metastable alloys with mechanical properties improved by comparison to counterparts obtained via classical thermo-mechanical treatments.

Characterization of Oxygen Defect Clusters in UO2+ x Using Neutron Scattering and PDF Analysis.

In hyper-stoichiometric uranium oxide, both neutron diffraction work and, more recently, theoretical analyses report the existence of clusters such as the 2:2:2 cluster, comprising two anion vacancies and two types of anion interstitials. However, little is known about whether there exists a region of low deviation-from-stoichiometry in which defects remain isolated, or indeed whether at high deviation-from-stoichiometry defect clusters prevail that contain more excess oxygen atoms than the di-interstitial cluster. In this study, we report pair distribution function (PDF) analyses of UO2 and UO2+ x ( x ≈ 0.007 and x ≈ 0.16) samples obtained from high-temperature in situ neutron scattering experiments. PDF refinement for the lower deviation from stoichiometry sample suggests the system is too dilute to differentiate between isolated defects and di-interstitial clusters. For the UO2.16 sample, several defect structures are tested, and it is found that the data are best represented assuming the presence of center-occupied cuboctahedra.

Improving atomic displacement and replacement calculations with physically realistic damage models.

Atomic collision processes are fundamental to numerous advanced materials technologies such as electron microscopy, semiconductor processing and nuclear power generation. Extensive experimental and computer simulation studies over the past several decades provide the physical basis for understanding the atomic-scale processes occurring during primary displacement events. The current international standard for quantifying this energetic particle damage, the Norgett-Robinson-Torrens displacements per atom (NRT-dpa) model, has nowadays several well-known limitations. In particular, the number of radiation defects produced in energetic cascades in metals is only ~1/3 the NRT-dpa prediction, while the number of atoms involved in atomic mixing is about a factor of 30 larger than the dpa value. Here we propose two new complementary displacement production estimators (athermal recombination corrected dpa, arc-dpa) and atomic mixing (replacements per atom, rpa) functions that extend the NRT-dpa by providing more physically realistic descriptions of primary defect creation in materials and may become additional standard measures for radiation damage quantification.

Understanding Local Structure versus Long-Range Structure: The Case of UO2.

A recent trend in the development of new optimized materials makes use of crystalline domains having nanometer sizes for which characterization methods at the atomic scale are mandatory. Amongst them is pair-distribution function analysis (PDF-analysis), a diffraction technique that has already shown that a short-range or "local" atomic structure of a given domain, having a lower symmetry than the average long-range structure, often exists in many compounds having valuable properties for industrial applications, such as pyrochlores, spinels, and doped ceria among others. However, the manner by which these domains are arranged to produce the average long-range structure is still an open question. Herein, the first structural model that accounts for both the local structure (inside a given domain) and the long-range structure (averaged over all domains) that is observed in the PDF of uranium dioxide is presented. The structural model describes domain walls in such a way as to preserve the uranium coordination polyhedron and to obey the needed symmetry rules. The proper description of domain walls is an important step in the understanding and the modelling of nanostructured materials.

Intricate disorder in defect fluorite/pyrochlore: a concord of chemistry and crystallography.

Intuitively scientists accept that order can emerge from disorder and a significant amount of effort has been devoted over many years to demonstrate this. In metallic alloys and oxides, disorder at the atomic scale is the result of occupation at equivalent atomic positions by different atoms which leads to the material exhibiting a fully random or modulated scattering pattern. This arrangement has a substantial influence on the material's properties, for example ionic conductivity. However it is generally accepted that oxides, such as defect fluorite as used for nuclear waste immobilization matrices and fuel cells, are the result of disorder at the atomic scale. To investigate how order at the atomic scale induces disorder at a larger scale length, we have applied different techniques to study the atomic composition of a homogeneous La 2 Zr 2 O 7 pyrochlore, a textbook example of such a structure. Here we demonstrate that a pyrochlore, which is considered to be defect fluorite, is the result of intricate disorder due to a random distribution of fully ordered nano-domains. Our investigation provides new insight into the order disorder transformations in complex materials with regards to domain formation, resulting in a concord of chemistry with crystallography illustrating that order can induce disorder.

Near transferable phenomenological n-body potentials for noble metals.

We present a semi-empirical model of cohesion in noble metals with suitable parameters reproducing a selected set of experimental properties of perfect and defective lattices in noble metals. It consists of two short-range, n-body terms accounting respectively for attractive and repulsive interactions, the former deriving from the second moment approximation of the tight-binding scheme and the latter from the gas approximation of the kinetic energy of electrons. The stability of the face centred cubic versus the hexagonal compact stacking is obtained via a long-range, pairwise function of customary use with ionic pseudo-potentials. Lattice dynamics, molecular statics, molecular dynamics and nudged elastic band calculations show that, unlike previous potentials, this cohesion model reproduces and predicts quite accurately thermodynamic properties in noble metals. In particular, computed surface energies, largely underestimated by existing empirical cohesion models, compare favourably with measured values, whereas predicted unstable stacking-fault energy profiles fit almost perfectly ab initio evaluations from the literature. All together the results suggest that this semi-empirical model is nearly transferable.

Disrupted coarsening in complex Cahn-Hilliard dynamics.

Predicting the pattern formation in a system maintained far from equilibrium is a complex task. For a given dynamics governed by the evolution of a conservative order parameter, recent investigations have demonstrated that the knowledge of the long time expression of the order parameter is sufficient to predict the existence of disrupted coarsening, i.e., the pinning of the inhomogeneities wavelength to a well defined value. However, there exists some dynamics for which the asymptotic form of the order parameter remains unknown. The Cahn-Hilliard-like equation used to describe the stability of solids under irradiation belongs to this class of equations. In this paper, we present an alternative to predict the patterning induced by this equation. Based on a simple ansatz, we calculated the form factor and proved that a disrupted coarsening takes place in such dynamics. This disrupted coarsening results from the bifurcation of the implicit equation linking the characteristic length of the dynamics (k_{m}^{∞})^{-1} to a control parameter describing the irradiation. This analysis is supported by direct simulations. From this paper, it clearly appears that the bifurcation of k_{m}^{∞} is a criterion for disrupted coarsening.