Anter El-Azab

Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals

We present a continuum dislocation dynamics model that predicts the formation of dislocation cell structure in single crystals at low strains. The model features a set of kinetic equations of the curl type that govern the space and time evolution of the dislocation density in the crystal. These kinetic equations are coupled to stress equilibrium and deformation kinematics using the eigenstrain approach. A custom finite element method has been developed to solve the coupled system of equations of dislocation kinetics and crystal mechanics. The results show that, in general, dislocations self-organize in patterns under their mutual interactions. However, the famous dislocation cell structure has been found to form only when cross slip is implemented in the model. Cross slip is also found to lower the yield point, increase the hardening rate, and sustain an increase in the dislocation density over the hardening regime. Analysis of the cell structure evolution reveals that the average cell size decreases with the applied stress, which is consistent with the similitude principle.

Phase field modeling of the effect of porosity on grain growth kinetics in polycrystalline ceramics

We present a phase field model for investigating grain growth in polycrystalline ceramics containing porosity. Grain growth in such materials is complicated by the interaction between the pores and the grain boundaries, which tends to hinder the kinetics of grain growth. In addition to grain-boundary migration, the model takes into consideration pore-surface diffusion and, whenever effective, other diffusion mechanisms such as volume diffusion and grain-boundary diffusion. The pore-surface diffusion controls the pore mobility. A direct relationship between the model parameters and the material properties is established, which facilitates the quantitative analysis of grain growth. The model is used to investigate the conditions under which porosity is effective in controlling grain growth. Application of the model to ceria shows that grain growth law in this material is sensitive to the level of porosity. In particular, the grain growth in ceria gradually changes from boundary controlled growth to pore controlled growth as porosity increases. The effects of porosity, temperature, grain boundary and surface mobility on grain growth were investigated. The model results agree well with published grain growth experiments.

Migration mechanisms of oxygen interstitial clusters in UO2

Understanding the migration kinetics of radiation-induced point defects and defect clusters is key to predicting the microstructural evolution and mass transport in nuclear fuels. Although the diffusion kinetics of point defects in UO(2) is well explored both experimentally and theoretically, the kinetics of defect clusters is not well understood. In this work the migration mechanisms of oxygen interstitial clusters of size one to five atoms (1O(i)-5O(i)) in UO(2) are investigated by temperature-accelerated dynamics simulations without any a priori assumptions of migration mechanisms. It is found that the migration paths of oxygen interstitial clusters are complex and non-intuitive, and that multiple migration paths and barriers exist for some clusters. It is also found that the cluster migration barrier does not increase with increasing cluster size and its magnitude has the following order: 2O(i) < 3O(i) < 1O(i) < 5O(i) < 4O(i). Possible finite-size effects are checked with three systems which are of different sizes. The results show good agreement with other available experimental and theoretical data. The cluster migration sequence might explain the interesting relationship measured experimentally between the oxygen diffusivity and stoichiometry in UO(2+x).

Phase field modeling for grain growth in porous solids

Concurrent evolution of grain size and porosity in solids is a technically important problem involving curvature-driven motion of grain boundaries and the pore motion by surface diffusion. A phase field approach comprising a system of Cahn–Hilliard and Allen–Cahn equations has been developed recently to tackle this problem. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. As a case study, the model was used to investigate the effect of porosity on the kinetics of grain growth in CeO2 in 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four-grain junctions were found to move along with the migrating boundary, while edge pores (on the boundary between two grains) were found to easily separate from the boundary. The simulations showed that pore breakaway leads to abnormal grain growth. The simulations also showed that grain growth kinetics in CeO2 changes from boundary controlled to pore controlled as the amount of porosity increases. The kinetic growth parameters such as the growth exponent and the rate constant (or equivalently the activation energy) were found to depend strongly on the precise amount and distribution of porosity, which reconciles the different experimental results reported for grain growth in CeO2.

A sharp interface model for void growth in irradiated materials

A thermodynamic formalism for the interaction of point defects with free surfaces in single-component solids has been developed and applied to the problem of void growth by absorption of point defects in irradiated metals. This formalism consists of two parts, a detailed description of the dynamics of defects within the non-equilibrium thermodynamic frame, and the application of the second law of thermodynamics to provide closure relations for all kinetic equations. Enforcing the principle of non-negative entropy production showed that the description of the problem of void evolution under irradiation must include a relationship between the normal fluxes of defects into the void surface and the driving thermodynamic forces for the void surface motion; these thermodynamic forces are identified for both vacancies and interstitials and the relationships between these forces and the normal point defect fluxes are established using the concepts of transition state theory. The latter theory implies that the defect accommodation into the surface is a thermally activated process. Numerical examples are given to illustrate void growth dynamics in this new formalism and to investigate the effect of the surface energy barriers on void growth. Consequences for phase field models of void growth are discussed.

The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip

A recent continuum dislocation dynamics formalism (Xia and El-Azab 2015 Model. Simul. Mater. Sci. Eng. 23 055009) has been enriched by incorporating an improved cross slip model. 3D discrete dislocation dynamics simulations were used to collect cross slip rate data in the form of time series that were analysed to estimate the correlation time for cross slip, which was subsequently used as a time scale for local window averaging of the collected cross slip rate data. This time averaging filters out the cross slip rate fluctuations over time intervals less than the correlation time, thus resulting in relatively smoother time series for the cross slip rates. The coarse grained series were further cast in the form of smooth trends with superposed fluctuations and implemented in continuum dislocation dynamics simulations using a Monte Carlo scheme. This approach resulted in a significant improvement of the predicted stress–strain response and a more realistic dislocation cell structure evolution. The similitude law for the average cell size evolution with inverse of stress, however, remains unaffected by the cross slip rates used in continuum dislocation dynamics.

Oxygen transport in off-stoichiometric uranium dioxide mediated by defect clustering dynamics

Oxygen transport is central to many properties of oxides such as stoichiometric changes, phase transformation, and ionic conductivity. In this paper, we report a mechanism for oxygen transport in uranium dioxide (UO2) in which the kinetics is mediated by defect clustering dynamics. In particular, the kinetic Monte Carlo method has been used to investigate the kinetics of oxygen transport in UO2 under the condition of creation and annihilation of oxygen vacancies and interstitials as well as oxygen interstitial clustering, with variable off-stoichiometry and temperature conditions. It is found that in hypo-stoichiometric UO(2-x), oxygen transport is well described by the vacancy diffusion mechanism while in hyper-stoichiometric UO(2+x), oxygen interstitial cluster diffusion contributes significantly to oxygen transport kinetics, particularly at high temperatures and high off-stoichiometry levels. It is also found that di-interstitial clusters and single interstitials play dominant roles in oxygen diffusion while other larger clusters have negligible contributions. However, the formation, coalescence, and dissociation of these larger clusters indirectly affects the overall oxygen diffusion due to their interactions with mono and di-interstitials, thus providing an explanation of the experimental observation of saturation or even drop of oxygen diffusivity at high off-stoichiometry.

Irradiation-induced composition patterns in binary solid solutions

A theoretical/computational model for the irradiation-driven compositional instabilities in binary solid solutions has been developed. The model is suitable for investigating the behavior of structural alloys and metallic nuclear fuels in a reactor environment as well as the response of alloy thin films to ion beam irradiation. The model is based on a set of reaction-diffusion equations for the dynamics of vacancies, interstitials, and lattice atoms under irradiation. The dynamics of these species includes the stochastic generation of defects by collision cascades as well as the defect reactions and diffusion. The atomic fluxes in this model are derived based on the transitions of lattice defects. The set of reaction-diffusion equations are stiff, hence a stiffly stable method, also known as the Gear method, has been used to numerically approximate the equations. For the Cu-Au alloy in the solid solution regime, the model results demonstrate the formation of compositional patterns under high-temperature particle irradiation, with Fourier space properties (Fourier spectrum, average wavelength, and wavevector) depending on the cascade damage characteristics, average composition, and irradiation temperature.

Fission Products in Nuclear Fuel: Comparison of Simulated Distribution with Correlative Characterization Techniques

During the fission process in a nuclear reactor, uranium dioxide (UO2) fuel material is irradiated, forming fission products (FPs). The addition of FPs alters the path phonons travel in UO2, detrimentally altering the thermal conductivity of the fuel. [1] To improve fuel performance, a fundamental understanding of the role of insoluble FPs, such as Xenon (Xe), during microstructural evolution is critical. Correlative characterization techniques where atom probe tomography (APT) is paired with transmission electron microscopy (TEM) can provide unique insights into the segregation behavior of FPs. Coupling these techniques with computer simulations of fission product distribution provide deeper understanding of FP migration during service. Although there are limitations with each of these techniques in isolation, significant insight into material behavior can be gained with the concurrent and synergistic pairing of multiple experimental and computational techniques.

Why Materials Theory

© L p i Materials science is an interdisciplinary field with the broad objectives of understanding the structure and properties of materials and the discovery of new materials. In his historical account of this field titled The Coming of Materials Science (Cahn et al. 2003), R. W. Cahn referred to the middle of the past century as the time materials science was born out of metallurgy. Materials science has expanded since then to cover the science of ceramics, polymers, semiconductors, and numerous functional materials. Since the inception of materials science, experiment has been a central theme underlying investigation of the structure and properties of materials while modelling was aimed initially at the interpretation of experimental results. However, with the need to understand increasingly complex materials structures and the connection of materials structure with materials behaviour, advanced theoretical concepts from the fields of physics, chemistry, mechanics, applied mathematics, and statistics were introduced. Thus, the development of rigorous models for materials structure, materials defects, microstructure evolution, and the behaviour of materials became a second thrust of materials science. Over the past three decades, the theory of materials has worked hand in hand with experiments to interpret results and to explore materials behaviour under conditions that at present cannot be probed directly by experiments. Concurrently, materials research began to exploit the rapidly increasing power of computers to solve theoretical models and to generate structural and property related data through simulations. This in turn enabled materials discovery for applications, including batteries (Liu et al. 2015) and structural materials (Schmitz et al. 2011). The availability of advanced simulation tools capable of predicting the structure and behaviour of materials over varying length and time scales and the possibility of integrating such tools into materials design marked the coming of integrated computational materials engineering (ICME) (Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security et al. 2008), an approach integrating simulation tools at all relevant scales for the concurrent design of materials, processes, and products. Furthermore, the quest for accelerated materials discovery has ushered in the era of the materials genome (MG), where experiments, computational tools, and big data (Materials Genome Initiative Strategic et al. 2014) are combined to accelerate materials discovery. Advances in computing, data acquisition, and the discovery and design of materials have also led to the application of the principles of informatics to materials (Rajan 2005), whereby information based on the structure and property of materials and their connections are surveyed to enable MGand ICME-type efforts. At this point in time, it is fair to state that materials research is driven by materials discovery and engineering. In this regard, understanding the structure of materials and