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Multiscale Defect Formation and Transport in Materials in Extreme Environments


The lifetime and properties of materials operating under extreme conditions are determined by complex interactions stemming from the formation of internal defects at the atomic length and time scales. The research conducted in this dissertation is focused on the study of atomic defect formation and transport under such conditions, and the development of atomically-based tools with enhanced resolution and predictive capabilities. Our attention is placed on two such far-from-equilibrium conditions with important real world implications: materials irradiated in nuclear environments and materials deforming under shock loading.

In the former, prolonged exposure to irradiation by energetic neutrons or ions, resulting in atomic collision cascades, leads to the formation, transport and aggregation of vacancies and self-interstitial atoms (SIAs) into clusters. This leads to an evolution of the microstructure and thus also the material properties, making the problem truly multiscale in both time and space. In addition, energy barriers for the thermally activated processes that govern this evolution are inhomogeneous, varying spatially due to non-uniform internal stress and temperature fields. Because of these complexities, and the many scales involved, typical efforts to model such phenomena face severe coarse-graining, often neglecting spatial heterogeneities altogether and using mean-field approaches.

In this dissertation, we develop computational models of point defect formation and transport in spatially heterogeneous stress and temperature fields. To accomplish this, first an atomistically-based description of point defects is developed using a combination of molecular statics calculations and continuum elasticity theory. This enables an accurate representation of point defect strain fields and their interaction energies in various strain fields. The continuum representation has been found to be accurate to within several percent of the atomistic calculations and was successfully tested against highly accurate first principles calculations in a published study.

Using the described point defect representation, we have performed calculations of the dislocation bias factor for irradiated metals, using a spatially-resolved rate theory solution we developed based on the finite element method. The flexibility of the model is fully exploited, leading to calculations with heightened resolution; accounting for the spatially-dependent, energetically favorable SIA orientations, one-dimensional diffusion mechanisms near the dislocation core, and full anisotropic elasticity. Our results for iron have shown that the effects of preferred SIA orientations should not be ignored near the dislocation core. Implementing minimum energy SIA configurations in iron decreases repulsive interactions and increases absorption, ultimately leading to much larger bias factors. On the other hand, we also find the use of anisotropic elasticity in the calculations to decrease bias factors by 45\% compared to those obtained using the isotropic formulation. An anisotropic implementation of the dislocation strain fields, however, gives larger interaction energy gradients, leading to increased drift diffusion and larger bias (12\% and 6\% increase in Fe and Cu, respectively). One-dimensional migration also plays a significant role in decreasing the bias, but its effect is greatly diminished when anisotropy and SIA orientations are accounted for.

Following the rapid transient stage of helium-vacancy cluster (bubble) nucleation under irradiation, the bubble growth phase proceeds over macroscopic timescales. Due to the complex nature of the problem, prediction of the time-dependent bubble size distribution in the helium-vacancy phase space has remained elusive. In this dissertation we approach the problem in two ways, both accounting for full material spatial resolution. In the first, we use a previously developed reduced set of rate equations to track the average bubble size through time, in a two-dimensional specimen under the typical stress and temperature gradients seen in plasma-facing components in fusion environments. With temperature gradients long known to have several orders of magnitude greater effect on bubble diffusion than associated stress gradients, our results conclusively revealed the important role of stress gradients on the near-surface average bubble size profile due to point defect diffusion processes.

Extending this spatially-dependent rate theory approach to capture the full bubble size distribution surface, we have developed a novel approach based on the theory of nonlinear stochastic differential equations. Here, we provide a framework to describe the full helium bubble size distribution as a function of time and space, in irradiated metals under stress and temperature gradients. Our findings show the important role of stochastic atomic fluctuations on the dispersion of the distribution around the mean. We find for smaller average bubbles sizes (early in the simulation), the spread of the distribution is large and stable. As bubbles begin to grow larger, the stochastic fluctuations have a reduced effect and the distribution begins to shrink, corresponding to a more uniformly sized bubble population. Recommendations are also made regarding how to advance the simulations in the future by including phenomena such as bubble coalescence.

To characterize the response of metals to shock loading, extensive molecular dynamics (MD) simulations have been performed. In light of recent experimental results obtained by laser-induced shock-loading on single-crystal nanopillars, MD simulations were performed on both nanofilm and nanopillar structures, the difference being the geometry and imposed boundary conditions in the directions transverse to the propagation direction of the shock wave. The dynamic response of the structures to shock loading was analyzed over a wide spectrum of impact stresses. State variables (stress, velocity, temperature, etc.) were computed as functions of time and position along the specimen. The deformation mechanisms observed in nanopillars was found to differ significantly from those found in the nanofilms and bulk samples. Specifically, in nanofilms, we found the presence of periodic boundary conditions require much larger impact stresses to induce plasticity ($> 35$ GPa) compared to nanopillars, where free surfaces play an important role. In nanopillars, comparison to the experiments explained the observed surface activation at lower than expected stresses ($\sim 1$ GPa), due to dislocation nucleation and termination at the free surfaces. Additional simulations of spallation were also performed. Results showed the formation of voids occurrs at the intersections of stacking faults at the spall plane. The growth and coalescence of these voids leads to the full spallation of the material. In these cases the [100] oriented crystals showed increased resilience to spallation compared to the [111] crystals. The results of this work have contributed to a greater understanding of the deformation mechanisms at work in metal nanostructures exposed to ultra-high strain rate loading conditions.

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