Machine learning method to determine concentrations of structural defects in irradiated materials

TL;DR

This work tackles the challenge of predicting irradiation-induced defect concentrations across wide ranges of temperature, pressure, and irradiation rate. It introduces a data-driven surrogate that trains neural networks on cluster dynamics data (Centipede) to predict steady-state defect concentrations for uranium nitride, with networks dedicated to each defect type. The approach achieves roughly 7.4% average accuracy across defect types and offers about a 10^4-fold speedup over direct cluster-dynamics simulations, enabling efficient integration into multiscale models and rapid diffusivity predictions. The method is broadly applicable to other irradiated materials and can be extended to include extended defects, improving design-space exploration for nuclear materials.

Abstract

The formation and subsequent growth of structural defects in an irradiated material can strongly influence the material's performance in technological and industrial applications. Predicting how the growth of defects affects material performance is therefore a pressing problem in materials science. One common computational approach that is used to examine defect growth is cluster dynamics, a method which employs a system of mean-field rate equations to track the time evolution of concentrations of individual defect types. However, the computational complexity of performing cluster dynamics can limit its practical implementation, specifically in the context of exploring a broad set of physical conditions corresponding to, for example, different temperatures and pressures. Here, we present a machine learning approach to circumvent the computational challenges of performing cluster dynamics while maintaining high accuracy in the prediction of defect concentrations. The method is illustrated on the nuclear material uranium nitride but is broadly applicable to other materials. The developed data-driven method is shown to accurately capture complex correlations between material properties, temperature, irradiation conditions, and the concentration of defects.

Figures (10)

• Figure 1: Schematic diagram of the data-driven methodology developed in this work. The defect concentrations obtained from cluster dynamics simulations are used to train a collection of neural networks, one for each of the $N$ defect types tracked in the model. After training, each network can be used to predict the corresponding defect concentration $c$ over a broad range of state points corresponding to different physical conditions. The collection of predicted concentrations can then be used to predict macroscopic properties $\mathcal{P}$ of the material such as atomistic diffusion values and volumetric swelling rates.
• Figure 2: Phase diagram of UN. The white markers are representative state points used in the training data.
• Figure 3: Schematic of the general form of the feed-forward neural network architecture used in this work. The inputs are temperature, partial pressure of N$_2$, and fission rate and the output is the concentration of an individual defect. Each of the $l$ hidden layers consists of $n$ nodes.
• Figure 4: Concentrations of (a) a single nitrogen interstitial N$_\text{i}$, (b) a cluster of a U vacancy and a N vacancy {V$_\text{U}$:V$_\text{N}$}, and (c) a cluster of a Xe-based double N vacancy {Xe:2V$_\text{N}$}. These values were calculated from Centipede across varying temperatures, N$_2$ pressures, and fission rates. Temperature is shown on the $x$-axis, partial pressure of N$_2$ is shown with color, blue being the lowest and yellow being the highest pressure. The data shown in each plot is a combination of data from the training, testing, and validation sets.
• Figure 5: True vs. predicted plots of (a) the best performing neural network corresponding to an N interstital, (b) the median performing neural network corresponding to a cluster of a single U and N vacancy, and (c) the worst performing neural network corresponding to a Xe-based double N vacancy. The color of each marker represents the temperature with scale shown in the color bar on the right. The data shown in each plot is from the testing set.