Modeling of silver transport in cubic SiC: Integrating molecular dynamics, bounds averaging, and uncertainty quantification

TL;DR

This work develops a physics-informed, microstructure-aware model for silver transport in polycrystalline 3C-SiC by integrating MD-derived diffusivities for Σ3 and Σ9 grain boundaries with literature data for other GB types, using a bounds-averaging approach to obtain $D_{ ext{eff}}(T)$. A Bayesian calibration against experimental diffusion data yields credible intervals for the effective Arrhenius parameters and reveals a positive correlation between $\ln D_{0, ext{eff}}$ and $Q_{ ext{eff}}$. To reconcile model predictions with experiments, the authors introduce a trap-based multiplicative correction $D'_{ ext{eff}}$, derived from first principles and incorporating desorption energy $Q_t$, resulting in $D'_{ ext{eff}}(T) = \alpha D_{ ext{eff}}$ with $Q_{ ext{eff}} + Q_t$ governing the temperature dependence. Sensitivity analysis identifies the trap desorption energy $Q_t$ and the diffusivity of Σ9/Σ27 GBs as the dominant factors shaping Ag transport, underscoring the importance of microstructure and nano-porosity in predictive simulations. The framework enables seamless embedding into higher-scale fuel-performance models (e.g., BISON) to improve predictions of Ag release in TRISO fuels.

Abstract

Silver released from TRISO fuel particles can migrate through the SiC layer and deposit on reactor components, posing radiation hazards and operational challenges. Despite numerous proposed mechanisms, the precise pathway of silver transport through intact 3C-SiC remains unresolved. We present a physics-informed model for estimating the effective diffusivity of silver in polycrystalline 3C-SiC. Molecular dynamics (MD) simulations yield diffusivities for {Σ3} and {Σ9} grain boundaries (GBs), while literature values are used for other GB types and the bulk. These are combined using a bounds-averaging approach accounting for distinct GB transport properties. Bayesian inference of experimental data provides credible intervals for effective Arrhenius parameters and reveals a correlation between activation energy and pre-exponential factor. Although the homogenized model captures GB-mediated transport mechanisms, it overpredicts silver diffusivity relative to experiments. To resolve this, a multiplicative correction based on reversible trapping at nano-pores is introduced. It is derived from first principles and is shown to reproduce observed transport behavior. Sensitivity analysis identified trap desorption energy and {Σ9} GB diffusivity as dominant factors influencing Ag transport. The resulting framework provides a mechanistic description of Ag transport suitable for integration into higher-scale fuel performance models.

Figures (9)

• Figure 1: (Color online) Relative effective diffusivity computed using our averaging method (Method 1) and the percolation-based method by Chen and Schuh Chen2007 (Method 2), as a function of the GB-to-bulk diffusivity ratio $D_\text{GB}/D_b$.
• Figure 2: (Color online) (a) Construction of the $\Sigma 3 \{ 112 \}$ GB via the superposition of two symmetric crystals along the $\{112\}$ plane, which results in the energetically unfavorable $p2'mm' (1 \times 1)$ model. (b) Type A of the $p2'mm' (1 \times 2)$ symmetric reconstruction model of the $\Sigma 3 \{ 112 \}$ GB. C atoms are gray and Si atoms are light brown.
• Figure 3: (Color online) (a) Polar variant of the $\Sigma 9$ GB that contains C-C wrong bonds, i.e., Type A. (b) Polar variant of the $\Sigma 9$ GB that contains Si-Si wrong bonds, i.e., Type B. (c) Non-polar variant of the $\Sigma 9$ GB that contains both types of wrong bonds, i.e., Type C. C atoms are gray and Si atoms are light brown.
• Figure 4: (Color online) (a) MSD versus time plot for C-rich $\Sigma 9$ GB at 1400 K with 5--10 Ag atoms. (b) MSD versus time plot for Si-rich $\Sigma 9$ GB at 1500 K with 0.1 at.% Ag atoms. All Ag atoms have been inserted randomly in the GB width.
• Figure 5: Arrhenius plots of Ag diffusion in $\Sigma 3$ GBs ($D_0 = 3.69 \times 10^{-9}$ m$^2$/s, $Q$ = 1.02 eV), C-rich $\Sigma 9$ GBs ($D_0 = 4.50 \times 10^{-8}$ m$^2$/s, $Q$ = 0.88 eV), Si-rich $\Sigma 9$ GBs ($D_0 = 5.51 \times 10^{-9}$ m$^2$/s, $Q$ = 0.46 eV), and non-polar $\Sigma 9$ GBs ($D_0 = 1.24 \times 10^{-9}$ m$^2$/s, $Q$ = 0.33 eV). All supercells contain 0.1 at.% Ag, which corresponds to 105 Ag atoms out of 105,705 total atoms in the $\Sigma 3$ supercells and 194 Ag atoms out of 194,594 total atoms in the $\Sigma 9$ supercells. $\Sigma 3$ diffusivity is fitted at 2000--2800 K, whereas $\Sigma 9$ diffusivity is fitted at 1000--2000 K. Linear fits yield effective activation energies and pre-exponential factors. Data points represent diffusivities averaged across five independent simulations. Error bars represent standard error.