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Nanocrystalline (NC) materials are intrinsically unstable against grain growth. Significant research efforts have been dedicated to suppressing the grain growth by solute segregation, including the pursuit of a special NC structure that minimizes the total free energy and completely eliminates the driving force for grain growth. This fully stabilized state has been predicted theoretically and by simulations but is yet to be confirmed experimentally. To better understand the nature of the full stabilization, we propose a simple two-dimensional model capturing the coupled processes of grain boundary (GB) migration and solute diffusion. Kinetic Monte Carlo simulations based on this model reproduce the fully stabilized polycrystalline state and link it to the condition of zero GB free energy. The simulations demonstrate the emergence of a fully stabilized state by the divergence of capillary wave amplitudes on planar GBs and by fragmentation of a large grain into a stable ensemble of smaller grains. The role of solute diffusion in the full stabilization is examined. Possible extensions of the model are discussed.
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This content will become publicly available on February 1, 2026
Theoretical Model and Experimental Application for Solute Diffusion in Leaching Test With Time-Dependent Boundary Conditions
Abstract Measuring the diffusion coefficient of clay-based liner materials is important in estimating and predicting long-term barrier performance in waste containment facilities. Various theoretical models, including the finite cylindrical model, have been commonly used to determine the diffusion properties of clay-based liner materials in leaching tests. However, the assumption of zero-concentration boundary conditions of the traditional finite cylindrical model contradicts the measured variation of concentration in real leaching tests, likely resulting in (1) underestimated and unconservative diffusion coefficient, or (2) requirement of a relatively large liquid-to-soil ratio and frequent leachate replacement in the experiment to maintain the zero-concentration boundary condition. In this study, a theoretical model was developed to evaluate the solute diffusion process within a soil specimen under arbitrary, time-dependent concentration boundary conditions. The proposed model, incorporating the time-dependent boundary conditions, provides efficient calculations of the concentration distribution and the cumulative fraction leached of solute across the soil specimen. The example application of the proposed model to experimental data demonstrates the capability of the proposed model to determine apparent diffusion coefficients of clay-based liner materials without introducing errors associated with the assumption of a zero concentration boundary condition. The proposed model provides a comprehensive method to investigate the dynamic transport behaviors of solutes through clay-based liner materials in future studies.
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- Award ID(s):
- 2143145
- PAR ID:
- 10608897
- Publisher / Repository:
- ASME
- Date Published:
- Journal Name:
- ASME Journal of Heat and Mass Transfer
- Volume:
- 147
- Issue:
- 2
- ISSN:
- 2832-8450
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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