Abstract
Composition-dependent interdiffusion coefficients are key parameters in many physical processes. However, finding such coefficients for a system with few components is challenging due to the underdetermination of the governing diffusion equations, the lack of data in practice, and the unknown parametric form of the interdiffusion coefficients. In this work, we propose InfPolyn, Infinite Polynomial, a novel statistical framework to characterize the component-dependent interdiffusion coefficients. Our model is a generalization of the commonly used polynomial fitting method with extended model capacity and flexibility and it is combined with the numerical inversion-based Boltzmann–Matano method for the interdiffusion coefficient estimations. We assess InfPolyn on ternary and quaternary systems with predefined polynomial, exponential, and sinusoidal interdiffusion coefficients. The experiments show that InfPolyn outperforms the competitors, the SOTA numerical inversion-based Boltzmann–Matano methods, with a large margin in terms of relative error (10× more accurate). Its performance is also consistent and stable, whereas the number of samples required remains small.
Highlights
In many industrial processes that involve diffusion, e.g., alloy solidification, heat treatment, coating and electric packaging, the characterization of composition-dependent interdiffusion coefficients is a crucial task, as it quantifies a diffusion process clearly.The classic approach is based on Boltzmann-Matano analysis [1,2] which transforms the diffusion system into a linear system of equations
In most of the experiments, our model shows an excellent performance with only 40 electron probe micro-analysis (EPMA) measurements, which is very desirable in practical interdiffusion coefficient estimations
Where for each coefficient in the polynomial aijt,r, the superscript r represents the degree of polynomial and the value of them are generated independently from uniform distributions
Summary
In many industrial processes that involve diffusion, e.g., alloy solidification, heat treatment, coating and electric packaging, the characterization of composition-dependent interdiffusion coefficients is a crucial task, as it quantifies a diffusion process clearly.The classic approach is based on Boltzmann-Matano analysis [1,2] which transforms the diffusion system into a linear system of equations. A pseudobinary approach is introduced by considering only two components diffused into the diffusion zone This method takes advantage of its time independence in the first-order linear equations and is very efficient when the pseudobinary condition is strictly satisfied in experiments. Zhang and Zhao [10] suggested a forward-simulation approach by iteratively optimizing the interdiffusion coefficients with repeated forwardsimulations, similar to the classic inference approach for inverse problems. Such a method is shown to be accurate and stable, it incurs an overwhelming computational cost because each iteration requires a complete diffusion simulation with a fine spatialtemporal grid
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