Regularization inverse method for variable binary diffusivity measurements

Alonso V. Jaques, Jeffrey C. LaCombe

Research output: Contribution to journalArticle

2 Citations (Scopus)


Boltzmann-Matano (and related) inverse methods are used extensively in the determination of interdiffusivities in alloys. In the course of analyzing experimental data to determine concentration dependent diffusivities, numerical integrations and differentiations of the concentration profile are performed. With experimental data that contains point-to-point scatter, challenges such as calculating the local slope result. Smoothing of the experimental data is often performed prior to analysis using a variety of approaches. This can introduce artifacts into the data and affects the confidence in the estimated interdiffusivities. We present here, a new approach to the so-called Boltzmann-Matano-type inverse method for calculating concentration-dependent interdiffusion coefficients in binary alloys. This method starts with a regularization formulation from the calculus of variations to estimate a smoothed form of the noisy concentration data. This is then integrated into the inverse estimation process through an optimization routine. This process minimizes or eliminates the necessity of arbitrary filtering or smoothing parameters, and does not require foreknowledge of the functional form of D(C). The regularization inverse method presented is less subjective, is self-consistent (i.e., regularized concentration profiles are consistent with the diffusion equation), and results in increased accuracy in the estimated diffusion coefficients in comparison with existing inverse methods. © ASM International.
Original languageEnglish
Pages (from-to)195-202
Number of pages8
JournalJournal of Phase Equilibria and Diffusion
Publication statusPublished - 1 Jun 2012

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