Modeling silicon and aluminum diffusion in electrical steel
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Modeling Silicon and Aluminum Diffusion in Electrical Steel Jose Barros, Benny Malengier, Roger Van Keer, and Yvan Houbaert
(Submitted July 12, 2005) High silicon (Si) and aluminum (Al) electrical steel with improved magnetic properties can be produced by hot dipping in a molten Al-25 wt.% Si bath followed by diffusion annealing. The hot dipping deposits a Si-rich layer on top of the substrate, which is subsequently diffused into the bulk at high temperatures. The final properties of the material depend on the resulting concentration profiles, therefore a model capable of simulating the Si and Al diffusion is required. The first steps toward such a model are presented. The lack of knowledge of the ternary interdiffusion coefficients for the Al-Si-Fe system is overcome by reducing the coupled system of diffusion equations to a single partial differential equation (PDE), utilizing the diffusion path. Then by using a Levenberg-Marquardt inverse method, the apparent diffusion along this path can be determined. The direct problem was solved by a second-order space discretization, reducing the diffusion equation to a nonlinear system of ordinary differential equations (ODEs), which consequently can be solved with standard procedures for ODE.
1. Introduction
The aim of this study is to show the first steps toward such a model.
Electrical steel is an excellent soft magnetic material used for the construction of electrical motors and transformers. Its composition is basically high-purity Fe-Si or Fe-SiAl alloys; normally the alloying content never exceeds 3 wt.%. Beyond this concentration the material becomes very brittle because of the concurrence of the ordering phenomena D03 and B2, and it is not possible to perform cold rolling.[1] However, the magnetic properties, namely power losses and magnetostriction, are optimized when the alloying content reaches 6.5 wt.%. These higher-silicon content alloys can only be manufactured if an additional final step is introduced in the production route of electrical steel: enrichment by surface deposition of Si and Al and their diffusion into the bulk material. Recent research has shown that the magnetic and mechanical properties of the high-Si electrical steel produced by diffusion depend strongly on the shape of the diffusion profile obtained after the annealing.[2] The different applications of the electrical steel require different magnetic and mechanical properties, hence a diffusion model capable of predicting the diffusion profiles depending on the different conditions of the production process (e.g., annealing temperature, time, Si and Al content of the substrates, microstructure before the diffusion annealing) is necessary. This article is a revised version of the paper printed in the Proceedings of the First International Conference on Diffusion in Solids and Liquids - DSL-2005, Aveiro, Portugal, July 6-8, 2005, Andreas Öchsner, José Grácio and Frédéric Barlat, eds., University of Aveiro, 2005. Jose Barros and Yvan Houbaert, Department of Metallurgy and Materials Science,
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