Host Atom Diffusion in Ternary Fe-Cr-Al Alloys
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he technological importance of iron-rich ferritic alloys of the ternary Fe-Cr-Al system, there are no solid data available on host atom mobilities in these materials. Earlier investigations concentrated on interdiffusion experiments and their evaluation via Boltzmann–Matano (BM)-based methods. Although some of them were very comprehensive, even the most relevant ones suffer from limitations such as measurements at one temperature only[1,2] or in a narrow temperature interval only,[3,4] or the use of industrial Fe-Cr-Al-based materials.[3,4,5] None of them directly compares interdiffusion coefficients and (isotope) tracer diffusivities obtained on the same material. Most of these limitations are also given for the work on other Fe-based ternary systems like Cu-Ni-Fe[6,7] or Fe-Ni-Cr.[8] As to the theoretical approaches used in these earlier publications, BM-based data evaluation procedures were used to supply the phenomenological diffusivity matrix which was then used either to compare classical models (e.g., Onsager vs Darken[7]) or to investigate correlation phenomena,[9] i.e., atomistic jump mechanisms. While most of the authors are rather optimistic on the physical DIANA ROHRBERG, Researcher, KARL-HEINZ SPITZER, GU¨NTER BORCHARDT, and RAINER SCHMID-FETZER, Professors, LARS DO¨RRER and MICHAEL H. G. JACOBS, Senior Researchers, and ANNA J. KULIN´SKA, Postgraduate Student, are with the Institut fu¨r Metallurgie, TU Clausthal, 38678 ClausthalZellerfeld, Germany. Contact e-mail: [email protected] ANNA FRACZKIEWICZ, Professor, is with the E´cole Nationale Supe´rieure des Mines de Saint-E´tienne, 158, cours Fauriel, 42023 Saint-E´tienne Cedex 2, France. TORSTEN MARKUS, Associate Professor, is with the Forschungszentrum Ju¨lich GmbH, Institut fu¨r Energie- und Klimaforschung, 52425 Ju¨lich, Germany. Dedicated to Prof. Jean Le Coze on the occasion of his 70th birthday. Manuscript submitted February 20, 2013. Article published online September 6, 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A
meaning of their results, some of them are skeptical, see, e.g., Stringer and coworker[1] p. 2775, ‘‘…leaving it to the reader to assess the relative values and the reasonableness of the criteria adopted….’’ Further, van Loo and coworkers[6] give a definitely negative answer to their two questions, ‘‘(1) Are the experimentally found interdiffusion coefficients material constants? (2) Is the reduced matrix formalism correct?…’’ (which means that off-diagonal phenomenological coefficients in the classical diffusivity matrix are neglected). More recently advanced numerical methods were applied[10] to inverse modeling in order to obtain the diffusivity matrix (see Reference 11 and references therein). Because of the lack of confidence conveyed by the classical (i.e., BM-based) data evaluation procedure, we decided to adopt a different approach: In the present work, we use an alternative model (whose key elements were presented in Reference 11) to extract selfdiffusivities from interdiffusion experiments (at high temperature) and to compare them t
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