CADiff – the inter and reactive diffusion simulation tool
Bartłomiej Wierzba1
, Maciej Pietrzyk2
, Marek Danielewski1
1Interdisciplinary Centre for Materials Modelling, Faculty of Materials Science and Ceramics.
2AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland.
DOI:
https://doi.org/10.7494/cmms.2008.1.0186
Abstract:
The CADiff software is presented in the paper. The method based on the extended Darken and Wagner models, allows to simulate the inter and reactive diffusion processes. The diffusion fluxes are defined in the volume fixed reference frame. The Darken method is extended to include the non ideal alloys showing different partial molar volumes and boundary conditions taking into account both the diffusion and the surface reactions. The CADiff simulation tool allow to compute a wide range of interdiffusion processes starting from the Fick constitutive diffusion flux formula to the combined Darken-Onsager approach. They allow to model pure interdiffusion in multi-component systems as well as a wide class of the reaction-diffusion problems associated with solid state chemistry, corrosion, surface treatment etc.
Cite as:
Wierzba, B., Pietrzyk, M., Danielewski, M., (2008). CADiff – the inter and reactive diffusion simulation tool. Computer Methods in Materials Science, 8(1), 47 – 53. https://doi.org/10.7494/cmms.2008.1.0186
Article (PDF):
Keywords:
Diffusion, Interdiffusion, Reactive diffusion, Oxidation, Selective oxidation, Wagner method, Chemical
References:
CADiff software available at: https://www.cmms.agh.edu.pl/public_repo/
Danielewski, M., Filipek, R., Milewska, A., 2000, Interdiffusion in Oxidized Multicomponent Alloys, Solid State Phenomena, 72, 23.
Danielewski, M., Filipek, R., Walec, T., Milewska, A., 2001, Interdiffusion driven by the reactive diffusion, interdiffusion in oxidized alloys, Met. Phys. Adv. Tech., 19, 155.
Holly, K., Danielewski, M., 1994, Interdiffusion in Solids, Free Boundary Problem for r-Component One Dimensional Mixture Showing Constant Concentration, Phys. Rev. B, 50, 13336-13343.
Danielewski, M., Wierzba, B., 2007, Mechano-Chemistry; Diffusion in Multicomponent Compressible Mixtures, Physica A, doi:10.1016/j.physa.2007.10.015.
Danielewski, M., Wierzba, B., 2008, Diffusion Processes Determining the Oxidation Rate of Multicomponent Alloys, Corr. Sci, 50, 1161-1168.
Darken, L.S., 1948, Diffusion, Mobility and Their Interrelation through Free Energy in Binary Metallic Systems, Trans. AIME, 174, 184-201.
Gesmundo, F., Viani, F., Niu, Y., Douglass, D.L., 1993, The Transition from the Formation of Mixed Scales to the Selective Oxidation of the Most-Reactive Component in the Corrosion of Single and Two-Phase Binary Alloys, Oxidation of Metals, 40, 373.
Gesmundo, F., Castello, P., Viani, F., Niu, Y., Philibert, J., 1997, An Approximate Treatment of the Transient State in the Corrosion of Binary Alloys Forming the Most-Stable Oxide. Part I: Solid-Solution Alloys, Oxidation of Metals, 47, 91.
Kubaschewski, O., 1949, von Goldbeck, J., Inst. Metals, 76, 255.
Manning, J.R., 1971, Z. Naturforsch. 26a, 69.
Murch, G.E., Belova, I.V., 2005, Phenomenological Coefficients in Solid-State Diffusion: an Introduction, Diffusion Fundamentals, 2, 8.1-8.13.
Nernst, W., 1889, Die elektromotorische Wirkamkeit der Ionen, Z. Phys. Chem., 4, 129-140.
Onsager, L., 1931, Reciprocal relations in reversible processes, Phys. Rev., 37, 405-426.
Planck, M., 1890, Ber die potentialdierenz zwischen zwei verdnnten lsungen binrer elektrolyte, Ann. Phys. Chem., 40, 561-576.
Smigelskas, A.D., Kirkendall, E., 1947, Zinc Diffusion in Alpha Brass, Trans. A.I.M.E., 171, 130-142.
Vegard, L., 1921, Die Konstitution der Mischkristalle und die Raumfullung der Atome, Z. Phys., 5, 17-26.
Wagner, C., 1952, Theoretical analysis of the diffusion processes determining the oxidation rate of alloys, J. Electrochem. Soc., 99, 369-380.
Wagner, C., 1956, Oxidation of alloys involving noble metals, J. Electrochem. Soc. 103, 571-580.
Wagner, C., 1956, Formation of composite scales consisting of oxides of different metals, J. Electrochem., Soc. 103, 627-633.
Wagner, C., 1959, Reaktionstypen bei der Oxydation von Legierungen, Z. Elektrochem., 63, 772-782.
Wierzba, B., Danielewski, M., Bachorczyk-Nagy, R., Pietrzyk, M., 2007, The Stress Field in Cu-Fe-Ni Diffusion Couples, Def. and Diff. Forum, 264, 47-54.