# DIFFUSION “SURPRIZES” IN INTERDIFFUSION MODELS

## Main Article Content

## Abstract

*Optimized algorithm of solution diffusion problem was described by using the non-equidistant space coordinate scale. The quasi-stationary model of reactive diffusion is described. The optimal diffusion-based phase growth and competition in binary system algorithm are introduced. *

*Numeric modeling of phase growth and competition for one, two, and three intermediate phases is performed by two alternative ways. First, phase layer growth is computed under steady-state approximation and with zero solubility of A in B and B in A. Second, phase growth in multiphase binary couple is computed by direct numeric solving of the second Fick’s law over total diffusion couple with* *interdiffusion coefficient being a* *piecewise continuous function** of concentration, equal to zero everywhere beyond the homogeneity ranges of intermediate and marginal phases. Both approaches provide parabo;ic laws for infinite diffusion couples and giva similar descriptions of the phase growth kinetics.*

*It was shown that for the single intermediate phase growth case the parabolic growth law is valid till the beginning of the parent phase depletion. The intermediate phase growth slows down after parent phase depletion. For twophase growth case the parabolic growth law can be valid for the phase that is placed near the parent phase.* *For three intermediate phase growth when the central phase partial diffusion coefficient is greatest than the nearest phases diffusion coefficients phase can grow, compete and inhibit nearest phases.*

*The inert markers motion around diffusion pair interface plane model was developed and optimized. The Kirkendal plane instability and bifurcation was investigated. *

*The model demonstrates that the markers, initially distributed in the vicinity of contact interface, may be further redistributed between moving attractors. At the same time, the stable K-planes are marker attractors.* *Furthermore, the K-plane that refers to the V=(1/2t)*X intersection line with velocity curve V(X) at the positive derivative of dC/dX**, is unstable**. In this case the inert markers disperse from unstable K-plane to stable K-planes if **they exist.*

## Article Details

## References

Gurov, K. P., Kartashkin, B. A., & Ugaste, Y. E. (1981) Mutual diffusion in multiphase metallic systems, “Nauka”, p. 360.

Gusak, A. M., & Yarmolenko, M. V. (1993). A simple way of describing the diffusion phase growth in cylindrical and spherical samples. Journal of applied physics, 73(10), 4881-4884. Retrieved from https://doi.org/10.1063/1.353805

Gusak, A. M., Zaporozhets, T. V., Lyashenko, Y. O., Kornienko, S. V., Pasichnyy, M. O., & Shirinyan, A. S. (2010). Diffusion-controlled solid state reactions: in alloys, thin films and nanosystems. John Wiley & Sons. Retrieved from ISBN: 978-3-527-64156-7

Gusak, A. M., Zaporozhets, T. V., Lyashenko, Y. O., Pasichna, V. M. (2021) Models of solid phase reactions - new results. Another. SG NTM "New course", Kharkiv. Retrieved from ISBN 978-617-7886-17-3

Van Dal, M. J. H., Gusak, A. M., Cserháti, C., Kodentsov, A. A., & Van Loo, F. J. J. (2001). Microstructural stability of the Kirkendall plane in solid-state diffusion. Physical review letters, 86(15), 3352. Retrieved from https://doi.org/10.1103/PhysRevLett.86.3352

Van Dal, M. J. H., Gusak, A. M., Cserháti, C., Kodentsov, A. A., & Van Loo, F. J. J. (2002). Spatio-temporal instabilities of the Kirkendall marker planes during interdiffusion in β'-AuZn. Philosophical magazine A, 82(5), 943-954. Retrieved from https://doi.org/10.1080/01418610208240011

Kodentsov, A. A., Paul, A., Van Dal, M. J. H., Cserháti, C., Gusak, A. M., & Van Loo, F. J. J. (2008). On the spatial stability and bifurcation of the Kirkendall plane during solid-state interdiffusion. Critical reviews in solid state and materials sciences, 33(3-4), 210-233. Retrieved from https://doi.org/10.1080/10408430802462958