This paper proposes a model to simulate the diffusion of impurities in bcc atomic lattices. It works with three-dimensional volume, divided in small cubic elements (voxels), containing more than one atomic cell each.
Once the domain is discretized, impurities jump from one voxel to another according to certain probability that takes into account the composition and geometry of the target voxel.
In the present work, a model was applied to a prismatic volume and in order to deduce the relationship between the atomic jumping frequency and the temperature two different cases were studied. One consists of a Fe matrix with Cr impurities, and the other is based on a Cr matrix with Fe impurities. Results obtained from these simulations were compared with profiles obtained by Dictra software.
Results for the atomic jumping frequencies were fitted to an Arrhenius type equation, as shown in following expressions:
From these equations it is possible to obtain an activation energy for the atomic jumping phenomenon of ∼306 kJ/mol and ∼411 kJ/mol for the Fe-matrix and Cr-matrix systems, respectively. These energies match the empirical measured values for the diffusion of Cr and Fe impurities, 250 kJ/mol and 407 kJ/mol, respectively.
Results obtained in this work assure that the proposed model is suitable for simulating the three-dimensional diffusion of substitutional impurities in Cr and Fe bcc systems. It could be easily expanded to other bcc matrix systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)