External force field during diffusion – sedimentation in condensed matter

Bartek Wierzba , Wojciech Nowak, Patrycja Wierzba, Jan Sieniawski

Rzeszow University of Technology, Faculty of Mechanical Engineering and Aeronautics, al. Powstańców Warszawy 12, 35-959, Rzeszów, Poland.

DOI:

https://doi.org/10.7494/cmms.2017.1.0570

Abstract:

In this paper numerical description of the external force field during interdiffusion is discussed. Two methods of modeling the sedimentation process will be presented. Mainly, the steady state and evolutionary approximation. The proposed approaches will based on the generalized Darken method. The main equations will be the mass conservation and equation of Both presented approximations will based on the method of lines to solve numerically the ordinary differential equations (ODEs) system resulting from the space discretization (Schiesser, 1991). The uniform grid, which contained N mesh points along the x direction, respectively, was used and the concentrations and drift velocity were defined at points xk. The applied discretization led to the system of ODEs in time variable. The evolutionary method will based additionally on the adaptive step-size Runge–Kutta-Fehlberg modification. The six evaluations of the functions from the fifth-order Runge–Kutta algorithm were used to make other combinations implemented in the fourth-order Runge–Kutta method. The difference between these two estimates served as an estimate of the truncation error. Hence, the step size was adjusted (Press, 1992). The results of the proposed methods will be compared and discussed.motion. Thus the simultaneous action of backstress, external forces and of Kirkendall shift during interdiffusion in metals is described by self-consistent scheme. The diffusion flux is than determined by both, chemical and mechanical potentials – j=Di grad(ui).

Cite as:

Wierzba, B., Nowak, W., Wierzba, P., Sieniawski, J. (2017). External force field during diffusion – sedimentation in condensed matter. Computer Methods in Materials Science, 17(1), 18 – 21. https://doi.org/10.7494/cmms.2017.1.0570

Article (PDF):

Keywords:

Sedimentation, Darken method, Equation of motion

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