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. 2020 Feb 26;13(5):1051.
doi: 10.3390/ma13051051.

Kinetic Modeling of Grain Boundary Diffusion: The Influence of Grain Size and Surface Processes

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Free PMC article

Kinetic Modeling of Grain Boundary Diffusion: The Influence of Grain Size and Surface Processes

Justina Jaseliunaite et al. Materials (Basel). .
Free PMC article

Abstract

Based on rate equations, the kinetics of atom adsorption, desorption, and diffusion in polycrystalline materials is analyzed in order to understand the influence of grain boundaries and grain size. The boundary conditions of the proposed model correspond with the real situation in the electrolytes of solid oxide hydrogen fuel cells (SOFC). The role of the ratio of grain boundary and grain diffusion coefficients in perpendicular and parallel (to the surface) concentration profiles is investigated. In order to show the influence of absolute values of grain and grain boundary diffusion coefficients, we select four different cases in which one of the diffusion coefficients is kept constant while the others vary. The influence of grain size on diffusion processes is investigated using different geometrical models. The impact of kinetic processes taking place on the surface is analyzed by comparing results obtained assuming the first layer as a constant source and then involving in the model the processes of adsorption and desorption. It is shown that surface processes have a significant influence on the depth distribution of diffusing atoms and cannot be ignored. The analytical function of overall concentration dependence on grain and grain boundary volume ratio (Vg/Vgb) is found. The solution suggests that the concentration increases as a complementary error function while Vg/Vgb decreases.

Keywords: adsorption; grain boundary diffusion; kinetic modeling; mass transfer; polycrystals; rate equations; solid oxide fuel cells.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Schematic presentation of the solver.
Figure 2
Figure 2
Geometry of models with different grain sizes, in a.u.: (a) 30, (b) 42, (c) 66, (d) 90, and (e) 138. Grain boundary width is fixed for all models at 6 a.u.
Figure 3
Figure 3
Calculated concentration distribution images with concentration contours of models (ae) (see Figure 2) for Case 1, Case 2, and Case 3 (see Table 2).
Figure 4
Figure 4
Parallel to the surface concentration profiles for different models at position i = 141 a.u.: at left side for Case 1 and at right side for Case 2.
Figure 5
Figure 5
Parallel to the surface concentration profiles for (b) model (see Figure 2) at depth i = 141 a.u: at left side without adsorption/desorption and at right side with adsorption and desorption.
Figure 6
Figure 6
Parallel to the surface concentration profiles for the first 10 monolayers: at left side without adsorption/desorption and at right side with adsorption and desorption; at top for Case 1 and at bottom for Case 2.
Figure 7
Figure 7
The quantitative comparison of diffusion in grains of polycrystalline material of different models (see Figure 2) with corresponding monocrystalline material of the same volume at three different moments of time and for Cases 1 and 2.
Figure 8
Figure 8
Average concentration dependencies (points) on relative volume Vg/Vgb at different moments of time and for cases with and without adsorption/desorption. Lines are fitting results using the error function in Equation (8): (a) Case 1; (b) Case 2.
Figure 9
Figure 9
Dependencies on time (points) of coefficients (a) a and (b) b from Equation (8) (values from (Table 3)) for Case 1 and Case 2 with and without adsorption/desorption processes. In (a) lines are fitting of points with function q⋅t1/2, and q values are indicated in (a).

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