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Diffusion and Mass Transfer
Within a microstructure, there is generally mass transfer whenever there are gradients in chemical potential. There are three processes that are important to model to have mass transfer within the microstructure:
2) Grain Boundary Diffusion - mass transfer along a grain boundary
3) Precipitation/Dissolution - mass transfer between a grain and grain boundary
(1D) or (3D)Mass Flux
(1D) or (3D)where C is chemical concentration or potential, D is diffusion constant (d is also, but may have different units), and q is mass flux.
We first discretize the elle data structure into a series of triangles.
We then assign the attributes of each flynn to the triangles contained
in it and then run the diffusion code.
where C0 is the concentration in Triangle-0, Q1 is the flux from Triangle-1 into Triangle-0, A0 is the area of Triangle-0, and L1 is the length of the boundary between Triangle-1 and Triangle-0.
Flux into Triangle 0 from Triangle 1: q1 = k (C1-C0)L1/A0Total change in concentration in Triangle-0 per time = total influx/volume:
The concentration or chemical potential on each grain boundary segment is determined by the values at each of the end-point nodes. Each node carries attributes, which are allowed to diffuse as the grain boundary diffusion code is run.
where C0 is the concentration at Node-0, q1 is the flux from Node-1 into Node-0, x1 is the length of the boundary segment between Node-1 and Node-0, and w1 is the width of the boundary segment between Node-1 and Node-0.
Flux into Node-0 from Node-1: q1 = k (C1-C0)/x1Total change in concentration at Node-0 per time = total influx/volume:
last updated 17 November 1999