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## Diffusion and Mass TransferWithin 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.
C is the concentration in Triangle-0,
_{0}Q
is the flux from Triangle-1 into Triangle-0,
_{1}A is the
area of Triangle-0, and _{0}L is the length of the boundary
between Triangle-1 and Triangle-0.
_{1}Flux into Triangle 0 from Triangle 1:Total change in concentration in Triangle-0 per time = total influx/volume: 2) Grain Boundary Diffusion
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. whereC is the concentration at Node-0, _{0}q
is the flux from Node-1 into Node-0, _{1}x is the length
of the boundary segment between Node-1 and Node-0, and _{1}w
is the width of the boundary segment between Node-1 and Node-0.
_{1}Flux into Node-0 from Node-1:Total change in concentration at Node-0 per time = total influx/volume: last updated 17 November 1999 |