GB_MODEL

Grain-boundary and dislocation assisted diffusion is implemented by assuming that these contributed to the diffusion by using the same frequency factor and a modified bulk activation energy. The grain-boundaries and the dislocations contribute to the total amount of diffusion according to the weighted fractions.

Syntax

gb_model

 

The parameters are entered separately for each region in order to different expression for different phases.
 

The used expressions for the grain-boundary and dislocation contributions are:

expression for the grain-boundary and dislocation contributions

expression for the grain-boundary and dislocation contributions

where

  • frequency-factor in the bulk: frequency-factor in the bulk
  • activation energy in the bulk: activation energy in the bulk
  • Bulk diffusion activation energy multiplier (typical value 0.5): bulk diffusion activation energy multiplier (typical value 0.5)
  • bulk diffusion activation energy multiplier (typical value 0.8): bulk diffusion activation energy multiplier (typical value 0.8)

The weighted calculated value for the mobility mobility M is then evaluated from:

weighted calculated value for the mobility calculated from this equation

where

  • grainboundary thickness : grain boundary thickness (typical value 0.5·10-9 or 0.5·10-10)
  • grainsize as a function of time and temperature: grain size as a function of time and temperature (typical value 25·10-6)
  • dislocation density as a function of time and temperature: dislocation density as a function of time and temperature
  • burgersvector : burgers vector (typical value 1·10-10)
  • mobility in the bulk: mobility in the bulk (δ/d being the fraction of grain boundaries in the bulk and fraction of dislocations in the bulk being the fraction of dislocations in the bulk)