kawin.GrainBoundaries

class kawin.GBFactors(self)

Defines nucleation factors for bulk, dislocation,  
surface, edge and corner nucleation 
 
This includes: surface area, volume, GB area removal, Rcrit and Gcrit 
 
Attributes 
---------- 
gbRemoval - factor to multiply by r**2 to get area of grain boundary removed 
areaFactor - factor to multiply by r**2 to get surface area of precipitate 
volumeFactor - factor to multiply by r**3 to get volume of precipitate 

kawin.GBFactors.setNucleationType(self, site)

Sets nucleation site type 
 
Parameters 
---------- 
site - int 
    Index for site type based off list on top of this file 

kawin.GBFactors.setFactors(self, gbEnergy, gamma)

Calculated area, volume and GB removal factors 
 
Parameters 
---------- 
gbEnergy - float 
    Grain boundary energy 
gamma - float 
    Interfacial energy between precipitate and bulk 

kawin.GBFactors.Rcrit(self, dG)

Critical radius for nucleation 
This is only done for GB nucleation 
    Bulk and dislocation nucleation needs to account for shape factors 
 
R* = 2 * (b * \gamma_{\alpha \alpha} - a * \gamma_{\alpha \beta}) / (3 * c * dG) 
 
Parameters 
---------- 
dG - float 
    Volumetric driving force 

kawin.GBFactors.Gcrit(self, dG, Rcrit)

Critical driving force for nucleation 
 
G* = 4/27 * (b * \gamma_{\alpha \alpha} - a * \gamma_{\alpha \beta})^3 / (c * dG)^2 
 
or in terms of R* 
G* = -R*^2 * (b * \gamma_{\alpha \alpha} - a * \gamma_{\alpha \beta} + c * r* * dG) 
 
This is calculated in terms of R* since there is a check in the nucleation calculation that will 
increase R* to minimum radius if R* is too small (very low nucleation barriers) 
 
Parameters 
---------- 
dG - float 
    Volumetric driving force 
Rcrit - float 
    Critical radius for nucleation