Model of the crystal structure

o Phase field model -- some of both crystals everywhere

  • Mass fraction of round crystal type at every point as u(t)
  • Square crystal type at every point is 1-u(t)

o Thermodynamics of mixed phases at mild temperatures

  • Two wells in the energy potential -> two phases
  • Energy barrier between two phases -> inhibits change
  • Pressure gradient determines the lower energy state
    • Squares prefered if dp is large
    • Rounds prefered if dp is small

o Thermodynamics of mixed phases at cold temperatures

  • Three wells in the energy potential
  • Allows for persistant equal mixture of phases
  • Inhibits square or round formation

o Simplified model

u' = - dE(u,dp,T) / du

  • Decrease energy as rapidly as possible
  • Changes mass fraction of crystal types

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