title: Alpha factor
text: # Alpha factor
  
  The α-factor is used to predict the solid–liquid interface type of a material during solidification.
  
  ## Method
  
  According to John E. Gruzleski in his book Microstructure Development During Metalcasting (1996):
  
  α = $(L/k*T_E)*(η/v)$
  
  where L is latent heat of fusion; k is Boltzmann’s constant; $T_E$ is equilibrium freezing temperature; η is the number of nearest neighbours an atom has in the interface plane; and v is the number of nearest neighbours in the bulk solid.
  
  Since $L/T_E$ = $ΔS_f$
  
  where $ΔS_f$ is the molar entropy of fusion of the material.
  
  α = $ΔS_f/k(η/v)$
  
  According to Martin Glicksman in his book Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts (2011):
  
  α = $ΔS_f/R_g(η_1/Z)$
  
  where $R_g$ is the universal gas constant. $(η_1/Z)$ is similar to previous, always 1/4 < $(η_1/Z)$ < 1.
  
  