Alpha factor
# 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.

