Alpha factor explained

The α-factor is a dimensionless quantity used to predict the solid–liquid interface type of a material during solidification. It was introduced by physicist Kenneth A. Jackson in 1958. In his model, crystal growth with larger values of α is smooth, whereas crystals growing at smaller α (below the threshold value of 2) have rough surfaces.^{[1] [2]}

Method

According to John E. Gruzleski in his book Microstructure Development During Metalcasting (1996):

\alpha = (L)/(⋅ kT _{E}) (η)/(v) where L is the latent heat of fusion; k is the Boltzmann constant; T _{E} is the freezing temperature at equilibrium; 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.

As

(L)/(T _{E}) = \Delta S _{f} , where \Delta S _{f} is the molar entropy of fusion of the material,\alpha = (\Delta S _{f})/(k) ⋅ (η)/(v) ^[3]

According to Martin Glicksman in his book Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts (2011):

\alpha = (\Delta S _{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.^[4]

Notes and References

1. Bennema . P. . 1993 . Morphology of crystals determined by alpha factors, roughening temperature, F faces and connected nets . Journal of Physics D: Applied Physics . 26 . 8B . B1–B6 . 10.1088/0022-3727/26/8b/001.
2. Web site: Kenneth A. Jackson (1930 - 2022) . . 2024-04-01 . 2022 . Don . Uhlmann . Vincent . Fratello.
3. Book: Gruzleski . John E. . Microstructure Development During Metalcasting . 1996.
4. Book: Glicksman . Martin . Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts . 2011.