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
kTE
η
v

where

L

is the latent heat of fusion;

k

is the Boltzmann constant;

TE

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
TE

=\DeltaSf

, where

\DeltaSf

is the molar entropy of fusion of the material,

\alpha=

\DeltaSf
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=

\DeltaSf
Rg
η1
Z
where

Rg

is the universal gas constant.
η1
Z
is similar to previous, always
1
4

<

η1
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.