{{short description|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.<ref>{{cite journal|last=Bennema |first=P. |year=1993 |title=Morphology of crystals determined by alpha factors, roughening temperature, F faces and connected nets |journal=Journal of Physics D: Applied Physics |volume=26 |number=8B |pages=B1–B6 |doi=10.1088/0022-3727/26/8b/001}}</ref><ref>{{cite web|url=https://www.nae.edu/312073.aspx |title=Kenneth A. Jackson (1930–2022) |website=National Academy of Engineering |access-date=2024-04-01 |year=2022 |first1=Don |last1=Uhlmann |first2=Vincent |last2=Fratello}}</ref>
== Method == According to John E. Gruzleski in his book ''Microstructure Development During Metalcasting'' (1996): : <math>\alpha = \frac{L}{kT_\mathrm{E}}\cdot\frac{\eta}{v} </math> where <math>L</math> is the latent heat of fusion; <math>k</math> is the Boltzmann constant; <math>T_\mathrm{E}</math> is the freezing temperature at equilibrium; <math>\eta</math> is the number of nearest neighbours an atom has in the interface plane; and <math>v</math> is the number of nearest neighbours in the bulk solid.
As <math>\frac{L}{T_\mathrm{E}} = \Delta S_f</math>, where <math>\Delta S_f</math> is the molar entropy of fusion of the material, : <math>\alpha = \frac{\Delta S_f}{k} \cdot \frac{\eta}{v}</math> <ref name="gruzleski">{{cite book |last1=Gruzleski |first1=John E. |title=Microstructure Development During Metalcasting |date=1996}}</ref>
According to Martin Glicksman in his book ''Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts'' (2011): : <math>\alpha = \frac{\Delta S_f}{R_\mathrm{g}} \cdot\frac{\eta_1}{Z}</math> where <math>R_\mathrm{g}</math> is the universal gas constant. <math>\frac{\eta_1}{Z}</math> is similar to previous, always <math>\frac{1}{4} < \frac{\eta_1}{Z}</math> < 1.<ref name="glicksman">{{cite book |last1=Glicksman |first1=Martin |title=Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts |date=2011}}</ref>
== References == {{reflist}}
Category:Materials science
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