Alpha factor

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.

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. \alpha = \frac{L}{kT_\mathrm{E}}\cdot\frac{\eta}{v} where L is the latent heat of fusion; k is the Boltzmann constant; T_\mathrm{E} is the freezing temperature at equilibrium; \eta 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 \frac{L}{T_\mathrm{E}} = \Delta S_f , where \Delta S_f is the molar entropy of fusion of the material, \alpha = \frac{\Delta S_f}{k} \cdot \frac{\eta}{v} According to Martin Glicksman in his book Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts (2011): \alpha = \frac{\Delta S_f}{R_\mathrm{g}} \cdot\frac{\eta_1}{Z} where R_\mathrm{g} is the universal gas constant. \frac{\eta_1}{Z} is similar to previous, always \frac{1}{4} < 1.

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