Alpha factor

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

: $\backslash alpha\; =\; \backslash frac\{L\}\{kT\_\backslash mathrm\{E\}\}\backslash cdot\backslash frac\{\backslash eta\}\{v\}$

where $L$ is the latent heat of fusion; $k$ is the Boltzmann constant; $T\_\backslash mathrm\{E\}$ is the freezing temperature at equilibrium; $\backslash eta$ 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 $\backslash frac\{L\}\{T\_\backslash mathrm\{E\}\}\; =\; \backslash Delta\; S\_f$, where $\backslash Delta\; S\_f$ is the molar entropy of fusion of the material,

: $\backslash alpha\; =\; \backslash frac\{\backslash Delta\; S\_f\}\{k\}\; \backslash cdot\; \backslash frac\{\backslash eta\}\{v\}$ {{cite book |last1=Gruzleski |first1=John E. |title=Microstructure Development During Metalcasting |date=1996}}

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

: $\backslash alpha\; =\; \backslash frac\{\backslash Delta\; S\_f\}\{R\_\backslash mathrm\{g\}\}\; \backslash cdot\backslash frac\{\backslash eta\_1\}\{Z\}$

where $R\_\backslash mathrm\{g\}$ is the universal gas constant. $\backslash frac\{\backslash eta\_1\}\{Z\}$ is similar to previous, always < 1.{{cite book |last1=Glicksman |first1=Martin |title=Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts |date=2011}}

{{reflist}}

Category:Materials science

{{CMP-stub}}