Maximum crystal growth rate and its corresponding state

Summary

For the temperature dependence of linear crystal growth rate, the activation energy for the molecular transport could be expressed in terms of the equation of either WLF or Arrhenius. On the basis of the Arrhenius expression, the corresponding state of the crystal growth rate was formulated theoretically as

$${{\ln ({G \mathord{\left/ {\vphantom {G {G_{max} }}} \right. \kern-\nulldelimiterspace} {G_{max} }})} \mathord{\left/ {\vphantom {{\ln ({G \mathord{\left/ {\vphantom {G {G_{max} }}} \right. \kern-\nulldelimiterspace} {G_{max} }})} {\ln ({{G_{max} } \mathord{\left/ {\vphantom {{G_{max} } {G_o }}} \right. \kern-\nulldelimiterspace} {G_o }})}}} \right. \kern-\nulldelimiterspace} {\ln ({{G_{max} } \mathord{\left/ {\vphantom {{G_{max} } {G_o }}} \right. \kern-\nulldelimiterspace} {G_o }})}} = {{(T_{cmax} - T)^2 } \mathord{\left/ {\vphantom {{(T_{cmax} - T)^2 } {T(T_m - T)}}} \right. \kern-\nulldelimiterspace} {T(T_m - T)}}.$$