Cahn-Hilliard theory with triple-parabolic free energy. I. Nucleation and growth of a stable crystalline phase

Nucleation and growth of a stable crystalline phase are described in the fr amework of a single-order-parameter Cahn-Hilliard theory. A piecewise parab olic free energy-order parameter relationship composed of three parabolas i s adopted with a negative curvature coefficient (lambda(1)) for the central part. An analytical solution of the problem is presented. The work of form ation of critical fluctuations, the temperature coefficient of their interf acial free energy, and the Tolman length are found to be sensitive to the v alue of lambda(1), whereas the steady-state growth rate is rather insensiti ve. It is demonstrated that for systems of known free-energy order paramete r relationship, the triple-parabola approximation is useful in obtaining qu alitative and semiquantitative results for nucleation and growth rates. (C) 2000 American Institute of Physics. [S0021-9606(00)52605-1].