Two-dimensional nucleation in crystal growth: thermodynamically consistent description of the nucleation work

Abstract

In the scope of Gibbs's theory of capillarity, a thermodynamically consistent formula is derived for the work W to form a two-dimensional (2D) nucleus on a growing molecularly smooth crystal face. The derivation is based on a newly introduced dividing line (DL) called conservative, because it defines the nucleus as having size-independent specific line energy κ 0. The thermodynamically consistent formula for W accounts for the annulment of the nucleation work at the spinodal of the adsorption monolayer on the crystal face. Expressions are given for the radii R C and R T of the 2D nucleus defined by the conservative DL and by the line of tension, respectively. As a side result, the R T dependence of the specific line energy κ T of the 2D nucleus defined by the line of tension is determined. Provided the inequality κ T⩽ κ 0 is satisfied, the analysis is valid for 2D nuclei of any size, i.e. for 2D nucleation in the entire range of conditions between the binodal and the adsorption spinodal. It is found that, due to the annulment of W at this spinodal, the rates of 2D nucleation and of nucleation-mediated crystal growth are higher than those determined by using the classical nucleation theory.