Figure 2.07. Critical Radius for Nucleation of a Spherical Cap. This diagram shows the Gibbs energy change for nucleation of a new phase on a surface as a spherical cap as a function of the radius of the base of the cap. Move the |ΔT| slider to overstep the reaction and see the critcal radius for spherical cap nucleation. The scale of the graph can be changed by clicking the "Change Scale" button in the upper right.
There are separate sliders to change the model values for the various parameters used in the calculation of the diagram including the interfacial Gibbs energy of the surface of the spherical cap and for the interfacial Gibbs energy of the base of the spherical cap. The shape of the spherical cap in terms of the ratio (H/B) of the height (H) of the cap to the width (B) of the base may be changed and is shown cross section with 0.1 steps by a reddish shape.
The critical radius (= B/2) and the associated critical volume (nm3) of a spherical cap nucleus are shown. The critical volume is also given in terms of formula units for the chemical formula used to define the volumetric Gibbs energy change in units of J/mole. The number of atoms in the critical volume of the nucleus is found by multipying the number of forumla units by the number of atoms in the formula.
For small values of |ΔT|, some values of H/B show a critical volume for a spherical cap nucleus that is smaller than the critical volume for a spherical nucleus (also shown). This means that in some cases, the opportunity to nucleate on a surface will facilitate nucleation of a new phase because fewer formula units must be added to the nucleus to reach the critical radius.
