Determining the free energy barrier to nucleation of crystallites independent of the barrier to growth: A direct non-Arrhenius method

Abstract

No method is currently available to measure the free energy barrier W* to nucleation of erystallites in amorphous solids, independent of the barrier to growth. The existing methods measure the combined process of nucleation and growth and can not directly give the free energy barrier to nucleation. For example, in a frequently employed method W* is obtained as the difference between the activation energy of the quasi-steady-state rate of nucleation J. ~x 1 / T exp[-(Ea + W*) / kT] and that of the growth rate of crystallites [1,2]. Here Ea is the activation enthalpy for diffusion of atoms in an amorphous solid, k is Boltzmann constant. However, it can be shown that the previous method measures the activation enthalpy rather than the activation free energy barrier to nucleation as it intended to measure. The method equates Ea + W* k T to the absolute slope of Jss on an Arrhenius plot and obtains W* by subtracting Ed -k T from the slope. However, W* as the activation free energy can always be separated into the activation enthalpy A H ( g . ) and entropy T A S ( g . ) , W* = A H , T A S . . Consequently, the absolute slope of Jss on an Arrhenius plot equals Ea + A H . kT , and thus the previous method measures the activation enthalpy AH. rather than the activation free energy barrier W*. It is surprising that the problem identified above has always been overlooked in applications. Another noteworthy fact is the error associated with the previous method can be comparable or even larger than the absolute value it intended to measure. In the previous method both activation energies are obtained based on an Arrhenius plot of J. and the growth rate, respectively, the error is thus a sum of the errors associated with the measurements of J, and the growth rate.