The apparent activation energy and pre-exponential kinetic factor for heterogeneous calcium carbonate nucleation on quartz

Nucleation occurs widely in materials synthesis and natural environments. However, in the nucleation rate equation, values for the apparent activation energy (E_a) and the pre-exponential kinetic factor (A) are thus far unknown because real-time nanoscale observations are difficult to perform. Here we experimentally determine E_a and A using heterogeneous calcium carbonate nucleation on quartz as a model system. Nucleation rates are measured with in situ grazing incidence small-angle X-ray scattering and ex situ atomic force microscopy, and the experiments are conducted with a fixed supersaturation of IAP/K_sp(calc) = 10^1.65 at 12, 25, and 31 °C. E_a is calculated as 45 ± 7 kJ mol⁻¹, and A is 10^{12.0 ± 1.1} nuclei μm⁻² min⁻¹, or 10^{2.9 ± 1.3} mol m⁻² min⁻¹. Increasing the temperature shortens the induction time, but does not change nucleus sizes. These parameter values are critical for predicting and controlling the nucleation of materials.