  The phenomenon of burst nucleation in solution, in which a period of apparent
chemical inactivity is followed by a sudden and explosive growth of nucleated
particles from a solute species, has been given a widely accepted qualitative
explanation by LaMer and co-workers. Here, we present a model with the
assumptions of instantaneous thermalization below the critical nucleus size and
irreversible diffusive growth above the critical size, which for the first time
formulates LaMer's explanation of burst nucleation in a manner allowing
quantitative calculations. The behavior of the model at large times is derived,
with the result that the average cluster size, as measured by the number of
atoms, grows linearly with time, while the width of the cluster distribution
grows as the square root of time. We develop an effective numerical scheme to
integrate the equations of the model and compare the asymptotic expressions to
results from numerical simulation. Finally, we discuss the physical effects
which cause real nucleation processes in solution to deviate from the behavior
of the model.
