A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at sufficient rate from a given fraction solid, growth velocity first increases, and then decreases rapidly when solute fields of adjacent particles overlap. An approximate analytical solution for the spherical particle growth velocity is then developed and shown to be valid until the solute fields begin to overlap. A particle stability model is next presented, building on the above analytic solution. This model permits prediction of the maximum cooling rate at which a semi-solid slurry or reheated semi-solid billet can be cooled while still retaining the spherical growth morphology. The model shows that particle stability is favored by high particle density, high fraction solid and low cooling rate. The predictions of the stability model are found to be in good quantitative agreement with experimental data collected for Al-4.5wt%Cu alloy. Engineering applications of the results obtained are discussed.