A simple dynamical Ising model on a fixed lattice with a single bond energy parameter has been used to simulate the kinetics of diffusion during solid-state phase transformations in binary metallic alloys. The results of these simulations are compared with direct real-space measurements of the atomic distributions of elements in alloys, obtained with the positionsensitive atom probe. Despite the simplicity of the model, there is good quantitative agreement between the development of microstructure in the simulation and the nucleation and growth of cobalt-rich precipitates in copper-cobalt alloys.