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The kinetic behavior of precipitation in a supersaturated Ni-12.5 at.% Si alloy single-crystal has been Studied by the small-angle neutron scattering (SANS) technique to supplement earlier transmission electron microscopy (TEM) and wide-angle X-ray diffraction (XRD) work. The SANS measurements performed at room temperature on quenched specimens subjected to isothermal anneals at 673, 723, 778 and 823 K for up to 125 h have revealed the presence of an interference peak in the scattering function. The particle size, determined according to the Guinier approximation, is found to obey the t1/3 coarsening law at long aging times. For short aging times below 773 K, a deviation from the t 1/3 law is seen signifying a classical `growth' stage prior to coarsening - an observation consistent with our previous in situ XRD work. The activation energy for solute diffusion is determined to be 278.4 kJ mol-1 using the rate constants governing the growth of particle size and is 255.8 kJ mol-1 using the variation of the mean interparticle distance. Enhanced diffusion due to quenched-in excess vacancies is observed below 773 K. The dynamical scaling law appears to be followed for the data obtained in the coarsening stage. A disruption of scaling occurs at the point when the particle growth changes from a parabolic rate behavior to a cubic coarsening rate.