  Using an atom-vacancy exchange algorithm, we investigate the kinetics of the
order-disorder transition in an fcc A_3B binary alloy model following a
temperature quench from the disordered phase. We observe two clearly distinct
ordering scenarios depending on whether the final temperature T_f falls above
or below the ordering spinodal T_{sp}, which is deduced from simulations at
equilibrium. For shallow quenches (T_f>T_{sp}) we identify an incubation time
tau_{inc} which characterizes the onset of ordering through the formation of
overcritical ordered nuclei. The algorithm we use together with experimental
information on tracer diffusion in Cu_3Au alloys allows us to estimate the
physical time scale connected with tau_{inc} in that material. Deep quenches,
T_f<T_{sp}, result in spinodal ordering. Coarsening processes at long times
proceed substantially slower than predicted by the Lifshitz-Allen-Cahn t^{1/2}
law. Structure factors related to the geometry of the two types of domain walls
that appear in our model are found to be consistent with Porod's law in one and
two dimensions.
