  The time evolution of structure factors in the disordering process of an
initially phase separated lattice depends crucially on the microscopic
mechanism which drives the disordering, such as Kawasaki dynamics or vacancy
mediated disordering. Monte Carlo (MC) simulations show unexpected ``dips'' in
the structure factors, which mean-field theory completely fails to capture. The
disordering via vacancies is slower by a surprisingly large constant factor
compared to Kawasaki dynamics. A phenomenological model is introduced in order
to understand the dips, and an analytical solution of Kawasaki dynamics is
derived, in excellent agreement with simulations. An outline is given on how to
extend the analytical solution to the more complicated case of a wandering
vacancy.
