We have improved our vectorized Monte Carlo code for spin-exchange kinetics in diamond lattice by including next-nearest-neighbour interaction. The cluster multiple-labelling technique has been extended to the case of clusters of the ordered AB phase. The output data are sent to a workstation and visualized with computer graphics techniques. Preliminary results of the long range order parameter versus reduced temperature at two different concentrations (c = 0.2 and c = 0.5) have been obtained. The evolution towards equilibrium states is usually very fast (within 2000 MCS/atom). However at low reduced temperatures states of metastable equilibrium occur, in particular antiphase domains. The initial configuration at c = 0.5 turns out to be formed by two interwoven AB antiphase domains, which have been analyzed by computer graphics. This peculiar structure has been attributed to the fact that the concentration …