This dissertation presents an investigation of ordering in FCC based systems using the pair potential approximation in the ground state and mean field limits. The theoretical approach is used to explain the occurrence of observed equilibrium phases and characteristics of thermodynamic instabilities, in particular, spinodal ordering and decomposition. It is shown that the stability of non-integer domain sizes in long period superstructures such as Al{sub 3}Ti and Ag{sub 3}Mg may result from the tendency of a system to reduce the number of non-dominant ordering waves, thus producing domain sizes that have rational fraction form n/m. This conclusion is used to explain the domain size stability with respect to variations in temperature and electron concentration. The cation ordering in the precipitate phases in calcite and dolomite is analyzed by analogy with ordering in FCC based metals. The ordered phases in calcite and dolomite are shown to be consistent with pair potential minima at {l brace}100{r brace} and {l brace}1/2, 1/2, 1/2{r brace} positions in reciprocal space respectively. 32 refs., 6 figs.