Atomistic simulation techniques are used to model a range of sulfates. Two widely different sets of potentials have been developed. The first is based on shell model, electron-gas potentials; the second is a rigid ion model which treats inter- and intra-molecular forces differently. The success of the potential models has been demonstrated by comparing calculated and experimental lattice parameters and elastic constants. The structures and energetics of surfaces of barite (BaSO4) are examined in detail, allowing for the effects of surface relaxation. The two lowest-energy surfaces are {001} and {210} which dominate the calculated equilibrium morphology.