Laboratory surface science under ultrahigh vacuum (UHV) conditions allows us to simulate the growth of ices in astrophysical environments. Using the techniques of temperature programmed desorption (TPD), reflection-absorption infrared spectroscopy (RAIRS) and microbalance methods, we have studied binary ice systems consisting of water (H2O) and variety of other species including carbon monoxide (CO), at astrophysically relevant conditions of temperature and pressure. We present results that demonstrate that the morphology of water ice has an important influence on the behaviour of such systems, by allowing processes such as diffusion and trapping that can not be understood through a knowledge of the binding energies of the species alone. Th...