The growth rate of NH4NO3 phase III crystals is measured and interpreted using two models. The first is a standard crystal growth model based on a spiral growth mechanism, the second outlines the concept of kinetical roughening. As the crystal becomes rough a critical supersaturation can be determined and from this the step free energy. The step free energy versus temperature turns out to be well represented by a Kosterliz-Thouless type model. Further a phenomenological treatment of some peculiar growth observations is given.