Periodic density functional theory and surface thermodynamics were combined in a model for the relative stability of rutile-structured MgF2 surfaces in a mixed H2O/HF gas phase. We performed DFT calculations for surfaces (001), (100), (101) and (110), considering H2O and HF adsorption, as well as hydroxylation of the surfaces. The influence of temperature and composition of the gas phase on the surface energies was explored using ab-initio thermodynamics. We found that the relative stability of the surfaces, which depends on their composition, is governed by the thermodynamic equilibrium between gas phase and solid. As a consequence, the morphology of the crystallites strongly varies depending on these parameters.