Equilibrium thermodynamic calculations are used to construct predominance diagrams of the Ti–O, Cr–O, and Zn–O systems and implications for the growth of Ti:Sapphire, ruby, and ZnO crystals are discussed. For each of these systems, a growth atmosphere yielding an oxygen partial pressure that stabilizes the desired oxidation state of the metal is proposed on the basis of the performed computations. The effectiveness of these atmospheres is demonstrated in crystal growth experiments. (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)