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Phase equilibria that are relevant for the growth of Bi2MO4 have been studied experimentally, and the ternary phase diagrams of Bi2O3-PdO2-Pd and Bi2O3-Cu2O-CuO and its isopleth section Bi2O3-CuO were redetermined. It is shown that every melting and crystallization process is always accompanied by a redox process at the phase boundary and that for both title compounds, the valence of the transition metal is lowered during melting. Vice versa, during crystal growth, O-2 must be transported through the melt to the phase boundary. Based on these new insights provided by our thermodynamic studies, Bi2CuO4 single crystals with a length of up to 7 cm and a diameter of 6 mm were grown by the OFZ technique to be used for investigations of magnetic, electronic and thermal transport properties. The grown crystals were characterized by powder X-ray diffraction, Laue, magnetization and specific heat measurements.