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For use in quantitatively modeling the growth of gold-seeded semiconductor nanowires in the vapor-liquid-solid mode, we calculate the difference of chemical potential between a liquid melt formed of group III and group V atoms dissolved in gold and the corresponding solid III-V binary compound. Fits to our results are provided for seven compounds as simple polynomials of the concentrations in the III-V-Au liquid and temperature. We find that the difference of chemical potential increases with the group III and group V concentrations, decreases with increasing temperature, and can easily reach several hundreds of meV per III-V pair. We discuss these values and variations in the light of published experimental results, in particular as regards the crystalline structure adopted by the nanowires during growth.