Precipitation in Mg-Zn alloys was analyzed by means of first principles calculations. Formation energies of symmetrically distinct hcp Mg1-xZnx (0 < x < 1) configurations were determined and potential candidates for Guinier-Preston zones coherent with the matrix were identified from the convex hull. The most likely structures were ranked depending on the interface energy along the basal plane. In addition, the formation energy and vibrational entropic contributions of several phases reported experimentally (Mg4Zn7, MgZn2 cubic, MgZn2 hexagonal, Mg21Zn25 and Mg2Zn11) were calculated. The formation energies of Mg4Zn7, MgZn2 cubic, and MgZn2 hexagonal Laves phases were very close because they were formed by different arrangements of rhombohedral and hexagonal lattice units. It was concluded that beta_1^ precipitates were formed by a mixture of all of them. Nevertheless, the differences in the geometrical arrangements led to variations in the entropic energy contributions which determined the high temperature stability. It was found that the MgZn2 hexagonal Laves phase is the most stable phase at high temperature and, thus, beta_1^ precipitates tend to transform into the beta_2^ (MgZn2 hexagonal) precipitates with higher aging temperature or longer aging times. Finally, the equilibrium beta phase (Mg21Zn25) was found to be a long-range order that precipitates the last one on account of the kinetic processes necessary to trigger the transformation from a short-range order phase beta_2^ to beta .
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