  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 .
