  A class of proposed coherent precipitate structures (Guinier-Preston zones)
in the Al-Mg-Si alloy are investigated using first-principles density
functional theory methods. The cluster expansion method is used to extract
effective interaction parameters, providing the means for large scale energy
calculations of alloy structures. The Mg$_1$Si$_1$ L$1_0$ structure and
structures related to the Mg$_5$Si$_6$ $\beta''$ phase are studied in more
detail, and e.g., precipitate/matrix interface energies are presented. Using
direct first-principles calculations we show that the former phase is
dynamically unstable and thus must be stabilized by the surrounding Al matrix.
Monte Carlo simulations and free-energy techniques are used to study the Al
rich side of the phase diagram with the current CE parameters, and kinetic
Monte Carlo simulations are used to study clustering in the disordered phase.
The implications of our findings are discussed in the framework of classical
nucleation theories, and we outline possible nucleation mechanisms.
