Influence of thermomechanical loads on the energetics of precipitation in magnesium aluminum alloys

We use first principles calculations to study the influence of thermomechanical loads on the energetics of precipitation in magnesium-aluminum alloys. Using Density Functional Theory simulations, we present expressions of the energy of magnesium-aluminum binary solid solutions as a function of concentration, strain and temperature. Additionally, from these calculations, we observe an increase in equilibrium volume (and hence the equilibrium lattice constants) with the increase in concentration of magnesium. We also observe an increase in the cohesive energy of solutions with increase in concentration, and also present their dependence on strain. Calculations also show that the formation enthalpy of $\beta$ phase solutions to be strongly influenced by hydrostatic stress, however the formation enthalpy of $\alpha$ phase solutions remain unaffected by hydrostatic stress. We present an expression of the free energy of any magnesium aluminum solid solution, that takes into account the contributions of strain and temperature. We note that these expressions can serve as input to process models of magnesium-aluminum alloys. We use these expressions to report the influence of strains and temperature on the solubility limits and equilibrium chemical potential in Mg-Al alloys. Finally, we report the influence of thermomechanical loads on the growth of precipitates, where we observe compressive strains along the $c$ axis promotes growth, whereas strains along the $a$ and $b$ directions do not influence the growth of precipitates.