We extend a first principles based hierarchical multi-scale model scheme for describing a fully coherent precipitate in a host lattice to 3D simulations. As our test system, the needle-shaped main hardening Al–Mg–Si alloy precipitate β′′ is chosen. We show that computational costs do not impose practical limits on the modelling: the scheme can probe the full interface energy for physically sized and well isolated precipitates. Examining a series of energetically competitive bulk β′′ configurations, we highlight a series of results: (i) the scatter in the structural parameters for different β′′ configurations clearly exceeds experimental uncertainties also when interaction with the host lattice is taken into account. (ii) Structural and compositional β′′/Al interfaces generally coincide. This implies that precipitate stoichiometry is retained only for the two β′′ configurations with the lowest formation energy (compositions Mg5Al2Si4, Mg4Al3Si4). (iii) β′′–Mg4Al3Si4 emerges as a minimum energy configuration for large precipitates. Finally, (iv) more complete modelling, with precipitates surrounded by Al in all three dimensions, is expected to highlight a non-negligible influence of the precipitate misfit along the main growth (needle) direction.