We propose an extension of the axial next nearest neighbour Ising (ANNNI) model to a general number of interactions between spins. We apply this to the calculation of stacking fault energies in magnesium—particularly challenging due to the long-ranged screening of the pseudopotential by the free electron gas. We employ both density functional theory (DFT) using highest possible precision, and generalized pseudopotential theory (GPT) in the form of an analytic, long ranged, oscillating pair potential. At the level of first neighbours, the Ising model is reasonably accurate, but higher order terms are required. In fact, our ‘ AN N NI model’ is slow to converge—an inevitable feature of the free electron-like electronic structure. In consequence, the convergence and internal consistency of the AN N NI model is problematic within the most precise implementation of DFT. The GPT shows the convergence and internal consistency of the DFT bandstructure approach with electron temperature, but does not lead to loss of precision. The GPT is as accurate as a full implementation of DFT but carries the additional benefit that damping of the oscillations in the AN N NI model parameters are achieved without entailing error in stacking fault energies. We trace this to the logarithmic singularity of the Lindhard function.

Twin boundaries have been shown to deviate from the twinning planes in hcp metals, and facets have often been observed in twin interfaces. This study presents a twinning disconnection-based model for faceting in single, double and triple twin boundaries in magnesium. Primary twinning disconnections predicted via symmetry arguments are shown to produce commensurate facets in single twin boundaries, which are then transformed into commensurate facets in double twin boundaries via the action of secondary twinning disconnections. In contrast, it is shown that for triple twin boundaries with tension-compression-tension twinning sequence, no commensurate facets can be produced by the action of tertiary twinning disconnections. The effect of facets on the macroscopic orientation of twin interfaces is discussed. Theoretical findings are validated by a transmission electron microscopy study of a hot rolled Mg-1.18wt%Al-1.77wt%Nd alloy. Single and double twins are observed, as well as rare triple twins, and the interface between the matrix and a triple twin is captured for the first time. Facets consistent with theoretical predictions are imaged via high-resolution TEM and macroscopic deviations of the boundaries from the primary twinning planes are measured.