We report on a combined computational and experimental examination of coherent precipitation in a Mg-Nd alloy, a prototypical Mg-rare earth alloy. Three-dimensional phase field simulations are conducted to predict the composition and morphology of precipitates, a unique family of hierarchically ordered phases that are metastable in a wide Nd concentration range. Predictions are compared to experimental high-angle annular dark-field scanning transmission electron microscopy observations. The phase field model thermodynamic description is parameterized entirely from first-principles calculations. The simulations predict an elevated Nd composition in that is above the stress-free equilibrium value. The elevated Nd concentration in is in very good agreement with experimental observations and arises from a large misfit strain energy penalty and the low curvature of the free energy well. The phase field simulations predict that isolated precipitates are lenticular with a β′′′ habit plane, and are approximately equiaxial when viewed along the β′′′ direction. The predicted habit plane and precipitate dimensions are shown to be generally consistent with experimental observations, within the uncertainty introduced by density functional theory calculations of the stress-free transformation (misfit) strain and by precipitate interactions not accounted for in the simulations. Contrary to the predictions for isolated precipitates, some experimentally observed precipitates are elongated along the β′′′ direction relative to the β′′′ direction. This elongation is frequently correlated with a particular arrangement of two orientation variants of . A phase field simulation of two precipitates in this arrangement is shown to exhibit similar β′′′ elongation.