Fig. 4

Bonding character from DFT calculations. a Mg lattice supercells showing Nd and Zn solutes as 1st and 2nd nearest neighbors (NN), only Nd solute, and pure Mg. The encircled Mg atom was displaced along the [0001]α to calculate the restoring force. b Plot of DFT-calculated force as function of displacement along [0001]α. The inset histogram shows the calculated bond stiffness increases with Zn addition. Charge isosurface using Δρ = 0.015 eÅ−3 in panels c–e shows the valence electron delocalization along [0001]α in solid solution, bulk γ″, and γ″–Mg supercells in Mg–Nd–Zn system