Consider two potential alloying strategies for enhancing the electrical conductivity of aluminum (Al): adding small amounts of magnesium (Mg) as a substitutional solute or introducing lithium (Li) atoms into interstitial sites.
The atomic radii are: Al =143pm, Mg =160pm, Li =152pm. Aluminum crystallizes in a face-centered cubic (fcc) lattice.
(a) On separate diagrams, construct a three-dimensional representation of one fcc unit cell for each alloying strategy: (i) 5\,\% Mg substitutional; (ii) 5\,\% Li interstitial. Use clear symbols to differentiate Al from the solute atoms and indicate all solute positions.
(b) For each diagram, label one complete edge of the unit cell with the lattice parameter a and denote at least one nearest-neighbor distance between Al and the solute atom.
(c) Using only geometric considerations from your diagrams and the radii provided, determine whether lattice strain is greater for Mg substitution or Li interstitial incorporation. Explain your reasoning thoroughly.
(d) Based on your conclusion in part (c), evaluate which alloying strategy is more likely to maintain or improve electrical conductivity, and justify your choice in terms of electron scattering mechanisms at the particle level.