Calculations. Density functional theory (DFT) calculations were performed with the CASTEP planewave pseudopotential code. The calculations used the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and Vanderbilt ultrasoft pseudopotentials. MAX crystal structures from the Inorganic Crystal Structure Database were used as starting models (ICSD606236 for Nb2AlC and ICSD160755 for Nb4AlC3). Prior to the EFG calculations, atomic positions were optimized (with lattice parameters held constant) until the force on any atom was smaller than 10 meV×Å -1 . All calculations used a planewave energy cut-off energy of 600 eV and a Monkhorst-Pack 39 grid with a spacing finer than 2p ´ 0.04 Å -1 to sample the Brillouin zone. Computed EFG parameters were used as the starting point to fit the experimental Al and 93 Nb spectra.