Solid-solution formation in binary aluminium-based alloys is due essentially to the combined effects of the size and valence of solvent and solute atoms, as expected by the four Hume-Rothery rules. The lattice parameter of aluminium in the solid solution of the sputtered Al−Fe films is [Al-a (Å)=4.052−6.6×10⁻³Y]. The increasing and decreasing evolution of the lattice parameter of copper [Cu-a (Å)=3.612+1.8×10⁻³Z] and aluminium [Al-a (Å)=4.048−1.6×10⁻³X] in the sputtered Al-1.8 to 92.5 at. % Cu films is a result of the difference in size between the aluminium and copper atoms. The low solubility of copper in aluminium (<1.8 at % Cu) is due to the valences of solvent and solute atoms in contrast with other sputtered films prepared under similar conditions, such as Al−Mg (20 at. % Mg), Al−Ti (27 at. % Ti), Al−Cr (5at. % Cr) and Al−Fe (5.5 at. % Fe) where the solubility is due to the difference in size.