The Lattice Spacings of Solid Solutions of Different Elements in Aluminium

H. J. Axon , W. Hume-Rothery


Measurements have been made of the lattice spacings of solid solutions of lithium, magnesium, silicon, copper, zinc, germanium and silver in aluminium. The lattice of aluminium is expanded by the solution of magnesium or germanium, and contracted by the solution of lithium, silicon, copper or zinc. No change in lattice spacing can be detected when silver is dissolved in aluminium, although microscopic examination shows that a solid solution is formed, and this is confirmed by the absence of any diffraction lines other than those of the solid solution in aluminium. If the lattice spacing/composition curve for dilute solutions is extrapolated to 100% of solute, the resulting lattice spacing refers to a hypothetical face-centred cubic modification of the solute, and the corresponding closest distance of approach of the atoms is called the apparent atomic diameter (A.A.D.) of the solute when in solution in aluminium. Previous work enables the corresponding A.A.D. values to be deduced for the above solute elements when dissolved in univalent copper, silver or gold, and in divalent magnesium. The differences between the A.A.D. values of a given element when dissolved in various solvents are discussed, and it is suggested that they are controlled by the interplay of four factors: (1) the relative volume per valency electron in crystals of the solvent and solute, (2) the relative radii of the ions of solvent and solute, (3) Brillouin zone effects, and (4) the difference between solvent and solute in the electrochemical series. If this line of approach adopted be correct, it follows that it is only in exceptional circumstances that the so-called Vegard's law will apply to metallic solid solutions.