Atomic diameters, atomic volumes and solid solubility relations in alloys

Abstract The use of the concepts of favourable and unfavourable size factor in predicting solid solubilities in metallic systems is discussed. The original concept of Hume-Rothery, Mabbott and Channel-Evans involved the use of atomic diameters which were defined as the closest distances of approach of atoms in the crystals of the elements. Atomic diameters defined in this way give a much better correlation with solid solubilities than do the Goldschmidt atomic diameters and a slightly better correlation than the Pauling single bond metallic radii. Recent suggestions that atomic diameters should be replaced by atomic volumes are reviewed and it is shown that the atomic volumes do not correlate well with the solid solubilities in alloy systems. In spite of the different crystal structures involved, the atomic volumes in the sequences Cu→ Zn → Ga→ Ge, Ag → Cd → In and Au → Hg → Tl show an almost exactly linear increase with atomic number.