The lattice spacings of the primary solid solutions in magnesium of the metals of Group IIIB and of tin and lead

The lattice spacings of the primary solid solutions in magnesium of aluminium, gallium, thallium, tin and lead have been accurately measured. The new data confirm that the effect of increasing the valency of the solute is to tend to expand the lattice of magnesium. Thus, although the inter-atomic distance for tin is smaller than the corresponding distances for indium and thallium, the contraction in the 'a'-spacing of magnesium-tin alloys is markedly less than in the indium and thallium alloys. Lead expands the lattice of magnesium. The 'a'-spacing-composition curves for the systems studied are smooth and continuous. In contrast, the 'c'-spacing curves show a change in direction at an electron concentration of approximately $2\cdot 0075$, that is, at $0\cdot 75$ atomic per cent of a three-valent solute and $0\cdot 375$ of a four-valent solute. It is at this point that an overlap of electrons from the first Brillouin Zone for the magnesium structure occurs in the 'c' direction, in addition to the already existing overlap in the 'a' direction. For solutes of favourable 'size factor' the variation in axial ratio with composition, after the onset of the second overlap, is proportional to the electron concentration, and is therefore twice as great per atomic per cent for a four-valent solute as for a three-valent solute. The apparent atomic diameters of the above elements in dilute solid solution in magnesium, as deduced by extrapolation of the lattice spacing-composition curves to 100% of solute, are in agreement with the requirements of the Brillouin Zone theories of metals. The results confirm the suggestion that indium, thallium, white tin and lead are incompletely ionized in the elementary state.