The apparent sizes of atoms in metallic crystals with special reference to aluminium and indium, and the electronic state of magnesium

Abstract

The interatomic distances in crystals of alloys cannot be accounted for by assigning a fixed atomic radius to each kind of atom, and the causes of this variation are discussed with special references to the Brillouin zone characteristics of different structures. According to the theory of Jones, the effect of an overlap across the side of a Brillouin zone is to compress the zone at right angles to the face concerned, and so to expand the crystal lattice in the same direction. This expansion is not a property of an atom which can be transferred to any of its alloys, but is a characteristic of a structure with sufficient electrons to produce an overlap. The lattice spacings of alloys of aluminium and indium with copper, silver, gold, and magnesium are examined, and the apparent sizes of the aluminium and indium atoms are discussed, and are shown to be in agreement with the theory. The previous suggestion, that in metallic aluminium the atoms exist in an incompletely ionized state, is improbable, and is no longer required in order to explain the facts. New experimental data for the lattice spacings of solid solutions of aluminium and indium are presented, and these show that, whilst the curves connecting the a parameter with the composition are smooth and continuous, the corresponding curves for the c parameter show an abrupt change in direction at about 0.75 atomic % of indium or aluminium. This is taken to imply that, although in metallic magnesium with two electrons per atom, the overlap of the first Brillouin zone is in the a direction only, the structure is so near to the stage at which the c overlap sets in that the addition of less than one electron per hundred atoms causes the c overlap to take place.