Nonclose-packed structures

Key points: A common nonclose-packed metal structure is body-centred cubic; a primitive cubic structure is occasionally encountered. Metals that have structures more complex than those described so far can sometimes be regarded as slightly distorted versions of simple structures.

Fig. 3.21 The structures of the metallic elements at room temperature. Elements with more complex structures are left blank.

Not all elemental metals have structure based on close-packing and some other packing patterns use space nearly as efficiently. Even metals that are close-packed may undergo a phase transition to a less closely packed structure when they are heated and their atoms undergo large-amplitude vibrations. One commonly adopted arrangement has the translational symmetry of the body- centred cubic lattice and is known as the body-centred cubic structure (cubic-I or bcc) in which a sphere is at the centre of a cube with spheres at each corner (Fig. 3.22a). Metals with this structure have a coordination number of 8 because the central atom is in con tact with the atoms at the corners of the unit cell. Although a bcc structure is less closely packed than the ccp and hcp structures (for which the coordination number is 12), the difference is not very great because the central atom has six second-nearest neighbours, at the centres of the adjacent unit cells, only 15 per cent further away. This arrangement leaves 32 per cent of the space unfilled compared with 26 per cent in the close-packed structures (see Example 3.3). A bcc structure is adopted by 15 of the elements under standard conditions, including all the alkali metals and the metals in Groups 5 and 6. Accordingly, this simple arrangement of atoms is sometimes referred to as the ‘tungsten type’. The least common metallic structure is the primitive cubic (cubic-P) structure (Fig. 3.23), in which spheres are located at the lattice points of a primitive cubic lattice, taken as the corners of the cube. The coordination number of a cubic-P structure is 6. One form of polonium (-Po) is the only example of this structure among the elements under normal conditions. Solid mercury (-Hg), however, has a closely related structure: it is obtained from the cubic-P arrangement by stretching the cube along one of its body diagonals (Fig. 3.24a); a second form of solid mercury (-Hg) has a structure based on the bcc arrangement but compressed along one cell direction (Fig. 3.24b). Although antimony and bismuth normally have structures based on layers of atoms, both convert to a cubic-P structure under pressure and then to close-packed structures at even higher pressures. Metals that have structures more complex than those described so far can sometimes be regarded, like solid mercury, as having slightly distorted versions of simple structures. Zinc and cadmium, for instance, have almost hcp structures, but the planes of close-packed atoms are separated by a slightly greater distance than in perfect hcp. This difference suggests stronger bonding between the close-packed atoms in the plane than between the planes: the bonding draws these atoms together and, in doing so, squeezes out the atoms of the neighbouring layers.

Fig. 3.22 (a) A bcc structure unit cell and (b) its projection representation.

Fig. 3.23 (a) A primitive cubic unit cell and (b) its projection representation.

Fig 3.24 The structures of (a) -mercury and (b) -mercury that are closely related to the unit cells with primitive cubic and body-centred cubic lattices, respectively.

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مواضيع ذات صلة

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids

Atomic radii of metals

Polytypism

The close packing of spheres

Lattices and unit cells

The orbitals

Bonding and antibonding orbitals

Hybridization