Crystal

A complete description of the structure of a crystal involves several levels of detail. Metallic crystals are discussed first for simplicity, because the atoms are all of the same type, and can be regarded as spherical in shape. However, the basic concepts are the same for all solids.

If the spheres are represented by points, then the pattern of repeating points at constant intervals in each direction in a crystal is called the lattice. Fourteen different lattices can be obtained geometrically (the Bravais lattices). If lines are drawn through analogous points within a lattice, a three-dimensional arrangement of structural units is obtained. The smallest possible repeating structural unit within a crystal is called the unit cell, much like a brick is the smallest repeating unit (the unit cell) of a brick wall.

The 14 unit cell types are based on seven types of crystal systems. These are the cubic, triclinic, monoclinic, orthorhombic, trigonal, tetragonal, and hexagonal systems. The specific crystal system and type of unit cell observed for a given solid is dependent on several factors. If the particles that make up the solid are approximately spherical, then there is a tendency for them to pack together with maximum efficiency. Close-packed structures have the maximum packing efficiency, with 74% of the crystal volume being occupied by the particles. Close-packing occurs in two different ways: cubic close-packing (ccp), which gives rise to cubic unit cells (the face-centered cube), and hexagonal close-packing (hcp), which gives hexagonal unit cells.

The placement of atoms that produces each of these arrangements can be described in terms of their layering. Within each layer, the most efficient packing occurs when the particles are staggered with respect to one another, leaving small triangular spaces between the particles. The second layer is placed on top of the first, in the depressions between the particles of the first layer. Similarly, the third layer lies in the depressions of the second. Thus, if the particles of the third layer are also directly over depressions of the first layer, the layering pattern is ABCABC, in which the fourth layer is a repeat of the first. This is called cubic close-packing, and results in the face-centered cubic unit cell. Such close-packed structures are common in metals, including calcium, strontium, aluminum, rhodium, iridium, nickel, palladium, platinum, copper, silver, and gold. If the third layer particles are also directly over particles of the first, the repeating layer pattern is ABAB. This is called hexagonal close-packing, and produces the hexagonal unit cell. This packing arrangement also is observed for many metals, including beryllium, magnesium, scandium, yttrium, lanthanum, titanium, zirconium, hafnium, technetium, rhenium, rubidium, osmium, cobalt, zinc, and cadmium.

Other layering patterns in which the particles are not close-packed occur frequently. For example, particles within a layer might not be staggered with respect to one another. Instead, if they align themselves as in a square grid, the spaces between the particles also will be square. The second layer fits in the depressions of the first; the third layer lies in depressions of the second, and over particles of the first layer, giving the layering pattern (ABAB) with a space-filling efficiency of 68%. The resulting unit cell is a body-centered cube. Metals which have this arrangement of atoms include the alkali metals, barium, vanadium, niobium, tantalum, chromium, molybdenum, tungsten, manganese, and iron.