Atomic arrangements in crystalline solids can be described by a network of lines called a
space lattice. Each space lattice can be described by specifying the atom positions in a repeating unit cell. The crystal structure consists of space lattice and motif or basis. Crystalline materials possess long range atomic order such as most metals. But some materials such as many polymers and glasses possess only short range order. Such materials are called semicrystalline or amorphous. There are seven crystal systems based on the geometry of the axial lengths and interaxial angles of the unit cells. These seven systems have a total of 14 sublattices (unit cells) based on the internal arrangements of atomic sites within the unit cells.
In metals the most common crystal structure unit cells are: body-centered cubic
(BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) (which is a dense
variation of the simple hexagonal structure).
Crystal directions in cubic crystals are the vector components of the directions resolved along each of the component axes and reduced to smallest integers. They are indicated as [uvw]. Families of directions are indexed by the direction indices enclosed by
pointed brackets as (uvw). Crystal planes in cubic crystals are indexed by the reciprocals of the axial intercepts of the plane (followed by the elimination of fractions) as (hkl). Cubic crystal planes of a form (family) are indexed with braces as {hkl}. Crystal planes in hexagonal crystals are commonly indexed by four indices h, k, i, and l enclosed in parentheses as (hkil). These indices are the reciprocals of the intercepts of the plane on the a1, a2, a3, and c axes of the hexagonal crystal structure unit cell. Crystal directions in hexagonal crystals are the vector components of the direction resolved along each of the four coordinate axes and reduced to smallest integers as [uvtw].
Using the hard-sphere model for atoms, calculations can be made for the volume, planar,
and linear density of atoms in unit cells. Planes in which atoms are packed as tightly as possible are called close-packed planes, and directions in which atoms are in closest contact are called close-packed directions. Atomic packing factors for different crystal structures can also be determined by assuming the hard-sphere atomic model. Some metals have different crystal structures at different ranges of temperature and pressure, a phenomenon called polymorphism.
Crystal structures of crystalline solids can be determined by using x-ray diffraction analysis techniques. X-rays are diffracted in crystals when the Bragg’s law conditions are satisfied. By using the x-ray diffractometer and the powder method, the crystal structure of many crystalline solids can be determined.
