A
chemical substance in the solid state may form
crystals in which the
atoms,
molecules, or
ions are arranged in space according to one of a small finite number of possible
crystal systems (lattice types), each with fairly well defined set of lattice parameters that are characteristic of the substance. These parameters typically depend on the
temperature,
pressure (or, more generally, the local state of
mechanical stress within the crystal),
electric and
magnetic fields, and its
isotopic composition. The lattice is usually distorted near impurities,
crystal defects, and the crystal's surface. Parameter values quoted in manuals should specify those environment variables, and are usually averages affected by measurement errors. Depending on the crystal system, some or all of the lengths may be equal, and some of the angles may have fixed values. In those systems, only some of the six parameters need to be specified. For example, in the
cubic system, all of the lengths are equal and all the angles are 90°, so only the
a length needs to be given. This is the case of
diamond, which has at 300
K. Similarly, in
hexagonal system, the
a and
b constants are equal, and the angles are 60°, 90°, and 90°, so the geometry is determined by the
a and
c constants alone. The lattice parameters of a crystalline substance can be determined using techniques such as
X-ray diffraction or with an
atomic force microscope. They can be used as a natural length standard of nanometer range. In the
epitaxial growth of a crystal layer over a substrate of different composition, the lattice parameters must be matched in order to reduce strain and crystal defects. == Volume ==