**1-1.lattice parameter**:

The lattice constant, or lattice parameter, refers to the constant distance between unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice constants, referred to as a, b, and c. However, in the special case of cubic crystal structures, all of the constants are equal and we only refer to a. Similarly, in hexagonal crystal structures, the a andb constants are equal, and we only refer to the a and c constants. A group of lattice constants could be referred to as lattice parameters. However, the full set of lattice parameters consist of the three lattice constants and the three angles between them.

For example the lattice constant for a common carbon diamond is a = 3.57Å at 300 K. The structure is equilateral although its actual shape can not be determined from only the lattice constant. Furthermore, in real applications, typically the average lattice constant is given. As lattice constants have the dimension of length, their SI unit is the meter. Lattice constants are typically on the order of several angstroms (i.e. tenths of a nanometre). Lattice constants can be determined using techniques such as X-ray diffraction or with an atomic force microscope.

In epitaxial growth, the lattice constant is a measure of the structural compatibility between different materials. Lattice constant matching is important for the growth of thin layers of materials on other materials; when the constants differ, strains are introduced into the layer, which prevents epitaxial growth of thicker layers without defects.