celleparametre

Celleparametre, or cell parameters, are the geometric values that define the size and shape of a crystal’s unit cell. They consist of three edge lengths, a, b, and c, and the three interaxial angles, alpha, beta, and gamma, between those edges. Together, these six quantities establish the basic framework of the crystal lattice and set the cell’s volume and overall geometry.

The edge lengths are typically expressed in angstroms, while the angles are given in degrees. The particular set of lattice parameters, along with the symmetry described by a space group, determines the crystal system (such as cubic, tetragonal, orthorhombic, monoclinic, triclinic, or rhombohedral) and the distinction between conventional and primitive cells. For example, in a cubic system a = b = c and alpha = beta = gamma = 90 degrees, whereas in a monoclinic system alpha = gamma = 90 degrees and beta is not 90 degrees.

The unit cell volume can be calculated from the parameters using a general formula that involves a, b, c and the cosines of the angles, reflecting how deviations from orthogonality and equality of edges alter space filling. Lattice parameters directly affect crystal packing, density, and many physical properties inferred from structure, such as anisotropic expansion and vibrational behavior.

Determination of cell parameters is a primary outcome of crystallographic experiments, commonly X-ray, neutron, or electron diffraction, followed by refinement against observed diffraction data. Databases of crystal structures routinely catalog the cell parameters and their uncertainties, providing essential inputs for modeling, comparison, and materials design.