Lattice parameter

A lattice parameter is a length or angle that specifies a crystal unit cell’s dimensions and shape. The three edge lengths and three interaxial angles together define its geometry.

Unit cell: The repeating structural unit whose translations generate a crystal lattice. Its edges and angles are the geometric quantities specified by lattice parameters.
X-ray crystallography: A method that determines atomic structures by analyzing X-ray diffraction from crystals. Diffraction measurements can be used to refine the unit-cell dimensions and angles.
Thermal expansion: The change in a material’s dimensions as its temperature changes. Temperature-dependent lattice parameters quantify expansion at the atomic scale.
Interplanar spacing: The perpendicular distance between successive parallel planes in a crystal. It is derived from lattice parameters and plane orientation, rather than being a cell parameter itself.
Crystal lattice: An infinite periodic arrangement of points representing translational order in a crystal. Lattice parameters specify the geometry of the repeating translations that generate it.
Bragg's law: The relation connecting X-ray wavelength, crystal-plane spacing, and diffraction angle. Measured diffraction angles reveal plane spacings that constrain lattice parameters.
Vegard's law: An empirical rule that lattice parameters vary approximately linearly with composition in some solid solutions. Cell dimensions can estimate composition when the rule applies.
Atomic coordinates: Fractional or Cartesian positions specifying where atoms lie within a unit cell. Cell parameters set the cell geometry, while coordinates locate atoms inside it.
Bravais lattice: One of fourteen three-dimensional lattice types classified by translational symmetry. Each Bravais type imposes characteristic relationships among unit-cell lengths and angles.
Miller indices: Integer labels for the orientation of planes and directions in a crystal lattice. Plane spacings indexed by Miller indices depend on the unit-cell parameters.

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