The distance between adjacent points in a crystal lattice.Lattice spacing is the distance between adjacent points in a crystal lattice, the repeating three-dimensional arrangement of atoms, ions, or molecules in a solid. It is a fundamental structural parameter that determines many physical properties of a material, including its density, mechanical strength, and electronic behavior. In a perfect crystal, the lattice spacing is uniform, but real materials often have defects or strains that alter it locally. The spacing is typically on the order of a few angstroms (10^-10 meters), comparable to the size of an atom.
The concept emerged from the early 20th-century work on X-ray crystallography by Max von Laue, William Henry Bragg, and William Lawrence Bragg, who demonstrated that crystals act as diffraction gratings for X-rays. The first measurements of lattice spacing were made in 1912–1913.
In a crystal, atoms are held in equilibrium positions by a balance of attractive and repulsive forces. The lattice spacing is the equilibrium distance that minimizes the total energy of the system. It can be measured directly using X-ray diffraction, where the constructive interference of X-rays scattered by the periodic lattice follows Bragg's law: nλ = 2d sinθ, where d is the lattice spacing. The spacing depends on the atomic species, bonding type, and external conditions like temperature and pressure. For example, heating a crystal increases atomic vibrations and typically expands the lattice, while applying pressure compresses it.
Lattice spacing is used to characterize materials in semiconductor manufacturing, to calibrate X-ray and neutron diffractometers, and to study phase transitions and stress in engineering alloys.
The lattice spacing of silicon, about 0.543 nanometers, is so precisely known that it was used to redefine the kilogram in 2019 via the Avogadro project.
| d | variable | Interplanar spacing of the crystal lattice — lattice spacing metre |
| θ | variable | Glancing angle of incidence (and reflection) relative to the planes — angle radian |
| n | variable | Order of reflection (positive integer) — diffraction order |
| λ | variable | Wavelength of the incident wave — wavelength metre |
| sin | operator | Trigonometric sine of the angle — sine function |
