Miller indices calculator ( planar spacing distance in bcc system)

Description

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.
In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written (hkℓ), and each index denotes a plane orthogonal to a direction (h, k, ℓ) in the basis of the reciprocal lattice vectors. For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted a); similar to the reciprocal lattice. Thus, in this common case, the Miller indices (hkℓ) simply denote normals/directions in Cartesian coordinates.
The body-centered cubic system (cI) has one lattice point in the center of the unit cell in addition to the eight corner points. It has a net total of 2 lattice points per unit cell (1⁄8 × 8 + 1).
For cubic crystals (in body-centered cubic system) with lattice constant a, the spacing d between adjacent (hkℓ) lattice planes can be calculated by the integers h,k,l and the atomic radius.

Related formulas

Variables

dbccThe spacing distance between adjacent (hkℓ) lattice planes (Å)
rThe atomic radius (Å)
hInteger (dimensionless)
kInteger (dimensionless)
lInteger (dimensionless)