Cubic crystal system 2026-10-14
The cubic crystal system has cubic point symmetry. Its three cubic Bravais lattices are primitive, body-centered, and face-centered. The body-centered cubic lattice is one member of that classification.
For the cubic crystal system, the Miller indices satisfy
The inverse squared interplanar spacings have ratios approximately . With the lattice constant close to , the appropriate squared-index sums are . Thus the four powder diffraction rings are
The braces collect all symmetry-related lattice planes with the same interplanar spacing. In particular, is forbidden for both a body-centered cubic lattice and a face-centered cubic lattice, but occurs for a primitive cubic lattice. These observations identify the Bravais lattice as primitive cubic lattice, with a multi-atom atomic basis, consistent with a perovskite structure.
Each ring independently gives :
Their average is . Allowing for the rounded measured angles, a suitable final value is
A larger centred unit cell could relabel reflections, but would conflict with the stated approximate lattice constant.