C-centered orthorhombic lattice 2026-10-20
A Bravais lattice with three perpendicular conventional axes and lattice points at and . A translation by half a diagonal of an face preserves the complete crystal motif; apparent centering of unlabelled molecular centers alone is insufficient.
Past exam of the materials science course of the University of Cambridge 2016 Paper 1 1 a i Solution 2026-10-20
This is a C-centered orthorhombic lattice. The translation takes each A molecule to another A molecule and each B molecule to another B molecule. Thus the conventional cell has two lattice points.
A two-molecule crystal motif can be chosen as A at and B at . Attaching that same motif to both C-centered lattice points produces all four molecules, hence eight iodine atoms per conventional cell.
The centers alone appear face-centered, but exchanges A and B orientations. It is not a translation symmetry of the oriented molecular solid. An F-centered assignment would discard essential motif information.
Past exam of the materials science course of the University of Cambridge 2018 Paper 1 1 a Solution 2026-10-20
A Bravais lattice is a set of equivalent points generated by integer combinations of three independent translation vectors. A crystal motif is the arrangement of atoms attached identically to every lattice point. Together they specify the periodic crystal structure: lattice translations repeat the motif without changing its internal arrangement.
A unit cell is a region whose translations tile the structure. A primitive unit cell contains one lattice point after sharing boundary points with neighboring cells. A conventional cell can contain more than one lattice point to display the crystal's symmetry with simple axes and angles; for example, a conventional face-centered cube has four lattice points but a less visually symmetric primitive cell has one.
Rotational symmetry compatible with a periodic three-dimensional lattice has order or , as expressed by the crystallographic restriction theorem. A crystallographic fivefold axis is excluded from an ordinary periodic crystal. This statement concerns exact lattice symmetry; it does not exclude local fivefold atomic arrangements or nonperiodic ordered structures.