title: Lattice parameters from direct-space images at two tilts.
abstract: Lattices in three dimensions are oft studied from the "reciprocal space" perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes. Such data can come from electron-phase (or less easily Z contrast images) taken at two tilts, provided that one image shows two non-parallel lattice periodicities, and the other shows a periodicity not coplanar with the first two. We outline here protocols for measuring the 3D parameters of cubic lattice types in this way. For randomly oriented nano-crystals with cell side greater than twice the continuous transfer limit, orthogonal +/-15 degrees and +/-10 degrees tilt ranges might allow one to measure 3D parameters of all such lattice types in a specimen from only two well-chosen images. The strategy is illustrated by measuring the lattice parameters of a 10nm WC(1-x) crystal in a plasma-enhanced chemical-vapor deposited thin film.
authors.affiliation: Physics and Astronomy and Center for Molecular Electronics, University of Missouri-StL (63121), USA.
authors.forename: W
authors.initials: W
authors.lastname: Qin
authors.forename: P
authors.initials: P
authors.lastname: Fraundorf
mesh_terms: D000465:Algorithms; D003460:Crystallization / Q000379:methods; D007091:Image Processing, Computer-Assisted / Q000379:methods; D008854:Microscopy, Electron / Q000379:methods*; D012107:Research Design / Q000706:statistics & numerical data*