Lattice parameters from direct-space images at two tilts

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 nanocrystals with cell side greater than twice the continuous transfer limit, orthogonal +/- 15degrees and +/- 10degrees 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 10 nm WC1-x crystal in a plasma-enhanced chemical-vapor deposited thin film. (C) 2002 Elsevier Science B.V. All rights reserved.