Crystal lattice parameters from
direct space images at two tilts

W. Qin and P. Fraundorf
CME Scanned Tip and Electron Image Lab
Department of Physics & Astronomy
University of Missouri-StL, St. Louis MO 63121
arXiv:cond-mat/0001139

Lattices in 3D are oft studied by diffraction and hence a ``reciprocal-space'' perspective. Today, however, location as well as diffraction data can be incorporated into direct space images. From such images the full (or a superset) lattice of a crystal can be inferred from spacing/orientation data on three sets of lattice planes not sharing a common zone. Such data may be obtained from electron-phase or 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 discuss here how to find, and implement, protocols for measuring the 3D parameters of any lattice type in this way. In the case of crystals with cell side greater than twice the continuous transfer limit, we show that orthogonal +/-15 and +/-10 degree tilt ranges may allow one to measure 3D parameters of all cubic nanocrystal varieties 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.

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