Determination of lattice parameters from multiple CBED patterns: A statistical approach

This study deals with the uncertainty of the measurement of lattice parameters by CBED using the kinematic approximation. The analysis of a large number of diffraction patterns acquired on a silicon sample at 93 K with a LaB6 TEM without energy filter shows the presence of both the systematic and the random parts of errors. It is established that random errors follow the normal statistical distribution and that the precision quantified by the relative standard deviation is about 3–4×10−4 for lattice parameter measurements made from single pattern. The error sources are analyzed, different ways of enhancement are reviewed, and a new approach is proposed. It is shown that both accuracy and precision can be simply improved by taking into account multiple patterns analysis for the determination of the actual voltage, the single lattice parameter “a” or the complete set of lattice parameters. The precision of about 1.5–2×10−4 can be reached using a minimum of three HOLZ line patterns for the single “a” parameter and about 5×10−4 for the complete set of lattice parameters using six diffraction patterns. The use of multiple patterns also allows overcoming the non-uniqueness of solution linked to the CBED studies.