G. Mobus et O. Kienzle, Probability calculus for quantitative HREM. Part I: Monte-Carlo and point cloud techniques, ULTRAMICROS, 85(4), 2000, pp. 183-198
A new approach to a central question of modern high-resolution electron mic
roscopy (HREM) is presented: How precisely can we locate atom positions in
crystal defects using computer-controlled structure retrieval algorithms? T
he purpose is not just to give error bars for the determined atomic column
positions, but to derive estimations for the continuous probability functio
ns. In the first part of this two-part paper, we present techniques which a
nalyse point clouds of fluctuating fit-results for atom coordinates. The po
int clouds are obtained in a first approach from multiple input images diff
ering in noise, commonly known as Monte-Carlo error estimation. Furthermore
, we exploit the response obtained during a global optimisation-based refin
ement process for which all the trial structures are evaluated resulting in
a second type of point cloud. In comparison, the Monte-Carlo-type techniqu
e turns out to be the most robust one. Using examples from current research
on SrTiO3-bicrystals and Cu-Al2O3 interfaces, we study two largely differe
nt crystallographic and statistical situations. (C) 2000 Elsevier Science B
.V. All rights reserved.