Measurement of low-order structure factors by Convergent Beam Electron Diffraction.
This thesis describes the development and testing of a new technique for the
measurement of structure factors based on the matching of theoretical calculations
with experimental, energy-filtered zone-axis Convergent Beam Electron
Diffraction (CBED) patterns. The sum-of-squares difference between a set of
experimental diffraction intensities and a theoretical calculation is minimised by
varying a set of low-order structure factors until a best fit is obtained.
The basic theory required for the simulation of zone-axis CBED patterns is given.
Additional theory is developed specifically for the pattern matching method in
order to improve the efficiency of the matching calculation. This includes the
development of analytic expressions for the gradient of the sum-of-squares with
respect to each of the fitting parameters, and the addition of beams to the pattern
calculation by second-order perturbation theory.
The effects of random and systematic errors are considered by fitting to simulated
`noisy' data. A wide range of potential systematic error effects are investigated
and limits are found for errors in the accelerating voltage, Debye-Waller factor
and lattice parameter which reduce systematic errors to acceptable levels. These
tests also investigate the sensitivity of the method to structure factor variations,
which gives an indication of how many structure factors can be measured.
Finally, the method is applied to the measurement of low-order structure factors
from experimental Si  zone-axis patterns. The results are compared to the
best X-ray Pendellösung measurements available, and the bonding charge densities
obtained from both the zone-axis and X-ray measurements are constructed