Measurement of low-order structure factors by convergent beam electron diffraction

  • Martin Saunders

Student thesis: Doctoral ThesisPhD


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 [110] 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.

Date of Award1994
Original languageEnglish
Awarding Institution
  • University of Bath

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