The Measurement of Low-Order Structure Factors and Thickness

Abstract

In this chapter we discuss the accurate measurement of structure-factor amplitudes and specimen thickness by CBED. We assume that a simple, inorganic, small unit-cell crystal of known structure is to be analyzed. Then the refinement of a small number of low-order “bonding” reflections will allow a detailed three-dimensional map of the crystal charge density to be made. These low-order structure factors are refined together with other diffraction parameters such as the specimen thickness, the incident-beam directions, and the absorption coefficients. In general, these parameters are treated on an equal footing with the structure factors. The refined structure factors include the effect of Debye—Waller factors, so they are temperature dependent (see Section 3.1). (The refinement of lattice parameters is treated in Sections 5.4 and 3.6.) Earlier reviews of the subject can be found in Cowley (1967, 1969), Goodman (1978), and Spence and Carpenter (1986). A recent review of structure factor measurement by electron diffraction can be found in Spence (1992c). Sections 4.5 and 4.6 discuss the significance of the measured charge density and of the zero-order Fourier coefficient of potential.