Obtaining and Indexing Parallel-Beam Diffraction Patterns

Abstract

The core strength of TEM is that you can obtain both a DP and an image from the same part of your specimen (not to mention various spectra). To obtain the crystallographic data, a method for interpreting and indexing the DP is essential and this aspect is the theme for the next four chapters. We'll start in this chapter by considering classic selected-area diffraction (SAD) patterns (SADPs) and how to index them, but also introduce other related, if less widely used, parallel-beam diffraction methods. You can proceed to index your pattern in several ways, depending on how much information you already know about your specimen. We will begin the chapter by considering the experimental approach with the aim of being able to identify shortcuts whenever possible. The experienced microscopist will readily identify many patterns just by looking at them, but will still need to index new patterns or to identify unfamiliar ones. The fastest and most efficient experimental approach may take advantage of several concepts covered in the preceding two chapters and the following three. Today, sophisticated computer software is available which takes much of the tedium out of the indexing process. Most DPs in a TEM are single-crystal (spot) patterns because the area from which we can routinely obtain SADPs (< 1 mm) is smaller than typical grain sizes of most engineering materials. However, with increased emphasis on nanocrystalline materials (grain size < 0.1 mm), it is more usual for the DPs to contain contributions from many crystals and so ring/textured SADPs are increasingly common. (We'll cover convergent-beam (CBED) and other forms of micro/nanodiffraction patterns, which can come from regions < 10 nm, in Chapters 20 and 21.) Using the DP, we can identify the crystal (which we often already know) and its orientation (which we probably don't) with respect to both the beam and to any adjacent crystals. The positions of the allowed hkl reflections are characteristic of the crystal system. Indexing associates each spot or ring in the DP with a plane (hkl), or set of planes {hkl}, in the crystal. From the indexing of the spots, you can deduce the orientation of the crystal in terms of the zone axis [UVW] in which the indexed planes lie. If you want to know the orientation relationship between two crystals, you need to know more than one [UVW] for each crystal and, as we'll show, it is the determination of orientation relationships between different phases or differently oriented crystals that is the most useful information to come out of DP indexing. Orientation determination in the TEM is so important that we devote a complete chapter to the topic in the companion text. Now, computer control of both DP formation and DP indexing is very much the norm, but if you don't understand the principles, you shouldn't believe the computer output (GIGO). So we deliberately confine our discussion of computer-assisted indexing to the end of this chapter. BEAM DIRECTION It is convention to define [UVW] as the beam direction. This direction is normal to the plane of the DP and anti-parallel to the electron beam.