Chapter 5.1. Introduction

Precise and accurate lattice parameters can be obtained by X-ray methods, both polycrystalline and single crystal. The literature on X-ray lattice-parameter determination is voluminous, involving hundreds of publications. For powder-camera methods most of it is fairly old; summaries with sufficient detail for most purposes will be found in Klug & Alexander (1974) and Peiser, Rooksby & Wilson (1960). The proceedings of the symposium on Accuracy in Powder Diffraction held in Gaithersburg in 1979 (Block & Hubbard, 1980) are particularly valuable as a source of information on developments of all aspects of powder diffraction up to 1979; the publication includes a review of accuracy in lattice-parameter measurements (Wilson, 1980), which contains about twice as many references as Chapter 5.2 . A more recent symposium was held in Fremantle in 1987 (CSIRO, 1988); it contains several papers relevant to accuracy in lattice-parameter determination, as well as papers on other applications of powder diffractometry. References to papers published in these symposia are included in Chapter 5.2 where appropriate. A second Gaithersburg conference with the same title (Prince & Stalick, 1992) covered many aspects of powder diffraction, but not lattice-parameter determination. Unfortunately there seem to be no comparable reviews of single-crystal methods, so that Chapter 5.3 is somewhat more detailed than Chapter 5.2 .

Electron- and neutron-diffraction methods are less used and are (in general) less precise than X-ray methods. They are, however, applicable to some problems for which X-ray methods are inappropriate, and are described in Chapters 5.4 and 5.5 .

Whatever the radiation, perhaps the most important factor in obtaining accurate and precise lattice parameters is careful experimental technique; lack of care can produce larger errors than lack of the latest equipment. Measurements should be repeated to check the precision (reproducibility) of the determination; periodical check measurements of a standard specimen (for example, high-purity silicon) should be undertaken to check the accuracy (absence of, or satisfactory correction for, systematic errors).

The lattice parameter of silicon is discussed in Section 4.2.1 . There is said to be a difference between the lattice parameters of high-quality single-crystal silicon plates and silicon powder samples. The lattice parameter of the powder is reported as 1.5 × 10⁻⁵ nm lower at room temperature (Okada & Tokumaru, 1984; see also Hubbard, 1983).