Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 5.1, p. 490
doi: 10.1107/97809553602060000595

Chapter 5.1. Introduction

A. J. C. Wilsona

aSt John's College, Cambridge, CB2 1TP, England

A brief overview of Chapters 5.2 to 5.5 on the determination of lattice parameters using various methods is provided.

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[link]) and Peiser, Rooksby & Wilson (1960[link]). The proceedings of the symposium on Accuracy in Powder Diffraction held in Gaithersburg in 1979 (Block & Hubbard, 1980[link]) 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[link]), which contains about twice as many references as Chapter 5.2[link] . A more recent symposium was held in Fremantle in 1987 (CSIRO, 1988[link]); 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[link] where appropriate. A second Gaithersburg conference with the same title (Prince & Stalick, 1992[link]) 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[link] is somewhat more detailed than Chapter 5.2[link] .

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[link] and 5.5[link] .

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[link] . 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[link]; see also Hubbard, 1983[link]).


Block, S. & Hubbard, C. R. (1980). Editors. Accuracy in powder diffraction. Natl Bur. Stand. US Spec. Publ. No. 567.
CSIRO (1988). Papers presented at the International Symposium on X-ray Powder Diffractometry, Fremantle, Australia, 20–23 August 1987. Aust. J. Phys. 41(2), iv, 101–335.
Hubbard, C. R. (1983). New standard reference materials for X-ray powder diffraction. Adv. X-ray Anal. 26, 45–51.
Klug, H. P. & Alexander, L. E. (1974). X-ray diffraction procedures for polycrystalline and amorphous materials, 2nd ed. New York: John Wiley.
Okada, Y. & Tokumaru, Y. (1984). Precise determination of lattice parameter and thermal expansion coefficient of silicon between 300 and 1500 K. J. Appl. Phys. 56, 314–320.
Peiser, H. S., Rooksby, H. P. & Wilson, A. J. C. (1960). Editors. X-ray diffraction by polycrystalline materials, 2nd ed. London: Chapman & Hall.
Prince, E. & Stalick, J. K. (1992). Editors. Accuracy in powder diffraction. II. NIST Spec. Publ. No. 846.
Wilson, A. J. C. (1980). Accuracy in methods of lattice-parameter measurement. Accuracy in powder diffraction. Natl Bur. Stand. US Spec. Publ. No. 567.

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