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International Union of Crystallography (IUCr)

Commission on Crystallographic Nomenclature

A Commission Report

Acta Cryst. (1996). A52,770 - 781.

ATOMIC DISPLACEMENT PARAMETER NOMENCLATURE
Report of a Subcommittee on Atomic Displacement Parameter Nomenclature

By K.N. TRUEBLOOD (Chairman), Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095, USA,
H.-B. BÜRGI, Laboratorium für chemische und mineralogische Kristallographie, Universität Bern, Freiestrasse 3, CH-3012 Bern, Switzerland,
H. BURZLAFF, Institut für Kristallographie, Universitüt, Bismarckstrasse 10, D-91054 Erlangen, Germany,
J.D. DUNITZ, Laboratorium für organische Chemie, ETH Zentrum, CH-8092 Zürich, Switzerland,
C.M. GRAMACCIOLI, Dipartimento di Scienze della Terra, via Botticelli 23, I-20133 Milano,Italy,
H.H. SCHULZ, Institut für Kristallographie und Mineralogie, Universität, Theresienstrasse 41, D-80333 München, Germany,
U. SHMUELI, School of Chemistry, Tel Aviv University, 69 978 Tel Aviv, Israel, and
S.C. ABRAHAMS (ex officio, IUCr Commission on Crystallographic Nomenclature), Physics Department, Southern Oregon State College, Ashland, OR 97520, USA.

(Received 12 June 1995; accepted 2 May 1996)

Abstract

Modern x-ray and neutron diffraction techniques can give precise parameters that describe dynamic or static displacements of atoms in crystals. However, confusing and inconsistent terms and symbols for these quantities occur in the crystallographic literature. This report discusses various forms of these quantities, derived from probability density functions and based on Bragg diffraction data, both when the Gaussian approximation is appropriate and when it is not. The focus is especially on individual atomic anisotropic displacement parameters (ADPs), which may represent atomic motion and possible static displacive disorder.

The first of the four sections gives background information, including definitions. The second concerns the kinds of parameters describing atomic displacements that have most often been used in crystal structure analysis and hence are most commonly found in the literature on the subject. It includes a discussion of graphical representations of the Gaussian mean-square displacement matrix. The third section considers the expressions used when the Gaussian approximation is not adequate. The final section gives recommendations for symbols and nomenclature.

Table of Contents

• 1. Introduction
  • 1.1 Organization of this Report
  • 1.2 Background
  • 1.3 Notation for position and displacement vectors
  • 1.4 The structure factor and atomic displacements
  • 1.5 Comments about terminology
• 2. Displacement Parameters Based on the Gaussian Approximation
  • 2.1 Anisotropic displacement parameters
    • 2.1.1 Relationships between the anisotropic displacement parameters
    • 2.1.2 Construction of Cartesian mean-square displacement tensors
  • 2.2 Equivalent isotropic displacement parameters
  • 2.3 Graphical representations of the Gaussian mean-square displacement matrix
    • 2.3.1 Ellipsoids of constant probability
    • 2.3.2 Mean-square displacement surface
• 3. Beyond the Gaussian Approximation
• 4. Recommendations
• References
• About this document ...

(If you wish to access the continuous version of the Report, please click here. )

Established 15 February 1994 by the IUCr Commission on Crystallographic Nomenclature, with all members appointed by 7 June 1994, under the ground rules outlined in Acta Cryst. (1979). A35, 1072. H. Burzlaff resigned from the Subcommittee 2 January 1995. Final Report accepted 20 December 1995 by the IUCr Commission on Crystallographic Nomenclature.

We are especially indebted to Verner Schomaker for his critical reading and counsel on many drafts of this Report, to Hans Boysen for his special help with Section 3, and to Richard Marsh, Emily Maverick and Tullio Pilati for their advice.