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Incommensurate Crystallography$

Sander van Smaalen

Print publication date: 2007

Print ISBN-13: 9780198570820

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198570820.001.0001

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Incommensurate Crystallography
Oxford University Press

A.1 Data collection and data processing (Chapter 6)

Measurements of the intensities of Bragg reflections of incommensurate crystals requires measurements at setting angles corresponding to scattering vectors that cannot be indexed by three integers. The computer program DIF4 by K. Eichhorn (University of Karlsruhe) computes setting angles of reflections from indexings with up to six integers. Other, commercial diffractometer software sometimes allows the collection of data at a series of scattering vectors (h 1 h 2 h 3), where real-valued indices hi can be given. The latter can easily be calculated from the four-integer indexing by ad hoc software [eqn (2.5)]. Data processing is possible with HELENA (Spek, 1997) and REDUCE (Eichhorn, 1995).

The measurement with area detectors involves identical procedures for periodic and aperiodic crystals. Software for indexing and integration of measured images need to account for the particular positions of satellite reflections. Several commercially available software packages incorporate options for integration of data from aperiodic crystals, including EVAL by Bruker, CRYSALIS by Oxford Diffraction and X-AREA by STOE.

Refinements of the components of modulation wave vectors on area-detector data can be performed with NADA (Schönleber et al., 2001). Automatic indexing and refinement of lattice parameters and modulation wave vectors is possible with BAYINDEX (Pilz et al., 2002).

A.2 Structure refinements (Chapter 7)

The first general-purpose computer program for the refinement of modulated crystal structures against single-crystal X-ray diffraction data was REMOS by A. Yamamoto. REMOS82 was initially released in 1982 (Yamamoto, 1982c). The present version, REMOS95.1_3, is available from A. Yamamoto, Advanced Materials Laboratory, Tsukuba, 305-0044, Japan, or by download from the web site http://quasi.nims.go.jp/yamamoto/. It allows the refinement of modulated and composite crystals against either single-crystal or powder diffraction data.

The second, widely used computer program for structure refinement is JANA, originally written by Petricek et al. (1985). The present version, JANA2000, can be obtained from V. Petricek, Department of Crystallography of the Institute of Physics of the Academy of Sciences of the Czech republic, Cukrovarnicka 10, 162 53 Praha, Czech Republic, or by download from the web site http://www-xray.fzu.cz/jana/Jana2000/jana.html. A new major release, JANA2006, is currently under development. JANA2000 allows the refinement (p.239) of modulated and composite crystals against single-crystal or powder diffraction data. Important feature of JANA2000 is the plethora of possibilities for special functions and restrictions between parameters, including rigid-body modulations, non-crystallographic site symmetries, block-wave and saw-tooth-shaped modulation functions, anharmonic temperature parameters, and direct refinement of the parameters of the TLS formalism.

Other computer programs for structure refinements are of less general scope than the two programs introduced above, or support for them has been discontinued. They include

  1. 1. SIMREF Version 2.8 for Rietveld refinement against powder diffraction data, written by U. Amann, H. Ritter, J. Ihringer, J.K. Maichle and W. Prandl, Institut für Angewandte Physik der Universität Tübingen Auf der Morgenstelle 10, D-72070 Tübingen, Germany. SIMREF is available from http://www.uni-tuebingen.de/uni/pki/simref/simref.html.

  2. 2. XND for Rietveld refinement of incommensurately modulated structures against X-ray powder diffraction data. Written by J.–F. Bérar, Laboratoire de Cristallographie – CNRS, BP 166, 38042 Grenoble CEDEX 09, France; Email: berar@polycnrs-gre.fr.

  3. 3. MSR for the refinement of incommensurately modulated structures was developed around 1985 by W. A. Paciorek. More recent versions include efficient algorithms for computing the modulated atomic scattering factor (Paciorek and Uszynski, 1987; Paciorek and Chapuis, 1992; Paciorek and Chapuis, 1994).

  4. 4. A computer program for refinement of structures of crystals with one-dimensional, displacive modulations by Hogervorst (1986).

  5. 5. MINREF by Elsenhans (1990), especially developed for the refinement of incommensurate magnetic structures against neutron powder diffraction data.

A.3 Fourier maps and the maximum entropy method (Chapter 8)

Fourier maps and difference Fourier maps can be computed with the refinement programs REMOS95.1 and JANA2000, then producing maps based on observed structure factor amplitudes and calculated structure factors from the refinement (Section A.2).

Electron density maps according to the maximum entropy method (MEM) can be computed with BAYMEM, written by van Smaalen et al. (2003). BAYMEM can be obtained from S. van Smaalen, Laboratory of Crystallography, University of Bayreuth, D-95440 Bayreuth, Germany, or from the web site http://www.crystal.uni-bayreuth.de/BayMEM.html. BAYMEM allows MEM maps to be calculated for periodic and aperiodic crystals of arbitrary dimensions. It includes modules for the generation of PRIOR densities, for the extraction of modulation functions from electron density maps, and for the analysis of density maps according to Bader's Atoms in Molecules theory.

(p.240) A.4 Structure solution (Chapter 10)

A computer program, DIMS, for the application of direct methods to diffraction data of incommensurately modulated structures and composite crystals has been written by Fu and Fan (1994). DIMS can be obtained from H.–F. Fan at the web site http://cryst.iphy.ac.cn/VEC/Tutorials/DIMS/main.html. The most recent version has been described in the newsletter of the Commission on Crystallographic Computing of the IUCr (Fan, 2005).

Charge-flipping in superspace can be performed with the computer programs SUPERFLIP (Palatinus, 2004) and BAYMEM (Section A.3). SUPERFLIP can be obtained from L. Palatinus or from the web site http://superspace.epfl.ch/superflip/.

A.5 Structural analysis and plotting

t-Plots of many quantities can be made with the refinement programs JANA2000 and REMOS95 (Section A.2), and by MISTEK, available from S. van Smaalen.

Basic structures are usually plotted by one of many plotting programs for atomic structures of periodic crystals. The most recent version of DRAWXTL allows basic structures to be plotted of all subsystems of a composite crystal in a single plot (Finger et al., 2007). (p.241) (p.242) (p.243) (p.244) (p.245) (p.246) (p.247) (p.248)