International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 3.7, pp. 315-316

Section 3.7.4.2. Features particularly useful for powder crystallography

J. A. Kaduka,b,c*

aDepartment of Chemistry, Illinois Institute of Technology, 3101 South Dearborn Street, Chicago, IL 60616, USA,bDepartment of Physics, North Central College, 131 South Loomis Street, Naperville, IL 60540, USA, and cPoly Crystallography Inc., 423 East Chicago Avenue, Naperville, IL 60540, USA
Correspondence e-mail: kaduk@polycrystallography.com

3.7.4.2. Features particularly useful for powder crystallography

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A field which is particularly useful for identifying structural analogues is the ANX formula. This formula is generated according to the following rules:

  • (i) H+ is not taken into account, even if coordinates are available.

  • (ii) The coordinates of all sites of all other atoms must be determined.

  • (iii) Different atom types on the same positions (for example, in solid solutions) are treated as a single atom type.

  • (iv) An exception: if cations and anions occupy the same site they will not be treated as one atom type.

  • (v) All sites occupied by the same atom type are combined, unless the oxidation state is different. Thus, Fe2+(Fe3+)2O4 yields AB2X4, while (Fe2.667+)3O4 yields A3X4.

  • (vi) For each atom type, the multiplicities are multiplied by the site-occupancy factors and the products are added. The sums are rounded and divided by the greatest common divisor.

  • (vii) If the rounded sum equals zero, all sums are multiplied by a common factor so that the smallest sum equals unity, so no element will be omitted.

  • (viii) Cations are assigned the symbols A–M, neutral atoms are assigned N–R and anions are assigned X, Y, Z and S–W.

  • (ix) The symbols are sorted alphabetically and the characters are assigned according to ascending indices: AB2X4, not A2BX4.

  • (x) All ANX symbols with more than four cation symbols, three neutral atom symbols or three anion symbols are deleted.

The utility of these symbols is illustrated by the fact that the three garnets Mg3Al2(SiO4)3, Ca3(Al1.34Fe0.66)Si3O12 and (Mg2.7Fe0.3)(Al1.7Cr0.3)Si3O12 all yield ANX = A2B3C3X12.

Reduced-cell searches [see International Tables for Crystallography Volume A, Section 3.1.3[link] (de Wolff, 2016[link])] are particularly easy to carry out in the `Cell' section of Advanced Searches. Once a unit cell has been determined by indexing the powder pattern, it is always worth carrying out a reduced-cell search to identify potential isostructural compounds using lattice-matching techniques. It is often wise to first carry out such a search using relatively narrow tolerances (say, 1% on the lattice parameters) and then carry out additional searches using larger tolerances. Systematic searches of the subcells and supercells of a given unit cell, as could be carried out using the NBS*LATTICE program with the NIST Crystal Data Identification File (Mighell & Himes, 1986[link]; Mighell, 2003[link]), are not yet implemented.

Under the `Crystal Chemistry' section it is possible to search for crystal structures that contain bonds between particular atom types in a distance range. Such searches are particularly valuable in assessing the chemical reasonableness of crystal structures, such as the study by Sidey (2013[link]) on the shortest BIII—O bonds.

Because the ICDD Powder Diffraction File `01' entries contain the ICSD collection code in the comments, searching for the collection code of a hit in a search/match is particularly easy in the `DB Information' section. In this way, the relevant ICSD entry can be located without any ambiguity and the best structure for the problem at hand can be used to start the Rietveld refinement.

References

Mighell, A. D. (2003). The normalized reduced form and cell mathematical tools for lattice analysis – symmetry and similarity. J. Res. Natl Inst. Stand. Technol. 108, 447–452.Google Scholar
Mighell, A. D. & Himes, V. L. (1986). Compound identification and characterization using lattice-formula matching techniques. Acta Cryst. A42, 101–105.Google Scholar
Sidey, V. (2013). On the shortest BIII—O bonds. Acta Cryst. B69, 86–89.Google Scholar
Wolff, P. M. de (2016). International Tables for Crystallography, Vol. A, 6th ed., edited by M. I. Aroyo, pp. 709–714. Chichester: Wiley.Google Scholar








































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