Jump to ContentJump to Main Navigation
Show Summary Details

Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Boldyreva, Elena V. / Huppertz, Hubert / Petrícek, Václav / Tiekink, E. R. T.

12 Issues per year

IMPACT FACTOR increased in 2015: 2.560
Rank 8 out of 26 in category Cristallography in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 0.827
Source Normalized Impact per Paper (SNIP) 2015: 1.198
Impact per Publication (IPP) 2015: 1.834

See all formats and pricing
Just Accepted


Space filling of crystal structures A contribution to the graphical presentation of geometrical relationships in simple crystal structures

Erwin Parthé
Published Online: 2010-07-28 | DOI: https://doi.org/10.1524/zkri.1961.115.1-2.52


The well-known but little used concept of space filling proves to be an excellent method for presenting geometrical relationships of different simple crystal structures. By introducing the radius ratio into the equation for space filling it is possible to express space filling in a way which is independent of the particular size of the atoms involved, but is instead characteristic for each structure type. The shape of the space-filling curves allows one to distinguish homeotect structure types, structure types with commutative partial structures and structure types with identical partial structures. The features of space-filling curves can be related to the values in Laves' construction formula.

The space-filling concept can be used to find geometrical correlations which have heretofore been obscured by the differing methods used to describe various structures. By comparing space-filling values one can predict the possible pressure structures of compounds. Finally the space-filling diagram offers a convenient way to present geometrical structure arguments. This is demonstrated for the known relations applicable to valence compounds and Hägg compounds. This discussion is complemented by a further demonstration of the use of space-filling diagrams in respect to certain new relations found to be valid for monosilicides and borides.

About the article

Published Online: 2010-07-28

Published in Print: 1961-05-01

Citation Information: Zeitschrift für Kristallographie, ISSN (Online) 0044-2968, ISSN (Print) 1433-7266, DOI: https://doi.org/10.1524/zkri.1961.115.1-2.52. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Jingjing Wei, Nicolas Schaeffer, and Marie-Paule Pileni
Journal of the American Chemical Society, 2015
Zhijie Yang, Jingjing Wei, Pierre Bonville, and Marie-Paule Pileni
Journal of the American Chemical Society, 2015, Volume 137, Number 13, Page 4487
Zhijie Yang, Jingjing Wei, and Marie-Paule Pileni
Chemistry of Materials, 2015, Volume 27, Number 6, Page 2152
Nabiha T Elias and Toby S Hudson
Journal of Physics: Conference Series, 2012, Volume 402, Page 012005
M. J. Murray and J. V. Sanders
Philosophical Magazine A, 1980, Volume 42, Number 6, Page 721
K Schubert
Journal of the Less Common Metals, 1989, Volume 154, Number 1, Page 39
A.N. Alcaraz, R.S. Duhau, J.R. Fernández, Peter Harrowell, and D.B. Miracle
Journal of Non-Crystalline Solids, 2008, Volume 354, Number 27, Page 3171
A. Zaoui, M. Certier, M. Ferhat, W. Sekkal, O. Pagès, and H. Aourag
Computational Materials Science, 2000, Volume 17, Number 2-4, Page 400
A Zaoui
Materials Chemistry and Physics, 2003, Volume 77, Number 2, Page 310
H. Blank
Journal of Alloys and Compounds, 1998, Volume 268, Number 1-2, Page 180
Dong-Kyun Seo and Roald Hoffmann
Journal of Solid State Chemistry, 1999, Volume 147, Number 1, Page 26
Patrick I. O’Toole and Toby S. Hudson
The Journal of Physical Chemistry C, 2011, Volume 115, Number 39, Page 19037
M.D. Eldridge, P.A. Madden, and D. Frenkel
Molecular Physics, 1993, Volume 79, Number 1, Page 105
Erwin Parthé
Zeitschrift für Kristallographie, 2006, Volume 221, Number 5-7/2006
Paul Podsiadlo, Galyna V. Krylova, Arnaud Demortière, and Elena V. Shevchenko
Journal of Nanoparticle Research, 2011, Volume 13, Number 1, Page 15
X. Cottin and P. A. Monson
The Journal of Chemical Physics, 1995, Volume 102, Number 8, Page 3354
P Bartlett
Journal of Physics: Condensed Matter, 1990, Volume 2, Number 22, Page 4979
H. P. Beck and E. Gladrow
Zeitschrift f�r anorganische und allgemeine Chemie, 1979, Volume 453, Number 1, Page 79
Laura Filion and Marjolein Dijkstra
Physical Review E, 2009, Volume 79, Number 4
A. S. Mikhaylushkin, Toyoto Sato, Stefan Carlson, Sergei I. Simak, and Ulrich Häussermann
Physical Review B, 2008, Volume 77, Number 1
W. Klement, A. Jayaraman, and G. C. Kennedy
Physical Review, 1963, Volume 131, Number 2, Page 632
D. G. Pettifor and R. Podloucky
Physical Review Letters, 1984, Volume 53, Number 11, Page 1080
G. J. Piermarini and C. E. Weir
The Journal of Chemical Physics, 1962, Volume 37, Number 8, Page 1887

Comments (0)

Please log in or register to comment.
Log in