On the unit cell volume expansion in homogeneous series of isotypic structures of “ionic” inorganic compounds
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Egbert Keller
Abstract
Within a “homogeneous” series of (crystal-chemically) isotypic structures one and only one chemical element E of the sum formula is replaced successively by heavier elements of the same group of the periodic table. For corresponding series of “ionic” compounds, a (coarse) “expectation value” ΔVth for the unit cell volume expansion following the replacement of E(i) by E(j) (with i<j=row numbers in the periodic table) can be calculated by using the empirical formula ΔVth=56.5 (zE ΔρE(i) E(j)) – 0.80 (zE ΔρE(i) E(j))2, where zE is the number of atoms E per unit cell and ΔρE(i) E(j) is the linear statistical size (= radius) difference for the two elements E(i) and E(j). Two hundred and twenty-eight different series have contributed to the statistical evaluation of this formula. Series for which E are elements of low valence have been excluded a priori from the calculations if the residual atoms of higher valence by themselves form an infinite framework, as it was suspected, that in structures of this kind the “natural” volume expansion caused by the E(i) → E(j) size increase is hampered by the rigidity of this framework. Application of the above formula to structures of this kind clearly supports this suspicion only, if the framework is of dimensionality three. The results derived from all other investigated structures are qualitatively compatible with the “volume increments rule” published in the 1930s. This suggests that they should be applicable also to isotypic series of crystal structures defined in a less restricted manner.
Acknowledgements
The author thanks Dr. S. Rühl of the FIZ Karlsruhe, Germany, for providing him with a “light” version of the ICSD in ASCII format. He is also indebted to an anonymous referee for his/her hint regarding Biltz’ “raumchemische” investigations. Financial support by the “Deutsche Forschungsgemeinschaft” regarding the development of FINDIS (KE 793/4-1) is gratefully acknowledged.
References
[1] J. Lima-De-Faria, E. Hellner, F. Liebau, E. Makovicki, E. Parthé, Nomenclature or inorganic structure types. Acta Cryst.1990, A46, 1.10.1107/S0108767389008834Search in Google Scholar
[2] G. Bergerhoff, R. Hundt, R. Sievers, I. D. Brown, The inorganic crystal structure data base. J. Chem. Inf. Comput. Sci.1983, 23, 66.10.1021/ci00038a003Search in Google Scholar
[3] FIZ Karlsruhe, Inorganic Crystal Structure Database (ICSD), 2016, http://icsdweb.fiz-karlsruhe.de.Search in Google Scholar
[4] R. Allmann, R. Hinek, The introduction of structure types into the Inorganic Crystal structure Database ICSD. Acta Cryst.2007, A63, 412.10.1107/S0108767307038081Search in Google Scholar PubMed PubMed Central
[5] E. Keller, V. Krämer, Experimental versus expected halide-ion size differences; structural changes in three series of isotypic bismuth chalcogenide halides. Acta Cryst.2006, B62, 417.10.1107/S0108768106009359Search in Google Scholar PubMed
[6] E. Keller, C. Röhr, Structural changes within and between the two isotypic series ABiO2 (A=Na, K, Rb, Cs) and ASbO2 (A=K, Rb, Cs). Z. Kristallogr.2008, 223, 431.10.1524/zkri.2008.0045Search in Google Scholar
[7] P. Schultz, E. Keller, Strong positive and negative deviations from Vegard’s rule: X-ray powder investigations of the three quasi-binary phase systems BiSX1−xYx(X, Y=Cl, Br, I). Acta Cryst.2014, B70, 372.10.1107/S2052520614000766Search in Google Scholar PubMed
[8] E. Keller, Extraktion homogener isotyper Strukturserien aus der ICSD. Z. Kristallogr. Suppl.2009, 29, 24.Search in Google Scholar
[9] S. Rühl, FIZ Karlsruhe, Germany, 2013, personal communication.Search in Google Scholar
[10] E. Keller, V. Krämer, ‘Ionic’ size differences from bond-valence parameters and from ionic radii. Acta Cryst.2006, B62, 411.10.1107/S0108768106009335Search in Google Scholar PubMed
[11] E. Keller, SCHAKAL 99. Universität Freiburg, Germany, 2004.Search in Google Scholar
[12] Origin Lab Corporation, Origin, version 7.0303. Northampton, MA, USA, 2002.Search in Google Scholar
[13] W. Biltz, Raumchemie der festen Stoffe. L. Voss, Leipzig, 1934.10.1002/cber.19350680738Search in Google Scholar
[14] W. Klemm, H.-G. v. Schnering, Die molaren Volumina von Metall-Phosphiden. Z. Anorg. Allg. Chem. 1982, 491, 9.10.1002/zaac.19824910103Search in Google Scholar
[15] A. Baranov, M. Kohout, F. R. Wagner, Y. Grin, R. Kniep, W. Bronger, On the volume chemistry of solid compounds: the legacy of Wilhelm Biltz, Z. Anorg. Allg. Chem.2008, 634, 2747.10.1002/zaac.200800331Search in Google Scholar
[16] S. Adams, softBV. Universität Göttingen, Germany, 2004, http://www.softbv.net.Search in Google Scholar
[17] I. D. Brown, Chemical and steric constraints in inorganic solids. Acta Cryst.1992, B48, 553.10.1107/S0108768192002453Search in Google Scholar
Supplemental Material:
The online version of this article (DOI: 10.1515/zkri-2016-0005) offers supplementary material, available to authorized users.
©2016 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Graphical Synopsis
- Inorganic Crystal Structures
- On the unit cell volume expansion in homogeneous series of isotypic structures of “ionic” inorganic compounds
- Organic and Metalorganic Crystal Structures
- Syntheses and structures of two [Au(I)PPh3]-complexes with 2-aceneoxazolethiolates as ligands
- Three variants of novel Co(II) complex with NSAID mefenamic acid and N,N′-donor ligand neocuproine
- Invariom modeling of disordered structures: case studies on a dipeptide, an amino acid, and cefaclor, a cephalosporin antibiotic
- Mono urotropine adducts of some binary zinc xanthates and dithiocarbamates: solid-state molecular structures and supramolecular self-assembly
- Letter
- The Kepler tiling as the oldest complex surface structure in history: X-ray structure analysis of a two-dimensional oxide quasicrystal approximant
