Research PapersNo Access

INTERACTIONS FROM SELF-COORDINATION NUMBERS – A PHYSICAL RELATION WITHOUT FORMULA

J. HAUCK

Institut für Festkörperforschung, Forschungszentrum Jülich D–52425 Jülich, Germany

Search for more papers by this author

and

K. MIKA

Institut für Festkörperforschung, Forschungszentrum Jülich D–52425 Jülich, Germany

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0217979206034315Cited by:1 (Source: Crossref)

Abstract

A large number of homogeneous particles A with different A–A interactions like carbon atoms in diamond, CO₃ ions in CaCO₃, S₆ molecules in rhombic sulphur, colloid or micelle particles are ordered in such a way that the bulk structure can be characterized by the self-coordination numbers T_i, i =1-3 of nearest, second and third neighbors. There are about 500 sets with increased T_i values (aristotypes) and about 500 sets with reduced T_i values, which are obtained from characteristic lattice complexes. The number k=1,2,3, etc. of the (T₁ T₂ T₃) aristotype is added to the Wyckoff letters of standardized structures like 167-b9a9 or 148-a4 for the Ca(CO₃) or (S₆) structures with the centers of (CO₃) or (S₆) groups. Two or more particles A, B, etc. can belong to the same aristotype like Na and Cl atoms in NaCl or Li, Ag and Sb atoms in Li₂AgSb. All possible structures of an aristotype are within certain limits of T_i values in a T_i, i = 1-3 coordinate system, the structure map. The location of A, B, etc. positions on structure maps can be related with repulsive or attractive interactions at high or low T₂ values. The plate- or rod-like habit of single crystals can frequently be related to layered or rod-like packings (T₁ T₂ T₃) of the constituents.

Keywords:

PACS: 61.50.Ah, 61.66.-f, 61.50.Lt

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

M. N. Rudden and J. Wilson , Elements of Solid State Physics ( John Wiley , Chichester , 1992 ) . Google Scholar
N. Hunt, R. Jardine and P. Bartlett, Phys. Rev. E 62, 900 (2000), DOI: 10.1103/PhysRevE.62.900. Crossref, Web of Science, ADS, Google Scholar
F. C. Brown , The Physics of Solids ( Benjamin , New York , 1967 ) . Google Scholar
G. Burns , Solid State Physics ( Academic Press , Orlando , 1985 ) . Google Scholar
C. P. Royall, M. E. Leunissen and A. van Blaaderen, J. Phys.: Condens. Matter 15, 3581 (2003), DOI: 10.1088/0953-8984/15/48/017. Crossref, Web of Science, Google Scholar
S. M. Allen and E. L. Thomas , The Structure of Materials ( John Wiley , New York , 1999 ) . Google Scholar
J. M. MacLaren et al. , Surface Crystallographic Information Service, A Handbook of Surface Structures ( Reidel , Dordrecht , 1988 ) . Google Scholar
J. Hauck and K. Mika, Int. J. Mod. Phys. B 18, 115 (2004), DOI: 10.1142/S0217979204023684. Link, Web of Science, ADS, Google Scholar
J. Hauck and K. Mika, Int. J. Mod. Phys. B 17, 2053 (2003), DOI: 10.1142/S021797920301803X. Link, Web of Science, Google Scholar
W. Fischer and E. Koch, Intern. Tables for Crystallogr. A, ed. Th. Hahn (Reidel, Dordrecht, 1987) pp. 825–854. Google Scholar
J. Hauck and K. Mika, Cryst. Res. Technol. 40, 917 (2005), DOI: 10.1002/crat.200410457. Crossref, Web of Science, Google Scholar
W. Fischer, Z. Kristallogr. 138, 129 (1973). Crossref, Web of Science, Google Scholar
J. Hauck and K. Mika, Int. J. Mod. Phys. B 18, 1627 (2004), DOI: 10.1142/S0217979204024859. Link, Web of Science, ADS, Google Scholar
E. Parthé et al. , Gmelin Handbook of Inorganic and Organometallic Chemistry 4 ( Springer-Verlag , Berlin , 1993 ) . Google Scholar
N. G. Parsonage and L. A. K. Staveley , Disorder in Crystals ( Clarendon Press , Oxford , 1978 ) . Google Scholar
A. I. Kitaigorodskii , Organic Chemical Crystallography ( Consultants Bureau , New York , 1961 ) . Google Scholar
A. Yethiraj and A. van Blaaderen, Nature 421, 513 (2003), DOI: 10.1038/nature01328. Crossref, Web of Science, ADS, Google Scholar
S. Yoshimura and S. Hachisu, Progr. Colloid & Polymer Sci. 68, 59 (1983). Crossref, Google Scholar
J. M. Seddon, Ber. Bunsenges. Phys. Chem. 100, 380 (1996). Crossref, Web of Science, Google Scholar
J. Hauck and K. Mika, Prog. Solid State Chem. 28, 1 (2000), DOI: 10.1016/S0079-6786(00)00005-4. Crossref, Web of Science, Google Scholar
G. Bergerhoffet al., Acta Cryst. B 55, 147 (1999), DOI: 10.1107/S0108768198010969. Crossref, Web of Science, Google Scholar
H. G. von Schnering and R. Nesper, Angew. Chem. 99, 1097 (1987). Crossref, Google Scholar
S. Anderssonet al., Chem. Rev. 88, 221 (1988), DOI: 10.1021/cr00083a011. Crossref, Web of Science, Google Scholar
M. Lee, B. K. Cho and W. C. Zin, Chem. Rev. 101, 3869 (2001), DOI: 10.1021/cr0001131. Crossref, Web of Science, Google Scholar
A. Mueller and D. F. O'Brien, Chem. Rev. 102, 727 (2002), DOI: 10.1021/cr000071g. Crossref, Web of Science, Google Scholar
H. Follner, Fortschr. Miner. 66, 37 (1988). Google Scholar
S. Matthes , Mineralogie. Eine Einführung in die spezielle Mineralogie, Petrologie und Lagerstättenkunde ( Springer-Verlag , Berlin , 2001 ) . Google Scholar
C. Klein and C. S. Hurlbut , Manual of Mineralogy ( John Wiley , New York , 1985 ) . Google Scholar
E. Koch and W. Fischer, Intern. Tables for Cryst. C, eds. A. J. C. Wilson and E. Prince (Kluwer, Dordrecht, 1999) pp. 738–743. Google Scholar
F. Ducastelle , Cohesion and Structures 3 , eds. F. R. de Boer and D. G. Pettifor ( North-Holland , Amsterdam , 1991 ) . Google Scholar
M. Kaburagi, J. Phys. Soc. Jap. 44, 54 (1978), DOI: 10.1143/JPSJ.44.54. Crossref, Web of Science, ADS, Google Scholar
J. Hauck and K. Mika, Progr. Solid State Chem. 31, 149 (2003), DOI: 10.1016/j.progsolidstchem.2003.09.001. Crossref, Web of Science, Google Scholar