Homeotypic structures

Two structures are homeotypic if they are similar, but fail to fulfill the aforementioned conditions for isotypism because of different symmetry, because corresponding atomic positions are occupied by several different kinds of atoms (substitution derivatives) or because the geometric conditions differ (different axes ratios, angles, or atomic coordinates). An example of substitution derivatives is C (diamond)-ZnS (zinc blende)-Cu3SbS4 (famatinite). The most appropriate method to work out the relations between homeotypic structures takes advantage of their symmetry relations (cf. Chapter 18). 

For each main and subclass several homeotypic structure types may exist (Tables 5b, 6,7b). A structure type may belong to different families if different parts of the structure are considered to be the important Bauverband . 

ABSTRACT. Based on the nomenclature report of the lUCr (1990) the concepts of isopointal, isoconfigurational, Isotypic and homeotypic structures are described and illustrated by several examples. The notation proposed In this report for the crystal - chemical formulae is also developed, including the symbologies for close packings which are not closest, and for the condensation process of the structural units. 

In a report presented by Uma-de-Faria, Hellner, Liebau, Makovicky, Parth6 (1990) (henceforth denoted 1990 Report) a detailed analysis of this problem is made, and the following hierarchy of terms is proposed, based on the degree of stmctural similarity Isopointal, Isoconfigurational, crystal chemically Isotypic, and homeotypic structures ... 

Apart from these three main categories of related structures, there are other parental structures which are interesting to consider, the so-called homeotypic structures. They correspond to the relaxation of some of the isotypism conditions, such as ... 

These concepts and their historical development were summarized in a contribution by Laves (1944), translated and reported by Hellner (1979), in which conditions for calling crystal structures equal (isotypism), similar (homeotypism) or different (heterotypism) are discussed and exemplified. 

Ryhlewska, U., and Warzajtis, B. Interplay between dipolar, stacking and hydrogen-bond interactions in the crystal structures of unsymmetrically substituted esters, amides and nitriles of (R,R)-0,0 -dibenzoyltartaric acid, Acta Cryst., Sec. B. 2001, B57, 415-427. Isostructuralism in a series of methyl ester/methylamide derivatives of (R,R)-0,0 -dibenzoyl tartaric acid inclusion properties and guest-dependent homeotypism of the crystals of (2R,3R)-0,0 -dibenzoyltartaric acid diamide, Acta Cryst., Sec. B. 2002,B58, 265-271. 

The second polymorph, polymorph B, can be considered as homeotypic with CaCuP (AlB2-type) structure. The structure consists of undulating hexagonal sheets. Five such nets interpenetrate to file the void space in a single net. see Venkataraman, D. Lee, S. Moore, J. S. Zhang, P. Hirsch, K. A. Gardner, G. B. Covey, A. C. Prentice, C. L. Submitted for publication to Chemistry of Materials. 

For the Classification of Minerals , crystal-structure determinations improved the definitions of mineral species and varieties, assisted in the development of the concept of crystal structure types, helped to establish isotypic series and homeotypic and heterotypic groups, and pointed to the recognition of much broader crystallochemical relationships. The X-ray method appreciably simplified the generally unique characterization of a mineral species and led to a reduction in varieties and the discreditation of many minerals accepted up to that time, thereby eliminating countless superfluous mineral names . 

In this edition, the world of minerals is divided by chemical features into ten classes, each of which is subdivided, on chemical-structural principles, into divisions, subdivisions, groups of isotypic and homeotypic minerals, or individual minerals with unique structure types groups with two or more mineral names comprise minerals with similar structure or composition. The classification system and alphanumeric coding scheme used in this 9 edition of the Strunz Mineralogical Tables were presented at the 1994 IMA meeting in Pisa. They permit the insertion of thousands of new minerals in the future without changing the basic classification framework. 

Homeotypy. Homeotypic substances are those that have similar crystal structures, but with different crystallographic space groups and/or chemical compositions. 

This paper will give a survey of such an attempt for nearly all cubic structure types and their grouping in families main- and subdasses and homeotypic types it wfll further demonstrate the extension to crystal stmctures with non-cubic symmetry. 

Differences with respect to cell content (the number of atoms per unit cell). Crystals A and B are considered as homeotypic even then, if only parts of the Bau-verb3nde in A and B are equal from a topological point of view. These parts should be composed of those bondings, however, which are believed to be the most important for the structure types under consideration. 

Differences with respect to a replacement of points by polyhedra If a point of a Bauverband is replaced by a coordination polyhedron, this structure will also be called homeotypic with the original structure. 

Hellner, E. (1965). Descriptive Symbols for Crystal-Structure Types and Homeotypes Based on Lattice Complexes. Acta Ciyst. 19,703 - 712. lUPAC (1990). "Nomenclature of Inorganic Chemistry". Oxford Blackwell. 

BertheviUe B, Herrmannsdorfer T, Yvon K (2001) Structure data for K2MgH4 and Rb2CaH4 and comparison with hydride and fluoride analogues. J Alloys Compd 325 L13-L16 Hines J, Cambon O, Astier R et al (2004) Crystal structures of a-quartz homeotypes boron phosphate and boron arsenate structure-property relationships. Z Krist 219 32-37 Feldmann C, Jansen M (1995) Zurkristallchemischen Ahnlichkeit von Aurid- und Halogenid-lonen. Z anorg allgem Chem 621 1907-1912... 

Schubert (1989) points out that radius ratio considerations in LaFj would suggest coordination near LaFg, and the LaFj structure should therefore be homeotypic with CaFj. He then relates the LaFj structure to that of CaFj, compares the displacements to those of related structures, e.g., CaFj-YFj superstructures, and discusses crystal energetics. LaFj crystals were examined by DSC from 100 -500 K an anomaly which occurs in the Cp versus T curve is related to a phase transition in which the fluoride sublattice fuses (Aliev and Fershtat 1984). This phenomenon appears related to the high ionic conductivity of the tysonite-type fluoride phases. 

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