Isotypical structures

The crystal structures of two compounds are isotypic if their atoms are distributed in a like manner and if they have the same symmetry. One of them can be generated from the other if atoms of an element are substituted by atoms of another element without changing their positions in the crystal structure. The absolute values of the lattice dimensions and the interatomic distances may differ, and small variations are permitted for the atomic coordinates. The angles between the crystallographic axes and the relative lattice dimensions (axes ratios) must be similar. Two isotypic structures exhibit a one-to-one relation for all atomic positions and have coincident geometric conditions. If, in addition, the chemical bonding conditions are also similar, then the structures also are crystal-chemical isotypic. 

The ability of two compounds which have isotypic structures to form mixed crystals, i.e. when the exchange process of the atoms can actually be performed continuously, has been termed isomorphism. However, because this term is also used for some other phenomena, it has been recommended that its use be discontinued in this context. 

According to Parthe et al. (1993), a standardization procedure is necessary in the presentation of the relevant data characteristic of a crystal structure (see also Parthe and Gelato 1984). A convenient description of the structure types is then possible using the Wyckoff sequence (the letters of the occupied Wyckoff sites). This allows a finer classification of structure types and offers suggestions not only for recognizing isotypic structures but also possible structural relationships like substitution, formation of vacancy or filled-in structure variants. 

FIGURE 7.1(c) Antibody isotypes. Description of various antibody isotype structures and functions. 

Earlier discussion introduced the concept of using the characteristic truncated octahedral elements of the sodalite framework to explain the molecular architecture of the synthetic zeolites X and Y (see Section. 2.4.3). There are other structural correlations that can be drawn between felspathoids and zeolites, for example, that the cancrinite cage (11-hedron) is a face-sharing element seen in the LTL, ERI, OFF, and EOS frameworks. Furthermore, in nature, salt ion pairs are contained in felspathoid minerals and when these are removed the residual framework exhibits the zeolitic properties of ion exchange and reversible water loss. Other similarities arise in that zeolites can imbibe salt ion pairs, and isotypic structures... 

The powder pattern of Na3AlHfi shows significant similarities to the pattern of cryolite, Na3AlF6 [142, 143]. Rormebro et al. performed structure refinements and confirmed the isotypic structures of sodium hexaaluminate and cryolite [144]. The crystals structure (space group P2i/n) consists of isolated distorted [AlHg] octa-hedra (Figure 5.10). 

At last, the structures containing both zigzag chains and dimers are known. The isotypic structures KHXO4 contain half of the tetrahedra connected to the dimers, whereas the second half forms chains with a geometry shown in Figure 3 [27,50],... 

Phenylantimony(III) dihalides, PhSbX2 (X = Cl, Br, I), have isotypical structures and are all self-assembled via secondary bonding to form two-dimensional sheets, with all the phenyl groups on the same side of the plane [400]. In these compounds Sb interactions between adjacent molecules are also present. 

Isomorphism. VC, VN, and VO have isotypical structures and form solid solutions where nitrogen or oxygen can substitute for carbon over a wide range of homogeneity. These solutions may be considered as V(C,N,0) mixed crystals. VC forms solid solutions with the other monocarbides of Group V and TiC, and with TiN, NbN, and TaN. l... 

Structural type Representative compounds Spatial groups No. of structural units Isotype structures ... 

Each figure shows one projection of the unit cell, the coordination polyhedra of the phosphorus atoms and some structure peculiarities. In the case where atomic parameters of some phosphides are not refined they are given as for their respective prototype or other isotypic structure. STs are considered in order of increasing phosphorus content in the compound. The number near circles indicates the third coordinate of the atom. 

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