Crystal chemical formula

J. Lima-de-Faria, Crystal chemical formulae for inorganic structure types. In Modem Perspectives in Inorganic Crystal Chemistry (E. Parthe, ed.), p. 117. Kluwer, 1992. 

Common crystal-chemical formulae. Unit cell volumes and interatomic distances. In the analysis and description of a structure some calculation may be useful. A few common formulae are collected here. 

In the intermediate case, the ions of divalent metal do not form their own structural layer but are localized in the vicinity of vacant octahedrons [ Al2(OH)6] 2oo using OH" groups of this layer, as well as OH" groups and H2O molecules of the freshly formed third network of layered packing. In this case, interplanar distance is equal to 0.76 nm. Hence, the crystal chemical formula for this compound is [Me(0H)2-H20][Al2(0H) ]. It was obtained in Mg(OH)2 - A1(0H)3 system. The decomposition of such compounds at moderate temperatures (about 800°C) can result in the formation of stoichiometric spinels, which was demonstrated in [15]. 

Table 4. Crystal chemical formulas of theoretically possible complexes [1102(804)4] ...

Thus, polymorphism with the formation of monoclinic and tetragonal modifications is typical for U- and Th-compounds with general formula BM(X04)2 (X = P, As, V). These modifications differ in the packing of the XO4 anions, the orientation of anions around a cation, and the form of the (B,M)On coordination polyhedra (n = 8 or 9). The crystal chemical formula of the BM(P04)2 phosphates and their arsenate and vanadate analogues can be written as B0.5M0.5XO4, owing to the cation disorder. 

The blossoming of new materials has been so rapid that the nomenclature of ordered mesoporous materials is in the wild state in which zeolite nomenclature was thirty years ago. A set of rules for writing a standardized crystal chemical formula for both microporous and mesoporous materials has been established by the Physical Chemistry Division of the International Union for Pure and Applied Chemistry, through its Commission on Colloid and Surface Chemistry including Catalysis [65]. The impact of this nomenclature on the activity of the scientists dealing with mesoporous materials has still to be verified. 

Ideally, the crystal-chemical formula of micas can be written as /(73.xDx)[Z40io] 2... 

Features 1-4 imply that the crystal-chemical formula of a mica cannot be established on the basis of a chemical analysis only (even if it is complete) detailed structural knowledge is necessary. Structurally, the occupancy of a site can be obtained by combining chemical constraints (chemical analysis) with other information like the following. 

In the general crystal chemical formula, WY2 3Z40jo(OH)2, the various positions are occupied as follows ... 

The lUPAC recommendations on the nomenclature of microporous and mesoporous inorganic solids define a rather complex naming for porous materials based on its crystal chemical formula, which for zeolites with a confirmed FTC can be safely reduced to... 

CRYSTAL CHEMICAL FORMULAE FOR INORGANIC STRUCTURE TYPES... 

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. 

Crystal chemical formulae for Inorganic structure types... 

There is a difference between the ciystai chemicai formula of a structure and the symbol of a structure type. The crystal chemical formula of a structure (or structural formula of a compound) corresponds to the chemical formula of the compound with the addition of superscripts, subscripts, parentheses, etc., expressing its various structural characteristics. The symbol of a structure type represents a certain kind of structural arrangement and may be based on various notations such as alphabetic letters, lattice complexes or crystal chemical formulae. 

The crystal chemical formulae should give detailed structural information on the structural units, their constitution and way of packing, the interstitieil atoms and the coordination of the atoms, both interstitial and those contained in the structural units. The nomenclature should be as simple and self-explanatory as possible. 

TABLE 3. Examples of crystal chemical formulae of inorganic structures... 

The dimensionality is the number of dimensions in which a structurai unit has infinite extension, it ia zero for individual atoms and finite groups, and one, two or three for infinite chains, sheets and frameworks, respectiveiy. The corresponding symbols to be used in a crystal chemical formula are... 

Parthe, E. (1980). Crystal Chemical Formulae for Simple Inorganic Crystal Structures. Acta Cryst. B36,1 - 7. 

Problem 1 Considering that in the ZnS wurtzite stnjcture the S atoms form an hexagonal closest packing and the Zn atoms occupy tetrahedral interstices write the corresponding crystal chemical formula. 

Problem 2 Considering that in the AuCu the Au and Cu atoms have simileir radius and both form together a cubic closest packing, write its crystal chemical formula... 

Crystal chemical formulae. To describe the predicted and observed structural features we shall use crystal chemical formulae (Lima-de-Faria, Hellner, Uebau, Makovicky Parth, 1990) where one can denote in codified form... 

For more details on crysfol chemical formulae, peuticulaiy for the meaning of the symbols and the commas, semi-colons and small letters within the superscripted square brackets used in the crystal chemical formulae, see the contribution of Uma-de-Faria in this book. 

The same crystal chemical formula is also valid for wurtzite, a stacking variant of zinc blende. 

ZnP2 VEC = 4, thus N bo = 0 VECa = > l us AA = 2. With AA = 2 one may find an infinite anion chain or a closed anion ring. Simplest crystal chemical formula assuming an infinite chain ... 

The same crystal chemical formula applies also to isoelectronic a-CdP2 and ZnAs2, shown in Rgure 2, all being characterized by infinite anion chains. In a-CdP2 the chains are parallel, in ZnAs2 antiparallel and in red ZnP2 mutually perpendicular. The valence electron mles do not permit the prediction of which type of anion chain will occur in the structure. 

Figure 2 Structures of red ZnP2 and isoelectronic compounds with same crystal chemical formula.

CU2P7 VEC=. 4.111, thus Nnbo = 1/9 VECa = 5.286, thus AA = 19/7. One can formulate two equivalent crystal chemical formulae which differ only in the single non-bonding orbital being either on a P atom with two or on a P atom with three homonuclear bonds ... 

IngS/ The original crystol structure determination (Wadsten, Amberg Berg, 1980) revealed a defect tetrahedral structure which, based on the reported atom coordinations and atom contacts, can be described by the following crystal chemical formula ... 

One notes, that the structural features corresponding to this crystal chemical formula do agree with those observed experimentally. The problem, which remained unsolved for 10 years, h is now finally been settled. A recent reexamination (Deiseroth Pfeifer, 1991) has proven that the compound can not exist without Sn, its true composition being ln4SnS4. 

For simplicity the non-bonding orbitals are often omitted in the crystal chemical formulae or they are shown only for certain kinds of atoms. In the case of a tetrahedral structure the number of non-bonding orbitals assigned to an atom can easily be obtained by noting that the sum of the number of covalent bonds, given within the superscripted square brackets, and the number of non-bonding orbitals must be four. 

For both compounds a tetrahedral structure including all atoms is not possible because VEC < 4. However, both can have tetrahedral anion partial structures, which in the particular case, since for both VEC > 6, should consist of non-cyclic molecules. For Sr3AS4 there exist two possibilities, that is an unbranched chain of 4 As atoms, as shown in the drawing and actually found in Sr3AS4, or a chain of 3 anions which is branched, the anion in the middle of the chain being linked to a forth anion. Note, that in both the crystal chemical formulae and the drawings the non-bonding orbitals have not been indicated, however, it should not be difficult for the reader to verify that the listed values of N i ibo are correct. 

Problem 2 The following binary compounds are characterized by tetrahedral anion partial structures. Find out what the probable features of these charged anion partial structures might be and denote them by means of crystal chemical formulae. 

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