Structures of binary compounds

The relative sizes of the atoms or ions. The radius ratio (usually r+/r but sometimes r /r+, where r+ is the radius of the cation and r is the radius of the anion) is generally used to assess the relative sizes of ions. Small cations often fit in the tetrahedral or octahedral holes of a close-packed anion lattice. Somewhat larger cations can fit in the octahedral holes, bnt not in tetrahedral holes, of the same lattice. Still larger cations force a change in structure (as described in Section 7.1.4). 

The relative numbers of cations and anions. For example, a formula of M2X will not allow a close-packed anion lattice with cations exclusively in each octahedral hole because the number of cations is twice the number of octahedral holes The structure must have the cations in tetrahedral holes (this is theoretically possible because the ratio of tetrahedral holes to each anion is 2 1) or have an anion lattice that is not close-packed. 

The structures described in this section are generic, named for the most common compound with the structure. The focus in this section is on structnres where the constituent ions exhibit a high degree of ionic bonding. The effect of a relatively high covalent component on the structure of crystals is not considered here. The electronic structure of the ions, and the resulting ionic and covalent contributions to their bonds, must be considered to fully rationalize crystal structures. 

FIGURE 7.6 The Structure of Diamond, (a) Subdivision of the unit cell, with atoms in alternating smaller cubes. 

Sodium chloride O Sodium (or chloride) 9 Chloride (or sodium) (a) 

FIGURE 7-7 Sodium Chloride and Cesium Chloride Unit Cells. 

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Appendix, ICSD Codes, D and N Parameters of the Structures Used 43 Table A3 Structures of binary compounds. 

Villars, P., Mathis, K. and Hulliger, F. (1989) Environment classification and structural stability maps. In The Structures of Binary Compounds, eds. de Boer, F. and Pettifor, D. (North-Holland, Amsterdam), Vol. 2, p. 1. 

Hafner, J. (1989) The Structures of Binary Compounds. Cohesion and Structure, ed. 

Several families of ternary antimonides crystallize with structure types derived from those of binary types by an insertion of third component in the structure of binary compounds, i.e., LaFe4Pi2 from C0AS3, Y3Au3Sb4 from TI14P3, UsCrSbs fromMnsSis. 

On the other hand, Lopez et al.104 used molecular-dynamics simulations in systematically studying Cura xAux clusters with n = 13 or 14, and x ranging from 0 to n. Due to the small size of the clusters (13 or 14 atoms) it was possible to obtain a detailed description of the structure of all stoichiometries. The interatomic interactions were described with an approximate Gupta-like potential. They found that for n = 13 all clusters have an icosahedral-like structure. On the other hand, for n = 14 the pure Au and Cu clusters have different structures, and in this case it was found that all clusters, except for the pure Au one, prefers the same type of structure. This finding indicates that it is not trivial to guess the structure of binary compounds from those of the pure system. 

Pettifor DG (1986) The structures of binary compounds phenomenological structure maps. J Phys 019 285-313... 

As we have seen from the previous part, the structures of the stannides are connected in some way with the structures of other groups of compounds. Analysis shows, that the structures of the ternary stannides can be divided into three main groups. The first group contains the stannides obtained by an insertion of the third component in the structure of binary compounds. These types are presented in table 6. 

Structures of ternary stannides with the structures of binary compounds or their superstructures... 

Carbon forms a huge number of binary compounds with hydrogen. Three major categories of these compounds are alkanes, alkenes, and alkynes. An alkane has only single bonds between carbon atoms. The four simplest alkanes, which are shown in Figure 3-7. are methane, ethane, propane, and butane. An alkene, on the other hand, contains one or more double bonds between carbons, and an alkyne has one or more triple bonds between carbon atoms. Figure shows the structures of ethylene, the simplest alkene, and acetylene, the simplest alkyne. 

Solid solutions are very common among structurally related compounds. Just as metallic elements of similar structure and atomic properties form alloys, certain chemical compounds can be combined to produce derivative solid solutions, which may permit realization of properties not found in either of the precursors. The combinations of binary compounds with common anion or common cation element, such as the isovalent alloys of IV-VI, III-V, II-VI, or I-VII members, are of considerable scientific and technological interest as their solid-state properties (e.g., electric and optical such as type of conductivity, current carrier density, band gap) modulate regularly over a wide range through variations in composition. A general descriptive scheme for such alloys is as follows [41]. 

A similar procedure was also used by Villars to find atomic property expressions which could be used to distinguish the crystal structures of intermetallic compounds 182 sets of tabulated physical properties and calculated atomic properties were considered. These were combined, for binary phases, according to the modulus sums, differences and ratios. The best separations were obtained by using three-dimensional maps, which, for a binary AVB,., x [Pg.309]

These problems have of course different weights for the different metals. The high reactivity of the elements on the left-side of the Periodic Table is well-known. On this subject, relevant examples based on rare earth metals and their alloys and compounds are given in a paper by Gschneidner (1993) Metals, alloys and compounds high purities do make a difference The influence of impurity atoms, especially the interstitial elements, on some of the properties of pure rare earth metals and the stabilization of non-equilibrium structures of the metals are there discussed. The effects of impurities on intermetallic and non-metallic R compounds are also considered, including the composition and structure of line compounds, the nominal vs. true composition of a sample and/or of an intermediate phase, the stabilization of non-existent binary phases which correspond to real new ternary phases, etc. A few examples taken from the above-mentioned paper and reported here are especially relevant. They may be useful to highlight typical problems met in preparative intermetallic chemistry. 

Fergusson et al. were the first to report the existence of binary compounds with a general formula Se Sg in these melts. They carried out an extensive investigation by X-ray powder diffraction and by absorption spectroscopy in the infrared, visible, and ultraviolet regions over the whole composition range of molten mixtures of sulfur and selenium cooled down to 20 °C. They also examined phases obtained by recrystallization of the cooled melts from carbon disulfide. All phases were isomorphic with one of the allotropes of Sg and SCg indicating that the structures also consist of cyclic eight-membered molecules ... 

Earlier X-ray powder diffraction studies by de Haan and Visser provided similar results. These authors investigated the impact of the selenium content on the structure type of the crystals and deduced the existence of eight-memteed ring molecules but were unable to decide whether the crystals consisted of binary compounds of sulfur and selenium or simply of Seg and Sg. 

During this period, various aspects of Miedema s methods for predicting the heat of formation of binary compounds were assembled and eventually published in book form (de Boer et al. 1988). This included the application of the technique to predict the thermodynamic behaviour of some ternary compounds. Whilst only applicable to a restricted set of crystallographic structures, this was nevertheless a significant development, as a common objection to the CALPHAD approach was that the existence of ternary compounds could never be predicted solely from binary data. 

In this context the binary fluoride NbFa.s should be referred to also. In the structure of this compound isolated polynuclear groups NbeFia are 3-dimensionally infinitely linked by additional fluorines (296). This is the only exeimple of a fluoride so far, in which discrete Men-clusters have been observed, indicative of metal-metal bonding 279, 295). 

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