Infinite chain

The common structural element in the crystal lattice of fluoroaluminates is the hexafluoroaluminate octahedron, AIF. The differing stmctural features of the fluoroaluminates confer distinct physical properties to the species as compared to aluminum trifluoride. For example, in A1F. all corners are shared and the crystal becomes a giant molecule of very high melting point (13). In KAIF, all four equatorial atoms of each octahedron are shared and a layer lattice results. When the ratio of fluorine to aluminum is 6, as in cryoHte, Na AlF, the AIFp ions are separate and bound in position by the balancing metal ions. Fluorine atoms may be shared between octahedrons. When opposite corners of each octahedron are shared with a corner of each neighboring octahedron, an infinite chain is formed as, for example, in TI AIF [33897-68-6]. More complex relations exist in chioUte, wherein one-third of the hexafluoroaluminate octahedra share four corners each and two-thirds share only two corners (14). 

At room temperature and atmospheric pressure, 95% of the vapor consists of dimers (13). The properties of the vapor deviate considerably from ideal gas behavior because of the dimeri2ation. In the soHd state, formic acid forms infinite chains consisting of monomers linked by hydrogen bonds (14) ... 

AMMONIUM compounds). Diammonium dimolybdate [27546-07-2] (NH 2 2 7 " ble commercially as the tetrahydrate and prepared from MoO and excess NH in aqueous solution at 100°C, has an infinite chain stmcture based on MoO octahedra. In aqueous solution the behavior of Mo(VI) is extremely pH-dependent (4). Above pH 7 molybdenum(VI) occurs as the tetrahedral oxyanion MoO , but below pH 7 a complex series of concentration-, temperature-, and pH-dependent equiUbria exist. The best known of these equiUbria lead to the formation of the heptamolybdate,... 

The existence of a variety of other polyphosphide anions has been demonstrated. For example, P and P have been identified in LaP2 (72). Infinite chain stmctures for the polyphosphide anion have been reported for compounds such as KP and thallium pentaphosphide [11093-99-5] TIP. Cage anions such as P that include triply linked phosphoms atoms are found in Li P. ... 

Uranium pentafluoride [13775-07-0], UF, has been isolated under different conditions, leading to two different modifications, d and p. The former is a grayish white soHd, which is synthesized from the interaction of UF [7783-81-5] and HBr or by heating UF [10049-14-6] and UF to 80—100°C. The yellowish white P-modification is also obtained by reacting UF and UF, but at higher temperatures (150—200°C). The two different modifications of UF have both been stmcturaHy characterized. The a-form consists of infinite chains of octahedral UF units. The P-form has eight-coordinate uranium atoms with the fluorides in a geometry between dodecahedral and square antiprismatic. 

Bismuth Penta.fIuoride, Bismuth(V) fluoride consists of long white needles that have been shown to have the same stmcture as the body-centered, tetragonal a-polymorph of uranium hexafluoride. The density of the soHd is 5.4 g/mL at 25°C. The soHd consists of infinite chains of trans-bridged BiF polyhedra dimers and trimers are present in the vapor phase (22). Bismuth pentafluoride may be prepared by the fluorination of BiF or... 

The stmcture of kernite consists of parallel infinite chains of the Bion (6) composed of six membered rings (80). The polymeric nature of the anion is consistent with the slow rate of dissolution and crystallisation observed for kernite. 

The primary Cr—O bonded species is cbromium (VT) oxide, CrO, which is better known as chromic acid [1115-74-5], the commercial and common name. This compound also has the aliases chromic trioxide and chromic acid anhydride and shows some similarity to SO. The crystals consist of infinite chains of vertex-shared CrO tetrahedra and are obtained as an orange-red precipitate from the addition of sulfuric acid to the potassium or sodium dichromate(VI). Completely dry CrO is very dark red to red purple, but the compound is deflquescent and even traces of water give the normal mby red color. Cbromium (VT) oxide is a very powerful oxidi2er and contact with oxidi2able organic compounds may cause fires or explosions. 

P. D. Gujrati, Scaling theory of polydispersity, infinite chain and the Flory-Huggins approximation. Phys Rev B 40 5140-5143, 1989. 

Pure NI3 has not been isolated, but the structure of its well-known extremely shock-sensitive adduct with NH3 has been elucidated — a feat of considerable technical virtuosity.Unlike the volatile, soluble, molecular solid NCI3, the involatile, insoluble compound [Nl3.NH3] has a polymeric structure in which tetrahedral NI4 units are comer-linked into infinite chains of -N-I-N-I- (215 and 230 pm) which in turn are linked into sheets by I-I interactions (336 pm) in the c-direction in addition, one I of each NI4 unit is also loosely attached to an NH3 (253 pm) that projects into the space between the sheets of tetra-hedra. The stmcture resembles that of the linked Si04 units in chain metasilicates (p. 349). A further interesting feature is the presence of linear or almost linear N-I-N groupings which suggest the presence of 3-centre, 4-electron bonds (pp. 63, 64) characteristic of polyhalides and xenon halides (pp. 835-8, 897). 

Figure 22.4 Alternative representations of (a) infinite chains of vanadium atoms in VF5, (b) tetrameric structures of NbFs and TaFs, and (c) dimeric structure of MX5 (M = Mb, Ta X = Cl, Br).

More than 90% of the rocks and minerals found in the earth s crust are silicates, which are essentially ionic Typically the anion has a network covalent structure in which Si044-tetrahedra are bonded to one another in one, two, or three dimensions. The structure shown at the left of Figure 9.15 (p. 243), where the anion is a one-dimensional infinite chain, is typical of fibrous minerals such as diopside, CaSi03 - MgSi03. Asbestos has a related structure in which two chains are linked together to form a double strand. 

Silicate lattices. The red circles represent oxygen atoms. The black dot in die center of die red circle represents the Si atom, which is at the center of a tetrahedron. (Left) Diopside has a one-dimensional infinite chain. (Right) A portion of the talc structure, which is composed of infinite sheets. 

According to investigations performed by Pakhomov and Kaidalova [204], the crystal structure of NF NbC consists of infinite chains made up of distorted octahedral ions (NbOF4 ) linked by oxygen atoms. Ammonium cations, NH/, occupy the spaces between the chains, as shown in Fig. 30. The packing of the structural units in the NH4NbOF4 crystal can be described as a CsCl type structure in which CF ions are replaced by Nb02F4 complexes and Cs" ions are replaced by ammonium ions. 

NH4NbOF4 Infinite chains of octahedrons -Nb02F43 MNbOF4 (M=K, Rb, Cs) refers also to a chain-type structure. 

Nevertheless, the system, composed of chain fragments of oxyfluoroniobate complexes, is thermodynamically less stable. Dipole properties of fragments of a certain length are re-orientated so as to be linked into typical infinite chains. There is no doubt that the fragment re-orientation and linking process initiates the partial reduction of niobium to Nb4+ and the oxidation of fluoride to elementary fluorine. The process scheme can be presented as follows ... 

The crystal structure of MsM OF compounds, where M = NH4, K, Rb, is made up of infinite chains of oxyfluoroniobate octahedrons that are similar to MNbOF4 chain-type compounds. Infinite chains are separated by isolated complexes NbFy2, whose structure is similar to that found in the island-type compound K2NbF7. The structure of the M5Nb30Fi8 compounds was described and discussed in Chapter 3.2. Due to the separation of the chains, the displacement of the niobium ion is in the same direction in all chains. The above displacement leads to a spontaneous polarization value that is as high as 4-5 pC/cm2. 

The strongest mode observed near 800 cm 1 is polarized along c and is a totally symmetrical vibration mode (Ai) corresponding to the niobium-oxygen vibrations vs (NbO) of infinite chains (NbOF4 )n running along the c -axis. The mode observed at 615 cm 1 is polarized perpendicular to c and corresponds to the NbF vibrations of the octahedrons of the same chains. The mode at 626 cm 1 is attributed to NbF vibrations of isolated complex ions - NbF 2 . The lines at 377, 390 and 272 cm 1 correspond to deformation modes 8(FNbF) of the two polyhedrons. 

Ag(4,4 -bipy)N03 has a three-dimensional structure with silver ions diagonally coordinated by two bipy ligands (N-Ag-N 173.7°) in extended infinite chains, the chains being cross-linked by Ag-Ag bonds (2.970 A) [45]. 

We now discuss the effects of finite chain length. The difficulties arise from the definition of a bulk free energy term, when the very nature of the chains constrains the crystal thickness to be finite. There are two different approaches to this problem the first to be considered is due to Hoffman et al. [31] and is a simple modification of the infinite chain case, but is somewhat lacking in theoretical justification the second, due to Buckley and Kovacs [23], aims to correct this deficiency and suggests that the interpretation of experimental data given by Hoffman s approach is misleading. 

Hoffman assumes that aj, has the same interpretation as for infinite chain length, that is the surface tension of the fold surface. However, as pointed out above, effects of a non-folded surface are already included in AH[ Tm(0, p)] and AS[ 7, (0, p)], and at best a e could be regarded as the contribution to the surface tension from just the folds, but more realistically as a parameter which is related to the surface tension but which also varies with the thickness of the lamella, that is as the proportion of the number of folds to free ends in the surface changes. 

A different approach [23, 32] considers AF in Eq. (2.2) to consist of a part which must be defined with respect to infinite chain length plus an entropy of localization [33] due to the pairing of chain ends which becomes important in the case of closely stacked lamellar crystals [34]. It amounts to — Kin (Cp) per molecule, where C is a constant related to the flexibility of the chains in the melt, and which arises due to the conformations of the finite chain. Hence ... 

Metal-metal interactions in transition metal complexes containing infinite chains of metal atoms. T. W. Thomas and A. E. Underhill, Chem. Soc. Rev., 1972,1, 99-120 (70). 

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