Carbon crystal structures, lattice parameters

See Herzog, H.J. Crystal structure, lattice parameters and liquidus-solidus curve of the SiGe system, in Properties of Silicon Germanium and SiGe.Carbon. Erich Kasper and Klara Lyutovich, eds., London, INSPEC, 2000, p. 45. 

Crystal Structure and Lattice Parameters (nm) Orthorhombic, a = 0.283, b = 0.554, c = 1.1470 Cr3C2 is an intermediate carbide having carbon chains with C-C distance approximately 0.165 nm running through distorted metal lattice where the Cr atoms are at the corners of trigonal prisms and the carbon atoms in the center of the prisms.i li" ... 

Like NiO, CoO and FeO are characterized by the same crystal structure as MgO and have comparable lattice parameters, and, hence, can form CoO/MgO and FeO/MgO solid solutions. Therefore, it was expected that CoO/MgO and FeO/MgO would inhibit carbon deposition and metal sintering, just as Ni/MgO does, resulting in high stability (171). 

Linear carbon chains with variable crystal lattice parameters could be obtained. The carbon film is composed of a mixture of spb and sp-hybridized carbon atoms. Therefore we are dealing with carbynoid structures. Carbynoid crystals of 1 pm size were obtained. 

Reports on the crystal structure of selenourea rqrpeared in the early 1960s, which gave preliminary accounts of the unit-cell dimensions of selenourea [5]a,b] and information about the carbon-selenium double bond in the crystal structure of /V-phenyl-AT-benzoylselenourea [57c]. More accurate determination of the lattice parameters and atomic positions of selenourea was carried out at room temperature and at 173 K by Rutherford and Calvo in 1969 [52]. All of these reports assigned the structure to one of the enantiomorphous trigonal space groups P3 and P32 with Z=27, which differs from an earlier electron diffraction study based on space group Pnma with a = 6.48, b = 8.75, and c = 7.04 A and Z=4 [55a] that can be compared with the room-temperature phase of thiourea. The lattice parameters of selenourea firom these studies are listed in Table 6. 

The YbCo.gj carbide reported by Haschke and Eick (1970a) was not verified to exist in the ytterbium-carbon system by other workers. Its crystal structure was not determined by these authors. In contrast, the two forms of the YCq.s+z compound, the face-centered cubic Fe4N-type form and the rhombohedral CdCl-type form, have been well determined. Their lattice parameters are in good agreement with the systematic variation between those of the other heavy lanthanide hypocarbides, although the composition range for this diphase mixture was not determined. The only information about this material was provided by Spedding et al. (1958). They reported that a carbon-rich YbsC compound exists. 

Recently, Hoffmann et al. (1989) reported a series of the ErgRhjCij-type compounds present in the R-Rh-C system. These compounds RgRhjCjj (R=Y, Gd-Tm) are thermodynamically stable at 900°C and have a monoclinic structure, space group C2/m, with Z — 2 formula units per unit cell. The lattice parameters of these compounds have been measured by single-crystal X-ray diffraction. The structure contains a finite chain-like centrosymmetric polyanion [Rh5Ci2] with two Rh-Rh bonds (2.708 A) and six pairs of carbon atoms. The shortest distances between adjacent Rh5Ci2 clusters are the Rh-C distances of 2.94 A and the Rh-Rh distances of 3.27 A, and thus the Rh5Ci2 units may be treated as isolated from each other. This structure is characterized by three different kinds of C2 pairs. The C-C bond distances of 1.27, 1.32 and 1.33 A are between those of a triple bond (1.20 A) and a double bond (1.34 A) in hydrocarbons, and are the shortest found so far in ternary carbides of the rare earth metals with transition metals. 

The crystal structure of La202C2 determined from three-dimensional X-ray diffraction on a twin crystal is of monoclinic symmetry, space group C/2m (Seiver and Eick 1976). The lattice parameters are a = 7.069(8) A, b = 3.985(4) A, c = 7.310(9) A and p = 95.70(6)° the calculated density is 5.41 gcm". In this structure, the lanthanum atom has four oxygen and four carbon atoms situated in a distorted bicapped trigonal prismatic arrangement. Interatomic La-O distances range from 2.392(8) to 2.823(9) A and La-C distances from 2.86(1) to 3.11(1) A. The carbon atoms are present as C2 units with an interatomic C-C distance of 1.21(3) A. Oxygen atoms are tetrahedrally coordinated, as in the sesquioxide. 

Substitutions in the HA structure are possible. Substitutions for Ca, PO4, and OH groups result in changes in the lattice parameter as well as changes in some of the properties of the crystal, such as solubility. If the OH" groups in HA are replaced by F" the anions are closer to the neighboring Ca " ions. This substitution helps to further stabilize the structure and is proposed as one of the reasons that fluoridation helps reduce tooth decay as shown by the study of the incorporation of F into HA and its effect on solubility. Biological apatites, which are the mineral phases of bone, enamel, and dentin, are usually referred to as HA. Actually, they differ from pme HA in stoichiometry, composition, and crystallinity, as well as in other physical and mechanical properties, as shown in Table 35.7. Biological apatites are usually Ca deficient and are always carbonate substituted (COs) " for (P04). For... 

The carbides and nitrides of group 4-6 transition metals belong to the so-called Hagg compovmds (6). Hagg formulated a set of empirical rules for the crystal structures of interstitial solid solutions of transition metals. According to the rules, when the radius ratio r = rx/fmetai is less than 0.59, small atoms (such as carbon and nitrogen) occupy the interstitial sites of the simple crystal structures formed by the metal atoms. For the carbides and nitrides of Ti, V, Nb, Mo, and W, which have been extensively applied as catalysts, the radius ratios fall in between 0.491 r lr i) and 0.576 (rc/ry). They are indeed Hagg compounds (6). Table 1 summarizes the crystal structures and lattice parameters of carbides of Mo, W, V, Nb, and Ti. 

The structure of the space unit cell of deoxycholic acid (Fig. lOA) crystallized from acetone (79) has the following dimensions a = 25.8 A, b = 13.5 A, and c = 7.2 A. Since the lattice parameters did not change appreciably with various choleic acids of long-chain aliphatic substances such as alcohols, fatty acids, and esters (Fig. lOB), it was deduced that there were holes in the crystalline lattice of deoxycholic acids that could accommodate aliphatic compounds. The so-called coordination numbers or molecular ratios of the deoxycholic acid and its guest molecule are related to the number of carbons in the aliphatic chain of the guest compounds and therefore the chain length of the molecule. 

Fluoroapatite (F-apatite), chloroapatite (Cl-apatite) and carbonate apatite (CO -apatite) are derived from hydroxyapatite. In F-apatite and Cl-apatite, the F and Cl ions assume the position of the OH ions. When F and Cl ions are inserted in the Ca triangle, their position in relation to the OH in hydroxyapatite changes (Fig. 1-23). As a result, the lattice parameters change compared with those of hydroxyapatite (Young and Elliot, 1966). When F ions are inserted in place of OH ions, the -axis is reduced and the c-axis remains constant (F = apatite a = 9.382 A, c = 6.880 A). The insertion of Cl ions enlarges the unit cell (Cl apatite a = 9.515 A, c = 6.858 A). The crystal structure of fluoroapatite is shown in Appendix 19. 

Both crystal structures are monoclinic with two monomers or monomer units of different orientation per unit cell (Fig. 9.3 sketches only one of these two.). The chemical bond between two carbons of nearest neighbour diacetylenes (1,4-addition) results in the linear polymer chain and the small change in the lattice parameter along the b-axis prevents the destruction of the macroscopic single crystal during the topochemical reaction. Several surfaces of diacetylene crystals have been studied by atomic force microscopy (AFM) in order to investigate both, the single crystal surface structure and solid state reactions at the surface [129, 131]. 

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