Hexagonal crystal lattice

The structure of SWCNTs is characterized by the concept of chirality, which essentially describes the way the graphene layer is wrapped and is represented by a pair of indices (n, m). The integers n and m denote the number of unit vectors (a a2) along the two directions in the hexagonal crystal lattice of graphene that result in the chiral vector C (Fig. 1.1) ... 

Well-determined experimental values (see text) are in bold. cSymmetry-dictated equivalencies of the elastic coefficients for <5-FI MX (hexagonal crystal lattice) are indicated. 

There are two weak Bragg peaks in this diffraction pattern, which could not be indexed since they do not belong to the hexagonal crystal lattice with the established unit cell. As we will find out later (Chapters 6 and 7), these two peaks manifest the presence of a small amount of an impurity phase - a solid solution of Sn in Ni, which has a face-centered cubic crystal structure with the space group symmetry Fm3m and a = 3.543 A. Only one theoretically possible Bragg peak of the major hexagonal phase (003) is unobserved in this powder diffraction pattern because its intensity is below the limits of detection. 

The electron diffraction pattern shown in Figure 11.1(a) corresponds to the hexagonal crystal lattice with the lattice parameter varying from 0.490... 

The image provides evidence for the hexagonal crystal lattice of carbon atoms, which are seen on the tops of carbon chains. The crystal lattice parameter a was found to be equal to 0.486 nm. The result is in good agreement with the parameter of the hexagonal crystal lattice obtained by AFM and TEM (0.490 0.002 nm). 

According to empirical evidence, the Lennard-Jones potential (11.26) describes the interaction between molecules well. The Lennard-Jones potential does not depend on a bonding direction, therefore the molecular solids tend to have the largest possible number of neighbors. SoUd molecular crystals often have the face-centered cubic lattice or close hexagonal crystal lattice. 

Ice can crystallize forming 12 different structures. At atmospheric pressure the freezing water transforms into ice termed Ih that has a hexagonal crystal lattice. The Ic ice with the cubic crystal lattice is formed at low temperatures, that is at 143 K (-130 ° C). Phases of ice other than the Ih phases are produced by the application of high pressures. 

The structure of usual ice Ih is shown in Figure 15.4a. The X-ray investigation has revealed that the oxygen atoms form hexagonal crystal lattice similar to that of wurtzite ZnS. 

Figure 15.4 The crystal structure of ice. (a) Hexagonal crystal lattice of Ih ice the large circles are the oxygen atoms, the small circles are the hydrogen atoms, (b) A layer of the ice...

The most common apatite used in medicine and dentistry is hydroxyapatite (HA), a material with a hexagonal crystal lattice an ideal chemical formula, i.e., Ca,o(P04) (OH)2 ideal weight percents of 39.9 percent Ca, 18.5 percent P, and 3.38 percent OH and an ideal calcium-phosphate ratio of 1.67 (Fig. 13.5). The crystal structure and crystallization behavior of HA is strongly dependent on the substitutional nature of the ionic species. 

The only thermodynamically stable crystallographic modification of alumina is a-Al203, or comndum. Corundum has a hexagonal crystal lattice with the cell... 

Phosphorus pentoxide exists in at least four polymorphic forms as well as a glass. The common variety of laboratory and commerce already discussed (mp = 420 C, p = 2.30 g/cc) consists of large cage molecules (4.41a) arranged in a hexagonal crystal lattice with only weak van der Waals-type forces between the cages. This was sometimes known as the H form or Form T of the oxide. 

Martensitic Structures. If the cooling rates from the P field are siiffLdently rapid, an acicular or lath-like martensite is formed. In alloys with low concentrations of beta-stabilizing elements, the martensite has a distorted hexagonal crystal lattice, similar to that of a, and is referred to as a. Because of the fine lath width, oc is stronger than lamellar a, but not necessarily brittle. The other principal type of martensite (orthorhombic a") occurs upon the quenching of a P phase that contains intermediate concentrations of beta-stabilizing alloy elements (e.g., between 10 and 15 wt% vanadium). The a" martensite has an orthorhombic structure with a very fine, internally twinned microstructure. The orthorhombic a" martensite is mechanically soft. 

A complete understanding of the crystal structure of HA can be acquired from the in-depth knowledge of the spatial orientation or organization of a small number of constituent ions. The unit cell, a basic structural pattern of the constituent ions, of HA is a right rhombic prism that forms a simple hexagonic crystal lattice. The... 

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