Crystal lattice position

Usually the assumption is made that the spectrum of a moleculzir crystal is that of an array of molecules oriented in their crystal lattice positions but without any interaction. This model was tacitly used until it was formally proposed as a model by Ambrose, Elliott, and Temple (37), and independently by Pimentel and McClellan (1635). The... 

Where both cobalt and manganese are present in solution, the coprecipitation of hausmannite and C03O4 might be expected. Sinha et al. (25) found that random substitution of cobalt for Mn " or Mn could occur in such material occurrence of Co in manganese oxide crystal-lattice positions was noted by Bums (4). Apparently there are no thermodynamic data for mixed cobalt + manganese oxides, but the behavior of the ions can probably be represented over a considerable range of solid composition by a solid—solution model based on the equilibrium between the pure end members. Thus... 

RbCl interfacial water is due to a higher RbCl saturation solution concentration. The variation of interfacial water residence time is in excellent agreement with water self-diffusion coefficients. In bulk solutions, water molecules move faster when compared with water molecules at crystal lattice positions and interfacial water molecules as indicated by the short residence times and large diffusion coefficients. For water molecules in bulk KCl solution, the residence time (5.9 ps) and self-diffusion coefficient ( 2.5 X 10 m /sec) are very close to the values for pure water ( 5 ps and 2.5 x 10 mVsec, respectively) (Du and Miller 2007c Koneshan et al. 1998 Koneshan and Rasaiah 2000). 

The point defects, in turn, are classified as native (intrinsic) and substitution defects. The intrinsic point defects appear as a vacancy (the absence of an atom in a crystal lattice position) or as an interstitial defect (the presence of the host crystal atom in an interstitial position). The host crystal atoms can be substituted for another atom of a different chemical species at a regular lattice site or at the interstitial position (impurity center or substitution defect). The point defects can also be classified as neutral and charged relative to the host crystal lattice. The perturbation of a solid by... 

An important problem arising in the description of hydrogenated MX phases is that of the localisation sites of H atoms in the matrix. H-containing carbides and nitrides have been investigated rather extensively by the NMR, X-ray and neutron diffraction methods (see Rundqvist Tellgren and Andersson (1984)). The data obtained show that H atoms occupy crystal lattice positions, which are maximally distant from the p elements and are situated at least 2 A from one another. Different opinions exist in the literature (see, e.g., Shveikin et al (1984), Rundkvist et al... 

Alexandrite, like ruby, contains Cr ions but they are substituted in the lattice of chrysoberyl, BeAl204. The chromium ions occupy two symmetrically non-equivalent positions which would otherwise be occupied by aluminium ions. In this environment the 2 ground state of Cr is broadened, compared with that in ruby, by coupling to vibrations of the crystal lattice. 

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). 

Fig. 6. Radiation damage in graphite showing the induced crystal dimensional strains. Impinging fast neutrons displace carbon atoms from their equilibrium lattice positions, producing an interstitial and vacancy. The coalescence of vacancies causes contraction in the a-direction, whereas interstitials may coalesce to form dislocation loops (essentially new graphite planes) causing c-direction expansion.

In the analysis of crystal growth, one is mainly interested in macroscopic features like crystal morphology and growth rate. Therefore, the time scale in question is rather slower than the time scale of phonon frequencies, and the deviation of atomic positions from the average crystalline lattice position can be neglected. A lattice model gives a sufiicient description for the crystal shapes and growth [3,34,35]. 

Among the molecules, however, business is going on as usual. Iodine dissolves by the detachment of surface layer molecules from the iodine crystals. The rate at which this process occurs is fixed by the stability of the crystal (tending to hold the molecules in the surface layer) and the temperature (the thermal agitation tending to dislodge the molecules from their lattice positions). As the dissolving continues, the concentration of iodine molecules in the solution increases. 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

There are three different substituted benzene compounds with the formula C6H4F2. Assume that the benzene rings pack similarly into their crystal lattices. If the positions of the H and F atoms are statistically disordered in the solid state, which isomer will have the least residual molar entropy ... 

The crystal structure of 2-bromo-l,4-phenylenediyl bis(tran5-4-n-prop-ylcyclohexanoate) was determined by Hartung and Winter [114]. The molecules exhibit pseudo-centrosymmetry in consequence of a special kind of disorder within the crystal lattice. The peculiarity of the crystal structure is the disorder of the molecules with respect to the position of their bromine atoms which occupy the 2- or 5-position of the phenyl ring in a statistical manner. 

Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

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