Jumping crystals

Steiner, T., Hnfried, H. and Saenger, W. (1993) Jumping crystals X-ray structures of the three crystalline phases of ( ) -3,4- Di- O-acetyl-1,2,5,6-tetra- O-benzyl-myo-inositol. Acta Crystallogr. B, 49, 708-718. 

Crottaz, O., Kuhel, F. and Schmid, H. (1997) Jumping crystals of the spinels NiCr204 and CuCr204. /. Mater. Chem., 7, 143-146. 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

Adsorption Kinetics. In zeoHte adsorption processes the adsorbates migrate into the zeoHte crystals. First, transport must occur between crystals contained in a compact or peUet, and second, diffusion must occur within the crystals. Diffusion coefficients are measured by various methods, including the measurement of adsorption rates and the deterniination of jump times as derived from nmr results. Factors affecting kinetics and diffusion include channel geometry and dimensions molecular size, shape, and polarity zeoHte cation distribution and charge temperature adsorbate concentration impurity molecules and crystal-surface defects. 

Diffusion in the bulk of a crystal can occur by two mechanisms. The first is interstitial diffusion. Atoms in all crystals have spaces, or interstices, between them, and small atoms dissolved in the crystal can diffuse around by squeezing between atoms, jumping - when they have enough energy - from one interstice to another (Fig. 18.6). Carbon, a small atom, diffuses through steel in this way in fact C, O, N, B and H diffuse interstitially in most crystals. These small atoms diffuse very quickly. This is reflected in their exceptionally small values of Q/RTm, seen in the last column of Table 18.1. 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

In the use of piezoelectric crystals for stress-pulse measurements, it is convenient to describe the current pulse in terms of the initial current jump i for step loading based on Eq. (4.7) analogous to The piezoelectric cur-... 

The relaxation of a thermodynamic system to an equilibrium configuration can be conveniently described by a master equation [47]. The probability of finding a system in a specific state increases by the incoming jump from adjacent states, and decreases by the outgoing jump from this state to the others. From now on we shall be specific for the lattice-gas model of crystal growth, described in the previous section. At the time t the system will be found in the state. S/ with a probability density t), and its evolution... 

That is, the H-bonded network provides a natural route for rapid transport. This phenomenon of proton jumping thus occurs with little actual movement of the water molecules themselves. Ice has an electrical conductivity close to that of water because such proton jumps also readily occur even when the water molecules are fixed in a crystal lattice. Such conduction of protons via H-bonded networks has been offered as an explanation for a number of rapid proton transfers of biological significance. 

The practical importance of vacancies is that they are mobile and, at elevated temperatures, can move relatively easily through the crystal lattice. As illustrated in Fig. 20.21b, this is accompanied by movement of an atom in the opposite direction indeed, the existence of vacancies was originally postulated to explain solid-state diffusion in metals. In order to jump into a vacancy an adjacent atom must overcome an energy barrier. The energy required for this is supplied by thermal vibrations. Thus the diffusion rate in metals increases exponentially with temperature, not only because the vacancy concentration increases with temperature, but also because there is more thermal energy available to overcome the activation energy required for each jump in the diffusion process. 

Because each lithium atom has one valence electron and each molecular orbital can hold two electrons, it follows that the lower half of the valence band (shown in color in Figure 5) is filled with electrons. The upper half of the band is empty. Electrons near the top of the filled MOs can readily jump to empty MOs only an infinitesimal distance above them. This is what happens when an electrical field is applied to the crystal the movement of electrons through delocalized MOs accounts for the electrical conductivity of lithium metal. 

Diffusion has often been measured in metals by the use of radioactive tracers. The resulting parameter, DT, is related to the self-diffusion coefficient by a correlation factor/that is dependent upon the details of the crystal structure and jump geometry. The relation between DT and the self-diffusion coefficient Dsclf is thus simply... 

Ionic transport in solid electrolytes and electrodes may also be treated by the statistical process of successive jumps between the various accessible sites of the lattice. For random motion in a three-dimensional isotropic crystal, the diffusivity is related to the jump distance r and the jump frequency v by [3] ... 

FIGURE 5-15 Migration of the fluoride ion through the LaF3 lattice (doped with EuF2). The vacancies created within the crystal cause jumping of neighboring F- into the vacancy. 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

Sometimes the atomic arrangement of a crystal is such as not to permit the formulation of a covalent structure. This is the case for the sodium chloride arrangement, as the alkali halides do not contain enough electrons to form bonds between each atom and its six equivalent nearest neighbors. This criterion must be applied with caution, however, for in some cases electron pairs may jump around in the crystal, giving more bonds than there are electron pairs, each bond being of an intermediate type. It must also be mentioned that determinations of the atomic arrangement are sometimes not sufficiently accurate to provide evidence on this point an atom reported equidistant from six others may be somewhat closer to three, say, than to the other three. 

Of course, in real systems, the relative contributions of Coulomb and crystal-field effects are such as to place chromophores somewhere inbetween the weak-and strong-field limits. In that case, a real Txg F) A2g transition is not a pure two-electron jump, so that some intensity is observed. 

Here we comment on the shape of certain spin-forbidden bands. Though not strictly part of the intensity story being discussed in this chapter, an understanding of so-called spin-flip transitions depends upon a perusal of correlation diagrams as did our discussion of two-electron jumps. A typical example of a spin-flip transition is shown inFig. 4-7. Unless totally obscured by a spin-allowed band, the spectra of octahedral nickel (ii) complexes display a relatively sharp spike around 13,000 cmThe spike corresponds to a spin-forbidden transition and, on comparing band areas, is not of unusual intensity for such a transition. It is so noticeable because it is so narrow - say 100 cm wide. It is broad compared with the 1-2 cm of free-ion line spectra but very narrow compared with the 2000-3000 cm of spin-allowed crystal-field bands. 

Our crystal-ball predictions are that DMFCs will first be commercialized as portable power sources for military and civilian applications before the year 2010 and that there will then be a quantum jump in the technology to be in a position to drive DMFC-powered electric vehicles 10 years thereafter. 

Steady-state molecular beam studies of the reaction of methylacetylene on reduced Ti02 (001) surfaces were undertaken to determine whether this reaction could be performed catalytically under UHV conditions. A representative experiment is presented in Figure 1. Prior to each experiment, the surface was sputtered and annealed to a temperature between 400 K and 550 K surfaces prepared in this manner have the highest fraction of Ti(+2) sites (ca. 30% of all surface cations) of any surface we have been able to create by initial sputtering [3]. Thus these are the surfaces most active for cyclotrimerization in TPD experiments [1]. Steady-state production of trimethylbenzene (as indicated by the m/e 105 signal detected by the mass spectrometer) was characterized by behavior typical of more traditional catalysts a jump in activity upon initial exposure of the crystal to the molecular beam, followed by a decay to a lower, constant level of activity over a longer time scale. Experiments of up to 6 hours in duration showed... 

The conductivities of melts, in contrast to those of aqueous solutions, increase with decreasing crystal radius of the anions and cations, since the leveling effect of the solvation sheaths is absent and ion jumps are easier when the radius is small. In melts constituting mixtures of two salts, positive or negative deviations from additivity are often observed for the values of conductivity (and also for many other properties). These deviations arise for two reasons a change in hole size and the formation of new types of mixed ionic aggregates. 

The point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

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