Two-ion crystal

As explained in Section 10.2, a non-destructive mass measurement can be performed by measuring the characteristic oscillation frequencies of the COM and/or the BR mode of a two-ion crystal. These frequencies can be determined by exciting the COM and the BR mode motion with a periodic driving force (see Section 10.3.3). In Fignre 10.6 are shown the detected amplitude and the in-phase amplitude signals... 

Rohde, H. Guide, S.T. Roos, C.R Barton, P.A. Leibfried, D. Eschner, J. Schmidt-Kaler, F Blatt, R. Sympathetic ground-state coohng and coherent manipulation with two-ion crystals. J. Opt. B Quantum Semiclass. Opt. 2001, 3, S34—S41. 

Similar to the situation for a coupled pendulum, normal vibrations can be excited in a Wigner crystal. For example, the two-ion crystal has two normal vibrations where the two ions oscillate in the ion trap potential either in phase or with opposite phases. For the in-phase oscillations, the Coulomb repulsion between the ions does not influence the oscillation frequency because the distance between the... 

A nondestructive detection technique is often desirable. One such technique is based on the excitation of motional resonances of trapped species. The information about the species is encoded in the frequency of the resonance. This technique has been used in the past for mass spectrometry of ion clouds in the gas or fluid state [29,69]. For a two-ion crystal containing a single molecular ion sympathetically cooled by a single atomic ion, a high mass resolution has been demonstrated [31]. 

In deriving theoretical values for inter-ionic distances in ionic crystals the sum of the univalent crystal radii for the two ions should be taken, and corrected by means of Equation 13, with z given a value dependent on the ratio of the Coulomb energy of the crystal to that of a univalent sodium chloride type crystal. Thus, for fluorite the sum of the univalent crystal radii of calcium ion and fluoride ion would be used, corrected by Equation 13 with z placed equal to y/2, for the Coulomb energy of the fluorite crystal (per ion) is just twice that of the univalent sodium chloride structure. This procedure leads to the result 1.34 A. (the experimental distance is 1.36 A.). However, usually it is permissible to use the sodium chloride crystal radius for each ion, that is, to put z = 2 for the calcium... 

If two ions have the same radius and the same charge, they will enter a given crystal lattice with equal facility. 

If two ions have similar radii and different charge, the ion with the higher charge will enter a given crystal lattice more readily. 

Lyotropic lamellar (La) liquid crystals (LC), in a form of vesicle or planar membrane, are important for membrane research to elucidate both functional and structural aspects of membrane proteins. Membrane proteins so far investigated are receptors, substrate carriers, energy-transducting proteins, channels, and ion-motivated ATPases [1-11], The L liquid crystals have also been proved useful in the two-dimensional crystallization of membrane proteins[12, 13], in the fabrication of protein micro-arrays[14], and biomolecular devices[15]. Usefulness of an inverted cubic LC in the three-dimensional crystallization of membrane proteins has also been recognized[16]. 

If there is simultaneous diffusion of more than one component in the crystal, the flux of A in direction X depends on the individual diffusivities of all diffusing components (Darken, 1948), and the individual diffusivity coefficient in equations 4.87 and 4.88 is replaced by interdiffusion coefficient D i.e., for the simultaneous diffusion of two ions A and B,... 

The first satisfactory definition of crystal radius was given by Tosi (1964) In an ideal ionic crystal where every valence electron is supposed to remain localised on its parent ion, to each ion it can be associated a limit at which the wave function vanishes. The radial extension of the ion along the connection with its first neighbour can be considered as a measure of its dimension in the crystal (crystal radius). This concept is clearly displayed in figure 1.7A, in which the radial electron density distribution curves are shown for Na and Cl ions in NaCl. The nucleus of Cl is located at the origin on the abscissa axis and the nucleus of Na is positioned at the interionic distance experimentally observed for neighboring ions in NaCl. The superimposed radial density functions define an electron density minimum that limits the dimensions or crystal radii of the two ions. We also note that the radial distribution functions for the two ions in the crystal (continuous lines) are not identical to the radial distribution functions for the free ions (dashed lines). 

For the crystal composed of ions, the equality given in Eq. (9.33) is no longer valid, because the two ionic charge distributions, which partly shield the nuclear charges, are different. For the free-ion crystal, the values of the potential at the nuclear positions in NaF, evaluated according to Section 9.3.2, are... 

Another semiconducting fulleride salt, [Ru(bpy)3](C5o)2 with bpy = 2,2 -bipyridine, crystallizes on the Pt electrode surface out of dichloromethane solutions saturated with [Ru(bpy)3]PF5 within a few minutes [79]. The NIR spectra of benzonitrile solutions of this salt demonstrate that the only fulleride anion present is 55 . The temperature dependence of the conductivity is typical for a semiconductor, with the room temperature conductivity being 0.01 S cm and the activation energy 0.1 kj mol (0.15 eV). It was postulated that there is an electronic overlap between the two ions of this salt leading to a donation of electron density from the 55 to the ligand orbitals in the [Ru(bpy)3] " AI 0.7) [79]. 

The main difference between the two mechanisms as they relate to crystal size (discussed in Sec. 2.6) is that the cluster mechanism is three dimensional while the ion-by-ion one is mainly two dimensional. Crystal size in the former is limited largely by the amount of reactant per nucleus The more nuclei, the smaller the final crystal size, since the same concentration of reactants is divided over more nuclei. Temperature affects this by stabilizing (kinetically) smaller nuclei as temperature is lowered, thus increasing the number of nuclei at lower temperature. 

The authors note that in the two hydrated crystals, a system of stacked bases and strings of chloride ions are present. On the other hand, in the anhydrous crystal, an extensive hydrogen bonding network is not present. The guanines, instead, exist as ionic Gua2+Cl2 units and form parallel layers with interleaved chloride ions. EPR resonances from radicals other than thiyl radicals were observed near g = 2.0, but the radicals causing them were not the object of the investigation and were not characterized. 

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