Atom exchange frequencies

Fig. 12.4 The (squared) frequency of the motion along the reaction coordinate q for a symmetric atom exchange reaction. L is the range of the chemical barrier region, and the frequency is shown in units of the mean frequency of the unperturbed solvent. The range of frequencies in the solvent is indicated as a solid bar. The negative values for the solvent correspond to unstable solvent modes.

The equilibrium potential of a crystal is unambiguously determined by the exchange frequency of kink atoms. The concentration of kink sites has no effect on the potential, but the presence of kink atoms is essential for the establishment of the equilibrium potential. 

Correlation effects during vacancy diffusion in a metal A. As has already been shown, if the vacancy and the tracer atom exchange sites twice in succession, no net motion of the tracer atom takes place. We would like to be able to use the measured displacement of the tracer atom in order to calculate the jump frequency or the mobility of the vacancy. The jump frequency could then be used to calculate the diffusion coefficient in the metal A. In order to do this, then, we must calculate the probability of a repeated exchange of sites between a tracer and the same vacancy. The calculation is based upon the known geometry of the lattice and upon the assumption that the direction of a vacancy jump is independent of the direction of all previous jumps. This can be expressed quantitatively as follows Let xl (A ) be the mean square displacement of the tracer A and let xi (V) be the mean square displacement of the vacancy V after n jumps (lim n —> oo). The correlation factor is then defined, by means of eqs. (5-11), (5-19), and (5-20), as ... 

Tiesinga E, Verhaar BJ, Stoof HTC, van Bragt D. (1992) Spin-exchange frequency shift in cesium atomic fountain. Phys. Rev. A 45 2671-2674. 

FIGURE 12.8 (a) Deuterium-hydrogen exchange frequency (iwii) (solid line) and amount of moles of exchanged D atoms per mol of surface Pt (dashed line) in the PtXC-R catalyst as a function of contact time between the gas and the sample at 298 K. The catalyst has been previously treated under dynamic vacuum at 448 K for 1 h. (b) Schematic representation of the exchange processes I and 11. 

Despite these simplifications, a typical or F NMR spectrum will nomially show many couplings. Figure BTl 1.9 is the NMR spectrum of propan-1-ol in a dilute solution where the exchange of OH hydrogens between molecules is slow. The underlymg frequency scale is included with the spectrum, in order to emphasize how the couplings are quantified. Conveniently, the shift order matches the chemical order of die atoms. The resonance frequencies of each of the 18 resolved peaks can be quantitatively explained by the four... 

In Eq. (26), M is the hydrogen mass, X labels the mode, is the atomic eigenvector for hydrogen / in mode X, and co, is the mode angular frequency. is the number of quanta of energy Ao>, exchanged between the neutron and mode X. is a modified Bessel function. 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

---