Lattice motions

For example, in the case of H tunneling in an asymmetric 0i-H - 02 fragment the O1-O2 vibrations reduce the tunneling distance from 0.8-1.2 A to 0.4-0.7 A, and the tunneling probability increases by several orders. The expression (2.77a) is equally valid for the displacement of a harmonic oscillator and for an arbitrary Gaussian random value q. In a solid the intermolecular displacement may be contributed by various lattice motions, and the above two-mode model may not work, but once q is Gaussian, eq. (2.77a) will still hold, however complex the intermolecular motion be. 

DSP crystal, a detailed picture of the lattice motion and related displacements was constructed and related to the topochemical postulate and the mechanism of phonon assistance. Holm and Zienty (1972) have measured the quantum yield for the overall polymerization process of a,a -bis(4-acetoxy-3-methoxybenzylidene)-p-benzenediacetonitrile (AMBBA) crystals in slurries and reported it to be 0.7 on the basis of the disappearance of two double bonds ( = 1.4 if assigned on the basis of the number of double bonds consumed). 

Attempts have been made to lower the temperature of appearance of the sub-lattice motions. It was found that substitution in the I- sub-lattice of Agl, e.g. by WOj", stabilizes this structure up to rather low temperatures crystals of (AgI)1 JC(Ag2W04)JC show, for = 0.18, an Ag+ conductivity of 0.065 S/cm at 20°C. Addition of cationic species, for instance in Ag2HgI4, Ag4RbI6, and Ag7[N(CH3)4]I8 has a similar effect. 

One of the applications of TRXRD is to study complex systems where electric fields couple to multiple degrees of freedom. Though femtosecond laser pulses can generate THz radiation from ferroelectric LiTa03, the corresponding lattice motion remained undetected by optical measurements. Cavalleri and coworkers demonstrated the coherent modulation of the X-ray intensity at 1.5 THz [10], and assigned it as phonon-polariton mode of A symmetry (Fig. 3.3). Nakamura and coworkers detected the coherent LO phonon of CdTe... 

Coherent lattice motions can create periodic modulation of the electronic band structure. Time-resolved photo-emission (TRPE) studies [20-22] demonstrated the capability to detect coherent phonons as an oscillatory shift of... 

The cross-polarization (spin-spin) rate (Tcp) competes on an equal footing with the spin-lattice (motional) rate (Tip)". Now the cross-polarization rate is strongly field dependent (12,20,, 32) ... 

Professor G. Tammann, one of the pioneers of solid-state chemistry, considered the importance of lattice motion to reactivity. 

There has been a long history in theoretical efforts to understand H + H/Cu(lll) and its isotopic analogs because it represents the best studied prototype of an ER/HA reaction. These have evolved from simple 2D collinear quantum dynamics on model PES [386] to 6D quasi-classical dynamics on PES fit to DFT calculations [380,387,388], and even attempts to include lattice motion on ER/HA reactions [389]. These studies show that there is little reflection of incident H because of the deep well and energy scrambling upon impact, i.e., a % 1. Although some of the... 

Figure 1 2 10. The reduced Lifshitz parameter"z" - (ET - EF)/(EA- ET), where (EA- Er) is the full energy band dispersion in the c-axis direction, as a function of the number of holes in the G subband in A1 doped MgB2. The quantum uncertainty in the z value is indicated by the error bars that are given by D (

Similar QC studies have been made on Ni(l 0 0) [42,44]. One of these allowed for lattice motion and H penetration into the bulk [44], and we focus on those issues here. To accurately simulate the evolution of a large slab (1197 atoms in 7 layers) of Ni atoms, a sizable number of surface adsorbates, H migration into the bulk, and reactions between pairs of H atoms on the surface, we require a model PES were the H-metal and the H-H interactions in the presence of the metal are functions of the instantaneous positions of the Ni atoms. We used a many-body PES of the form [44] ... 

In Table 2, we summarize the results of 6 QC studies, in which the lattice atoms move or are held rigid, as indicated, and the initial coverage is in monolayers (ML). The incident energy is 0.07 eV, and periodic boundary conditions are used. The probabilities for primary reaction to form HD include both ER and HA contributions. It is apparent that allowing for lattice motion can significantly change reactivity and... 

The transition form the gas phase to conditions prevailing in solution and in solids can be made through the application of relaxation theories as has been shown by Bratos 91>. Gradually rotational fine structure is replaced by broadening due to energy dissipation involving the random solvent environment or lattice motions. 

It is obviously ideally suited to measuring the effect of the electron quantum fluctuations on the phonon frequency. What one immediately learns from Eq. (26) is that the propagator is quasistatic that is, the >m = 0 component dominates for T > co /2tt. This comes from the definition of the Matsubara frequencies for bosons [under Eq. (8)]. As far as the electrons are concerned, the atoms move very slowly (the adiabatic limit). If 2g2 gi> - g3 (see Fig. 5), the electrons are able to screen the slow lattice motion and thus soften the interactions. We are obviously interested in the 2kF phonons, which will be screened most effectively by the dominant 2kF charge response of the one-dimensional electron gas. 

Xj is related to the inverse of the rate of 3-bond motions, and the x -exponential term is introduced to account for out-of-lattice motions. 

A serious drawback of lattice gas models is their inadequacy to describe properly the commensurate - incommensurate phase transitions, often observed in real systems [144 - 150]. The possibility of the formation of incommensurate phases results directly from the finitness of potential berriers between adjacent potential minima and from the off-lattice motion of adsorbed particles. Although attempts have been made to extend the lattice-gas models and include the possibility of the formation of incommensurate solid phases [151,152], but it is commonly accepted (and intuitively obvious) that the continuous-space theories are much better suited to describe behaviour of adsorbed films exhibiting incommensurate phases. Theoretical calculations of the gas - solid potential for a variety of systems [88] have shown that, in most cases, the lateral corrugation is rather low. Nevertheless, it appears to have a very big influence on the behaviour of adsorbed layers. 

Figure 2.7 Artistic view of electron-phonon scattering. Lattice motions involving the displacement of polar modes can scatter the electron inelastically. The polar fluctuations create dipolar fields that can modulate the electron distribution. The electron responds to these stochastic fluctuations in local fields with a change in its energy and effective momentum transfer to the lattice. This process is depicted by comparing (a) and (b) to visualise the motion of the lattice atoms, leading to a change in direction or momentum of the electron from its initial path shown in (a).

Third, diffusion is often an integral part of the dynamics in real systems under non-UHV and even under UHV conditions. These involve nonzero coverages of multiple adsorbates, nonequilibrium surface structures of adsorbates, and other complications. It is clearly important to understand the simplest case of single-atom diffusion on a surface since this will underlie the more complex situations. A number of important conclusions have been learned from studies of atomic diffusion (1) lattice motion substantially increases the quantum mechanical diffusion constant as shown in Fig. 44 by... 

Both spin-lattice (motional) and spin-spin processes contribute to TjpCC). Experimental cross-polarization transfer rates from protons in the local dipolar field to carbons in an applied rf field can be used to determine the relative contributions quantitatively. This measurement also requires a determination of the proton local field. Methods for making both measurements have been developed in the last few years [1,2]. For polystyrenes, the spin-lattice contribution to TjpCCO s is by far the larger. This means that the TipCCVs can be interpreted in terms of rotational motions in the low-to-mid-kHz frequency range. 

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