Healing length

In the interpretation of these spectra it is assumed that the geometry (i.e., the layer statistics in the NMR layer model) of the particles does not change as a result of chemisorption but that the surface LDOS and the healing length are affected. In principle, this suggestion can be tested experimentally by comparing the lineshape in a double-resonance experiment on... 

Fig. 56. Effects of chemisorption on the Pt NMR spectrum of Pt/TiO,. Spectra taken at 80 K. Panels b-d are the same samples as those in F ig. 45 panels f-h are for samples under oxygen. The open symbols are scaled from experiments at 20 K. The changes under hydrogen can be described as a gradually increasing healing length (Fig. 55), which effectively sweeps all Gaussians in Fig. 48 to low field. The oxygen case is more complicated in f and g, the spin lattice relaxation at the surface peak does not obey time/temperature scaling (Fig. 45) so that some platinum must be in a nonmetallic environment.

A remarkable difference in the Pt spectra of oxide- and carbon-supported platinum is especially clear for the 2.5-nm sample the fuel cell material shows much less intensity at the bulk resonance position (1.138 G/kHz). A similar difference is shown by the spectrum for the 2.0-nm sample. In terms of the NMR layer model, this comparison means that the healing length is larger in the carbon-supported material. It is not clear whether this result is related to the conducting nature of the carrier or to the presence of the electrolyte comparisons between wet and dry samples are needed. 

Figure 2. Suppression of identical particle collisions. Full squares measured scattering cross-section for Beliaev damping as a function of the excitation wavenumber in units of the inverse healing length. The assumptions of our analysis are tested using hydrodynamic simulations (dashed line), and found to agree with Beliaev damping theory (solid line) and the experimental data. Corrections observed in the hydrodynamic simulation take into account the full inhomogeneity and finite size of the experimental system, and validate the approximations of our analysis.

Figure 7. Healing lengths, estimated from the iayer model analysis, plotted against the electronegativity. (Reprinted with permission from...

Fig. 8 Solid curve showing the relationship between the healing length and electronegativity as determined from Eq. (7). For comparison, we also show the three experimental points based on previous observations. See the text for details. (Reproduced with permission from Ref [10], Copyright by American Chemical Society 2000.)...

Films on Slightly Rough Substrates The Healing Length... 

FIGURE 4.7. Thin film on a rough substrate. The wavelength A is the characteristic pitch of the roughness to be compared with the healing length e-... 

If A is positive, the film is stable. When deposited on a wavy substrate characterized by a wavevector the film replicates the surface s modulation if < 1, whereas it remains planar if > 1 (see chapter 4). That is the reason why has been dubbed the healing length, as the film heals the roughness of the original surface. 

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