Distribution of width

The slice through a bulk crystal can differ from both the 111 plane and the 100 plane by small angles. This produces a kink in the face of the step. By an extension of the analysis that leads to step characterization, these kinks can also be characterized. For example, a plane with Miller indices 10,8,7 has 111 terraces seven atoms wide, 110 steps one atom high, and kinks of 100 orientation every two atoms. Because of the greater thermodynamic stability of the planes of low Miller index, these surfaces of ordered roughness are stable and can be prepared and studied. Since it is sensitive to periodicity over a domain about 20 nm in diameter, LEED sees the pattern associated with terraces of various widths and may be used to characterize these surfaces. Satisfactory LEED patterns do not require absolute uniformity of terrace width but may be obtained with experimental surfaces that display a distribution of widths. 

Microscopic disorder We consider a lattice the sites of which have disordered resonance energies, with a distribution of width Ae, but have the same intersite interactions (same dipole orientation and oscillator strength) as the perfect lattice. This is the so-called substitutional disorder model.122 We assume the disorder width to be smaller than the excitonic bandwidth (4< Be) and examine the bottom of the excitonic band, where the emitting and the absorbing K 0 states lie. In a renormalization-group scheme, we split the lattice into isometric domains of n sites, on which the excitation is assumed to be localized, and write the substitutional-disorder hamiltonian in this basis we thereby obtain a new disorder width An Aen-1/2 and a... 

The mean (T) is the center of gravity of the distribution (Figure 2.7) i.e. For the mean, the moment of the sums of the elementary areas of the relative distribution, of width dv, about the ordinate, equals the sum of the moments of the elements about the ordinate ... 

Several conclusions can be drawn from Eqs. (76) and (77). First, the influence of fluctuations is the largest when the number of open channels u is of the order of unity, because then the distribution Q k) is the broadest. Second, the effect of a broad distribution of widths is to decrease the observed pressure dependent rate constant as compared to the delta function-like distribution, assumed by statistical theories [288]. The reason is that broad distributions favor small decay rates and the overall dissociation slows down. This trend, pronounced in the fall-of region, was clearly seen in a recent study of thermal rate constants in the unimolecular dissociation of HOCl [399]. The extremely broad distribution of resonances in HOCl caused a decrease by a factor of two in the pressure-dependent rate, as compared to the RRKM predictions. The best chances to see the influence of the quantum mechanical fluctuations on unimolecular rate constants certainly have studies performed close to the dissociation threshold, i.e. at low collision temperatures, because there the distribution of rates is the broadest. 

LiC/cm. A Gaussian distribution about the draw direction characterises the chain axis reorientation in the stretched samples. The PVDF (draw ratio 3) has a Gaussian distribution of width 220 (half-width at e of maximum). Angular dependence of the magnetisation for the poled PVDF homopolymer films was not expected due to the low remanent polarisation of the samples. 

The width function is the normalized shape of the first mercury peak in the density profile, approximated as a Gaussian distribution of width [Pg.22]

Fig. 1. Simplistic view of a homogeneously broadened chromophore optical absorption spectrum at 0 K. The left-hand side shows the vibrational and phonon splitting of two electronic levels. The typical vibrational levels are split by 1000 cm", and the phonons form a quasi-continuous distribution of width approximately equal to 200 cm". The upper right-hand comer shows the absorption spectrum at 0 K with the sharp zero phonon lines of approximately 1 cm" width and the phonon wing with width approximately 200 cm". ... 

By superimposing each charged particle with a Gaussian charge distribution of width and of opposite sign, the total Coulomb interaction can be reformulated according to [59,64]... 

The fact that the lifetime t of an excited nuclear state is finite means that its energy has a certain distribution of width F, which, due to the Heisenberg uncertainty relationship, is connected to T by... 

Table 3. Local -minima for all phases of a model structure. The model intensity was falafled in order to show experimental errors by random numbers having a rectangular distribution of width 3%, 10%, 20%, 40% of the highest intensity maximum...

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