Profile widths, reflection

It is of interest to compare the half-widths at half-intensity of the spectral functions of the three systems shown in Fig. 3.2. These amount to roughly 140, 80 and 50 cm-1 for He-Ar, Ne-Ar and Ar-Kr, respectively, which are enormous widths if compared to the widths of common Doppler profiles, etc. The observed widths reflect the short lifetimes of collisional complexes. From the theory of Fourier transforms we know that the product of lifetime, At, and bandwidth, A/, is of the order of unity, Eq. 1.5. The duration of the fly-by interaction is given roughly by the range of the induced dipole function, Eq. 4.30 (1/a = 0.73 a.u. for He-Ar), divided by the mean relative speed, Eq. 2.12. We obtain readily ... 

E was the same as D except that the reflection profile widths were allowed to vary. The results were not changed. (from Immirzi, in preparation.)... 

Figure 14. The density profiles at different bubble radii for ( He)jy clusters with iV= 1.88x10 reflecting on the formation of a helium balloon with a finite thickness (AR = R — Rb) in the cluster. The profile thicknesses for the bubble and for the cluster surface obtained from this simple model are t, t2 = 6-lOA (see text). The exterior surface profile of the cluster was characterized by the 90-10% fall-off width W2, while the interior bubble profile was characterized by a 10-90% rise width wj. For N = 1.88 x 10 clusters wi = 6.2 A for Rt = 0 (no bubble), W2 = 7.8 A and wi = 6.2 A for Rj = 10.3 A, while W2 = 6.8 A and Wi = 12.3 A for Rb = 19.2 A. These results demonstrate that the cluster surface profile width n>2 remains nearly independent of the bubble size, while Wi increases with increasing the bubble radius.

Figure 7. Composite plot of neutron reflectivity reaction front interfacial width (open circles) and AFM RMS roughness (filled circles) versus post-exposure bake time. PEB temperature is 110 C. AFM roughness values have a relative uncertainty of 2 nm, while the deprotection profile width has a relative uncertainty of 3 nm.

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. 

Fig. 12. Interface width a as a function of annealing time x during initial stages of interdiffusion of PS(D)/PS(H) [95]. Data points are obtained by a fit with error function profiles of neutron reflectivity curves as shown in Fig. 11. Different symbols correspond to different samples. The interface width a0 prior to annealing is also indicated (T) and is subtracted quadratically from the data (a = [

The process profile is presented as a bar chart, with a separate bar for each parameter. The width of each bar reflects the relative importance of a parameter s maximum impact. The bar chart highlights process strengths and weaknesses. This is illustrated in Fig. 2.7, which shows the process profile for 1. It is immediately apparent that the weakness of the process is. its environmental abuse potential. 

Are the quantitative characteristics of the halos homogeneous in the same sample (width, maximum reflectivity, shape of profile) ... 

Peak Breadths And Reflection Profile Function. As has been mentioned, the individual reflection profiles tend to be broad for polymers. With both x-ray and neutron radiation the peaks exhibit large peak-widths. In a neutron diffraction pattern of isotactic polypropylene (A. Immirzi, work in progress) the peak width at half maximum, K j, had values ranging from 0.60° at 20= 14° to 1.00° at 26= 43° (X= 1.542 A), whilst, with the same... 

The line shapes are described by Voigt functions, which reflect the Lorentzian line profiles due to natural line width and Gaussian profiles due to Doppler broadening. The instrumental broadening by the rocking curve of the crystal, de-focusing and the finite resolution of the detector is described well by a Voigt profile shape too [3[. 

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