Reflectivity profile

Figure 3 A calculated reflectivity profile for a perdeuterated polystyrene film with a thickness of SO nm on a silicon substrate. The calculation was for a specimen where the interfaces between the specimen and air and the specimen and the substrate were sharp. This causes the reflectivity on average (shown by the dashed line) to decrease in proportion to k or 9. The separation distance between the minima of the oscillations diractly yields the thickness of the specimen, as shown.

One of the key advantages to time-of-flight reflectometers comes in the measurement of fluid surfaces. Simply delivering the neutrons onto the fluid surface at a fixed angle (without moving the specimen) and detecting the reflected neutrons yields the reflectivity profile. 

Figure 32. X-ray field intensities at extended Ge (220) lattice positions (0-9) for a perfectly collimated incident X-ray beam. An atomic adlayer whose center falls on one of these positions would have its characteristic fluorescence intensity modulated in the same fashion. The dashed curve represents the Bragg reflectivity profile. (From M. J. Bedzyk, Ph. D thesis, SUNY Albany, 1982.)...

As has already been emphasised, it is very difficult to approach a plane wave with the laboratory sources, which are properly described as spherical-wave sources. A single-crystal reflectivity profile from such a source will be dominated by the source profile rather than by the above formulae the integrated intensity expressions will be multiplied by the source profile function. 

Fig. 2.54 Neutron reflectivity profile for a symmetric PS-dPMMA diblock (Mw 30 kg moP1) as a function of incident wavevector (Russell 1990). The inset shows the scattering length density (b/V, the neutron scattering length per unit volume) profile normal to the film surface that was used to calculate the reflectivity profile shown as the solid line, This is typical of a block copolymer film containing a multilayer stack, with lamellae parallel to the surface.

X-ray reflectivity, AFM and optical microscopy have been used to probe lateral structure in a thin film of a symmetric PS-PMMA diblock that formed islands at the surface (Cai et al. 1993). The step height obtained from beating of fringes in the X-ray reflectivity profile was found to be in good agreement with a direct... 

Fig. 2.59 Neutron reflectivity profiles for a PS-riPMMA symmetric diblock copolymer (Mw = 29.7kgmor ) film of total thickness 5232 A (Menelle et al. 1992). Experiments were performed on samples annealed at the temperatures shown. The solid lines were computed using the scattering length density profiles shown in the insets, which show that the surface induces lamellar order even above the bulk ODT 157 8°C (the air-polymer interface is located at z - 0). 

Fig. 3.38 (a) Neutron reflectivity profile for a PS-PEO diblock (M = 15 kg mol-1,1.5% PEO) end-adsorbed from d-toluene onto quartz (Field et al. 1992a). The symbols indicate measured values, whilst the full line is a fit to a parabolic volume fraction profile, (b) Models for the density profile. The parabolic function was found to give the best fit to the data. 

Fig. 6.51 Volume fraction profiles determined from modelling reflectivity profiles for blends of a PS-PMMA diblock (M = 91.5kgmol, = 0.53) with 5wt% of rfPS...

Many things do, or may, go into making up each yj. At a mini -mium there is a background plus contributions from the "tails" of all nearby reflections (Fig. 2). Let G(0 -6H) represent the Htil individual reflection profile centered at the Bragg position, 0. Let y-jnH represent a net intensity, above background, contributed by the Bragg reflection and let yib be the background level at this i- fe position. Then... 

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... 

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.)... 

In some instances, intensities are still measured by visual estimation, although in general this practice has now been superseded by the use of one-dimensional microdensitometers. Typically, a radial scan is taken through the centre of each spot, the shape of the background is estimated and sketched in, and overlapping reflections are apportioned. The area under each reflection profile is then measured, and an empirical "arcing factor" is applied. In correcting for the Lorentz and... 

Neutron reflectometry studies on mixed DPPC/oleic acid monolayers have been conducted using the CRISP reflectometer at RAL. First, the stmcture of DPPC monolayers was determined by measuring reflectivity profiles from three different isotopic forms of the DPPC monolayer system. This was achieved using hydrogenated (h-DPPC) and chain perdeuterated (d-DPPC) phospholipids and two different subphases of D2O and ACMW. The monolayers were studied at three surface coverages of approximately 50, 60, and 70 A /molecule. Examination of the surface pressure-area isotherm reveals that the main LE/LC phase transition for DPPC monolayers occurs over this range of molecular area (Lewis and Hadgraft, 1990). 

In order to evaluate the three partial structure factors for the DPPC monolayers it is necessary to measure the reflectivity profiles / (Q) for three different isotopic forms of the DPPC/water system, which sets up three simultaneous equations of the form of Eq. 17. These systems are d-DPPC on ACMW (to give b = 0, as explained earlier), h-DPPC on D2O (to give bo = 0 when compared to b ,), and finally d-DPPC on D2O (to yield the cross-term boJ. 

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