Instrument resolution function

Figure 4. XRD date of curve 1 - without co-sputtering (only sputtering of ZnO Ga target) curve 2 - instrumental resolution function curve 3 - co-sputteiing (Tsubstrate=300°C) curve 4 -co-sputtering (Tsubstrate=500 C)...

Figure 5. Quasielastic neutron scattering spectrum of TMA+ cations in the sodalite cage of die aluminosilicate zeolite TMA-sodalite compared with the instrument resolution function.

Thus the exact incorporation of the instrument resolution function would entail the evaluation of this four dimensional integral for each data point, in addition to the convolution in t, required to incorporate the uncertainty in the measurement of time of flight. To reduce data processing times, the approximation is made in the data analysis that the resolution can be incorporated as a single convolution in t space, with a different resolution function Rm (J ) for each mass. Thus (17) is modified to... 

All direct depth profiling techniques used to study the surface segregation from binary polymer mixtures have a depth resolution [29] p limited to some 5-40 nm HWHM (half width at half maximum of the related Gaussian function). They cannot observe the real composition profile < )(z) (for the sake of comparison mimicked by mean field prediction (dashed line) in Fig. 16a) but rather its convolution (solid line in Fig. 16a) with an instrumental resolution function characterized by p. The total surface excess z however provides a good parameter, independent of resolution, as it has been concluded based on experimental data obtained using different direct techniques [170]. 

As we have just seen, the peak profile is the result of the convolution of a certain number of elementary contributions with various degrees of complexity. These functions usually depend on the diffraction angle, which means that the shape of the diffraction peaks varies with 6. With the exception of microstractural effects (see Part 2 of this book), the width of the peaks is directly determined by the various elements that comprise the diffractometer. The description of the evolution of this width according to the Bragg angle characterizes the device used. This is referred to as the instrumental resolution function. 

Figure 3.6. Instrumental resolution function of several diffractometers...

Figure 3.7. Calculation of the instrumental resolution function of a diffractometer equipped with a four-reflection monochromator and a curved position sensitive deteetor...

Fig. 10.17 (a) INS spectrum of /raw-polyacetylene, (b) calculated density-of-states convoluted with a Gaussian lineshape and the instrument resolution function and (c) as (b) including the effects of the Debye-Waller factor and phonon wings. Reproduced from [29] with permission of Elsevier. 

Figure 8.19 Incoherent dynamic structure factor measured with poly(vinyl chloride) for q = 1.5A 1 at temperatures above and below the glass transition temperature.358 K. The broken curve is the instrumental resolution function measured. (From Colmenero euifr13)...

In the fit it was assumed that iodine was predominantly present in the form of (in fact other forms like I5 were also tried, but gave no better fit) and that these groups were located in the cage between the sulphur atom and the nearest neighbouring side chain. The tilt angles of the side chains (two parameters) and of the plane of the main chains were used as fitting parameters. Furthermore it was opened for a chain position shift of every second polymer layer, so that the thiophene units were either located on top of each other or were shifted half the c-axis, as one moved from layer to layer along the b direction. The calculated intensities were folded with the instrumental resolution function for comparison with observation. 

The delta-function deconvolution method (FFT) was used to improve the spectral resolution and to remove the plural scattering effect at the core-loss edge in electron energy-loss spectroscopy (EELS). The zero-loss peak (used as an instrumental resolution function) works as a nonattenuation high-pass filter in this technique [17]. Reflectance spectra in the vacuum ultraviolet of microcrystalline 3-BN, prepared by plasma CVD (chemical vapor deposition), and of sintered (3-BN measured with synchrotron radiation in the energy range from 5 to 25 eV, show reflectance peaks near 11.4 and 14 eV and a broad peak near 18 eV. The peaks at 11.4 and 14.0 eV are assigned to the E and E2 peaks of the sphalerite-type semiconductor [18]. 

Equation 1 can be fitted to the experimental spectra after (i) multiplying by x n x) + 1), with X = fuo/k T and n(x) the Bose factor in order to account for the detailed balance, and (ii) convolution with the instrumental resolution function / ( >). The experimental intensity may be in fact written as... 

Two types of experiments have been carried out using FRES, segregation of various species at surfaces and interfaces, and polymer chain diffusion. In order to carry out depth profiling via FRES, the data are convoluted with an instrumental resolution function, typically Gaussian. 

Fig. 31. Schematic representation of the diffuse scattering around the (110) lattice point at + 1.2K in UAs. The reciprocal lattice projection is [iTO], Note the difference in scale in the K O] and [OOi/] direction. The instrumental resolution functions have a HWHM of A = 0.006 and Ai = 0.003 in appropriate reciprocal-lattice units. (From Sinha et al. (1981).)...

However, in molecular media such as polymers, polymer blends and polymer-based composite materials, positron or Ps will inhabit a different environment and have different lifetimes. As a result, the measured lifetime spectra in such systems will represent many decaying exponentials superposed with the instrumental resolution function. Figure 27.3b shows a typical lifetime spectrum in a polymer blend and its constituents. 

Line width and shape Instrumental resolution function Microstructure... 

Figure 36 Calculated and measured IINS spectra of p-Hi (left) and 0-H2 (right) in the small cage of S-II tetrahydrofuran clathrate hydrate. The top figures show the stick spectrum, while the one convolved with the instrumental resolution function is in the bottom figures. Reprinted figure with permission from M. Xu, L. Ulivi, M. Celli, D. Colognesi and Z. Bacci, Phys. Reu By 83, 241403 (2011). Copyright 2011 American Physical Society. (For a color version of this figure, please see plate 15 in color plate section.)...

Figure 21 (a) Proton NRA spectrum recorded using an incident beam of 0.7MeV He ions and simulation (red curve) calculated for pure perdeuterated polymer with 0.75 MeV incident beam, (b) After normalization (division of data by simulation, and conversion of channel to depth), the resulting volume fraction versus depth data may be fit using a simple model convolved with the instrumental resolution function. 

---