D-Spacings calculating

Thiol capping of stabilized NPs provides sufficient hydrophobicity to the particles to disperse easily in the polymer matrix. Fig.6 shows the WAXD spectra of pure PDMS, 2 vol% PDMS/Au and 4 vol% PDMS/Au. Its is found that pure polymer has d-spacing of 7 A, however for the PDMS/Au composite there are two peaks, one representing presence of Au NPs and the second peak is because of the polymer. Also the d-spacing calculated for PDMS/Au had shifted to 7.4 A, suggesting a more open matrix than the matrix of pure polymer. This will enable the volatile organic compounds to sorb and desorb easily, thus enhance the sensitivity of the sensor. 

Interdiffusion of bilayered thin films also can be measured with XRD. The diffraction pattern initially consists of two peaks from the pure layers and after annealing, the diffracted intensity between these peaks grows because of interdiffusion of the layers. An analysis of this intensity yields the concentration profile, which enables a calculation of diffusion coefficients, and diffusion coefficients cm /s are readily measured. With the use of multilayered specimens, extremely small diffusion coefficients (-10 cm /s) can be measured with XRD. Alternative methods of measuring concentration profiles and diffusion coefficients include depth profiling (which suffers from artifacts), RBS (which can not resolve adjacent elements in the periodic table), and radiotracer methods (which are difficult). For XRD (except for multilayered specimens), there must be a unique relationship between composition and the d-spacings in the initial films and any solid solutions or compounds that form this permits calculation of the compo-... 

In addition, an interesting, although negative, result has come from powder diffraction studies of the hexachloro compounds. We have examined Debye—Scherrer photographs of several samples known to contain predominantly hexachlorodibenzo-p-dioxins and have identified the patterns of at least three crystalline phases therein. (There are 10 possible isomers of hexachlorodibenzo-p-dioxin.) These patterns have been checked carefully against the calculated d-spacings and intensities of the 1,2,3,7,8,9-hexa isomer described by Cantrell, Webb, and Mabis (I) and also against an observed pattern supplied by Cantrell and believed to be from the low temperature phase of the same material. Yet to date we... 

Given the following "d-spacings" for the diffraction lines of a given cubic powder, calculate the h.k.l values of the pleme spacings. 

Each of the integrands in equations (2.18), (2.19), and (2.20) is the complex conjugate of the wave function multiplied by an operator acting on the wave function. Thus, in the coordinate-space calculation of the expectation value of the momentum p or the nth power of the momentum, we associate with p the operator (h/f) d/dx). We generalize this association to apply to the expectation value of any function f p) of the momentum, so that... 

To verify the mechanism presented, the quantum-chemical calculations of proton affinity, Aa, were carried out for modifiers, since the corresponding experimental data are quite rare. The calculations were performed for isolated molecules, since the properties of species in the interlayer space are probably closer to the gas phase rather than the liquid. The values of Ah were calculated as a difference in the total energy between the initial and protonated forms of the modifier. Energies were calculated using the TZV(2df, 2p) basis and MP2 electron correlation correction. Preliminarily, geometries were fully optimized in the framework of the MP2/6-31G(d, p) calculation. The GAMESS suite of ah initio programs was employed [10]. Comparison between the calculated at 0 K proton affinities for water (7.46 eV) and dioxane (8.50 eV) and the experimental data 7.50 eV and 8.42 eV at 298 K, respectively (see [11]), demonstrates a sufficient accuracy of the calculation. 

Let us calculate some of the angles relative to the vector in 3-D space as shown in Figure 13-1. To calculate these angles, we refer to Chapter 1, and if we proceed with our calculations we find... 

Figure 13-1 A point (X, Y, Z) = (2, 2, 6) located along a vector in 3-D space. Both the angle a (the angle to the x-axis) and the angle /3 (the angle to the y-axis), as illustrated in the figure are shown as a projection of the 3-D-vector (2,2,6) onto the (x, y) plane, and the proper calculations for both a and /3 from what is then a 2-D vector are correct as given in equations 13-1 and 13-2.

Figure 13-3 The geometric problem associated with calculating the length of a vector AB, given a point (x, z) = (2, 6) in 2-D space. Note that the angle 0 is equal to 90° — 71.57° = 18.3°.

Equation (15) has been successfully used to determine the relative amounts of anhydrous carbamazepine (C15H12N20) and carbamazepine dihydrate (C15H12N20 2H20) when they occur as a mixture [47]. The powder x-ray patterns of anhydrous carbamazepine and carbamazepine dihydrate revealed that the lines with d-spacings of 6.78 A (peak at 13.05° 26) and 9.93 A (peak at 8.90° 20) were unique to anhydrous carbamazepine and carbamazepine dihydrate, respectively (Fig. 5). In mixtures containing these two phases, anhydrous carbamazepine was first considered the unknown component while carbamazepine dihydrate was designated the matrix. The intensity ratios, Ai/(/ii)o were calculated (Table 4) for different values of xx (different weight fractions of... 

The 220/204 reflections and the 312/116 reflections were split, which is consistent with the tetragonal distortion of the crystal lattice49 (Fig. 6.15). Lattice parameters a and c were calculated from X-ray d spacings according to Eq. 6.5,... 

Figure 5.8 A Debye-Scherrer powder camera for X-ray diffraction. The camera (a) consists of a long strip of photographic film fitted inside a disk. The sample (usually contained within a quartz capillary tube) is mounted vertically at the center of the camera and rotated slowly around its vertical axis. X-rays enter from the left, are scattered by the sample, and the undeflected part of the beam exits at the right. After about 24 hours the film is removed (b), and, following development, shows the diffraction pattern as a series of pairs of dark lines, symmetric about the exit slit. The diffraction angle (20) is measured from the film, and used to calculate the d spacings of the crystal from Bragg s law.

The molecular size and the cross-sectional area of coumarine 1 were calculated to be 3.2x10.4x7.5 (A) and 78 A, respectively. From the data of observed d-spacings and the calculated molecular size, three possibilities for the conformation of coumarine molecules could be proposed. In the dl-type [shown in Fig. 5(a)], since the thickness of one aluminosilicate layer was about 9.6 A, the full clearance space was estimated to be about 3.6 A. This value was almost equal to the thickness of the planar coumarine molecule. Therefore, it was considered that coumarine molecules were "flat" on the silicate surfaces and covered each exchangeable cation site without any overlap. In the dh-type [shown in Fig. 5(b,c)], the measured d-spacing was 18.5 A, so that the interlamellar spacing was evaluated to be about 8.9 A, in which the coumarine... 

The crystallographic data for these phases, including tables of calculated d-spacings and intensities for X-ray powder diffraction patterns, have been collected in Chapter 13. Characterization by electron microscopy, a particularly important technique because of the nature of the materials, is reviewed in Chapters 14 and IS. 

Tables 1 through 7 giving positional and isotropic thermal parameters for most of the compounds discussed in this chapter. These data are taken, for the most part, from the literature, but, for a few materials that have not been structurally characterized, calculated positions are given. The tables also include lattice constants, space groups, and compositional data. Table 8 gives calculated x-ray powder diffraction information (26 (Cu), d-spacing, hkl, and intensity) for the same oxide compounds. In regard to the diffraction patterns, it should be remembered that preferred orientation and absorption effects, and cation substitutions will make the experimentally observed intensities differ from the calculated ones. Additional information on the crystal structures of high-Tc oxides can be found in a recent review (48).

The particle diameter D is related to the full width at half maximum A by the Debye-Scherrer equation D = 0.9 XIA cos0, where 20 is the diffraction angle and X is the X-ray wavelength. Table 27.1 lists the particle size and lattice plane spacing calculated using the strongest (h,k,l) peak for the Fe, W, Mo carbides, nitrides, oxynitrides and oxycarbides. It is important to note that the calculated particle size using the Debye-... 

Abbreviations CF - crystal field SH - spin Hamiltonian ZFS - zero-field splitting MA - magnetic anisotropy TIP - temperature-independent paramagnetism MP - magnetic parameter averaged (gav, /tip), axial (gz> g > D /up) CSC - complete space calculation. 

---