Diffraction Bragg

X-rays are collected and analy2ed in ema in one of two ways. In wds, x-rays are dispersed by Bragg diffraction at a crystal and refocused onto a detector sitting on a Rowland circle. This arrangement is similar to the production of monochromati2ed x-rays for xps described above. In the other approach, edx, x-rays are all collected at the same time in a detector whose output scales with the energy of the x-ray (and hence, Z of the material which produces the x-ray.) Detectors used for ema today are almost exclusively Li-drifted Si soHd-state detectors. 

There are restrictions on the values of the quantum numbers which elecuons can occupy in tluee-diirrensioiral metal structures which can be determined by application of tire Bragg diffraction equation... 

Wavelength Spectrometry (WDS) is based upon the phenomenon of Bragg diffraction of X rays incident on a crystal. The difiraction phenomenon is described by the expression ... 

Figure 1 Bragg diffraction. A reflected neutron wavefront (D, Dj) making an angle 6 wKh planes of atoms will show constructive interference (a Bragg peak maxima) whan the difference in path length between Df and (2CT) equals an integral number of wavelengths X. From the construction, XB = d sin 6.

Bragg diffraction on crystalline colloidal arrays Photonic crystal material is composed of a crystalline colloidal array that diffracts light at wavelengths determined by the optical lattice spacing, which is affected by the presence of analyte 5,14,15... 

For the evaluation of the response of the sensor, we selected several vapors of different polarity. The vapors included water (H20), acetonitrile (ACN), toluene, and dichloromethane (DCM). Solvent polarity and refractive index of tested vapors are listed in Table 4.346 47. The spectral range for the evaluation of the vapor responses of the colloidal crystal film was selected as 700 995 nm, which covered only the fundamental Bragg diffraction peak on the (111) planes of the colloidal crystal film to further reduce effects from possible stacking defects in the film as suggested in the literature44. 

The Bragg condition defines a cone of angles,, normal to the (hkl) planes. Alternatively, we use the Laue condition to specify the Bragg diffraction ... 

Given a zone axis, we can define an orthogonal zone axis coordinate, (x,y, ), with the z parallel to the zone axis direction. Let us take X along the g direction and y normal to the x-direction. Expressing the condition for Bragg diffraction (equation 6) in this coordinate, we have... 

The first term a i. h is the Miller index component h, which is an integer. Thus in the interference fimction it becomes unity since exp(2 ni)=l. This corresponds to strong Bragg diffraction when q=0. The second term when put in the interference fimction becomes... 

What can we gness about the solution It shonld clearly be a wave equation. We expect (from knowledge of Bragg diffraction) it to be a plane wave, or sums of plane waves. We nse capital K g and K j, for wavevectors inside the crystal to distinguish them from k g and k j, ontside the ciystal. Inside the crystal the allowed wavevectors should satisfy conservation of momentnm, that is Kg+h=Kh... 

A standard method for confirming coherence of the layers is the study of x-ray diffraction spectra. If the layers are coherent and there are enough of them to provide a relatively strong Bragg diffraction pattern, satelhtes due to superlattice (see Chapter 16) formation should appear on each side of the Bragg diffraction peak. Although detailed treatments can be found in the literature, we present below a simplified but rather useful formula for the determination of layer periodicity. 

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