Reflection of X-rays

Before the development of semiconductor detectors opened the field of energy-dispersive X-ray spectroscopy in the late nineteen-sixties crystal-spectrometer arrangements were widely used to measure the intensity of emitted X-rays as a function of their wavelength. Such wavelength-dispersive X-ray spectrometers (WDXS) use the reflections of X-rays from a known crystal, which can be described by Bragg s law (see also Sect. 4.3.1.3)... 

The modification improves performance and is interesting in connection with x-ray emission spectrography (Chapters 7, 8, and 9). It consists in measuring the intensity of tin Ka relative to that of scattered x-rays entering the detector from an analyzing crystal set for the reflection of x-rays 2.2 A in wavelength. As the tin coating becomes thicker, increased attenuation of the x-rays scattered by the iron cause s the intensity ratio to increase more rapidly than does the intensity of tin Ka. Table 6-3 contains performance data for the Quantrol on Method II (modified). The instrument can also be set up to use industrially a modification of Method III. 

Crystal broadening of monochromatic beams, 115, 116, 118 Crystal reflection of x-rays, efficiency, 116... 

The Rutile Structure.—A large number of compounds MX crystallize with the tetragonal structure of rutile, TiCfe. In this structure the position of the ion X is fixed only by the determination of a variable parameter by means of the intensity of reflection of x-rays from various crystal planes. In accordance with the discussion in a following section, we shall assume the parameter to have the value which causes the distances between X and the three ions M surrounding it to be constant. With this requirement the inter-atomic distance R and the edges a and c of the unit of structure are related by the equation R = (a/4 /2) [2 + (c/o)2]. In this way the inter-atomic distances in Table XII are obtained. In the case of magnesium fluoride the agreement is satisfactory. 

It was concluded by Zachariasen [Norsk geol. Tidsskrift, 8, 189 (1925) Z. physik. Chem., 119, 201 (1926)] from the intensities of reflection of x-rays that beryllium oxide does not contain Be++ and O" ions. However, it has since been shown by Claassen [ibid., 124, 139 (1926)] and Zachariasen himself [Z. Physik, 40, 637 (1926)] that if the electron distribution of the ions is taken into account, the x-ray measurements are compatible with an ionic structure. 

The verification of the suggested structures by the comparison of the observed and calculated intensities of reflection of x-rays has been begun. So far the calculations have been carried out for 18 even orders of re-... 

Now there are two physically distinct arrangements of the metal atoms corresponding to w = 0.030, the first with u = 0.030, and the second with u = — 0.030 and it is not possible to distinguish between them with the aid of the intensities of reflection of X-rays which they give. Let us consider the positions 24e. The structure factor for 24e is ... 

Whereas the XSW technique takes advantage of the standing wave established on the total reflection of X-rays from a mirror surface, a conceptually more straightforward approach is that of simply specularly reflecting an X-ray beam from an electrode coated with the film of interest, measuring the ratio of the intensities of the incident and reflected rays, and fitting the data, using the Fresnel equations, to a suitable model an approach similar to optical ellipsometry. 

Lenzen, R., Triimper, J. (1978), Reflection of X rays by neutron star surfaces , Nature 271, 216. 

Fig. 32. The integrated intensity of magnetic reflections of x-ray resonant exchange scattering measured for NdNi2BjC and SmNi2B2C. Dashed line and full line model calculations for a magnetic moment parallel to the tetragonal a-axis and c-axis, respectively (after Detlefs et al. 1997b).

Fig. 145. Reflection of X-rays in opposite directions by a non-centro-symmetric structure. The phase-differences of waves from different atoms are, except in special circumstances, the same for 002 as for 002 hence the intensities are the same. Hence the symmetry of an X-ray diffraction pattern ( L aue symmetry ) is the point-group symmetry of the crystal plus a centre...

Fig. 4. Reflection of X rays from internal crystal plane...

Two of the more direct techniques used in the study of lattice dynamics of crystals have been the scattering of neutrons and of x-rays from crystals. In addition, the phonon vibrational spectrum can be inferred from careful analysis of measurements of specific heat and elastic constants. In studies of Bragg reflection of x-rays (which involves no loss of energy to the lattice), it was found that temperature has a strong influence on the intensity of the reflected lines. The intensity of the scattered x-rays as a function of temperature can be expressed by I (T) = IQ e"2Tr(r) where 2W(T) is called the Debye-Waller factor. Similarly in the Mossbauer effect, gamma rays are emitted or absorbed without loss of energy and without change in the quantum state of the lattice by... 

This is not so strange as it may seem actually Bragg s law, which determines the reflection of X-rays, is also valid quite similarly for electron beams of the same wave length X. 

NOTE ON THE SELECTIVE REFLECTIONS OF X-RAYS BY CRYSTALS OF POTASSIUM BROMIDE... 

Armstrong, Duane and Havighurst, continuing the investigation of the reflection of X-rays by alkali halide crystals, found that if the crystals were carefully selected for perfection, by observing the sharpness of the photographic registration of a reflected X-ray beam, no effects were obtained which could be ascribed to selective reflection." Allison had also found that no such effect existed in the reflection of X-rays by barite. 

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