Wavelength of X-rays

TABLE 7.1 Wavelengths of X-Ray Emission Spectra in Angstroms Continued)... 

X-Ray Microscopy. Because of the short wavelength of x-rays, they have, for nearly 100 years, held out the hope of being utilized in order to significantly lower the diffraction limit of resolution when visible light is used. The difficulties of focusing x-rays and the relative weakness of x-ray sources have, until recently, fmstrated efforts to teach that goal (25). 

Two other items deserve mention. The various methods of measuring the wavelength of x-ray lines can be adapted to the location of absorption edges. The occurrence of three L, five M, etc., states, an early mystery, has now been satisfactorily explained with the aid of wave mechanics. 

Y. Cauchois and H. Ilulubei, Tables de Constantes et Donnees Numeriques. 1, Con-stantes Selectionnees. Longuers d Onde des Emissions X et des Discontinuites d Absorption X. (Tables of Constants and Numerical Data. 1. Selected Constants. Wavelengths of X-ray Emissions and of X-ray Absorption Discontinuities.), Hermann Cie., Editeurs, Paris, 1947. 

The short wavelength of x-rays naturally makes them difficult to focus. Electrons, on the other hand, can rather easily be controlled to give beams a few square microns in cross section, a fact that made possible the x-ray emission electron-microprobe (9.9). Clearly, such a concentrated electron beam striking one side of a suitable thin target can give rise to an x-ray spot on the other, and this spot can be small enough to be regarded as a point source of x-rays. 

X-rays are electromagnetic radiation lying between ultraviolet and gamma rays in the electromagnetic spectrum. The wavelength of x-rays is expressed in angstrom units (A) 1 A is equal to 10-8 cm. 

As mentioned above, the formalism of the reciprocal lattice is convenient for constructing the directions of diffraction by a crystal. In Figure 3.4 the Ewald sphere was introduced. The radius of the Ewald sphere, also called the sphere of reflection, is reciprocal to the wavelength of X-ray radiation—that is, IX. The reciprocal lattice rotates exactly as the crystal. The direction of the beam diffracted from the crystal is parallel to MP in Figure 3.7 and corresponds to the orientation of the reciprocal lattice. The reciprocal space vector S(h k I) = OP(M/) is perpendicular to the reflecting plane hkl, as defined for the vector S. This leads to the fulfillment of Bragg s law as S(hkI) = 2(sin ())/X = 1 Id. 

Y. Cauchois and C. Senemand, Wavelengths of X-ray Emission Lines and Absorption Edges, Volume 18 of International Tables of Selected Constants, Pergamon Press, Oxford, 1978. 

Using these units, the wavelengths of X-rays used in analytical work are in the range 1 10 A. 

X-ray detectors also come in several varieties (1) single-photon counters which yield accurate results but require up to several weeks to acquire the 10,000 -100,000 (lO lO ) reflections necessary to compile a complete data set for a protein crystal (2) image plates that operate much like photographic film but are 10 times more sensitive (3) area detectors, electronic devices that detect X-ray photons on a two-dimensional surface. Both fluorescent-type detectors, image plates and fast area detectors, are more sensitive at the shorter wavelengths of X-ray radiation from synchrotron sources. 

Figure 23-1 A part of the electromagnetic spectrum. The letters Vy By G, Y, O, R over the visible part of the spectrum refer to the colors of the light. The position marked "Ka line of Cu" is the wavelength of X-rays and most widely employed in X-ray diffraction studies of proteins and other organic materials.

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