Diffraction of X rays by crystals

FIGURE 1.5. The experimental setup used by Friedrich and Knipping to measure X-ray diffraction intensities. The important components consisted of an X-ray source to provide a finely collimated X-ray beam, a crystal to scatter X rays, and a detection system, such as photographic film, to measure the directions and intensities of the diffracted beams. The intensities so measured are related to the squares of the amplitudes of the scattered beams, but information on the relative phases of these scattered beams is lost. This same general experimental setup is currently used, although the source of X rays and the detection system are now much more sophisticated- 

During the twentieth century, as different types of diffraction have been found, we have come to understand that no firm distinction can be made between waves and particles. For example, neutrons and electrons,which would be considered particles according to classical mechanics, can be diffracted. With great perspicacity, William Henry Bragg wrote in 1912, The problem then becomes, it seems to me, not to decide between two theories of X rays, but to find, as I have said elsewhere, one theory which possesses the capacities of both.  

Several types of diffraction by crystals are now studied. Neutron diffraction can be used with great effectiveness to give information on molecular structure. These results complement those from X-ray diffraction studies, because there are different mechanisms for the scattering of X rays and of neutrons by the various atoms. X rays are scattered by electrons, while neutrons are scattered by atomic nuclei. Neutron diffraction is important for the determination of the locations of hydrogen atoms which, because of their low electron count, are poor X-ray scatterers. Electron diffraction, while requiring much smaller crystals and therefore being potentially useful for the study of macromolecules, produces diffraction patterns that are more complicated. Their interpretation is hampered by the fact that the diffracted electron beams are rediffracted within the crystal much more than are X-ray beams. This has limited the practical use of electron diffraction in the determination of atomic arrangements in crystals to studies of surface structure. 

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Bijvoet, J.M., Burgers, W.G. and Hagg, G. (1972) Early Papers on Diffraction of X-rays by Crystals (Int. Union of Crystallography, Utrecht) pp. 5. 

M. von Laue (Frankfurt) discovery of the diffraction of X-rays by crystals. 

X-ray diffraction occurs in the elastic scattering of X-ray photons by atoms in a periodic lattice. The scattered monochromatic X-rays that are in phase give constructive interference. Figure 4.4 illustrates how diffraction of X-rays by crystal planes allows one to derive lattice spacings by using the Bragg relation ... 

A great amount of information about the structure of crystals has been obtained by use of the x-ray diffraction method. The diffraction of x-rays by crystals was discovered by Max von Laue in 1912. Shortly thereafter W. L. Bragg discovered the Bragg equation, and in 1913 he and his father, W. H. Bragg, published the first structure determinations of crystals. 

Obviously, much of the development of crystallography predates the discovery of diffraction of X-rays by crystals. Early studies of crystal structures were concerned with external features of crystals and the angles between faces. Descriptions and notations used were based on these external features of crystals. Crystallographers using X-ray diffraction are concerned with the unit cells and use the notation based on the symmetry of the 230 space groups established earlier. 

One of the greatest and most surprising discoveries of our own age, that of the diffraction of X-rays by crystals (in 1912) was made by a mathematician, Max von Laue, by the sheer power of believing more concretely than anyone else in the accepted theory of crystals and X-rays. 

Unlike visible light, X rays cannot be focused, so we use diffraction of X rays by crystals to see molecules, but, to do this, the microscope lens must be replaced by a mathematical computation (a Fourier synthesis). 

Bragg s Law, the Bragg equation In diffraction of X rays by crystals, each diffracted beam can be considered to be reflected from a set of parallel lattice planes. If the angle between the diffracted X-ray beam (wavelength X) and the normal (perpendicular) to a set of crystal lattice planes is 90° - Ohki, and if the perpendicular spacing of the lattice planes is dhti, then ... 

Max von Laue (1879-1960). German physicist who was the first to observe and explain the phenomenon of x-ray diffraction in 1912 Laue was awarded Nobel Prize in Physics in 1914 for his discovery of the diffraction of x-rays by crystals . For more information about Laue see http //wvw.nobel.se/physics/laureates/1914/... 

Radiography was thus initiated without any precise understanding of the radiation used, because it was not until 1912 that the exact nature of x-rays was established. In that year the phenomenon of x-ray diffraction by crystals was discovered, and this discovery simultaneously proved the wave nature of x-rays and provided a new method for investigating the fine structure of matter. Although radiography is a very important tool in itself and has a wide field of applicability, it is ordinarily limited in the internal detail it can resolve, or disclose, to sizes of the order of 10 cm. Diffraction, on the other hand, can indirectly reveal details of internal structure of the order of 10 cm in size, and it is with this phenomenon, and its applications to metallurgical problems, that this book is concerned. The properties of x-rays and the internal structure of crystals are here described in the first two chapters as necessary preliminaries to the discussion of the diffraction of x-rays by crystals which follows. 

At first glance, the diffraction of x-rays by crystals and the reflection of visible light by mirrors appear very similar, since in both phenomena the angle of incidence is equal to the angle of reflection. It seems that we might regard the planes of atoms as little mirrors which reflect the x-rays. Diffraction and reflection, however, differ fundamentally in at least three aspects ... 

The diffraction of x-rays by crystals was discovered in 1912, and in 1913 the first determinations of the atomic arrangement in crystals were made by use of this technique by the British physicists W. H. Bragg and W. L. Bragg (father and son). Their work during this first year included the determination of the structure of diamond, as shown in the adjacent drawing. 

Figure 12.27 Diffraction of x-rays by crystal planes. As in-phase x-ray beams A and B pass into a crystal at angle 9, they are diffracted by interaction with the particles. Beam B travels the distance DE + EF farther than beam A. If this additional distance is equal to a whole number of wavelengths, the beams remain in phase and create a spot on a screen or photographic plate. From the pattern of spots and the Bragg equation, n = 2d sin 0, the distance d between layers of particles can be calculated.

In 1912. W 1. Bragg treated the diffraction of X-rays by crystals as shown in Figure 12-6. Here, a narrow beam of radiation strikes the cryslal surface at angle scattering occurs as a result of interaction of tile radiation with atoms located at O. P. and R. if the distance... 

The equation nA = 2d sin 9 is known as the Bragg equation. The important result of this equation is that at any particular angle of incidence 9, only X-rays of a particular wavelength fulfill the requirement of staying in phase and being reinforced, and are therefore diffracted by the crystal. Diffraction of X-rays by crystals forms the basis of XRD for crystal structure determination and is also the reason XRF spectrometry is possible, as will be seen. 

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