Atomic diffraction scattering

Figure 4 Interference pettern created when regularly spaced atoms scatter an incident plane wave. A spherical wave emanates from each atom diffracted beams form at the directions of constructive interference between these waves. The mirror reflection—the (00) beam—and the first- and second-order diffracted beams are shown.

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

X-ray diffraction. The mechanism by which atoms diffract or scatter electromagnetic radiation via the coupling of the electron cloud of the atom to the incident oscillating electric field was discussed in the section on SERS. The X-rays scattered by an atom are the resultant of the waves... 

Now consider the effect of anomalous scattering on the relative intensities of the diffracted rays in Scheme 2a and b when atom Y scatters anomalously with an intrinsic phase lead A< >(Y), and atom W scatters normally. Under such circumstances, the wave scattered by atom Y in Scheme 2a would lead that of atom W by a phase difference of + A< >(Y), and the wave scattered by atom Y in Scheme 2b would lag behind that of atom W by - + A(Y). These two phase differences are unequal in magnitude, so the corresponding amplitudes of their resultant waves, and the subsequent intensities, will be different, leading to a breakdown of Friedel s law. 

The determination of the atomic structure of surfaces is the cornerstone of surface science. Before the invention of STM, various diffraction methods are applied, such as low-energy electron diffraction (LEED) and atom beam scattering see Chapter 4. However, those methods can only provide the Fourier-transformed information of the atomic structure averaged over a relatively large area. Often, after a surface structure is observed by diffraction methods, conflicting models were proposed by different authors. Sometimes, a consensus can be reached. In many cases, controversy remains. Besides, the diffraction method can only provide information about structures of relatively simple and perfectly periodic surfaces. Large and complex structures are out of the reach of diffraction methods. On real surfaces, aperiodic structures such as defects and local variations always exist. Before the invention of the STM, there was no way to determine those aperiodic structures. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Neutron diffraction by crystals has been found valuable for locating hydrogen atoms (especially deuterium atoms, which scatter neutrons strongly), for studying the arrangement of magnetic moments, and for other special purposes. A summary is given by G. E. Bacon, Neutron Diffraction, Clarendon Press, Oxford, 1955. 

X-ray diffraction Scattering, mainly by electrons, followed by interference (A = 0.01-1 nm) Electron density map of crystal 10- sbut averaged over vibrational motion crystal —10 cm1 Location of light atoms or distinction between atoms of similar scattering factor difficult in presence of heavy atoms... 

Monoenergetic beams of atoms are scattered from ordered surfaces and detected as a function of scattering angle. This gives structural information on the outermost layer of the surface. Atom diffraction is extremely sensitive to surface ordering and defects. 

A multitude of concepts such as X-ray, neutron and electron diffraction, X-ray crystallography, low-angle scattering, powder diffraction, scattering by noncrystalline and amorphous solids, all refer to the same physical phenomenon. Whereas X-rays and electrons are scattered by extranuclear charge clouds, more massive particles like neutrons and a-particles are scattered on atomic nuclei. In principle, all of these processes are of the same type, as described for X-rays below. 

When the photon source has the wavelength of X rays (0.05 nm to 5nm), several processes can occur diffraction, absorption (by atoms), and scattering (Bragg s103 law or other). 

The low energy probe of atomic diffraction does not damage even delicate physisorbed overlayers, and it is sensitive to hydrogen, which is an important component of many surface systems of current interest. Electron scattering techniques are relatively insensitive to hydrogen because of its small scattering... 

Scattered waves from neighbouring atoms interfere in exactly the same way and unless the atoms are ordered as in a crystal, the total diffraction pattern is a function of the radial distribution of scattering density (atoms) only. This is the mechanism whereby diffraction patterns arise during gas-phase electron diffraction, scattering by amorphous materials, and diffraction... 

Other techniques used in surface structure determination include extended X-ray absorption fine structure (EXAFS), ion scattering, electron forward focusing, and helium atom diffraction. 

In isomorphous replacement, specific atoms in the crystal are attached to a heavy atom which scatters X-rays strongly, perturbing the diffusion pattern. Suitable tagging atoms are mercury, platinum or lanthanides, all of which have high electron densities. Structural analysis is made on the basis of comparing the diffraction patterns of the native macromolecule with that of the isomorphously tagged form. 

Thus, for a unit cell containing n atoms that scatter with amplitudes /i /2 "./n and phases v>, v>2. > V n. the resultant diffracted amplitude is given by... 

The reason that neutron diffraction is so much more effective than x-ray diffraction as a means for locating hydrogen atoms can be seen in the atomic scattering amplitudes given in Table 9-II (taken from reference 94, except for the neutron diffraction scattering factor for deuterons). 

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