Atoms diffraction patterns

Due to the weak scattering by H atoms, diffraction patterns from CH4 clusters are strikingly similar to Ar ones. On the other hand patterns from N2 clusters differ considerably since there is no scattering atom at the molecule center. Size effects are particularly appreciable in N2 clusters and can be... 

Fig. 7.8 Na Atomic diffraction patterns obtained for Na atoms with a standing laser wave, with a clear splitting of the diffraction peaks of 2hk (theory-dashed line, experiment-solid line). (Reprinted with courtesy and permission of the American Physical Society from Gould...

The diffraction pattern consists of a small number of spots whose symmetry of arrangement is that of the surface grid of atoms (see Fig. IV-10). The pattern is due primarily to the first layer of atoms because of the small penetrating power of the low-energy electrons (or, in HEED, because of the grazing angle of incidence used) there may, however, be weak indications of scattering from a second or third layer. 

Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. 

Another mode of electron diffraction, low energy electron diffraction or FEED [13], uses incident beams of electrons with energies below about 100 eV, with corresponding wavelengths of the order of 1 A. Because of the very strong interactions between the incident electrons and tlie atoms in tlie crystal, there is very little penetration of the electron waves into the crystal, so that the diffraction pattern is detemiined entirely by the... 

So it is essential to relate the LEED pattern to the surface structure itself As mentioned earlier, the diffraction pattern does not indicate relative atomic positions within the structural unit cell, but only the size and shape of that unit cell. However, since experiments are mostly perfonned on surfaces of materials with a known crystallographic bulk structure, it is often a good starting point to assume an ideally tenuinated bulk lattice the actual surface structure will often be related to that ideal structure in a simple maimer, e.g. tluough the creation of a superlattice that is directly related to the bulk lattice. 

In this section, we concentrate on the relationship between diffraction pattern and surface lattice [5], In direct analogy with the tln-ee-dimensional bulk case, the surface lattice is defined by two vectors a and b parallel to the surface (defined already above), subtended by an angle y a and b together specify one unit cell, as illustrated in figure B1.21.4. Withm that unit cell atoms are arranged according to a basis, which is the list of atomic coordinates within drat unit cell we need not know these positions for the purposes of this discussion. Note that this unit cell can be viewed as being infinitely deep in the third dimension (perpendicular to the surface), so as to include all atoms below the surface to arbitrary depth. 

Idistribution functions can be measured experimentally using X-ray diffraction. The regular arrangement of the atoms in a crystal gives the characteristic X-ray diffraction pattern with bright, sharp spots. For liquids, the diffraction pattern has regions of high and low intensity but no sharp spots. The X-ray diffraction pattern can be analysed to calculate an experimental distribution function, which can then be compared with that obtained from the simulation. 

Fig. 1. Structures of (O) atoms and corresponding electron and x-ray diffraction patterns for (a) a periodic arrangement exhibiting translational symmetry where the bright dots and sharp peaks prove the periodic symmetry of the atoms by satisfying the Bragg condition, and (b) in a metallic glass where the atoms are nonperiodic and have no translational symmetry. The result of this stmcture is that the diffraction is diffuse.

Crystal Structure. Diamonds prepared by the direct conversion of well-crystallized graphite, at pressures of about 13 GPa (130 kbar), show certain unusual reflections in the x-ray diffraction patterns (25). They could be explained by assuming a hexagonal diamond stmcture (related to wurtzite) with a = 0.252 and c = 0.412 nm, space group P63 /mmc — Dgj with four atoms per unit cell. The calculated density would be 3.51 g/cm, the same as for ordinary cubic diamond, and the distances between nearest neighbor carbon atoms would be the same in both hexagonal and cubic diamond, 0.154 nm. 

When a ledge is formed on an atomically smooth monolayer during tire formation of a thin film the intensity of the diffraction pattern is reduced due to the reduction in the beatrr intensity by inelastic scattering of electrons at the ledge-monolayer junction. The diffraction intensity catr thus be used during deposition of several monolayers to indicate the completion of a monolayer through the relative increase in intensity at tlris time. Observation of this effect of intensity oscillation is used in practice to count the number of monolayers which are laid down during a deposition process. 

From shock compression of LiF to 13 GPa [68] these results demonstrate that X-ray diffraction can be applied to the study of shock-compressed solids, since diffraction effects can be observed. The fact that diffraction takes place at all implies that crystalline order can exist behind the shock front and the required readjustment to the shocked lattice configuration takes place on a time scale less than 20 ns. Another important experimental result is that the location of (200) reflection implies that the compression is isotropic i.e., shock compression moves atoms closer together in all directions, not just in the direction of shock propoagation. Similar conclusions are reached for shock-compressed single crystals of LiF, aluminum, and graphite [70]. Application of these experimental techniques to pyrolytic BN [71] result in a diffraction pattern (during compression) like that of wurtzite. 

The F-actin helix has 13 molecules of G-actin in six turns of the helix, repeating every 360 A. Oriented gels of actin fibers yield x-ray fiber diffraction patterns to about 6 A resolution. Knowing the atomic structure of G-actin it was possible for the group of Ken Holmes to determine its orientation in the F-actin fiber, and thus arrive at an atomic model of the actin filament that best accounted for the fiber diffraction pattern. 

MIR), requires the introduction of new x-ray scatterers into the unit cell of the crystal. These additions should be heavy atoms (so that they make a significant contribution to the diffraction pattern) there should not be too many of them (so that their positions can be located) and they should not change the structure of the molecule or of the crystal cell—in other words, the crystals should be isomorphous. In practice, isomorphous replacement is usually done by diffusing different heavy-metal complexes into the channels of preformed protein crystals. With luck the protein molecules expose side chains in these solvent channels, such as SH groups, that are able to bind heavy metals. It is also possible to replace endogenous light metals in metal-loproteins with heavier ones, e.g., zinc by mercury or calcium by samarium. 

---