Atoms Bragg scattering

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

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). 

Finally, X rays of a certain X can specifically excite X-ray luminescence of the sample. Thus, Cu-Ka line will excite iron atoms, and Mo-K those of yttrium, producing a strong parasitic background which (imlike Bragg scattering) does not decrease with the increase of the Bragg angle - a most unwelcome complication. 

FIGURE 5.7 If we take the difference between the incident and reflected rays k and lc0 from (a) to form the diffraction vector s, then, by Bragg s law, it is clear that s must be identical to the reciprocal lattice vector h for any family of planes in diffracting position. This must be true no matter what the actual distribution of atoms, or scattering material, around the planes in the family may be. 

Therefore, to better approximate the real scattering efficiency of each atom, the scattering factor fj in the structure factor equation is multiplied by an exponential term that effectively reduces the fj as a function of sin 9, where 9 is the Bragg angle. The new term has the form... 

Once Xj,yj, and zy are known for each atom in the unit cell, it is possible to calculate and its components, Fc(hkl) and (aIM)l . This calculation is broken into two parts, one, AhU, involving a cosine function and the other, Bhu, involving a sine function (Fig. 16). For each atom the scattering factor at the value of sin0/A. appropriate for the diffracted beam, hid, is multiplied by a cosine or sine function that contains h,k,l and x,y,z in it. This is done for each atom in the structure, and the values are all summed to give A u and B. This entire computation is then repeated for every Bragg reflection. 

One of the important featmes of Bragg scattering is that the strength of the scattered beam depends on how well the atoms are localized at their ideal lattice locations. If the atoms are all located very close to the lattice positions defined by the interference pattern, they will all nearly satisfy the conditions for constructive interference, and the scattering will be strong. 

Since the specimen is thin compared to the mean free path of the incident electrons, most will not interact at all with the constituent atoms of the sample but will simply pass undeflected through the material. However, provided the sample is crystalline, some fraction of the incident electrons will be scattered from crystal planes within the material by Bragg diffraction, and give rise to characteristic spots or rings in an electron diffraction pattern. These diffracted electrons lose little or none of their incident energy in such Bragg scattering events and are said to be elastically scattered. 

J.N. Tan, J.J. Bollinger, B. Jelenkovic, D.J. Wineland, Long-Range Order in Laser-Cooled, Atomic-Ion Wigner Crystals Observed by Bragg-Scattering. Phys. Rev. Lett. 75, 4198... 

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