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Additional info for Elementary Solid State Physics
We start with the simplest possible situation, an x-ray beam scattered from a one-dimensional monatomic lattice, as illustrated in Fig. 5(a). 5 and can readily be evaluated. 2s) Physically, it is more meaningful to examine 52 than S, since this is the quantity which enters directly into calculations of intensity. al " - sin:(lr)s. 26) ' We now wish to see how this function depends on the scattering vector s. 26), 52 is the ratio of two oscillating functions having a common period s'a:2n, but, because N is much larger than unity in any practical case, the numerator oscillates far more rapidly than the denominator.
In effect the electrons absorb energy from the beam, and scatter it in all directions. But the electrons form a charge cloud surrounding the atom, so when we are considering scattering from the atom as a whole, we must take into account the phase differences between the rays scattered from the different regions of the charge cloud. We do this as follows: t In the remainder of this chapter fi rst-order reflections. and in the problem section, we shall consider only .. _ 38 ; )4.. 1 \ X-ray, Neutron, and Electron Difrraction in Crystals Consider a single electron, as shown X1 in Fig.
2 (a) Reflection of x-rays from a crystal. The reflected rays are nearly parallel because the detector is positioned far from the crystal. (b) Reflected intensity from a KBr crystal. The reflecting planes for the various peaks are indicated. difference between the paths of any two consecutive rays is an integral multiple of the wavelength. 3) where ,t is the wavelength and rays I ,? a positive integer. The path difference A between and 2 in the figure is L:TB+Ee -Ae,:2TB-Te,. , that the angles of incidence equal the angles of reflection.