Characterization of Materials by E. Lifshin (editor)

By E. Lifshin (editor)

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Example text

It may also apply to thin precipitate lamellae which have a lattice different from that of the matrix. In such a non-reflecting slab of thickness z the extinction distance is infinite since no diffraction occurs out of the transmitted or scattered beam. The system of Eqs. sj. We then obtain where To and So are the values of T and S at the entrance face of the vacuum lamellae, or in matrix form: T\ = /exp(-7iisz) Sjout V 0 0 \/T\ exp(nisz))\Sjin (1-149) We call this matrix the vacuum matrix and it is represented by F(z,s), where z is the (1-146) Note that $(a1)${a2) = Sia^a^.

E. The dynamic theory can also be developed directly from the Schrodinger equation. This approach can easily be generalized to many-beam situations. Moreover it leads to a simple geometrical construction of the wave vectors of the different beams propagating in the crystal. , K is corrected for refraction by maintaining the constant part of the lattice potential, but ignoring the periodic part. The periodic part of the lattice potential changes the wave vector of the incident wave to k0. We further assume that only one scattered wave with wave vector kg = k0 + g is excited, a part from the incident beam with wave vector k0.

1-132) and (1-133); moreover, we generally assume that the deviation parameters s1 and s2 may also be different in the front and rear parts of the crystal, simulating the presence of a "mixed" interface; the thicknesses of the two parts are called zt and z2 (Fig. 1-23). The transmission matrix for the front part is clearly M(z1,s1). The transmitted and scattered beams emerging from this front part are now incident on the second part with thickness z 2 . We shall represent the transmission matrix for this second part by ( y v I and determine the expressions for the elements X, Y9 U and V.

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