5. (a) Consider a crystal consisting of m + 1 lattice planes of spacing d. of...

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5. (a) Consider a crystal consisting of m + 1 lattice planes of spacing d. of total thickness t = md, being set for diffraction as depicted in Fig. 2. At the incidence angle OB, Braggs law is satisfied. Explain the phenomenon through which the angles 1 and 2 are the limiting angles at which the diffracted intensity falls to zero. < (b) Assuming a triangular shape for the diffraction peak, derive the Scherrer Equation < t = B cos 0B Where B is the Full Width Half Maximum of the triangular shaped diffraction peak < (c) For the case where m=10 in the figure, write down a complete list of the path differences, in wavelengths, between the ray scattered by each plane below the surface and that scattered by the surface plane, for a scattering angle of 201. What plane scatters a ray exactly out of phase with the ray scattered by the third plane below the surface? What is the path difference for these two rays? < < (d) Write down a similar list of path differences for rays scattered at an angle halfway between 20B and 201 and demonstrate that these rays do not cancel one another. 11 B D 01 02.0B B' C' D' A' d 1 2 3 t=md M L L'AM' N N' m Figure 2. 5. (a) Consider a crystal consisting of m + 1 lattice planes of spacing d. of total thickness t = md, being set for diffraction as depicted in Fig. 2. At the incidence angle OB, Braggs law is satisfied. Explain the phenomenon through which the angles 1 and 2 are the limiting angles at which the diffracted intensity falls to zero. < (b) Assuming a triangular shape for the diffraction peak, derive the Scherrer Equation < t = B cos 0B Where B is the Full Width Half Maximum of the triangular shaped diffraction peak < (c) For the case where m=10 in the figure, write down a complete list of the path differences, in wavelengths, between the ray scattered by each plane below the surface and that scattered by the surface plane, for a scattering angle of 201. What plane scatters a ray exactly out of phase with the ray scattered by the third plane below the surface? What is the path difference for these two rays? < < (d) Write down a similar list of path differences for rays scattered at an angle halfway between 20B and 201 and demonstrate that these rays do not cancel one another. 11 B D 01 02.0B B' C' D' A' d 1 2 3 t=md M L L'AM' N N' m Figure 2.