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061025 Quiz 5 XRD

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1 061025 Quiz 5 XRD

1 & 2) It was mentioned in Lab 1 that the diffraction pattern observed on a film or screen is the Fourier transform of the structure. Explain how a diffraction pattern with one peak (one d- spacing) is related to the real space structure of a crystal using the pairwise correlation function (rod throwing probability) and a Fourier transform of this function.

3) Show how the phase difference, φ = 2π/λ (S - S0) • AB can be obtained from a sketch of the diffraction from atoms A and B.

4) Construct the Sphere of Reflection by sketching a reciprocal lattice with an origin, (000) and the center of the diffraction measurement indicating 2θ and (S - S0)/λ. Why are only a few peaks seen when a perfect crystal diffracts with a single wavelength x-ray radiation?

5) Construct the limiting sphere and explain why Debye-Scherrer rings are seen from a powder pattern in a 2D photographic measurement such as was done in lab 2.

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