MatSE 405: Microstructure Determination Problem set #13; due Wednesday, April 24, in class.
1. (a) Calculate the x-ray index of refraction and critical angle for total external reflection for Cu Ka x-rays incident on Al2O3. (b) Compare your calculation for the index of refraction with the results of more sophisticated calculations at the LBL web-site.
2. Compare the strength of the x-ray atomic scattering factor fx (remember to multiply dimensionless x-ray scattering factor by the classical electron radius) to the strength of the atomic scattering factor for electrons fe for Fe at the Bragg angle of the (200) reflection. The bcc lattice constant of Fe is 0.29 nm. You can find a table of fe values here. You can find calculations of fx at this site. Scroll down the index and click on "scattering factors". Use the B=0 result.
3. Calculate the extinction length for x-rays and electrons for the (400) reflection of Si. Use l = 1.54 Å for x-rays and l = 3 pm for electrons. You can find a table of fe values here. You can find calculations of fx at this site. Scroll down the index and click on "scattering factors". Use the B=0 result. Recall that the extinction length of a two-beam diffraction condition is
 x = pcosqB N lFhkl ,
(1)
where qB is the Bragg angle, N is the number of unit cells per unit volume, and Fhkl is the structure factor of that unit cell. For x-rays, remember to multiply the dimensionless x-ray atomic scattering factor by the classical electron radius to get a structure factor with the correct units of length. Si is a diamond structure crystal with a lattice constant of 0.543 nm.

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On 17 Apr 2008, 08:48.