MatSE 405: Microstructure Determination |

Problem set #13; due Wednesday, April 24, in class.

- (a) Calculate the x-ray index of refraction and critical angle for total external reflection
for Cu K
_{a}x-rays incident on Al_{2}O_{3}. (b) Compare your calculation for the index of refraction with the results of more sophisticated calculations at the LBL web-site. - Compare the strength of the x-ray atomic scattering factor f
_{x}(remember to multiply dimensionless x-ray scattering factor by the classical electron radius) to the strength of the atomic scattering factor for electrons f_{e}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 f_{e}values here. You can find calculations of f_{x}at this site. Scroll down the index and click on "scattering factors". Use the B=0 result. - 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 f
_{e}values here. You can find calculations of f_{x}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

where qx = pcosq _{B}N lF_{hkl}, (1) _{B}is the Bragg angle, N is the number of unit cells per unit volume, and F_{hkl}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.

File translated from T

On 17 Apr 2008, 08:48.