X-ray Diffraction

Powder X-ray techniques allow the rapid identification of unknown mineral specimens on the basis of observed interplanar spacings and observed peak intensities. It is generally helpful to have some other information to narrow down the possibilities (e.g., looks like a silicate rather than an oxide mineral, occurs in a garden-variety rock, etc.). The exercises that follow test your ability to apply the Bragg Law (n&lamda; = 2d sin θ). The final portion of Part 1 involves interpretation of actual printouts from an X-ray diffractometer (XRD).

1. For a cubic crystal with a = 10.0 Å calculate the interplanar spacing for planes with the following Miller indices:
   1. (010) _______________     (020) _______________     (050) ________________
   2. For the same mineral, and using Cu Ka X-rays as a source (k = 1.5418 Å), calculate the value of 2θ at which you would expect to find a reflection from the (001) planes. Show your work.

       

       

       

       

       

2. For a cubic crystal, use trigonometry to determine the interplanar spacings missing from the list below:

   (111)   4.924 Å		(422)   1.742 Å
   (220)   ______Å		(511)   1.634 Å
   (311)   2.573 Å		(440)   ______Å
   (222)   ______Å		(531)   ______Å
   (400)   ______Å		(620)   1.350 Å

3. The sheet silicate minerals are composed of stacked sheets of silica tetrahedra that commonly have d-spacings of between 7 Å and 15 Å. For the two unknowns (A and B) that yielded the attached scans, assume that the first peak in each of the attached scans is a 'reflection' from (001). Use the value of h (not 2h), the k given on the scans, and Bragg's Law to calculate the interplanar spacing for the (001) planes.

   Assume that all subsequent peaks are (002), (003), (004) ... (00 µ). Muliply each d-value you determine for these subsequent peaks by µ to provide additional determinations of the (001) interplanar spacing. Be aware that some of the reflections in the (00 µ) series may be missing. Once multiplied by µ, each calculation should give you approximately the same number.

   Average your determinations for (001) to provide the best estimate of d001. Unknown A Unknown B

Due Date: You should be prepared to submit this completed Homework assignment on Monday, November 8 in class.