The Problem: A collection of ancient plaster figures has been uncovered. A small sample is taken: microscopic examination identifies calcite (CaCO3) and electron microprobe analysis reveals Ca, Si and Mg as the major heavier elements. A powder diffraction pattern is collected, which after initial data analysis, yields the parameters below (the third parameter "FWHM" is a measure of the peak width). Identify the two remaining phases in the sample. Explain, step by step, how you arrived at this solution. Comment on the solution.

ANSWERS TO THE PROBLEM SET 5

The following table identifies the various phases present in the plaster. The d-values indexed black are due to the calcite. The silicate (5-490) and magnesium carbonate (8-479) are indexed with blue and red respectively.

d (Å) I (%) FWHM(°)     d (Å) I (%) FWHM(°)     d (Å) I (%) FWHM(°)
4.27 28   0.27     2.237 4   0.23     1.700 5   0.35
3.86 12   0.30     2.128 8   0.23     1.672 6   0.23
3.343 82   0.25     2.102 6   0.35     1.659 2   0.24
3.035 100   0.28     2.095 18   0.27     1.626 4   0.29
2.845 3   0.28     1.980 4   0.23     1.604 8   0.28
2.742 12   0.35     1.939 2   0.37     1.587 2   0.29
2.503 2   0.36     1.927 5   0.29     1.541 12   0.23
2.495 15   0.28    1.913 17   0.28     1.525 5   0.28
2.458 10   0.22    1.875 17   0.28    1.518 4   0.30
2.284 29   0.43    1.817 15   0.22    1.510 4   0.42

The d-value indexed with the green is an overlap of calcite (113) and silica (102) peaks. This is also evident from thier high FWHM values. Similarly the d-value indextedThe d-value indexed with the violet is an overlap of (211) of magnesium carbonate and (217) of silica.


Comment: An excellent table which makes the solution (which is correct) very clear by the use of colour-coding for the phases including even special colours (green, violet) for overlap lines. Incidentally the violet should read as an overlap between calcite and silica, not magnesium carbonate and silica. The one criticism is that you did not give explanations of how you worked your way "step by step" to the solution and arrived at your answer (see model answer). Obviously you must have done the right things, but for full marks we also needed the explanation as well. Note that in the model answer given, for full certainty one must be able not only to account for all the lines in the pattern, but also provide plausible reasons why any expected line (from the silica/|MgCO3 files) cannot be seen.

5 + 5.5 + 5.5 Marks

Thus the mixture contains three phases of decreasing % content

  1. CALCITE
  2. SILICA
  3. MAGNESIUM CARBONATE

The presence these three phases is further confirmed from electron microprobe analysis which revealed the presence of Ca, Si and Mg.


Comment: Your final solution is correct and you point out that the solution is consistent with the microprobe results.
4 Marks


Overall Comment: A correct solution, excellent table, but more explanations could have been given.

Additional comments by JKC: HTML very much improved. Note that you should only have one pair of <HEAD> </HEAD> tags per document (at the top) and that you need to enclose the remainder in a pair of <BODY> </BODY> tags (as edited in my myself to this file).