Powder Diffraction Assignments

Answer to Problem Set 4

Question: 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.

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

Even if you do not have the ICCD-PDF you will be able to work through the problem by using the files below (selected from the ICDD-PDF). You are advised to work through the problem in the following sequence:

  1. Start by making use of the PDF entry for calcite:

  2. Home in on a potential second/third phase from the following range of entries in the Hanawalt search manual
    3. (you should note down the numerical address of your choice candidate; e.g. 7-215 or 21-1271; the number appears on the far right of the manual so you might have to expand your screen or move to the extreme right of the page once you have selected your choice):

  3. Repeat the process of (2) for a potential third/second phase from the following range
    4. , again noting down the numerical address of your choice:

  4. Once you have identified your potential second and third phases, you should obtain their full PDF patterns and then check that your two choices match the full card image in detail. To get the card image of either, enter the numerical code of one of them in the following dialogue box and enter (e.g. Vol. = 7 Card = 215). If you have made a correct choice (either one) then the full pattern will be returned to you; if you make the wrong choice then you will receive an error message and obviously you will have to re-try after more thought or correction! Eventually you should get both card images. If you cannot get anywhere after many attempts then e-mail Paul Barnes for help.

Vol. - Card
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Note that both volume number and card number must be filled in. (You can check that the above form works correctly by entering volume number 5 and card number 586. Submission of the form should return data for 5-586, which is calcite.)

You might find the following clues helpful:

Answer:

The sample consists of the next three phases:

  • CaCO3,
  • alpha-SiO2, and
  • MgCO3.

    The first step was to notice in the list above entires which belong to calcite, looking at its data card (5-586). Fifteen of them were found. From the remaining entries, one with the highest d (Å) value (4.27Å) was the first one. This I used to skim through the leading values in the first four given pages of the Hannawalt manual, allowing that the last decimal might not be the same as it is in the powder diffraction pattern. It resulted in the closest entry with card number 5-490, alpha-SiO2. This proved to be right.

    Then I again did removal of entries from the list which belonged to the already known phases (a couple of them proved to be from both of them). From the remaining five entries, the one with d = 2.742Å was the most prominent one. Using it with 30-33 pages of the Hannawalt manual, I found that the card nearest to the remaining values would be 8-479, i.e. MgCO3.

    Comment: in the last step (not in the first one, though) there was a possibility that the biggest d available value was not the biggest value of the unknown phase too, since that one could have already been covered (and excluded from the list used for the quest) by a value from already revealed two phases. But, this should not be a problem, since all entries in the Hannawalt manual are given several times, differently ordered.

    All the given entries are covered with this solution, so that can be inferred that no additional phases (containing Ca, Si, and/or Mg) are present in the sample (under the assumption that there are no further phases which reflections are totally covered with those from phases above).

    Student: Siniûa Prokic