Powder Diffraction Assignments

Answers to Problem Set 4 by Stewart F. Parker

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. The PDF entry for calcite (5-586) gives the following lines (and their intensities) in the range 4.5 - 1.5 Å:
    d( Å )3.8603.0352.845 2.4952.2852.0951.927 1.9131.8751.6261.604 1.5871.5251.5181.510
    Intensity121003 1418185 17248 2543

    Comparison with the table above shows that the "literature intensity" accounts for all of the observed intensity in these reflections except for the two at 2.284 Å (predicted 18, observed 29) and 1.510 Å (predicted 3, observed 4). The FWHM of these peaks is at least 50% greater than the majority of the other peaks, this strongly suggests that one or more of the other phases also contribute to these peaks.

  2. Home in on a potential second/third phase from the following range of entries in the Hanawalt search manual (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):

    The largest unassigned peak is at 3.343 Å, so this must belong to one or more of the additional phases. The electron microprobe data gives Ca, Si and Mg as the heavier elements. Typically, the microprobe can detect elements heavier than about sodium, so it is a reasonable first assumption that the other elements present (if any) must belong to the first row of the Periodic Table. I will assume that the Ca is all accounted for by the calcite, (if I am unable to assign another phase, I will relax this constraint). Looking through page 14 of the Hanawalt search manual in the d-spacing range 3.39 - 3.32  Å, there are a number of possible hits but the only one that contains only Si or Mg plus light elements is silica, SiO2. This is also chemically reasonable as a filler in plaster. The PDF number is 5-490 and the card was successfully retreived suggesting that it is a correct assignment! The PDF entry for silica gives the following lines (and their intensities) in the range 4.5 - 1.5 Å:
    d( Å )3.3432.458 2.2822.2372.1281.980 1.8171.8011.6721.659 1.6081.541
    Int. (Lit.)10012 12696 17<173 <115
    Int. (Obs.)10012 135105 18072 015

    The last two lines compare the PDF literature intensity with the observed ones, using the intensity of the 3.343 Å as 100%. The agreement is not perfect, but the overall pattern of intensities is well reproduced, giving confidence in the assignment. The apparently anomalous observed intensity of the 2.284 Å reflection is explained as overlap between reflections due to calcite and silica. This also explains the small shift for the silica line (predicted 2.282, observed 2.284 Å).

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

    The largest unassigned peak is at 2.742 Å, so this must belong to one or more of the additional phases. The electron microprobe data gives Ca, Si and Mg as the heavier elements, as Ca and Si have been accounted for, I will assume that the material must contain only Mg plus first row elements. Looking through page 32 of the Hanawalt search manual in the d-spacing range 2.74 - 2.70  Å, there are a number of possible hits but the only one that contains only Mg plus light elements is magnesium carbonate, MgCO3. The PDF number is 8-479 and the card was successfully retreived again suggesting that it is a correct assignment! The PDF entry for magnesium carbonate gives the following lines (and their intensities) in the range 4.5 - 1.5 Å:
    d( Å )2.7422.503 2.3182.1021.9391.769 1.7001.510
    Int. (Lit.)10018 445124 354
    Int. (Obs.)10017 050170 428

    The last two lines compare the PDF literature intensity with the observed ones, using the intensity of the 2.742 Å as 100%. The agreement is reasonable with the overall pattern of intensities reproduced. As these reflections are much weaker than those due to calcite and silica, the uncertainty in the intensity measurement will be aggravated when scaled to 100%. The apparently anomalous observed intensity of the 1.510 Å reflection is explained as overlap between reflections due to calcite and magnesium carbonate.

    At this stage there are no unassigned lines or lines with anomalous intensities or widths, so the analysis can be considered complete.