Mark Farnworth - Pilkington European Technical Centre

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.

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

    [5 Marks]

    A study of the PDF card for calcite shows that its reflections correspond to 15 of the 30 reflections in the Problem 5 data set. All agree, within 3 decimal places of each d-spacing - except for Calcite 2.285Å which in the dataset is 2.284Å. This minor discrepancy can be ignored since it is observed that the 2.284 reflection has an unusually large peak width (as does the 1.510Å reflection). Larger than expected peak widths may be due to an interferring reflections - see later). Further evidence of this is obtained by consideration of the 2.284Å reflection peak intensity. The Calcite PDF card shows that the 2.284Å reflection should have an intensity of 18 - if the main Calcite 3.035Å reflection is assigned a value of 100. The actual 2.284Å reflection intensity is 29, significantly higher than it should be, which indicates a contaminant contribution. An alternative explanation is increased intensity due to preferred orientation, although I consider this unlikely since the other reflection intensities are similar to those shown on the PDF card.

    The reflections that can be attributed to Calcite are highlighted in red in the table below.

    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


    Comment: You have got the right idea, noting both the question of intensities (i.e. not just the d-spacing values) and the relevance of the two anomalous lines (2.284, 1.510 Ang.); I also like your use of colour in the table.
    5 Marks

  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):

    • Four pages of entries taken from the Hanawalt search manual:
      Page: 13 (77 kBytes)
        14 (78 kBytes)
        15 (79 kBytes)
        16 (86 kBytes)

    [10 Marks]

    Of the unidentified reflections, the most intense (A) is d= 3.343Å, the second most intense (B) is d= 4.27Å, the third most intense (C) is d= 1.817Å and the 'equal' forth most intense (D) reflections are d= 2.742Å and d= 1.541Å. At this stage it was not known whether these five reflections were from the same phase and so this was borne in mind when searching the Hanawalt data pages 13 to 17.

    The plan was to proceed as follows:

    To assume that the three strongest unidentified reflections were from the same phase, to run down the left hand column (most intense reflection) of each page, find any values that were 3.343 +/- 0.002Å. For 'matches' to then check the second column (second most intense reflections) to see if it was 4.27 +/- 0.02Å and for these matches to then check the third column (third most intense reflections) to see if it was 1.817 +/- 0.002Å. I allowed some leeway (+/- values) to account for possible inaccuracies in the measured and reference pattern data. This method would search for the unknown reflections A then B then C.

    If the above method didn't work my second plan would have been to search the reflections A then C then D (i.e. B attributed to a third phase).

    My third plan would have been to search the reflections B then C then D (i.e. A attributed to a third phase).

    In practice, my first method worked, ICCD Pattern 5-490 SiO2 giving matches to the three most intense unidentified reflections. Further confirmation was achieved when the remaining 5 entries of the 5-490 data were compared with the unidentified reflections.

    Entry 4 (1.54Å) corresponded to reflection 1.541Å.
    Entry 5 (2.46Å) corresponded to reflection 2.458Å.
    Entry 6 (2.28Å) corresponded to reflection 2.284Å.It was noted that this occured at the same position as a Calcite reflection, this observation, therefore, explaining the unusually large FWHM for this reflection.
    Entry 7 (1.38Å) was outside the range of the measured data.
    Entry 8 (2.13Å) corresponded to reflection 2.128Å

    Comparison of the measured peak intensities for SiO2 with the intensities given in the silica PDF card showed a very good correspondence. For example, the silica 4.27Å reflection intensity should be 35% of the main 3.343Å SiO2 reflection intensity according to the PDF card. 35% of 82% is 28.7%, which is very similar to the 28% measured value. Similar calculation showed similar agreement for the other SiO2 reflections. It was also noted that the elements in SiO2 were consistent with the electron probe analysis. Si had been detected (light elements such as O, C and H are not readily detected by electron probe analysis).

    The silica ICDD Pattern Number 5-490 was typed into the dialogue box on the Problem Set 5 question sheet and the full pattern obtained. Comparison was made with the measured reflections.

    The reflections that can be attributed to silica are highlighted in blue in the table below.

    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


Comment: Again, all the right ideas, also taking into account the intensities and the status of the anomalous 2.284 line, and the use of colour in the table. Minor quibbles: the 2.284 line should ideally be both red and blue (since it satisfies both calcite and quartz) - maybe a violet colour!!?; also the missing 2 lines (1.801, 1.608) should be "explained away" on grounds of being extremely weak; in other words one must not only explain what is there, but also explain what is not there.
8.5 Marks

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