Powder Diffraction Assignment
Problem Set 5

Christy De Meyer

  1. the start: the ICDD-PDF entry for calcite

    The information obtained from the microscopic examination, the identification of calcite (= CaCO3), enables us to assign certain reflections in this X-ray diffractogram to this compound.

    diffractogram of
    the ancient plaster    		 ICCD-PDF entry
    for calcite
    d (Å) I (%) d (Å) I (%) remarks
    4.27 28 from another phase
    3.86 12 3.86 12 I and d identical + small FWHM
    peak form calcite
    3.343 82 from another phase
    3.035 100 3.035 100 I and d identical + small FWHM
    peak form calcite
    2.845 3 2.845 3 I and d identical + small FWHM
    peak form calcite
    2.742 12 from another phase
    2.503 2 from another phase
    2.495 15 2.495 14 I (14~15) and d the same + small FWHM
    peak form calcite
    + perhaps another small peak(?)
    2.458 10 from another phase
    2.284 29 2.285 15 d slightly different + I different
    + broad peak
    peak form calcite
    + peak from another compound
    2.237 4 from another phase
    2.128 8 from another phase
    2.102 6 from another phase
    2.095 18 2.095 18 I and d identical + small FWHM
    peak form calcite
    1.980 4 from another phase
    1.939 2 from another phase
    1.927 5 1.927 5 I and d identical + small FWHM
    peak form calcite
    1.913 17 1.913 17 I and d identical + small FWHM
    peak form calcite
    1.875 17 1.875 17 I and d identical + small FWHM
    peak form calcite
    1.817 15 from another phase
    1.700 5 from another phase
    1.672 6 from another phase
    1.659 2 from another phase
    1.626 4 1.626 4 I and d identical + small FWHM
    peak form calcite
    1.604 8 1.604 8 I and d identical + small FWHM
    peak form calcite
    1.587 2 1.587 2 I and d identical + small FWHM
    peak form calcite
    1.541 12 from another phase
    1.525 5 1.525 5 I and d identical + small FWHM
    peak form calcite
    1.518 4 1.518 4 I and d identical + small FWHM
    peak form calcite
    1.510 4 1.510 3 I (4~3) and d the same + broader FWHM
    peak form calcite
    + perhaps another small peak(?)


    Comment: You have got the right idea, and you have correctly noted the need to flag up the 2.284 and 1.510 lines. I take it you mean "peak from" rather than "peak form".
    5 Marks

  2. Second/third phase

    A number of peaks have already been identified as coming from CaCO3. If we look at the remaining unidentified peaks, one can easily notice a very sharp and intense peak at d=3.343Å. Looking in the Hanawalt search manual, more specific on pages 14 and 15 (in the 3.39 - 3.32 +/-0.02 range) and keeping in mind the information from electron microprobe analysis (Ca, Si ans Mg as major heavier elements), we can quickly find the compound SiO2. How did I found this result?
    Firstly, I searched the Hanawalt manual for compounds with the most intense peak at 3.34Å.
    Secondly, I checked the chemical composition (especially keeping an eye on the compounds which contain Mg, Ca and Si).
    Further examination included the comparison of the other d-values (and their order of intensity).
    This yields SiO2 (5-490) as second phase. I searched the ICCD-PDF entry for SiO2. As I did for CaCO3, I also indicated peaks of SiO2 in the pattern of the ancient plaster. (In bold)

    diffractogram of
    the ancient plaster    		 ICCD-PDF entry
    for calcite and SiO2
    d (Å) I (%) d (Å) I (%) remarks
    4.27 28 4.26 35, but 29
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    3.86 12 3.86 12 peak form calcite
    3.343 82 3.343 100, but here 82 d the same (I reference) + small FWHM
    peak form SiO2
    3.035 100 3.035 100 peak form calcite
    2.845 3 2.845 3 peak form calcite
    2.742 12 from another phase
    2.503 2 from another phase
    2.495 15 2.495 14 peak form calcite
    2.458 10 2.458 12, but 10
    relative to 82    		 I and d the same + small FWHM
    peak form SiO2
    2.284 29 2.285
    2.282    		 15
    12, but 10
    relative to 82    		 broad peak
    peak form calcite
    + SiO2
    2.237 4 2.237 6, but 5
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    2.128 8 2.128 9, but 7
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    2.102 6 from another phase
    2.095 18 2.095 18 peak form calcite
    1.980 4 1.980 6, but 5
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    1.939 2 from another phase
    1.927 5 1.927 5 peak form calcite
    1.913 17 1.913 17 peak form calcite
    1.875 17 1.875 17 peak form calcite
    1.817 15 1.817 17, but 14
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    There should be a very small reflection at 1.801Å
    but probably this one is lost in the background
    1.700 5 from another phase
    1.672 6 1.672 7, but 6
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    1.659 2 1.659 3, but 2
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    1.626 4 1.626 4 peak form calcite
    1.604 8 1.604 8 peak form calcite
    1.587 2 1.587 2 peak form calcite
    1.541 12 1.541 15, but 12
    relative to 82    		 I and d nearly the same + small FWHM
    peak form SiO2
    There should be a very small reflection at 1.601Å
    but probably this one is lost in the background
    1.525 5 1.525 5 peak form calcite
    1.518 4 1.518 4 peak form calcite
    1.510 4 1.510 3 peak form calcite

    There are still some gaps left in the spectrum. The highest peak left in this spectrum lies at an d=2.742Å. Thus, the third phase will not be found on pages 13-16.


    Comment: This is the correct solution. Your explanation of how to get the solution is clear, noting the elemental and intensity information to be used. Also note that the agreement should be in both positive and negative senses; i.e. you must also explain that there are no lines missing in the sample that are present in the data file - in fact there are 2 missing (see model answer) but this can be explained on account of their weak intensities.
    8 Marks

  3. third phase

    As the highest intensity of the third phase in the diffractogram is resulting from d=2.742Å, I checked pages 30-32 (2.79-2.75 +/-0.1 and 2.74-2.70 +/-0.1). One remark: all of the remaining peaks are broader (FWHM of +/- 0.35).
    Firstly, I searched the Hanawalt manual for compounds with the most intense peak at 2.74Å.
    Secondly, I checked the chemical composition (the compound must contain Mg).
    Further examination included the comparison of the other d-values (and their order of intensity).
    This yields MgCO3 ( 8-479) as third phase. Searching the ICCD-PDF entry and checking this composition on the pattern of the ancient plaster: (In Italic)

    diffractogram of
    the ancient plaster    		 ICCD-PDF entry
    for calcite and SiO2 and MgCO2
    d (Å) I (%) d (Å) I (%) remarks
    4.27 28 4.26 35, but 29
    relative to 82    		 peak form SiO2
    3.86 12 3.86 12 peak form calcite
    3.343 82 3.343 100, but here 82 peak form SiO2
    3.035 100 3.035 100 peak form calcite
    2.845 3 2.845 3 peak form calcite
    2.742 12 2.742 100, but here 12 d the same (I reference)
    peak form MgCO3
    2.503 2 2.503 18, but 2
    relative to 12    		 I and d nearly the same
    peak form MgCO3
    2.495 15 2.495 14 peak form calcite
    2.458 10 2.458 12, but 10
    relative to 82    		 peak form SiO2
    2.284 29 2.285
    2.282    		 15
    12, but 10
    relative to 82    		 broad peak
    peak form calcite
    + SiO2
    2.237 4 2.237 6, but 5
    relative to 82    		 peak form SiO2
    2.128 8 2.128 9, but 7
    relative to 82    		 peak form SiO2
    2.102 6 2.102 45, but 5
    relative to 12    		 I and d nearly the same
    peak form MgCO3
    There should be a very small reflection at 2.318Å
    but this one is certainly lost in the background
    2.095 18 2.095 18 peak form calcite
    1.980 4 1.980 6, but 5
    relative to 82    		 peak form SiO2
    1.939 2 1.939 12, but 1
    relative to 12    		 I and d nearly the same
    peak form MgCO3
    1.927 5 1.927 5 peak form calcite
    1.913 17 1.913 17 peak form calcite
    1.875 17 1.875 17 peak form calcite
    1.817 15 1.817 17, but 14
    relative to 82    		 peak form SiO2
    1.700 5 1.700 35, but 4
    relative to 12    		 I and d nearly the same
    peak form MgCO3
    There should be a very small reflection at 1.769Å
    but this one is certainly lost in the background
    1.672 6 1.672 7, but 6
    relative to 82    		 peak form SiO2
    1.659 2 1.659 3, but 2
    relative to 82    		 peak form SiO2
    1.626 4 1.626 4 peak form calcite
    1.604 8 1.604 8 peak form calcite
    1.587 2 1.587 2 peak form calcite
    1.541 12 1.541 15, but 12
    relative to 82    		 peak form SiO2
    1.525 5 1.525 5 peak form calcite
    1.518 4 1.518 4 peak form calcite
    1.510 4 1.510 3 peak form calcite
    there is a negletable signal from MgCO3


    Comment: Again correct solution with a clear explanation at how you arrived there; well spotted regarding the consistent FWHM of the remaining phases. Again note that one missing line in the sample needs to be excused (see model answer).
    8 Marks


    Additional Comment: Some additional comments should be made concerning (very) rough ideas of relative amounts of phases and their feasibility against the history of the find (see model answer).
    0 Marks


    Overall: A correct solution and clear explanation. Beautiful & outstanding tables.