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.

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.

The PDF entry for calcite (5-586) = gives the following lines (and their intensities) in the range 4.5 - 1.5 Å:


d( Å )	3.860	3.035	2.845	2.495	2.285	2.095	1.927	1.913	1.875	1.626	1.604	1.587	1.525	1.518	1.510
Intensity	12	100	3	14	18	18	5	17	2	4	8	2	5	4	3


Comparison with the table above shows that the "literature = intensity" accounts for all of=20 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.


Comment: Well done spotting the anomalous intensity/FWHM of two of the lines.
4.5 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)

   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=20 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=20 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 )	3.343	2.458	2.282	2.237	2.128	1.980	1.817	1.801	1.672	1.659	1.608	1.541
   Int. (Lit.)	100	12	12	6	9	6	17	<1	7	3	<1	15
   Int. (Obs.)	100	12	13	5	10	5	18	0	7	2	0	15

   
   The last two lines compare the PDF literature intensity with the = observed ones, using the intensity of the=20 3.343 Å as 100%. The agreement is not perfect, but the overall = pattern of intensities is well reproduced,=20 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).=20

   
   Comment: Excellent methodology, searching while keeping certain factors in mind, and spotting the overlap situation. Only criticism is that you should point out the obvious - that the two lines not accounted for (1.801 & 1.608) are very weak and therefore it is reasonable that they were not seen.
   8.5 Marks

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:
   • Four more pages of entries taken from the Hanawalt = search manual:

     Page:	30 (81 kBytes)
     	31 (32 kBytes)
     	32 (29 kBytes)
     	33 (81 kBytes)

   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=20 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 )	2.742	2.503	2.318	2.102	1.939	1.769	1.700	1.510
   Int. (Lit.)	100	18	4	45	12	4	35	4
   Int. (Obs.)	100	17	0	50	17	0	42	8

   
   The last two lines compare the PDF literature intensity with the = observed ones, using the intensity of the=20 2.742 Å as 100%. The agreement is reasonable with the overall = pattern of intensities reproduced. As these reflections=20 are much weaker than those due to calcite and silica, the uncertainty = in the intensity measurement will be aggravated when=20 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.

   
   Comment: Again good logic making good use of the Mg-microprobe information. You gave an implied reason for 2 peaks (in "Lit") not being observed.
   9 Marks

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

   
   Comment: I was after comments about the likelihood of the solution given it was ancient plaster, the overlapping lines and the microprobe information (see model answer). You did include all these points elsewhere in your answer.
   4 Marks

   
   Overall Comment: Correct solutions and good methodology used in the searching. I hope this assignment was useful in giving you some further grasp of the procedures involved in search/match analysis.

   
   Total Mark 26