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 date analysis, yields the parameters below (the third parameter "FWHM" is a measure of the peak width). Identify the two remaining phrases in the sample. Explain, step by step, how you arrived at this solution. Comment on the solution.
1. Given that one of the phases present in the data set below is calcite, I first printed the ICDD card for calcite, (5-586), and compared the d values and intensities of the standard calcite reflections to those listed in the given data set. Next to each peak associated with calcite I wrote the name calcite and the expected intensity of that reflection. See the data table reproduced below. I next examined the FWHM for the calcite peaks. The FWHM for calcite peaks averaged 0.28°. There are two notable exceptions to this average. The peak at 2.284Å has a FWHM of 0.43 ° and an intensity of 29 %, both of which are much larger than expected for calcite alone. The peak at 1.510Å has the expected intensity for calcite but its FWHM of 0.42° is much larger than the calcite average. These anomalies lead me to suspect that these peaks could be the expression of two (or more) superimposed reflections.
Comment: You have got the right idea, and I am
pleased to see that at this early stage you are including the peak width (FWHM)
and peak intensities in your considerations. Also your account of how you went
about the analysis is very clear.
5 Marks
2. While identifying the calcite peaks I recognised the telltale signs of the presence of my old, dear friend, quartz, from the two most intense peaks in the given data at 3.343 and 4.27 Ångstroms. If I had not recognised quartz directly I would have first located the Hanawalt group to which the d spacing of the most intense unidentified reflection, 3.343, would be allocated. Within the Hanawalt group, 3.39 - 3.32, I would have used the 2nd most intense unidentified reflection, 4.27 Å to locate possible phases. If perchance the 4.27 Å peak did not lead to an identification of the phase I would have continued to search the 3.39-3.32 Hanawalt group using the d spacings of the other unidentified peaks in decending order. The results of the microprobe analysis, the presence of Ca, Si and Mg as the major heavier elements, and other unidentified reflections would help the analyist home in on the correct phase identification.
I printed the ICDD card for quartz (46-1045) and compared its d values and intensities to the remaining unidentified (or too intense or too wide) peaks. The peaks that matched those of quartz were labled as was done for calcite. The FWHM for quartz appeared to be smaller on average (0.23°) than that for calcite. The 2.284 Å peak with the large FWHM of 0.43° was indeed composed of overlaping calcite and quartz peaks.
Comment: Yes of course this is the correct solution which
was aided by your personal familiarity with quartz . Again you have correctly
included the FWHM's, intensities, elemental information and the 2.284 line in your
considerations. I should point out that final agreement should include considerations
of both positive and negative aspects; i.e. you must also account for any missing
lines in the sample that are present in the data file - the model answer follows up
this point.
8 Marks
3. The third phase was identified by using the three most intense unidentified reflections at 2.742 Å (12%), 2.102 Å (6%) and 1.70 Å (5%). The Hanawalt group, 2.74 - 2.70, was searched for the 2.102 reflection followed by the 1.70 reflection. The phase was identified as magnesite. Magnesite was also a logical possibility given the presence of Mg in the sample. I printed the ICDD card for magnesite (8-479) and matched the remaining unidentified reflections to those of magnesite. The FWHM of the magnesite reflections averaged 0.35°, somewhat more than the FWHM averages of the other two phases. The unusually wide peak at 1.510 Å was indeed a composite of calcite and magnesite reflections.
| ICDD Phase and I% | d (Å) | I(%) | FWHM° | ICDD Phase and I% | d (Å) | I(%) | FWHM° |
|---|---|---|---|---|---|---|---|
| quartz - 16 | 4.27 | 28 | 0.27 | magnesite - 12 | 1.939 | 2 | 0.37 |
| calcite - 12 | 3.86 | 12 | 0.30 | calcite - 5 | 1.927 | 5 | 0.29 |
| quartz - 100 | 3.343 | 82 | 0.25 | calcite - 17 | 1.913 | 17 | 0.28 |
| calcite - 100 | 3.035 | 100 | 0.28 | calcite - 17 | 1.875 | 17 | 0.28 |
| calcite - 3 | 2.845 | 3 | 0.28 | quartz - 13 | 1.817 | 15 | 0.22 |
| magnesite - 100 | 2.742 | 12 | 0.35 | magnesite - 35 | 1.700 | 5 | 0.35 |
| magnesite - 18 | 2.503 | 2 | 0.36 | quartz - 4 | 1.672 | 6 | 0.23 |
| calcite - 14 | 2.495 | 15 | 0.28 | quartz - 2 | 1.659 | 2 | 0.24 |
| quartz - 9 | 2.458 | 10 | 0.22 | calcite - 4 | 1.626 | 4 | 0.29 |
| quartz - 8 calcite - 18 | 2.284 | 29 | 0.43 | calcite - 8 quartz<1 | 1.604 | 8 | 0.28 |
| quartz - 4 | 2.237 | 4 | 0.23 | calcite - 2 | 1.587 | 2 | 0.29 |
| quartz - 6 | 2.128 | 8 | 0.23 | quartz - 9 | 1.541 | 12 | 0.23 |
| magnesite - 45 | 2.102 | 6 | 0.35 | calcite - 5 | 1.525 | 5 | 0.28 |
| calcite - 18 | 2.095 | 18 | 0.27 | calcite - 4 | 1.518 | 4 | 0.30 |
| quartz - 4 | 1.980 | 4 | 0.23 | calcite - 3 magnesite - 4 | 1.510 | 4 | 0.42 |
Comment: This is the correct solution. Again note
that both positive and negative aspects must be mentioned (see model answer)
and that the intensities are reasonable.
8 Marks
Analysis of the data cet collected from material from ancient ancient plaster figures contains three phases, calcite (CaCO3), quartz (SiO2) and magnesite (MgCO3). The average FWHM is different for each phase indicating different crystallite sizes. The FWHM for quartz is 0.23°, for calcite the FWHM is 0.28°, and the FWHM for magnesite is 0.35°. These values for FWHM indicates that quartz has the largest crystallite size and magnesite has the smallest cryatallite size. The given intensity of the quartz peak at 4.27 Å of 28% is higher than the expected intensity of 16%. The given d spacing of 4.27 Å is also larger that the d spacing of 4.2549 Å expected from the ICDD card for quartz (46-1045). These slightly different values might arise from several different causes, eg texture from coarse grains of quartz or peak displacement due to misallignment of the diffractometer. The presence of a fourth phase is highly unlikely given the elemental composition and absence of additional unidentified peaks.
Comment: A good summing up which included the valid
point re probable different crystallite sizes of the 3 component phases. One
might make a rough estimate of the relative proportions of the 3 phases (see
model answer).
3 Marks
Comment: Overall a correct solution, well-explained
account and you have made some perceptive points.