Fraser Rowan - Assignment IV

Elucidation of powder diffraction pattern

All of the peaks shown to exist for the powder diffraction pattern obtained from ancient plaster can be accounted for using CaCO₃ (JCPDS 5-586), SiO₂ (JCPDS 5-490) and MgCO₃ (JCPDS 8-479). The assignments of each of the peaks are shown in table 1.

Table 1. D-spacing and Intensity of the pattern obtained from the analyte, CaCO₃ (black), SiO₂ (blue) and MgCO₃ (red), in columns 1&2, 3&4, 5&6 and 7&8, respectively. Reflections coloured in green indicate sharing between two patterns.

Columns 1 and 2, in table 1, show all the peaks identifying the analyte. The first step of the problem is to identify all peaks attributed to CaCO₃, (a known phase within the plaster). These peaks are highlighted in columns 1 and 2, in black and green. The d-spacing/intensity as reported by JCPDS 5-586 are shown in columns 3 and 4 for comparison. The most intense peak at 3.035Å belongs to the CaCO₃ which suggests that this phase is the main phase. The full width half maximum (FWHM) of the peaks at 2.284 and 1.510Å are significantly more broad than those of the other peaks present in the CaCO₃ pattern and are highlighted in green. This indicates that an overlap exists with peaks from secondary phases which are slightly shifted form that of the CaCO₃ pattern. These peaks should, therefore, not be ruled out from further investigation.

Comment: An excellent table; I like the use of colours to indicate phases, particularly the third colour (green) to cover the ambiguous lines (2.284 and 1.510).
5 Marks

The next step is to identify a second phase in the plaster using pages 13-16 of the Hanawalt Search Manual (HSM). Although only four pages are supplied, there are a significant number of entries. This is reduced by including only those containing Ca, Si or Mg. The next three most intense peaks (excluding those identified as CaCO₃) are 3.343, 4.27 and 1.817Å with intensities of 82, 28 and 15%, respectively. The remainder of the Hanawalt entries are investigated by comparing the d-spacings values in the extreme left column of the page to that of the most intense d-spacing: 3.343Å. When a match is identified the d-spacing in the second left column is compared to that of the second most intense d-spacing: 4.27Å. When a match occurred for the first and second intensities, the value in the third left column is compared to that of the reflection at 1.817Å. Using this method the second phase can be primarily identified, on page 14, as SiO₂. The JCPDS card, 5-586, is obtained and used to check against the remaining peaks. These peaks are marked off in table 1 in columns 5 and 6, and in the analyte column (1 and 2) in blue (and green).  As suspected from the FWHM,  the reflection at 2.284Å was a combination of two peaks rather than one. This peak is the product of the 113 reflection of CaCO₃ and the 102 reflection of SiO₂.

Comment: This is the correct solution. I like your use of the elemental information to cut down the number of choices. Note that the general intensities also match in a proportional way (as well as the d-spacings). Also note that 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

The remaining peaks are then placed into descending order: 2.742, 2.102, 1.700, 2.503 and 1.939Å with intensities of 12, 6, 5, 2 and 2%, respectively. Pages 30-33 of the HSM are employed in a similar manner to that previously described using 2.742, 2.102 and 1.700Å as the three most intense peaks. The final phase is identified on page 30 of the HSM to be MgCO₃. The other peaks are verified from JCPDS card 8-479 as belonging to MgCO₃. and are shown in columns 5 and 6, and in the analyte columns 1 and 2 in red (and green). The peak at 1.510Å shown to have a FWHM of 0.42 is a combination of the 119 reflection of CaCO₃ and the 211 reflection of  MgCO₃. It should be noted, however, that the contribution from the MgCO₃ reflection will be very slight due to its very low intensity. In a sample of pure MgCO₃ the 211 peak would have 4% of the intensity of the most intense peak: 1 0 4. In the analyte, the intensity of the 1 0 4 reflection is 12%, suggesting that the intensity of the 211 peak would be 0.48%.

Comment: Again the correct solution and my comments would mirror the previous case; note the missing line has to be excused.
8 Marks

Semi-quantitative information can be obtained from these results by comparing the intensities of the most intense peak from each pattern. This method is very much an over-simplification and many effects which contribute to the results are not considered. These effects can be divided into four categories: structural, instrumental, morphological and the nature of data analysis employed. Structural contributions include atomic scattering factor, structure factor, polarisation, multiplicity and temperature. Instrumental contributions include voltage drift, detector dead time, divergence slit aperture and axial divergence. Contributions from the morphology of the sample include micro-absorption, crystallite size, degree of crystallinity, residual stress and preferred orientation. Finally, contributions from the data analysis encompass the method of peak area measurement, degree of peak overlap, subtraction of background, whether Ka2 reflections have been stripped and the degree of data smoothing employed. However, bearing these factors in mind it would appear that by volume, 51.5% of the sample is CaCO₃ and the remaining 42.3 and 6.2% belong to SiO₂ and  MgCO₃, respectively.

Comment: Your final comments and percentages agree with the order I came up with in the model answer (calcite>quartz>magnesite) though personally I would have left off the post-decimal point numbers (i.e. 52, 42, 6% resp.).
4 Marks

General: A very pleasing answer, particular your dealing with the problem lines and the use of colour to illustrate the solution.