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So What About Multiple Phases?

Possibly the question you have been itching to ask is what happens in cases where there is more than one phase present, and indeed present in different proportions? In other words if the three strongest lines are found to be d1, d2 and d3, it is possible that all three belong to phase 1, or alternatively that d1 and d3 belong to phase 1 and d2 belongs to phase 2, and so on. Obviously the permutations are many and trying them all out manually might be too much. There are many ways of skinning this cat (i.e. solving this problem); we will illustrate one type of approach using the following question, the answer to which will be deliberately left unfinished as it will be used later as part of an assignment. For the latter you will be expected to use the extracted information given in the figures which follow.

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 and comment on the result.

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

If you do not have the ICCD-PDF you will be able to work usefully through the problem taking the following information in strict sequence:

  1. start by making use of the PDF entry for calcite

  2. home in on a potential second/third phase from the following range of entries in the Hanawalt search manual

  3. repeat the process of (2) for a potential third/second phase from the following range

  4. Once you have identified your potential second and third phases, you should obtain their full PDF patterns and then check that your two choices match the full patterns in detail. Obviously if you do not have the ICDD-PDF then you won't be able to perform this part until you receive the assignment.
Although this problem will be more fully dealt later during the assignment, it is still instructive to have a quick pre-look now. The following clues might guide you:

Although searching manually for multiple phases might seem daunting at first, the previous example serves to show that there are often clues that can be exploited. Further clues can even be "created" in some cases. A range of ideas follows:

Computer-searching for multiple phases can be quite different from manual methods. The computer is obviously far better-suited to the "brute force" approach of trying endless permutations of phase-line combinations, but even the computer tends to struggle when the number of phases exceeds around four, so more advanced strategies are also required in addition to the "tricks" discussed earlier (see "And Something More"). Sometimes it is beneficial to reverse the sense of information. One such example is the use of negative d spacing ranges: rather than say, positively, that two consecutive d spacings are found to be 2.0 and 2.4 Å, one could alternatively say, negatively, that there are no d spacings to be found between say 2.05 and 2.35 Å. The disadvantage of the positive statement is that it might apply to just one, or to two or more phases in a mixture, but you don't know which. However the negative statement applies to all phases singly and in combination. Another example is to compose towards rather than decompose from unknown patterns: that is, rather than subtract a phase's pattern from the unknown, with the risks of bad intensity representations that can follow, potential candidate patterns are added together to form a composite pattern which is compared with the unknown; this process can also be done including background as well as peak information. Given the continual improvement in computer processing/intelligence power we can expect a steady improvement in computer-aided methods for search/matching to multiple phase mixtures.

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© Copyright 1997-2006.  Birkbeck College, University of London.
  		Author(s): Paul Barnes
Martin Vickers