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So What About Multiple Phases? |
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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:
- start by making use of the PDF entry for
calcite
- home in on a potential second/third phase from the following range of
entries in the Hanawalt search manual
- Four pages of entries taken from the Hanawalt search manual:
Page: |
13 (77 kBytes) |
|
14 (78 kBytes) |
|
15 (79 kBytes) |
|
16 (86 kBytes) |
- repeat the process of (2) for a potential third/second phase from the
following range
- Four more pages of entries taken from the Hanawalt search manual:
Page: |
30 (81 kBytes) |
|
31 (32 kBytes) |
|
32 (29 kBytes) |
|
33 (81 kBytes) |
- 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:
- one of the two remaining phases will obviously reside within pages 13-16
of the Hannawalt manual;
- the other remaining phases will obviously reside within pages 30-33 of the
Hannawalt manual;
- use the peak width (FWHM) information and keep an open mind on the
two lines with very large peak widths;
- with the guidance here you will later be able to identify, with certainty,
the two remaining phases.
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:
- apportion lines to potential phases, aided by peak width
information (i.e. previous example);
- apportion lines to potential phases, aided by peak shape
information;
- apportion lines to potential phases following a re-collection of
the powder pattern after partial or full separation of the constituent phases
by physical means (e.g. sieving, flotation, filtration, convection);
- a common situation is that a mixture has a dominant phase plus minor
impurity phase(s), so one can safely assign the 3 strongest lines to the
dominant phase, search for then subtract the lines of the dominant phase and
then deal with the weak impurity phase(s);
- use microscope/microprobe examination to group chemical constituents by
phase (e.g. one crystallite morphology appears to contain only certain elements
while another crystal morphology appears to contain a different element
combination).
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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