Extrapolation of the likely composition of a mineral from mixed analyses

I have mentioned before the difficulties of using a microprobe to analyze very small phases. The electron beam with which we do the analysis can, with care, be focused to about 1 micron diameter (remember that there are 1,000 microns in every millimeter). However, should the mineral phase of interest be smaller than one micron, in any dimension, the analysis will yield the composition of not just that mineral, but of whatever happens to be next to it as well.

The below photo shows one of my experiments for which this was a problem. As with all back-scatter electron images the amount of brightness or darkness of any given part of the image is based on the composition of the sample in that location. Brighter areas contain more heavy elements, darker areas more light elements. The brightest grains in this image are the large pale grey crystals, which often have dark centers; these are garnets. The dark centers are the pyrope (Mg-garnet) seeds that were included in the experimental powder to give the new garnet, which is much higher in Fe (iron), a place to start growing from. The narrow stick-shaped crystals which occur in a group on the left hand side of the image are chloritoid. Unfortunately, as you can see by the scale bar on the bottom of the image, they are too narrow to obtain a good analysis. Through careful searching of the sample we found a few places where the chloritoid grains were slightly larger than the others—these were the ones we analyzed, in hopes that we would be lucky. Alas, 15 times we tried, and 15 times we failed to obtain an analysis which was only chloritoid, but instead they were "mixed" results of both chloritoid plus another phase.

How do I know for certain that they are mixed? Look at the below graphs and you can see for yourself. The upper graph shows the composition of all of those mixed analyses with respect to how much aluminum and how much silica they contain (blue-green hollow triangles). It also shows the region (grey circle) within which all of the matrix mica in this sample plots, and the location of where kyanite (Al₂SiO₅), also present in this sample, plots. As you can see, there is a clear trend going from the solid green triangle towards the mica, and another trend going from the solid green triangle towards the location of kyanite. The lower graph shows the trends for iron vs aluminum. By plotting this data for a variety of different combinations of elements I have come up with my best guess as to the composition of chloritoid is in this sample (solid bluish-green triangles). Is it as accurate as if I'd been able to get a good measurement? No. Does it give me information I can use when doing other parts of my data analysis? Yes, yes it does. Playing with graphs is one of the fun parts of my job—the information they convey communicates so very clearly.

play with the data long enough and it becomes possible to find a way to see patterns in it

One of the things I’ve been struggling with in my current research is how best to communicate the results from the various experiments I’ve run. My experiments have thus far yielded a total of ten different phases, with as many as seven of them appearing in a single experiment. I use two different capsules at each pressure and temperature at which I run experiments; each capsule has a different bulk composition. Therefore I’ve been displaying the result graphically, by using 8-pointed stars divided into an inner ring for one of the composition types, and an outer ring for the other. The resultant triangles representing the phases present are either left blank if it isn’t present or filled in with colour-coding if it is. One phase, quartz, is always present (save for when we reduce the starting SiO2 to eliminate it), so it doesn’t need a triangle of its own, and another occurs only in one high-P run, so it appears as a different colour triangle replacing one attached to a low-P phase; this is why I’ve been able to get away with using only eight points for the star.

However, there are times when it is necessary to communicate with text or a table, rather than with an illustration, and this is where I’d been stymied. I simply wasn’t seeing much in the way of a pattern with my data in terms of mineral assemblages. A mineral assemblage is the group of minerals which are all stable at the same pressure/temperature; they would have been the products of the reaction(s) which produced the assemblage. (When doing experiments we talk of phases rather than minerals—a phase is a particular composition of a mineral (many minerals can have more than one possible compositions, so may be considered a family of mineral phases)—in general only one phase within a family will be stable at a given set of conditions) .

Today I finally discovered a way to organize my data so as to see patterns in the assemblages. This required using colour coding and playing with the data, combining them into groups until I was able to determine that the “important” phases of the list of 10 are talc, garnet, and biotite. The others are either ubiquitous (quartz, chloritoid and muscovite) or only show up in a few of the runs and can be considered "minor" (zoisite, lawsonite, kyanite, carbonate). Once I’d worked that out, I was able to split the data into four groups each of which are +/- the minor phases and + the ubiquitous phases.

However, it was also necessary to consider each of the two bulk compositions separately to see the relationships between the groups, and I had to draw circles around the stars on my original P-T diagram to see how the groups relate to pressure and temperature. (I love having a drawing program which lets one draw circles on layers that can be made visible or invisible, so that one can see only the circles relevant to a single composition at one time.) Once I had all of the groups for each bulk composition circled it was easy to see that:

The experiments using the metagreywacke composition only have groups A, B, and C thus far. These groups plot on diagonal trends for this composition such that with respect to temperature B is less than both A and C, but with respect to pressure C is less than both B and A.

The experiments with metapelitic composition have groups A to D which plot in a grid such that with respect to temperature B is less than A while D is less than C and with respect to pressure C is less than A while D is less than B.

Now that I can see these patterns I shall really look forward to obtaining the results from future experiments to see how they relate to this overall pattern.

routine + templates makes things easier

With each of the experiments I am running I inflict elevated pressure and temperature on two different tiny gold capsules full of powder. One of them is always full of powder “NM” while the other contains powder “NP”. Even though it is generally possible to tell the two capsules apart before they go into the piston cylinder (by making a sketch of the actual shape of the welded ends, since no two are ever quite the same), the pressure they are subjected to generally means that it is harder to tell them apart when they come out. Fortunately, it is possible to use the microprobe to do a scan over a largish patch of the sample and obtain numbers which are, more or less, representative of the bulk composition of that region.

The first time I did this it felt difficult to compare those numbers with the actual, known, bulk composition of the samples, since this rough-area scan is never going to give precisely the same numbers as the bulk composition. The growth of minerals within the powder has caused some elements to be concentrated in some minerals, and other elements in other minerals. However, in general, the relative differences between the two bulk compositions can still be distinguished via the rough scan. Therefore I set up a spreadsheet with graphs, plotting the original, known, bulk composition in one colour (hollow symbols for NM and solid symbols for NP), and the rough area scans of the first experiment in another. Sure enough just as the original bulk NM is higher in Al₂O₃ and lower in K₂O FeO and CaO than is NP, so the first experiment has one capsule with higher Al₂O₃ and lower FeO, K₂O, and CaO than the other. The second experiment repeated the pattern, but now that I’ve added the third the graph is even easier to read, for now the symbols for the NP bulk plot in one distinct clump on each graph, whilst the ones for the NM bulk composition samples plot in another. This means that from here on out, I need only enter in the new data into the spreadsheet, and in a second’s glance at the chart I’ll know which is which.

Somehow, I really enjoy these tricks which make life easier. Besides, it is fun to set up the charts and graphs.

Two weeks left to finish analyzing the data from my first three experiments and prepare my poster for AGU. Somehow, I suspect that this will keep me as quiet on the blog front as the past couple of weeks when I had both unpacking to do and thesis corrections to make (since my household goods and the examiner’s report arrived on the same day).

The tool I learned to use today, and what I discovered when I applied it

My life recently has reduced itself to not much more than working on the thesis in progress, or taking the occasional walk for exercise; I’ve even chosen to miss out on social events I would have otherwise attended in my push to “finish”. However, as I work I keep discovering new things I need to learn in the process. I once heard that the learning curve on a PhD project is exponential, and, truly, I believe it—it seems to me that I am learning ever so much more every day now in this very late stage of the project than I did in the early months of working on it (and, for the record, during those early months, I was astounded by just how very much I was learning compared to my prior rates of information acquisition).

One of this week’s new lessons was how to apply a t-test in an Excel spreadsheet. When my advisor gave me back chapter five, with comments and suggestions for improvement, one of the things he said was that the variation of some of the abundances for some of the trace elements in the monazite for the grains which grew in the Cambrian looked on the graph like they might, perhaps, vary by age of the grains. The “vary by age” we are talking here is very minor—these crystals grew ~505 Million years ago, give or take a handful of million years. How long did that growth period take? If it was fast it might have been just a couple million years, but if it was slow it could have taken tens of millions of years. In the latter case, it would be possible for there to be changes in the growing conditions (temperature/pressure) over the time period. If there were changes in the temperature and pressure during the metamorphic episode it is possible that during that period different minerals would be stable at different times during the event. It is known that how much of any given trace element is incorporated into monazite is based, in part, on what other minerals are growing or breaking down at the same time the monazite is growing. Since monazite tends to be a small mineral (generally <> 1 mm, and sometimes > 1 cm)) tend to out-compete it for any elements they are fond of if they are growing at the same time, or if the large mineral is breaking down, they tend to release trace elements, which the monazite can then incorporate into its own crystal structure.

Therefore, to test this, part of my day was spent going back to the results of my monazite analyses, sorting them by age to get all of the ones from the ~505 Million year old growing episode together, then sorting them back out into their individual samples again, then sorting each sample by first one, and then another trace element, then doing a t-test for each element to compare all of the analyses from a single sample which are high in that element with those which are low in that element. If the “t Stat” number reported is larger than the “t Critical two-tail” number then I can say that, yes, there is a statically valid difference in the ages of the two groups. However, for the samples from the first region I’ve tested, I can’t say that. Statically, the ages for those analyses high in these elements are indistinguishable from those which are low in those elements. Therefore, the factor which is more likely to effect how much of each of those trace elements wound up in the monazite is probably just a simple “how close was each grain of monazite to the other minerals which were either giving off, or taking up, those elements?”.

Having done all of that for this region, I next need to repeat the process for the other regions, write up the results (in less general terms!) in the thesis, and move on to the next task on the list…