I spend my days making graphs

There are a variety of techniques used to determine the temperature and pressure at which a group of metamorphic minerals grew. All of them have been built up over the decades by dedicated scientists who combine information from the study of thermodynamics and various experiments wherein real minerals have been made to grow in laboratory conditions. The one I have been using involves a suite of computer programs, which, if given the composition of the rock sample, will plot a diagram showing all of the possible combinations of minerals which grow from those ingredients at any given temperature and pressure. If all of the minerals present have uniform compositions, then it is a simple matter of comparing the list of minerals that are present with the list of minerals which should be present and thereby get a good guess as to the temperature and pressure at which they grew (how good will depend on if the "field" for that particular set of minerals is a large or small one).

However, if there are minerals which are "zoned" (their composition changes from the center to the rim), it complicates things. You see, for this technique to work, all of the minerals have to be in “equilibrium”, which means that the chemical reactions which make them have to have “gone to completion”. An entire zoned mineral, by definition, can’t all be in equilibrium with everything else present, but it is possible for the outermost bit of it to be in equilibrium with everything else present, and the inner portion to be “frozen” and no longer participating in the chemical reactions which are taking place outside of it. When this happens, the “bulk composition” of the wherein the chemical reactions are happening is constantly changing as some of the ingredients get “frozen” in the center of the zoned crystal. In such a case if you know the composition of the entire rock sample these diagrams only tell you what minerals could have been present way back when that zoned mineral first started growing, which list may or may not bear any relationship to the ones which are present now.

So, how can you read the diagram when there are zoned minerals present? You can’t tell what minerals were there at the time your zoned mineral first started growing, because as that mineral grew it subtracted some of ingredients from the surrounding rock, and “froze” them into its “core”. This process caused the remaining list of ingredients present to be sufficiently changed that the list of possible minerals present at any given temperature and pressure also changes. This is not unlike comparing the list of what you might be able to make for dinner on any given evening without going grocery shopping. They day you first stock the house up with food the list of meals you might make from the ingredients on hand will be much larger than it will be a week or two later (if you don’t go food shopping in between) and have been using up some of your ingredients in the meanwhile.

So the “trick” I use is to consider my zoned mineral (in this case, garnet) as being made up of proportions of four specific ingredients. Just as different cake recipes might call for differing amounts of flour, butter, eggs, and sugar, and still be a cake, so a garnet will have differing amounts of iron (Fe), magnesium (Mg), calcium (Ca), and manganese (Mn). (These elements, being of similar size, all manage to fit into the same slot in the crystal structure.) How much of each is incorporated into the growing garnet at any given time will depend both upon the ingredients available and the temperature and pressure at which the garnet is growing. Therefore if we make a diagram which shows the expected changes in quantity of each of those four ingredients in garnet (at different temperatures and pressures) it is possible to find the spot on the diagram which corresponds to the garnet being studied.

I do this by measuring the composition of my garnet using an electron microprobe and making a note of how much of each of those four ingredients (Fe, Mg, Ca, and Mn) is present in the center of the garnet. I then highlight the lines in the graph corresponding to each of those numbers, and where the four lines intersect marks the temperature and pressure of the first growth of garnet. Often this works, and there is much rejoicing. Sometimes it doesn’t.

There can be any number of reasons why it doesn’t work—perhaps I’ve not actually measured the center of the garnets. Perhaps the composition I started with for the whole rock doesn’t actually match the composition that was present when the garnet started growing. Perhaps the composition of the rock has changed with time as fluids carried in new ingredients and carried away old ones.

Creating these diagrams, they joys of having them work, and the frustrations when they don’t are a normal part of my life as a graduate student. Biologists get to play with plants or animals, chemists get to work in a laboratory, I spend my days entering lists of numbers into a file, setting the program calculating based upon those numbers, and, when it is done (it can take quite a while—these calculations are actually quite complex, which is why we delegate them to a computer), opening images in a drawing program to see the results in a graphical format. Once I’ve got results the fun part begins—where I think about what the numbers mean, and how my rocks could have been buried deeply enough to grow these minerals in the first place, and how they managed to get back up to the surface so that I could collect them in the second.