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finally, some more words!
I just spent all of yesterday and most of today on a single task, which, alas, did not wind up giving me any usable results. However, having tried *ten* different attempts, and having been intrigued at how little the graphs changed, despite some fairly major changes in the starting composition, I did add another 1,138 words to the thesis explaining what I did and what it shows, in addition to what it fails to show.
It failed to give me an estimate of the temperature and pressure of the initial growth of the garnet core. In theory, if you know the composition of the entire rock Perplex will plot a diagram showing all of the possible combinations of minerals which grow from those ingredients at any given temperature and pressure. If none of the minerals are zoned, then it is a simple matter of comparing the list of minerals that *is* present with the list of minerals which *should be* present and 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”. Zoned minerals, by definition, can’t *all* be in equilibrium with everything else present. But it is possible for the outermost bit to be in equilibrium with everything else present, and the inner portion to be “frozen” and no longer participating in the chemical reactions. When this happens, the “bulk composition” of the part wherein the chemical reactions is 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 you can only use Perplex to tell you what minerals could have been present way back when that zoned mineral first started growing.
But that is only one mineral, so how, then, can you read the diagram—you can’t know what the other minerals were then, because with the subtracting of some ingredients frozen into the core of the zoned mineral the remaining pile of ingredients is sufficiently changed that the list of possible minerals present at any given temperature and pressure 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. If you’ve just stocked 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 your ingredients in the mean while.
So the “trick” we use is to consider our zoned mineral (in my case, garnet) as being made up of “end-members” Just as a salad might have differing amounts of green leafy plants, tomato, avocado, and carrot and still be a salad, so a garnet will have differing amounts of iron (Fe), magnesium (Mg), calcium (Ca), and manganese (Mn). How much of each will depend 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 amount of each of those four ingredients in garnet it is possible to find the spot on the diagram which corresponds to our garnet. 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. 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. In today’s case I was working with estimates of that composition by working backwards—I know what minerals are present now, and what their current composition is. In theory, one can multiply their composition by their relative amount and get a composition for the entire sample. However, when I tried this I had two of the end member lines nicely intersecting, and the other two plotting off of the map. So I wondered if, perhaps, I’d gotten the estimate of their relative proportions wrong and so I changed the relative amounts of each mineral and tried again (spreadsheets are your friend when doing things like this—you need only change one number in one cell, and the others change themselves). It turns out that one can make some *major* changes in the relative proportions of the minerals and those two lines which intersect continue to intersect at exactly the same spot, and the two lines which plot somewhere off the edge of the graph continue to plot off of the graph. So I let myself get distracted and do 10 different versions of this, some with *really* different starting compositions and confirmed that while the size and shape of many of the fields change, the lines for the garnet core don’t move much.
With any luck tomorrow’s sample will work better than today’s did…
It failed to give me an estimate of the temperature and pressure of the initial growth of the garnet core. In theory, if you know the composition of the entire rock Perplex will plot a diagram showing all of the possible combinations of minerals which grow from those ingredients at any given temperature and pressure. If none of the minerals are zoned, then it is a simple matter of comparing the list of minerals that *is* present with the list of minerals which *should be* present and 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”. Zoned minerals, by definition, can’t *all* be in equilibrium with everything else present. But it is possible for the outermost bit to be in equilibrium with everything else present, and the inner portion to be “frozen” and no longer participating in the chemical reactions. When this happens, the “bulk composition” of the part wherein the chemical reactions is 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 you can only use Perplex to tell you what minerals could have been present way back when that zoned mineral first started growing.
But that is only one mineral, so how, then, can you read the diagram—you can’t know what the other minerals were then, because with the subtracting of some ingredients frozen into the core of the zoned mineral the remaining pile of ingredients is sufficiently changed that the list of possible minerals present at any given temperature and pressure 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. If you’ve just stocked 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 your ingredients in the mean while.
So the “trick” we use is to consider our zoned mineral (in my case, garnet) as being made up of “end-members” Just as a salad might have differing amounts of green leafy plants, tomato, avocado, and carrot and still be a salad, so a garnet will have differing amounts of iron (Fe), magnesium (Mg), calcium (Ca), and manganese (Mn). How much of each will depend 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 amount of each of those four ingredients in garnet it is possible to find the spot on the diagram which corresponds to our garnet. 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. 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. In today’s case I was working with estimates of that composition by working backwards—I know what minerals are present now, and what their current composition is. In theory, one can multiply their composition by their relative amount and get a composition for the entire sample. However, when I tried this I had two of the end member lines nicely intersecting, and the other two plotting off of the map. So I wondered if, perhaps, I’d gotten the estimate of their relative proportions wrong and so I changed the relative amounts of each mineral and tried again (spreadsheets are your friend when doing things like this—you need only change one number in one cell, and the others change themselves). It turns out that one can make some *major* changes in the relative proportions of the minerals and those two lines which intersect continue to intersect at exactly the same spot, and the two lines which plot somewhere off the edge of the graph continue to plot off of the graph. So I let myself get distracted and do 10 different versions of this, some with *really* different starting compositions and confirmed that while the size and shape of many of the fields change, the lines for the garnet core don’t move much.
With any luck tomorrow’s sample will work better than today’s did…