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Unformatted text preview: 20001“ Kohn and Spear 1 CALCULATING THE AMOUNT OF DISSOLVED GARNET
The method assumes a starting map with raw pixel values and (free) NIH Image software: (a) From several spot measurements, it is useful (although not required) to transform the raw
Mn intensity map into an XSPS map. Note that background corrections for garnets are so similar
that even a few points will allow accurate conversion. Determine the lowest XMH, by outlining
the lowest Mn region and measuring. (b) Cut out the core by drawing a closed contour along the minimum XMn and filling the interior. (c) Using thresholding, delineate (White out) the rim area of increased Mn. Using the wand tool,
outline the edge of the garnet and measure the area and mean concentration. This gives a
background measurement of core plus low Mn—inclusions in the rim region. (d) Using thresholding, black out the rim area and remeasure the same area delineated in (c).
This gives the total area and mean concentration of the entire garnet. (e) For simplicity, we assume that the lowest XMn value once extended to the edge of the garnet.
The area of dissolved garnet is then calculated via the equation: A(rir.n, original) = [A(d) x C(d)—A(c) x C(c)]/[XMn(lowest)] where A and C are area and mean concentration, and (c) and (d) refer to the measurements in
steps (c) and (d). Alternatively, the amount of dissolved rim can be determined from the
current rim volume times the excess Mn (mean XMn  minimum XMH) divided by the minimum
XMD. [Note that in these firstorder calculations, the lowest measured XM" is used as a pmxy for
the mean XM“ of the dissolved rim. Depending on one’s preferences, this estimate can be refined
iteratively by constructing a model XM” profile for the original garnet (e.g., with steadily
decreasing XMn towards the rim), estimating a new mean XMn for that profile, and using that as
the lowest XV“ in the calculation. The new estimate of the amount of dissolved garnet can then
be used to infer a new Mn profile and mean XMD, etc] (e) For simplicity, we assume that the measured X Fe and XMg at the “troug ” are constant over
the part of the garnet that dissolved, so these contents are multiplied by the volume of garnet
dissolved to yield the amounts of Fe and Mg ﬂuxed into the matrix via garnet dissolution.
Alternatively one could assume XFE and XMK proﬁles for the dissolved rim. Finally, the ﬂuxes of
Fe and Mg caused by diffusional exchange with the matrix biotite must also be considered,
although they are typically an order of magnitude less than the ﬂuxes due to garnet dissolution.
For Fe or Mg, we difference the assumed original concentration and the average Fe or Mg
concentration of the diffusionally affected rim. These Fe and Mg ﬂuxes are then subtracted
from the amount of Fe and Mg in the current biotite to yield the original biotite composition. Note that sensu stricto this approach applies only for central—cut garnets, and assumes both that
current area modes are directly proportional to volume percents, and that dissolution is
uniformly radial. Noncentral cuts (overrepresentation of the rim) and nonuniform dissolution
(contribution of higher Mn garnet than at the Mn trough) will both tend to cause overestimation
of the degree of dissolution. Also, this method uses area measurements for estimating amounts
of garnet that have dissolved, which works best for small amounts of dissolution (<~20%). For
larger amounts and greater accuracy, area measurements can be converted to volumes, as we
did with DlI58. Our approach is simplest when biotite is the only ferromagnesian mineral
present, because biotite takes so little Mn. In instances where a new mineral is produced (e. g,
retrograde chlorite), the Mn content of that mineral must be considered in the mass balance, as
well as its FeMg concentration and partitioning with other matrix minerals such as biotite. Kohn and Spear 2 Finally, this technique is a useful diagnostic tool and can be used to select for those samples that
are E strongly influenced by dissolution. MEASUREMENTS AND CALCULATIONS EUR SAMPLE DH58. Total area of thin section = 490 m2. Grt mode 27.35% {determined from the areas of all garnets (36 m2), divided by the area of the
thin section] Bt mode 2 27:2% (determined from digital optical images 2 ~0.00532 mol biotite/ cm3). Bt Fe/(Fe + Mg) (matrix) 2 1.222 molpfu/(1.222+1.088 mol pfu) = 0.529 XSPS at Mn trough = 0.02 KM” at Fe / (Fe + Mg) trough: 0.60 Km at Fe/ (Fe + Mg) trough: 0.11 Present area of analyzed Grt: 8.7 mm2 (=135766 pixels*64 um2 / pixel) Present volume of Grt: 19.3 mm?1 (assuming spherical geometry) Present radius of Grt: 1.66 mm (assuming spherical geometry) Area of Grt rim with increased Mn: 46030 pixels * 64 um2 : 2.95 1111112. Volume of Grt rim with increased Mn: 8.9 mm3 (assuming spherical geometry, =~3 volume
percent for the rock based on similar profiles in other garnets). Average XSps between trough and edge: 0.0584 (i.e., 0.0384 excess relative to the Mn trough) Volume of dissolved Grt: 8.9 mm3 x 0.0384/002 = 17.1 mm3 (or ~6 volume %) Original volume of Grt: ~36.4 mm3 Original area of Grt: ~13.3 mmz. Original radius of Grt: ~2.06 mm. Grt Fe concentration: 0.60 x 0.0261 = 0.015660 mol/cm3 Grt (60% Almandine) Grt Mg concentration: 0.11 x 0.0261 2 0.002871 mol/cm3 Grt (11% Pyrope) Bt Fe concentration: 1.222 x 0.0197/ 3 = 0.008024 mol/cm3 Bt (1.222 moles pfu) Bt Mg concentration: 1.088 x 0.0197/3 : 0.007145 mol/cm3 Bt (1.088 moles pfu) Bt Fe (moles, final) 2 0.008024 x 0.27 : 0.002166 mol/ cm3 of rock Bt Mg (moles, final) = 0.007145 x 0.27 = 0.001929 mol/cm3 of rock Grt Fe (moles, added by dissolution) 20.015660 x 0.06 = 0.000940 mol/ cm3 of rock Grt Mg (moles, added by dissolution) = 0.002871 x 0.06 = 0.000172 mol/cm3 of rock Grt Fe (moles, added by diffusion) = 0.03 x 0.02610 x 0.04 x 3 = 0.000094 mol/cm3 of rock.
(Maximum amount is 0.08 mole percent; minimum is 0; 0.04=value used; 0.03=mode). Grt Mg (moles, added by diffusiOn) = negligible. Bt Fe(moles, original) 2 0.002166  0.000940  0.000094 : 0.001132 mol/cm3 of rock Bt Mg(moles, original) 2 0.001929  0.000172 2 0.001757 mol/cm3 of rock Bt Fe/(Fe + Mg) (original) = 0.390 Bt mode (original) ~ (0.001132 + 0.00175'7)/(0.002166 + 0.001929) x 27% = 19% Note that on a volume basis, the molar concentrations for garnet and bio tite are:
Fe in Almandine: 0.0260 mol/cm3 Mg in Pyrope: 0.0265 mol/cm?L Fe in Annite: 0.0194 mol/cm3 Mg in Phlogopite: 0.0200 mol /crn'"' So for typical garnets and biotites, the molar concentrations are approximately:
Garnet: 0.0261 mol (cub. site)/ cm3 Biotite: 0.0197 mol (oct. site)/ cm3 ...
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This note was uploaded on 03/19/2012 for the course GEOLOGY 6 taught by Professor Rm during the Spring '12 term at UNAM MX.
 Spring '12
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