metamorphic projections and isograds projections the geosciences are a visual science. we understand concepts better when we look at ca
Metamorphic Projections and Isograds
The geosciences are a visual science. We understand concepts better
when we look at cartoons and diagrams and field examples. We
understand metamorphic reactions and resultant mineral assemblages
better when we can visualize the changes in diagrams. Unfortunately,
visualization beyond two dimensions is tricky and beyond three
dimensions impossible. We can draw diagrams in two dimensions that
depict three oxide components of rocks and minerals (triangular
diagrams), but few minerals and even fewer rocks are composed of only
three oxides. For example, the simple "type metamorphic reaction",
calcite + quartz = wollastonite + CO2, uses four oxides to express all
the minerals -- CaO, MgO, SiO2, and CO2.
What to do? Metamorphic geochemists commonly use diagrams that are
projections -- one or more oxides are omitted from the diagram or
combined with other oxides to get the number down to three. FeO & MgO
are often combined because they substitute for each other and can be
considered as "one oxide". In the projection used here, no oxides are
combined, but H2O and CO2 are not plotted. The rationale for doing
this is best explained in thermodynamic terms. In non-thermodynamic
terms, the resulting diagrams are considered to always contain a
non-plotted fluid consisting of H2O and CO2.
The CMS (CaO-MgO-SiO2) projection applies to rocks containing minor
amounts of other common oxides such as Al2O3, MgO, and FeO. It thus
applies to carbonate rocks or siliceous carbonate rocks (e.g. sandy
dolomites, cherty carbonates). Rocks or minerals are plotted (on a
mol% basis) by ignoring H2O and CO2. So ---
Dolomite CaMg(CO3)2 = CaO + MgO + 2CO2
we plot as 50%CaO, 50% MgO
Talc Mg3Si4O10(OH)2 = 3 MgO + 4SiO2 + H2O
we plot as 57% SiO2, 43% MgO
Projections and Reactions
We use the projection to (1) illustrate the metamorphic reactions and
(2) determine which different mineral assemblages are produced by a
reaction, and (3) which bulk compositions (rocks) will contain those
different mineral assemblages. To do that, we need these principles:
(1) All stable minerals at any P&T (in any particular triangle) are
connected by tielines, but the tielines cannot cross. At T1 below, the
line connecting qtz & mineral B is a tieline.
(2) Resulting internal triangles show the stable mineral assemblages.
The arrangements of tielines are a geometrical visualization of
chemistry, or chemography. At T1, possible mineral assemblages are
magnesite + qtz + dolomite and dolomite + qtz + calcite. MgO-rich
compositions would have the first assemblage and CaO-rich compositions
assemblage (in actuality, MgO-rich compositions are rarely found in
sedimentary environments). Compositions involving dolomite + qtz would
simply have dolomite + qtz.
(3) Tielines change at metamorphic reactions. Between T1 and T2, this
isograd reaction occurred:
3 Dol + 4 Qtz + H2O = Talc + 3 calcite + 3 CO2
The tieline Dol + qtz (LHS) gave way to talc + calcite (RHS).
Three-mineral assemblages are now qtz + calcite + talc, calcite + talc
+ dol, and dol + talc + magnesite. What assemblage would a protolith
containing dolomite and a little chert now show? Answer: calcite +
talc + dolomite. Would that same assemblage show up in all protolith
compositions? Answer: no.
(4) Minerals do not become unstable ("disappear") with rising
temperature unless they appear as the only mineral on the LHS of a
reaction. Example: at temperatures above the Dol + Q reaction, talc
appears, but neither Dol nor qtz disappears.
Isograd Reactions at Alta
Observed mineral assemblages can, for the most part, be explained as
the result of the following reactions, the sequence representing
increasing grade (temperature) of metamorphism. Each corresponds to a
mapped isograd in the field. As we'll see below, the reactions depend
upon fluid composition as well as temperature, but if fluid
composition is the same throughout the area along an isograd, then the
mapped isograd is a line of constant paleotemperature.
(1) 3 CaMg(CO3)2 + 4 SiO2 + H2O = Mg3Si4O10(OH)2 + 3 CaCO3 + 3 CO2
dolomite quartz talc calcite
(2) 2 Mg3Si4O10(OH)2 + 3 CaCO3 = Ca2Mg5Si8O22(OH)2 + CaMg(CO3)2 + H2O
talc calcite tremolite dolomite
(3) Ca2Mg5Si8O22(OH)2 + 3 CaCO3 +2 SiO2 = 5 CaMgSi2O6 + H2O + 3 CO2
tremolite calcite quartz diopside
We don't map isograd (3), for reasons that will become apparent.
(4) Ca2Mg5Si8O22(OH)2 + 11 CaMg(CO3)2 = 8 Mg2SiO4 + 13 CaCO3 + H2O + 9
tremolite dolomite forsterite calcite
(5) CaCO3 + SiO2 = CaSiO3 + CO2
calcite quartz wollastonite
We don't map the wollastonite isograd because it is not applicable to
most of the rocks. After you read the material below, can you figure
(6) CaMg(CO3)2 = CaCO3 + MgO + CO2
dolomite calcite periclase
The chemography of the talc isograd was shown above, and the other
isograds are shown on the following page. The areas marked "sandy
dolostone" etc. represent bulk compositions of rocks.
The T-X Projection
If we write the equilibrium constant for (1), it is:
atc acc3 fCO23
adol3 aqtz4 fH2O
and, if the minerals are not solid solutions, their activities are
unity, and so
Keq = fCO23 / fH2O
Because the equilibrium constant always varies with temperature, it
follows that the temperature at which the talc isograd reaction will
occur will vary with the fugacities (or partial pressures) of the
volatile species CO2 and H2O, or, stated another way, with the
composition of a CO2-H2O fluid present in the metamorphic aureole.
The temperatures of the reactions have been determined experimentally
as a function of fluid composition and appear in the diagram below.
CO2/ (H2O + CO2) in a metamorphic fluid
Carbonate-silicate isograd reactions as a function of temperature and
fluid composition at a total pressure (total pressure constant) of 1
kbar, equivalent to about 4 km of overload. (The temperatures are not
particularly sensitive to total pressure.) The arrows denote a
possible fluid compositional path during prograde metamorphism at
The possible fluid path in the figure begins, at low temperature,
fairly H2O-rich, reflecting original sedimentary pore water. At high
temperatures, it becomes more CO2-rich because it is buffered by
metamorphic mineral assemblages. For example, the talc isograd
reaction consumes only 1 mole H2O but produces 3 moles CO2. The path
is constrained by the need to cross reactions that correspond to the
observed isograds in the order observed for common lithologies in the
field. For example, the path shown correctly predicts both a talc and
a tremolite isograd, separated by about 50 deg. At high temperature,
the path is shown swinging back toward H2O-rich compositions; this
interpretation reflects the need to cross the periclase isograd at a
temperature lower than the magma temperature. If tht trend is correct,
it could not have been produced by metamorphic mineral buffering and
may have been due to the ingress of magmatic water into country rocks
near the pluton.
The work below should appear as an appendix in your report.
(a) Using the diagrams provided, figure out the mineral assemblage
that each protolith in the table below would exhibit in each of the
metamorphic zones. Produce a similar table in your appendix.
*Dolostone immediately surrounding a chert nodule
(b) Why are tremolite and forsterite observed commonly, whereas
wollastonite and diopside are observed uncommonly?
(c) Suppose that the metamorphic fluid composition lay to the CO2-rich
side of points A & B in the diagram. Write, with balanced reactions,
the isograd reactions that would be encountered during prograde
metamorphism. Note that there are two diopside isograds.
(d) Produce a set of diagrams analogous to the set in the guidebook
for the CO2-rich path. Hand in those diagrams.
(e) Produce a table analogous to the table above for the new prograde
path. Hand in the table.
(f) Indicate in detail why a path to the left of A&B was chosen rather
than a path to the right of A&B. No speculation is necessary here; a
path to the right predicts several mineral or isograd occurrences that
simply are not observed. You should be able to come up with several
separate details. Hints: Details involve talc, diopside, and