The Earth as a whole has a wide range of redox
conditions, from the metallic iron (Fe)-nickel core,
through the ferrous (Fe
2
) silicate mantle, to the hy-
drosphere and oxygen-rich atmosphere, where ferric
(Fe
3
) minerals such as hematite and goethite are sta-
ble. At sea level, P
total
1 bar approximately for air
and, because the mole fraction of oxygen in it is 0.21,
from Dalton’s law (equation 3.24) the partial pressure
of oxygen P
O
2
0.21 bar. At equilibrium, this P
O
2
must be equal to the fugacity of oxygen in a melt at the
surface of the Earth, thus setting an upper limit of
f
O
2
0.21 bar (10
0.68
bar) on the oxygen fugacity in
natural melts. Only in lunar basalts and in very rare ter-
restrial basalts that formed from magma intruded into
and reduced by interaction with coal does iron occur in
the metallic state, or as wüstite (FeO). Most magmas
have oxygen fugacities such that magnetite is the stable
phase, that is, the shaded region of Figure 3.14. As as-
cending magmas contact near-surface meteoric ground
waters or the oxygen-rich atmosphere, Fe
2
in the
magma can be at least partly oxidized to Fe
3
, de-
pending on kinetic factors. At highest oxygen fugaci-
ties hematite is stable. Hence, iron-rich basaltic lavas
extruded onto the surface are locally red because of the
presence of very finely divided particles of hematite.
Provided magnetite persists in equilibrium with
hematite in an HM buffer, decreasing T results in the
system’s experiencing decreasing oxygen fugacity as
oxygen is consumed in production of hematite. Once
all of the magnetite is gone, the system leaves the buffer
curve and enters the field of stable hematite, and T and
f
O
2
are no longer interdependent variables.
How do other factors, such as confining pressure
(P) and P
H
2
O
, in magmatic systems influence redox
equilibria? As for P, Kress and Carmichael (1991) show
that, provided the magma system remains closed, any
change in P less than 30 kbar (i.e., depths above the up-
per mantle) changes the oxygen fugacity by less than
one-half of a log unit. Therefore, the oxidation state of
a closed magma system rising from a source in the up-
per mantle will essentially reflect the oxidation state of
that source. For example, if a closed magma system
originates on the QFM buffer, it virtually stays on it
during ascent. As for dissolved water in melts, it has
commonly been assumed that more water-rich melts
would be more oxidized because of the thermal disso-
ciation of water into oxygen and hydrogen ions and the
loss of the more easily diffusing hydrogen. However,
there is increasing evidence (Moore et al., 1995) that
dissolved water by itself has no effect on the oxidation
state of iron in natural melts.
3.5.5 Fe-Ti Oxide Buffers: Oxygen
Geobarometers and Geothermometers
Buffer reactions like the ones just described provide
the means of evaluating the intensive variables in mag-
matic systems at which minerals crystallized under
equilibrium conditions using their chemical composi-
tions and thermodynamic models. Equilibria involving
oxygen and minerals are the basis for oxygen geo-
barometers (indicating f
O
2
of crystallization) and geo-
thermometers (T).
Since the pioneering and now classic publication of
Buddington and Lindsley (1964), the chemical compo-
sition of coexisting oxide phases in the system FeO-
Fe
2
O
3
-TiO
2
has been an important source of informa-
tion on the f
O
2
and T of the magma in which they have
crystallized. Two major solid-solution series occur in
this system: cubic, or isometric, ulvöspinel-magnetite
solid solutions essentially between Fe
2
TiO
4
and Fe
3
O
4
and rhombohedral ilmenite-hematite solid solutions
essentially between FeTiO
3
and Fe
2
O
3
. The composi-
tions of the two solid solutions are strongly dependent
on f
O
2
and T. Hence, determinations of the composi-
tions of an equilibrium pair of cubic and rhombohedral
Fe-Ti oxides in a rock, usually by electron microprobe
analysis, give the values of the f
O
2
and T at which they
equilibrated. This is the method used by Hildreth
(1983) to determine f
O
2
and T in the rhyolite-dacite-
andesite magma sequence plotted in Figure 3.14.
Ghiorso and Sack (1991) provide detailed instruc-
tions for recalculating the compositions of natural ox-
ides, which always contain Mn, Al, V, and so on, in
solid solution, before plotting in terms of Fe and Ti,
and for evaluating whether the coexisting compositions
represent equilibrium. Carmichael et al. (1974, p. 87)
demonstrate that confining pressure, P, has little effect
on the equilibrium compositions; an increase in P from
1 to 5000 bars on the solid phases at 1000°C only in-
creases log f
O
2
by 0.073.
3.6 KINETICS
The basic questions with regard to changes in the states
of petrologic systems are: In what direction does a spon-
taneous process proceed, and how fast will it proceed?
The answer to the first question is that systems move to-
ward a more stable state of lower Gibbs free energy or
chemical potential. With regard to the second question,
there is usually some inertia or resistance to the chang-
ing of a state. A metastable state seldom has unre-
stricted access to a lower energy more stable state be-
cause of an activation energy barrier or hump between
the initial and final states (Figure 3.5). High-T minerals,
such as diamond and olivine, are mostly metastable
at the cool, wet, oxygen-rich surface of the Earth. Yet
these minerals do not convert into stable minerals, such
as clays, carbonates, gypsum, and hematite, while sitting
in museum drawers in a human lifetime, and they had
not done so for millennia before they were collected
from exposures at the surface of the Earth.
66 Igneous and Metamorphic Petrology