Trace Element in
Behavior in
Crystallization
Lecture 28
Melting Beneath Mid-Ocean
Ridges
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The most common kind of melting on Earth
is at mid-ocean ridges.
Once the parcel of mantle has risen above
the initial melting depth, melt from below
will continually stream through it and will
react with the solid in an attempt to reach
equilibrium with it.
Despite the complexity of the melting
process, the batch melting equation gives
a reasonably good approximation of
incompatible element concentrations in
the melt as a function of the average
degree of melting.
Beneath mid-ocean ridges, the average
degree of melting will be less than the
maximum degree of melting, because
different parcels of mantle follow different
paths. Only mantle directly beneath the
ridge is able to rise the maximum amount,
and hence melt the maximum amount. In
the simple case, the average extent of
melting is one half the maximum extent.
Other ratios are possible for other models of
mantle flow.
The presence of water will depress the
solidus, producing melting earlier.
Trace Elements During
Crystallization
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As for melting, we can imagine two possibilities: equilibrium and fractional
crystallization.
Equilibrium crystallization occurs when the total liquid and total solid
remain in equilibrium throughout the crystallization. If we define X as the
fraction crystallized, then
Cil
1
=
Ci0 DX + (1- X)
The limit of trace element enrichment or depletion occurs when X = 1,
when Cℓ/C˚ = 1/D.
Fractional crystallization, which assumes only instantaneous equilibrium
between solid and liquid, is a more generally applicable model of
crystallization. In this case, trace element concentrations in the melt are
governed by:
Ci
= (1- X)D-1
o
Ci
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If D is very large, Cℓ/Co approaches 0 as X approaches 1, and it
approaches ∞ as X approaches 1 if D is very small.
For multiphase crystallization, we can replace it with the bulk distribution
coefficient as we defined it earlier.
Fractional Crystallization
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Though fractional crystallization
can, in principle, produce
extreme trace element
enrichment, this rarely occurs. A
melt that has crystallized 90% or
more would have major element
chemistry very different and very
different partition coefficients,
and usually larger ones. This limits
the enrichment of incompatible
elements.
However, highly compatible
elements (elements with
solid/liquid partition coefficients
greater than 1, such as Ni) do
have concentrations that
approach 0 in fractionated
melts.
In Situ Crystallization
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We think about how magmas
might crystallize in a magma
chamber and use these same
basic equations to build more
sophisticated models.
In in situ crystallization, we
imagine crystallization occurs in a
crystal-rich mush on the margin
of the chamber, where heat is
being lost. Melt in the mush
connects with the free magma in
the chamber only by diffusion.
This leads to a less enrichment of
incompatible elements as
crystallization proceeds.
CL æ M L ö
=ç 0÷
0
èM ø
C
o
fA (
Cf
CL
-1)/( fA -1)
ƒA is rhe fraction of returning liquid and Cf is
the concentration in that liquid.
f is the fraction of liquid remaining
(and returning to magma chamber in
the mush zone).
RTF Magma Chambers
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We know a little about how
volcanoes work. In particular,
they don’t completely empty
during eruption. On long time
scales (thousands of years),
we can consider them to be
continually refilled, tapped
(erupted), and undergoing
fractional crystallization.
Thus they are open systems.
Our equations thus far have
been for closed systems.
Open systems can lead to
different styles of enrichment,
and, ultimately in extreme
cases, steady-state
concentrations after many
cycles.
Trace Element Ratios
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Incompatible elements ratios are less
sensitive to fractional crystallization and
partial melting than are absolute
abundances, particularly if they are of similar
incompatibility. For large extents of melting,
the ratio of two incompatible elements in a
magma will be similar to that ratio in the
magma source.
One approach is to plot the ratio of two
incompatible elements against the
abundance of the least compatible of the
two. This kind of plot is sometimes referred to
as a process identification plot because
fractional crystallization and partial melting
have very different slopes.
Crystallization produce rather flat slopes on
such a diagram. Partial melting produces a
steeper slope and the slope produced by
aggregates of fractional melts is similar to
that of equilibrium partial melting. In situ
crystallization can produce a range of slopes
depending on the value of ƒ, but a value of
0.25 is probably most reasonable.
Summary
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Incompatible element abundances are strong functions of degree of
melting (more so for fractional), compatible element abundances are
only weakly dependent on extent of melting.
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Moderate amounts of fractional crystallization do not have dramatic
effects on incompatible element concentrations. Concentrations of
highly compatible elements dramatically decrease with extent of
fractional crystallization.
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The RTF model does have significantly greater effects on incompatible element concentrations than simpler
models, however.
This all works out nicely: compatible elements are good qualitative
indicators of the extent of fractional crystallization and incompatible
elements are good indicators of the degree of melting.
Both geochemical and experimental evidence indicates that alkali
basalts and are the products of lower degrees of melting than tholeiites
such as MORB, which are generally produced by ~8 to 15% average
extent of melting.
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Two simplifications are important for partial melting. When D ≪ F, the enrichment is 1/F for batch melting. If
D is large (i.e., D ≫ F), the depletion of the element in the melt is rather insensitive to F. In either case, when F
approaches 0, the maximum enrichment or depletion is 1/D.
Highly undersaturated rocks such as nephelinites are probably produced by the smallest degrees of melting
(1% or less).
Incompatible element ratios are less sensitive to fractional crystallization
and partial melting than are absolute abundances, particularly if they
are of similar incompatibility.
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For relatively large extents of melting, the ratio of two incompatible elements in a magma will be similar to
that ratio in the magma source.