文档介绍：Chapter 2
Fractional Melting
During batch melting, melt always remains in equilibrium with solid. In
contrast, during fractional melting, melt is extracted as soon as it is
generated and only the last drop of extracted melt is in equilibrium with
the solid.
Table . Mass balance during fractional melting. Note that, in contrast with batch
melting, there are no exchanges between the extracted melt and the residual solid
(no two-way arrows in the table).
Source Residual Extracted
Solid Melt
the mass of an
There are several ways to derive the fundamental equation for fractional
melting. Here we choose an approach that can be easily understood.
The mass conservation for a trace element requires
C,(l-F)+CF=C,. ()
-
C, is the concentration in the solid and C is the concentration in the
accumulated extracted melt and is related to the instantaneous melt C,
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24 Quantitative Geochemistry
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C = - IC,dF.
F
The solid is in equilibrium with the instantaneous melt, or, the last drop
of the extracted (aggregated) melt by the following relationship
c, = C;D, ()
and D is the bulk partition coefficient.
Note that the residual solid is in equilibrium with instantaneous melt,
rather than extracted melt. The relationship between c and C, can be
rewritten as
-
d(CF)
c. =- ()
’ dF
bining Eqs. (), (), and (), we obtain the differential
equation
-
d(CF) -
D(1- F)- +CF =Co,
dF
or
d(CF) dF
- - 1
Co-CF Dl-F
This is a fundamental equation for fractional melting. D can remain
constant or change with fundamental equation for fractional
melting is a differential equation while that for batch melting is an
algebraic equation. If Dchanges, it is more difficult to derive the
equations for fractional melting than batch melting due to the necessity
of solving differential equations for fractional melting.
. Modal Fractional Melting with