Geoscience Reference
In-Depth Information
4. During crystal growth from their melt, elements partition across the interface with,
for element
i
,
C
i
min
=
K
i
min
/
liq
C
liq
. The position of the mineral-melt interface is set
at
x
0, the growth rate
V
is constant, and the density change during crystallization
is neglected. We will assume that diffusion in the solid (
x
=
0) is slow enough to
be neglected and that the diffusion coefficient of
i
in the melt (
x
<
0) is
D
liq
. Write
the advection fluxes on each side of the interface, the diffusion flux in the liquid,
and the overall transport balance of element
i
during crystallization. This situation is
reminiscent of sedimentation. What is the major difference?
5. Experiments by van Orman
et al.
(2001)
determined the parameters for Nd diffusion
in pyrope crystals. The pre-exponential term is
D
Nd
0
>
10
−
9.2
m
2
s
−
1
and the activa-
=
300 kJ mol
−
1
. It is determined that the core of a spherical garnet
of 1 cm radius contains about 1 ppm Nd. Concentration decreases in the depleted
rim to a zero value at the surface and this is thought to be the result of a metamor-
phic pulse with a steady temperature of 800
◦
C. The thickness of the depleted rim
(diffusion boundary layer) is 0.1 micron and we assume that concentration decreases
linearly between the core and the surface. The specific weight of garnet is 3.5 g cm
−
3
.
Calculate the total flux of Nd in kg s
−
1
out of the garnet during the metamorphic
pulse.
6. Helium is lost by diffusion from an apatite crystal assumed to be spherical with a
radius
a
of 100 microns (
tion energy
E
Nd
=
μ
m) during a short episode of reheating (
t
=
200 000 years
at 100
◦
C). The parameters for He diffusion in apatite are
D
He
0
0.064 m
2
s
−
1
and the
=
activation energy
E
He
148 kJ mol
−
1
. Calculate the parameter
D
He
t
/
a
2
and
=
τ
=
the fraction of He lost at the end of the thermal disturbance.
7. Using the parameters given in the previous exercise, what is the closure temperature
of He diffusion in apatite for a cooling rate of 10 K Ma
−
1
? Hint: use a guess for the
temperature to calculate
then
T
c
, and proceed by successive refinements.
8. Cygan and Lasaga
(1985)
determined that the parameters for Mg diffusion in pyrope
garnet are
D
Mg
0
θ
239 kJ mol
−
1
.
If the cooling rate is 10 K Ma
−
1
, what is the closure temperature of Mg exchange
between a spherical garnet of 1 cm radius and its neighbors?
9. A very large number of different
39
Ar-
40
Ar analyses of K-feldspar in granites and
gneisses showed that the Ar diffusion parameters are
E
Ar
10
−
9
m
2
s
−
1
and the activation energy
E
Mg
=
9.8
×
=
190 kJ mol
−
1
=
and
10
5
s
−
1
, where
a
is the “effective” diffusion radius (McDougall and Har-
rison,
1999
). Calculate the closure temperature for Ar diffusion in feldspar for a
cooling rate of 20 K Ma
−
1
.Thevalueof
D
Ar
0
was also determined on homoge-
neous gem-quality material; by comparison with the previous data, it was shown that
the “effective” diffusion radius
a
is only 6
D
Ar
0
/
a
2
=
μ
m. Discuss the implications of these
observations for chronology.
10. Discuss the significance of the apparent temperatures given by (a) fractionation of
oxygen isotopes between minerals and (b) Fe-Mg fractionation between co-existing
clinopyroxene and orthopyroxene.
11. Groundwater percolates through the sedimentary basement at a velocity of 10m a
−
1
.
Rock volumic porosity is one percent and we neglect the difference in density between
water and sediment. Let
D
i
be the partition coefficient of element
i
between the matrix
