Diffusion in Earth’s Deep Interior: Insights
from High-Pressure Experiments
Jim Van Orman
Department of
Geological Sciences
Case Western Reserve
University
COnsortium for Materials Properties
Research in Earth Sciences
COMPRES is an NSFsupported consortium
that supports study of
Earth material properties,
particularly at high
pressures and
temperatures (Earth
interior conditions).
Interior of the Earth
The crust and
upper mantle are
composed of the
familiar silicate
minerals.
In the deep
mantle, these
transform to
denser highpressure forms.
Mantle Mineralogy
To study these and other materials,
COMPRES supports user facilities,
including several synchrotron X-ray
facilities where high-pressure
experiments are performed.
Advanced Photon Source
Synchrotron facilities
also house very large
presses that allow
study of somewhat
larger samples.
Mounted on a stage that
can move the press with
micron precision to put the
sample at the focal point of
the X-ray beam.
Mafic melt viscosity
experiment by Lara
Brown, Chip Lesher,
et al., UC-Davis
Diffusion in Earth’s Deep Interior: Insights
from High-Pressure Experiments
What is Diffusion?
Diffusion is the transport of matter by random hopping of atoms.
It is a fundamental step in many important chemical and physical
processes.
http://www.johnkyrk.com/diffusion.html
Atoms initially confined to a plane spread
out with time according to a simple
mathematical law, based on the theory of
a random walk.
How rapidly they spread depends on the
diffusion coefficient. Diffusion is
*much* more rapid in gases and liquids
than in minerals.
How can
diffusion
happen in a
crystal?
Gas
Crystal
In a perfect crystal, diffusion is extremely difficult
But crystals are never perfect...
dislocations
grain
boundaries
Diffusion by a
vacancy mechanism
More vacancies =
faster diffusion
Vacancies move much
faster than the atoms
themselves
Diffusion in the Deep Earth (1):
Maintaining a Heterogeneous Mantle
Subduction makes the mantle
chemically heterogeneous
Convective and
diffusive mixing
On what length scales
can the heterogeneity
be preserved?
Diffusion in the Deep Earth (2):
Chemical Transfer at the Core-Mantle Boundary
Diffusion in the Deep Earth (3):
Diffusion and Viscosity
diffusion
coefficient
viscosity
Stokes-Einstein Equation
Diffusion in Deep
Earth Materials
at High Pressure
1. Solid Iron-Nickel
Alloys (Inner Core)
2. MgO (Lower
Mantle)
What are the
fundamental controls on
the diffusion rates?
High-Pressure Experiments
Pressure =
Force/Area
Multi-Anvil
Press
Sample size ~1 mm
1. Diffusion in
Iron-Nickel
Alloys at High
Pressure
Fe
Ni
Homologous Temperature Scaling
For Close-Packed Metals
Inner Core
Does it hold at high pressure?
Fe-Ni Diffusion Profiles
12 GPa, 1600 oC
Yunker and Van Orman, 2007
100
Fe concentration (atomic %)
.5 hours
80
2 hours
60
40

Boltzmann-Matano
1 dx  c
Dc     xdc
2t dc c 0
10 hours
20
0
-200
0
200
x-position (microns)
400
600
Melting curve
1 atmosphere
DFe-Ni vs Composition
Yunker and Van Orman, 2007
log Diffusion coefficient (m
2
/s)
-12.0
-12.2
-12.4
-12.6
12 GPa
1600 oC
2 hr
-12.8
-13.0
-13.2
0
20
40
60
Fe concentration (atomic %)
80
100
DFe-Ni vs Pressure at Constant Homologous
Temperature
/s)
-12
log Diffusion coefficient (m
2
T/T m=.874
90% Fe
-13
-14
-15
Yunker and Van Orman, 2007
-16
0
5
10
Pressure (GPa)
15
20
logDFe-Ni vs Pressure
Yunker and Van Orman, 2007
/s)
-12
log Diffusion Coefficient (m
2
1600°C
90%Fe
-13
-14
Goldstein et al. (1965)
Constant activation volume
-15
-16
0
5
10
15
Pressure (GPa)
20
25
logDFe-Ni vs Pressure
Yunker and Van Orman, 2007
/s)
-12
log Diffusion Coefficient (m
2
1600°C
90%Fe
-13
-14
Goldstein et al. (1965)
Constant activation volume
This experiment
-15
-16
0
5
10
15
Pressure (GPa)
20
25
logDFe-Ni vs Pressure
Yunker and Van Orman, 2007
/s)
-12
log Diffusion Coefficient (m
2
1600°C
90%Fe
-13
D  D0 exp gTm T 
-14

Goldstein et al. (1965)
Constant activation volume
This experiment
Homol. Temp scaling
-15
-16
0
5
10
15
Pressure (GPa)
20
25
Inner core viscosity (Harper-Dorn
creep regime)

1 kT
 
2
Ý 2AHD Db
~1011 - 1012 Pa s
Suggests that inner core behaves like a fluid on the
timescale of Earth rotation, and is free to super-rotate
instead of being gravitationally locked to the mantle.
Inner core anisotropy an active deformation feature,
rather than growth texture?
2. Diffusion in MgO
(Mg,Fe)O is thought to
represent ~15-20% of the
lower mantle.
Prior Studies of Self-Diffusion in MgO
(Atmospheric Pressure)
Mg
O
Van Orman and Crispin, in press, Reviews in Mineralogy & Geochemistry
Diffusion in MgO at High Pressure
Sample retrieved from experiment at
2000 oC and 25 GPa
25Mg, 18O
Experiments
were designed
to measure
lattice and
grain boundary
diffusion of
both Mg and O
enriched
Van Orman et al., 2003
Van Orman et al., 2003
Ab Initio Calculation
Cation diffusion in MgO is predicted to become slower
with increasing depth in the lower mantle (except just
above the core-mantle boundary).
A surprise: Al3+ diffuses rapidly in MgO
Al2O3
MgO polyxtl
Van Orman et al., 2003
MgO xtl
Al3+ impurities in MgO:
Cation vacancies are created to
maintain electrical neutrality.
These are attracted to Al3+ and
tend to form pairs (and higher
order clusters at low
temperature). These defect
associates have been known
about for decades, but their
influence on diffusion has been
largely neglected.
Al-vacancy pairs enhance the
mobility of Al, but diminish
the mobility of the vacancy
(and thus the mobility of other
cations that diffuse using
vacancies).
Spinel
MgAl2O4
MgO
E-probe scan
Diffusion
experiments to
determine Alvacancy binding
energy and pair
diffusivity
1 atm to 25 GPa
1577 to 2273 K
Van Orman et al., 2009
Van Orman et al., 2009
Diffusion profiles were fit to a theoretical model to determine
binding energy and diffusivity of the Al-vacancy pairs. Binding
energies for all experiments at atmospheric pressure are -50 ±
10 kJ/mol (2), consistent with theoretical values of -48 to -53
kJ/mol (Carroll et al., 1988) and have no clear pressure
dependence.
However…
The diffusion coefficient of the Al-vacancy
pair does depend on pressure.
V = 3.22 cm3/mol
(+/- 0.25)
Similar to pressure dependence for
Mg self-diffusion (3.0 cm3/mol)
Van Orman et al., 2009
What about other trivalent cations?
Crispin and Van Orman, 2010
-10.5
-11
4000 ppm
log D (m2/s)
-11.5
Ga (0.62Å)
-12
-12.5
Al (0.535 Å)
-13
-13.5
-14
-14.5
Cr (0.615Å)
-15
-15.5
0.00042
0.00047
0.00052
0.00057
Sc (0.745Å)
0.00062
Temperature-1 (K-1)
0.00067
Diffusivity and Ionic Radius
Crispin and Van Orman, 2010
1.E-12
Ga
Al
logD (m2/s)
Sc
Sc
1.E-13
Cr
1.E-14
0.5
0.55
0.6
0.65
0.7
Ionic Radius (Angstroms)
0.75
0.8
Why is chromium so slow?
• Cr3+ 1s2 2s2 2p6 3s2 3p6 3d3
Crystal field effect
The crystal field effect
seems to explain
differences in the
diffusivity of other
transition metals.
• Fe2+ 6 d electrons
– 3 t2g, 2 eg, 1 t2g
• Co2+ 7 d electrons
– 3 t2g, 2 eg, 2 t2g
Wuensch and Vasilos, 1962
• Ni2+ 8 d electrons
– 3 t2g, 2 eg, 3 t2g
(Similar to Cr3+)
260
Crispin and Van Orman, 2010
Activation Energy (kJ/mol)
240
Cr
3+
220
Co
200
180
Ga
2+
Ni
2+
3+
Fe
2+
160
0
-50
-100
-150
-200
Crystal Field Stabilization Energy (kJ/mol)
-250
A transition in the electronic structure of Fe2+ in MgO is
one of the exciting discoveries in mineral physics in the
last decade (Badro et al., 2003).
Marquardt et al. (2009) Science
• At high pressure, the
two electrons in eg
orbitals in Fe2+ move
to t2g orbitals.
• This so-called “spin”
transition affects a
wide range of
properties (density,
seismic wave speeds).
• It may also have a
strong influence on
diffusion.
-12
Crispin and Van Orman, 2010
Fe
-13
2
log D (m /s)
-14
Co
Ni
-15
-16
Co(ls)
-17
-18
-19
-350
Fe(ls)
-300
-250
-200
-150
-100
-50
Crystal Field Stabilization Energy (kJ/mol)
0
Conclusion:
How might electronic spin transitions affect diffusion
length scales in the mantle?
High Spin
Low Spin?
Spin transitions may slow the diffusion of transition metals
significantly. This would:
1)Make chemical exchange across the core-mantle boundary more
difficult.
2)Make chemical heterogeneity in the deepest mantle more
difficult to erase.