diffusion in earth’s deep interior: insights from high-pressure experiments
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Diffusion in Earth’s Deep Interior: Insights from High-Pressure Experiments. Jim Van Orman Department of Geological Sciences Case Western Reserve University. CO nsortium for M aterials P roperties R esearch in E arth S ciences. - PowerPoint PPT PresentationTRANSCRIPT
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 NSF-supported consortium that supports study of Earth material properties, particularly at high pressures and temperatures (Earth interior conditions).
Interior of the Earth
In the deep mantle, these transform to denser high-pressure forms.
In the deep mantle, these transform to denser high-pressure forms.
The crust and upper mantle are composed of the familiar silicate minerals.
The crust and upper mantle are composed of the familiar silicate minerals.
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
http://www.johnkyrk.com/diffusion.html
What is Diffusion?What is Diffusion?
Diffusion in Earth’s Deep Interior: Insights from High-Pressure Experiments
Diffusion is the transport of matter by random hopping of atoms. It is a fundamental step in many important chemical and physical processes.
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.
Gas
Crystal
How can diffusion happen in a crystal?
How can diffusion happen in a crystal?
In a perfect crystal, diffusion is extremely difficultIn a perfect crystal, diffusion is extremely difficult
dislocations
grain boundaries
But crystals are never perfect...But crystals are never perfect...
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
On what length scales can the heterogeneity
be preserved?
Convective and diffusive mixingConvective and diffusive mixing
Diffusion in the Deep Earth (2):Chemical Transfer at the Core-Mantle Boundary
Diffusion in the Deep Earth (3):Diffusion and Viscosity
Stokes-Einstein Equation
diffusioncoefficient
viscosity
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-AnvilPress
Sample size ~1 mm
Ni
Fe
1. Diffusion in Iron-Nickel Alloys at High Pressure
Homologous Temperature Scaling For Close-Packed Metals
Inner Core
Does it hold at high pressure?
Fe-Ni Diffusion Profiles12 GPa, 1600 oC
100
80
60
40
20
0
Fe concentration (atomic %)
6004002000-200
x-position (microns)
2 hours
10 hours
.5 hours
€
D ′ c ( ) =−12t
dxdc
⎛ ⎝ ⎜
⎞ ⎠ ⎟′ c
xdc0
′ c
∫
Boltzmann-Matano
Yunker and Van Orman, 2007
DFe-Ni vs Composition
-13.2
-13.0
-12.8
-12.6
-12.4
-12.2
-12.0
log Diffusion coefficient (m
2/s)
100806040200
Fe concentration (atomic %)
12 GPa1600 oC2 hr
Melting curve1 atmosphere
Yunker and Van Orman, 2007
DFe-Ni vs Pressure at Constant Homologous Temperature
-16
-15
-14
-13
-12
log Diffusion coefficient (m
2/s)
20151050
Pressure (GPa)
T/T m=.87490% Fe
Yunker and Van Orman, 2007
-16
-15
-14
-13
-12
log Diffusion Coefficient (m
2/s)
2520151050
Pressure (GPa)
Goldstein et al. (1965) Constant activation volume
1600°C90%Fe
logDFe-Ni vs PressureYunker and Van Orman, 2007
-16
-15
-14
-13
-12
log Diffusion Coefficient (m
2/s)
2520151050
Pressure (GPa)
Goldstein et al. (1965) Constant activation volume This experiment
1600°C90%Fe
logDFe-Ni vs PressureYunker and Van Orman, 2007
-16
-15
-14
-13
-12
log Diffusion Coefficient (m
2/s)
2520151050
Pressure (GPa)
Goldstein et al. (1965) Constant activation volume This experiment Homol. Temp scaling
1600°C90%Fe
€
D = D0 exp −gTm T( )
logDFe-Ni vs PressureYunker and Van Orman, 2007
Inner core viscosity (Harper-Dorn creep regime)
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?
€
η =σ2 ˙ ε
≈1
2AHD
kTDb
~1011 - 1012 Pa s
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
25Mg, 18O enriched
Experiments were designed to measure lattice and grain boundary diffusion of both Mg and O
Sample retrieved from experiment at 2000 oC and 25 GPa
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).
MgO polyxtl MgO xtlAl2O3
A surprise: Al3+ diffuses rapidly in MgO
Van Orman et al., 2003
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).
MgOSpinelMgAl2O4
Diffusion experiments to determine Al-
vacancy binding energy and pair
diffusivity
1 atm to 25 GPa1577 to 2273 K
E-probe scan
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.
Van Orman et al., 2009
V = 3.22 cm3/mol(+/- 0.25)
The diffusion coefficient of the Al-vacancy pair does depend on pressure.
Similar to pressure dependence for Mg self-diffusion (3.0 cm3/mol)
Van Orman et al., 2009
However…
Al (0.535 Å)
What about other trivalent cations?
Crispin and Van Orman, 2010
Diffusivity and Ionic RadiusDiffusivity and Ionic Radius
Sc
Crispin and Van Orman, 2010
Why is chromium so slow?Why is chromium so slow?
• Cr3+ 1s2 2s2 2p6 3s2 3p6 3d3 Crystal field effect
Wuensch and Vasilos, 1962
• Fe2+ 6 d electrons– 3 t2g, 2 eg, 1 t2g
• Co2+ 7 d electrons– 3 t2g, 2 eg, 2 t2g
• Ni2+ 8 d electrons– 3 t2g, 2 eg, 3 t2g
(Similar to Cr3+)
The crystal field effect seems to explain differences in the diffusivity of other transition metals.
0 -50 -100 -150 -200 -250160
180
200
220
240
260
Ga3+
Cr3+
Ni2+Co2+
Act
ivat
ion
Ene
rgy
(kJ/
mol
)
Crystal Field Stabilization Energy (kJ/mol)
Fe2+
Crispin and Van Orman, 2010
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).
• 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.
Marquardt et al. (2009) Science
-350 -300 -250 -200 -150 -100 -50 0
-19
-18
-17
-16
-15
-14
-13
-12
Fe(ls)
Co(ls)
log
D (
m2 /s
)
Crystal Field Stabilization Energy (kJ/mol)
Fe
CoNi
Crispin and Van Orman, 2010
High Spin
Conclusion:How might electronic spin transitions affect diffusion
length scales in the mantle?
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.