P - GET

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P - GET

High-Pressure Deformation and Synchrotron Radiation, or
Mantle Rheology at Mantle Pressures
Paul Raterron
[email protected]
High-Pressure Deformation and Synchrotron Radiation:
Introduction
Materials plasticity
Rheological laws
Notions of crystal plasticity
Dislocation / Diffusion creep
High-P (> 3 GPa) deformation devices & synchrotron X rays
Deformation-DIA apparatus (D-DIA)
In situ strain, stress & LPO measurements
DT-Cup and DT-25
Rotational Drickamer apparatus (RDA)
Radial diffraction in the Diamond anvil cell (DAC)
Mantle rheology at mantle pressures
Olivine and enstatite single-crystal rheology at high P
From single crystal to aggregate plasticity
2
Paul Raterron – CNRS Lille – Fosterite 2015
Earth’s deep interior: extreme pressures and temperatures
Transition zone (410 – 670 km)
24 GPa , 1700 - 2300 K
Lower mantle (670 – 2900 km)
136 GPa , ~3000 K (CMB)
Inner Core (> 5100 km)
365 GPa , ~6000 K
3.65 Mbar
Modified from Kellogg et al., Science, 1999
Inner Core: e.g., Sun and Song, EPSL, 2008
Extreme P , T Conditions
Upper Mantle (< 410 km)
P < 14 GPa , T < 1700 K
140 kbar
An Earth made of rock-forming crystals
Upper mantle (< 410 km)
60% olivine ~30% pyroxenes ~10% pyrope
Transition zone (410 – 670 km)
ringwoodite wadsleyite
~40% majorite
Lower mantle (670 – 2900 km)
bridgmanite +
Mg-perovskite
Core
Fe + ~4% Ni
+ ~10 wt.% O, S, Si,…
~12% Ferropericlase
~8% CaSiO3
Rocks are polycrystalline: complex rheology
Disclinations
(Cordier et al., 2014)
Diffusion
(Cobble)
Dislocations
(glide, cross slip)
Diffusion
(Nabarro-Herring)
Dislocations
(climb)
Grain-boundary sliding
(e.g., Hansen et al., 2011)
5
Understanding Earth’s mantle dynamics
1 - Deformation data on Earth’s materials at relevant (extreme) P and T
2 - Quantification of minerals/rocks plastic responses
3 - Extrapolation to Earth’s relevant (natural) low-stress and strain-rate conditions
6
Introduction
Rheological laws
DT-Cup and DT-25
7
Notions on materials plasticity : rheological laws
p
 E * + PV * 

m

ε = Aσ   fO 2 exp −


RT
d 


n 1
High-T power law :
σ1
dε =
dL
L(t)
 L
dL
=> Strain ε = Ln 
L(t )
 Lo 
Differential stress
σ = σ1 −σ 3
Viscosity
η=
ε =
dε
dt
σ
= Bσ 1− n
ε
Note:
fO2 , fH2O , aSiO2 , etc.
8
Notions on materials plasticity : dislocation creep
Edge dislocation glide
Dislocation slip system
[uvw] (hkl)
Mantle silicates
dε/dt = A σ3 to 5 => η = σ-2 to -4/A
Non-newtonian viscosity
Glide
plane
(hkl)
Texture (CPO, LPO)
Random polycrystal
Deformed polycrystal
hkl
Burgers
vector
[uvw]
[uvw]
Notions on materials plasticity : dislocation creep
Courtesy Carlos Tomé, LANL
Dislocation-creep seismological implications
Texture (LPO, CPO)
[100 ]
[010]
Seismic anisotropy
[001]
SC olivine
Elastic anisotropy
=>
Velocity anisotropy
Vp
(km/s)
Vs
anisotropy
220 km
attenuation
Vs
anisotropy
Ohuchi et al., EPSL, 2011
11
Gung et al., Nature, 2003
Notions on materials plasticity : diffusion creep
Cobble creep (GB diffusion)
dε/dt = A σ /d3
Nabarro-Herring creep (bulk)
dε/dt = A σ /d2
η stress independent
Newtonian viscosity
No LPO / No Seismic anisotropy ?
Source www
(Miyazaki et al., Nature, 2013)
Random lattice orientations
GBS
Source www
12
Notions on materials plasticity : grain boundary sliding (GBS)
GBS
dε/dt = A σ2/d2
dis-GBS
dε/dt = A σ3/d
Non-newtonian viscosity
LPO / Seismic anisotropy ?
Quadruple junction
Accomodated by dislocation glide (dis-GBS)
13
Introduction
Rheological laws
DT-Cup and DT-25
14
High-P rheology : which deformation apparatus ?
Courtesy G. Shen
Upper mantle + TZ (3 < P < 27 GPa)
Lower mantle + Core (P > 27 GPa)
=>
Large Volume Presse (LVP):
=>
Diamond Anvil Cell (DAC):
Deformation-DIA apparatus(D-DIA)
Deformation T-Cup (DT-Cup) – DT-25
Radial diffraction
15
Deformation-DIA (D-DIA)
Main ram
(backward)
Deformation-DIA (D-DIA)
Wang et al. (2002)
P < 17 GPa
T < 1900 K
ε < 40%
Inner pistons
(forward)
Courtesy Bill Durham, MIT
16
Thermal gradient in the D-DIA cell
Z (mm)
1700
5 GPa
+3
Temperature (K)
1500
1300
1100
0
900
y = -154,22x2 + 38,08x + 1 673,00
R² = 0,97
700
WC anvil
500
-3
-2
a)
-1
0
1
2
3
-3
Z position (mm)
WC anvil
Over 2 mm at cell centre : ∆T ~ 155 K/mm
Raterron et al., RSI, 2013
17
Pressure during D-DIA runs
Pressure (GPa)
6
T = 1673 K
5
P ~ 5.0 (±0.5) GPa
4
0
5
10
15
20
Specimen Strain (%)
18
Strain, P & stress measurements
d-spacing
variations
ε = f (σ , P, T ,...)
NSLS X17-B2 beamline
Diffracted beam : σ
(2 dhkl sin θ = λ)
Transmitted
beam : ε
Synchrotron
X rays
19
In situ σ and ε measurements
cBN anvils
EDX detector 1
10
Coutesy: M. Vaughan
5
YAG
σ1
σ (diffraction)
9
Conical slit
Incident
Specimen
white X-ray
Modified from Raterron & Merkel, J. Syn. Rad., 2009
ε (radiography)
20
Deformation-DIA (D-DIA) at NSLS X17-B2
10-element EDX detector
1
5
10
9
Anvil:
Sintered
diamond
or
cBN
Conical slit : fixed 2θ
Deformation-DIA (D-DIA) at NSLS X17-B2
CCD camera
10-element
EDX detector
Conical slit (front part)
Deformation-DIA (D-DIA) at ESRF ID06
23
6-Axis Deformation Apparatus at PETRA III Extension (DESY, Hamburg)
24
Courtesy Nori Nishiyama, DESY
ε measurement : X-ray radiography
60
Piston
Al2O3
50
Fayalite
Fe2SiO4
Fa100 alpha
SC olivine
5,32E-5 s-1
Strain (%)
40
SC olivine
Mg1.8Fe0.2SiO4
7,98E-5 s-1
30
20
2,20E-5 s-1
3,07E-5 s-1
10
2,43E-5 s-1
1,40E-5 s-1
0
1250
1300
1350
1400
1450
1500
Time (min)
ESRF – ID06
25
25
In situ σ measurement : X-ray diffraction
dhkl < dhkl
Singh et al. (1998)
alumina d110
σ1
2.392 Å
Det.# 5
σ1 min.
Det. # 1
σ1 max.
2.386 Å
ψ
σ
Sij : elastic compliances
σ : differential stress
Unit cell <V> = f (P, T)
26
High-P steady state deformation conditions
ε = f (σ , P, T ,...)
Constant strain rate
ε
Constant differential stress σ
20
dԑ/dt = 4.8 × 10-5 s-1
16
Specimen Strain (%)
Differential Stress (GPa)
1
12
8
4
Alumina
{012}
0,8
{104}
{110}
{113}
0,6
{024}
{116}
0,4
{214}
596 ±±80
20MPa
MPa
<σ > == 624
(EPSC model)
0,2
{300}
0
0
0
1 000
2 000
3 000
Time (s)
4 000
5 000
0
5
10
15
20
Specimen Strain (%)
27
Alumina dhkl-stress EPSC simulation
EPSC : Elastoplastic self-consistent
Eshelby
σ
28
In situ LPO measurements
Peak position (dhkl = f(Ψ)) => P(T), Stress value and orientation
Peak intensity (Ihkl = f(Ψ)) => LPO
020
021
101
002
131
112
130
041
210
(1/dhkl)
Bollinger et al., JAC, 2012
29
1
Correction factor Fcorr
Correction factor for sensitivity
Correction factor for sensitivity
and shadow effect
5
9
Detector number
Fcorr = ∑ Ipeak / ∑ Iref
Icorr = Ipeak / Fcorr
6
Forsterite
Mg2SiO4
1100°C
010
001
100
Inverse pole figure (IPF) of
compression direction
from in situ X-ray data
IPF from EBSD data
on run product
8
Forsterite
Mg2SiO4
1100°C
(010) glide plane
[100] Burgers vector (?)
Deformation T-Cup (DT-Cup)
T-Cup
+
Hexagonal anvil
Hunt et al. , Rev. Sci. Instr., 2014
33
34
P → 18.8 GPa
T → 1573 K
Strain ε → 56%
35
Deformation T-25 (DT-25)
25 mm
36
Rotational Drickamer Apparatus (RDA)
RDA
Yamazaki & Karato
Rev. Sci. Instr., 2001
P → 23 GPa
T → 1800 K
High strain: γ > 6
Wadsleyite : Nishihara et al. , PEPI, 2008
37
20°
Incident X rays
Top anvil
Cylindrical
sleeve
PEEK
4 mm
Pyrophyllite
Bottom
anvil
Ringwoodite
Mg1.8Fe0.2SiO4
Miyagi et al. , PEPI, 2013
38
Nishihara et al. , PEPI, 2008
Radial diffraction in the DAC
40 µm
80 µm
Pressure range
 0-50 GPa: routine
 60-300 GPa: possible
Homogeneous heating to 1500K
Local heating to 4000 K
0°
Synchrotron
x-rays
~25 µm
90°
δ
30-40 keV
In-situ measurement
Courtesy Sébastien Merkel, Université de Lille
- texture
- stress (strain)
- sample dimensions
40
Stress and LPO measurements
Courtesy Sébastien Merkel, Université de Lille
41
In situ measurement: hcp-Co, 42 GPa, 300K (Merkel and Yagi, Rev. Sci. Instrum., 2005)
δ
Courtesy Sébastien Merkel
42
Monochromatic beam
Angle dispersive X-ray Diffraction
δ
360° =
0
EPSC model for the deformed aggregate
δ
Q parameter : a measure of d-spacing response to stress
(Singh et al., J. Appl. Physics, 1998)
43
HT Radial diffraction in the DAC
Electrical contacts
Sample, heaters,
gasket...
Opening 70ºx70º
Thermocouples
Inconel body
Liermann et al. , Rev. Sci. Instr., 2009
HT Radial diffraction in the DAC
Heater (graphite)
Insulating layer (alumina)
Synthetic mica KMg3(AlSi3O10)F2
Fusion: 1378 ºC
RX
Amorphous Boron + epoxy
Diameter: 400 µm
Hole: 80 µm
~ 10 mm
Thermocouple
Power requirements :
~ 2V, 100 A for 1000 K
1/8'' ~ 3 mm
Max. temperature: ~ 1500 K
400 µm
Introduction
Rheological laws
DT-Cup and DT-25
46
Observables or constraints
Seismic velocity / anisotropy
Viscosity
Depth (km)
LVZ
220 km
δln(Vs) (%)
Gung et al., Nature 2003
Viscosity (Pa.s)
after Forte & Mitrovica, Nature, 2001
47
Experiments and modeling
Seismic velocity / anisotropy
[100 ]
[010]
Viscosity
[001]
ε = f (σ , P, T ,...)
Ocean geotherm, 60-km depth, 10-15 s-1, γ = 0.5
Observed / Computed LPO
Flow laws / computations
48
From single-crystal to aggregate plasticity
σ
b
a
c
Single crystal deformation
=>
Individual slip-system rheological law
ε = Aσ
n
fO2m exp −
E * + PV *
RT
High-P deformation data
(e.g., olivine, Raterron et al., PEPI, 2012)
Room-P deformation data
(e.g., olivine, Bai et al., JGR, 1991)
Aggregate
Mantle P, T, σ,…, conditions
Classical / empirical modeling
Computational modeling
49
Dislocation slip-system activity at high P ?
Olivine
σ1 // [011]c
σ1 // [110]c
b
a
1 to 2 mm
c
[100](010)
σ1 // [101]c
a
b
c
a
c
[001](010)
[001](100)
[100](001)
50
b
a
[100](010)
c
6 mm
b
c
a
[001](010)
Raterron et al., Am. Mineral., 2007
51
Raterron et al. , PEPI, 2009
52
Enstatite
σ1 // [110]c
σ1 // [011]c
a
b
1 to 2 mm
b
a
[001](100)
c
c
[001](010)
53
Orthoenstatite vs protoenstatite
a
M1
M1
b
Mg2
Mg2
Orthoenstatite (Pbca)
Jahn, Acta Cristal. Section A, 2010
Protoenstatite (Pbcn)
54
Enstatite slip-system activity at high P
E * + PV *
ε = Aσ exp −
RT
n
protoenstatite
1-atm rheological laws
Mackwell, GRL, 1991
0
orthoenstatite [101]c crystals
[001](100) slip system
log10 (Strain Rate , s-1)
-1
-2
-3
-4
-5
This study
-6
0
1
2
3
4
5
-1
P/RT (10 Pa mol J )
5
6
55
E * + PV *
ε = Aσ exp −
RT
n
orthoenstatite
P=1.3 GPa rheological law
Ohuchi et al., CMP, 2011
log10 (Strain Rate , s-1)
-2
orthoenstatite [011]c crystals
-3
-4
-5
This study
-6
0
1
2
3
4
P/RT (105 Pa mol J-1)
5
6
56
E * + PV *
ε = Aσ exp −
RT
n
30 EN_011 - DEF1
P=6.4(2) GPa
Τ =1586 K
σ =803(89) MPa
P=6.2(2) GPa
Τ =1600 K
σ =578(89) MPa
Specimen strain (%)
25
20
15
DEF3
DEF2
10
5
0
500
P=5.9(3) GPa
Τ =1611 K
σ =759(90) MPa
𝑛𝑛𝐸𝐸𝐸𝐸 = 𝑛𝑛𝑂𝑂𝑂𝑂 × ln
𝑛𝑛𝑂𝑂𝑂𝑂 = 3.5
𝜀𝜀𝐸𝐸𝐸𝐸
̇i
𝜀𝜀𝐸𝐸𝐸𝐸
̇ ii
�ln
=>
𝜀𝜀𝑂𝑂𝑂𝑂
̇i
𝜀𝜀𝑂𝑂𝑂𝑂
̇ ii
𝑛𝑛𝐸𝐸𝐸𝐸
101c Enstatite
550
600
650
Time (min)
700
011c SC olivine
750
800
57
E * + PV *
ε = Aσ exp −
RT
n
2
Enstatite [011]c crystals
P=5 GPa ; T= 1400 MPa
Ln(Strain Rate, s-1)
0
-2
-4
-6
-8
-10
-12
-14
-16
5
6
Ln(Stress, MPa)
7
8
58
E * + PV *
ε = Aσ exp −
RT
n
Enstatite [011]c crystals
P=5 GPa ; σ = 300 MPa
Ln(Strain Rate, s-1)
-9
-11
-13
-15
-17
-19
7,0E-05
7,5E-05
8,0E-05
8,5E-05
9,0E-05
9,5E-05
1/RT (J-1 mol)
59
Dislocation slip-system activity in the mantle
10
1800
20-Ma ocean
Adiabat
Normalized Strain Rate
Temperature (K)
1600
1400
1200
Continent
1000
800
600
400
Ol [011]c
20-Ma ocean
Ol [110]c
1
Ol [101]c
0,1
0,01
OPx [101]c
0,001
OPx [011]c
200
0
100
200
300
Depth (km)
400
0,0001
50
(a)
150
200
250
300
Depth (km)
10
Normalized Strain Rate
100
Continent
Ol [011]c
Ol [110]c
1
Ol [101]c
0,1
0,01
OPx [101]c
0,001
OPx [011]c
0,0001
(b)
50
100
150
200
Depth (km)
250
300
60
From single-crystal to aggregate plasticity
σ
b
a
c
CRSS : critical resolved shear stress
Slip-system flow law
=> slip-system CRSS
σ
Viscoplastic self-consistent
(VPSC) simulation
Eshelby
GSF energy (ab initio)
=> slip-system Peierls stress
(olivine, Durinck et al., PCM, 2005)
=> relative CRSS
« Diffusion »
(isotropic mechanism)
Computational modeling for olivine aggregate
σ
70% SC olivine
+
Dislocation slip systems, …
Biphase
aggregate
30% diopside
Diff.
Second-Order (SO) model
(Ponte Castañeda, JMPS, 2002)
+
Isotropic mechanism (n = 1)
(Si diff., Dohmen et al. 2002)
E*=530 kJ/mol ; V*=0
« Diffusion »
62
Computational modeling for peridotite aggregate
.
20-Ma ocean geotherm / γ = 10-15 s-1 / QFM-2
SC olivine
1,0
1.0
[100](010)
[001](010)
[001](100)
CRSS ( MPa)
[100](001)
[100](021)
[001]{110}
0,5
0.5
a/c slip transition
0,0
0.0
50
100
150
200
250
300
350
400
Depth (km)
Raterron et al., PEPI, 2014
63
.
Diopside
20-Ma ocean geotherm
dγ/dt = 10-15 s-1
30
DIOPSIDE
<1-10>{110}
[001]{110}
CRSS ( MPa)
[010](100)
[001](100)
20
10
0
50
90
130 170 210 250 290 330 370 410
Depth / km
64
.
70% SC olivine
+
15
390-km depth
Flow stress (MPa)
30% diopside
Reasonable
stress
10
Second-Order (SO) model
(Ponte Castañeda, JMPS, 2002)
activity > 50%
5
+
Isotropic mechanism (n = 1)
0
10
20
30
40
50
60
70
80
Isotrope mechanism activity (% )
90 100
(Si diff., Dohmen et al. 2002)
E*=530 kJ/mol ; V*=0
65
.
a slip/a+c
60 km Depth
n ~ 6.1
c (010)
100
010
001
60 km
a (010)
240 km
Isotropic
390 km Depth
n ~ 1.4
a slip/a+c
390 km
c (010)
Aggregate shear strain
Taketo
home
From Single-crystal
aggregate plasticity
*** Key points to take home ***
1 - Constraining Mantle dynamics and seismic features requires high-P > 3 GPa
rheological data
2 - In high-P experiments, P, T and strain rates are well constrained ; stress
exhibits large uncertainty; yet rheological laws are accessible
3 - Extrapolation of aggregate rheology to mantle P, T and stress conditions
requires multiscale approaches which integrate individual mechanisms
67
High-Pressure Deformation and Synchrotron Radiation, or
Thank You
Caroline Bollinger
GFZ, Bayreuth, Germany
Olivier Castelnau
PIMM, CNRS, Arts et Métiers, ParisTech
Jiuhua Chen
FIU, Miami, USA
Fabrice Detrez
MSME, Université Paris Est
Guillaume Fraysse
UMET, CNRS, Lille
Jennifer Girard
Yale University, USA
Caleb Holyoke
Akron Université, USA
Sébastien Merkel
UMET, Université de Lille
68

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