Rheology II Transport properties

Patrick Cordier

Mineral Physics Group - UMET - Université Lille 1 & CNRS

CIDER Summer Program: Flow In the Deep Earth Santa Barbara CA July 2016 The unreachable Earth Mechanical properties of wadsleyite

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Nishihara et al., 2008 5000 Kawazoe et al., 2013 Kawazoe et al., 2010 (MPa)σ 4000 Hustoft et al., 2013 Farla et al., 2015 3000

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0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of ringwoodite

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Hustoft et al., 2013 5000 Kavner et al., 2001 Meade and Jeanloz, 1990 (MPa)σ 4000 Miyagi et al., 2014 Nishiyama et al., 2005 3000

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0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of bridgmanite

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Merkel et al. 2003

6000 Meade et al. 1990 (MPa)σ Girard et al. 2015

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0 0 500 1000 1500 2000 2500 3000 T (K) Constitutive equations

Q − ε∝ σ n. e kT

Mackwell, 2008

Also need to take high- pressure into account: Q+PV Extrapolating to natural timescales

Q − ε∝ σ n. e kT

-7.0

-8.0

-9.0 Extrapolation to natural conditions

-10.0

-11.0

-12.0 The pitch drop experiment

The University of Queensland pitch drop experiment (started 1927)

Here featuring, Professor John Mainstone (taken in 1990, two years after the seventh drop and 10 years before the eighth drop fell).

Professor John Mainstone died on 23 August 2013, aged 78, after having watched the experiment 52 years

Bitumen η = 2.3 1011 Pa.s What if….

Galileo Galilei (Leyden 1638) From crystals to mantle flow From flow crystals to mantle

© B. Schuberth Can we bridge bridge scales ? Deforming crystals

transport of matter Diffusion creep

• Nabarro (1948) - Herring (1950) creep

+ − ⎛σ b3 ⎞ C −C C+ C exp = 0 ⎜ ⎟ J = −D gradC ≈ αD ⎝ kT ⎠ v v d C+

3 − ⎛−σ b ⎞ C = C0 exp⎜ ⎟ ⎝ kT ⎠ DsdσΩ - ε! = α C d 2kT

d 2kT σ = ε! αDsdΩ

Newtonian Diffusion creep in the mantle

Glišovic et al. (2015) Shearing crystals

(001) Shearing crystals

Ringwoodite (20 GPa) (110) plane

Easy shear path along the ½[-110] direction

Defines the Burgers vector Ritterbex et al. (2015) Slip systems

Ringwoodite (20 GPa)

Slip along <110> in: {001} {110} {111} Ritterbex et al. (2015) We learnt: Slip systems

Plasticity of crystals - Schmid & Boas (1950)

{hkl}

Uchic et al. 2004 We don’t understand: stresses

τmax/µ = 0.2-0.3

Two to four orders of magnitude too large

Need for defects: dislocations The Volterra defects

Vito Volterra (1860-1940) Vito Volterra, Sur les Distorsions des corps élastiques, Gauthier-Villars, Paris, 1960 Crystal defects: dislocations

Egon Orowan Sir Geoffrey Ingram Taylor Michael Polanyi

1934 Dislocaons duality

Near field: atomistic Far field: elastic

µb σ = f (θ) 2πr Long-range interactions Dislocaons respond to stress

External loading σ

!" F

!" " !" Peach & Koehler (1950) force : F = σ. b × L ! velocity v From dislocaons to plascity: the toolbox

• 3D dislocation dynamics

MgO J. Amodeo et al. Mechanics of Materials 71 (2014) 62–73

• 2.5 D dislocation dynamics

Olivine Boioli et al. (2015) • Orowan equation

Dislocation velocity Strain rate Dislocation density Burgers vector modulus Dislocation velocities: can we measure ?

New approack based on nanomechanical testing of olivine in the TEM Nanomechanical testing in the TEM The Push-to-Pull device (Hysitron®)

Collaboration with H. Idrissi Antwerpen, Belgium & C. Bollinger, Bayreuth, Germany

Hair Nanomechanical testing in the TEM

Nanomechanical testing in the TEM

Nanomechanical testing in the TEM

Dislocation velocities: can we calculate ? Dislocation core modeling

Perovskite MgSiO3 : orthorhombic: 20 atoms / unit cell

LAMMPS molecular statics

30 000 atoms

Antoine Kraych’s PhD Atomic structure of dislocations

[100] x

[001]

[010] [100] screw dislocation in bridgmanite at 30GPa

Density of Burgers vector in (010) planes (30GPa)

Dislocation position along [001] (Å) Dislocation gallery

Bridgmanite

[100](010)

[010](1 OO) Dislocation gallery

l/2<111>{101} Wadsleyite

Stacking fault

1h [111](101) Dislocation gallery

(100)(010) Wadsleyite Dislocation gallery

1/2<110>{110}

112<110>{1 ll} P>lJ ... _ 1 Ringwoodite Dislocation gallery

Post-perovskite

[100](010) Stop 2

• We know: the << crystallography of defects >>

/ '\. [\' ' • We don't know: their << dynamics >>

Questions: • Do dislocations move easily when stress is applied ? • What is their velocity • How doest it depend on stress ? temperature ? Lattice friction: the brutal force

150 (a)

-> 100 <.--' ...... ,0 llJ 50

Peierls stress

o.oos O.OIS Lattice friction

0,7 0,6 (1) : 0 GPa 0,5 [100](010) in bridgmanite at 30 GPa "O>< 0,4 ...... ~ 0,3 0,2 0,1 0 1----....,,,,,,,~~:__-1--~-L--~~~:::=~..... ---1 (2): 2.1 GPa

(3): ·'-"' GPa

o.oos E 0.01 O.OIS

(4)

- 20 - 15 - 10 -5 0 5 10 15 20 x(Â) Lattice friction: calculation of the Peierls potential

The "Nudged Elastic Band" (NEB) method ~ energy barrier

--0-· (100)(010) 1.4 ...... [010)(100) 1.2

'::ô' 1 ...... > ..!.. 0.8 o.. :;::.;: 0.6

0.4

0.2

Qr..L:-~-----'~~-----L~~----'-~~----L..~~-31<1 0 0.2 0.4 0.6 0.8 xl a' Kraych et al. EPSL in revision Dislocations: how they move

6 (a) [100](010) 5

-~4:a ~ ~ ~ 3 -u > u~ 2 V,. ~ cc 1

(1) (2) (3) (4) (5) (6) 0 -----'(1) - 15 - 10 - 5 0 5

---...... (2)

(4)

5 10 Dislocation position (Â) Kraych et al. EPSL in revision Wadsleyite: Peierls stresses

10000 [100](010) • 9000 E

8000

7000 - %[111](101)

6000 CU - Nishihara et al., 2008 ~ :!! 5000 iiKawazoe et al. , 2013 -t:> .a. Kawazoe et al. , 2010 4000 XHustoft et al. , 2013

~~ Faria et al., 2015 3000

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0 0 500 1000 1500 2000 2500 3000 T (K} Ringwoodite: Peierls stresses Lattice friction in MgSi03 Perovskite

35 [010](001)

30 [100] (001) T •••. / ._T'/ .• .?' 25 T'~· ,. /~ --...---. T' i ~--...~ "- I =... 20 û) ...... ,._ - 1 15 . _..- .

10 2 easiest slip systems: [100](010) 5 [010](100)

o i--~~--~~~---~~----....-~~--~~~---~~----.~___. 20 40 60 80 100 120 140 Pressure (GPa) Lattice friction in MgSi03: from bridgmanite to post-perovskite

18 16 Mantle

14 pv [100](01 O) a..ro <.9 12 "'C -a. t:> 10 < en '+' en Q) "'C L.. "'C .+J 8 en < en L.. Q) 6 Q) a.. 4

2 ppv [100](01 O) + 0 20 40 60 80 100 120 140 Pressure, GPa Stop 3

• We know: the intrinsic resistance that the crystal opposes to dislocation motion: the

Peierls stress s -;;- "r o.. J 0 ~~ l ~ .,.. l- i

E 0.01 O.OIS / '\. ~ • We don't know: how temperature helps to overcome this lattice friction

(/) (/) ...... ~ Cf)

Temperature Modeling dislocation mobility

• Core structure Stress assisted thermal activation : (i;, T} • Peierls Potential

Kink pair mechanism : /1 v

Modeling rare events:

Wadsleyite; 1700K, 1 GPa: 1OOps MgSi03 perovskite: kink pair mechanism

20 w

1 - 16 ... 0.8 ~ 0.6

0.4

0.2

0 2 4 6 ' 10 12 14 16 18 20 22 24 26 28 30 32 xla

4

o l____L_____L~_J_____L_~L____L_____L~_J__--=~ 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 't l 'tp

Transient state theory

, L vvb ( Afl*(r)) v = a · w * ( r) · w * (r) ·exp - kT

Antoine Kraych's PhD Dislocation velocities

5 10 PV T =2000 K P=30 GPa Rwd T =1800 K P=20 GPa 1 OO 01 T =1600 K P= 0 GPa ...-.. en 5 ._..--E 1 o- ~ +-' () 0 1 o-10 -Q) > Q) "'O 1 o-15 - CJ 10-20

1 o-25 ------500 1000 1500 2000 2500 3000 3500 Resolved shear stress 't (MPa) From dislocations to plasticity: a ractical exam le

Orowan equation i = p b v(r, T) Kraych et al. EPSL submitted

0 1 ' '. 10 Il"",,. .. » Zl" •• !) tt

'b2 r;; C = -k ln (vv a v.P~î • • 2 2w*2 E ,,L.~------'-._,/ The strain rate is here Dislocation Glide in Ringwoodite (20 GPa)

18 Kavner et al., 2001 1 • Hustoft et al., 2013 1 M 1

16 Miyagi et al., 2014 1 >< Nishiyama et al., 2005 1 e 1

14 Meade and Jeanloz, 1990 • i -Cl) Cl) Q.) "­ +-' . 10-s -1 Cl) 10 E= S 0) c 1/2<110>{111} ·-"- 8 Q.) Q.) c 6 ·-0) c w 4

2 ,,,,,,,,,,, ,,,,,.,, ..... ,,,,,,.,, ..... u,,,,, ...... • •••• 0 --~--~----~--~--~~--··_... _... _ .. ___. _···-··-··-· ----- 0 500 1000 1500 2000 2500 3000 3500 4000 T (K) Ritterbex et al. (2015) PEPI Dislocation Glide in Wadsleyite (15 GPa)

10 Hustoft et al., 2013 1 1 Kawazoe et al., 2010 -•-- [100](010) screw Kawazoe et al., 2013 • ~ 8 -a.. Nishihara et al., 2008 ...,..,---+----t (!) Faria et al., 2015 ...,..,---+----t en -en Q) 6 ~ ...... en . 10-s S -1 O> E= c ~ 4 Q) Q) c ·-0> c w 2 ...... screw ······ •·········· ······· ······· 0 •• ·•·····•···· ········ 0 500 1000 1500 2000 2500 3000 3500 4000 4500 T (K) Ritterbex et al. Am. Mineralogist in press MgSi03 perovskite (30 GPa)

14 _...... P = ___ 30 __. GPa___ _...... ,....; i = ___10- ,...... _5 s ______- 1 ; p = 1013 m- 2 _...... ,.... ___ ,...... _____..

• Meade et al. 1990 12 A Merkel et al. 2003 • Girard et al. 2016

...... _ ...... [100) (010) ...... -­ ...... - -- ...... MgO - --- ..... 2 ~(110){100} ...... !(110}{110} ~-----~:_ ___J o c:::~~~~~...=:::::::=:::::d 0 500 1000 1500 2000 2500 3000 T(K) Kraych et al. EPSL submitted - Results on MgO from Amedeo et al. Phil. Mag. 2012 Stop4

• We know: the intracrystalline flow properties of major high pressure minerais

l 12.. . t ~ .... :I

. - • ,. ''°' ,,.. - Vit - Tiit) Courtesy J. Girard / " ~ • We don't know the mechanical properties of the << rock >> From the grain to the aggregate

Collaboration with O. Castelnau & K. Derrien ENSAM, Paris • Visco Plastic Self Consistent modelling

• Finite Elements modelling

Equivalent strain

Building an aggregate From the grain to the aggregate

Collaboration with O. Castelnau & K. Derrien 10000 ENSAM, Paris

9000

8000 work in progress ! 7000

6000 -ca Nishihara et al. , 2008 a. iiKawazoe et al., 2013 :E 5000 Kawazoe et al., 2010 -b 4000 X Hustoft et al., 2013 Faria et al. , 2015 3000 • This study

2000

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0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 T (K} Stop 5

• We can model (and we agree with) mechanical data obtained in laboratory conditions ----~ - 1• - l 16 ...... 2 1• ...... ----- i 12 1 +rW- -··­ 1 10 ( :ll"".1 - ···t1·- ·-- i : t 111'<11~lll) I 'f.i- • ï1 ;.1·. ... • 112<110>4uq . -- - -Tl'Q- - - -- 2 o.____.__._~~-...... 1 0 500 1000 1500 2000 2500 ~ - 4000 T1K1 • But we can do the same at mantle strain­ rates (no extrapolation !) Dislocation Glide in Wadsleyite (15 GPa)

1000 [100] (010) screw

800 1 1h<111>{101} screw ! 1 -«S 1 a.. 600 1 ~ 1 . 10-16 -1 1 E = S -(/) 1 1 (/) ! Upper ! ~ransition! a: 400 1 1 0 i Zone i 1 1 200 1

0 L-~.&..-~..L-~..L_~...L-~...... __~...... :===...... --=::::::..... ~ 1000 1200 1400 1600 1800 2000 2200 2400 2600 T (K) Ritterbex et al. Am. Mineralogist in press Dislocation Glide in Ringwoodite (20 GPa)

1200 \ . 10- 16 - 1 \ E= S 1000

800 1/2<110>{111}

-li) 600 li) a:: u 400 "\ 1 '\ 1 1/2<110>{110} .,__ ! Lower Î ' . ! Tra;:~:on i! 200 '··""!1 1

i i i~ .i 0 i b·-··- 1000 1200 1400 1600 1800 2000 2200 2400 2600 T (K) Ritterbex et al. (2015) PEPI MgSi03 perovskite (30 GPa)

4.5 P = 30 GPa 4

3.5

3 ,,,,.-._ ...... ro ...... ~ 2.5 ...... Cl ...... ~ ...... \/). 2 ... \/)...... [100] (010) ~ Bg ...... u 1.5 ...... _ 1 -- 0.5 [010] (100) ------0 ~~~~~ 1000 1500 2000 2500 3000 T(K) Kraych et al. EPSL submitted - Results on MgO from Amedeo et al. Phil. Mag. 2012 MgSi03 perovskite (60 GPa)

P= 60 GPa

3.5

3 [010] (100) ~ es 2.5 ...._.., r/J 2 r/J ~ u 1.5 MgO 1 ~( 110 ) {110} 0.5 li ~ (110 ) { 100} o ~~~~------...J---4-_._~___J__._~--'-~ 1000 1500 2000 2500 3000 T(K) Kraych et al. EPSL submitted - Results on MgO from Amedeo et al. Phil. Mag. 2012 MgSi03 post-perovskite (120 GPa)

1.0 ----...... ------.------.------.------E = 10·14 s·1 8 2 0.8 p = 10 m· ro P5 0.6

(j)- (j) 5 0.4 [110](1 OO) MgO 100 GPa 0.2 [100](010) ppv 120 GPa

ÜL------'-~""------'---'---'----l..----l---'--==c==J 0 500 1000 1500 2000 2500 Temperature, K A. Goryaeva in prep Which mechanism ?

Diffusion creep ? Stop 6

• We understand, model, quantify dislocation glide

/ '\. ~ • But creep in the mantle would involve glide and climb ! What is climb ?

•••••••••••••••••••••••••••• • Point defects (vacancies) diffuse •••••••••••••••••••••• •••••••••••••••••••••• toward the dislocations •••••••••••••••••••••• ••••••••••••••••••••••

. ~ .A. I'\. c Î-, T T • They are absorbed (or emitted) I , T > ."'. f-~-< o- ~ -~ ~ -

..., The dislocation moves away from its glide plane 2n Ds/d ( (rn) ) V cumb = ln R/ r c b exp kT - 1 lnterplay between glide and climb [1 OO] dislocations

Olivine 10 1 102 103 104 1o 5 / Ratio v9 vc 1800

1700

.....-.. ~ 1600 r-

1500

1400 0 100 200 300 400 500 cr (MPa) lnterplay between glide and climb [1 OO] dislocations

Unlaxlal tension 2.5 ' glide -- Single slip· + dffmb glide+climb -- 2.0 Po= 1.4 1012m- 2 T= 1600 K ;, 1.5 a= 4-0 MPa •

~0 -a. w 1.0

0.5

o ~-~--~--~-__._--~ 8pm 0 0.5 1.0 1.5 2.5 time (106 s) ~•

10 ~ ,. ' + f "t + 8 A f ,." +

++b X - b 2 4 6 8 10 2 4 6 8 10 X (µm) X yim) Gliae only Initial configuration Boioli et al. Phys Rev B 2015 lnterplay between glide and climb [1 OO] dislocations

Unlaxlal tension 2.5 ' glide -- Single slip· + dffmb glide+climb -- 2.0 Po= 1.4 1012m- 2 T= 1600 K ;, 1.5 a= 4-0 MPa •

~0 -a. w 1.0

0.5

o ~-~--~---'------'---~ 8pm 0 0.5 1.0 1.5 time (106 s) ~•

100 10

50

++b ·50 X - b -100 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 X (µm) X yim) X (µm) Initial configuration Gliae only Glide + Climb lnterplay between glide and climb [1 OO] dislocations

Unlaxlal tension Single •slip· + dffmb

E .B11m :,.

1.8 At steady state: nearly constant dislocation density u------0 U OA OJe o.8 UJ t.2 tA tîme(1a'I) Boioli et al. Phys Rev B 2015 Activation enthalpy

(a) to.s .,.._____,,...._.,...._____,,._....,...._____...;.---...... ____.. 10"' 10.. 7 -1r ~°'- 1'ftl"Iwi "W 1r1 10"n 1cr12

10~3 ...... ~...... -...... - ...... 5-1 8.2 i&iA 8-8 6.8 '1 7al 1a411i(K)

glide creep diffusion (eV) 5.7 4.7 4.25

nn:iid:et al. Fei et al. Earth Planet. Sei. Lett. 345,95 (2012) Am. l\.1in. (2ffJ7) Fei et al. Nature 498 (2013) Boioli et al. Phys Rev B 2015 Stress exponent

(b) 10-5

10-6

10·1

10-8

~ ~- 10.g 'êoll 10·10

1 o·11

10·12

10·13 10 100 a (MPa)

T(K) 1700 1600 1500 1400 3.1 3.2 3.2 2.9

Boioli et al. Phys Rev B 2015 Olivine rheology at low temperature [001] glide

10-08 10-10 10-12 10-14

M -1 T=lOOO K V) 10-16 -w 10-18 10 T=900 K A 10-20 1

10-22 T=800 K ce======14 1 10-24 10 100 1000 a (MPa) Boioli et al. EPSL 2015 Creep in the lower mantle

(A) Olivine Ratio v I Ve -~ 0 .... 1800

1700

g 1600 ~

1500

1400 0 500 1000 1500 2000 2500 3000 o (MPa)

(B) Ringwoodite 10·10 1o ·6 10·2 102 1o 5 (C) Bridgmanite 10·20 -.----r-r- Ratio Vg / Ve Vg / Vc 2000 2200

1900 2100 g 1800 g 2000 ......

1700 1900

1600 1800 0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000 a (MPa) a (MPa) lntroducing pure climb creep

• Strain is produced by dislocation climb

• Dislocations act as sources .l. and sinks of point defects (vacancies)

~ • Disloca.tions exchange 1- vacanc1es

• The characteristic diffusion length is determined by the dislocation density

Pure climb creep Modelling pure climb cree~

a (A) Lx (B) 4 t .. 0.05 î=1900 K 0.04 P=24GPa +- -+ t o~ a=40 MPa >. ...J 0.03 Xv=10 5 0 0 ~ 0 a --- 0 J 0.02 0 0 0.01

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 + time (108 s)

400 4 * "* 200 3 CO' ~ .. CO' Ê a. E a. 0 0 ~ ::?...... :::1. ~ >- Il >- 2 t:) t::l -200 -200 ... -400 0 0 2 3 4 5 1.5 2 2.5 3 3.5 X (µm) X (µm) Modelling pure climb creep in bridgmanite

T=1900 K; P=24 GPa; Xv=10-5

CLIMB p =1012 m-2 0 •

8 -2 CLIMB Po=10 m ------N-H d=0.1 ------mm ••••••••••••• COBLE d=0.1 mm ••••••••••• • •••••• •••• •••••••••••• ························ ------N-H d=10 mm

•••••••••• CO BLE d=10 mm •••••••••• •• • •• • ••• • •••••• • 10-25 L--~~.i..--.....J~·~··~•••••••••••••...L_L-J....-J...... L_J._~~__..L_~-L-~~-1-.L.....L...LJ 1 10 100 stress (MPa) Pure climb creep: Avery important mechanism for planetary interiors rheology

A few tacts:

• Strain is produced by dislocation climb

.l. • Strain is not produced by shear: no crystal preferred orientations ~1- • No grain size dependence

• Controlled by diffusion, but rheology may not be linear

Pure climb creep Stop 7

• Diffusion creep • Dislocation creep • Pure climb creep

/ " ~ • What about grain boundaries ? Toward a more general elastic field

Collaboration with C. Fressengeas & V. Taupin, Metz theory

-+ - 1= = Displacement field: u Rotation vector: w = --w: X 2

- -+ - Total distortion tensor: U = grad u Curvature tensor: K = grad w

------Cauchy stress: a= C: E Couple stress tensor: M =A: K

Equilibrium condition div a = 0 Equilibrium condition div M = 0

1 Energy: E cauchy = -aiJ EiJ Energy: 2 T oward a more general elasto-plastic field theory

- Compatibility equations: curl U = 0 curl K = 0

Incompatible elasto-plasticity:

Nye's dislocation density tensor: Disclination density tensor: --- a = curl u e = -curl u p 8 = curl K e = -curl K p

Burgers vector: closure defect obtained Frank vector: closure defect obtained by by integrating the incompatible elastic integrating the incompatible elastic distortions along a circuit C curvature along a circuit C T oward a more general elasto-plastic field theory

- curl K = 0

Disclination density tensor: --- Screw 8 = curl K e = -curl K p dislocation

Frank vector: closure defect obtained by integrating the incompatible elastic curvature along a circuit C (e) (/) Disclinations

You remember ? Disclinations

(a) (b) Disclinations were recently evidenced in metals, here Al

Beausir & Fressengeas (2013)

Di5cÎ:inations Dislocation and disclinations analysis by EBSD

OOM - naturally deformed Cordier et al. Nature 2014 T0548 mylonitic harzburgite from Experimentally deformed the Oman ophiolite at 1200°c (Sumail massif)

12p~

f.l mœ

-i!. 1 ~ UD ~ l i i 'Il 'S :a~ i 1 lili. -11 "4'"3 Q.iO 61!JDIJ[ -+Al~GBaM o MG.BSlH '*''TfiPl&pm~ crnJyN A TiîQleiUJWî&n oJdf B :J[ mrnn::-.- :::u: ::u:m Grain boundary modeling based on disclinations

Displacement Dislocation Grain density boundary

Dislocation/ Disclination continuous Rotation Disclination density modeling Atomistic configuration

Sun et al. IJP 2016 Grain boundary modeling based on disclinations

Forsterite: (011 )/[1 OO] tilt grain boundary with misorientation 60.80° (coll S. Jahn)

3.6nm Grain boundary modeling based on disclinations

Forsterite: (011 )/[1 OO] tilt grain boundary with misorientation 60.80° (coll S. Jahn)

• .. •

E 23 1.1 6 0.788 0.42 1 0.0530 .. -0.315 • • -0.682 Si -1.05 • •

Sun et al. Phil Mag 2016

Shear -coupled boundary migration

Œ;tS(m~ 1.mme+9 1.0aae+9 1e~9 1e+9

1e+9' sl ,82e'f9 -1 .82e+9

8a~Crad/m2)

~199.+19 '4ê+19 2ê+19 -0 •2-e+19 ~ l .O!Be>t9 ~œ9 Q.62 118+9 -4Ae+l9' 0.6 OA

le+O D.2 a -0.06 Final stop: Thank you 1

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www.rheoman.eu

Funding: ERG advanced grant n°290424 Multiscale Modeling of the Rheo/ogy of the Mantle (RheoMan)