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Dislocation Glide in Ringwoodite (20 Gpa)

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Dislocation Glide in Ringwoodite (20 Gpa) 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 10000 9000 8000 7000 6000 Nishihara et al., 2008 5000 Kawazoe et al., 2013 (MPa) Kawazoe et al., 2010 σ 4000 Hustoft et al., 2013 Farla et al., 2015 3000 2000 1000 0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of ringwoodite 10000 9000 8000 7000 6000 Hustoft et al., 2013 5000 Kavner et al., 2001 (MPa) Meade and Jeanloz, 1990 σ 4000 Miyagi et al., 2014 Nishiyama et al., 2005 3000 2000 1000 0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of bridgmanite 14000 12000 10000 8000 Merkel et al. 2003 (MPa) 6000 Meade et al. 1990 σ Girard et al. 2015 4000 2000 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 Can we bridge scales ? Schuberth © B. © 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) <uvw>{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 plas.city: 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 2000 1000 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.
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