Mineralogy – Petrophysics: Deformation processes & compositional evolution in the lithosphere and asthenosphere

This class & the next one’s program: How do the lithosphere and asthenosphere deform? Long-term viscoplastic (ductile) deformation mechanisms: Dislocation creep, diffusion creep, grain boundary sliding How do these crystal-scale processes translate in terms of macroscopic mechanical behavior : flow laws + on Friday Deformation – crystallographic orientations – anisotropy of physical properties in the mantle

Andréa Tommasi [email protected] elastic Rheological behaviors & macroscopic deformation

elasto- visco- plastic Rupture (brittle deformation) viscous plastic

the 3 processes may coexist f(T/Tm,σ…)

Ductile (solid state) magmatic flow flow ductile deformation crystal plasticity dislocation creep diffusion creep recrystallization grain boundary dislocation glide sliding / migration visco-plastic viscous behavior behavior σ = σ + f (ε) σ ∝ε y linear – non-linear? Crystal plasticity = major process in ductile deformation

ü ductile deformation (change in shape ± crystals orientation) without loss of physical continuity (≠ brittle behavior)

ü viscoplastic behavior : ifσ ≥ σ ⇒ σ ∝ε y

Ice Ih hexagonal

Which processes ? Ice deformation at HT (-5°C)

Deformation = change in shape and orientation (color) of the crystals

Dislocation glide & polycrystalline ice Dynamic recrystallization in-situ deformation: pure shear C. Wilson - Univ. Melbourne, Australia 0%

Dislocation creep in the "lab" @ 800°C & 10-6s-1 Heavitree quartzite: "coarse grained" 200µm Initial material undeformed (diagenetic growth only)

42% shortening

Microstructure = signature of the crystal-scale mechanisms Dell'Angelo & Tullis activated to accommodate the imposed macroscopic strain JStructGeol 1986 Solid-state flow: Ductile deformation (creep)

dislocation glide Function of: linear: dislocations - mineral structure - T dislocation - , creep σ ε Motion of defaults in the - f(H2O, O2)… crystals’ structure

point: vacancies twinning

diffusion

grain boundary sliding needs an additional mechanism! Deformation of metals : shear along well-defined crystallographic planes

Frenkel's early model

high energy cost : rupture and reconstruction of a large number of atomic bonds Ø crystal strength much higher than observed experimentally Solution? Solution? Defaults in the crystalline structure

Localized shearing Instantaneous strain

strain = f(time)

dislocation

Same final result, but lower energy consumption! the principle…

Displacement by a crystal lattice unit = Burgers vector b

Deformation = motion of dislocations = dislocation glide Dislocations in 3D = dislocation loops

• The dislocation line separates the sheared volume of the crystal from the non-sheared one

• The Burgers vector is the dislocation motion (shear) direction How do we observe dislocations? § decoration (olivine)

Kamchatka xenolith, Soustelle et al. J. Petrol. 2010 § transmission electron microscopy (TEM) Dislocations imaging by TEM

Deformation of the crystal lattice in the vicinity of a dislocation

transmitted electrons diffracted electrons L: dislocation line θ: deviation relatively to Bragg angle Dislocations : TEM

Using an aperture, one may select

• the transmitted electrons

Dislocations in glide configuration in a Zr alloy Foto H. Leroux, LSPES- USTLille Dislocations : TEM

Using an aperture, one may select

• the diffracted electrons

Dislocations in olivine © H. Couvy, USTLille Dislocation glide

Burgers vector strain rate

ε˙ ∝ ρmbv

glide velocity (depends on σ)

density of free dislocations 2 ⎛ σ ⎞ ρm ∝⎜ ⎟ ⎝ µb⎠ shear modulus

3 ε! ∝σ Dislocation glide : activation energy

Dislocation glide: reorganisation of atomic bonds

Ø f(σ, T)

Ø f (crystal structure): some planes & directions are favored because bonds are weaker olivine crystal seen along the [100] direction

(Mg,Fe) () = planes [] = directions

Si02 tetraedra Covalent bonds = strong!

[100] 4.98A Cations: Mg, Fe Ionic bonds [010] = weak [001] 10.21 A (010) 5.99 A (001) (011) (Mg,Fe)

Dislocation glide : crystals orientation evolution!

within a grain (crystal):!

(001) (010) (011)

strain = motion of dislocations on well-defined crystal 1! planes & directions

n ⎛ s ⎞ 2! s τ r γ˙ = ⎜ s ⎟ ⎝ τ 0 ⎠ But in a real rock there are neighbors! Dislocation glide : crystals orientation evolution! motion of dislocations on well-defined crystal planes & directions = crystal deformation has a limited degree 1! of freedom

strain compatibility è rotation of the crystal! 2! Ø development of a crystal preferred orientation! = all crystals tend to a common orientation!

3! Z

Z X

X Y

lherzolite, xenolith Tahiti obstacle = grain boundary, another dislocation, impurity…

accumulation of dislocations = tangling = forests increase of the crystal internal energy ➣ hardening

http://zig.onera.fr/~devincre/DisGallery/index.html ➣ To continue to deform, one needs to continuosly increase the stress … Consequences? ➣ System stops deforming ➣ or… Change in deformation mechanism in a small-scale Sinistral strike-slip shear zone in a tonalite, SE-Brazil Experimental data: change in mechanical behavior as a function of strain rate & temperature hardening clinopyroxenite temperature strain rate

At low strain rates and HT = steady state Hardening avoided by a process that is "slow" and T dependent! Solid-state flow: Ductile deformation (creep)

dislocation glide Function of: linear: dislocations - mineral structure - T dislocation - , creep σ ε Motion of defects in the - f(H2O, O2)… crystals structure

point: vacancies twinning

diffusion

grain boundary sliding needs an additional mechanism! Point defects in a crystal interstitial

vacancy difusion = mass transport motion of atoms & vacancies

Vacancies & atoms move in opposite directions, but it is the vacancies that move along large distances difusion = mass transport motion of atoms & vacancies F(mineral, T, …)

Fick law (1-D) – flux is a function ∂c of the diffusivity D & J = −D. of the concentration gradient ∂x from high stress (compressive) to low stress (extensive) regions

Changes the shape, but not the orientation of the crystals Diffusion mechanisms grain boundary - Nabarro-Herring creep : intracrystalline diffusion - Coble creep: diffusion along grain boundaries

- not an empty space! Ø rocks are cohesive Vacancies & atoms move in opposite directions - region of discontinuity (arrows indicate atoms flow, but it is the vacancies in the crystalline arrangement = more that really move along large distances!) defects An easily observable mass diffusion process: Grain boundary migration

Static grain growth: octachloropropane Park, Ree & Means, J. Virtual Explorer 2000

Jessel & Bons – Simulation using ELLE – J. Virtual Explorer 2000 virtualexplorer.com.au/.../lectures/lec2.html Grain boundary migration in olivine : HT deformation or static recrystallization (HT, but no deformation) Diffusion is a well-understood physical process… Einstein law (the drunk guy walking…) Γ: frequency of steps a : amplitude of the step 2 t : observation time d = Γa t d : walked distance

In a crystal: ⎛ ΔG ⎞ Γ = ν.exp⎜ − m ⎟ ⎝ RT ⎠ Γ= probability of successful atomic jumps ν= vibration frequency of the atoms (≈1013Hz) ΔG = enthalpy reduction (migration energy) m 1 2 cm2s-1 D = Γ.Nv.a D= atomic diffusion coefficient 2 Nv = vacancy concentration (# empty sites/ total # sites) T ì = Γ ì = D ì a = interatomic distances

Strain rate = transport velocity

Forces (Fext): F - Applied (external) stresses ext - Internal stresses due to dU/dx, < v >= D where U is the elastic energy kT associated with dislocations (depends on the dislocation density and hence on stress) v ∝ F T ì = v ì E 1,E+00 D ∝ exp(− RT ) 1,E-02 exp − E 1,E-04 ( RT ) 1,E-06 v ∝ T 1,E-08

1,E-10 E ∼ 100 − 300kJ / mol 1/T 1,E-12 R = 8.31J / mol / K exp(-E/RT)/T 1,E-14 800 900 1000 1100 1200 1300 1400 1500 dislocation = distortion of the crystal lattice ➣ elastic energy « ideal » interatomic distances not respected Coble vs. Nabarro-Herring creep ε˙ = v /l → l ∝ d ε˙ ∝ F → F ∝σ ˙ exp 1 ε ∝ (− T)

σV δD ε˙ = A ⋅ B B RT d 3

Dv = intracrystalline diffusion coeff. D grain boundary diffusion coeff σV D b = ε˙ = A ⋅ V Db >> Dv V 2 A= adimensional constant RT d V = molar volume R = ideal gaz constant d = grain size

δ = grain boundary thickness

Usually the 2 processes are associated … General diffusion creep flow: σV εσ˙ = A 2 Deff ε! = A p exp(kTd−E / RT )

d Dv = intracrystalline diffusion coeff. Db = grain boundary diffusion coeff D Db >> Dv 1 < p < 3;πEδ ∼b100A=− adimensional300k constantJ / mol D eff = Dv (1+ ) V = molar volume R = ideal gas constant dDv NA = Avogadro constant k = Boltzmann constant d = grain size R = kb NA δ = grain boundary thickness Effective diffusion creep needs small grain sizes & high temperature Diffusion creep

compression

extension

Does it exist in nature? Under which conditions?

- experimental evidence = linear relation between stress & strain rate

- absence of crystal preferred orientations??? May crystal preferred orientations develop during diffusion creep?

Current ‘paradigm’: Diffusion creep does not produce crystal preferred orientations, since it does not create strain incompatibility.

But some (recent) experimental observations & models challenge this « assumption »:

• Wheeler, J. (2009). The preservation of seismic anisotropy in the Earth's mantle during diffusion creep. Geophysical Journal International, 178(3), 1723-1732. • Miyazaki, T., Sueyoshi, K., & Hiraga, T. (2013). Olivine crystals align during diffusion creep of Earth/'s upper mantle. Nature, 502(7471), 321-326. • Sundberg, M., and R. F. Cooper (2008), Crystallographic preferred orientation produced by diffusional creep of harzburgite: Effects of chemical interactions among phases during plastic flow, J. Geophys. Res.,113, B12208, doi: 10.1029/2008JB005618 • Walker, A.N., Rutter, E.H., Brodie, K.H., 1991. Experimental study of grain-size sensitive flow of synthetic, hot- pressed calcite rocks, in: Knipe, R.J., Rutter, E.H. (Eds.), Deformation Mechanisms, Rheology and Tectonics. The Geological Society, London, pp. 259-284 • Pieri, M., Kunze, K., Burlini, L., Stretton, I., Olgaard, D. L., Burg, J. P., & Wenk, H. R. (2001). Texture development of calcite by deformation and dynamic recrystallization at 1000K during torsion experiments of marble to large strains. Tectonophysics, 330(1), 119-140. • Heidelbach, F., Stretton, I., Langenhorst, F., & Mackwell, S. (2003). Fabric evolution during high shear strain deformation of magnesiowüstite (Mg0. 8Fe0. 2O). Journal of Geophysical Research: Solid Earth (1978–2012), 108(B3). Deformation mechanisms maps dry olivine polycrystals (dunite) dislocation glide

dislocation creep

diffusion creep slow strain rates < 10-16 s-1

May another process help enhancing strain rates? Grain boundary sliding assisted by diffusion

Diffusion accommodates strain incompatibility problems (voids & overlaps)!

≠ from pure diffusion creep? equiaxed grains???

Grain growing from a lower plane (rocks is a 3D object!) T=1350-1450°C ≥1.e-4 s-1

Extreme elongation >> 100% Initial without localisation or rupture 515% Grain size < equilibrium one olivine + MgO 315% Initial

84%

Grain growth = F(strain) PROBLEM!

399% 515%

n=2; p=1.5 315%

TEM: very few dislocations Calcite (mylonitic limestone) Does it exists in nature?

Locally… very fine-grained small scale (cm) bands within shear zones

Olivine (peridotite ultramylonite) BOURCIER ET AL.: MULTISCALE STUDY OF NACL DEFORMATION

size of the microstructure and the type of constitutive because of the very different characteristic sizes of the behavior. See, e.g., Salmi et al. [2012] for a review of pro- microstructures, the considered ranges of gage lengths are posed definitions. A common way to define the size of an very different for the three materials. It is clearly observed RVE consists in studying the evolutions of the statistical that, as expected, the fluctuations attenuate when the gage fluctuations of some quantity defined by an averaging length is enlarged, but they never vanish. A possible quanti- procedure over domains of a given size as a function of this fication of the RVE size consists in choosing the gage length size. We adopt such a procedure here. More specifically, we that leads to a standard deviation below 10% of the average investigate the statistical fluctuations of experimentally mea- strain. With such a choice, it is found that the hot-pressed sured average strains over domains of a given size as a func- material seems to be homogeneous for an RVE diameter tion of this size, or in other words, the fluctuations of the larger than 1500 mm, while this limit is close to 100 mm local strains relative to some gage length ΔL as a function for the fine-grained material, and to 2000 mm for the of this length. Fluctuations are quantified by means of the coarse-grained one. These important results permit us to strain distribution function of the von Mises equivalent define for each microstructure the pertinent scale for the strain, as well as by its standard deviation. These quantities study of the micromechanisms of deformation. For instance, need to be analyzed over domains that are larger than the we verify that the fine-grained samples may be studied at a RVE size, i.e., over “macroscale” domains, or at least large much finer scale than the other two. This finer scale can only “mesoscale” domains. Results are plotted in Figure 5: the be addressed by SEM investigations. Note also that for the strain distributions as function of the local strain normalized hot-pressed material, the standard deviation of local strains JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 118, 511–by526, the averagedoi:10.1002/jgrb.50065, strain over the investigated 2013 ROI are given for does no longer diminish when the gage length is enlarged four gage lengths, and the continuous evolutions of the stan- above 2.5 mm. This can be explained by the existence of dard deviation of the same quantity with respect to gage the macroscopic heterogeneity shown in Figure 4 [4] and length are plotted for the three microstructures. Note that commented in section 4.1. This macroscale heterogeneity

BOURCIER ET AL.: MULTISCALE STUDY OF NACL DEFORMATION while a more quantitativeMultiscale investigation experimentalat mesoscale is 4.2. investigation Quantification of Representative of crystal Volume plasticity Element and outlined in section 5. Itgrain should be emphasized boundary that the sliding actual Size in From synthetic Strain Fields halite using digital image characteristic dimensions of these three scales of analysis [39] The representative volume element is a central con- depend on the microstructure under consideration. It is thus cept for the micromechanical analysis of materials. There of high interest to quantifycorrelation the size of an RVE, which is the is an extensive literature addressing this question, and in purpose of the following section. particular the size of an RVE in relation to the characteristic M. Bourcier,1 M. Bornert,2 A. Dimanov,1 E. Héripré,1 and J. L. Raphanel1 Received 20 September 2012; revised 14 December 2012; accepted 19 December 2012; published 19 February 2013.

[1] There is a renewed interest in the study of the rheology of halite since salt cavities are considered for waste repositories or energy storage. This research benefits from the development of observation techniques at the microscale, which allow precise -4 -1 characterizations of microstructures, deformation mechanisms, and strain fields. TheseFigure 8. Intragranular plasticity observed at microscale in coarse-grained sample thanks to relative motion of the markers Amb PT, 10 s techniques are applied to uniaxial compression tests on synthetic halite doneIntragranular with a slip classical press and with a specific rig implemented in a scanning electron microscope. Digital images of the surface of the sample have been recorded at severalbands: loading stages. Surface markers allow the measurement of displacements by means of digital image Fine grained correlation techniques. Global and local strain fields may then be computeddislocation using ad hoc glide data processing. Analysis of these results provides a measure of strain heterogeneityBOURCIER at ET AL.: MULTISCALE STUDY OF NACL DEFORMATION30-80µm various scales, an estimate of the size of the representative volume element, and most importantly an identification of the deformation mechanisms, namely crystal slip plasticity and grain boundary sliding, which are shown to be in a complex local interaction. Indeed, the applied macroscopic loading gives rise locally to complex stress states owing to relative crystallographic orientations, density and orientation of interfaces, and local deformation history. We have quantitatively estimated the relative importance of crystal slip plasticity and grain boundary sliding for different microstructures and evidenced their dependence on grain size. The two mechanisms of deformation and their link to the microstructure should thus be considered when modeling polycrystalline viscoplasticity. Figure 9. Grain boundary sliding inducing an opening of a cavity at a triple junction in a coarse-grained sample (no markers). Figure 6. 2DCitation: DIC results fromBourcier, in situ SEM M., M.test on Bornert, coarse-grain A.ed Dimanov, material. (1) E. Microstructure He´ ripre´ , and (SEM J. L. image). Raphanel (2013), Multiscale experimental (2) MacroscopicCoarseinvestigation stress/strain grained of curve. crystal (3) Equivalent plasticity and strain grain maps boundary at mesoscopic sliding (left) in and synthetic microscopic halite using digital image correlation, 520 (right) scales.J. Intracrystalline Geophys. Res. slip Solid bands Earth develo,p118 inhomogeneously, 511–526, doi:10.1002/jgrb.50065. within individual grains, and grain boundary200-250 sliding is often observed.µm Strain concentrated 1. Introduction of phenomenological constitutive relations (see for instance, Minor, local Senseny et al. [1992]; Langer [1984]). [2] The mechanical propertiesat of halite grain have been exten- [3] More recently, in the frame of the compressed air energy accommodationsively studied over several decades,boundaries: because halite is a rock storage projects [Crotogino et al., 2001], salt caverns have forming mineral with geotechnical and industrial applica- been considered for the storage of “green energy” in the form mechanismtions. Geological storage of liquidgrain and gaseous boundary hydrocar- of compressed air. The specifics of these new projects, namely bons in deep caverns is a worldwide current situation low overall stress levels, cyclic loading with short characteris- [Carter and Hansen, 1983; Bérestsliding, et al., 2005], but and the not po- tic times, temperature and humidity fluctuations, have pointed tential for geological storage of nuclear wastes in deep salt out the limits of a purely phenomenological approach, and Figure 10. 2D DIC results, equivalent strain from in situ SEM test on fine-grained material at a micro- mines is strongly envisaged by someonly countries, for instance motivated micromechanical investigations for which the Germany or the United States. These studies, mostly based scopic scale. (1) Microstructure, (2) macroscopic stress/strain curve, and (3) strains map: Localization experimentalalong grain identi boundariesfication indicates of the important physical contribution mechanisms of GBS to the global deformation. on macroscopic mechanical testing, aim at the characteriza- associatedMore with important the deformation of the material is the founda- tion of the macroscopic behavior of halite and the derivation tion of the modeling effort. turned[4] out Despite to be much the fact less pronounced that recent in investigations the other tests for of naturalGBS is also observed. Indeed, such very local observations 1Laboratoire de Mécanique des Solides, CNRS UMR 7649, École whichrock the salts areas [Schléder investigated et al at., macroscale 2007; Desbois to produce et al these., 2010]permit pro- to precisely detail the activity of each mechanism Figure 7. SlipPolytechnique, lines observed 91128, at the Palaiseau surface of Cedex, the coarse-grained France. sample; SEM imagingresultsvide in secondarysigni were muchficant smaller. insights on the active deformation mechan-and to retrieve the history of their interplay. Referring to electron mode. 2Laboratoire Navier, Université Paris-Est, CNRS UMR 8205, École des isms in natural conditions, the natural material is howevergrain numbers as noted in Figure 6, we can see at first the Ponts ParisTech, 77455, Marne la Vallée Cedex 2, France. activation of plastic deformation (CSP) in grain 1. However, 519 4.3.not Coarse-Grainedwell suited for Halite our experiments, which requirealmost small at the same time, some deformation is concentrated at Corresponding author: J. L. Raphanel, Laboratoire de Mécanique des samples,[40] In this a section, good one reproducibil analyzes theity, local controlled strain fields composition, in the interface between grains 1 and 3; it can be shown to be Solides, CNRS UMR 7649, École Polytechnique, 91128 Palaiseau Cedex, theand coarse-grained microstructure, halite. i.e., One gra recallsin size that this distribution, material is porosity,GBS, probably induced by the crystallographic incompati- France. ([email protected]) characterizedwater content. by polygonal Consequently, grains in with our sizes study, varying as in be- manybility other in terms of intragranular crystal plasticity between tween 250 and 500 m (Figure 1b) and very low porosity ©2013. American Geophysical Union. All Rights Reserved. laboratory investigations,m synthesized halite has beenthese used. grains. At this early stage of deformation, grain 3 behaves (less than 1%). Two scales of observation have been consid- 2169-9313/13/10.1002/jgrb.50065 This may be done at a relatively low cost, starting within anpure almost rigid manner. With increasing loads and macro- ered for strain mapping (see Figure 6 and Table 1), covering scopic axial deformations, we can observe activation of crys- respectively (almost) the mesoscale of an RVE and a partic- tal plasticity in grain 2, while the bands of deformations in 511ular microscale field focused on a triple junction, with grain 1 become more intense and closely spaced. With further respective gage lengths of 8 and 1.6 mm. Intracrystalline loading, grain 3 finally exhibits intragranular plasticity plasticity is attested both by the observation of slip lines at denoted by bands that have almost the same orientation as the surface (Figure 7) and the computation of an intragranu- the bands of deformation in neighboring grain 2. lar equivalent strain showing discrete bands of deformation within the grains. When the slip direction is parallel to the observation surface, no slip lines are observed in the SEM 4.4. Fine-Grained Material images, but gliding can be quantified anyway thanks to the [42] The fine-grained material needs to be observed at a displacement of markers and DIC, as illustrated in Figure 8. much finer scale because of its grain size,which is in the in- This mechanism is complemented by grain boundary sliding terval between 30 and 80 mm. Again, two scales are consid- at some grain boundaries, as illustrated in Figure 9 and by ered (see Figure 10 and Table 1), with corresponding gage localization near some grain interfaces (Figure 6). In this lengths of 18 and 6 mm, respectively. But now, the larger material both mechanisms do coexist within an RVE as view should be considered as a high definition “macroscale” evidenced by the mesoscale maps. field, while the smaller one is a “large mesoscale” view [41] In the considered microscale zoom around a triple (scale in excess of the previously defined mesoscale). Note junction, plastic slip (CSP) seems to dominate, but some that the DIC data of the larger scale have been used to

521 Does the upper mantle ever have a Newtonian behavior?

Grain sizes in mantle rocks are usually > 1mm… Ø too big for GBS (this depends on how we extrapolate the lab data!)

The experiments were effective deformation by these processes occurs (the Hiraga et al. data) show a stress exponent of 2

Stress exponents ~ 2 also predominate in the deformation experiments on fine-grained olivine aggregates (combination of Intracrystalline (dislocation) processes and grain boundary accommodated deformation

Later this week – seismic anisotropy…

Ø Probably the whole (upper) mantle has a non-Newtonian behavior!

Deformation mechanisms maps dry olivine polycrystals (dunite) dislocation glide

dislocation creep

diffusion creep slow strain rates < 10-16 s-1

Diffusion plays an essential in dislocation creep: avoids hardening due to dislocation pinning obstacle = grain boundary, another dislocation, impurity… accumulation of dislocations = tangling = forests increase of the crystal internal energy ➣ hardening

http://zig.onera.fr/~devincre/DisGallery/index.html

How to avoid dislocations pinning? Dislocation reorganisation : recovery Experimental data: change in mechanical behavior as a function of strain rate & temperature temperature strain rate

clinopyroxenite

Dislocation creep

Deformation by dislocation glide, but hardening avoided by diffusional processes Solid-state flow: Ductile deformation (creep)

dislocation glide produces strain

linear: dislocations Function of: dislocation - mineral structure creep - T Motion of defects in the - σ ,ε crystals structure - f(H2O, O2)…

point: vacancies twinning

diffusion

avoids hardening: recovery & recrystallization grain boundary sliding needs an additional mechanism! Deformation processes and rheology of the mantle lithosphere

Experimental deformation of olivine single crystals and polycrystals @ 850-1100°C, 300 MPa, dry conditions

Paterson press, Montpellier

Demouchy et al (2013), Demouchy et al (2014a,b) [001] glide Olivine deformed @ 900-950°C & 300 MPa

TEM : [001] glide &

[001] glide dislocation interactions

062 Straight [001] screw dislocations: high lattice friction

Non screw segments interact elastically

Edge-trapped dislocation dipoles [001] glide

Straight screw dislocations

[001] glide lattice friction g: -2-2-2 curved non- Non screw segments screware curved segments:No lattice friction lowEasy glide friction producing screw segments Dipoles act as obstacles hardening which control plastic glide

Further interactions lead to entanglements TEM images by P. Cordier, Lille g: 062

g: 062 Olivine deformed @ 900-950°C & 300 MPa Recovery by breakup of [001] dislocations dipoles into [001]prismatic glide loops (self-climb)

g: 062

Cordier et al (in prep)

Straight [001] screw dislocations: [001] glide high lattice friction obstacles

[001] glide obstacles

Fluctuated dipole Self-climb

Fluctuated dipole Self-climb

Boioli et al. EPSL submitted Break-up of dipoles into prismatic loops (diffusion)

Break-up of dipoles into prismatic loops (diffusion) How to avoid the blocking of dislocations? Dislocation reorganisation : recovery ➣ change of glide plane

Edge dislocations : climb

Needs vacancies glide climb motion: diffusion ➣ f(T) Climb movie How reorganising the dislocations & forming a subgrain boundary decreases the stored + elastic energy in a crystal - Stade 1 : Dispersed + dislocations + - -

+

- How reorganising the dislocations & forming a subgrain boundary decreases the stored elastic energy in a crystal +

- Stade 2 : +

+ -

-

+

- +

- How reorganising the dislocations & forming a subgrain boundary decreases the stored elastic energy in a crystal +

Stade 3: : - Annihilation + Superposition of the compression + & extension domains -

- +

- +

- How reorganising the dislocations & forming a subgrain boundary decreases the stored elastic energy in a crystal

Stade 4 : Subgrain boundary No long-distance elastic stresses How to avoid the blocking of dislocations? Dislocation reorganisation : recovery ➣ formation of dislocations walls & subgrains E➘ How to avoid the blocking of dislocations? Dislocation reorganisation : recovery ➣ formation of dislocations walls & subgrains

Subgrain boundary= misorientation <15°

➣ Dynamic recrystallization by subgrain rotation Create a new grain (nucleation) by forming a new grain boundary within an existing grain / dynamic = during deformation Tilt walls = formed mainly by edge dislocations Subgrain boundary = normal to Burgers vector Rotation axis = normal to Burgers vector & to the normal to the glide plane

2 families of subgrain boundaries = 2 families of slip systems Dislocation walls and subgrains + dynamic recrystallization by subgrain rotation

Quartz-mylonite Crossed-polarized light

"hexagonal" subgrains: crystal symmetry control on slip systems A 2nd diffusion-assisted process that helps softening the crystals: Grain boundary migration

Jessel & Bons – Simulation using ELLE virtualexplorer.com.au/.../lectures/lec2.html

HT Deformation in octachloropropane A 2nd diffusion-assisted recovery and recrystallization process: Grain boundary migration

motor 1: D stored elastic energy (ρ of dislocations) Ø dynamic recrystallization (synkinematic) motor 2: decrease in surface energy è grain growth) Ø static recrystallization (post-kinematic) 5560 GUlLLOPE AND POIRIER.' DYNAMIC RECRYSTALLIZATION OF HALITE

TøC T/T,. date the strain heterogeneity [Pontikis, 1977]. Finally, the

8OO 1 anglebetween adjacent subgrains increases to a point(0 > 15ø ) where they can no longer be recognizedas subgrainsbut become grains in their own right. It follows that the new

7OO recrystallizedgrains preserve the spatial arrangement of the o.9 polygonizationsubgrains: they are small, equiaxed, and ho- mogeneousin size, with rather straight, mostly tilt boundaries trending along planes normal to {110} glide planes. The Laue 600 0.8 patterns show broken rings typical of polycrystals,with a strong preferred orientation correspondingto a common [ 100] axis of rotation normal to the plane of plane strain. This, of 5OO o.t' course, becomes less apparent for very large deformations TION when the strain is no longer plane. DynamicN recrystallisationMigration recrystallization. The final structure in minerals results : 4OO ¸ ¸ 0.6 from the growth of one or severalsubgrains or grains already Continuousobtained by rotationrecrystallization recrystallization.The grains areby hetero- subgrain rotation and/or nucleation + grain geneousin size, and some of them may be quite large(> 1 mm) 3OO with bulging or scalloped and corrugated boundaries com- o.s monly associatedwith migration.There is no obviouspre- boundary migration ferred orientation. ZOO VOL. 84, NO. HI0 JOURNAL OF GEOPHYSICAL RESEARCH SEPTEMBER 10, 1979 H AL•TE ROT. Dynamic migration recrystallizationis distinguishedfrom a PURE o o.• possiblerapid static recrystallization at the end of the experi- 5'00pprn Sr re* Z• ment by the fact that growing new grains have themselvesa OiEUZ, E I-1 lOO ___ polygonization substructure,an evidencefor the fact that they were deformed while growing [Nicolas and Poirier, 1976]. The 0.5 Dynamic RecrystallizationDuring Creep of Single-CrystallineHalite: experimental resultsare summarized in Table 1.

RESULTS An Experimental Study lOOO 33 16 i 1 8 d t•m RecrystallizationDoma•'ns i t _ M. G UILLOPE to 2 5 50 75 10o cr ha,- Two regionswere found in the temperature-stressplane: in 1 2.5 5 ?'.5' lo [o-?}x],mthefirst one, Centreonly d'Etudesrotation Nucldaires recrystallization de Saclay,is Sectionpossible; de Recherchesinthe de Mdtallurgie Physique,Boite Postale 2, 91190 Gif sur Yvette, France Fig. 2. Criticalcurve in the a, T planebetween the domainsof secondone, migration recrystallizationoccurs (Figure 2). rotationrecrystallization (below) and migrationrecrystallization Rotation recrystallization. Rotation recrystallization isthe J.P. POIRIER (above).The dashed part of the curve for Sr++-doped NaCIhas been only possible mode for all stresses below a critical temperature extrapolated.The subgrainsizes (d) correspondingto the applied stresseshavebeen given inabscissae. Thetwo stippled domains corre- (which depends slightly on stress) Institutand defor Physiquestresses du below Globe, a Universit• Paris V1, 75230 Paris Cedex 05, France spondto naturaldeformation conditions of haliteafter Carter and critical valueof stressat temperatureshigher than the critical 5560 GUlLLOPE AND POIRIER.' DYNAMIC RECRYSTALLIZATION OF HALITE Heard[1970] and Heard [1972]. temperature. Singlecrystals of pure and impure halite havebeen dynamically recrystallized during compression creep at temperaturesbetween 250 ø and 790øC and stressesbetween 1.5 and 120 bars. Recrystallizationwas found to occurby two differentTøC mechanisms: at lower temperaturesand stressesT/T,.the newdate grains theresult strainfrom heterogeneity [Pontikis, 1977]. Finally, the the rotation of subgrainswithout grain boundary migration (rotation recrystallization),and at higher subgrain rotation 8OO 1 anglebetween adjacent subgrains increases to a point(0 > temperaturesand stressesthe final texture resultsfrom the migration of the high-anglegrain 15ø ) boundarieswhere they ofcan no longer be recognizedas subgrainsbut the rotated subgrains.Migration recrystallizationwas shownto occur for critical stressbecomeand temperature grains in their own right. It follows that the new conditions,allowing rapid grain boundarymigration. A curve separatesthe two domainsin the a, T plane 7OO recrystallizedgrains preserve the spatial arrangement of the and movesto highertemperatures and stressesfor crystalsof higherimpurity content;o.9 for polygonization natural crystals,subgrains: they are small, equiaxed, and ho- only rotation recrystallizationcan occur. In each recrystallizationregime the recrystallizedmogeneousgrain in size size, is with rather straight, mostly tilt boundaries uniquely related to the applied stress,thus yielding two different geopiezometers,5562 which trending should alongGUlLLOPEnot planes be AND POIRIER: normal DYNAMIC to {110} RECRYSTALLIZATION glide planes. OF TheHALITE Laue 600 migration applied indiscriminatelyto natural tectonitesto determinelithospheric or mantle0.8 deviatoricpatternsstresses. showThe broken rings typical of polycrystals,with a experimentalresults are interpretedby the Li•cke et Stfiwe theory for impurity-controlledgrain boundary strong preferred orientation correspondingto a common [ 100] migration. axis of rotation normal to the plane of plane strain. This, of 5OO o.t' course, becomes less apparent for very large deformations TION when the strain is no longer plane. INTRODUCTION are formedN by progressivemisorientation Migration recrystallization.of polygonized sub-The final structure results 4OO from the growth of one or severalsubgrains or grains already Dynamicrecrystallization canbe defined as a solidstate ¸ grains, ¸ without grain 0.6boundary migration [Nicolas and Poirier, obtained by rotation recrystallization.The grains are hetero- processleading tothe creation ofa new(and usually different) 1976]. This mechanism, distinctgeneous fromin size,the andnucleation some of themand may be quite large(> 1 mm) grainstructure inthe course ofplastic 3OOdeformation ofcrystal- growth mechanism (theonly withknown bulgingin metals), or scallopedhas been and corrugatedrec- boundaries com- linesolids. The differences between the old and recrystallized ognized inquartz and o.solivine monlytectonites associated[White, with 1973; migration. Poirier There is no obviouspre- structurescanreside inone or several ofthe following features: and Nicolas, 1975]. The purpose ferred oforientation. the present study was to ZOO preferredorientation of the grains(petrofabric), mis- H gather AL•TE moreinformationROT. onthe Dynamic relationship migrationbetween recrystallization deforma- is distinguished from a orientationbetween adjacent grains, and grain size and shape. tion PUREand odynamic recrystallizationo.• possibleandrapid more staticspecifically recrystallizationonthe at the end of the experi- 5'00pprn Sr re* Z• ment by the fact that growing new grains have themselvesa OiEUZ, E I-1 Dynamicrecrystallization, asopposed lOOto static (or annealing) conditions ___ of occurrence of recrystallization involving grain recrystallization,occurs simultaneously withdeformation in boundary migration ('migration' polygonizationrecrystallization)or substructure,rotationan evidence for the fact that they 0.5 were deformed while growing [Nicolas and Poirier, 1976]. The Fig. 3. Samplerecrystallized by rotation(X 17);a = 4 bars,T =certain 650øC, conditions• = 65%.Etched of stress,(100) cleavagestrain, surface. temperature, The purity, etc., of subgrainswithout migration('rotation' recrystallization). boundariesof recrystallizedgrains have been underlined in black.The figuresin thegrains indicate the rotation in degrees experimental resultsare summarized in Table 1. aboutto the[100] axis normal to the surface(e.g., 33 means33 ø anticlockwise,andthe same 3-• microscopicmeans 33 ø clockwise).elementary processes thatcause or Wechose the mineral halite (NaCl) for the following reasons: controldeformation arealso responsible fordynamic recrys- (1) It iseasily available insingle crystals ofknown purity;RESULTS (2) lOOO 33 16 i 1 8 d t•mFig. 6. SampleRecrystallization recrysta!!izedby Doma•'ns migration (x30); • = 34 bars, T = 480øC, • = 71%. Etched surface.Newly tallization[Nicolas and Poirier, 1976]. Therefore i if the micro- its recrystallization t canrecrystallizedbe_ studied grain Bin isuniaxial seenconsuming creepgrain testsA, in whichwith- the polygonization substructure has already a high mis- orientation. Notice the scallopedboundary betweenA and B. structureofa paleodeformedrockcan be ascribed to 2to 5 dynamic 50 out 75 confining 10o pressure crat ha,-temperatures Two regionslowerwere thanfound 800øC; in the (3)temperature-stress plane: in 1 2.5 5 ?'.5' lo recrystallization,it may be of great value as a markerof the itshigh-temperature the boundary[o-?}x],mdeformationfor thethe purefirst mechanisms crystalone, occurs only at rotation the are samereasonably temper- recrystallization ously increased ispossible; to take intoin the account the increasein cross physicaland mechanical conditions prevailingFig. 2. Criticalduring curve the inlast the a, well T planeknown; between (4)the atureit domains is asprobably the transitionof secondabetween rather one, extrinsic good migration and model intrinsic recrystallizationforregimes other sectionoccurs and maintain(Figure a constant 2). stress. However, for experi- rotationrecrystallization (below) and migrationrecrystallizationin the samematerial [Poirier, Rotation 1972].recrystallization. Rotation mentsrecrystallizationat high temperatures,isifthe a partial unloadingby 50% is tectonicepisode, assuming, ofcourse, (above).we know The dashedhow topart relate of the curve ductile for Sr++-doped minerals; NaCIandhas (5) been theonly study possible of itsmoderecrystallization for all stresses belowmadeis beforea critical the criticaltemperature strain •c is reached, the deformation extrapolated.The subgrainsizes (d) correspondingtoEffect theof appliedRecrystallization onthe Creep Curve continuesata lower creep rate; and when the critical strain is thevarious features ofthe recrystallized structure toparame- interesting inits own Rotationright recrystallization as the information has no effectongathered the creepcurve, may bereached, a suddenacceleration can be seenon thecreep curve stresseshavebeen given inabscissae. helpfulThetwo in stippled understanding domains corre-better (which the mechanicsdepends slightlyof emplacementon stress) and for stresses below a ters characteristicof these conditionsspond (e.g.,to naturaltemperaturedeformation or conditions of haliteafter sinceCarter it proceedsand by critical continuous valuerotation of stressof the subgrainsat temperaturesdur- correspondinghigher than to very therapid criticalmigration recrystallization even if ing steadystate creep. In our experiments,migration recrys- the final stressafter unloadingis smaller than the critical stress).A recent instance ofthis approach Heardcan[1970] be and found Heard in [1972]. the ofsalt domes. tallization causesno temperature. perceptibleacceleration of creep during stress.This behavior can be understoodif one considersthat useof therecrystallized grain size as a geopiezometerfor Thepurpose ofthethe course present of a typicalstudyexperiment istwofold: when the (1)load tois continu-find out the structure corresponding to the higherstress tr• is preserved deformedmantle rocks [Twiss, 1977; Mercier et al., 1977;the respective temperature andstress domains where migra- Nicolas,1978]. tionor rotation recrystallization occurand (2) to compare the However,one knows very little of dynamic recrystallization recrystallized grainsize paleopiezometers inboth cases with a andits mechanisms inminerals. Most of our still very imper- view to assessing theirvalue as indicators ofstress inthe crust and mantle. fect knowledgecomes from experimentsat fast strain rates on metals[Sellars, 1978].A few experimentshave beenperformed on olivine [At)• Lallemantand Carter, 1970;Mercier et al., EXPERIMENTALTECHNIQUES 1977],calcite [Griggs et al., 1960],and quartz rocks[Green et Material al., 1970; Tullis et al., 1973] in conditionsof solid confining pressure,where the physicalparameters are difficult to control We usedcrystals of three different impurity contents:(1) and to measureaccurately. Hobbs [1968] studied the recrys- very pure syntheticsodium chloride singlecrystals (50 X 50 tallization of quartz single crystalsunder confining pressure mm) containingless than 10 ppm impurities(mostly Ca ++ and and was the first to produce evidencefor a dynamic recrys- Mg ++), purchasedfrom Hatshaw Chemicals,(2) singlecrys- tallization mechanismwhereby smaller individual new grains tals containing500 ppm Sr++ ions, preparedby diffusionof SrCI: into the pure Harshaw materialas describedby Poirier Copyright (D 1979 by the AmericanGeophysical Union. [1972], and (3) natural singlecrystals from Dieuze (Moselle, Fig. 7. Detail of the migratingboundary between grains A and B of Figure 5 (x 200). The boundaryis convextoward Paper number 9B0589. 5557 grain A and consumesboundaries of rotation recrystallizedsmaller grains in A (deepetching). The substructurein B is in 0148-0227/79/009B-0589501.00 the processof formation.

Fig. 3. Samplerecrystallized by rotation(X 17);a = 4 bars,T = 650øC,• = 65%.Etched (100) cleavagesurface. The boundariesof recrystallizedgrains have been underlined in black.The figuresin thegrains indicate the rotation in degrees aboutto the[100] axis normal to the surface(e.g., 33 means33 ø anticlockwise,3-• means 33 ø clockwise). Recrystallization (nucleation) starts in high stress domains Enstatite (opx): Recrystallization along kink bands

High dislocation density A 2nd diffusion-assisted recovery and recrystallization process: Grain boundary migration

2 mn

Olivine Dunitic xenolith 30 mn Tommasi et al EPSL 2004

15 h

Static grain growth: octachloropropane Park, Ree & Means, J. Virtual Explorer 2000 octacloropropane C3Cl8

Deformation by “dislocation creep”, but under ≠ strain rate conditions Park, Ree & Means, J. Virtual Explorer 2000

High strain rate (fast deformation) Dynamic recrystallization by bulging Grain size reduction

Low strain rate (slow deformation) Dynamic recrystallization by subgrain rotation and grain boundary migration No grain size reduction Quartz : dynamic recrystallization processes vary with increasing T

bulging

subgrain rotation Temperature

grain bondary migration Viscoplastic deformation of ice

dislocation creep = dislocation glide + dynamic recrystallization

polycrystalline ice - HT in-situ deformation: pure shear C. Wilson - Univ. Melbourne, Australia In experiments, a change in macroscopic mechanical behavior is usually interpreted as due to a change in dominant deformation mechanism. Can you explain the data on this figure?

How may we identify the mechanisms active during and after deformation in natural systems (Earth)? Microstructures & deformation regimes

Dislocation creep: • Grain elongation (produced by glide, may be erased by recrystallization) • Undulose extinction, deformation bands & subgrains (microstructures directely related to dislocations = may be erased by annealing) • At high stress (or LT) dynamic recrystallization may produce grain size reduction & a bimodal grain size distribution (porphyroclasts vs. neoblasts) • HT: sinuous or polygonal grain boundaries : migration synkinematic grain growth hinders grain size reduction • Crystallographic preferred orientation (CPO) = preserved even in annealed (statically recrystallized) rocks

Diffusion creep or diffusion-assisted grain boundary sliding: • Fine-grained material (µm) • Weak elongation may exist, but generaly absent • Absence of intracrystalline deformation features (Undulose extinction, deformation bands & subgrains) • Absence of CPO? Experimental deformation : calcite + 1% qz - 900 K – 10-5s-1

High stress regime ~ low T in nature © GFZ Postdam Crystals elongation & undulose extinction, almost no recrystallization Ø dislocation glide dominant Quartz: crystals elongation & undulose extinction + recrystallization producing a very fine grained matrix

High stress regime ~ low T. Why? Quartz: crystals elongation & undulose extinction + recrystallization producing a very fine grained matrix

Is this rock less or more deformed than the previous? Quartz: subgrains + some (low range) grain boundary migration

Intermediate stress / T regime. Why? Quartz: grain boundary migration (+ subgrains)

Low stress / high T regime. Why? Quartz: grain boundary migration very high T deformation + annealing (granulite facies) Do you see why? Paleowattmeters: A scaling relation for dynamically recrystallized grain size

Nicholas J. Austin* Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Brian Evans* 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA

ABSTRACT also dissipated, but a fraction, λ, is responsible During dislocation creep, mineral grains often evolve to a stable size, dictated by the deforma- for increases in internal energy owing to grain- tion conditions. We suggest that grain-size evolution during deformation is determined by the boundary area. If the total strain rate can be par- rate of mechanical work. Provided that other elements of microstructure have achieved steady titioned between dislocation and diffusion creep, ˙ ˙ state and that the dissipation rate is roughly constant, then changes in internal energy will be then β = Wdisl/Wtot, and the dissipation rate is proportional to changes in grain-boundary area. If normal grain-growth and dynamic grain-size θ˙ = (1 – β)σε˙ + (1 – λ)(β)σε˙. (4) reduction occur simultaneously, then the steady-state grain size is determined by the balance of irr those rates. A scaling model using these assumptions and published grain-growth and mechani- Incorporating Equation 4 into Equation 3 and cal relations matches stress–grain-size relations for quartz and olivine rocks with no fi tting. For rearranging yields marbles, the model also explains scatter not rationalized by assuming that recrystallized grain −cγ size is a function of stress alone. When extrapolated to conditions typical for natural mylonites, σε = d . (5) d 2 red the model is consistent with fi eld constraints on stresses and strain rates. βλ The stable grain size is often posited to occur Keywords: recrystallization, deformation, rheology, calcite, quartz, olivine, grain size, piezometers, when grain growth and reduction rates are equal localization, dissipation. (de Bresser et al., 1998; Hall and Parmentier, 2003). When no mechanical work is done, the INTRODUCTION 1990). Clearly, a theoretical understanding of total grain-size evolution rate must equal the Reduced grain size is a common and striking recrystallization is necessary to interpret natural static growth rate. Lacking any specifi c infor- feature of mylonites. Creep experiments indi- microstructures. mation on how (or if) growth and reduction Dynamic recristallizationcate that average grain size evolves to a stable processes couple, we assume they are linearly Relation recrystallized grain size - stress ˙ ˙ ˙ value (ds) determined by the deformation condi- SCALING BETWEEN POWER independent: dtot = dred = dgr.

tions. Early work suggested that ds was inversely AND GRAIN SIZE Thus, related to stress (σ) (Twiss, 1977), and, thus, During deformation, external forces do work −cγ mylonite grain sizes have been used to infer (per unit volume) at a rate of W˙ = σε˙ + σ˙ε, σε = (d − d ). (6) tot βλd 2 tot gr paleostresses (e.g., Stipp and Tullis, 2003): where a dot denotes a time derivative, and σ and ε are differential stress and incremental strain, Assuming that deformation does not modify d = Aσ –m, (1) s respectively. For simplicity, we consider uniaxial normal grain growth kinetics, then the rate of ˙ –1 1–p where A and m are empirically determined. The stress and coaxial strain. If σ varies less rapidly growth is dgr = Kg exp[–Qg/RT]p d , where p 1000 Stress depends on application of this- strain idea ratewas clouded by evidence than grain size, then, on some time scale, σ˙ = 0 is the exponent in the normal grain growth law. - temperature ˙ of independent infl uence of metamorphic condi- and Wtot = σε˙. The rate that work is done equals The total grain-size evolution rate is ˙ tions (Etheridge and Wilkie, 1981). More recent the rate of increase in internal energy, Eint, plus 2 d ⎛ −Qg Paleo-piezometer: ˙ βλσε ⎞ −1 1− p Zhang et al. 2000 workers have suggested that d is also a function the rate of energy dissipation, θ , including heat dtot = + K g exp p d . (7) Grain size (µm) s irr ⎜ ⎟ Van der Wal 1993 In reality, grain size depends on the work rate, cγ ⎝ RT ⎠ Karato et al. 1980 of temperature or strain rate (Poirier and Guil- production and any other irreversible increases Jung & Karato 2001b that is, on both stress and strain rate 100 lopé, 1979; de Bresser et al., 1998, 2001; Drury, in entropy (Poliak and Jonas, 1996; Bercovici The steady-state grain size occurs when the 1 10 100 Stress (MPa) 2005). At present, there is no universally accepted and Ricard, 2005). If the stored energy associ- total evolution rate is zero:

Deformation mechanisms dependtheory on grainto explain size… the relationship between ds and ated with free dislocations rapidly attains steady ⎛ −Qg ⎞ May dynamic recrystallization result in a change from dislocation to −1 the deformation conditions, but factors to be state, then the rate of change of internal energy K g exp⎜ ⎟ p cγ diffusion creep? Under which conditions? 1+ p ⎝ RT ⎠ considered are transitions in the recrystallization is proportional to the rate of change of grain ds = , (8) mechanism (Poirier and Guillopé, 1979; Rutter, boundary area: βγσε 1995), stabilization of the grain size at values bal- into which β may be substituted, yielding: −cγ ancing diffusion and dislocation creep (de Bresser Eint = 2 dred , (2) Q d ⎛ − g ⎞ −1 et al., 1998, 2001), subgrain nucleation and grain- K g exp⎜ ⎟ p cγ 1+ p ⎝ RT ⎠ growth rates (Shimizu, 1998), and nucleation-site where c is a geometric constant, d is the grain ds = . (9) density (Sakai and Jonas, 1984). size at time t, and γ is the average specifi c grain λσεdisl Field observations of nominally single-phase boundary energy. Then, Finally, if the rock deforms by power-law creep,

rocks often indicate a gradation in recrystallized n ⎛ Qdisl ⎞ −cγ ε = ε 0σ exp− , then ⎝⎜ ⎠⎟ grain size from protomylonite to ultramylonite Wν = σε = 2 dred + θirr . (3) RT (e.g., de Bresser et al., 2002, and references d -m′ ⎛ Q′ ⎞ therein). If stress is the only parameter deter- Grain growth rates in calcite rocks during dif- d = κ⋅σ ⋅exp− , (10) s ⎝⎜ RT ⎠⎟ mining ds, then one may infer that the most fusion creep do not differ from normal, static 1 highly deformed rocks have seen the highest growth rates (Walker et al., 1990; Austin and p+1 ⎡cKγ g ⎤ ⎛ n +1⎞ stresses, in contradiction to localization theory Evans, 2005), so we postulate that the mechani- where κ = ⎢ ⎥ , m′ = ⎜ ⎟, and ˙ λεp 0 ⎝ p +1⎠ for nondilating materials (e.g., Hobbs et al., cal work done by diffusion creep, Wdiff = σε˙diff, is ⎣ ⎦ completely dissipated. Part of the work done on QQg − disl ˙ Q′ = . *E-mails: [email protected], [email protected]. the material by dislocation creep, Wdisl = σε˙disl, is ()p +1

© 2007 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. GeologyGEOLOGY,, April April 2007; 2007 v. 35; no. 4; p. 343–346; doi: 10.1130/G23244A.1; 4 fi gures. 343 experimental deformation = extension - olivine – 1200°C & 10-5s-1

® W. Ben Ismail

necking = high stress olivine – low T (~900°C) deformation Mylonite = basal thrust of the Oman ophiolite

1mm HT deformation of mantle rocks (olivine-rich): grain elongation & undulose extinction well-developed subgrains & grain boundary migration = dislocations glide + diffusion active = DISLOCATION CREEP

High or low stress? Deformation mechanisms maps dry olivine polycrystals (dunite)

dislocation glide

dislocation creep

diffusion creep

Remember: Experimental points used to define these maps are obtained in a very limited T, strain rate, and grain size range => lots of extrapolation!!! 4 M. Thielmann, B.J.P. Kaus / Earth and Planetary Science Letters 359–360 (2012) 1–13

at the top boundary and shear-stress free at the side and the (see also Fig. S1). The effect of shear heating on the state of stress bottom boundaries, that additionally have imposed normal velo- in the lithosphere can be illustrated with 1D stress profiles city conditions in such a way that the whole domain is com- (Fig. 2): whereas the maximum of the second invariant of shear pressed (and thickened) with an overall constant background stress tII remains at 900 MPa in models without shear heating, it strain rate e_BG (denoted by arrows in Fig. 1A). is significantly smaller in all other models. The shear heating efficiency x significantly influences the timing, the temperature increase inside the shear zone and the 3. Results state of stress in the lithosphere. In the models shown here, the maximum temperature increase is located near the brittle–ductile 3.1. Influence of shear heating on lithospheric deformation transition, where Peierls creep is the dominant deformation mechanism (due to the large stresses at this location). Models We ran several models (27 in total) in which we varied without Peierls plasticity show the same behavior but with (i) cohesion and friction angle and (ii) the shear heating efficiency lithospheric stresses 200 MPa (the maximum value of tII is The shallow (cold) lithospheric mantle :  x (see Table S3 in supplementary material for a detailed summary 1.2 GPa compared to 1 GPa in models with Peierls creep  of employed model parameters). included) higher prior to the formation of lithospheric-scale faults a key layer controllingOf these the parameters, plates’ the shear heating mechanical efficiency x is the most behavior(Fig. S2). During the initial model stages, faults form in the mantle important one (Fig. 2). Although brittle parameters like the friction lithosphere due to Mohr–Coulomb plasticity, but ultimately a angle and cohesionWhich also exhibit some is influenceits actual in lithospheric- rheologysingle thermally? weakened shear zone develops. In order to test scale localization, they only change the general behavior when the influence of elasticity, we performed several models with a extreme values are assumed (e.g. when we employ a friction angle viscoplastic rheology (see Fig. S5 and Table S3). As in the visco- 6 of 151 and a cohesion of 10 Pa (see Fig. S3), lithospheric localiza- elasto-plastic models, we observe the formation of a lithospheric- tion does not occur for x 0:5, but when choosing a friction angle scale shear zone. The effect of elasticity is twofold: (i) it delays the ¼ 2 of 301 and a cohesion of 10 Pa as an extremely low value (see onset of formation of a lithospheric-scale shear zone by reducing Fig. S4), lithospheric deformation does not deviate significantly the amount of work being converted to heat, but (ii) helps from the simulation shown in Fig. 2, where a friction angle of localization by converting elastically stored energy to heat in 6 301 and a cohesion of 10 Pa is employed). the shear zone, which results in an extreme short-term increase During the initial stage of all models, deformation is domi- in velocity and a significant rise in temperature. In the viscoplas- nated by isostatic equilibration, which is caused by the differ- tic case, localization is less catastrophic and results in more New experimental data for ences in lithospheric thicknesses and the initial horizontal free moderate temperature increases (also see Fig. S5). surface. This stage (not shown) lasts no longer than 0.1 Ma, and is followed by lithospheric-scale folding, with faults forming in olivine at LT + dislocation the shallower crust due to Mohr–Coulomb plasticity (first row 3.2. Lithospheric-scale localization regimes of Fig. 2). Deformation is localized in brittle faults but remains dynamics modeling distributed in the ductile parts of the lithosphere, and until this To gain insight into the physics of shear-heating induced stage all models develop similarly. With ongoing compression, lithospheric-scale localization, we ran a total of 42 2D numerical however, a single stable lithospheric-scale shear zone develops in simulations with a wet olivine rheology, in which we varied the models with shear heating (x 0:5,x 1), which is followed by compression strain rate e_BG and the thermal age of the lithosphere ¼ ¼ subduction initiation. The model without shear heating (x 0), on U (see also Table S4). We employed x 1 in these simulations ¼ ¼ the other hand, develops two conjugate shear zones and does for several reasons: (i) Experimental evidence: Chrysochoos not result in subduction initiation. Deformation, instead, remainsHuismansand Belmahjoub & Beaumont (1992) Natureused 2011 infrared techniques to accurately distributed between several lithospheric-scale faults and with observe the temperature increase in a sample during compression no specific fault being ‘‘chosen’’ to take up all the deformation and found that x lies between 0.4 and 0.9, approaching the latter Yield stresses >500 MPa

Fig. 2. Comparison between three simulations (Loc17, Loc22, Loc27) with no shear heating (x 0), 50% shear heating efficiency (x 0:5) and 100% shear heating efficiency Thielmann¼ & Kaus EPSL 2012¼ (x 1). Colors correspond to the logarithm of the second invariant of strain rate, different levels of gray denote different rock units. White lines denote 800, 1000 and ¼ 1200 1C isotherms. The rheology in all three simulations is visco-elasto-plastic. Viscous rheology is given by Peierls and dislocation creep. In the rightmost column, 1D stress envelopes of the second stress invariant tII are plotted that were extracted at the left boundary of the 2D models (colors correspond to the different runs). Note that not the whole model domain is plotted, but rather a zoom on the relevant part. 46 S. Demouchy et al. / Physics of the Earth and Planetary Interiors 220 (2013) 37–49 factors such as the finite strength of the solid pressure medium and ine rheology at low temperature may be the lack of precision of the piston friction, which have been detailed by Tullis and Tullis stress estimations in DIA and D-DIA experiments, since they can (1986). Finally, the relatively low confining pressure in our study only be indirectly estimated from the broadening/refinement may have not allowed to achieve high enough stresses (>1 GPa) (i.e., for DIA set up) or shift (i.e., for D-DIA set up) of the X-ray dif- to affect the slip systems previously reported for olivine in aggre- fraction peaks by the polycrystalline olivine itself or by external gates, i.e., [100](010) or [001](010) at high temperature. pistons. Recent experiments performed in D-DIA press have attempted to deform olivine at low temperature and high pressure (above 3 GPa) to avoid any risk of sample failure (Raterron et al., 2004; 4.4. New semi-empirical flow law and consequences for deformation of Mei et al., 2010; Long et al., 2011). In this type of experiment, the uppermost mantle the stresses increase as a function of decreasing temperature as for low-pressure experiments. Final differential stress obtained To constrain the rheology of the lithospheric mantle, one needs by Mei et al. (2010) are significantly higher than results from Gri- to be able to extrapolate laboratory-based measurements to signif- icantly slower strain rates. Most of the mechanical data compared ggs’s apparatus experiments (Durham and Goetze, 1977; Phakey New flow law for olivine at lithospheric conditions et al., 1972), which are in turn higher than results from this study above, even if obtained with different methods and showing evi- and from Demouchy et al. (2009). Thus one can then question the dencebased of composite on all behavior, existing agree with data each at other. 500-1100°C One may thus & <3GPa relevance of a strong pressure effect (i.e., under a pressure too high for the uppermost mantle) and discard the results (Mei et al., 2010; Long et al., 2011). Nevertheless, when results from Long et al. (a) 5 1 (2011) are normalized to a strain rate of 10À sÀ , the differential stresses are in satisfying agreement with the hardness measure- strain rate =10-5 s-1 ments of Evans and Goetze (1979). Finally, Raterron et al. (2004) experiments imply strengths significantly lower than all other existing data sets. As already discussed in the introduction, a pos- sible explanation for the inconsistency between different DIA and LT flow laws D-DIA datasets (i.e., at high pressure) and with other data on oliv- Demouchy et al (2013)

HT flow laws

(a)

500-1100°C <3 GPa

Demouchy 2013 experiments on olivine crystals (b)

(b)

Fig. 10. Differential stresses (MPa) versus temperature (°C) (a) for all available 5 1 mechanical data. All stresses were normalized to a strain rate of 10À sÀ (with Eq. (1)) except for a single datum point from Meade and Jeanloz (1990), see details in the main text. (b) Differential stresses (MPa) versus temperature (K). Fits to the data Fig. 9. Log–log diagram of differential stress (MPa) versus temperature (°C) for selection (for pressure 63GPa and temperatures between 500 and 1000 °C, and a 5 1 5 1 identical strain rate (10À sÀ ) for the olivine crystals deformed in this study (a) for strain rate of 10À sÀ ). The different models (best model is model 3) obtained in maximal stresses and (b) for a strain of 0.8%. For comparison, the results from this study, as well as flow laws from G78: (1978), E&G79: Evans and Goetze (1979), Phakey et al. (1972) and Durham and Goetze (1977) and the change of the slip Rat04: Raterron et al. (2004) and H&K2003: Hirth and Kohlstedt (2003), Faul2011: system as a function of temperature proposed by Goetze (1978) are also shown. Faul et al. (2011) are also shown. Flow law parameters are reported in Table 2. Deformation processes and rheology of the mantle lithosphere Experimental deformation of olivine polycrystals @ 900-950°C & 300 MPa,

134 S. Demouchyinitial et al. /grain Tectonophysics size 623 (2014)2-4µ 123m–135 (Paterson press, Montpellier)

o strain-hardening observed in the deformation curvesDemouchy (Fig. 2 et). Atal (2014) lower Temperature ( C) strain rates, relevant of the shallow mantle, such recovery processes 400 600 800 1000 should be more active and may, in theory, permit to reach steady 3000 H&K 2003 WET H&K 2003 state. Therefore the high stresses reported here must represent an E&G 1979 ppm wt H2O F&al 2011 10 upper bound strength for olivine-rich rocks at low temperature. 2500 D&al 2013 50 D&al 2013 We may, however, compare the recent flow law by Demouchy PoEM 21, this study PoEM 22, this study et al. (2013) with the maximal stresses obtained for the deformed 2000 aggregates with the predictions of the recent flow law by Lab -5 -1 Demouchy et al. (2013), which is derived from deformation experi- 10 s ments on olivine single-crystals at low temperature and high pressure. 1500 The data were normalized to a common strain rate of 10−5 s−1 by recalculating the temperature using the method proposed by Goetze Stress (MPa) 1000 (1978):

500 • • −1 Mantle Rln = 1 εexp εn -14 -1 Tcorr 10 s ¼ 0Texp þ Q 1 0 600 800 1000 1200 1400 @ A Temperature (K) where Tcorr is the corrected temperature for a given experiment, Texp is • the absolute temperature of the experiment, R is the gas constant, and ε • Fig. 12. (a) Differential stresses (MPa) versus temperature (K). Stresses were normalized 5 1 and εn are the strain rate of the experiment and the strain rate desired to a strain rate of 10− s− ; thick dashed black and gray lines are for flow laws from Evans for the normalizationà (here Max 10 −stresses5 s−1), respectively. consistent The activation with en-flow lawand Goetze derived (1978), medium from dot-dash LT data black and on gray single-crystals lines are for Faul et al. (2011) and ergy Q is supposed to be 450,000 J/mol, as in the low temperature H&K 2003: thin solid black and gray lines are for Hirth and Kohlstedt (2003) and thick fl flow law reported by Demouchy et al. (2013). The mechanical data solid black and gray lines are for Demouchy et al. (2013). Wet olivine ow laws for olivine But… steady state not achieved incontaining low temperature trace amount of H (i.e., experiments 10 and 50 ppm H2O wt. using the calibration of Paterson from the present deformation experiments on olivine aggregates are re- (1982) used in Hirth and Kohlstedt (2003). Differential stresses (MPa) versus temperature ported in Fig. 12 alongAre with previouslythe LT flow established laws high representative temperature (K). of Stresses the were lithosphericfirst normalized to amantle strain rate of behavior 10−5 s−1, and then? extrapolated to a flow laws for dry and wet olivine (Faul et al., 2011; Hirth and strain rate of 10−14 s−1. Kohlstedt, 2003) and the low temperature flow laws for dry olivine (Demouchy et al., 2013; Evans and Goetze, 1979). The results from from Demouchy et al. (2013), which thus appears as an upper bound for this study are in good agreement with the recent low temperature the strength of olivine-rich rocks at lithospheric conditions. These flow law (Demouchy et al., 2013) obtained from experiments in results suggest that the occurrence of low melt fractions or the incorpo- which the samples did not fail by brittle fracture. This suggests that ration of hydrogen in the olivine atomic structure or shear heating are this flow law defines an upper bound for the strength of olivine at low not required to reconcile the observed low strength of Earth's upper- temperature, where recovery processes in olivine are not efficient. It most mantle and the experimentally obtained flow laws. also corroborates the conclusion that a dry mantle lithosphere has a Supplementary data to this article can be found online at http://dx. much lower strength than predicted by extrapolation of the high- doi.org/10.1016/j.tecto.2014.03.022. temperature experimental data. It also suggests that water-weakening in olivine, partial melting or shear heating might not be required to explain the low strength of the mantle lithosphere as proposed by Acknowledgments Demouchy et al. (2012) and Fei et al. (2013). A Marie Curie fellowship awarded to SD (PoEM: Plasticity of Earth 5. Conclusions Mantle, FP7-PEOPLE-20074-3-IRG, No. 230748-PoEM) supported this study. C. Nevado and D. Delmas are thanked for providing high-quality Deformation experiments in tri-axial compression on olivine aggre- thin sections for SEM and TEM. J. Oustry is sincerely thanked for his gates were performed at 900 °C, a temperature relevant of the upper- help in the mechanical workshop. D. Mainprice is thanked for the use most mantle and at a confining pressure of 300 MPa. Rheological data of his petrophysical software. The TEM and EBSD-SEM national facilities exhibit a complex behavior, with no steady-state, but a strong apparent in Lille and Montpellier are supported by the Institut National de Sci- strain hardening and absence of evidence of elastic deformation or ences de l'Univers (INSU) du Centre National de la Recherche fi stick-slip behavior. High resolution EBSD provides robust evidence Scienti que (CNRS, France), the Conseil Régional Languedoc-Roussillon (microstructures and CPO) for viscoplastic deformation accommodated (France), and by the Conseil Régional du Nord-Pas de Calais, (France). by dislocations motion, but TEM and electron tomography were neces- sary to fully identify the slip systems activated, which are characterized References by both [001] and [100] glide on multiple planes with predominance of non-basal planes for [001] glide. The high variety of glide planes con- Bai, Q., Mackwell, S., Kohlstedt, D., 1991. High-temperature creep of olivine single crystals. fi 1. Mechanical results for buffered samples. J. Geophys. Res. 96 (B2), 2441–2463. rms the stress dependence of the dislocation glide mechanisms in oliv- Barnard, J.S., Sharp, J., Tong, J.R., Midgley, P.A., 2006a. High-resolution three-dimensional ine. Characterization by TEM, including electron tomography, is thus imaging of dislocations. Science 313, 319. essential for a precise determination of glide plane by imaging the de- Barnard, J.S., Sharp, J., Tong, J.R., Midgley, P.A., 2006b. Three-dimensional analysis of fi formed crystal at micro-scale. On the other hand, EBSD maps provide dislocation networks in GaN using weak-beam dark- eld electron tomography. Phil. Mag. 86, 4901–4922. the necessary and complementary statistical approach to study a de- Bascou, J., Tommasi, A., Mainprice, D., 2002. Plastic deformation and development of formed polycrystalline solid. We conclude that the use of those two clinopyroxene lattice preferred orientations in eclogites. J. Struct. Geol. 24, techniques must become systematically paired. 1357–1368. fi fl Bunge, H.-J., 1982. Texture Analysis in Materials Science. Butterworths, London, p. 593. Although the lack of steady state hinders the de nition of a ow law, Byerlee, J., Brace, W., 1968. Stick slip stable sliding and earthquakes — effect of rock type the strength of olivine-rich rocks at temperatures of the lithospheric pressure strain rate and stiffness. J. Geophys. Res. 73, 6031–6032. http://dx.doi.org/ mantle predicted on the basis of the present experimental data is signif- 10.1029/JB073i018p06031. Chakraborty, S., 2010. Diffusion coefficients in olivine, wadsleyite and ringwoodite. In: icantly lower than inferred from the extrapolation of high-temperature Zhang, Y., Cherniak, D. (Eds.), Diffusion in Minerals and Melts. Reviews in Mineralogy flow laws. It is in agreement with the recent low temperature flow law and Geochemistry, 72, pp. 603–639. http://dx.doi.org/10.2138/rmg.2010.72.13. More on Patrick’s Cordier talk on Saturday…

Major lesson from these data: increasing temperature does not compensate for too high strain rates. Extrapolation of lab data to nature over 9-10 orders of magnitude in strain rate is a major weakness in our predictions of the mechanical behavior of the lithospheric mantle. Some additional reading

Basic textbooks Passchier and Trouw (2005) Microtectonics Nicolas and Poirier (1976) - Crystalline plasticity and solid state flow in metamorphic rocks

More advances : Poirier, J.P. (1985) Creep of crystals: high-temperature deformation processes in metals, ceramics, and minerals Karato, S-I. (2008) Deformation of Earth Materials: An Introduction to the Rheology of Solid Earth, Cambridge University Press

On the web : http://virtualexplorer.com.au/special/meansvolume/contribs/jessell/ http://www.geo.umn.edu/orgs/struct/microstructure/ http://www.atmos.albany.edu/geology/webpages/wdmovies/wdmoviep.html http://virtualexplorer.com.au/special/meansvolume/contribs/tullis/SlideSet/ deformation_micro.html http://serc.carleton.edu/NAGTWorkshops/structure/visualizations/microstructures.html