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 y ⇒ σ ∝ε 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 - σ ,ε creep 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 - σ ,ε creep 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 = D (1+ ) V = molar volume eff v 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,