GEOS 5505 2 Intragranular Deformation Mechanisms Bons Jessell

GEOS 5505 2 Intragranular Deformation Mechanisms Bons, Jessell

Intragranular Defomation Mechanisms “Stress” Dislocation Glide Grain Boundary Sliding Twinning Fracturing Bulk Rotation Recrystallisation Lattice Rotation Frictional Sliding Grain Boundary Migration Recovery Climb Kinking Phase Change Diffusive Mass Transfer “Chemistry” Atomic Intragranular Diffusional Creep Intergranular GEOS 5505 2017 Microstructures Jessell

Crystal Defects 0 D Vacancy 2 D Subgrain boundary 0 D Interstitial 2 D Grain/Phase boundary 1 D Dislocation 3 D Grain/Second Phase GEOS 5505 2017 Microstructures Jessell

Why are defects so important? • They can speed up the process of crystal growth by orders of magnitude (geometry) • The distorted crystal lattice around defects provides rapid diffusion pathways within crystals (geometry) • They are intimately involved in several deformation mechanisms (kinematics) • Provide a driving force for many deformation processes (dynamics) • Can weaken the strength of a crystal by several orders of magnitude (dynamics) • The movement of dislocations can lead to the formation of crystallographic preferred orientations GEOS 5505 2017 Microstructures Jessell

Dissolution-precipitation creep and diffusional creep • These deformation mechanisms involve diffusion • Of vacancies through grains or grain boundaries • Of dissolved matter through fluid GEOS 5505 2017 Microstructures Jessell

Diffusional creep stress • Vacancies are empty sites in the crystal lattice • Vacancies can diffuse through a crystal • Directed diffusion can lead to a change of shape of the crystal: deformation • Stress can drive the direction of diffusion GEOS 5505 2017 Microstructures Jessell

Two paths of vacancy motion GEOS 5505 2017 Microstructures Jessell

Possible Diffusional Creep Microstructure Detrital quartz grain in a calcite shear zone. They are single crystals with no evidence of rotation recrystallisation in wings. The lace network on surface reflects cte-qtz triple junctions. Michel Bestmann GEOS 5505 2017 Microstructures Jessell

Vacancy transport = material transport • Movement of a vacancy • Vacancy swaps places with a neighbouring atom • When one vacancy jumps to a neighbouring site • One atom jumps into the vacancy site • Transport of vacancies in one direction = Transport of material in the opposite direction GEOS 5505 2017 Microstructures Jessell

A flow law for diffusion creep • The deformation rate is determined by • The number of vacancies • CV in [mol m-3] • The strength of vacancies • their size in molecular volume W in [m 3 mol-1] • The velocity of vacancies • The flux J in [mol m-2 s-1] • We need to determine these to get the flow law: GEOS 5505 2017 Microstructures Jessell

Fl ux Coble creep Flux of vacancies is through grain boundaries • We need to know the flux of vacancies • We already know the gradients in vacancy concentration as a function of stress with b = grain shape factor GEOS 5505 2017 Microstructures Jessell

Coble creep If width of grain boundary is u, then all vacancies go through area ug Number f of vacancies going through area ug: Volume V arrives on surface of crystal, removing a layer of width w: This means that the crystal shortens with a rate of +∆sn/2 ug -∆sn/2 +∆sn/2 V w -∆sn/2 g g GEOS 5505 2017 Microstructures Jessell

Flow laws for diffusional creep Two types: Nabarro-Herring creep Coble creep Linear (Newtonian) viscous flow: Grain size sensitive: small grains fast flow Temperature sensitive: faster at high T GEOS 5505 2017 Microstructures Jessell

Microstructures • When diffusional creep is active • Stresses are too low to produce dislocations • No driving force for dynamic recrystallisation • Surface energy only driving force for recrystallisation • Absence of dynamic recrystallisation could indicate diffusional creep • Or the absence of deformation… • Or thermal overprint… • Diffusional creep can sometimes be seen by mapping (trace) elements grain GEOS 5505 2017 Microstructures Jessell

Flow by glide of dislocations • An edge dislocation is the edge of an extra half lattice plane • A dislocation is the edge of a zone along which the crystal has been translated • Glide of the edge dislocation through the whole crystal leads to: • A unit of strain • Annihilation of the dislocation GEOS 5505 2017 Microstructures Jessell

Dislocations are important for their • geometry - each dislocation represents a small angular distortion of the lattice, a lot of them together can result in a curved crystal lattice, or a sharp misorientation across a boundary. Dislocations can also act as fast diffusion pathways. • kinematics - the movement of dislocations results in the accumulation of deformation within a crystal. The deformation of a material by the movement of dislocations is known as crystalline plasticity • dynamics - the distortion around a dislocation provides an driving force for other processes such as grain boundary migration GEOS 5505 2017 Microstructures Jessell

Flow by glide of dislocations • An edge dislocation is the edge of an extra half lattice plane • A dislocation is the edge of a zone along which the crystal has been translated • Glide of the edge dislocation through the whole crystal leads to: • A unit of strain • Annihilation of the dislocation GEOS 5505 2017 Microstructures Jessell

Flow by climb of dislocations • An edge dislocation can also climb by adding or removing vacancies • Adding vacancies gradually removes the extra half plane, resulting in • A unit of strain • Annihilation of the dislocation GEOS 5505 2017 Microstructures Jessell

Dislocations in reality • Dislocations can be revealed • By etching for a normal microscope • With a transmission electron microscope • The dislocation line length in one cubic meter of heavily cold deformed brass can get as high as 1 light year. GEOS 5505 2017 Microstructures Jessell

Molecular dynamics Atomic interactions simulated using a many-body description of the atomic bonding Systems up to 1011 atoms Time scale of 1 ns (200000 timesteps) Very high strain rates e. g. 5. 10+8 s-1 Schiøtz et al 1998 GEOS 5505 2017 Microstructures Jessell

Quartz molecular dynamics Molecular Dynamics has the potential to provide: fundamental constraints on atom, dislocation and grain boundary behaviour Quartz (Nye) MD Experiment Elastic constants x 10 -11 (m 2/newton) s 11 s 12 s 44 s 33 s 14 1. 27 -0. 17 2. 01 0. 97 -0. 15 -0. 43 Bulk modulus (Pa) 3. 289 x 1010 Young’s modulus 7. 874 x 1010 1. 27 -0. 21 2. 28 0. 93 -0. 16 -0. 48 4. 17 x 1010 7. 87 x 1010 GEOS 5505 2017 Microstructures Jessell

Why not just perform MD simulations? 160 billion atoms (50003) or a cube of copper a 10 -6 m on each side. 8 hours wall clock and around 10 -10 s of simulated time (running at 10 -14 speed, dedicated machines, e. g. Anton can run at 10 -10) Single thin section equivalent volume of rock perhaps 10 -2 m deformed for 10+13 s 90 ms-1 impact on polycrystal 5 x 10 -9 ms-1 impact on polycrystal GEOS 5505 2017 Microstructures Jessell

But… Size: 1010 too small Time: 1020 too fast GEOS 5505 2017 Microstructures Jessell

Discrete Dislocation Dynamics GEOS 5505 2017 Microstructures Jessell

Creating dislocations • Dislocations are created by deformation • No deformation: no dislocations • Main source of dislocations: Frank-Reed source GEOS 5505 2017 Microstructures Jessell

Dislocation glide and interaction GEOS 5505 2017 Microstructures Jessell

Flow by dislocation movement • Dislocations bound an area where the crystal has been translated • A small "quantum" of strain • "quantum" size defined by Burger's vector • How fast does a crystal deform under a certain stress? • What is the flow law? • Basically, we need to know • How many dislocations? • How strong are they? • How fast do they glide? r�=dislocation density = no of dn lines per cm 2 or total line length per cm 3 • near perfect artificial crystal 102 cm-2 • annealed or as grown crystal 105 cm-2 • cold worked crystal 108 to 1011 cm-2 GEOS 5505 2017 Microstructures Jessell

Orowan's equation • Orowan's equation is a very basic equation for the rheology of materials that deform by the movement of dislocations • Orowan's equation relates the strain rate to • The Burger's vector b • How much does one dislocation contribute to strain? • The dislocation density • How many dislocations contribute to strain? • The dislocation velocity • How fast does one dislocation contribute to strain? Shortcut to slide 55… Orowan’s equation: now empirically: and at low v: so GEOS 5505 2017 Microstructures Jessell

Dislocation glide 1. Dislocation climb difficult, low grain boundary mobilities, high dislocation density contrasts; leads to dislocation glide accommodated by recovery and bulging grain boundary migration. GEOS 5505 2017 Microstructures Jessell

Recovery-controlled creep • Also known as dislocation creep or power-law creep • Small obstacles are overcome by thermal agitation alone: athermal regime (T > Tc) • Large obstacles (dislocation tangles) can disappear by climb-controlled annihilation of dislocations • Climb rate is controlled by thermally activated diffusion of vacancies GEOS 5505 2017 Microstructures Jessell

Power-law creep • The general form of the flow law for dislocation creep is of the type: • The stress exponent (n) is usually 3 -5, not always 3! • Assumptions on stress dependence parameters Dislocation density & source density • Relationship between diffusion rate and stress High T, low s: lattice diffusion: n = 3 Low T, high s: diffusion through dislocation cores: n = 5 "pipe-diffusion": GEOS 5505 2017 Microstructures Jessell

Dislocation glide vs dislocation creep Mobility of grain boundaries increases, grain boundary migration and rotation recrystallisation both active, with rapid migration of grain boundaries dominating. GEOS 5505 2017 Microstructures Jessell

Recapitulating • Derivation of flow laws • Low T: Dislocation glide • High T: Dislocation creep GEOS 5505 2017 Microstructures Jessell

Deformation Mechanism Maps Dislocation creep NH creep Coble creep • Dislocation creep: • GRAIN-SIZE INSENSITIVE (GSI) • Strain rate is independent of grain size for dislocation creep • Horizontal lines • Diffusional creep: • GRAIN-SIZE SENSITIVE (GSS) • Strain rate is dependent of grain size for diffusional creep GEOS 5505 2017 Microstructures Jessell

Cr str ysta de eng l-pl te crea th e asti mp s x c er es w pon regi at ur ith enti me, e all y de pt h ar ine h l gt th en ep str =d e, sure gim es re pr al ith ion w ict se Fr rea inc Burov, 2011 GEOS 5505 2017 Microstructures Jessell

Conclusions • Defects are the carriers of deformation • Dislocations are also carriers of misorientation and driving forces for other grain scale processes • Competition between deformation mechanisms can be analysed in terms of minimum work, however this ignores the feedback between activity of mechanisms and microstructure evolution, and other processes that affect these microstructures • We can derive flow laws from first principals, but we can only assign specific parameters empirically GEOS 5505 2017 Microstructures Jessell