GEOS 5505 2 Intragranular Deformation Mechanisms

1. GEOS 5505 2 IntragranularDeformation Mechanisms Bons, Jessell

2. IntragranularDefomation Mechanisms Dislocation Glide “Stress” Grain Boundary Sliding Frictional Sliding Fracturing Bulk Rotation Rotation Recrystallisation Lattice Rotation Grain Boundary Migration Recovery Twinning Climb Diffusional Creep Kinking Phase Change Atomic Intragranular Intergranular “Chemistry” Diffusive Mass Transfer

3. Crystal Defects 0D Interstitial 0D Vacancy 1D Dislocation 2D Subgrain boundary 2D Grain/Phase boundary 3D Grain/Second Phase

4. 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

5. Dissolution-precipitation creep and diffusional creep • These deformation mechanisms involve diffusion • Of vacancies through grains or grain boundaries • Of dissolved matter through fluid

6. 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

7. Two paths of vacancy motion

8. 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-cte-qtz triple junctions. Michel Bestmann

9. 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

10. 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 [m3 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:

11. Coble creep Flux 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

12. Volume V 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 Coble creep Number f of vacancies going through area ug: +∆sn/2 +∆sn/2 ug V w -∆sn/2 -∆sn/2 g g If width of grain boundary is u, then all vacancies go through area ug

13. Flow laws for diffusional creep Nabarro-Herring creep Coble creep Two types: Linear (Newtonian) viscous flow: Grain size sensitive: small grains  fast flow Temperature sensitive: faster at high T

14. Microstructures grain • 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

15. 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

16. 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

17. 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

18. 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

19. 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.

20. 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

21. 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(m2/newton) s11 1.27 1.27 s12 -0.17 -0.21 s44 2.01 2.28 s33 0.97 0.93 s13 -0.15 -0.16 s14 -0.43 -0.48 Bulk modulus (Pa)3.289x10104.17x1010 Young’s modulus 7.874x10107.87x1010

22. Why not just perform MD simulations? 160 billion atoms (50003) or a cube of copper a 10-6 m on each side. 8 hourswallclock and around 10-10 s of simulated time (running at 10-14 speed, dedicated machines, e.g. Anton canrunat10-10) Single thin section equivalent volume of rock perhaps 10-2 m deformed for 10+13 s 90 ms-1 impact on polycrystal 5x10-9 ms-1 impact on polycrystal

23. But… Size: 1010 too small Time: 1020 too fast

24. Discrete Dislocation Dynamics

25. Creating dislocations Dislocations are created by deformation No deformation: no dislocations Main source of dislocations: Frank-Reed source

26. Dislocation glide and interaction

27. Flow by dislocation movement • r =dislocation density = no of dn lines per cm2 or total line length per cm3 • near perfect artificial crystal 102cm-2 • annealed or as grown crystal 105cm-2 • cold worked crystal 108 to 1011cm-2 • 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?

28. Orowan's equation b Shortcut to slide 55… Orowan’s equation: now empirically: and at low v: so • 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 • 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?

29. Dislocation glide • Dislocation climb difficult, low grain boundary mobilities, high dislocation density contrasts; leads to dislocation glide accommodated by recovery and bulging grain boundary migration.

30. 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

31. 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":

32. 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.

33. Recapitulating • Derivation of flow laws • Low T: Dislocation glide • High T: Dislocation creep

34. 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

35. Frictional regime, strength linear increase with pressure=depth Crystal-plastic regime, strength exponentially decreases with temperature  depth Burov, 2011

36. 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