1. 1 Structural Geology Microstructural View of Deformation Lecture 20 – Spring 2016

2. 2 Dislocation Interaction Dislocation D 1 is assumed to move past D 2 After passing l 2, D 2 is offset by b 1, creating a jog Part of l 2 is now along D 1, but the Burger vector is different Figure 9.22 in text

3. 3 Pinning a Dislocation This creates a different CRSS, and this pins the dislocation, anchoring a segment of l 2 This increases the resistance to dislocation movement, decreasing the strain rate, and causing strain hardening

4. 4 Imaging Dislocations The dislocation density, N, is the total length of dislocations within a unit volume of crystal Dimensionally, this is length/length 3, or per length 2 Excellent crystals, grown from a melt, have values of N of 10 6 /cm 2 Strained crystals can be several orders of magnitude more

5. 5 Dislocation Lengths A strained quartz crystal with a volume of 1 cm 3 might have a dislocation length of 10 10 cm, or 100,000 km, assuming N = 10 10 /cm 2 So the length of a dislocation must be very small

6. 6 Transmission Electron Microscope We cannot see such small lengths with optical microscopes It is necessary to use more energetic radiation, with smaller wavelengths, to see dislocations The usual method is to use a transmission electron microscope (TEM), which passes a beam of electrons through the sample

7. 7 Magnification Magnifications up to 500,000x can be achieved To image dislocations, magnifications in the 10,000-100,000x range are sufficient The beam is transmitted through a very thin foil of the sample, typically a few hundred nanometers thick

8. 8 Diffraction Around Dislocation The images reveal dislocations because the dislocation causes a change in the electronic field around the dislocation The beam is defracted, and shows up as a dark region in the image

9. 9 Dislocations in Olivine Straight dislocations are seen in the upper half, loops in the lower left, and parallel dislocations in the lower right The dislocations here terminate against the edges of the thin foil In larger samples, the dislocations will be longer Figure 9-5 in text

10. 10 TEM Images of Calcite Mixed dislocations is seen at a line near A Figure 9.23 in text

11. 11 Dislocations in Ringwoodite Dark-field image of a relatively coarse- grained specimen ( 5μm), transformed and deformed at 16 GPa, 1,400 K The dislocation density is 10 14 m -2, which is consistent with a stress of 1 GPa

12. 12 Microstructural Analysis We distinguish four mechanisms in the microstructural analysis:  Recovery  Recrystallization  Superplastic creep  Deformational Twinning (previously discussed)

13. 13 Formation of Subgrains Such dislocation walls lower the total strain energy, relative to a crystal with dislocations scattered evenly throughout the crystal Figure 9.24 in text

14. 14 Tilt Boundaries Dislocations arrays in tilt boundaries may be visible optically Figure 9.25 in text

15. 15 Subgrain The angular mismatch at a boundary is defined as:  2sin(θ/2) = b/h  where θ is the angular mismatch, b is the Burger vector, and h is the spacing of individual dislocations in the wall A subgrain is the area of a grain enclosed by a low- angle tilt boundary Low-angle means < 10º Higher angles represent recrystallized grains, which will be discussed

16. 16 Undulatory Extinction In thin section, undulatory extinction is the result of subgrain formation Minerals like quartz, calcite, olivine, and pyroxene are particularly prone to exhibit this phenomenon Figure 9.26 in text

17. 17 Formation of Undulatory Extinction Temperature- activated rearrangement of dislocations produces the low- angle grain boundaries, and the process is called recovery Click movie to play

18. 18 Recrystallization Internal strain energy can be removed by a higher-temperature process called recrystallization Undulatory extinction disappears, and new grains, with grain boundary angles near 120º, appear

19. 19 Recrystallization Microstructure Field of view about 2 mm Mylonitic marble, southern Ontario Recrystallization forms high-angle grain boundaries that separate strain-free grains Figure 9.27 in text

20. 20 Foam Microstructure These angles are also seen in soap foam, and the structure is sometimes called a foam microstructure

21. 21 Grain Size Decrease If differential stress is present during recrystallization, the grain sizes generally decrease The process is known as dynamic recrystallization Sheared rocks, such as mylonites, are a common example of dynamic recrystallization

22. 22 Dynamic Recrystallization A specific stress on a grain produces a specific density of dislocations This increase in dislocation density leads to a decrease in grain size (and recrystallized grain size), such that recrystallized grain size can be used as a paleo stress gauge or paleopiezometer Click movie to play

23. 23 Mylonites Mylonites are characterized by having a grain size smaller than the rocks from which they form Mylonite comes from “mylos”, a Greek word meaning milling This is a misnomer, and really applies to rocks formed by cataclasis However, the name was applied without knowledge that mylonites form by dynamic recrystallization, and has stuck

24. 24 Mylonite in Thin Section Quartz ribbon (q) was originally an equant grain in a granite, but has been stretched (in a taffy-like manner) into an elongate grain The fine-grained matrix (m) is composed of minerals that recrystallized during deformation Field of View 4 x 2.7 mm, Cross Polarized Light

25. 25 Temperature Requirements The temperature range required for dynamic recrystallization depends on the mineral:  Calcite>300ºC  Quartz>350ºC  Feldspar>450ºC

26. 26 Mechanisms of Recrystallization The two major mechanisms of recrystallization are  Rotation recrystallization  Migration recrystallization

27. 27 Subgrain Transformation The original subgrain boundary does not move significantly The subgrains eventually become recognizable as grains in their own right Figure 9.29a in text

28. 28 Core-Mantle Structure The resulting structure, with the core relatively free of deformation, but the outer edge heavily recrystallized, is called a core-mantle structure Figure 9.30 in text

29. 29 Minerals Showing Rotation Recrystallization Rotation recrystallization has been observed in  Calcite  Quartz  Halite  Olivine

30. Migration Recrystallization Involves growth of one grain at the expense of another The boundary of one grain grows through its neighbor The growing grain has a lower dislocation density than the grain being consumed  At the grain boundary, atoms in the grain being consumed rearrange themselves to match the lattice of the growing grain  It is easier to rearrange atoms in this grain, since its high dislocation density means its bonds are already weakened Overall, this lowers the strain energy of the system 30

31. 31 Bulge Nucleation The growing grain bulges into the other grain, and the process is sometimes called bulge nucleation Figure 9.29b in text

32. 32 Minerals Showing Migration Recrystallization Migration recrystallization has been observed in:  Quartz  Feldspar  Halite

33. Paleostress Since dislocation migration depends on differential stress, we have another means of estimating paleostress Paleostress estimates depend on knowing the operative recrystallization method This also allows us to use the grain size of recrystallized grains as a paleopiezometer (pressure meter) 33

34. 34 Differential Stress and Grain Size Paleostress is difficult to estimate, so this tool could be quite useful More work is needed, but one relationship is clear:  σ d = Ad -I,  where A and I are empirically derived parameters, which differ for each mineral, and d is grain size measured in μm - A is expressed in MPa

35. 35 Grain Size Diagram In general, small grain sizes in recrystallized rocks indicate high strain rates, while large grains sizes indicate low strain rates Figure 9.31 in text

36. Superplastic Creep, aka GBSS Occurs at relatively high temperatures It is grain-size sensitive, with grains sliding past each other during deformation The grains slide without friction, because volume and grain-boundary diffusion are fast enough to keep gaps from forming between grains 36

37. 37 Neighbor Switching Deformation is accomplished by neighbor switching Figure 9.32 in text

38. 38 Nearly Viscous Rheology The strain rate is inversely proportional to the grain size  Where r is in the range of 2-3 Superplasticity approaches an exponent of 1 for n in equation 9-14, which means that it is nearly a viscous rheology, whereas dislocation creep is a non-linear rheology, and therefore not viscous

39. 39 Deformation Map Image (Ashby Diagram) Schematic example of a defomation map Figure 9.33 in text

40. 40 Dry Calcite Map Geologically reasonable strain rate region is shaded Figure 9.34a in text

41. 41 Wet Calcite Map Undulation in pressure solution region results from competition between change of solubility of calcite and fluid concentration as temperature increases Figure 9.34b in text

42. 42 Dry Quartz Map Geologically reasonable strain rate region is shaded Figure 9.35a in text

43. 43 Wet Quartz Map Region of dashed strain-rate contours represents the inhibition of pressure solution through the decrease in pore water concentration Figure 9.35b in text

44. 44 Feldspar Deformation Map Schematic deformation mechanism map after Tullis and Yund (1991) Blue indicates creep regimes for dry feldspar aggregates and red indicates wet feldspar aggregates Dashed lines indicate strain rate at which the experiments were conducted (10 -5 s -1 ) The bold dashed lines indicate a geologically relevant strain rate of 10 -14 s -1

45. 45 Olivine Deformational Map Olivine is the dominant mineral of the upper mantle Instead of homologous temperature, depth is plotted, assuming a geothermal gradient that decreases with depth, which is realistic The temperature regime is 300ºC at the surface to 1850ºC at 500 km depth The effects of pressure can also be accommodated Pressure increases the flow strength of olivine and decreasing the strain rate Figure 9.36 in text

46. 46 Marble Bench Sag Even the sag rate of marble benches can be estimated! Figure 9.38 in text