1) Introduction

We can define microstructures (based in part on a Hobbs, Means & Williams 1976 definition) to be: "the small-scale arrangement of geometric and mineralogical elements within a rock."

This of course begs the question as to what small-scale means, and we will be going on a tour of microstructures in this course at increasing scales:
 

Atomic scale (eg defects) ->
intra-crystalline (eg twinning) ->
inter-crystalline (eg porphyroblasts) ->
multi-grain interactions (eg shear bands, continuum mechanics)
 
Microstructures are also called fabrics by some people, or microfabrics.

• To establish the link between process, environment & microstructure via general constitutive equation eg Dorn 1957
• The (Micro)structure is a function of the competing processes in a rock: (PROCESS RATE=DRIVING FORCE*KINETICS) as they act on an initial (Micro)structure. By understanding this relationship we can interpret microstructures in terms of the history of temperature (T) , pressure (s), the CO2 fluid pressure (ƒCO₂) and other boundary conditions that control both the driving force and the kinetics

• To provide evidence of deformation processes, which in turn provides:
• evidence of rheology during deformation, which is important for geodynamic interpretation
• interpretation of deformation history
• evidence of metamorphic environment
• interpretation of seismic anisotropy
• microstructural geochemistry

3) How do we study microstructures

• Field work
• measurement of cleavages & lineations, etc (Hobbs, Means & Williams 1976)

measurement of numerous types of sense of shear (aka kinematic) indicators Passchier, C.W. & Trouw, R.A.J. 1996.

• Lab analysis

• Observation
• microscopy - optical thin section analysis
• SEM - Scanning Electron Microscope - observes surfaces only c.f. reflected light microscopy
• TEM - Transmission Electron Microscope - thin foil samples c.f. transmitted light microscopy
• Cathodoluminescence (CL)-displays trace chemical variations
• Quantitative analysis
• Crystallographic Preferred Orientations (CPO)
• Grain Shape Foliations (GSF)
• Grain Size Distributions
• AVA (mapping crystallographic orientations across a thin section)
• Stable isotope studies
• Experiments
-rock mechanics/fabric (Tullis & Tullis 1986)
-info with ceramics, metals, ice: All crystals the same, sort of (Ashby & Brown 1981)
-other crystalline analogues (Means 1989)
-numerical simulation (Jessell & Lister 1990)

4) Deformation Mechanisms & Processes

a) Definitions: Deformation Mechanisms are processes that lead to a change in shape of rock
 

• There are many types of deformation mechanisms which have been recognised in rocks and other crystalline materials, such as ceramics and metals. We provide a table of deformation mechanisms and processes and the effects they have on microstructure.

• grain boundary migration
• rotation recrystallisation
• metamorphic reaction

i)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
ii) Defects in crystals:
• Point 0-D known as point defects
• vacancies, interstitials, discrete 2nd phase

• Line: 1-D known as dislocations
 
• 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 energy source for other processes such as grain boundary migration.
• Plane: 2-D boundaries between different grains or parts of grains
• grain boundaries, twins, internal phase boundaries, stacking faults
• Grain boundaries will be discussed in much more detail in Lecture 2.

these two processes involve the non-random motion of point defects and can cause a change in shape of a crystal, and are thus deformation mechanisms. The movie just below shows vacancies moving through a crystal, and this is known as Nabarro-Herring Creep. If the vacancies diffuse around the grain margins, it is known as Coble Creep. Click on the picture below to see how vacancy diffusion works.

The images below are of detrital quartz grains 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. They probably formed as a result of Coble and/or Nabarro-Herring creep. Images courtesy of Michel Bestmann (michel@geol.uni-erlangen.de Institut für Geologie und Mineralogie, Schloßgarten 5, 91054 Erlangen, Germany)

d) Direct Observation of dislocations:

• Etch pits (acids preferentially etch intersection of dislocation with crystal surface)
• Decoration by heat treatment (trace elements precipitate on dislocations)
• Transmission Electron Microscopy (TEM)- a very thin 0.2-3 µ specimen is required
i) Bright field image. This TEM image shows the interior of a quartz grain experimentally deformed by Alice Post whilst doing her PhD at Brown University. iii) Undulose extinction demonstrates the effect of large numbers of dislocations producing a curved lattice

e) Movement of dislocations:

• Slip Systems: any given mineral will favour dislocation motion in particular crystallographically controlled directions. The plane in which the dislocation moves is called the slip plane, and the direction in which it moves is called the slip direction.
• Burgers vector: the length of the dislocation of the crystal lattice caused by a single dislocation is known as the Burgers vector, and this will be constant for any one slip system.
• The Critical Resolved Shear Stress (CRSS) is the stress (as resolved onto the slip plane in the slip direction)  needed to cause dislocation motion, ie break shortest bonds. Typically it decreases with increasing temperature for all slips systems in a mineral, however it may not decrease at the same rate for all systems.
• edge dislocation movement results in part of the crystal moving perpendicular to the dislocation line

• screw dislocation movement results in part of the crystal moving parallel to the dislocation line

• climb is a diffusive process whereby the dislocation line moves perpendicular to the dislocation line direction, but within the plane of the extra half-plane of atoms.

• stacking faults- are planar features where a
• loops if you take a dislocation line and follow it round and it joins back up with itself, this is known as a loop, and is by its nature made up of a combination of screw and edge dislocations, with a cylindrical volume of "slipped" crystal within the loop. As the loop grows, the volume of slipped crystal thus grows with it.

• Frank-Reed sources are "loop generators" that occur as impassable defects in a crystal hold up the passage of a dislocation. If two such defects occur as neighbours, an automatic loop generator is formed. This is what a dislocation Frank-Read source looks like. See Dislocation dynamics section in Lab 1 for further examples. This simulation shows one inclined slip plane with loops being generated continuously.

• tilt boundaries- sub-grain boundaries made up of arrays of edge dislocations

• twist boundaries- sub-grain boundaries made up of arrays of screw dislocations

f) Rheology of dislocation glide:
 

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

this is OROWANS EQN, where V = ave mobile dislocation velocity

at low V, V is proportional to the stress which gives:

g)Twinning

Unlike dislocation glide,  movement of a twin boundary significantly and permanently alters the orientation of the crystal. The orientation of the twin plane, and the misorientation across the twin boundary will be precisely the same for any particular type of twin, and the process of twinning is essentially instantaneous, there is not a gradual change in crystallographic orientation, as the twin boundary moves across a region, the crystal lattice flips, and a discrete increment of deformation is attained. Further deformation of the grain may cause more material to become twinned, but it does not further deform the twinned volume (at least not by the same type set, other twins, or other mechanisms may of course be activated). Deformation twins can often be distinguished from growth twins (that form during crystal growth) by being thinner, and having wedge shaped terminations. They are particularly important in the low temperature deformation of calcite, and the deformation of plagioclase. Here is a movie of twin development in bischovite, a hydrated magnesium salt, made by Janos Urai.

h) Kinking

Kinking superficially looks like twinning, however the relationship between the misorientation across a kink band boundary, and the orientation of the kink band boundary and the amount of deformation caused by the kink are not predictable. Micas often deform by kinking, which involves slip on the basal plane.

The movement of one grain past another, in pure material this may be accomplished by dislocation or diffusive mechanisms.

A beautiful molecular dynamics simulation of copper nano-crystals undergoing grain boundary sliding during vertical extension was performed by Jakob Shiotz (J. Schiotz, F. D. Di Tolla, and K. W. Jacobsen, Nature, 391, 561 (1998)). Here the sphere shading relates to the local crystal structure: White atoms are in a perfect face centred cubic environment. Light gray atoms are in local hexagonal close packing order, which for example corresponds to stacking faults. Atoms in any other environment (in grain boundaries and dislocation cores) are colored dark grey.

i) Other deformation processes:

• neighbour switching

The switching of grain relationships (needs grain boundary sliding and diffusion to cooperate to allow this).

• rigid body rotation- rotation of grain without any internal deformation. A ball undergoes rigid body rotation (or bulk rotation) when you roll it along the ground. Very rigid grains in a soft matrix will typically rotate in non-coaxial deformation regimes (see discussion on porphyroblasts in lecture 4). Similarly a feldspar lath in a granite melt can rotate with essentially no internal deformation if the melt is sheared.

• granular flow

• fracture- the brittle cracking of a mineral, often followed by sliding on or pulling apart of the fracture surfaces

• phase change- a change in the crystallography of the crystal, without a change in its bulk chemistry.

• Pressure Solution- The long-range (multiple grain) diffusive mass transfer of material. See lecture 5.

j) Deformation mechanism maps

These are graphs in typically stress-temperature space (but also grain size-temperature and others) which show which deformation mechanisms dominate under which conditions FOR A PARTICULAR MINERAL. They are contoured in strain rates, showing the strain rate that would be achieved by that process alone under the appropriate conditions. They only show dominance in terms of which mechanism is likely to account for the most strain, the label in any particular field does NOT mean that no other mechanism or process is active, and it does NOT mean that the microstructural development will be controlled by that labeled mechanism, in fact it does not even mean that the deformation mechanism is the dominant process in terms of microstructural evolution. It would be nice if we had general Microstructral process mechanism maps, an example of which is shown at the end of Lecture 3.