L7 - Mineral Creep Flashcards
What is elastic deformation? (2)
Recoverable
Material returns to its original shape if force removed
What is plastic deformation? (2)
Permanent
The material keeps shape if force removed
How does the lower crust and mantle deform? (1)
By solid-state thermally-activated creep
What does creep involve? (1)
What is it like if scaled up to xal size? (1)
The motion of discontinuities at the crystal lattice scale
Continuous fluid deformation
What is the creep equation? (1)
strain rate = A(σ^n)(d^-p)(C(OH)^r)exp(-(E+PV)/RT)
What defines diffusion creep? (1)
What does this mean? (2)
n=1
stress = constants * strain rate (at given P,T therefore a Newtonian fluid)
constants = viscosity
What are the controls on viscosity? (3)
Temperature
Grain size
Hydration state
How does T affect viscosity? (1)
Strain rate involves exp(-(E+PV)/RT)
How does grain size affect viscosity? (3)
Strain rate involves d^-p
p=2 for diffusion through grains
p=3 for diffusion on grain boundaries
How does the hydration state affect viscosity? (4)
One suggestion: H+ presence compensated by an increase in the density of -ve vacancies
OR H+ presence may change configuration and strength of bonds
so E required for switching is lower
Either way, the effect of ppm of water in the lattice of anhydrous minerals can dramatically reduce the creep strength
How does deformation by diffusion creep happen? (1)
The motion of point defects through the crystal/along grain boundaries
What types of point defects are there? (3)
Lattice vacancies
Substituted ions in lattice sites
Ions in non-lattice sites (interstitial)
What limits the rate of diffusion creep? (1)
Number of locations in the lattice in which the energy is high enough for a vacancy and ion to swap places in response to an applied stress
How does deformation by dislocation creep happen? (1)
The motion of planar defects in the lattice through it
How does dislocation creep depend on physical constants? (3)
Same for T and hydration state as diffusion creep
p=0 so independent of grain size
n=3-5
What are the implications of n being 3-5 for dislocation creep? (
Behaviour is like a non-Newtonian fluid
Law can be written as σ = A(E^(1/n - 1))strain rate
Effective viscosity is lower if the deformation is faster
Deformation gets concentrated in shear bands (narrower as n increases)
What is E in the constitutive law for dislocation creep? (3)
The second invariant of the strain rate tensor
Given by sqrt(strain rate_ij*strain rate_ij)
Measures how fast the material is straining
What is the rate-limiting factor in dislocation creep? (2)
Dislocations offset each other
Need to be straightened out by diffusion for dislocation to continue
What are deformation maps used for? (1)
What is an important result from them?
Can work out the rheology of a given mineral under a given set of conditions
For geologically-relevant T and σ, viscosities are such that large deformations can take place over geological timescales
How is the dominance of diffusion or dislocation creep affected by changes to stress, grain size, and T? (2)
Diffusion dominant if they decrease
Dislocation dominant if they increase
What viscosity value is obtained for the convecting mantle? (1)
What is the context of this? (1)
10^19 to 10^21 Pa s
Conditions close to the transition between creep types
What would happen over time to a warped xal lattice if dislocation creep occurs? (3)
Formation of sub grains
Grain size reduction
Diffusion creep occurs
Because dislocations move easier in some orientations, what does dislocation creep result in? (1)
What has this view led to? (1)
What has recent work shown?
Production of arrays of grains with a dominant alignment of the crystallographic axes
Suggestion that anywhere with significant seismic anisotropy must be deforming by dislocation creep
Diffusion creep can also produce a dominant lattice orientation
How can we constrain mantle rheology to ensure experimental results for deformation maps are correct? (5)
Look at glacial isostatic adjustment
Equation relating uplift to ice sheet size and mantle viscosity
w = w_m*exp(-t/τ_r)
w is vertical position of the surface, w_m is position when ice melted, t is time, τ_r is 4πη/ρgλ
Using λ = 3000km, η = 10^21 Pa s
What is a second independent constraint on mantle rheology? (3)
Why is there a difference? (1)
Look at postseismic ductile relaxation of the lower lithosphere
Ask what distribution of mantle η can reproduce the observed surface motions
The estimate is 10^18 to 10^19 Pa s for the upper mantle, and >10^20 Pa s for the lower crust
Looking at different rheologies, underneath Scandinavia (glacial uplift method) is Pre-Cambrian shields
What needs to be known for deformation maps to be applied to the lithosphere, and what is known currently about these constraints? (3)
T: decent guess, good using xenoliths
Hydration state: maybe guess, better with xenoliths
Composition: mantle is an ok guess, crust is weak guess
