L7 - Mineral Creep

Question 1

What is elastic deformation? (2)

Answer 1

Recoverable

Material returns to its original shape if force removed

Question 2

What is plastic deformation? (2)

Answer 2

Permanent

The material keeps shape if force removed

Question 3

How does the lower crust and mantle deform? (1)

Answer 3

By solid-state thermally-activated creep

Question 4

What does creep involve? (1)

What is it like if scaled up to xal size? (1)

Answer 4

The motion of discontinuities at the crystal lattice scale

Continuous fluid deformation

Question 5

What is the creep equation? (1)

Answer 5

strain rate = A(σ^n)(d^-p)(C(OH)^r)exp(-(E+PV)/RT)

Question 6

What defines diffusion creep? (1)

What does this mean? (2)

Answer 6

n=1
stress = constants * strain rate (at given P,T therefore a Newtonian fluid)
constants = viscosity

Question 7

What are the controls on viscosity? (3)

Answer 7

Temperature
Grain size
Hydration state

Question 8

How does T affect viscosity? (1)

Answer 8

Strain rate involves exp(-(E+PV)/RT)

Question 9

How does grain size affect viscosity? (3)

Answer 9

Strain rate involves d^-p
p=2 for diffusion through grains
p=3 for diffusion on grain boundaries

Question 10

How does the hydration state affect viscosity? (4)

Answer 10

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

Question 11

How does deformation by diffusion creep happen? (1)

Answer 11

The motion of point defects through the crystal/along grain boundaries

Question 12

What types of point defects are there? (3)

Answer 12

Lattice vacancies
Substituted ions in lattice sites
Ions in non-lattice sites (interstitial)

Question 13

What limits the rate of diffusion creep? (1)

Answer 13

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

Question 14

How does deformation by dislocation creep happen? (1)

Answer 14

The motion of planar defects in the lattice through it

Question 15

How does dislocation creep depend on physical constants? (3)

Answer 15

Same for T and hydration state as diffusion creep
p=0 so independent of grain size
n=3-5

Question 16

What are the implications of n being 3-5 for dislocation creep? (

Answer 16

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)

Question 17

What is E in the constitutive law for dislocation creep? (3)

Answer 17

The second invariant of the strain rate tensor
Given by sqrt(strain rate_ij*strain rate_ij)
Measures how fast the material is straining

Question 18

What is the rate-limiting factor in dislocation creep? (2)

Answer 18

Dislocations offset each other

Need to be straightened out by diffusion for dislocation to continue

Question 19

What are deformation maps used for? (1)

What is an important result from them?

Answer 19

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

Question 20

How is the dominance of diffusion or dislocation creep affected by changes to stress, grain size, and T? (2)

Answer 20

Diffusion dominant if they decrease

Dislocation dominant if they increase

Question 21

What viscosity value is obtained for the convecting mantle? (1)
What is the context of this? (1)

Answer 21

10^19 to 10^21 Pa s

Conditions close to the transition between creep types

Question 22

What would happen over time to a warped xal lattice if dislocation creep occurs? (3)

Answer 22

Formation of sub grains
Grain size reduction
Diffusion creep occurs

Question 23

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?

Answer 23

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

Question 24

How can we constrain mantle rheology to ensure experimental results for deformation maps are correct? (5)

Answer 24

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

Question 25

What is a second independent constraint on mantle rheology? (3)
Why is there a difference? (1)

Answer 25

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

Question 26

What needs to be known for deformation maps to be applied to the lithosphere, and what is known currently about these constraints? (3)

Answer 26

T: decent guess, good using xenoliths
Hydration state: maybe guess, better with xenoliths
Composition: mantle is an ok guess, crust is weak guess