D-DIA (Deformation DIA)High-P and T, homogeneous stress/strain

(Durham, Wang, Getting, Weidner)

Rotational Drickamer Apparatuslarge strain (radial distribution), high P-T

(Yamazaki, Xu, Nishihara)

ZirconiaAlumina

MgO

Sample assembly for a rotational DrickamerApparatus(torsion tests on a thin disk-shaped sample to large strain)

A change in geometry of a strain-marker

stress-distribution in a RDA

(Mg,Fe)O, ~12 GPa, ~1473 K

Large-strain shear deformationof wadsleyite

Effects of Phase Transformation

1. Grain-size2. Crystal structure, bonding3. Internal stress/strain (“transformation plasticity)

Rheology of deep mantle mineralsAt present, only results from analog materials are availableHigh-pressure deformation experiments are preliminaryNeed for direct, quantitative high-pressure studies

A first-order phase transformation is associated witha finite volume change that causes an internal stress/strain, which may modify the rheological behavior(transformation plasticity).

The role of internal stress

In the Orowan equation, the dislocation density may be controlled by the “internal stress”.

.

€

˙ ε = b ρ v

€

ρ = b

− 2

σ

int

μ( )

2

€

σ

int

: internal stress

€

˙ ε ˙ ε 0

≈′ σ tr′ σ 0( )

n−1

Problem 16-8Show that a high dislocation density and resultant (possible) enhancement of

deformation due to a phase transformation occurs only when

€

τR

>> τ

T

where

€

τ

R , T

ar e

the characteristic times of dislocation recovery and transformation respectively[Paterson, 1983].Hint: assume the following relations for the kinetics of a phase transformation and ofdislocation recovery:

€

ρ

a

t( ) = ρ

T

1 − exp−

t

τ

T

( )[ ]

dislocation generation

and

€

ρ t( ) = ρ

0

−ρ

0

− ρ

s

( ) 1 − exp−

t

τ

R

( )[ ]

dislocation recovery

where

€

ρ

0 , s

are the initial and the steady-state dislocation density respectively1.

Solution

1 T he use of a first-order kinetics as opposed to the second-order kinetics (see Chapter

10) is justified because we consider annihilation of dislocations with equal sign.

Physical Processes Controlling the Grain-Size

1. Grain growth (static: driving force=boundary energy)2. Dynamic recrystallization

(dynamic: driving force= dislocation energy)3. Phase transformation

Driving forces for grain-boundary migration

Grain-boundary energy -> grain-growthDislocation energy -> dynamic recrystallizationChemical energy -> grain-size reduction

€

F =

δ g

V

= 6

γ

r

δ r

r

~ 3

γ

r

€

F = μ b2

Δ ρ

Driving forces for grain-boundary migration

: grain-boundary energy

: dislocation energy

A schematic diagram of the sample capsule for wet annealing ran.

75Au-25Pd capsule

Wadsleyite

Olivine

Metal foil

Talc + Brucite(1 : 7 in molar ratio)

1 mm

oxygen fugacity for various buffer systems

Infrared absorption spectra

Grain-growth in wadsleyite

1

2

3

4

5

0 0.5 1 1.5 2

log

10

(GS

n -GS0n)

log10

t (h)

olivine n = 3

olivine n = 2

wadsleyite n = 3

wadsleyite n = 2

1573 K(µ

mn )

Log

(G

S^n

-GS

0^n)

A comparison of grain-growth kinetics in olivineand wadsleyite (under nominally “dry” conditions)

-50

-48

-46

-44

-42

-40

-38

-36

5 5.5 6 6.5 7 7.5 8

10000/(T, K)

Mo capsule 4h

Re capsule 1h

Re capsule 4h

ln k

(m

3 /s)

H*=140+/-20 kJ/mol

€

GS

n

− GS( )

o

n

= k

n

T , P , C( ) t

€

k

n

= Af

O 2

r

C

OH

q

exp −

H

*

RT

( )

r~0.5q~1H*~140 kJ/mol

fO2 effect

Secondary phase particles have an important effect on grain-growth (Zener pinning).Grain-growth in two-phase mixture is completelydifferent from that in a single-phase aggregates(controlled by the Ostwald ripening).Very few studies have been done on two-phaseaggregates (Yamazaki et al., 1996).

Zener pinning

When excess energy needed for a moving boundaryto pass over secondary particles exceed the driving forcefor migration, then grain-boundary migration stops.

LZ=4a/3f

a: size of secondary-phase particlesf: the volume fraction of secondary phase particles

If the size of the secondary phase particles can increase,then continuing growth is possible.

Grain-growth kinetics controlled by the Ostwald ripening

€

L

4

t( )

− L

4

0( )

=

32 π γ Ω δ D

B

c

0

27 RTf

3

t : boundary diffusion

€

L

3

t( )

− L

3

0( )

=

128 γ Ω D c

0

81 RTf

3

t : bulk diffusion

Kinetics is proportional to the solubility and diffusion coefficient of growing material in the matrix.