linking microstructures and reactions

Linking Microstructures and Reactions

Porphyroblasts, poikiloblasts, and pseudomorphing

Part 1Introduction, and some theory

A Metamorphic “Reaction”

Muscovite + Quartz = Andalusite + K-feldspar + H2O

KAl3Si3O10(OH)2 + SiO2 = Al2SiO5 + KAlSi3O8 + H2O

Metamorphic “reactions”

Notional reaction• Balanced chemical equation in a model system, e.g.

Ms + Qtz = And + Kfs + H2O, considered as a univariant relation between phase components in system KASH

Equilibrium relation• A notional reaction among phase components in a real rock, considered

as being in chemical equilibrium. e.g. Ms + Qtz = And + Kfs + H2O in a rock with white mica, …

Elementary reactions• Actual processes within rocks, responsible for chemical and mineralogical

change on the small scale.Overall reaction• Sum of elementary reactions, expressing overall chemical or assemblage

change in real or model system, e.g. Ms + Qtz => And + Kfs + H2O considered as a number of dissolution and precipitation reactions, linked by transport in intergranular fluid.• Driven by overall G, partitioned among the elementary reactions

Typical metamorphic microstructure

Granoblastic texture• Result of mutual adjustment

of grain boundaries in the solid state

Preferred orientations• Response to stress and

deformation

Not yet considering microstructures related to

reactions

Disequilibrium textures common

because:• Driving forces (surface and strain energy differences) are

small compared to chemical energy differences.• Deformation drives microstructures away from equilibrium.• Mineral growth may be controlled by reactant supply and

transport pathways, even while chemical equilibrium is being approached.

Obvious reactions: Coronas and symplectites

• Microstructures of reaction in high grade environments without aqueous fluid

Three-layer corona texture(Opx, Crd, Sil) betweenquartz and sapphirine

Symplectic intergrowths of Opxwith sapphirine and spinel

invading garnet

Typical metamorphic microstructures

Prograde metamorphism• Porphyroblasts• Poikiloblasts• Evidence that matrix grain size

has coarsened• Reactants and products not

generally in contact• Compositional zoning (if

present): prograde growth zoning

Retrograde metamorphism• Pseudomorphs• Reaction rims• Intergrowths (symplectites,

etc.)• Grain size reduction• Reactants and products in

contact with each other• Compositional zoning: frozen-in

diffusion gradients

Prograde metamorphic reaction processes

Involve several distinct steps• Nucleation of new mineral:

• assemble initial cluster of atoms into new structure

• Reaction at mineral surfaces:• detach material from

reactant minerals• add material to growing

minerals• Transport material to sites of

growth:• e.g. by diffusion in grain

boundaries or intergranular fluid

Breakdown of reactants

in matrix

Nucleus of product

Transport to growing surfaces

Growing grain of product

Heat Supply

Metamorphic reactions at the grain-boundary scale

Elementary reactionsPractical approximations to elementary reactions are

probably of two kinds:• Replacement reactions

Grain boundary (with fluid present?) moves through solid phases, material is transferred across the boundary and reassembled.

– Coupling between breakdown of one phase and growth of other (see Putnis 2002 Min Mag)

– Not usually isochemical– Constrained to conserve volume approximately

• Solid-fluid reactionsPrecipitation, Dissolution Grain boundary advances or retreats against fluid.

AB

B

Overall reactions at the local scale

Ms + Qtz => And + Kfs + H2ODriven by overall G, partitioned among the elementary reactions

Mechanism 1 may involve at least:• 2 dissolution reactions, • 2 precipitation reactions, • linked by transport in intergranular fluid

Mechanism 2 may involve at least:• 4 replacement reactions

Ms -> And; Qtz -> AndMs -> Kfs; Qtz -> Kfs

• linked by transport in grain boundaries +/- intergranular fluid

Overstepping: energy and temperature

Large S (e.g. dehydration) Small S (solid-solid)

G G

T

T

GG

T

TAssuming the required driving force is similar, a dehydration reaction will

run closer to its equilibrium temperature than a solid-solid reaction.The temperature overstepping needed to drive a solid-solid reaction (e.g.

the polymorphic transition Ky Sil) could be rather large.

Energy barriers and reaction rates

Thermally activated processes Temperature dependence of rate described by Arrhenius relationship

• where Ea = activation energy (height of barrier), pre-exponential factor A = frequency factor

• Net flow over barrier depends on G

RTEa

eARate

Activation energy

Reactants

ProductsG (free energy difference)

Rates of reaction at interfaces

(Transition State Theory)

Net rate RN = R+ - R- = k · (1 – eG/RT) · e-Ea/RT

close to equilibrium G<<RT, this approximates toRN = k · G/RT · e-Ea/RT

“linear kinetics”

Activation energy • In principle is characteristic of the process (nature of bonds to be broken)• In practice, for overall reaction, don’t know its physical significance• Comparative values:

Dissolution/growth 60 kJ/moleDiffusion in aqueous fluid < 20 kJ/moleDiffusion in grain boundaries 125 kJ/moleDiffusion in mineral lattice 250 kJ/mole

Rate of nucleation

= A . e-G*/RT

where A = a frequency factorand G* = an activation energy

Nucleation rate

-8

-4

0

4

8

12

0 20 40Overstep (delta T)

log

(rat

e pe

r m

3 pe

r s)

2

3*

316

GG

Surfaceenergy

Geometricalfactor

Overstepping

Interplay between nucleation and growth

log time

log

over

step

growth on nuclei

nucleation

not much

lots

notmuch

lots

Fastheating

Slowheating

hornfelsic texture

porphyro-blasts

Interplay between nucleation and growth

Rate laws:• nucleation rate has a very sharp exponential dependence

on overstepping.• growth rates are roughly linearly dependent on

overstepping.Effect of heating rate:• Slow T increase:

– After first nuclei form, enough time for transport and growth before nucleation rate increases.

– Small number of large crystals, at favourable sites in the rock.= porphyroblasts

• Fast T increase:– Nuclei form, but no time to grow before more nuclei form at

progressively less favourable sites.= fine-grained "hornfels"

Effect of heating rate

• Slow heating, sparse nucleation:biotite porphyroblasts

• Rapid heating, abundant nucleation:biotite hornfels

Both photomicrographs at same scale, ca. 2.5 mm across

Time-temperature-transformation and grain size distributionsO

vers

tep

Log time

v. fine

fine

medium

coarse

Heating rate

Principal factors controlling grain size patterns

• Heating rate• Reaction rate• Critical overstep

for nucleation