Transcript Microstructures of Reaction Part 1

Linking Microstructures and Reactions
Porphyroblasts, poikiloblasts, and
pseudomorphing
Part 1
Introduction, 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 DG, 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) between
quartz and sapphirine
Symplectic intergrowths of Opx
with sapphirine and spinel
invading garnet
Typical metamorphic microstructures
Prograde metamorphism
Retrograde metamorphism
• Porphyroblasts
• Pseudomorphs
• Poikiloblasts
• Reaction rims
• Evidence that matrix grain size
has coarsened
• Intergrowths (symplectites,
etc.)
• Reactants and products not
generally in contact
• Grain size reduction
• Compositional zoning (if
present): prograde growth
zoning
• Reactants and products in
contact with each other
• Compositional zoning: frozenin diffusion gradients
Prograde metamorphic reaction processes
Involve several distinct steps
• Nucleation of new mineral:
• assemble initial cluster of
atoms into new structure
Breakdown
of reactants
in matrix
Growing grain
of product
• 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
Nucleus of
product
Transport to
growing surfaces
Heat Supply
Metamorphic reactions at the grain-boundary scale
Elementary reactions
Practical 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.
B
– 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 reactions
Precipitation, Dissolution
Grain boundary advances or retreats against fluid.
B
A
Overall reactions at the local scale
Ms + Qtz => And + Kfs + H2O
Driven by overall DG, 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 -> And
Ms -> Kfs; Qtz -> Kfs
• linked by transport in grain boundaries +/- intergranular fluid
Overstepping: energy and temperature
Large DS (e.g. dehydration)
DG
G
DT
Small DS (solid-solid)
G
DG
DT
T
T
Assuming 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
Activation energy
Reactants
DG (free energy difference)
Products
Thermally activated processes
Temperature dependence of rate described by Arrhenius relationship
Rate  A  e
•
where Ea = activation energy
(height of barrier),
pre-exponential factor A =
frequency factor
•
Net flow over barrier depends on
DG
Ea

RT
Rates of reaction at interfaces
(Transition State Theory)
Net rate
RN = R+ - R- = k · (1 – eDG/RT) · e-Ea/RT
close to equilibrium DG<<RT, this approximates to
RN = k · DG/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/mole
Diffusion in aqueous fluid
< 20 kJ/mole
Diffusion in grain boundaries
125 kJ/mole
Diffusion in mineral lattice
250 kJ/mole
Rate of nucleation
= A . e-G*/RT
where A = a frequency factor
Nucleation rate
and G* = an activation energy
Surface
energy
16 
*
G 

2
3 DG
3
Overstepping
log (rate per m3 per s)
Geometrical
factor
12
8
4
0
-4
-8
0
20
40
Overstep (delta T)
Interplay between nucleation and growth
growth on nuclei
lots
not
much
log overstep
hornfelsic texture
nucleation
lots
porphyroblasts
Fast
heating
not much
Slow
heating
log time
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 distributions
Principal factors
controlling grain
size patterns
• Heating rate
• Reaction rate
• Critical overstep
for nucleation
Overstep
v. fine
fine
medium
coarse
Heating rate
Log time