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Linking Microstructures and Reactions. Porphyroblasts, poikiloblasts, and pseudomorphing Part 1 Introduction, and some theory. A Metamorphic “Reaction”. Muscovite + Quartz = Andalusite + K-feldspar + H 2 O KAl 3 Si 3 O 10 (OH) 2 + SiO 2 = Al 2 SiO 5 + KAlSi 3 O 8 + H 2 O. - PowerPoint PPT Presentation
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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