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

Metamorphic “reactions” Notional reaction Balanced chemical equation in a model system, e.g. Ms + Qtz = And + Kfs + H 2 O, 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 + H 2 O 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 + H 2 O 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) between quartz and sapphirine Symplectic intergrowths of Opx with 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 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. –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. ABB

Overall reactions at the local scale Ms + Qtz => And + Kfs + H 2 O Driven 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 -> And Ms -> 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G TT T G GG T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 Thermally activated processes Temperature dependence of rate described by Arrhenius relationship where E a = activation energy (height of barrier), pre-exponential factor A = frequency factor Net flow over barrier depends on  G Activation energy Reactants Products  G (free energy difference)

Rates of reaction at interfaces (Transition State Theory) Net rate R N = R + - R - = k · (1 – e G/RT ) · e -E a /RT close to equilibrium G<<RT, this approximates to R N = k · G/RT · e -E a /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/growth60 kJ/mole Diffusion in aqueous fluid< 20 kJ/mole Diffusion in grain boundaries125 kJ/mole Diffusion in mineral lattice250 kJ/mole

Rate of nucleation = A. e -G*/RT where A = a frequency factor and G* = an activation energy Nucleation rate Overstep (delta T) log (rate per m3 per s) Surface energy Geometrical factor Overstepping

Interplay between nucleation and growth log time log overstep growth on nuclei nucleation not much lots not much lots Fast heating Slow heating 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 distributions Overstep Log time v. fine fine medium coarse Heating rate Principal factors controlling grain size patterns Heating rate Reaction rate Critical overstep for nucleation