Linking Microstructures and Reactions

1. Linking Microstructures and Reactions Porphyroblasts, poikiloblasts, and pseudomorphing Part 1 Introduction, and some theory

2. A Metamorphic “Reaction” Muscovite + Quartz = Andalusite + K-feldspar + H2O KAl3Si3O10(OH)2 + SiO2 = Al2SiO5 + KAlSi3O8 + H2O

3. 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

4. Granoblastic texture Result of mutual adjustment of grain boundaries in the solid state Preferred orientations Response to stress and deformation Typical metamorphic microstructure Not yet considering microstructures related to reactions

5. 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.

6. 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 spinelinvading garnet

7. 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 Typical metamorphic microstructures

8. Breakdown of reactants in matrix Growing grain of product Nucleus of product Transport to growing surfaces Heat Supply 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

9. B A B 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.

10. Overall reactions at the local scale Ms + Qtz => And + Kfs + H2O Driven by overall DG, partitioned among the elementary reactions Mechanism 1may involve at least: • 2 dissolution reactions, • 2 precipitation reactions, • linked by transport in intergranular fluid Mechanism 2may involve at least: • 4 replacement reactionsMs -> And; Qtz -> AndMs -> Kfs; Qtz -> Kfs • linked by transport in grain boundaries +/- intergranular fluid

11. Large DS (e.g. dehydration) Small DS (solid-solid) DG G G DG DT DT T T Overstepping: energy and temperature 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.

12. 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 DG Activation energy Reactants DG (free energy difference) Products Energy barriers and reaction rates

13. Rates of reaction at interfaces (Transition State Theory) Net rateRN = R+ - R- = k · (1 – eDG/RT) · e-Ea/RTclose to equilibrium DG<<RT, this approximates toRN = 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

14. Nucleation rate 12 8 Surface energy Geometrical factor 4 log (rate per m3 per s) 0 -4 -8 0 20 40 Overstep (delta T) Overstepping Rate of nucleation = A . e-G*/RT where A = a frequency factor and G* = an activation energy

15. growth on nuclei lots not much hornfelsic texture log overstep nucleation lots porphyro-blasts Fast heating not much Slow heating log time Interplay between nucleation and growth

16. 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"

17. Slow heating, sparse nucleation:biotite porphyroblasts Rapid heating, abundant nucleation:biotite hornfels Effect of heating rate Both photomicrographs at same scale, ca. 2.5 mm across

18. v. fine fine Overstep medium coarse Heating rate Log time Time-temperature-transformation and grain size distributions Principal factors controlling grain size patterns • Heating rate • Reaction rate • Critical overstep for nucleation