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##### Kinetics and Dynamics of melts and crystals

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**Thermodynamics requires equilibrium**At equilibrium nothing happens Kinetics define the path towards equilibrium Viscosity: shear stress (force/area, ) that needs to be overcome to move a certain distance: Stress results in flow deformation measured as a velocity gradient dv/dy or change in shape, strain rate d/dt. =dv/dy=d/dt Transport phenomena Materials, atoms, energy Kinetics and Dynamics of melts and crystals**Chemical diffusion**Related to closure temperature for minerals Closure temperature: temperature for a mineral below which there is no significant exchange with its surroundings. Three routes of diffusion: Surface Grain boudary Volume Ficks’ first law: The flux of material through a unit area is proportional to the concentration gradient: Ji=-Di(c/x) D: Diffusion coefficient (cm2/sec) Fick’s first law holds for steady state In a time dependent system Ficks’ second Law describes the time dependent concentration variations:**Kinetics-crystal growth**Abrupt changes in trace element composition. Causes for abrupt changes? Consequences for crystal growth**Chemical diffusion**Diffusion coefficient is dependent on temperature. In fluid governed by the Stokes-Einstein equation: In solid dependence can be formulated as the Arrhenius equation: D=D0exp(-Ea/RT) Different mechanism of diffusion Diffusion in melts much faster than solids**Chemical diffusion**Good first order estimate of diffusion distance: x=√(Dt)**Diffusion of heat**Equation governing diffusion of heat very similar to chemical diffusion k is thermal conductivity Rock 2-3W/m.degree Thermal diffusivity, =k/C, where C is specific heat. is ability to conduct heat. Thermal diffusivity 10-4 to 10-5 cm2/sec. Contact aureole of a 35 Ma batholith in 1.4 Ga country rock**Crystallization-1**Why is undercooling required before crystallization takes place? Why is overheating required before boiling occurs? Surface or interfacial energy units J/cm2. Euhedral crystals, grow without tension or restriction. Anhedral crystals, bounded by non-rotational surfaces**Nucleation-1**Two independent processes: nucleation and growth Influences the texture of the rock. Nucleus: Angstroms in size Nucleation Homogeneous: spontaneous fluctuations in uniform disordered phase. Heterogeneous: nucleation on an existing surface (seed). Homogeneous nucleation: a embryotic crystal will become stable when the energy released by crystallization is larger then the surface energy**Nucleation-2**Nucleii become stable when they are larger than the “critical” radius rc. Critical value where G will decrease or G/r=0, or How does Gr vary with T? Gr-TS Surface energy correlates with viscosity, low viscosity fluids lower surface energy. Rapid cooling leads to greater supersaturation? Minerals with large entropy change will nucleate at less undercooling Large entropy change: large change in structure**Crystal Growth**Degree of undercooling effects crystal shape With increasing degree of undercooling: Skeletal-dendritic-feathery-spherulite: Important componants: Interface phenomena-attaching of atoms Diffusion of ions thorugh the melt Removal of heat from the crystal surface Decrease in growth rate with large degree of undercooling due to increased viscosity of melt • Kink, screw dislocation are best places for growth as the new unit will be surrounded on three sites by other units, next down is the step and least favorable way to grow is through addatom. • Crystal growth is often not the same in all directions**Crystal growth-3**Boundary layer control Grainsize determined by nucleation density If growth rate is slow many nucleii can form: small crystal size, high cooling rate: How?? • Rapid ascent • Release of volatiles**Overprinting**Melt inclusion in Qtz Partial resorbtion Reaction rim Qtz xenocryst Oscillatory zoning; not strictly Dunite 1200 grain boundary triple junction Smallest surface area Ostwald ripening. Decrease in surface area**Vesiculation**Growing bubbles Bubble formation easier in melts that have some crystals in them: heterogeneous nucleation In static melt bubble is spherical High density of bubbles: pumice or scoria**Fibrous pumice 93% void**Bubble growth Maximum packing as uniform spheres 74%, non-uniform spheres 86% Many pumices and scoria:70-80%; reticulite 95-98% voids Growth influenced by: Melt viscosity Coalescense Diffusion in melt Ostwald ripening Rate of ascent, loss of heat, decompression Volatile concentration and solubility Explosive volcanism: 3-6wt% water Exsolution of water out of melt increasing melt viscosity, decreases melt density. Faster ascent viscous melt exceed relaxation time: bubbles rupture the walls: explosive volcanism, fragmentation Presence of lapilli, ask and blocks: (no burst walls), uneven distribution of strain. Reticulite**Kinetic paths and fabric**Fabric are noncompositional properties Fabric related to crystallization path Glass: highly disordered High silica glass: obsidian Contains crystallites(very small xxs)**Glass**Perlitic, hydrated glass Vitrophyric: flow layered Layering made by micro crystals Spherulitic, sperules of microcrystalline material**Mozaic of small xx, too small to be identified by**microscope: High xx nucleation rate versus growth rate Aphyric: devoid of phenocrysts Cryptocrystalline: xx observed by X-ray Microcrystalline: xx observed by microscope Porphyritic: Bimodal xx-size population Aphanitic microcrystalline Porphyritic aphanitic Intergranular: random orientation of microlites Felsitic, microcrystalline, porphyritic, aphanitic texture**XX can be observed and identified by eye**Phaneritic Magmatic intrusions. Slower cooling Equigranular: single population of xx-size Large grainsize: slow cooling either in place or in a magma chamber Seriate texture: pegmatite: large range of xx sizes. Open system behavior**Phenocrysts set in a groundmass**• Two stage cooling: • Slow cooling, small undercooling, followed by rapid heat loss • But what about porphyritic intrusives: • Different nucleation rates. Alkali feldspar is slow to nucleate. In silicic systems solidus and liquidus are close together (they are near-eutectic melts) large undercooling not possible • Sudden change in composition: degassing, release of water would result in sudden shift in the solidus Porphyritic Poikolitic or ophitic Porphyritic phaneritic granodiorite Oikocrysts (large xx) surrounded by smaller grains**Grain shape**• Euhedral=hypidiomorhic=uninhibited crystallization • Can be skeletal, dendritic and feathery. • Skeletal can cause melt inclusions • Gradation to: subhedral: partly bounded by crystal phases • To anhedral or xenomorphic: not bounded by own crystal phases • Hypidiomorphic: mixture of euhedral, subhedral and anhedral grains Poikolitic texture of diabase with euhedral plagioclase xx Hypidiomorphic texture of gabbro, euhedral magnetite(black) and plagioclase and olivines among anhedral pyroxenes; (a) isotropic fabric; (b) laminated fabric (anisotropic)**Inhomogeneous grains Crystallization path**Zoning: normal, reversed, oscillatory Reaction rims mineral out of equilibrium with melt. Rapakivi texture plagioclase rimming an alkali feldspar Subsolidus decomposition and exsolution Andasine core, thin rim of labradorite**Interpretation of textures**Textures and fabric are the results of processes occurring on geological time scales Order of crustallization criteria: Phenocryst and groundmass mineral comparison Reaction rims Mineral inclusions Relative euhedralism Three different pathways for creating ophitic texture Need to be careful with euhedral criteria**Exsolution of fluids**Vesicular: containing vesicles Amygdaloidal: vesicles are filled with secondary phase; vesicles are now called amygdules Vesicular silisic glass: pumice or pumiceous texture Basaltic and andesitic pumice: scoria Vugs: exsolved fluids in crystalline magmas Miarolitic cavity: vugs in phaneritic rocks; these void spaces often have euhedral xx growing in it.**Fabrics and fragmentation**Fragmented material: volcanoclastic Categorize them by Size: Ash (<2mm), lapilli (2-64mm),bombs (>64mm) Composition: lithic: clasts polygranular, vitroclasts: clasts of glass Heritage: cognate: derived from the magma; xenocrysts and xenoliths Process of fragmentation: autoclastic: blocks on the margins of lavaflows, relatively low energy. Pyroclastic process: violent eruption produces ejecta and tephra. Groundhugging avalanches: pyroclastic flows: Cause of explosiveness: Exsolution of volatiles Hydromagmatic: addition of water Consolidation: Welded tuff**Anisotropic fabric**Flow layering**Stress and deformation**Normal stress:perpendicular to plane Shear stress: tangential to the plane Hydrostatic press or confining pressure: the same in all directions Deformation result of non-hydrostatic pressures. Deformation: Translation (displacement) Roration Distortion (strain) Elastic behavior Yield strength maximum stress underwhich a body still behaves elastic. At higher stresses it behave splastic. Viscous behavior: Newtonian stress and strain rate are linear related Brittle behavior: breaking apart Ductile behavior material flows (still behaves plastic)**Rheology of magma**Magma has resistance to flow: stress and strain rate are not linear related. Non-Newtonian fluid. Magma has: Yield strength, y. Shear strength. , has to overcome yield strength before deformation will take place: =y+a(dv/dt), a is apparent viscosity Crystals increase viscosity: a= +(1-BX)-2.5. X is volume of crystals, B=1.35**For Newtonian fluids type of flow (laminar or turbulet) is**determined by its Reynolds number Re=D/. V is velocity, D is hydraulic radius (geometry factor): 4 times the cross sectional area perpendicular to flow divided by the wetted perimeter; for pipe D=4r2/2r. Magma flow**Density**Melt density: 2.8-2.2g cm-3. Extrapolating to other P, T: coefficient of isothermal compressibility:; and Coefficient of (isobaric) expansion, . For crystalline solids =1-2 x 10-11 Pa-1, =1-5x10-5K-1.**Buoyancy**Upward force: positive bouyancy Terminal velocity given by Stokes’s law: Conductive cooling**Convection**Conduction and convection: reaction to thermal gradient. Thermal gradient result in compositional and density gradients • In magma chamber: conductive heat loss at the top results in a T-gradient and results in cooler and denser melts at the top. • Cool melts sink: starts convection due to gravitational instability. • Whether convection will take place depends on the Raleigh number: dimensionless number: ratio of buoyancy forces obver resistive forces (drag): h=vertical thickness of fluid