Metamorphism of metapelites: calculations of equilibrium assemblages and numerical simulations of the crystallization of garnet

Abstract This work uses a simplified model of equilibrium to predict the assemblage sequence and compositional zoning in garnet that should result from prograde metamorphism of common bulk compositions of pelitic rocks. An internally-consistent set of model thermodynamic data are derived for natural mineral compositions from natural assemblages. Equilibrium assemblages can be calculated for pelitic compositions with excess quartz and either muscovite or K-feldspar at any pressure and water pressure. The compositions and abundances of phases in equilibrium assemblages can be calculated where the elements Mg, Fe and Mn are exchanged among phases. The prograde metamorphic assemblage sequences and the effects of pressure on assemblages, predicted by the simulation method presented here, are similar enough to natural observations to suggest that the simulations can be used to analyse natural equilibrium and growth processes. The calculated phase diagrams at moderate and high crustal pressures explain the mineral assemblage sequence produced by prograde metamorphism in common pelitic compositions. Garnet appears by continuous reaction of biotite and chlorite as the garnet-biotite-chlorite divariant field migrates toward higher Mg/Fe ratios over the bulk composition. Staurolite appears in common bulk compositions when garnet and chlorite become incompatible. An aluminum silicate phase can appear when staurolite and chlorite react. Staurolite breaks down at an extremum point to produce garnet. Continuous reaction of biotite and sillimanite causes growth of abundant garnet. The reaction sequence involving garnet, staurolite and aluminum silicates is probably different at low pressure, but the main reason that staurolite and garnet are rare is the restricted compositional range over which their assemblages exist. Andalusite appears by the divariant reaction of chlorite and cordierite appears at low temperature in low pressure assemblages for common bulk compositions by the extremumpoint breakdown reaction of chlorite. Compositional zoning of garnet and the systematic variation of biotite composition in metamorphic sequences indicate that garnet is probably fractionated during growth. Fractionation of garnet causes garnet-consuming, univariant reactions to become multivariant. The metastable persistence of garnet should reduce the abundance and stability range of staurolite. Fractionation of even small quantities of garnet should deplete the equilibrating bulk composition of Mn, but have little effect otherwise. The simulations show that the prograde assemblage sequence in pelitic rocks can be complex in detail, with some assemblages lasting over temperature intervals of only a few degrees. The major prograde reactions that release water are the breakdown of chlorite to form garnet at low grade and the breakdown of muscovite at high grade. The volume of water released by formation of garnet at high grade is also important. These reactions have the capacity to buffer water pressure. The density of anhydrous pelitic rock increases markedly when chlorite breaks down and by the continuous reaction forming garnet at high grade. The heat content is controlled principally by heat capacity and continuous reactions. Discontinuous reactions have little thermal buffering capacity. Simulations of garnet fractionation show that commonly-observed garnet zoning profiles can be formed by garnet growth in the assemblage garnet-biotite-chlorite in common bulk compositions. A reversal of Fe-zoning in garnet can occur when garnet resumes growth above staurolite grade in the assemblage garnetbiotite-sillimanite. Discontinuities in zoning profiles can be caused only by disequilibrium. The disequilibrium can be due to either metastable persistence during a hiatus in growth or to growth by irreversible reaction. Because the appearance of garnet is controlled by a continuous rather than a discontinuous reaction, the appearance of garnet is very sensitive to bulk composition. The early development of garnet is also sensitive to the pressure and water pressure of metamorphism. As a consequence the first garnet isograd is of limited thermometric value. Metastable persistence of kyanite and manite at high grades could reduce the abundance of garnet and allow biotite to persist. Metastable persistence would also limit the of cordierite formation.     

A Natural Example of Metastable Reactions Involving Garnet and Sillimanite

The broad objective of this work is to develop models of reactionthat can be used to understand dynamic processes. The kineticsof reactions can be significant factors affecting heat and masstransfer, and the kinetic inhibition of equilibration enablesus to trace the history of natural samples. Samples were selectedfrom a metamorphic aureole for study because they show measurabledisequilibrium, and the approximate P—T path and timeof metamorphism are known. Detailed analysis of compositional variations of crystals andreaction textures suggests that biotite was being produced bythe breakdown of garnet at a faster rate than it was consumedby reaction with sillimanite. Some of the compositional variationsof biotite and cordierite can be explained by the process ofintergranular diffusion; however, the co-existence of metastablebiotite and sillimanite and the widespread distribution of Fe-richbiotite in the sample argue for a partial equilibrium modelfor which reaction rate was controlled by surface kinetic processes. Quantitative modelling was accomplished by breaking the overallreaction into three component reactions. The rate of one ofthese component reactions through time can be estimated fromgarnet zoning profiles, and the relative abundance of productphases is used then to estimate the absolute rates of the othercomponent reactions. A plausible interpretation of the datais that rate of dissolution of sillimanite was the rate-controllingprocess, and took place at a rate of 10^–7 to 10^–8cm/year in this sample. Analysis of this sample illustrates possible significant effectsof the kinetics of reaction in dry rocks in the deep crust.Even though biotite would have been unstable at final equilibriumand the overall reaction did not involve significant gain orloss of water, the particular kinetic path under taken resultedin production of biotite and consumption of water at the stageof reaction preserved in this sample.     

Designing a personal guidance system to aid navigation without sight: progress on the GIS component

Abstract

This paper reports on progress towards the development of a personal guidance system for a blind navigator. The system is being developed in light of the unique problems facing the blind traveller, which are discussed first. The system consists of four modules: a locator unit, a detailed spatial database, an algorithm for path selection and a user interface. Suggestions are offered for alternative ways of handling the locator problem using a global positioning system or a database query system. The nature of the geographic information system (GIS) to be used as a host for the database is discussed, followed by brief statement of the criteria for choosing an algorithm for path selection and suggestions on types of user interfaces best suited to the system. A report on a pilot-study GIS is presented. Special problems of database and system design are highlighted.     

Contact Metamorphic Reactions and Processes in the Mt. Tallac Roof Remnant, Sierra Nevada, California

Contact metamorphic facies in a large roof remnant within thecomposite Sierra Nevada batholith vary from actinolite hornfelsto pyroxene-hornfels facies. Hornblende-hornfels facies rockssurround most plutons. The pyroxene-hornfels facies, definedby the appearance of hypersthene in mafic rocks, occurs onlywhere two aureoles overlap. The rate of reaction of biotite plus quartz to hypersthene plusK feldspar plus water in the pyroxene-hornfels facies was controlledby the rate of escape of water. The reactants are still presentin the rocks; hypersthene was not stable where water pressurewas as high as load pressure but was able to form locally aswater vapor escaped and water pressure fell below load pressure. The reaction of epidote to andradite took place in the high-gradepart of the hornblende-hornfels facies and in the pyroxene-hornfelsfacies rocks. Hydrothermal experiments show that this reactiontakes place in the range 575 to 600 C at 2,000 bars. The highestcrystallization temperature within the hypersthene-bearing rocksis estimated to have been 750 C. The recrystallization temperatureof the clinopyroxene-bearing mafic hornfelses in the hornblende-hornfelsfacies is estimated to have been 625 to 650C, and that ofthe hornblende-bearing mafic hornfelses to have been 525 to550C. Interpretation of the fabric of the hypersthene rocks suggeststhat most of the heat was transferred to the walls by conductionand radiation. The main effect of hot magmatic vapor was toproduce a retrograde zone at the end of the recrystallizationperiod. The duration of the high-temperature phase of the metamorphismis estimated to be of the order of 10⁵ years.