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The formation of metamorphic garnet during isobaric heating is simulated on the basis of the classical nucleation and reaction rate theories and Gibbs free energy dissipation in a multi-component model system. The relative influences are studied of interfacial energy, chemical mobility at the surface of garnet clusters, heating rate and pressure on interface-controlled garnet nucleation and growth kinetics. It is found that the interfacial energy controls the departure from equilibrium required to nucleate garnet if attachment and detachment processes at the surface of garnet limit the overall crystallization rate. The interfacial energy for nucleation of garnet in a metapelite of the aureole of the Nelson Batholith, BC, is estimated to range between 0.03 and 0.3 J/m at a pressure of ca. 3,500 bar. This corresponds to a thermal overstep of the garnet-forming reaction of ca. 30°C. The influence of the heating rate on thermal overstepping is negligible. A significant feedback is predicted between chemical fractionation associated with garnet formation and the kinetics of nucleation and crystal growth of garnet giving rise to its lognormal-shaped crystal size distribution. [ABSTRACT FROM AUTHOR]

Garnet in metapelites from the Wölz Complex of the Austroalpine crystalline basement east of the Tauern Window characteristically consists of two growth phases, which preserve a comprehensive record of the geothermal history during polymetamorphism. From numerical modelling of garnet formation, detailed information on the pressure–temperature–time ( P–T–t) evolution during prograde metamorphism is obtained. In that respect, the combined influences of chemical fractionation associated with garnet growth, modification of the original growth zoning through intragranular diffusion and the nucleation history on the chemical zoning of garnet as P and T change during growth are considered. The concentric chemical zoning observed in garnet and the homogenous rock matrix, which is devoid of chemical segregation, render the simulation of garnet growth through successive equilibrium states reliable. Whereas the first growth phase of garnet was formed at isobaric conditions of ∼3.8 kbar at low heating/cooling rates, the second growth phase grew along a Barrovian P–T path marked with a thermal peak of ∼625°C at ∼10 kbar and a maximum in P of ∼10.4 kbar at ∼610°C. For the heating rate during the growth of the second phase of garnet, average rates faster than 50°C Ma−1 are obtained. From geochronological investigations the first growth phase of garnet from the Wölz Complex pertains to the Permian metamorphic event. The second growth phase grew in the course of Eo-Alpine metamorphism during the Cretaceous. [ABSTRACT FROM AUTHOR]

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure–temperature–time ( P– T– t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P– T– t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P– T– t trajectory. The results of garnet growth simulation can be used to infer the P– T– t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion. [ABSTRACT FROM AUTHOR]

Magnesian metamorphic rocks with metapelitic mineral assemblage and composition are of great interest in metamorphic petrology for their ability to constrain P– T conditions in terranes where metamorphism is not easily visible. Phase–assemblage diagrams for natural and model magnesian metapelites in the system KFMASH are presented to document how phase relationships respond to water activity, bulk composition, pressure and temperature. The phase assemblages displayed on these phase diagrams are consistent with natural mineral assemblages occurring in magnesian metapelites. It is shown that the equilibrium assemblages at high pressure conditions are very sensitive to a(H2O). Specifically, the appearance of the characteristic HP assemblage chloritoid–talc–phengite–quartz (with excess H2O) in the magnesian metapelites of the Monte Rosa nappe (Western Alps) is due to the reduction of a(H2O). Furthermore, the mineral assemblages are determined by the whole-rock FeO/(FeO+MgO) ratio and effective Al content X A as well as P and T. The predicted mineral associations for the low- and high- X A model bulk compositions of magnesian metapelites at high pressure are not dependent on the X A variations as they show a similar sequence of mineral assemblages. Above 20 kbar, the prograde sequence of assemblages associated with phengite (with excess SiO2 and H2O) for low- and high- X A bulk compositions of magnesian metapelites is: carpholite–chlorite → chlorite–chloritoid → chloritoid–talc → chloritoid–talc–kyanite → talc–garnet–kyanite → garnet–kyanite ± biotite. At low to medium P– T conditions, a low- X A stabilises the phengite-bearing assemblages associated with chlorite, chlorite + K-feldspar and chlorite + biotite while a high- X A results in the chlorite–phengite bearing assemblages associated with pyrophyllite, andalusite, kyanite and carpholite. A high- X A magnesian metapelite with nearly iron-free content stabilises the talc–kyanite–phengite assemblage at moderate to high P– T conditions. Taking into account the effective bulk composition and a(H2O) involved in the metamorphic history, the phase–assemblage diagrams presented here may be applied to all magnesian metapelites that have compositions within the system KFMASH and therefore may contribute to gaining insights into the metamorphic evolution of terranes. As an example, the magnesian metapelites of the Monte Rosa nappe have been investigated, and an exhumation path with P– T conditions for the western roof of the Monte Rosa nappe has been derived for the first time. The exhumation shows first a near-isothermal decompression from the Alpine eclogite peak conditions around 24 kbar and 505°C down to approximately 8 kbar and 475°C followed by a second decompression with concomitant cooling. [ABSTRACT FROM AUTHOR]

A theoretical model of the polarization properties of a 'Zeiss-type' coelostat is presented and discussed in detail. The Muller matrix describing the modification of the Stokes vector of the incident radiation as a result of the multiple reflections on the coelostat mirrors is derived as a function of the solar coordinates, the geometrical configuration of the coelostat, and the parameters defining the optical properties of the mirrors. These parameters, or more particularly, the index of refraction n and the extinction coefficient k, have been evaluated by means of laboratory measurements performed on a series of specimens having characteristics similar to those of the coelostat mirrors. The geometry of the coelostat configuration is described in full detail. The theoretical model has been then particularized to the case of the Donati Solar Tower in Arcetri, and some experimental measurements have been performed to check the correctness of the model. These measurements show the basic adequacy of the mathematical model, although some offset terms are found in the Stokes parameters U and V. [ABSTRACT FROM AUTHOR]