THERIA_G: a software program to numerically model prograde garnet growth

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 diffusio

Prograde garnet growth along complex P-T-t paths: results from numerical experiments on polyphase garnet from the Wölz Complex (Austroalpine basement)

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 ∼3.8kbar 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 ∼10kbar and a maximum in P of ∼10.4kbar at ∼610°C. For the heating rate during the growth of the second phase of garnet, average rates faster than 50°CMa−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 Cretaceou

Permian high-temperature metamorphism in the Western Alps (NW Italy)

During the late Palaeozoic, lithospheric thinning in part of the Alpine realm caused high-temperature low-to-medium pressure metamorphism and partial melting in the lower crust. Permian metamorphism and magmatism has extensively been recorded and dated in the Central, Eastern, and Southern Alps. However, Permian metamorphic ages in the Western Alps so far are constrained by very few and sparsely distributed data. The present study fills this gap. We present U/Pb ages of metamorphic zircon from several Adria-derived continental units now situated in the Western Alps, defining a range between 286 and 266 Ma. Trace element thermometry yields temperatures of 580-890°C from Ti-in-zircon and 630-850°C from Zr-in-rutile for Permian metamorphic rims. These temperature estimates, together with preserved mineral assemblages (garnet-prismatic sillimanite-biotite-plagioclase-quartz-K-feldspar-rutile), define pervasive upper-amphibolite to granulite facies conditions for Permian metamorphism. U/Pb ages from this study are similar to Permian ages reported for the Ivrea Zone in the Southern Alps and Austroalpine units in the Central and Eastern Alps. Regional comparison across the former Adriatic and European margin reveals a complex pattern of ages reported from late Palaeozoic magmatic and metamorphic rocks (and relics thereof): two late Variscan age groups (~330 and ~300 Ma) are followed seamlessly by a broad range of Permian ages (300-250 Ma). The former are associated with late-orogenic collapse; in samples from this study these are weakly represented. Clearly, dominant is the Permian group, which is related to crustal thinning, hinting to a possible initiation of continental rifting along a passive margin

Characterisation of a garnet population from the Sikkim Himalaya: insights into the rates and mechanisms of porphyroblast crystallisation

The compositional zoning of a garnet population contained within a garnet-grade metapelitic schist from the Lesser Himalayan Sequence of Sikkim (India) provides insight into the rates and kinetic controls of metamorphism, and the extent of chemical equilibration during porphyroblast crystallisation in the sample. Compositional profiles across centrally sectioned garnet crystals representative of the observed crystal size distribution indicate a strong correlation between garnet crystal size and core composition with respect to major end-member components. Systematic steepening of compositional gradients observed from large to small grains is interpreted to reflect a progressive decrease in the growth rate of relatively late-nucleated garnet as a result of an increase in interfacial energies during progressive crystallisation. Numerical simulation of garnet nucleation and growth using an equilibrium approach accounting for chemical fractionation associated with garnet crystallisation reproduces both the observed crystal size distribution and the chemical zoning of the entire garnet population. Simulation of multicomponent intracrystalline diffusion within the population indicates rapid heating along the pressure–temperature path, in excess of 100 ∘C Myr- 1. Radial garnet growth is correspondingly rapid, with minimum rates of 1.4 mm Myr- 1. As a consequence of such rapid crystallisation, the sample analysed in this study provides a close to primary record of the integrated history of garnet nucleation and growth. Our model suggests that nucleation of garnet occurred continuously between incipient garnet crystallisation at ∼ 520 ∘C, 4.5 kbar and peak metamorphic conditions at ∼ 565 ∘C, 5.6 kbar. The good fit between the observed and predicted garnet growth zoning suggests that the departure from equilibrium associated with garnet nucleation and growth was negligible, despite the particularly fast rates of metamorphic heating. Consequently, rates of major element diffusion in the intergranular medium during garnet crystallisation are interpreted to have been correspondingly rapid. It is, therefore, possible to simulate the prograde metamorphic history of our sample as a succession of equilibrium states of a chemical system modified by chemical fractionation associated with garnet crystallisation

Petrological consequences of variations in metamorphic reaction affinity

The extent to which kinetic barriers to nucleation and growth delay the onset of prograde metamorphic reaction, commonly known as overstepping, is related to the macroscopic driving force for reaction, termed reaction affinity. Reaction affinity is defined in the context of overstepping as the Gibbs free-energy difference between the thermodynamically stable, but not-yet-crystallized, products and the metastable reactants. Mineral reactions which release large quantities of H2O, such as chlorite-consuming reactions, have a higher entropy/volume change, and therefore a higher reaction affinity per unit of temperature/pressure overstep, than those which release little or no H2O. The former are expected to be overstepped in temperature or pressure less than the latter. Different methods of calculating reaction affinity are discussed. Reaction affinity 'maps' are calculated that graphically portray variations in reaction affinity on equilibrium phase diagrams, allowing predictions to be made about expected degrees of overstepping. Petrological consequences of variations in reaction affinity include: (i) metamorphic reaction intervals may be discrete rather than continuous, especially in broad multivariant domains across which reaction affinity builds slowly; (ii) reaction intervals may not correspond in a simple way to reaction boundaries and domains in an equilibrium phase diagram, and may involve metastable reactions; (iii) overstepping can lead to a 'cascade effect', in which several stable and metastable reactions involving the same reactant phases proceed simultaneously; (iv) fluid generation, and possibly fluid presence in general, may be episodic rather than continuous, corresponding to discrete intervals of reaction; (v) overstepping related to slowly building reaction affinity in multivariant reaction intervals may account for the commonly abrupt development in the field of certain index mineral isograds; and (vi) P-T estimation based on combined use of phase diagram sections and mineral modes/compositions on the one hand, and classical thermobarometry methods on the other, may not agree even if the same thermodynamic data are used. Natural examples of the above, both contact and regional, are provided. The success of the metamorphic facies principle suggests that these kinetic effects are second-order features that operate within a broadly equilibrium approach to metamorphism. However, it may be that the close approach to equilibrium occurs primarily at the boundaries between the metamorphic facies, corresponding to discrete intervals of high entropy, dehydration reaction involving consumption of hydrous phases like chlorite (greenschist-amphibolite facies boundary) and mica (amphibolite-granulite facies boundary), and less so within the facies themselves. The results of this study suggest that it is important to consider the possibility of reactions removed from equilibrium when inferring the P-T-t evolution of metamorphic rocks

Quantitative analysis of fatigue cracks in laminated carbon fibre-reinforced polymer composites using micro-computed tomography

A phenomenological study was carried out on laminated carbon fibre-reinforced polymer composites subjected to constant amplitude fatigue loading. Visualization of damage progression was performed using a high-resolution Skyscan micro-computed tomography unit which provided detailed information on propagation of initially occurring cracks throughout fatigue life at specific intervals. Quantitative analysis of image sequences of virtual cross-sections throughout the three orthogonal planes of the sample resulted in defining fatigue crack growth rates, da/dn for each plane, which was interpreted in terms of the three damage modes: opening (mode I), in-plane shear (mode II) and out-of-plane shear (mode III). By applying linear elastic fracture mechanics laws, strain energy release rates were calculated and then used in a cohesive zone model formulation to define model parameters. Considering a bi-linear triangular cohesive zone model curve, maximum traction and maximum separation were calculated for each of the three damage modes, differentiating between modes II and III in a novel manner

Toward a quantitative model of metamorphic nucleation and growth

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/m2 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