The Bancroft terrane and the associated Central Metasedimentary Belt boundary thrust zone represent the northern part of the Central Metasedimentary Belt (CMB) of the Canadian Grenville Province. Only a few direct pressure and temperature calculations based on phase equilibrium petrology methods exist in the central Bancroft terrane, and this study applies thermodynamic approaches such as garnet isopleth geothermobarometry to fill this gap and investigate the metamorphic history of the northern CMB. Four metapelitic rock samples were collected in the vicinity of the enigmatic Bancroft shear zone, which approximates the border between the Bancroft terrane and the Elzevir terrane to the south. Garnet isopleths for these samples only intersect if a certain amount of excess oxygen is added to the bulk rock composition corresponding to a Fe3+/Fetot ratio of 0.33–0.38. The northernmost sample records metamorphic peak conditions of approximately 1 GPa and 780 °C, whereas the southernmost sample, which is located in the Elzevir terrane, records a peak metamorphic pressure of approximately 0.9 GPa at a temperature of 520 °C. The latter result contradicts previous pressure estimates of the region and the proposed metamorphic field gradient but is based on a poorly constrained sample in terms of thermodynamic modeling. Hence, we conclude that the metamorphic field gradient in the northern CMB conceals two different P–T trajectories. Such a scenario is commonly observed in crustal thickening models and suggests that the cold upper plate (Elzevir terrane) was thrust over the warm lower plate (Bancroft terrane) in a northwesterly direction.

This paper introduces the software solution Bingo‐Antidote for thermodynamic calculations at equilibrium based on iterative thermodynamic models. It describes a hybrid strategy combining the strength of Gibbs energy minimization (GEM) and inverse thermobarometry models based on the comparison between the modelled and observed mineral assemblage, modes and compositions. The overall technique relies on quantitative compositional maps acquired by electron probe micro‐analyser for obtaining a mutually consistent set of observed data such as bulk rock and mineral compositions. Thus it offers the opportunity to investigate metamorphic rocks on a microscale. The scoring part Bingo integrates three statistical model quality factors Qasm for the assemblage, Qvol for the mineral modes, Qcmp for the mineral compositions combined in a global evaluation criterion Qtotal that quantifies how the model reproduces the observations for the investigated volume. The input parameters of GEM affecting the model quality such as pressure, temperature and eventually some components of the bulk composition (e.g. the molar amount of hydrogen, carbon or oxygen) or activity variables of fluids and gases (e.g. aH2O , aCO2 , f(O2)) can be optimized by inversion in Antidote using several mapping stages followed by a direct search optimization. Examples of iterative models based on compositional maps processed with Bingo‐Antidote demonstrate the utility of the program. In contrast to the qualitative interpretation of phase diagrams, the inversion maximizes the benefits of GEM and permits the derivation of statistically ‘optimal’ pressure–temperature conditions for well‐equilibrated samples. In addition, Bingo‐Antidote opens new avenues for petrological investigations such as the generation of chemical potential landscape maps.

Thermodynamic modeling of compositionally mapped microdomains and whole-rock compositions is used to constrain the pressure–temperature (P–T) evolution of sapphirine granulites and migmatitic paragneisses from the Gruf Complex of the Central Alps. The P–T paths and conditions estimated from granulite microdomains and whole-rock compositions are consistent with one another, indicating that the estimates from both types of compositions are accurate. The sapphirine granulites were heated to ultra-high temperature conditions of 900–1000 °C and 7.0–9.5 kbar as they were decompressed from ca. 800 °C and 9–12 kbar, resulting in garnet breakdown. In a subsequent step, nearly isothermal decompression led to the development of cordierite-bearing coronae and symplectites. By ca. 27 Ma, the sapphirine granulites had been exhumed to the midcrustal level of the migmatitic paragneisses, which were undergoing peak metamorphism at ca. 675–750 °C and 5–7 kbar. These results are consistent with a geodynamic model that invokes heat advection to the lower crust closely following the continental-subduction (ultra-high pressure) stage of the Alpine orogeny. The most plausible geodynamic model consistent with the results of this study is breakoff of a southward subducting lithospheric slab, resulting in asthenospheric mantle flow.

Accessory phosphate minerals, such as monazite and xenotime, are commonly used as geochronometers to provide timing constraints on tectonometamorphic events recorded by the host rocks within which they occur. However, the formation and recrystallization of accessory minerals, and their interaction with major mineral phases, are still poorly understood. As a consequence, linking ages obtained from accessory minerals to the metamorphic pressure-temperature (P-T) paths obtained primarily from major mineral phases, such as garnet, remains challenging. While there have been studies that have advanced our understanding of the behaviour of various accessory minerals through thermodynamic modelling, limited examples are available to test their reliability in natural metamorphic rocks. This study incorporates phosphate minerals into one of the most commonly used thermodynamic data sets for phase equilibria modelling. This refined methodology is tested by modelling the detailed P-T-time (t) paths for rocks from two different regions of the Himalaya, one subsolidus and one that experienced suprasolidus conditions. The results obtained from our integrated models yield direct information on the behaviour of monazite and xenotime growth/breakdown along the calculated P-T paths. This allows us to tie different age populations obtained from the accessory minerals directly to the P-T paths derived from major mineral phases and facilitates a refined understanding of the P-T-t histories of those rock specimens.

Numerical Modelling and Receiver Function Imaging of the Mantle Transition Zone in Different Geodynamic Scenarios

Deep mantle plumes and associated increased geotherms are expected to cause an upward deflection of the lower–upper mantle boundary and an overall thinning of the mantle transition zone between about 410 and 660 km depth. We use subsequent forward modelling of mineral assemblages, seismic velocities, and receiver functions to explain the common paucity of such observations in receiver function data. In the lower mantle transition zone, large horizontal differences in seismic velocities may result from temperature‐dependent assemblage variations. At this depth, primitive mantle compositions are dominated by majoritic garnet at high temperatures. Associated seismic velocities are expected to be much lower than for ringwoodite‐rich assemblages at undisturbed thermal conditions. Neglecting this ultralow‐velocity zone at upwelling sites can cause a miscalculation of the lower–upper mantle boundary on the order of 20 km.

The astonishing progress of personal computer technology in the past 30years as well as the availability of thermodynamic data and modeling programs have revolutionized our ability to investigate and quantify metamorphic processes. Equilibrium thermodynamics has played a central role in this revolution, providing simultaneously a physico-chemical framework and efficient modeling strategies to calculate mineral stability relations in the Earth's lithosphere (and beyond) as well as thermobarometric results. This Perspectives contribution provides a review of the ingredients and recipes required for constructing models. A fundamental requirement to perform thermodynamic modeling is an internally consistent database containing standard state properties and activity-composition models of pure minerals, solid solutions, and fluids. We demonstrate how important internal consistency is to this database, and show some of the advantages and pitfalls of the two main modeling strategies (inverse and forward modeling). Both techniques are commonly applied to obtain thermobarometric estimates; that is, to derive P-T (pressure-temperature) information to quantify the conditions of metamorphism. In the last section, we describe a new modeling strategy based on iterative thermodynamic models, integrated with quantitative compositional mapping. This technique provides a powerful alternative to traditional modeling tools and permits use of local bulk compositions for testing the assumption of local equilibrium in rocks that were not fully re-equilibrated during their metamorphic history. We argue that this is the case for most natural samples, even at high-temperature conditions, and that this natural complexity must be taken into consideration when applying equilibrium models.

Crystallization experiments of basaltic andesite mafic endmember from the 24 ka Lower Pollara eruption (Salina, Aeolian Islands, Italy) were investigated at 200 MPa, 950–1100 °C, in the H2O activity (aH2O) range ~0.3 to 1, and at two ranges of oxygen fugacity (fO2) between ~FMQ to FMQ+1 and ~FMQ+2 to FMQ+3.3 (log bars, FMQ is fayalite-magnetite-quartz). Comparison of the produced phase assemblages and phase compositions with the natural sample reveals that the storage conditions were ~1050 °C, ~2.8 wt% H2O in the melt (aH2O ~0.5), and relatively oxidizing (~FMQ+2.5). The composition of plagioclase in the groundmass indicates a period of cooling to ≤950 °C. The overall differentiation trends of the Salina volcanics can be explained by fractional crystallization close to H2O saturated conditions (~5 wt% H2O in the melt at 200 MPa) and most likely by accumulation of plagioclase, i.e., in basaltic andesites, and by various degree of mixing–mingling between the corresponding differentiates. The slightly elevated K2O contents of the most mafic basaltic andesites that can be found in the lowermost unit of the Lower Pollara pyroclastics reveal earlier processes of moderately hydrous fractional crystallization at higher temperature (>~1050 °C). Fractional crystallization with decreasing influence of H2O causes a moderate decrease of MgO and a significant increase of K2O relative to SiO2 in the residual liquids. It is exemplarily shown that the crystallization of SiO2-rich phases at high temperature and low aH2O of only moderately K2O-rich calc-alkaline basalts can produce shoshonitic and high potassic rocks similar to those of Stromboli and Volcano. This suggests that the observed transition from calc-alkaline to shoshonitic and high potassic volcanism at the Aeolian Arc over time can be initiated by a general increase of magmatic temperatures and a decrease of aH2O in response to the extensional tectonics and related increase of heat flow and declining influence of slab-derived fluids.

Thermodynamic datasets are essential for phase equilibrium computations, from which metamorphic pressure and temperature conditions of rocks can be estimated. In addition, they are used to model rock properties such as volume or density. The theoretical framework for thermodynamic volume modeling is imposed by the equation of state (EOS), which can be represented using many possible formulations. Until the 1990's, the Bridgman Power Series was a popular approach to model mineral volumes. Many experiments were fitted to this equation and input parameters for almost every mineral exist. Unfortunately, the equation has a drawback and does not allow the extrapolation of mineral volumes to pressures above 1 GPa. In this paper, an inverted EOS is introduced which uses the same input parameters as the Bridgman Power Series. Converting the fit parameters of the Bridgman Power Series to commonly used physical input parameters at reference conditions (K-00, K-00', and alpha(00), alpha'(00)) allows extrapolation of mineral volumes to very high pressure ( 20 GPa). The results from this study show in detail how the extended EOS improves the volumes of solid mineral phases such as coesite, jadeite and forsterite above 1 GPa, while retaining consistent volumes at low pressure temperature conditions. In this manner, the extended EOS also improves the phase equilibrium computations of the thermodynamic datasets built on the Bridgman Power Series. The proposed inverted EOS could be easily implemented by thermodynamic software packages with no modification of the dataset because the same input parameters are used.

We provide new insights into the prograde evolution of HP/LT metasedimentary rocks on the basis of detailed petrologic examination, element-partitioning analysis, and thermodynamic modelling of well-preserved Fe–Mg–carpholite- and Fe–Mg–chloritoid-bearing rocks from the Afyon Zone (Anatolia). We document continuous and discontinuous compositional (ferromagnesian substitution) zoning of carpholite (overall X Mg = 0.27–0.73) and chloritoid (overall X Mg = 0.07–0.30), as well as clear equilibrium and disequilibrium (i.e., reaction-related) textures involving carpholite and chloritoid, which consistently account for the consistent enrichment in Mg of both minerals through time, and the progressive replacement of carpholite by chloritoid. Mg/Fe distribution coefficients calculated between carpholite and chloritoid vary widely within samples (2.2–20.0). Among this range, only values of 7–11 correlate with equilibrium textures, in agreement with data from the literature. Equilibrium phase diagrams for metapelitic compositions are calculated using a newly modified thermodynamic dataset, including most recent data for carpholite, chloritoid, chlorite, and white mica, as well as further refinements for Fe–carpholite, and both chloritoid end-members, as required to reproduce accurately petrologic observations (phase relations, experimental constraints, Mg/Fe partitioning). Modelling reveals that Mg/Fe partitioning between carpholite and chloritoid is greatly sensitive to temperature and calls for a future evaluation of possible use as a thermometer. In addition, calculations show significant effective bulk composition changes during prograde metamorphism due to the fractionation of chloritoid formed at the expense of carpholite. We retrieve P–T conditions for several carpholite and chloritoid growth stages (1) during prograde stages using unfractionated, bulk-rock XRF analyses, and (2) at peak conditions using compositions fractionated for chloritoid. The P–T paths reconstructed for the Kütahya and Afyon areas shed light on contrasting temperature conditions for these areas during prograde and peak stages.

Understanding the relationships between density and spatio-thermal variations at convergent plate boundaries is important for deciphering the present-day dynamics and evolution of subduction zones. In particular, the interaction between densification due to mineralogical phase transitions and slab pull forces is subject to ongoing investigations. We have developed a two-dimensional subduction zone model that is based on thermodynamic equilibrium assemblage calculations and includes the effects of melting processes on the density distribution in the lithosphere. Our model calculates the “metamorphic density” of rocks as a function of pressure, temperature and chemical composition in a subduction zone down to 250 km. We have used this model to show how the hydration, dehydration, partial melting and fractionation processes of rocks all influence the metamorphic density and greatly depend on the temperature field within the subduction system. These processes are largely neglected by other approaches that reproduce the density distribution within this complex tectonic setting. Our model demonstrates that the initiation of eclogitization (i.e., when crustal rocks reach higher densities than the ambient mantle) of the slab is not the only significant process that makes the descending slab denser and generates the slab pull force. Instead, the densification of the lithospheric mantle of the sinking slab starts earlier than eclogitization and contributes significantly to slab pull in the early stages of subduction. Accordingly, the complex metamorphic structure of the slab and the mantle wedge has an important impact on the development of subduction zones.

This study presents the theory, applicability, and merits of the new THERIAK_D add‐on for the open source Theriak/Domino software package. The add‐on works as an interface between Theriak and user‐generated scripts, providing the opportunity to process phase equilibrium computation parameters in a programming environment (e.g., C or MATLAB®). THERIAK_D supports a wide range of features such as calculating the solid rock density or testing the stability of mineral phases along any pressure‐temperature (P‐T) path and P‐T grid. To demonstrate applicability, an example is given in which the solid rock density of a 2‐D‐temperature‐pressure field is calculated, portraying a simplified subduction zone. Consequently, the add‐on effectively combines thermodynamics and geodynamic modeling. The carefully documented examples could be easily adapted for a broad range of applications. THERIAK_D is free, and the program, user manual, and source codes may be downloaded from http://www.min.uni‐kiel.de/∼ed/theriakd/.

Thermodynamic databases are an essential tool to predict complex equilibrium mineral assemblages and mineral properties like mineral volumes. They consist of numerous thermodynamic data of various minerals, extracted from experiments. Each database follows its own methodology in calculating chemical and physical properties. Therefore a direct comparision between different database predictions was avoided, due to the contrasting methodolgies and philosophy. Here, we present a direct comparison between the databases of Berman [1] and Holland & Powell [2][3], focusing on mineral volumes [4]. For this propose, a reevaluation of the equation of states was nesscary. In this context, we identify an error also implemented in common thermodynamic softwares, concerning the calculation of excess volume. Even after treating the excess energy correctly, volumes show significant discrepancies between the different database predictions. These discrepancies impact geodynamic interpretations and geothermobarometrical estimations, due to the fact that the Gibbs free energy and rock density depends on mineral volumes. The imagination that pressure can vary by 4 kbar, temperature by 150 C or rock-density up to 30 %, by changing the thermodynamic database is dramatic. These enormous differences must be considered keeping in mind that calculations were done for well studied minerals (e.g. quartz and forsterite). The results play an important role for studies of geodynamic interpretations extracted from thermobarometric software packages like Perple_X, Theriak-Domino or Thermocalc. It is important to estimate the influence of the thermodynamic database on Gibbs free energy, volume and rock density. Summarizing, more experimental data will lead to a better comprehension of these discrepancies.

Away from active plate boundaries the relationships between spatiotemporal variations in density and geothermal gradient are important for understanding the evolution of topography in continental interiors. In this context the classic concept of the continental lithosphere as comprising three static layers of different densities (upper crust, lower crust, and upper mantle) is not adequate to assess long‐term changes in topography and relief in regions associated with pronounced thermal anomalies in the mantle. We have therefore developed a one‐dimensional model, which is based on thermodynamic equilibrium assemblage computations and deliberately excludes the effects of melting processes like intrusion or extrusions. Our model calculates the “metamorphic density” of rocks as a function of pressure, temperature, and chemical composition. It not only provides a useful tool for quantifying the influence of petrologic characteristics on density, but also allows the modeled “metamorphic” density to be adjusted to variable geothermal gradients and applied to different geodynamic environments. We have used this model to simulate a scenario in which the lithosphere‐asthenosphere boundary is subjected to continuous heating over a long period of time (130 Ma), and demonstrate how an anorogenic plateau with an elevation of 1400 m can be formed solely as a result of heat transfer within the continental lithosphere. Our results show that, beside dynamic topography (of asthenospheric origin), density changes within the lithosphere have an important impact on the evolution of anorogenic plateaus.