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THERIAK_D: An add‐on to implement equilibrium computations in geodynamic models
Abstract
[1] 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/.
... Such complex solutions are characteristic of multi-site interactions, each site behaving in a different way, or of reciprocal relationships involving end-members dependent in composition that can be treated as dependent in G (Powell & Holland, 1993b) or independent (Wood & Nicholls, 1978;Vidal et al., 2005). A model for clinopyroxene involving four end-members-diopside (CaMgSi 2 O 6 ), hedenbergite (CaFeSi s O 6 ), jadeite (NaAlSi 2 O 6 ) and omphacite (Ca 0Á5 Na 0Á5 Al 0Á5 Mg 0Á5 Si 2 O 6 )-is complex, because omphacite is a linear combination of diopside and jadeite with respect to composition, but not with respect to G, as ordering within the split M2 and M1 sites Molar volume data for forsterite as a function of pressure (or depth), calculated along a thermal gradient of 8 C km -1 calculated for different EOS using Theriak_D (Duesterhoeft & de Capitani, 2013). Dataset HP98 uses the Murnaghan EOS; an inflection point is observed at 24 kbar, which is a typical feature of this type of function; the volume is predicted to decrease from 0 to 6 kbar. ...
... This principle has been largely followed by THERIAK-DOMINO, PERPLE_X and GIBBS. As a result, several add-ons and extensions have been developed: LitMod (Afonso et al., 2008), LitMod3D (Fullea et al., 2009), PreMDB (Siret et al., 2009), PHMEGP (Zunino et al., 2011) and Rcrust (Mayne et al., 2016) for PERPLE_X; Theriak_D (Duesterhoeft & de Capitani, 2013), Theria_G (Gaidies et al., 2008), GRTMOD and myDomino (by E. Kelly) for THERIAK-DOMINO. ...
The astonishing progress of personal computer technology in the past 30 years 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.
... Gibbs free-energy minimizations were performed using Theriak-Domino. The Theriak_D add-on for the Theriak-Domino software package supports testing the stability of mineral phases along any P-T path and P-T grid or calculating the solid rock density (Duesterhoeft and de Capitani, 2013). Bulk composition used for calculation represented the rock sample analyzed by X-ray fluorescence spectroscopy at Potsdam University (Table 8). ...
Metamorphic evolution of an epidote–lawsonite blueschist sample characterized by the coexistence of lawsonite and epidote from Sivrihisar area (Tavşanlı Zone) was studied herein in terms of petrology and mineral equilibria. Based on the textural evidence and phase composition, 2 prograde stages, defined by assemblage-I and -II, and 1 retrograde stage were recognized. Assemblage-I indicates epidote-blueschist facies conditions (12 ± 1 kbar / 485 ± 10 °C). Assemblage-II is characterized by the coexistence of epidote and lawsonite (17 ± 1 kbar / 515 ± 10 °C) corresponding to the interface of lawsonite blueschist and epidote blueschist facies. Phase diagram calculations and mineral compositions revealed that along this interface, an equilibrium field with lawsonite and epidote is stable. This closed-equilibrium field is controlled by high aH2O and an elevated Fe3+/Al ratio of minerals. Pressure-temperature (P–T) estimates and textural observations indicated a counter-clockwise path during the subduction and exhumation history. The preservation of lawsonite and epidote during the retrograde stage pointed to the fact that the path followed the stability field of lawsonite and epidote during exhumation.
... to investigate the LBC compositions using Bingo-Antidote. For modelling, the GEM are performed by theriAk (de Capitani & Brown, 1987) and were implemented into mAtlAB ® using the strategy of the addon theriAk_d (Duesterhoeft & de Capitani, 2013). Five groups of recipes are defined in Table 2 and briefly described in the following. ...
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 for the assemblage, for the mineral modes, for the mineral compositions combined in a global evaluation criterion 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. , , 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.
... The model presented in this report differs from those reviewed above in that it is strongly based on the observation of preserved garnet growth zones in natural rocks; no provision for intracrystalline diffusion is made. GRTMOD is written in MATLAB © and interacts with Theriak (de Capitani & Brown, 1987) using the extension Theriak_D (Duesterhoeft & de Capitani, 2013). ...
This contribution presents an approach and a computer program (GRTMOD) for numerical simulation of garnet evolution based on compositions of successive growth zones in natural samples. For each garnet growth stage, a new local effective bulk composition is optimized, allowing for resorption and/or fractionation of previously crystallized garnet. The successive minimizations are performed using the Nelder-Mead algorithm; a heuristic search method. An automated strategy including two optimization stages and one refinement stage is described and tested. This program is used to calculate pressure-temperature (P-T) conditions of crystal growth as archived in garnet from the Sesia Zone (Western Alps). The compositional variability of successive growth zones is characterized using standardized X-ray maps and the program XMapTools. The model suggests that Permian garnet cores crystallized under granulite-facies conditions at T>800 °C and P = 6 kbar. During Alpine times, a first garnet rim grew at eclogite-facies conditions (650 °C, 16 kbar) at the expense of the garnet core. A second rim was added at lower P (∼11 kbar) and 630 °C. In total, garnet resorption is modeled to amount to ∼9 vol% during the Alpine evolution; this value is supported by our observations in X-ray compositional maps. © 2017 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart.
... The electronic annexes comprise a modified version of the Theriak-Domino software package (de Capitani and Petrakakis, 2010) including the extended EOS, a new database file JUN92hp.bs with the examples of this study and the THERIAK_D add-on (Duesterhoeft and de Capitani, 2013). Berman (1988) that were fitted to the experimental data of Levien and Prewitt (1981) up to 5.19 GPa. ...
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 (κ00, κ′00, and α00, α′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.
XMapTools is a MATLAB©-based graphical user interface program for electron microprobe X-ray image processing, which can be used to estimate the pressure–temperature conditions of crystallization of minerals in metamorphic rocks. This program (available online at http://www.xmaptools.com) provides a method to standardize raw electron microprobe data and includes functions to calculate the oxide weight percent compositions for various minerals. A set of external functions is provided to calculate structural formulae from the standardized analyses as well as to estimate pressure–temperature conditions of crystallization, using empirical and semi-empirical thermobarometers from the literature. Two graphical user interface modules, Chem2D and Triplot3D, are used to plot mineral compositions into binary and ternary diagrams. As an example, the software is used to study a high-pressure Himalayan eclogite sample from the Stak massif in Pakistan. The high-pressure paragenesis consisting of omphacite and garnet has been retrogressed to a symplectitic assemblage of amphibole, plagioclase and clinopyroxene. Mineral compositions corresponding to ~165,000 analyses yield estimates for the eclogitic pressure–temperature retrograde path from 25 kbar to 9 kbar. Corresponding pressure–temperature maps were plotted and used to interpret the link between the equilibrium conditions of crystallization and the symplectitic microstructures. This example illustrates the usefulness of XMapTools for studying variations of the chemical composition of minerals and for retrieving information on metamorphic conditions on a microscale, towards computation of continuous pressure–temperature-and relative time path in zoned metamorphic minerals not affected by post-crystallization diffusion.
Subduction is primarily driven by the densification of the downgoing
oceanic slab, due to dynamic P-T-fields in subduction zones. It is
crucial to unravel slab densification induced by metamorphic reactions
to understand the influence on plate dynamics. By analyzing the density
and metamorphic structure of subduction zones, we may gain knowledge
about the driving, metamorphic processes in a subduction zone like the
eclogitization (i.e., the transformation of a MORB to an eclogite), the
breakdown of hydrous minerals and the release of fluid or the generation
of partial melts. We have therefore developed a 2D subduction zone
model down to 250 km that is based on thermodynamic equilibrium
assemblage computations. Our model computes the "metamorphic density" of
rocks as a function of pressure, temperature and chemical composition
using the Theriak-Domino software package at different time stages. We
have used this model to investigate how the hydration, dehydration,
partial melting and fractionation processes of rocks all influence the
metamorphic density and greatly depend on the temperature field within
subduction systems. These processes are commonly neglected by other
approaches (e.g., gravitational or thermomechanical in nature)
reproducing the density distribution within this tectonic setting. The
process of eclogitization is assumed as being important to subduction
dynamics, based on the very high density (3.6 g/cm3) of eclogitic rocks.
The eclogitization in a MORB-type crust is possible only if the rock
reaches the garnet phase stability field. This process is primarily
temperature driven. Our model demonstrates that the initiation of
eclogitization of the slab is not the only significant process that
makes the descending slab denser and is responsible for the slab pull
force. Indeed, our results show that the densification of the downgoing
lithospheric mantle (due to an increase of pressure) starts in the early
subduction stage and makes a significant contribution to the slab pull,
where eclogitization does not occur. Thus, the lithospheric mantle acts
as additional ballast below the sinking slab shortly after the
initiation of subduction. Our calculation shows that the dogma of
eclogitized basaltic, oceanic crust as the driving force of slab pull is
overestimated during the early stage of subduction. These results
improve our understanding of the force budget for slab pull during the
intial and early stage of subduction. Therefore, the complex metamorphic
structure of a slab and mantle wedge has an important impact on the
development and dynamics of subduction zones. Further Reading:
Duesterhoeft, Oberhänsli & Bousquet (2013), submitted to Earth
and Planetary Science Letters
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.
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. [1] Berman (1988). Journal of Petrology 29, 445-522.
[2] Holland & Powell (1998) Journal of Metamorphic Geology 16,
309-343. [3] Holland & Powell (2011) Journal of Metamorphic Geology
29, 333-383. [4] Duesterhoeft, Zaehle, De Capitani, Oberhänsli
& Bousquet (2012, in prep.) Submitted to Contributions to Mineralogy
and Petrology.
In this paper, the term "equilibrium assemblage diagrams" refers to diagrams strictly based on assemblages predicted by Gibbs free energy minimization. The presented Theriak/Domino software uses a unique algorithm of scanning and bookkeeping, which allows to compute completely and automatically a great variety of diagrams: phase diagrams, pseudo-binary, pseudo-ternary, isopleths, modal amounts, molar properties of single phases or bulk-rock properties like total Delta G, volume of solids, etc. The speed and easiness of use makes thermodynamic modeling accessible to any student of Earth sciences and offers a powerful tool to check the consistency of thermodynamic databases, develop new solution models, plan experimental work, and to understand natural systems. The examples described in this paper demonstrate the capacity of the software, but also to show the usefulness and limitations of computed equilibrium assemblage diagrams. For most illustrations, a metapelite (TN205) from the eastern Lepontine Alps is used. The applications include the interpretation of complex diagrams, mineral reactions, the effect of Al content on the equilibrium assemblages, the interpretation of Si per formula unit in white mica, understanding some features of garnet growth, dehydration and isothermal compressibility, a broadening of the concept of AFM diagrams, combining equilibrium assemblage diagram information with thermobarometry, and comparing the results produced with different databases. Equilibrium assemblage diagrams do not always provide straightforward answers, but mostly stimulate further thought.
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.
The average chemical compositions of the continental crust and the oceanic crust (represented by MORB), normalized to primitive mantle values and plotted as functions of the apparent bulk partition coefficient of each element, form surprisingly simple, complementary concentration patterns. In the continental crust, the maximum concentrations are on the order of 50 to 100 times the primitive-mantle values, and these are attained by the most highly incompatible elements Cs, Rb, Ba, and Th. In the average oceanic crust, the maximum concentrations are only about 10 times the primitive mantle values, and they are attained by the moderately incompatible elements Na, Ti, Zr, Hf, Y and the intermediate to heavy REE.
By incorporating generalized concepts, the mechanics of phase diagram calculations for multivariable systems have been reduced to a simple algorithm which has been automated with a computer program called Vertex. Vertex is based on an abbreviated combinatorial algorithm which derives a piecewise linear approximation of the isopotential thermodynamic surface for a system. Computations can be terminated at different levels in this sequence to obtain a composition, mixed-variable, or Schreinemakers diagram. It is also possible to trace low variance equilibria between pseudocompounds representing the same phase. The computational variables for Vertex may include related variables such as the composition or activity of a saturated phase (for example, a fluid). A variety of buffering and sectioning constraints can also be imposed within Vertex to simplify the phase diagrams of complex systems. -from Author
The complete consumption of the oceanic domain of a tectonic plate by subduction into the upper mantle results in continent subduction, although continental crust is typically of lower density than the upper mantle. Thus, the sites of former oceanic domains (named suture zones) are generally decorated with stratigraphic sequences deposited along continental passive margins that were metamorphosed under low-grade, high-pressure conditions, i.e., low temperature/depth ratios (< 15°C/km) with respect to geothermal gradients in tectonically stable regions. Throughout the Mesozoic and Cenozoic (i.e., since ca. 250 Ma), the Mediterranean realm was shaped by the closure of the Tethyan Ocean, which likely consisted in numerous oceanic domains and microcontinents. However, the exact number and position of Tethyan oceans and continents (i.e., the Tethyan palaeogeography) remains debated. This is particularly the case of Western and Central Anatolia, where a continental fragment was accreted to the southern composite margin of the Eurasia sometime between the Late Cretaceous and the early Cenozoic. The most frontal part of this microcontinent experienced subduction-related metamorphism around 85-80 Ma, and collision-related metamorphism affected more external parts around 35 Ma. This unsually-long period between subduction- and collision-related metamorphisms (ca. 50 Ma) in units ascribed to the same continental edge constitutes a crucial issue to address in order to unravel how Anatolia was assembled. The Afyon Zone is a tectono-sedimentary unit exposed south and structurally below the front high-pressure belt. It is composed of a Mesozoic sedimentary sequence deposited on top of a Precambrian to Palaeozoic continental substratum, which can be traced from Northwestern to southern Central Anatolia, along a possible Tethyan suture. Whereas the Afyon Zone was defined as a low-pressure metamorphic unit, high-pressure minerals (mainly Fe-Mg-carpholite in metasediments) were recently reported from its central part. These findings shattered previous conceptions on the tectono-metamorphic evolution of the Afyon Zone in particular, and of the entire region in general, and shed light on the necessity to revise the regional extent of subduction-related metamorphism by re-inspecting the petrology of poorly-studied metasediments. In this purpose, I re-evaluated the metamorphic evolution of the entire Afyon Zone starting from field observations. Low-grade, high-pressure mineral assemblages (Fe-Mg-carpholite and glaucophane) are reported throughout the unit. Well-preserved carpholite-chloritoid assemblages are useful to improve our understanding of mineral relations and transitions in the FeO-MgO-Al2O3-SiO2-H2O system during rocks’ travel down to depth (prograde metamorphism). Inspection of petrographic textures, minute variations in mineral composition and Mg-Fe distribution among carpholite-chloritoid assemblages documents multistage mineral growth, accompanied by a progressive enrichment in Mg, and strong element partitioning. Using an updated database of mineral thermodynamic properties, I modelled the pressure and temperature conditions that are consistent with textural and chemical observations. Carpholite-bearing assemblages in the Afyon Zone account for a temperature increase from 280 to 380°C between 0.9 and 1.1 GPa (equivalent to a depth of 30-35 km). In order to further constrain regional geodynamics, first radiometric ages were determined in close association with pressure-temperature estimates for the Afyon Zone, as well as two other tectono-sedimentary units from the same continental passive margin (the Ören and Kurudere-Nebiler Units from SW Anatolia). For age determination, I employed 40Ar-39Ar geochronology on white mica in carpholite-bearing rocks. For thermobarometry, a multi-equilibrium approach was used based on quartz-chlorite-mica and quartz-chlorite-chloritoid associations formed at the expense of carpholite-bearing assemblages, i.e., during the exhumation from the subduction zone. This combination allows deciphering the significance of the calculated radiometric ages in terms of metamorphic conditions. Results show that the Afyon Zone and the Ören Unit represent a latest Cretaceous high-pressure metamorphic belt, and the Kurudere-Nebiler Unit was affected by subduction-related metamorphism around 45 Ma and cooled down after collision-related metamorphism around 26 Ma. The results provided in the present thesis and from the literature allow better understanding continental amalgamation in Western Anatolia. It is shown that at least two distinct oceanic branches, whereas only one was previously considered, have closed during continuous north-dipping subduction between 92 and 45 Ma. Between 85-80 and 70-65 Ma, a narrow continental domain (including the Afyon Zone) was buried into a subduction zone within the northern oceanic strand. Parts of the subducted continent crust were exhumed while the upper oceanic plate was transported southwards. Subduction of underlying lithosphere persisted, leading to the closure of the southern oceanic branch and to subduct the front of a second continental domain (including the Kurudere-Nebiler Unit). This followed by a continental collisional stage characterized by the cease of subduction, crustal thicknening and the detachment of the subducting oceanic slab from the accreted continent lithosphere. The present study supports that in the late Mesozoic the East Mediterranean realm had a complex tectonic configuration similar to present Southeast Asia or the Caribbean, with multiple, coexisting oceanic basins, microcontinents and subduction zones.
Internally consistent standard state thermodynamic data are presented for 67 minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2. The method of mathematical programming was used to achieve consistency of derived properties with phase equilibrium, calorimetric,
and volumetric data, utilizing equations that account for the thermodynamic consequences of first and second order phase transitions,
and temperature-dependent disorder. Tabulated properties are in good agreement with thermophysical data, as well as being
consistent with the bulk of phase equilibrium data obtained in solubility studies, weight change experiments, and reversals
involving both single and mixed volatile species. The reliability of the thermodynamic data set is documented by extensive
comparisons (Figs. 4–45) between computed equilibria and phase equilibrium data. The high degree of consistency obtained with
these diverse experimental data gives confidence that the refined thermodynamic properties should allow accurate prediction
of phase relationships among stoichiometric minerals in complex chemical systems, and provide a reasonable basis from which
activity models for minerals may be derived.
For the pressure calibration of EXAFS data taken at p ⩽ 10 GPa, isothermal equations of state (EOS) are needed with pressure, p, as the independent and relative volume, V/V0, as the dependent variable. We found a total of seven such equations in the literature and invented two new ones. All equations are expressed in terms of two (three) parameters, viz. the bulk modulus and its first (and second) pressure derivatives at p = 0. The equations are applied to shock wave compression data of 15 elements and compounds and the mean squared deviations between data and fits are calculated. Our two-parameter EOS yields the smallest mean squared deviations, whereas our three-parameter EOS gives results comparable to two other EOS from the literature. Intercomparison of the results obtained from the different EOS shows that we can determine the bulk modulus and its first and second pressure derivatives at p = 0 with errors of the order of 1, 10 and 100%, respectively.
TEMSPOL is an open MATLAB code suitable for calculating temperature and lateral anomaly of density distributions in deep subduction zones, taking into account the olivine to spinel phase transformation in a self-consistent manner. The code solves, by means of a finite difference scheme, the heat transfer equation including adiabatic heating, radioactive heat generation, latent heat associated with phase changes and frictional heating. We show, with a few simulations, that TEMSPOL can be a useful tool for researchers studying seismic velocity, stress and seismicity distribution in deep subduction zones. Deep earthquakes in subducting slabs are thought to be caused by shear instabilities associated with the olivine to spinel phase transition in metastable olivine wedges. We investigate the kinematic and thermal conditions of the subducting plate that lead to the formation of metastable olivine wedges. Moreover, TEMSPOL calculates lateral anomalies of density within subducting slabs, which can be used to evaluate buoyancy forces that determine the dynamics of subduction and the stress distribution within the slab. We use TEMSPOL to evaluate the effects of heat sources such as shear heating and latent heat release, which are neglected in commonly used thermal models of subduction. We show that neglecting these heat sources can lead to significant overestimation of the depth reached by the metastable olivine wedge.
A general algorithm for the computation of chemical equilibria in complex systems containing non-ideal solutions has been developed. The method is a G-minimization based on repeated linear and nonlinear programming steps. A computer program (THERIAK) based on this algorithm has been written and was used to solve a great variety of problems, ranging from a simple blast furnace calculation to liquid-liquid unmixing in a four component silicate melt. The computing times are in the magnitude of to 2 seconds for each calculation. The method can also be used to test the consequences of thermodynamic models and data in systems of interest to many fields, including chemistry, geochemistry and metallurgy.
Phase diagrams of hydrous mid-ocean ridge (MOR) basalts to 330 km depth and of hydrous peridotites to 250 km depth are compiled for conditions characteristic for subduction zones. A synthesis of our experimentally determined phase relations of chlorite, lawsonite, epidote-zoisite, amphibole, paragonite, chloritoid, talc, and phengite in basalts and of phase relations from the literature of serpentine, talc, chlorite, amphibole, and phase A in ultramafics permits calculation of H2O contents in hydrous phase assemblages that occur in natural compositions. This yields the information necessary to calculate water budgets for descending slabs. Starting from low-grade blueschist conditions (10–20 km depth) with H2O contents between 5 and 6 wt% for hydrated oceanic crust, complete dehydration is achieved between 70 and >300 km depth as a function of individual slab geotherms. Hydrous phases which decompose at depth below volcanic arcs are lawsonite, zoisite, chloritoid, and talc (± phengite) in mafic compositions and chlorite and serpentine in peridotite. Approximately 15–35% of the initially subducted H2O are released below volcanic arcs. The contribution of amphibole dehydration to the water budget is small (5–20%) and occurs at relatively shallow depth (65–90 km). In any predicted thermal structure, dehydration is a combination of a stepwise and a continuous process through many different reactions which occur simultaneously in the different portions of the descending slab. Such a dehydration characteristic is incompatible with `single phase dehydration models' which focus fluid flow through a unique major dehydration event in order to explain volcanic fronts. As a consequence of continuously progressing dehydration, water ascending from the slab will be generally available to depth of ca. 150–200 km. The fluid rising from the subducting lithosphere will cause partial melting in the hot portion of the mantle wedge. We propose that the volcanic front simply forms above the mantle wedge isotherm where the extent of melting is sufficient to allow for the mechanical extraction of parental arc magmas. Thermal models show that such an isotherm (ca. 1300°C) locates below volcanic fronts, slab surface depths below such an isotherm are compatible with the observed depths of the slab surface below volcanic fronts.
The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.
Phase diagrams involving solid solutions are calculated by solving sets of non-linear equations. In calculating P–T projections and compatibility diagrams, the equations used for each equilibrium are the equilibrium relationships for an independent set of reactions between the end-members of the phases in the equilibrium. Invariant points and univariant lines in P–T projections can be calculated directly, as can coordinates in compatibility diagrams. In calculating P–T and T–x/P–x pseudosections – diagrams drawn for particular bulk compositions – the equilibrium relationship equations are augmented by mass balance equations. Lines in pseudosections, where the mode of one phase in the lower variance equilibrium is zero, and points, where the modes of two phases are zero, can then be calculated directly. The software, THERMOCALC, allows the calculation of these and a range of other types of phase diagram. Examples of phase diagrams and phase diagram movies, with instructions for their production, along with the THERMOCALC input and output files, and the MathematicaTM functions for assembling them, are presented in this paper, partly in hard copy and partly on the JMG web sites (http://www.gly.bris.ac.uk/www/jmg/jmg.html, or equivalent Australian or USA sites).
The Inaccessible Earth: An Integrated View of its Structure and Composition
- G. C. Brown
- A. E. Mussett
Shortcourse: Thermodynamic Modeling of Mineral Reactions: An Introduction to Program Gibbs
- F. Spear
- J. Pyle
- L. Storm