R. Powell

Relating formulations of the thermodynamics of mineral solid solutions; activity modeling of pyroxenes, amphiboles, and micas

Abstract In a thermodynamic description of a mineral solid solution, it is customary to select a minimal group of end-members that constitutes an independent set, and yet in practical calculations it commonly occurs that a different independent set or subset is required. Given the simplification of the symmetric formalism, it is straightforward to derive the enthalpies of formation of dependent end-members as well as the interaction energies between the end-members in the new independent set, in terms of those in the original set. For example, a simplified ternary solid solution of Fe-free Ca-amphiboles might be described with independent end-members tremolite, tschermakite, and pargasite, and yet some calculations may require the use of end-members such as edenite or hornblende. Not only are their end-member properties dependent on those of the first three, but the mixing properties of any of the binary joins involving edenite or hornblende are dependent on those in the original independent set. Examples drawn from pyroxenes, amphiboles, and biotite micas show that such dependencies may prove invaluable in using experimental information or heuristics to help constrain the mixing properties of complex solid solutions. In particular, it is found that in non-ideal solid solutions that involve Fe and Mg distributed over two or more non-equivalent sites, equipartition of Fe and Mg implies extreme restrictions on the ratios of the interaction parameters and the magnitude of the Fe-Mg exchange energy. The thermodynamics can only be formulated generally and consistently when Fe- Mg ordering is explicitly included, and this is done most simply via ordered Fe-Mg endmembers.

An order-disorder model for omphacitic pyroxenes in the system jadeite-diopside-hedenbergite-acmite, with applications to eclogitic rocks

Abstract A new thermodynamic model for sodic pyroxenes involving jadeite-diopside-hedenbergite-acmite is presented. This model allows for ordering of Mg, Al, Fe2+, and Fe3+ on the M1 sites, with coupled Na and Ca ordering on the M2 sites. It is calibrated on the basis of experiments in three chemical subsystems together with available information on ordering in different pyroxenes and on the limited calorimetric data. Central to the determination of the parameters of the model is the use of relationships among the end-member Gibbs energies and the interaction energies in the various possible non-independent sets of end-members. An important aspect of this model, which uses the symmetric formalism, is that Fe-Mg (FM) and Al-Fe3+ (AF’) mixing is not assumed to be ideal. The model accounts successfully for the experiments at both 600 °C and at higher temperatures involving ordered and disordered pyroxenes coexisting with albite and quartz in NCMAS, NCFAS, NF’AS systems as well as the available calorimetry. It is also able to predict the positions and slopes of tielines in coexisting jadeite + omphacite and omphacite + augite found in nature at lower temperatures. Although the model requires a large number of energy parameters, some of these are not critical to the behavior of the model, while for others the constraints from experiment, calorimetry, ordering state and solvi lead to very limited allowable combinations. The model places some restrictive constraints on the shape of the phase relations in the jadeite.augite.acmite system. Petrological applications of the model are illustrated via a phase diagram example for a MORB bulk composition eclogite.

Deep crustal metamorphism during continental extension: modern and ancient examples

Granulite facies metamorphism in the lower levels of continental crust which is undergoing extension is indicated by unusually high heat flow in modern-day extensional regimes. For certain geometries of extension, particularly those involving crustal-penetrative detachment zones, this metamorphism may occur on a regional scale. The predicted pressure-temperature-time (P-T-t) paths for such metamorphism involve heating into the granulite facies at constant or decreasing pressure during extension, followed by cooling at constant or increasing pressure after extension stops, and thus they differ considerably from P-T-t paths of metamorphic terrains formed by continental convergence. Many granulite terrains from both the Precambrian and Phanerozoic record preserve P-T-t paths which involve substantial, essentially isobaric, cooling. In such terrains granulite facies metamorphism is typically associated with recumbent structures characterised by subhorizontal stretching lineations which are attributed to intense non-coaxial deformation. Such deformation may be expected for the deep crustal expression of detachment zones. These terrains may provide ancient examples of deep crustal metamorphism during extensional tectonics. Extensional tectonics is attracting widespread interest in the geological community, and geologists, in particular structural geologists, have begun to investigate the features which may be considered diagnostic of ancient extensional tectonic regimes [1]. Recently, extension associated with continental rifting has been proposed as a mechanism for the generation of high-T/low-P metamorphic terrains [2-4], and there is now a need to define the criteria by which metamorphism associated with extensional tectonics may be distinguished from the metamorphism of the more familiar terrains of continental convergence zones. In this contribution we discuss the evidence for deep crustal metamorphism during continental extension, the pressure-temperature-time (P-T-t) paths associated with such metamorphism, and, finally, a number of examples of deep crustal metamorphism which may have been associated with extensional tectonics, The observation that heat flow through con

Thermodynamics of order-disorder in minerals: II. Symmetric formalism applied to solid solutions

Abstract The thermodynamics of order-disorder in mineral solid solutions are handled with symmetric formalism, whereby the mineral is treated as a solid solution between an independent set of end-members with which the range of composition and states of ordering of the phase can be represented. An n-component mineral, requiring s independent order parameters to represent the state of order in the mineral, involves an independent set of n + s end-members. Symmetric formalism involves ideal mixing-on-sites with regular-solution activity coefficients. It is applied to omphacite, orthopyroxene, ferromagnesian clinoamphibole, and alkali feldspar. The model for omphacite, with a single order parameter, successfully produces the topology of paired miscibility gaps with tricritical points at their apices and with a critical curve connecting them. Ferromagnesian orthopyroxene is shown to behave effectively as an ideal solution at all geologically relevant temperatures. Cummingtonite- grunerite solid solutions are slightly positively nonideal in either a two-site or a three-site model. Na-K alkali feldspars with order-parameter coupling involving tetrahedral site occupancies can show the essential topologic relationships in this system, with only one independent binary interaction energy. The power of symmetric formalism comes from the simplicity of its representation of the thermodynamics of minerals and its flexibility with few adjustable parameters.

A Compensated-Redlich-Kwong (CORK) equation for volumes and fugacities of CO2 and H2O in the range 1 bar to 50 kbar and 100–1600°C

We present a simple virial-type extension to the modified Redlich-Kwong (MRK) equation for calculation of the volumes and fugacities of H2O and CO2 over the pressure range 0.001–50 kbar and 100 to 1400°C (H2O) and 100 to 1600°C (CO2). This extension has been designed to: (a) compensate for the tendency of the MRK equation to overestimate volumes at high pressures, and (b) accommodate the volume behaviour of coexisting gas and liquid phases along the saturation curve. The equation developed for CO2 may be used to derive volumes and fugacities of CO, H2, CH4, N2, O2 and other gases which conform to the corresponding states principle. For H2O the measured volumes of Burnham et al. are significantly higher in the range 4–10 kbar than those presented by other workers. For CO2 the volume behaviour at high pressures derived from published MRK equations are very different (larger volumes, steeper (∂P/∂T)V, and hence larger fugacities) from the virial-type equations of Saxena and Fei. Our CORK equation for CO2 yields fugacities which are in closer agreement with the available high pressure experimental decarbonation reactions.

Some isostatic and thermal consequences of the vertical strain geometry in convergent orogens

Abstract The thermal and isostatic consequences of continental deformation, particularly surface elevation, horizontal buoyancy forces and metamorphism in the crust, depend to a considerable extent on the way in which strain is distributed between the crust and the mantle lithosphere [1]. Since these vertical strains may be strongly “decoupled” by processes such as convective thinning or detachment of the lower thermal boundary layer [2], with the extent of this “decoupling” varying in space and time in an orogen [3], it is useful to parameterise the vertical strain on the scale of the crust, ƒ c , and lithosphere, ƒ 1 , respectively. We illustrate this parameterisation by considering the thermal and isostatic consequences of a number of ƒ c −ƒ 1 paths which may develop during the convergent deformation of a thermally-stabilised lithosphere. Three qualitatively distinct ƒ c −ƒ 1 paths in orogens are distinguished on the extent of “decoupling” between vertical strains in the crust and mantle lithosphere. Type 1 paths involve no decoupling, so the vertical strain in the lithosphere is homogeneous. For a given ƒ c , Type 1 paths result in relatively low surface elevation and low-intermediate metamorphic temperatures appropriate for the development of glaucophane-schist and Barrovian metamorphic assemblages. Type 2 paths allow decoupling due to processes such as convective thinning of the mantle lithosphere on the orogenic timescale but only after considerable initial lithospheric thickening. Type 2 paths lead to relatively high surface elevations, for a given ƒ c , and intermediate to high metamorphic temperatures only after the mantle lithosphere is thinned. The increase in potential energy associated with mantle lithospheric thinning (resulting in an increase in buoyancy forces by as much as 10 13 Nm −1 ) will quickly terminate convergent deformation, with the result that metamorphic heating will postdate the thickening deformation, and may induce extensional collapse of the orogen. Type 3 paths involve efficient mantle lithosphere thinning as the crust thickens with a consequence being, particularly, the possibility of relatively high metamorphic temperatures during active crustal thickening. For a given driving force, convergent deformation along a Type 3 path will be terminated at relatively small ƒ c providing an appropriate setting for the development of high T —low P metamorphic assemblages.

Metamorphic evolution of aluminous granulites from Labwor Hills, Uganda

Sapphirine-cordierite-quartz and spinel-cordierite-quartz form relic assemblages of probable Archaean age in Fe-rich aluminous metapelites from Labwor Hills, Uganda, and reflect an unusually high temperature metamorphism (∼1,000° C) at pressures in the vicinity of 7–9 kbars and a(O2) near the magnetite-hematite buffer. Subsequent reaction textures include the replacement of spinel and cordierite by sillimanite and hypersthene and formation of sapphirine-hypersthene-K-feldspar-quartz symplectites which are interpreted as pseudomorphs after osumilite. A petrogenetic grid appropriate to these assemblages suggests these reaction textures may be due to cooling at constant or increasing pressure and constant a(O2), or decreasing a(O2) at constant temperature and pressure. The former interpretation is supported by the coexistence of ilmenohematite and magnetite during the development of the reaction textures, and by the comparatively low Al2O3-contents of secondary hypersthene. This pressure-temperature path implies that: (1) metamorphism occurred at deep levels within normal thickness crust, probably less than 40–45 km thick, due to an extreme thermal perturbation induced either by emplacement of mantle-derived magmas or by thinning of the subcontinental lithosphere in an extensional tectonic regime, (2) the excavation and surface exposure of the granulites is due to a subsequent, postgranulite facies metamorphism, crustal thickening most probably involving their incorporation into an allochthonous upper crustal thrust sheet during the formation of the Mozambique foldbelt.

PT Paths from modal proportions: application to the Koralm Complex, Eastern Alps

Thermodynamic pseudosections portray those parts of a petrogenetic grid that are relevant to a given bulk composition and the reactions appearing on them can therefore be used directly to infer the PT path that the rock followed. However, for many ‘normal’ bulk compositions the use of pseudosections is hampered by the fact that they display only few large fields of high thermodynamic variance in the PT range of interest. Here it is discussed how modal information on reaction progress within these fields can be used to determine PT path information for thermodynamically high variant metamorphic assemblages. We use this information on reaction progress to contour pseudosections for modal proportions of minerals using the software package THERMOCALC. The approach is applied to di- tri- and quadrivariant assemblages from the Koralm complex in the eastern Alps. A PT path for these rocks is derived from modal considerations and compared with interpretations of mineral composition contours on the same pseudosection and with conventional thermobarometry. It is shown that at least part of the complex must have cooled initially near isobarically from prevalent peak conditions around 700°C and 14 kbar before the rocks commenced a Barroviantype decompression path.

Thermodynamics of order-disorder in minerals: I. Symmetric formalism applied to minerals of fixed composition

Abstract Thermodynamics of order-disorder in minerals may be approached by treating the mineral as a solid solution between an independent set of end-members with which the range of possible states of ordering of the phase can be represented. Thus, a mineral of fixed composition (a one-component phase), requiring s independent order parameters to represent the state of order in the mineral, involves an independent set of s + 1 end-members. This approach is applied by means of symmetric formalism, with the entropy part of the Gibbs energy taken to be the ideal configurational entropy of mixing using a mixing-onsites formulation, and the enthalpy part taken to be that of a regular solution between the s + 1 end-members. Symmetric formalism is shown to be formally identical to the generalized Bragg-Williams or point approximation, and its treatment of convergent and nonconvergent cation ordering is compared with that of the Landau theory. Its flexibility in describing a wide range of order-disorder behavior is illustrated with applications to sillimanite, spinel, albite, and potassium feldspar, the latter two involving order-parameter coupling.

How well established is isobaric cooling in Proterozoic orogenic belts? An example from the Arunta inlier, central Australia

Orogenic pressure-temperature paths can only be deduced from metamorphic textures if they formed during a single metamorphic event, rather than recording the effects of two or more separate events. Erroneous tectonic models are likely to result if textures formed in several events are ascribed to one event. We illustrate this problem for the Arunta inlier in central Australia, which has been considered to be a good example of an isobarically cooled terrain. Rocks of the Anmatjira Range in the central Arunta inlier, which has been described in terms of isobaric cooling, actually record the effects of two low-pressure, granulite facies, metamorphic events of similar peak metamorphic grade, M 1 and M 2 , that are separated in time by a period of basin development and deposition of a succession of sedimentary rocks. Correlations of stratigraphic, structural fabric, and metamorphic texture data allow the effects of M 1 and M 2 to be distinguished. Without this fine control, the textures formed by superposition of M 1 upon M 2 , considered as a manifestation of one event, could easily be interpreted as indicating isobaric cooling, because the overprinting assemblages are of similar pressure but slightly lower temperature than the original assemblages. We call this apparent isobaric cooling; in fact, we now recognize textures reflecting decompression that formed immediately following the peaks of both M 1 and M 2 . It is now a matter for conjecture whether isobaric cooling is more apparent than real in other terrains for which it has been recorded.