Isobaric Paths Research Articles

Temperature, Pressure, and Length-Scale Dependence of Solvation in Water-like Solvents. I. Small Solvophobic Solutes.

We analyze the role of temperature, pressure, and solute's molecular size on the pattern of isochoric and isobaric solvation of small hard-sphere solutes in TIP4P/2005 water and in a water-like "Jagla" solvent exhibiting unusual thermodynamics. To this end, we employ molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy along isobaric and isothermal paths covering solvent's stable liquid and supercritical states as well as supercooled and "stretched" liquid states. Results are found to be consistent with the most primitive scaled-particle theory and the Gaussian model of small-length-scale solvation. The temperature and pressure dependence of solvation quantities embraces solvent's water-like unusual thermodynamic behavior: its density is reflected in the solvation free energy; the isochoric solvation energy and entropy; and the isothermal density derivative of the solvation free energy, its isobaric thermal expansivity in the isobaric solvation enthalpy and entropy, and its isothermal compressibility in the partial molecular volume. The solute's size or length-scale dependence is found to combine with solvent's water-like behavior to produce the "convergence thermodynamics" picture characteristic of aqueous solutions of nonpolar solutes, which is unequivocally found here to be the mapping of the water-like density maximum into the isobaric solvation enthalpy and entropy versus temperature curves for a set of solutes of varying sizes.

Deciphering the Jurassic\u2013Cretaceous evolution of the Hamadan metamorphic complex during Neotethys subduction, western Iran

The Hamadan high-grade metapelites in the northwestern part of the Sanandaj–Sirjan zone, Iran, show a polymetamorphic evolution with relics of a garnet-bearing metamorphic mineral assemblage (M1), a contact metamorphic overprint (M2) related to the emplacement of the Middle to Late Jurassic Alvand composite pluton and a Buchan-type regional metamorphic event (M3) marked by 40Ar/39Ar ages in the 80–70 Ma range that is associated with penetrative ductile deformation producing a foliation and a thermal overprint onto the M2 assemblages. The M1 event is exclusively preserved as small garnet grains and mineral inclusions contained therein, incorporated into M2-stage cordierite porphyroblasts. Distinct metamorphic zones are developed over a region of ~ 600 km2, which are partly correlated with distance to the composite pluton: zones (1) cordierite + K-feldspar hornfels, and (2) andalusite ± cordierite hornfels that surround the Alvand composite pluton at a distance of up to 5 km. These two zones are clearly related to M2 metamorphism associated with pluton emplacement. Zones (3) staurolite schist, (4) andalusite schist, and (5) sillimanite schist are found outside of the contact aureole and are considered to be the result of regional M3 metamorphism in the eastern part distant to the Alvand composite pluton. Conventional thermobarometry shows that temperatures in the area vary between ~ 560 and 660 °C for zones 1 and 2 and ~ 490 and 690 °C for zones 3–5. Phase equilibria modelling in the MnNCKFMASHT system indicates two distinct isobaric prograde paths at low pressures, at ~ 2.7 kbar for zones 1 and 2 and slightly higher pressures of around 3.5–5.5 kbar for zones 3–5. U–Th–Pb monazite geochronology revealed overlapping ages of 168 ± 11 Ma and 149 ± 19 Ma in the hornfels (1 and 2) and schistose (3–5) zones, respectively. These ages are similar to the intrusion age of the Alvand composite pluton (153.3 ± 2.7 to 166.5 ± 1.8 Ma) and are interpreted to reflect heating due to the emplacement of the composite pluton (M2 contact metamorphic event). However, 40Ar/39Ar dating of white mica and amphibole yielded plateau ages ranging from 80 to 69 Ma over the entire transect. The formation of schistosity in zones 3–5 postdates the intrusion and is thus related to M3 metamorphism. The white mica fabric indicates formation of the foliation during M3 garnet growth, which is followed by local retrogression of garnet to chlorite during exhumation. Consequently, the 40Ar/39Ar white mica and amphibole ages likely indicate reheating during M3 to more than ca. 500 ± 25 °C (argon retention temperature in amphibole). These data establish the occurrence of a Cretaceous, Buchan-style regional metamorphic event that had not been firmly identified before. Subsequent Late Cretaceous exhumation of the Hamadan complex with its high-grade metapelites is due to extension along the Tafrijan–Mangavi–Kandelan fault, which represents a major ductile low-angle normal fault. Metamorphic temperatures coupled with mineral ages from this and published work suggest a fast stage of cooling with a rate of ~ 6 °C/Ma during exhumation after M3 metamorphism.

Vibrational dynamics of confined supercooled water.

The quest for a possible liquid-liquid coexistence line in supercooled water below its homogeneous nucleation temperature is faced by confining water within a porous silica substrate (MCM-41). This system is investigated by synchrotron radiation infrared spectroscopy, exploring both the intramolecular and the intermolecular vibrational dynamics, in the temperature range from ambient down to ∼120 K, along several isobaric paths between 0.7 kbar and 3.0 kbar. Upon lowering the temperature, the OH-stretching band shows that the intramolecular vibrational dynamics continuously evolves from predominantly liquidlike to predominantly icelike. An abrupt change in the line shape of the intermolecular vibrational band between 220 K and 240 K, depending on the pressure, is the signature of nucleation of ice within the MCM-41 pores. These findings do not support the presence of two liquid phases and provide evidence for the coexistence of liquid water and ice in water confined in MCM-41.

Exploring fractionation models for Martian magmas

AbstractMartian primary compositions, i.e., magmas that did not experience fractionation and/or contamination after extraction from the mantle, occur as a subset of Martian meteorites and a few lavas analyzed on the planet's surface by rovers. Eruptions of primary magmas are rare on Earth and presumably on Mars. Previous studies of fractional crystallization of Martian primary magmas have been conducted under isobaric conditions, simulating idealized crystallization in magma chambers. Polybaric fractionation, which occurs during magma ascent, has not been investigated in detail for Martian magmas. Using the MELTS algorithm and the pMELTS revision, we present comprehensive isobaric and polybaric thermodynamic calculations of the fractional crystallization of four primary or parental Martian magmas (Humphrey, Fastball, Y‐980459 shergottite, and nakhlite parental melts) using various pressure‐temperature paths, oxygen fugacities, and water contents to constrain how these magmas might evolve. We then examine whether known Martian alkaline rock compositions could have formed through fractional crystallization of these magmas under the simulated conditions. We find that isobaric and polybaric crystallization paths produce similar residual melt compositions, but given sufficient details, we may be able to distinguish between them. We calculate that Backstay (Gusev Crater) likely formed by fractionation of a primary magma under polybaric conditions, while Jake_M (Gale Crater) may have formed through melting of a metasomatized mantle, crustal assimilation, or fractional crystallization of an unknown primary magma. The best fits for the Backstay composition indicate that consideration of polybaric crystallization paths can help improve the quality of fit when simulating liquid lines of descent.

Extension of the Wu–Jing equation of state for highly porous materials: Thermoelectron based theoretical model

A thermodynamic equation of state (EOS) for thermoelectrons is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS and the Wu–Jing (WJ) model, [Q. Wu and F. Jing J. Appl. Phys. 80, 4343 (1996)] an extended Hugoniot EOS model is developed which can predict the compression behavior of highly porous materials. Theoretical relationships for the shock temperature, bulk sound velocity, and the isentrope are developed. This method has the advantage of being able to model the behavior of porous metals over the full range of applicability of pressure and porosity, whereas methods proposed in the past have been limited in their applicability.

A new equation of state for porous materials with ultra-low densities

A thermodynamic equation of state is derived which is appropriate forinvestigating the thermodynamic variations along isobaric paths to predictcompression behaviours of porous materials. This equation-of-state model istested on porous iron, copper, lead and tungsten with different initial densities.The calculated Hugoniots are in good agreement with the correspondingexperimental data published previously. This shows that this model cansatisfactorily predict the Hugoniots of porous materials with wide porosity andpressure ranges.

A New Hugoniot Equation of State for Shocked Porous Materials

A thermodynamic equation of state (EOS) is derived to be appropriate forinvestigating the thermodynamic variations along isobaric paths to predictthe compression behaviour of porous materials. This EOS model is tested onporous iron, copper, lead and tungsten with different initial densities. Thecalculated temperature and Hugoniot are in good agreement with thecorresponding experimental and theoretical data published previously. It isinteresting that this model can satisfactorily predict the shock behaviour ofporous materials over a wide range of porosity and pressure.

Pressure-Induced Charge Delocalization in Manganites Studied by Means of Infrared Spectroscopy

Infrared absorption spectra of the La 0.75 Ca 0.25 MnO 3 manganite have been collected over the spectral range 600-1100 cm m 1 along isobaric paths at P =0,2,4, and 7 GPa in the 240-320 K temperature range. The pressure dependence of the insulator-to-metal transition temperature T IM has been determined from the spectra analysis and the first PT phase diagram of a manganite in the high-pressure regime is presented and discussed.

Pressure and temperature dependences of the relaxation dynamics of cresolphthalein-dimethylether: Evidence of contributions from thermodynamics and molecular interactions

The relaxation dynamics of a low molecular supercooled liquid, cresolphthalein-dimethylether (KDE), has been investigated in the vicinity of glass transition temperature by dielectric relaxation measurements. Glass transition is approached and studied by the use of isothermal and isobaric paths. Under isobaric condition, the departure of the correlation function of the α-relaxation from exponential decay with time (nonexponentiality) is even less than the intermediate liquids such as glycerol. However, the Tg-scaled temperature dependence of the α-relaxation time, τ, resembles “fragile” glass-formers like orthoterphenyl (OTP). Thus KDE, like propylene carbonate (PC) that has in common a basic chemical structural unit, is an exception to the correlation between “fragility” and nonexponentiality found to hold for most glass formers. The dielectric relaxation measurements with the application of pressure show that KDE has large pressure coefficient of the glass transition temperature, (dTg/dP)P→0, or large activation volume, typically of “fragile” glass-formers. However, unlike “fragile” glass-formers, the change of the scaled activation volume with log τ for KDE is slow, comparable with that of glycerol. The dielectric dispersion of KDE as a function of frequency at different pressure and temperature combinations has an excess high frequency wing but no resolved Johari–Goldstein β-relaxation, resembling that of intermediate liquids. Thus the variable pressure and temperature measurements of the relaxation dynamics show that KDE (and likewise PC) behaves like a “fragile” liquid in some properties and an intermediate liquid in other properties. Previously it has been proposed that there are two distinct factors that determine the molecular dynamics of glass formers, one from thermodynamics and the other from cooperative many-body dynamics. We explain this split character of KDE and PC by the prominence of the thermodynamics factor, possibly due to the unique basic chemical structural unit they have in common. The prominent thermodynamics factor gives rise to properties, such as the Tg-scaled temperature dependence of the α-relaxation time and large (dTg/dP)P→0, that resemble “fragile” liquids. While the cooperative many-body dynamics in KDE and PC is weak as evidenced by low degree of nonexponentiality of the α-relaxation correlation function. Consequently some properties, including the shape of the dielectric dispersion, coincide with that of intermediate liquids. The explanation is supported by the comparison of adiabatic calorimetric data of PC and OTP to show that indeed the thermodynamics factor in PC is like that of a very “fragile” liquid.

Phase equilibrium constraints on the viscosity of silicic magmas II: implications for mafic–silicic mixing processes

Isobaric crystallisation paths obtained from phase equilibrium experiments show that, whereas in rhyolitic compositions melt fraction trends are distinctly eutectic, dacitic and more mafic compositions have their crystallinities linearly correlated with temperatures. As a consequence, the viscosities of the latter continuously increase on cooling, whereas for the former they remain constant or even decrease during 80% of the crystallisation interval, which opens new perspectives for the fluid dynamical modelling of felsic magma chambers. Given the typical dyke widths observed for basaltic magmas, results of analogue modelling predict that injection of mafic magmas into crystallising intermediate to silicic plutons under pre-eruption conditions cannot yield homogeneous composition. Homogenisation can occur, however, if injection takes place in the early stages of magmatic evolution (i.e. at near liquidus conditions) but only in magmas of dacitic or more mafic composition. More generally, the potential for efficient mixing between silicic and mafic magmas sharing large interfaces at upper crustal levels is greater for dry basalts than for wet ones. At the other extreme, small mafic enclaves found in many granitoids behave essentially as rigid objects during a substantial part of the crystallisation interval of the host magmas, which implies that finite strain analyses carried out on such markers can give only a minimum estimate of the total amount of strain experienced by the host pluton. Mafic enclaves carried by granitic magmas behave as passive markers only at near solidus conditions, typically when the host granitic magma shows near-solid behaviour. Thus they cannot be used as fossil indicators of direction of magmatic flow.

Modelización del proceso de episienitización (decuarcificación-albitización): formulación cinética y transporte advectivo en medio continuo

The development of episyenites from Sierra de Guadarrama has been modelized. The process mainly consists in a coupled process of dequartztification-albitization. The model is based on pure advective mass transport in a continuum medium, where the reactive process is formulated from a kinetic point of view. It is demonstrated the possibility of its formation through the action of low-salinity fluids (2,32 wt % NaCl equiv.), partially equilibrated with a biotite monzogranite, linked to isobaric reaction paths across negative geothermal gradients, intersecting the quartz retrograde solubility field, and associated to a quick fluid-resident mobilisation due to the environment tectonic opening. The model explains the albitic nature of the alteration against former models. These predict microcline formation from the gradient relations ∂logKmic/∂T > ∂logKab/∂T (0.05739 and 0.05735) and ∂logKKCl/∂T < ∂logKNaCl/∂T (-0.038 and -0.036). Albite formation arises from the anortite component presence, because ∂logKan/∂T =0,1293 ≻ ∂logKmic/∂T. Non-equilibrium relations are very small, which implies that alteration intensity arises from the circulation of huge fluid volumes. This process feature together the kinetic rate constants result in a small change, spatial and temporal, of the fluid composition, being practically null for its main components (Na, K and, subordinately to these, the pH). The model also shows the necessity of handling geochemical systems as complex as possible. In this way, the proposed aqueous speciation proves that pH evolution along decreasing temperature is not necessarily acid, but inlet fluid pH dependent due to the calculated concentrations show that its behaviour mainly depends as much from Hel as from the NaOH base dissociation.

Analysis of small‐ and large‐scale increases of reactive nitrogen observed during the Second Airborne Arctic Stratospheric Expedition

An analysis of the data obtained during AASE II was made to characterize small‐ (δx &lt; 24 km) and large‐scale (30 &lt; δx &lt; 260 km) increases of reactive nitrogen species. By using the NOx/NOy ratio, the increases were classified into fresh emissions and aged air parcels. The sources of the NOy increases were then assessed by the freshness of the increases and by examining the correlation (or absence thereof) between NOy and other trace species including tracers of various NOx sources: for example, aircraft emissions, lightning, the stratospheric source, and sources in the boundary layer. We found that the majority (43%) of NOy increases in the upper troposphere and lower stratosphere were due to displacement of constant mixing ratio surfaces relative to isobaric flight paths. Aircraft emissions were the second most abundant (17%). The next significant contributor was surface emissions, including fossil fuel combustion and biomass burning. Only two lightning spikes were found, apparently due to the winter season and emphasis on high latitudes in the AASE II experiment. The relative contribution from each source to the increases (or positive variability) represents a measure of the relative source strength. However, it is important to note that our findings on the relative contribution of each source to the NOy increases should not be applied directly to estimating the relative source strength of the ambient or background NOy abundance. Knowledge of the detailed temporal and spatial distribution of the relative contribution of each source is needed. This requires a substantially higher precision for the instruments of tracer gases than those used in this study.

Thermodynamic equation of state and application to Hugoniot predictions for porous materials

A thermodynamic equation of state (EOS) is derived which is appropriate for investigating the thermodynamic variations along isobaric paths. By using this EOS, a Hugoniot EOS model with a unified theoretical basis is proposed for predicting the shock compression behavior of porous materials. The model is tested on 2024 aluminum, copper, and tungsten which are the typical materials with low, intermediate, and high shock impedance, respectively, and commonly used as standards. The calculated Hugoniots for these three materials with different initial densities are in good agreement with the corresponding experimental data published previously. It shows that this Hugoniot EOS model can satisfactorily predict the Hugoniot of porous materials over a wide pressure range.

P- V- T equation of state of (Mg,Fe)SiO 3 perovskite: constraints on composition of the lower mantle

Unit-cell volumes (V) of Mg 1− x Fe x SiO 3 perovskite ( x = 0.0 and 0.1) have been measured along several isobaric paths up to P = 11 GPa and T = 1300 K using a DIA-type, cubic anvil high-pressure apparatus (SAM-85). With a combination of X-ray diffraction during heating cycles and Raman spectroscopy on recovered samples, pressure and temperature conditions were determined under which the P- V- T behavior of the perovskite remains reversible. At 1 bar, perovskites of both compositions begin to transform to amorphous phases at T ≈ 400 K, accompanied by an irreversible cell volume contraction. Electron microprobe and analytical electron microscopy studies revealed that the iron-rich perovskite decomposed into at least two phases, which were Fe and Si enriched, respectively. At pressures above 4 GPa, the P- V- T behavior of MgSiO 3 perovskite remained reversible up to about 1200 K, whereas the Mg 0.9Fe 0.1SiO 3 exhibited an irreversible behavior on heating. Such irreversible behavior makes equation-of-state data on Fe-rich samples dubious. Thermal expansivities ( α V ) of MgSiO 3 perovskite were measured directly as a function of pressure. Overall, our results indicate a weak pressure dependence in α V for MgSiO 3. Analyses on the P- V- T data using various thermal equations of state yielded consistent results on thermoelastic properties. The temperature derivative of the bulk modulus, ( ∂K T ∂T ) P , is −0.023(±0.011) GPa K −1 for MgSiO 3 perovskite. Using these new results, we examine the constraints imposed by α V and ( ∂K ∂T ) P on the Fe (Mg + Fe) and (Mg + Fe) Si ratios for the lower mantle. For a temperature of 1800 K at the foot of an adiabat (zero depth), these results indicate an overall iron content of Fe (Mg + Fe) = 0.12(1) for a lower mantle composed of perovskite and magnesiowüstite. Although the (Mg + Fe) Si ratio is very sensitive to the thermoelastic parameters of the perovskite and it is tentatively constrained between 1.4 and 2.0, these results indicate that it is unlikely for the lower mantle to have a perovskite stoichiometry.

Dielectric studies of liquid crystals under high pressure II. Low frequency relaxation process in 4-n-pentyl-4′-cyanobiphenyl in relation to theories of the nematic state

Abstract The results of high pressure dielectric studies of 4-n-pentyl-4′-cyanobiphenyl (5CB) are analysed in terms of theories of the nematic state. The retardation factor g∥ = τ∥/τ0 and the effective, single-particle potential of mean torque were calculated at the nematic–isotropic transition temperature T NI and along the isothermal, isobaric and isochoric paths within the nematic phase of 5CB. The potential of mean torque is compared with the order parameter known for the same conditions. The values of parameter γ relating the potential to the volume is discussed.

Comparison of Isothermal and Isobaric Water Retention Paths in Nonswelling Porous Materials

Water in porous media near the Earth's surface is subject to large fluctuations in pore water pressure and temperature, often causing significant changes in the degree of saturation. Quantitative comparisons of isothermal versus isobaric water retention are necessary to accurately predict changes in saturation due to the coupled influence of changes in the pore water matric potential ψ and temperature T. Yet there is a lack of experimental measurements of isobaric (i.e., constant ψ) water retention, inhibiting comparisons between isobaric and isothermal processes. In the present study the influence of the chronological sequence of changes in ψ and T is examined to determine whether the volumetric water content θ for any given final ψ‐T condition is independent of the ψ‐T sequence, when θ changes monotonically. To obtain the necessary data for these comparisons, isothermal water retention experiments were performed over a range in ψ from 0 to −100 kPa, and isobaric water retention experiments were performed at 20° and 80°C on core samples of a sandy soil and a nonwelded tuff. Results provide further evidence that the effect of T on ψ is considerably greater than estimates based on pore water capillary theory. For these materials the thermal enhancement of ψ was 4–12 times greater than capillary theory would predict. The effect of T on θ during isobaric water retention was several times greater for drying (warming) conditions than for wetting (cooling) conditions at a given ψ, resulting in net losses in θ ranging from 3 to 30%. For a given final ψ at 80°C, virtually identical θ values were obtained regardless of the chronological sequence of isothermal and isobaric drainage paths for both materials. This confirms the validity of unique θ (ψ, T) surfaces describing monotonic changes in θ as functions of both ψ and T in nonswelling porous materials. Determination of these θ (ψ, T) response surfaces for drying and wetting should yield water retention envelopes, useful in modeling water retention in near‐surface environments where both ψ and T vary.

Implications of post-thrusting extension and underplating for P-T-t paths in granulite terranes:A Grenville example

Mineral zoning studies in several granulite terranes have yielded nearly isobaric retrograde pressure-temperature ( P-T ) paths with significant path dispersion. Explanations include magmatic underplating, incomplete isostatic rebound following thrusting, and cooling after tectonic denudation associated with crustal extension. One-dimensional thermal models help to interpret the P-T-t (time) paths generated by such processes. Basaltic underplating yields P-T paths in good agreement with data for the Grenville province of Ontario, but yields T-t paths that disagree strongly with thermochronometry. In addition, seismic, heat-flow, and gravity data from the Grenville province are not consistent with a mafic lower crust. Calculations based on simple thrust models agree with the T-t data, but yield isothermal rather than isobaric initial P-T paths, and consistently underestimate the pressure at which peak temperature is achieved. The only model we found that fits both the P-T and T-t data incorporates a post-thrusting episode of tectonic denudation near the peak of metamorphism. This model also suggests that the temperature dependence of diffusion in garnet may explain the difference between measured isobaric and isothermal paths in granulites and amphibolites.

Effect of physical ageing on mechanical behaviour of an elastomeric glass under combined pressure and temperature

Abstract The relaxation or physical ageing behaviour of a polyurethane elastomeric glass (Solithane 113, Tg = −20°C at atmospheric pressure) has been studied at various states of pressure and temperature (P, T), near and far away from the glass transition. Those (P, T) states were reached via either isobaric or isothermal paths. The relaxation behaviour of these glasses has been found to be a function of P, T and the path. The Young's modulus (E) has been determined as a function of ageing time. When all the experimental data, obtained at various (P, T) states for a specific path, were replotted in the form of log E vs. 1 P for an isothermal glass and log E vs. 1 T for an isobaric glass, all the curves appear to converge to a specific value of E. The value was chosen as E∞, the ’near-equilibrium’ modulus. The relaxation behaviour was analysed by a parameter δ E = E ∞ −E(P,T,t) E ∞ When δ E ⋍ 1 is used to define a glass transition, the pressure-dependent glass transition lines for isobaric glasses are found to be entirely different from those for isothermal glasses. This may be the result of the pressure rate and temperature rate used. The non-equilibrium behaviour of E of the glass was analysed by an equation analogous to Kovac's equation for the kinetics of relaxation, namely − d δ E (P,T,t) d t = δ E (P,T,t) τ(P,T,δ E ) where δE(P,T) is the relative departure of E(P,T,t) from E∞. In general, the isobaric glasses at a specific state (P,T) relaxed faster, relatively, than isothermal glasses for the experimental conditions of heating rate or pressurization rate.

Order–disorder phase transitions in NH4BrxCl1–x crystals

Single crystals of NH4BrxCl1–x have been investigated ultrasonically over a wide range of pressure, temperature, and composition. Using the elastic constant c44 as a convenient probe, we have established the p–T–x phase diagram in the region where the orientations of NH4+ ions undergo long-range ordering. Two critical surfaces exist: one corresponding to ’’ferro’’ ordering and one corresponding to ’’antiferro’’ ordering. These surfaces intersect in a line of triple points closely related to the bicritical points in magnetic spin–flop systems. The adiabatic elastic constants c11 and C′ (as well as the acoustic absorption associated with these waves) have also been measured along several isobaric paths. The results are consistent with the existence of a master p–T phase diagram valid for all values of x.