Self-consistent Thermodynamic Model Research Articles

Loss of thermodynamic stability in amorphous materials

The primary relaxation dynamics near the glass transformation temperature Tg exhibits universal features in all glass formers with two-level tunneling states (Low Temp. Phys. 35, 282 (2009)). Researchers have long sought the signature of an underlying “true” ergodic-nonergodic transition at a certain thermodynamic instability temperature Te. Here the relaxation timescale for glass-forming materials is analyzed using a self-consistent thermodynamic cluster model in combination with the concept of cluster percolation. The ergodic hypothesis is violated near a crossover from Gaussian to non-Gaussian (Poisson) cluster-volume fluctuations associated with finite-size fractal-cluster distributions. The transition of compact-structured “ergodic” clusters into hole-like glassy nanoclusters is attributed to critical-size thermal fluctuations. An ergodic-nonergodic phase diagram with Te is constructed in a model-independent form in terms of the glass fragility parameter for organic and inorganic liquids and amorphous solids. In all cases, the ergodic-instability temperature is below and close to the glass transition temperature, and the distance between the two characteristic temperatures decreases with increasing fragility of the material.

Inferring the thermochemical structure of the upper mantle from seismic data

SUMMARY We test a mineral physics model of the upper mantle against seismic observations. The model is based on current knowledge of material properties at high temperatures and pressures. In particular, elastic properties are computed with a recent self-consistent thermodynamic model, based on a six oxides (NCFMAS) system. We focus on average structure between 250 and 800 km. We invert normal modes eigenfrequencies and traveltimes to obtain best-fitting average thermal structures for various compositional profiles. The thermochemical structures are then used to predict long-period waveforms, SS precursors waveforms and radial profiles of attenuation. These examples show the potential of our procedure to refine the interpretation combining different data sets. We found that a mixture of MORB and Harzburgite, with the MORB component increasing with depth, is able to reproduce well all the seismic data for realistic thermal structures. If the proportions of MORB with depth do not change, unrealistic negative thermal gradients below 250 km would be necessary to explain the data. Equilibrium assemblages, such as pyrolite, cannot fit the seismic data. The elastic velocities predicted by the reference mineral physics model tested are too low at the top of the lower mantle, even for the fastest (and most depleted) composition, that is, harzburgite. An increase in V P of 1 per cent and in VS of 2 per cent improves the data fit significantly and is required to find models that fit both traveltimes and normal modes, indicating the need for further experimental measurements of these properties at the simultaneously elevated pressure–temperature conditions of the lower mantle. Extending our procedure to other seismic and density data and interpreting the 3-D structure holds promise to further improve our knowledge of the thermochemical structure of the upper mantle. In addition, the same database of material properties can be used in dynamic models to test whether the thermochemical structure inferred from geophysical observations is consistent with the Earth’s evolution.

Thermodynamic assessment of La–Si and Mg–La–Si systems

Based on available phase equilibria and thermodynamic data, thermodynamic assessment has been carried out for La–Si binary system using CALPHAD approach. A set of self-consistent thermodynamic model parameters was obtained. The solution phases including Liquid, BCC, FCC, DHCP and Diamond_A4 were modeled as substitutional phases, of which the excess Gibbs energies being formulated with the Redlich–Kister polynomial function. And six intermediate compounds were treated as stoichiometric phases. Incorporated with thermodynamic parameters of Mg–La and Mg–Si binary systems cited from literatures, an isothermal section at 773 K of Mg–La–Si ternary system was thermodynamically optimized, including four ternary stoichiometric compounds (τ 2 , τ 3 , τ 4 and τ 5 ) and one semi-stoichiometric compound (τ 1 ). The calculated phase equilibria and thermodynamic properties agreed well with experimental data.

Effect of phonon anharmonicity on the thermal and elastic properties of stabilized δ-plutonium

The Debye temperature, bulk modulus, density, and molar heat capacity of a Pu0.95Al0.05 alloy have been calculated as functions of the temperature using a self-consistent thermodynamic model developed according to a quasi-classical approach that takes into account the effect of phonon anharmonicity on the acoustic and thermodynamic properties of metals. The results of self-consistent numerical simulation of the thermal and elastic properties are compared to the available experimental data and theoretical results obtained using alternative approaches. It is established that the phonon anharmonicity plays a significant role in the formation of elastic and thermal properties of the system under consideration.

Thermodynamic investigation of the galvanizing systems, I: Refinement of the thermodynamic description for the Fe–Zn system

The thermodynamic description for the Fe–Zn system was updated using CALPHAD approach. A set of self-consistent thermodynamic model parameters for this system was obtained by considering the available experimental data. Compared with the previous thermodynamic modeling, the present assessment with fewer parameters shows not only a better agreement with the experiments but also sounder physical meaning. The present CALPHAD modeling coupled with the ab initio calculations were used to predict the enthalpies of formation of the solid phases in the Fe–Zn system.

Thermodynamic Description of the Mg-Mn, Al-Mn and Mg-Al-Mn Systems Using the Modified Quasichemical Model for the Liquid Phases

A self-consistent thermodynamic model of the Mg-Mn, Al-Mn and Mg-Al-Mn systems has been developed. The major difference between this work and the already existing assessments of these systems is the application of the modified quasichemical model for the liquid phase in each system while most of the existing descriptions use the random mixing model. In the absence of key data for the Mg-Mn system, the calculated thermodynamic properties from the model have been found comparable to other similar systems and the estimated critical temperature of the Mg-Mn liquid miscibility gap using the available empirical equation has been found to be in acceptable agreement with the calculated value. A comparison between the current work and the most recent work on the Al-Mn system that uses the same model for the liquid phase reveals that better agreement with the experimental data with less number of model parameters has been achieved in the current work. Kohler symmetric extrapolation model with only one ternary interaction parameter has been used to calculate the ternary Mg-Al-Mn system. The thermodynamic description of the Mg-Al-Mn system has been verified by extensive comparison with the available experimental data from numerous independent experiments. The model can satisfactorily reproduce all the invariant points and the key phase diagram and thermodynamic features of the ternary as well as the constituent binary systems.

Thermodynamic assessment of the Nd–Zn system

The Nd–Zn binary system has been optimized by CALPHAD method, using the available experimental thermodynamic and phase diagram information. The system contains eight intermetallic compounds: NdZn, NdZn 2, NdZn 3, Nd 3Zn 11, Nd 13Zn 58, Nd 3Zn 22, Nd 2Zn 17 and NdZn 11. They were treated as stoichiometric compounds. The standard enthalpies of formation of these compounds were calculated in this work. Good agreement was obtained between the calculation and experimental results. A set of self-consistent thermodynamic model parameters was derived.

A selfconsistent thermodynamic model of a metal solid (Using aluminum as an example)

The fundamental principles of a selfconsistent thermodynamic approach to a simultaneous calculation of the entire set of basic thermodynamic functions of an elementary nonmagnetic metal, taking into account the thermal phonon anharmonicity and the concomitant Debye temperature θ dependence, are reported. It is shown that given a step-by-step analysis, the Debye temperature includes not only lattice but also electronic parameters, which could be interpreted as an indirect thermodynamic evidence of electron-phonon interaction in metals. The model adequacy, both in terms of its quantitative and qualitative validity, is shown by the example of aluminum.

A new calculation of the work of formation of bubbles and drops

The thermodynamic basis of surface tension for bubbles and drops is reformulated to take into account the variation in surface tension for very small, growing or incipient bubbles and drops. After assessing the magnitudes involved by means of conventional theory, a model is put forward for this variation that avoids the supposition of extreme pressures at small sizes in the simple model. The parameter of this new model is then set by consideration of the properties of real gases, determined by analysis of the incipient bubble and then extended, it is argued, to the incipient drop. van der Waals' model of a real gas is used to show how this combines with the Lewins model in a self-consistent approach to the thermodynamics of surface tension for bubbles and drops. The changes from the simple theory will then allow a revision of the dynamic statistical theory of auto-nucleation and a reassessment of the critical sizes for imposed or heterogeneous nucleation, based on a simple and self-consistent thermodynamic model.

Thermodynamic modeling of post-entrapment crystallization in igneous phases

Inclusions of quenched silicate liquid in igneous phenocryst phases represent important windows into the pre-eruption chemistry of volcanic rocks. Melt inclusions are subject to a variety of potential modifications after entrapment, which obscure the connection between final inclusion composition, and entrapment conditions. We concentrate on the effects of post-entrapment crystallization (PEC) in the cooling inclusion. PEC is neither an isobaric nor an isochoric process. Pressure decreases between 2 and 27 bars per degree of cooling, depending on the chemistry of melt and host and on the degree of PEC. In the equilibrium case, between about 50% and 65% of this pressure effect is due to thermal expansivity of the liquid, 10–35% from thermal expansivity of the host, and 5–40% from mass transfer between the inclusion and host. This complicates the application of simple element-partitioning schemes for back-calculating the effects of post-entrapment crystallization except in the simplest cases. We present a thermodynamic algorithm for PEC correction. This method is based on the self-consistent thermodynamic model set used in the MELTS software package. The algorithm moves backward through the PEC process, incrementally adding equilibrium crystal composition to the liquid while accounting for consequent variations in pressure and oxygen fugacity. Entrapment conditions are assumed to have been reached when the instantaneous liquidus solid composition most closely matches that of the bulk host crystal. Besides giving information on the degree of PEC and initial inclusion composition, the proposed algorithm can provide constraints on the pressure, temperature and oxygen fugacity at the time of entrapment. Olivine- and orthopyroxene-hosted inclusions from Popocatépetl, Mexico help constrain pre-eruption conditions for mixed magmas from recent eruptive products. Feldspar-hosted inclusions from Satsuma-Iwojima, Japan suggest that these magmas were substantially undersaturated with respect to supercritical vapor phase at the time of entrapment and underwent on the order of 29% post-entrapment crystallization. Quartz-hosted inclusions can potentially be employed in more silicic compositions, but this will require refinement of existing thermodynamic models.

Quantum dot solar concentrators

The luminescent properties of core-shell quantum dots are being exploited in an unconventional solar concentrator, which promises to reduce the cost of photovoltaic electricity. Luminescent solar collectors have advantages over geometric concentrators in that tracking is unnecessary and both direct and diffuse radiation can be collected. However, development has been limited by the performance of luminescent dyes. We present experimental and theoretical results with a novel concentrator in which the dyes are replaced by quantum dots. We have developed a self-consistent thermodynamic model for planar concentrators and find that this three-dimensional flux model shows excellent agreement with experiment.

Self-Consistent Thermodynamic Description of a Nonmetallic Nonferromagnetic Solid (using silicon as an example)

An algorithm is developed for constructing a self-consistent thermodynamic model of the Debye type to simultaneously describe the temperature dependences of the entire complex of the basic thermal properties of a nonferromagnetic nonmetallic isotropic solid. Silicon is used as an example to demonstrate that, even within simplified model assumptions about the values of thermodynamic parameters, it is possible to make a very satisfactory self- consistent description of thermodynamic parameters of a solid in a wide temperature range of many hundreds of kelvins.

A new approach to modelling quantum dot concentrators

Luminescent collectors have advantages over geometric concentrators in that tracking is unnecessary and both direct and diffuse radiation can be collected. However, development has been limited by the performance of luminescent dyes. We have recently proposed a novel concentrator in which the dyes are replaced by quantum dots (QDs). Advantages over dyes include that the absorption threshold can be tuned by choice of dot diameter, and that the red shift between absorption and luminescence is related to the spread of dot sizes. In this paper we discuss how we have developed a self-consistent thermodynamic model for planar concentrators which allows for re-absorption by the QDs.

Thermodynamic assessment of the La–In system

Optimized descriptions of the phase diagram and thermodynamic properties of the La–In system are obtained from the experimental phase diagram and thermodynamic data by means of the computer program THERMO-CALC. A set of self-consistent thermodynamic model parameters is derived. The system contains seven intermetallic compounds. The standard enthalpies of formation of the seven compounds are calculated. Good agreement is obtained between the calculation and experimental results.

Thermodynamic assessment of the Pt–Sn system

The phase diagram and thermodynamic data of the Pt–Sn (Platinum–Tin) system have been assessed by the CALPHAD technique. A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the system. The intermediate phases are modeled as stoichiometric compounds. The calculated phase diagram and thermodynamic properties using the optimized model parameters agree very well with the experimental data.

A thermodynamic assessment of the La–Sn system

The phase diagram and thermodynamic data of the La–Sn (Lanthanum–Tin) system have been critically assessed by means of the computer program THERMO–CALC. A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the La–Sn system. With the optimized model parameters, the La–Sn phase diagram and the thermodynamic properties agree well with respective experimental data.

Thermodynamic modeling of the Cr-Pd and Mo-Pd systems

To assist the quantitative design of ultra-high strength (UHS) quantum steels containing Pd, a set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the Cr-Pd and Mo-Pd systems. These thermodynamic parameters are of importance to control the kinetics of solid-solid phase transformations, such as martensitic transformation, and precipitation of M2C carbide and austenite, relevant to the design of UHS steels in the Fe-C-Co-Cr-Mo-Ni-Pd system. The present thermodynamic modeling complements our previous report on the thermodynamic modeling of the Co-Pd, Fe-Pd, and Ni-Pd systems to facilitate quantitative design of UHS quantum steels.

Colloidal Dispersions in Lyotropic Lamellar Phases

Phase behavior studies and small-angle neutron scattering measurements of nonionic lamellar phases that contain dispersed colloidal particles show a strong interplay between semiflexible bilayers and particles. Addition of charged silica particles to lamellar phases formed with either mixtures of the nonionic surfactant n-dodecylpentaoxyethylene glycol monoether (C12E5) or C12E5 and hexanol (C6E0) in water changes the temperature of the phase transition from the single lamellar phase to its adjacent two-phase region. Close to the ternary phase boundary, particles weaken the long-range correlation between the highly undulated surfactant bilayers, as evidenced from the changes in the structure factor of the bilayers measured in the small-angle neutron scattering experiments. A self-consistent thermodynamic model is developed based on the free energy contributions of the binary interactions describing the phase behavior of the C12E5−water−colloid mixture. This model shows the effect of concentration, temperature, particle size, and bilayer rigidity on the phase behavior, and agrees well with the measurements.

Thermodynamic modeling of the nickel-lead-tin system

A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of nickel-lead (Ni-Pb) and nickel-tin (Ni-Sn) systems. Sublattice descriptions are used for thermodynamic modeling of the η-Ni3Sn, λ-Ni3Sn, η-Ni3Sn2, λ-Ni3Sn2, and Ni3Sn4 phases. A three-sublattice and a four-sublattice model are used to describe the molar Gibbs energies of η-Ni3Sn2 and λ-Ni3Sn2, respectively, and also to describe the second-order phase transition from η-Ni3Sn2 to λ-Ni3Sn2. In the majority of the cases, the agreement between the experimental data and the calculated values is very good. Since the experimental Ni-Pb-Sn ternary-phase diagrams are not known, several isothermal sections are calculated based on thermodynamic principles. They are of practical importance as related to microelectronics soldering applications.

Thermodynamic modeling of the Pd-X (X=Ag, Co, Fe, Ni) systems

A set of self-consistent thermodynamic model parameters is presented to describe the phase equilibria of the Ag-Pd, Co-Pd, Fe-Pd, and Ni-Pd systems. In most cases, the calculated values using the optimized model parameters agree very well with the experimental data. The FePd and FePd3 phases with large homogeneity ranges are described by the compound energy formalism. At present, insufficient thermodynamic data are available for these two phases. Therefore, experimental data on the heat of formation and/or the first-principle calculation of cohesive energies will be very useful for further refinement of thermodynamic parameters of FePd and FePd3 phases.