Self-consistent Thermodynamic Model Research Articles

Earth shaped by primordial H2 atmospheres.

Earth's water, intrinsic oxidation state and metal core density are fundamental chemical features of our planet. Studies of exoplanets provide a useful context for elucidating the source of these chemical traits. Planet formation and evolution models demonstrate that rocky exoplanets commonly formed with hydrogen-rich envelopes that were lost over time1. These findings suggest that Earth may also have formed from bodies with hydrogen-rich primary atmospheres. Here we use a self-consistent thermodynamic model to show that Earth's water, core density and overall oxidation state can all be sourced to equilibrium between hydrogen-rich primary atmospheres and underlying magma oceans in its progenitor planetary embryos. Water is produced from dry starting materials resembling enstatite chondrites as oxygen from magma oceans reacts with hydrogen. Hydrogen derived from the atmosphere enters the magma ocean and eventually the metal core at equilibrium, causing metal density deficits matching that of Earth. Oxidation of the silicate rocks from solar-like to Earth-like oxygen fugacities also ensues as silicon, along with hydrogen and oxygen, alloys with iron in the cores. Reaction with hydrogen atmospheres and metal-silicate equilibrium thus provides a simple explanation for fundamental features of Earth's geochemistry that is consistent with rocky planet formation across the Galaxy.

The Thermodynamic Modelling of the Zn Slag Fuming with the Use of Coal and Ammonia

Slag fuming process is used to extract zinc from the lead blast furnace slags and recently for the extraction of multiple elements from the complex primary and recycling feed streams, making the thermochemistry of the process challenging. To meet new challenges, computer models with predictive powers outside of the range of normal process conditions are necessary. These models cannot rely exclusively on sets of existing process data and must have a foundation in thermodynamics combined with reasonable kinetic factors. The accuracy of predictions largely depends on the quality of thermodynamic data, including phase equilibria, elemental distributions, and calorimetry measurements. Present study demonstrates the recent developments of the self-consistent thermodynamic model for the gas/slag/matte/metal/speiss/solid phases within the Cu-Pb-Zn-Fe-Ca-Si-O-S-Al-Mg-As-Sb system, applied to zinc fuming, with attention to the phase equilibria and partitioning of minor elements in the process. As a demonstration of calculations far outside of normal operations, the use of ammonia as an alternative to coal is investigated. It was shown that from the thermodynamic point of view the process can reach the same final concentration of zinc and the heat balance of the reactor in the same amount of time when coal is replaced in the process by ammonia.

Thermal and Elastic Properties of CexTh1 –xO2 Mixed Oxides: A Self-Consistent Thermodynamic Approach

A self-consistent thermodynamic model of thorium dioxide and its dilute alloy Ce0.05Th0.95O2, which are of great importance for atomic power engineering, has been constructed based on generalized Debye and Einstein models. In terms of this model, the temperature dependences of the bulk modulus, density, and heat capacity of the systems have been obtained. The anharmonicity of the acoustical and optical modes of the crystal lattice and its change in passing from ThO2 to Ce0.05Th0.95O2 has been discussed.

Тепловые и упругие свойства смешанных оксидов Ce-=SUB=-x-=/SUB=-Th-=SUB=-1-x-=/SUB=-O-=SUB=-2-=/SUB=-: самосогласованный термодинамический подход

AbstractA self-consistent thermodynamic model of thorium dioxide and its dilute alloy Ce_0.05Th_0.95O_2, which are of great importance for atomic power engineering, has been constructed based on generalized Debye and Einstein models. In terms of this model, the temperature dependences of the bulk modulus, density, and heat capacity of the systems have been obtained. The anharmonicity of the acoustical and optical modes of the crystal lattice and its change in passing from ThO_2 to Ce_0.05Th_0.95O_2 has been discussed.

Experimental investigation and thermodynamic modeling of an innovative molten salt for thermal energy storage (TES)

A novel computational thermodynamic approach based on thermodynamic principles was applied to design and develop innovative molten salt mixtures for thermal energy storage. In this work, the eutectic composition of the NaCl-NaF-Na2CO3 ternary system was predicted based on experimental data via computational thermodynamic approach. Substitutional solution model (SSM) was used to describe the Gibbs energies for all liquid phases. Thus, a set of self-consistent thermodynamic model parameters was obtained for three subsystems and the parameters were used to predict the eutectic composition of the NaF-NaCl-Na2CO3 ternary system. Results manifested that the predicted eutectic point of the ternary system were located at T = 849 K and XNaF = 21.66 mol%, XNaCl = 41.87 mol% and XNa2CO3 = 36.47 mol%. By means of Differential Scanning Calorimetry method, the predicted results were verified experimentally and the agreement between the measured and predicted values was satisfactory. Thermal-physical properties for eutectic salt mixtures, such as enthalpies of fusion, heat capacity, density and thermal stability, were also determined experimentally via thermal analysis methods in this work. Through computational thermodynamics approach, an innovative eutectic salt was designed and developed as thermal energy storage (TES) materials at high temperatures, especially it can be serve as candidate thermal energy storage materials for next generation concentrated solar power (CSP) plants.

Phonon Anharmonicity and Thermodynamic Properties of Strongly Correlated Iron Monosilicide

Two computational approaches – a thermodynamic model based on results of ab initio calculations of the ground state and the self-consistent thermodynamic model have been applied to study thermal and elastic properties of iron monosilicide. It is shown that conventional DFT fails to reproduce experimental data for this strongly correlated compound. In addition, we have performed comparative analysis of anharmonicity of the acoustic and optical phonons in FeSi and their impact on the temperature dependencies of thermodynamic properties of FeSi.

Thermodynamic simulation of the elastic and thermal properties of cobalt monosilicide

A self-consistent thermodynamic model is used to calculate the temperature dependences of the heat capacity, the thermal expansion coefficient, the bulk compression modulus, the density, Debye temperature, and the Gruneisen parameter of CoSi in the temperature range 0–1400 K. The calculation results agree well with the existing experimental data and can be used to predict the properties of CoSi in the temperature range that has not been experimentally studied. Cobalt monosilicide is shown to have a significant phonon anharmonicity, which can be caused by an electron–phonon interaction, and this anharmonicity should be taken into account in the simulation of its thermoelectric properties.

Self-consistent modeling of thermal and elastic properties of unconventional superconductor PuCoGa5

A self-consistent thermodynamic model of PuCoGa5 is developed, which for the first time takes into account the anharmonicity of both acoustic phonons, described within a Debye model, and optical phonons, considered in an Einstein approximation. Within the framework of this model, we have calculated the temperature dependencies of lattice contributions to heat capacity, bulk modulus, volumetric coefficient of thermal expansion, Debye and Einstein temperatures and their Grüneisen parameters. The electronic heat capacity of PuCoGa5 is obtained, which demonstrates an unusual temperature dependence with two maxima. In addition, it is shown that an abnormal low temperature behavior of the bulk modulus of PuCoGa5 is not caused by the effects of lattice anharmonicity and is most likely due to the valence fluctuations, which is in agreement with previous studies.

Phonon anharmonicity and Gruneisen parameters of alpha-plutonium

A self-consistent thermodynamic model of alpha-phase of plutonium is constructed. The calculations of thermal and elastic properties of α-Pu, carried out within this model, demonstrate that anomalously strong temperature dependence of the bulk modulus and unusually high value of the coefficient of thermal expansion of α-Pu are caused by its strong lattice anharmonicity. The isothermal and isobaric Gruneisen parameters of α-Pu and δ-Pu Pu0.96Ga0.04 are calculated. It is shown that wide spread of the values of Gruneisen parameter of α-Pu, obtained previously from different experimental data, is explained by the dependence of Gruneisen parameter of α-Pu on temperature.

Lattice anharmonicity and thermal properties of strongly correlated Fe1–x Co x Si alloys

The temperature dependences of the thermal and elastic properties of strongly correlated metal alloys Fe1–xCoxSi (x = 0.1, 0.3, 0.5) with different atomic chiralities have been calculated in the framework of the self-consistent thermodynamic model taking into account the influence of lattice anharmonicity. The lattice contributions to the heat capacity and thermal expansion coefficient of the alloys have been determined using the experimental data. It has been demonstrated that the invar effect in the thermal expansion of the lattice observed in the magnetically ordered region of Fe0.7Co0.3Si and Fe0.5Co0.5Si is not related to the lattice anharmonicity, even though its appearance correlates with variations in the atomic chirality.

Phonon anharmonicity of iron monosilicide

A self-consistent thermodynamic model of the crystal lattice of FeSi is developed. In the framework of this model calculations of the heat capacity, coefficient of thermal expansion and bulk modulus of FeSi in a wide temperature range are carried out. On the basis of comparison with the experimental data, electronic contribution to the heat capacity of FeSi is obtained, the temperature dependence of which is caused by the insulator to metal transition, accompanied by disappearance of the energy gap in the electronic spectrum. We have found strong phonon anharmonicity of FeSi, which is manifested in substantial reduction of the Debye temperature and Gruneisen parameter with increasing temperature. The obtained values for the Gruneisen parameter of the crystal lattice of FeSi correlate with the estimations of the Gruneisen parameters for individual branches of the phonon spectrum of FeSi measured in neutron and synchrotron experiments.

A self-consistent thermodynamic model of metallic systems. Application for the description of gold

A self-consistent thermodynamic model of metallic system is presented. The expression for the Gibbs energy is derived, which incorporates elastic (static) energy, vibrational energy within the Debye model, and electronic part in Hartee-Fock approximation. The elastic energy is introduced by a volume-dependent anharmonic potential. From the Gibbs energy all thermodynamic quantities, as well as the equation of state, are self-consistently obtained. The model is applied for the description of bulk gold in temperature range 0 ≤ T ≲ 1300 K and external pressure up to 30 GPa. The calculated thermodynamic properties are illustrated in figures and show satisfactory agreement with experimental data. The advantages and opportunities for further development of the method are discussed.

Molecular dynamics simulations and thermodynamic modeling of NaCl–KCl–ZnCl2 ternary system

The NaCl–KCl–ZnCl2 ternary system is examined and modeled using the CALPHAD methodology in conjunction with molecular dynamics (MD) simulations. In particular, MD simulations are used for calculating liquid enthalpies of mixing as a function of composition for the ternary and its binary sub-systems. In addition, key structural features are obtained from MD that is then used for informing the employed two-sublattice ionic liquid model (Na+1, K+1: Cl−1, ZnCl2), which describes the ternary liquid phase. The structure of the simulated liquid systems show that Zn+2 cations primarily exhibit 4-fold coordination in addition to a smaller percentage of 5-fold followed by 3-fold coordination; in contrast, the coordination of both Na+ and K+ cations are distributed between 2- and 4-fold states. The optimized self-consistent thermodynamic model parameters show good agreement with MD data obtained in this work and available experimental literature data.

A thermodynamic model of thermal end elastic properties of curium

A self-consistent thermodynamic model of curium is developed. In the framework of this model the temperature dependencies of heat capacity, coefficient of thermal expansion, bulk modulus and Debye temperature of Cm are calculated. It is shown that the phonon anharmonicity of Cm is weaker than in the case of Np and δ-Pu, but stronger than in lanthanides.

Heat capacity of solid tantalum: Self-consistent calculation

A review is given of the results of calculations of the heat capacity C(T) of solid tantalum in a wide temperature range from helium temperatures to the melting point of metal T m . Calculation of the heat capacity of the metal within the framework of a self-consistent thermodynamic model (SCTDM) of a solid body versus the experimental (reference) data on C(T) is performed. In the range from the Debye temperature θ0 ∼ 250 K to the beginning of the premelting region T ∼ 0.8T m , the standard SCTDM ensured an adequate description of the tantalum heat capacity with a mean square error of less than 0.5 J K−1 mol−1. At lower and higher temperatures, extra models are needed. A number of thermodynamic characteristics of the element are determined whose values were previously absent or needed verification.

The influence of phonon anharmonicity on thermal and elastic properties of neptunium

A self-consistent thermodynamic model describing the thermal and elastic properties of α- and β-phases of neptunium was developed. The presence of strong phonon anharmonicity of Np is established. The obtained results are in good agreement with the experimental data and enable to predict the Np properties in wide temperature range.

Thermodynamic simulation of thermophysical and elastic properties of plutonium

A self-consistent thermodynamic model taking into account phonon anharmonicity effects is used for calculating the temperature dependences of the lattice components of thermophysical and elastic properties of the alpha-phase of plutonium. The theoretical curves are in good agreement with experimental data and make it possible to compare the mechanisms of formation of thermophysical and elastic properties of the alpha- and delta-phases of plutonium. The entropy of both phases is estimated, the role of the lattice magnetic anharmonicity is analyzed, and the key question concerning the reasons for stabilization of the delta-phase of plutonium relative to its α-phase is considered.

Thermodynamic modeling of the (U,La)O2±x solid solution phase

Lanthanide (Ln) fission products have high fission yields and are known to form solid solutions with UO2 over a wide range of composition. As part of a larger effort to predict phase stability of the mixed metal oxide (U,Ln)O2±x solid solution phase, a comprehensive and self-consistent thermodynamic model for (U,La)O2±x has been developed through the use of the compound energy formalism (CEF) as implemented in the CALPHAD (CALculation of PHAse Diagram) computational thermodynamic approach. The reported experimental oxygen chemical potentials for both hyper- and hypo-stoichiometric (U,La)O2±x have been assessed and used to evaluate interaction parameters for the phase representation. The lattice stability of hypothetical “LaO2” in the CaF2 structure necessary to describe the Gibbs energy of end-members for the La-doped UO2 solution phase has been obtained from first-principles calculations based on density functional theory. With respect to LaO1.5 it is determined to equal +8739J/mol. Good agreements between the calculated and experimental oxygen partial pressures have been obtained by introducing interaction parameters for the mixing between U and La in the metal cation sublattice. Calculated partial pressures of oxygen in equilibrium with the (U,La)O2±x solution phase at various temperatures are presented.

Effect of phonon anharmonicity on the thermophysical and elastic properties of platinum

A self-consistent thermodynamic model is constructed, which describes the effect of anharmonicity of crystal lattice on heat capacity, coefficient of thermal expansion, density, and bulk modulus of palladium. Fairly good agreement with experimental data is obtained within the model being developed, and the contribution to heat capacity associated with the effect of anharmonicity is identified. Significant increase is demonstrated of the effect made by lattice anharmonicity on the thermo-physical properties in the region of temperatures significantly exceeding the Debye temperature.

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

The temperature dependences of the total heat capacity and the lattice components of the bulk modulus, the volume thermal expansion coefficient, and the mean-square deviation of atoms from the equilibrium positions of nearly magnetic δ-plutonium (using the Pu0.96Ga0.04 alloy as an example) have been calculated within the framework of the self-consistent thermodynamic model. The electronic heat capacity has been calculated using the results obtained in terms of the self-consistent spin-fluctuation theory based on the inclusion of the strong magnetic anharmonicity, which leads to a splitting of the electronic spectra by fluctuating exchange fields. On this basis, the effect of phonon anharmonicity not only on the lattice heat capacity but also on other thermal and elastic properties has been considered.