High Temperature Thermodynamics Research Articles

A novel process for producing Al-Si alloy utilizing aluminum-silicon oxide extracted from coal fly ash

As a kind of solid waste rich in aluminum and silicon resources, the comprehensive utilization of coal fly ash (CFA) will be of great significance to reduce environmental pollution and improve economic benefits. This work proposed a facile and environmentally friendly cleaning process for producing Al-Si alloy by molten salt electrolysis from CFA extract, aluminum-silicon oxide (ASO). The dissolution behavior and dissolution reaction mechanism of ASO were studied by high temperature visual dissolution experiment, thermodynamics analysis and phase analysis. Due to the chemical reaction between ASO and cryolite-based melt, ASO powder dissolves rapidly in melt and the dissolution rate of ASO is not determined by the phase compositions but by the mass ratio of Al2O3/SiO2. For replenishing the oxide concentration in the electrolyte as quick as possible, the proper mass ratio of Al2O3/SiO2 is in the range of 0.75–7.5. The electrochemical co-reduction behavior of Si (IV) and Al (III) ions on the W electrode was performed by cyclic voltammetry and square wave voltammetry. The results indicated that the reduction of Si (IV) ion in the melt was a two-step irreversible process. Hypoeutectic Al-Si alloy and eutectic Al-Si alloy were prepared by galvanostatic electrolysis using ASO as raw material. This innovative technology can realize high-value recycling of CFA resources and low carbon emission, low energy consumption production of Al-Si alloy.

Sustainable space technologies—Strategies toward a predictive aerothermal design of re-useable space transportation systems

This paper presents a review of current aerothermal design and analysis methodologies for spacecraft. It briefly introduces the most important system architectures, including rockets, gliders, and capsule-based configurations, and gives an overview of the specific aerothermal and thermo-chemical effects that are encountered during their different flight phases and trajectories. Numerical and experimental design tools of different fidelity levels are reviewed and discussed, with a specific focus placed on the present limitations and uncertainty sources of models for the wide range of physical phenomena that are encountered in the analyses. This includes high temperature thermodynamics, chemical effects, turbulence, radiation, and gasdynamic effects. This is followed by a summary of current predictive capabilities and research foci, with missing capabilities identified. Finally, a future strategy toward an efficient and predictive aerothermal design of re-useable space transportation systems is proposed.

Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon

Silicon is indispensable in semiconductor industry. Understanding its high-temperature thermodynamic properties is essential both for theory and applications. However, first-principle description of high-temperature thermodynamic properties of silicon (thermal expansion coefficient and specific heat) is still incomplete. Strong deviation of its specific heat at high temperatures from the Dulong–Petit law suggests substantial contribution of anharmonicity effects. We demonstrate, that anharmonicity is mostly due to two transverse phonon modes, propagating in (111) and (100) directions, and can be quantitatively described with formation of the certain type of nanostructured planar defects of the crystal structure. Calculation of these defects' formation energy enabled us to determine their input into the specific heat and thermal expansion coefficient. This contribution turns out to be significantly greater than the one calculated in quasi-harmonic approximation.

Terahertz saturable absorption from relativistic high-temperature thermodynamics in black phosphorus

Terahertz saturable absorption from relativistic high-temperature thermodynamics in black phosphorus

Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon

Planar Defects as a Way to Account for Explicit Anharmonicity in High Temperature Thermodynamic Properties of Silicon

Impact of increased temperatures on the geochemical behaviour of trivalent actinides in aquatic systems

Abstract. The Safety Case for a radioactive waste repository in deep geological formations requires detailed chemical and thermodynamic information on the stored radionuclides in their relevant oxidation states. Although a comprehensive summary of critically evaluated thermodynamic data is available via the blue book series of the NEA-TDB (“Nuclear Energy Agency – Thermochemical Database”), the majority of this data is limited to ambient conditions (Grenthe et al., 2020). In the case of the disposal of high-active, heat-producing waste, however, the near-field of the repository will experience increased temperatures at early operative phases for several hundred or a few thousand years. Radionuclides may come into contact with aquatic solutions or brines at elevated temperatures in the case of early canister failure. Besides other factors of the overall disposal concept (e.g. the geometry of the repository, type and amount of stored radionuclide inventories), host rock characteristics themselves limit the extent of the allowable temperature increase. For example, in clay formations the maximum temperature should stay at around or below ∼100∘C in order to avoid an irreversible change in the host rock retention capacity, whereas rock salt allows much higher temperatures of up to 200 ∘C. Increased temperatures will have a distinct impact on the geochemical behaviour of radionuclides, potentially affecting their mobility and retention in the near field. Besides reactions at the solid–liquid interface (e.g. dissolution/precipitation reactions of the waste matrix, sorption reactions of the radionuclides to surfaces), complexation reactions with inorganic and organic ligands present in the aqueous phase potentially affect migration behaviour of the radionuclides. A quantitative thermodynamic description of these processes requires standard stability constants (log⁡βn0(T)), as well as standard reaction enthalpies and entropies (ΔrHm,n0, ΔrSm,n0). The precise experimental determination of these data for all relevant radionuclide/ligand reactions requires a vast amount of time and effort. In this regard, reliable extrapolation methods in particular for standard stability constants valid for 25 ∘C to higher temperatures are considered to support a comprehensive description. Recently, the German Federal Ministry of Education and Research (BMBF)-funded collaborative research project “Therm AC” focused on the experimental determination of new thermodynamic data at higher temperatures, as well as the comparison with the analogous results yielded by extrapolation methods. The Thermochemical Database Project of the OECD-NEA (NEA-TDB) is currently in the process of preparing a comprehensive state-of-the-art report on the high temperature thermodynamics of radionuclides, further emphasizing the particular relevance of this interesting topic. Within this contribution, a critical overview on the recent advances in the field of high temperature studies of radionuclides in aqueous solutions will be given. Besides summarizing information on key technical aspects relevant for high temperature studies, the effect of increased temperatures on the complexation of trivalent actinides with chloride will be discussed in more detail in order to illustrate newly derived in-depth understanding of the impact of increased temperatures on the (geo)chemical behaviour of trivalent actinides on the molecular scale (Skerencak-Frech et al., 2014).

Low-Temperature Mechanical Instabilities Govern High-Temperature Thermodynamics in the Austenite Phase of Shape Memory Alloy Constituents: Ab Initio Simulations of NiTi, NiZr, NiHf, PdTi, and PtTi

Recent studies on the constituent binaries of common NiTi-based shape memory alloys (NiTi, NiZr, NiHf, PdTi, PtTi) have led to questions regarding the accuracy of current phase diagrams, including the existence of theoretical phases, and the atomistic nature of stability in observed martensitic and austenitic phases. These issues are investigated here with ab initio molecular dynamics. Theoretically identified ground state structures are found to become mechanically unstable well below room temperature, while the experimentally determined martensite structures are found to be stabilized by anharmonic effects at elevated temperatures. The martensite phases of all binaries are found to transition to a common austenite structure (cubic B2), with transition temperatures in agreement with available experiments. Interestingly, the B2 structures are unstable at low temperature but are stabilized by large anharmonic effects that also govern the martensitic transition. An observed signature of this anharmonicity is the transitory symmetry breaking of B2 to a distorted, glassy structure known as B2’. The energy of the observed B2’ structure is quantified at low temperatures and, across the binaries, is found to be linearly correlated to the anharmonic energy and entropy of transition from the martensite phases to high-temperature B2. The implication of this finding is the properties of the low-temperature B2’ structure govern anharmonicity and ultimately the high-temperature transitions to B2. Means of utilizing these results to simplify the characterization of the austenite thermodynamics and associated transitions important to the shape memory effect are discussed. A reduced order model is presented that captures the competition between crystal lattice energy differences (B2 vs martensite) and the degree of anharmonicity characterized by the B2-B2’ energy differences for these sytems.

Microalgae to biofuels through hydrothermal liquefaction: Open-source techno-economic analysis and life cycle assessment

Hydrothermal liquefaction is a promising conversion technology in algae biofuel research due to its ability to agnostically convert proteins, carbohydrates, and lipids to biocrude. The high-temperature conditions that define this conversion process require the material to maintain a subcritical liquid state, which complicates the assessment of accurate thermochemical properties due to the required pressure. To clarify this issue, this work compares the estimated performance of algal hydrothermal liquefaction between different thermodynamic models. A process model was developed in Aspen Plus from a robust assessment of current literature. Techno-economic assessment and life-cycle assessment metrics are derived from this model and used as key performance indicators. The baseline fuel price contribution of hydrothermal liquefaction is $0.45 per liter gasoline equivalent. Independently decreasing the temperature from 350 °C to 260 °C while maintaining yield reduces the conversion cost by 19%, illustrating the importance of understanding the high-temperature thermodynamics of the system. Different thermodynamic property models can vary fuel conversion cost results by $0.07 per liter gasoline equivalent. The baseline global warming potential is +23 g CO2 eq MJ−1 and the net energy ratio is 0.30. Environmental metrics beyond global warming potential and net energy ratio are also discussed for the first time. Uncertainties in conversion performance are bounded through a scenario analysis that manipulates parameters such as product yield and nutrient recycle to produce a range of economic and environmental metrics. The work is supplemented with an open source model to support future hydrothermal liquefaction assessments and accelerate the development of commercial-scale systems.

High-temperature thermodynamics of ZnO–NH4Cl–H2O system

On the basis of the principles of simultaneous equilibrium, conservation of mass, and aqueous electronic charge neutrality and the correspondence principle of ion entropy, the high-temperature thermodynamics of the ZnO–NH4Cl–H2O system was studied to predict solubility and construct Zn species distribution. The model was constructed precisely by using the MATLAB program. The total Zn2+ concentration in the solution was affected significantly by temperature and total ammonium concentration. ZnNH3Cl3− was the predominant species in the ZnO–NH4Cl–H2O system. The solubility of zinc diammine chloride in NH4Cl solution (>2 mol·L−1) in the temperature range of 303–353 K was determined using equilibrium experiments, which had results that agreed well with the theoretical value. The data and high-temperature thermodynamic model used in this paper are reliable.

Thermodynamics of rotating quantum matter in the virial expansion

We characterize the high-temperature thermodynamics of rotating bosons and fermions in two- (2D) and three-dimensional (3D) isotropic harmonic trapping potentials. We begin by calculating analytically the conventional virial coefficients $b_n$ for all $n$ in the noninteracting case, as functions of the trapping and rotational frequencies. We also report on the virial coefficients for the angular momentum and associated moment of inertia. Using the bn coefficients, we analyze the deconfined limit (in which the angular frequency matches the trapping frequency) and derive explicitly the limiting form of the partition function, showing from the thermodynamic standpoint how both the 2D and 3D cases become effectively homogeneous 2D systems. To tackle the virial coefficients in the presence of weak interactions, we implement a coarse temporal lattice approximation and obtain virial coefficients up to third order.

Recent Developments in High Temperature Thermodynamic Properties of Nuclear Reactor Oxide Fuel

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Mach stem deformation in pseudo-steady shock wave reflections

The deformation of the Mach stem in pseudo-steady shock wave reflections is investigated numerically and theoretically. The numerical simulation provides the typical flow patterns of Mach stem deformation and reveals the differences caused by high-temperature gas effects. The results also show that the wall jet, which causes Mach stem deformation, can be regarded as a branch of the mainstream from the first reflected shock. A new theoretical model for predicting the Mach stem deformation is developed by considering volume conservation. The theoretical predictions agree well with the numerical results in a wide range of test conditions. With this model, the wall-jet velocity and the inflow velocity from the Mach stem are identified as the two dominating factors that convey the influence of high-temperature thermodynamics. The mechanism of high-temperature gas effects on the Mach stem deformation phenomenon are then discussed.

High-temperature thermodynamics of spin-polarized Fermi gases in two-dimensional harmonic traps

Using a second-order quantum virial expansion, we theoretically study the high-temperature thermodynamics of spin-polarized Fermi gases with $p$-wave interaction confined in two-dimensional harmonic traps. The second virial coefficient is calculated based on the energy spectrum of two harmonically trapped fermions. We find that the two-body spectrum can correctly be evaluated only when the $p$-wave effective range is properly considered, which is referred to as the well-known Wigner's bound. According to the quantum virial expansion, the high-temperature thermodynamics of the system is then discussed based on the two-body solutions. In addition, we investigate the high-temperature behavior of $p$-wave contacts in harmonic traps within the quantum virial expansion, which characterize a set of universal relations of strongly interacting spin-polarized Fermi gases. Our results can provide an accurate benchmark at high temperature for future numerical simulations as well as high-precision thermodynamic measurements of harmonically trapped spin-polarized Fermi gases in two dimensions.

Combined computational and experimental investigation of high temperature thermodynamics and structure of cubic ZrO2 and HfO2

Structure and thermodynamics of pure cubic ZrO2 and HfO2 were studied computationally and experimentally from their tetragonal to cubic transition temperatures (2311 and 2530 °C) to their melting points (2710 and 2800 °C). Computations were performed using automated ab initio molecular dynamics techniques. High temperature synchrotron X-ray diffraction on laser heated aerodynamically levitated samples provided experimental data on volume change during tetragonal-to-cubic phase transformation (0.55 ± 0.09% for ZrO2 and 0.87 ± 0.08% for HfO2), density and thermal expansion. Fusion enthalpies were measured using drop and catch calorimetry on laser heated levitated samples as 55 ± 7 kJ/mol for ZrO2 and 61 ± 10 kJ/mol for HfO2, compared with 54 ± 2 and 52 ± 2 kJ/mol from computation. Volumetric thermal expansion for cubic ZrO2 and HfO2 are similar and reach (4 ± 1)·10−5/K from experiment and (5 ± 1)·10−5/K from computation. An agreement with experiment renders confidence in values obtained exclusively from computation: namely heat capacity of cubic HfO2 and ZrO2, volume change on melting, and thermal expansion of the liquid to 3127 °C. Computed oxygen diffusion coefficients indicate that above 2400 °C pure ZrO2 is an excellent oxygen conductor, perhaps even better than YSZ.

High temperature thermodynamics of spinodal decomposition in arc deposited TixNbyAlzN coatings

Using first principles calculations and experimental methods we show that B1 structured solid solution TixNbyAlzN can be grown. The mixing free energy surface indicates that the alloys should decompose. Theoretical analysis of the thermodynamic driving force towards the spinodal decomposition shows that the force can be different in alloys with equally low thermodynamic stability but different Nb content, indicating that the detailed picture of the decomposition should also be different. Electron microscopy and nanoindentation underlines different age hardening of the samples. We demonstrate that an alloy with the optimized composition, Ti0.42Nb0.17Al0.41N combines high thermal stability and age hardening behavior.

High-temperature thermodynamics of the honeycomb-lattice Kitaev-Heisenberg model: A high-temperature series expansion study

We develop high temperature series expansions for the thermodynamic properties of the honeycomb-lattice Kitaev-Heisenberg model. Numerical results for uniform susceptibility, heat capacity and entropy as a function of temperature for different values of the Kitaev coupling $K$ and Heisenberg exachange coupling $J$ (with $|J|\le |K|$) are presented. These expansions show good convergence down to a temperature of a fraction of $K$ and in some cases down to $T=K/10$. In the Kitaev exchange dominated regime, the inverse susceptibility has a nearly linear temperature dependence over a wide temperature range. However, we show that already at temperatures $10$-times the Curie-Weiss temperature, the effective Curie-Weiss constant estimated from the data can be off by a factor of 2. We find that the magnitude of the heat capacity maximum at the short-range order peak, is substantially smaller for small $J/K$ than for $J$ of order or larger than $K$. We suggest that this itself represents a simple marker for the relative importance of the Kitaev terms in these systems. Somewhat surprisingly, both heat capacity and susceptibility data on Na$_2$IrO$_3$ are consistent with a dominant {\it antiferromagnetic} Kitaev exchange constant of about $300-400$ $K$.

High-temperature thermodynamics of silver: Semi-empirical approach* *Project supported by the Major Research Project, UGC, New Delhi, India (Grant No. 42-771/2013 (SR)).

We report high-temperature thermodynamics for fcc silver by combining ab initio phonon dynamics to empirical quadratic temperature-dependent term for anharmonic part of Helmholtz free energy. The electronic free energy is added through an interpolation scheme, which connects ambient condition free electron gas model to Thomas–Fermi results. The present study shows good agreement with experimental and reported findings for several thermal properties, and the discrepancy observed in some caloric properties is addressed. The decreases in the product of volume thermal expansion coefficient and isothermal bulk modulus and in the constant volume anharmonic lattice specific heat at high temperature are the clear evidences of proper account of anharmonicity. The present study also reveals that T 2–dependent anharmonic free energy is sufficient for correct evaluation of thermal pressure and conventional Grüneisen parameter. We observe that the intrinsic phonon anharmonicity starts dominating above characteristic temperature, which is attributed to higher order anharmonicity and can be related to higher order potential derivatives. We conclude that the uncorrelated and largeamplitude lattice vibrations at high temperature raise dominating intrinsic thermal stress mechanism, which surpasses the phonon-anharmonism and requires future consideration.

Quasi-coarse-grained dynamics: modelling of metallic materials at mesoscales

A computationally efficient modelling method called quasi-coarse-grained dynamics (QCGD) is developed to expand the capabilities of molecular dynamics (MD) simulations to model behaviour of metallic materials at the mesoscales. This mesoscale method is based on solving the equations of motion for a chosen set of representative atoms from an atomistic microstructure and using scaling relationships for the atomic-scale interatomic potentials in MD simulations to define the interactions between representative atoms. The scaling relationships retain the atomic-scale degrees of freedom and therefore energetics of the representative atoms as would be predicted in MD simulations. The total energetics of the system is retained by scaling the energetics and the atomic-scale degrees of freedom of these representative atoms to account for the missing atoms in the microstructure. This scaling of the energetics renders improved time steps for the QCGD simulations. The success of the QCGD method is demonstrated by the prediction of the structural energetics, high-temperature thermodynamics, deformation behaviour of interfaces, phase transformation behaviour, plastic deformation behaviour, heat generation during plastic deformation, as well as the wave propagation behaviour, as would be predicted using MD simulations for a reduced number of representative atoms. The reduced number of atoms and the improved time steps enables the modelling of metallic materials at the mesoscale in extreme environments.

A Study for Initial Solidification of Sn-Pb Alloy During Continuous Casting: Part II. Effects of Casting Parameters on Initial Solidification and Shell Surface

The initial shell solidification of liquid steel in the mold has significant influence on both surface and internal quality of the final slab, and it is mainly determined by the high transient high temperature thermodynamics occurring in the mold. This study investigated the effects of casting parameters like casting temperature, mold oscillation frequency, and stroke on the initial solidification of a Sn-Pb alloy through the use of a mold simulator to allow the clear understanding of the inter-relationship between irregular shell solidification, heat transfer, negative strip time (NST), and casting conditions. Results suggested that the shell surface oscillation marks (OMs) are strongly depending upon the fluctuations of meniscus responding temperatures and heat flux. An abrupt sudden fluctuation of high frequency temperature and heat flux at the meniscus during the NST would deteriorate the shell surface and leads to deep OMs. The fluctuations of responding temperature and heat flux are determined by the NST, meniscus solidification, and oil infiltration, which in turn are influenced by casting conditions, like casting temperature, oscillation frequency, stroke, etc.

Tunable high-temperature thermodynamics of weakly interacting dipolar gases

We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperatures, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the $s$-wave scattering length for the bosonic system is tunable and its absolute value is made small, then the $s$-wave interactions dominate and the dipolar gas behaves like a weakly interacting Bose gas with isotropic $s$-wave interactions. If the generalized scattering lengths for the fermionic system are tunable, then the dipole length can enter linearly in the virial equation of state, enhancing the dipole-dipole effects in the thermodynamic observables.