Phenomenological Thermodynamic Model Research Articles

The re-entrant transition from the molecular to atomic phases of dense fluids: The case of hydrogen.

A simple phenomenological thermodynamic model is developed to describe the chemical bonding and unbonding in homonuclear diatomic systems. This model describes the entire phase diagram of dimer-forming systems and shows a transition from monomers to dimers, with monomers favored at both very low and very high pressures, as well as at high temperatures. In the context of hydrogen, the former region corresponds to hydrogen present in most interstellar gas clouds, while the latter is associated with the long sought-after fluid metallic phase. The model predicts a molecular to atomic fluid transition in dense deuterium, which is in agreement with recently reported experimental measurements.

Theory-guided materials design of multiphase alloys with superior stiffness at finite temperatures

Aiming at designing Mg alloys with a significantly increased stiffness at elevated temperatures, we propose a high-precision multi-scale methodology to compute temperature-dependent elastic modulus of homogeneous multiphase alloys. The proposed method combines (i) first-principles calculations of temperature- and solid solubility-dependent elastic properties in individual phases with (ii) a two-level multiphase homogenization at the continuum level and (iii) a phenomenological thermodynamic modeling by the CALPHAD approach. According to the post-average approximation during the calculation, the stresses and strains of individual phases in the alloy are superimposed before undergoing the average approximation. This is different from the traditional method which consider forces as acting axially assumptions of isostrain and isostress model and followed by numerical averaging. We applied the proposed method in light-weight Mg-alloys, in particular, a three-phase alloy with the composition Mg0.878Al0.083Si0.039, and verified it through experimental measurements. The present work identifies that MgxAlySi1-x-y with 0 ≤ x ≤ 0.87 and 0 ≤ y ≤ 0.87-x are candidate compositions with Young's modulus exceeding 60 GPa at 623 K.

Computing grain boundary “phase” diagrams

AbstractGrain boundaries (GBs) can be treated as two‐dimensional (2‐D) interfacial phases (also called “complexions”) that can undergo interfacial phase‐like transitions. As bulk phase diagrams and calculation of phase diagram (CALPHAD) methods serve as a foundation for modern materials science, we propose to extend them to GBs to have equally significant impacts. This perspective article reviews a series of studies to compute the GB counterparts to bulk phase diagrams. First, a phenomenological interfacial thermodynamic model was developed to construct GB lambda diagrams to forecast high‐temperature GB disordering and related trends in sintering and other properties for both metallic and ceramic materials. In parallel, an Ising‐type lattice statistical thermodynamic model was utilized to construct GB adsorption (segregation) diagrams, which predicted first‐order GB adsorption transitions and critical phenomena. These two simplified thermodynamic models emphasize the GB structural (disordering) and chemical (adsorption) aspects, respectively. Subsequently, hybrid Monte Carlo and molecular dynamics atomistic simulations were used to compute more rigorous and accurate GB “phase” diagrams. Computed GB diagrams of thermodynamic and structural properties were further extended to include mechanical properties. Moreover, machine learning algorithms were combined with atomistic simulations to predict GB properties as functions of four independent compositional variables and temperature in a 5‐D space for a given GB in high‐entropy alloys or as functions of five GB macroscopic (crystallographic) degrees of freedom plus temperature and composition for a binary alloy in a 7‐D space. Other relevant studies are also examined. Future perspective and outlook, including two emerging fields of high‐entropy grain boundaries (HEGBs) and electrically (or electrochemically) induced GB transitions, are discussed.

Thermodynamic Calculation of Fe–N and Fe–Ga Melting Diagrams at Pressures from 0.1 MPa to 7 GPa

This paper presents results of melting-diagrams’ calculations for the Fe–N and Fe–Ga systems at atmospheric pressure (0.1 MPa) and at high pressures (3, 5, and 7 GPa). Thermodynamic calculations are performed within the models of phenomenological thermodynamics. As shown, the increase of pressure results in destabilization of high-temperature b.c.c.-Fe modification in Fe–N system and stabilization of Fe4N equilibrium with the liquid phase. In Fe–Ga system, the intermetallic compounds Fe3Ga, Fe6Ga5, Fe3Ga4, and FeGa3 retain their stability up to pressure of 7 GPa. The stabilization of Fe4N equilibrium with the liquid phase at high pressures indicates that the Fe4N can be a competing phase in the gallium-nitride crystallization from the Fe–Ga–N system melt.

A numerical investigation of the nucleation and the propagation of NiTi martensitic transformation front under impact loading

A numerical investigation of NiTi SMA alloy under impact loading is presented in this paper. It is aimed at better understanding the observed behavior of NiTi SMA specimen loaded at impact velocities (up to 50m/s). A phenomenological thermodynamic model with an explicit integration frame is chosen and implemented as a user's law in Abaqus explicit commercial code. The parameters of the model are determined from the usual thermal-mechanical testing data without any tuning. The comparison between numerical and experimental results shows a satisfactory agreement, which proves the pertinence of the proposed numerical model.Using this numerical model, the reason of the experimentally observed inconstant strain level ahead of the phase transformation front is found. Instead of a material feature of NiTi SMA under impact loading, such a phenomenon is only due to the loading condition. Virtual tests at very high impact velocities are performed. Steep impulses without a rising time is chosen in order to have only one transformation front propagating inside the specimen, knowing that it is not possible to obtain such a simple condition in a real tensile test. A steady transformation front is observed and there is an asymptotical speed limit of this propagating front when the impact velocity increases. This speed limit is higher than the shear elastic wave speed but lower than the longitudinal elastic wave speed.

Quantum-Mechanical Assessment of the Energetics of Silver Decahedron Nanoparticles.

We present a quantum-mechanical study of silver decahedral nanoclusters and nanoparticles containing from 1 to 181 atoms in their static atomic configurations corresponding to the minimum of the ab initio computed total energies. Our thermodynamic analysis compares T = 0 K excess energies (without any excitations) obtained from a phenomenological approach, which mostly uses bulk-related properties, with excess energies from ab initio calculations of actual nanoclusters/nanoparticles. The phenomenological thermodynamic modeling employs (i) the bulk reference energy, (ii) surface energies obtained for infinite planar (bulk-related) surfaces and (iii) the bulk atomic volume. We show that it can predict the excess energy (per atom) of nanoclusters/nanoparticles containing as few as 7 atoms with the error lower than 3%. The only information related to the nanoclusters/nanoparticles of interest, which enters the phenomenological modeling, is the number of atoms in the nanocluster/nanoparticle, the shape and the crystallographic orientation(s) of facets. The agreement between both approaches is conditioned by computing the bulk-related properties with the same computational parameters as in the case of the nanoclusters/nanoparticles but, importantly, the phenomenological approach is much less computationally demanding. Our work thus indicates that it is possible to substantially reduce computational demands when computing excess energies of nanoclusters and nanoparticles by ab initio methods.

A phenomenological base semi-physical thermodynamic model for the cylinder and exhaust manifold of a natural gas 2-megawatt four-stroke internal combustion engine

This paper presents the application of a systematic methodology to obtain a semi-physical model of phenomenological base for a 2 MW internal combustion engine to generate electric power operating with natural gas, as a function of the average thermodynamic value normally measured in industrial applications. Specifically, the application of the methodology is focused on the cylinders, exhaust manifold, and turbocharger turbine sections. The proposed model was validated with actual operating data, obtaining an error rate not exceeding 5%, which allow a thermal characterization of the Jenbacher JMS 612 GS-N based on the model. A parametric analysis is conducted; considering the volumetric efficiency, the output electric power, the effective efficiency, the exhaust gas temperature, the turbine mass flow, the specific fuel consumption under the nominal operation conditions, which is 1.16 bar in the gas pressure, 65 °C in the cooling water temperature, 35 °C in the average ambient temperature, and 1500 rpm. The results of this model can be used to evaluate the thermodynamic performance parameters of waste heat recovery systems. On the other hand, new control strategies and the implementation of state observers for the detection and diagnosis of failures can be developed based on the proposed model.

Large impact of strain on the electro-optic effect in (Ba, Sr)TiO3 thin films: Experiment and theoretical comparison

(001)-epitaxial (Ba0.5Sr0.5)TiO3 (BST) thin films with different magnitudes of compressive strain were fabricated on SrRuO3/SrTiO3 substrates by pulsed laser deposition, and their electro-optic (EO) properties were characterized by modulation ellipsometry at different temperatures. All fabricated films showed an increased paraelectric-to-ferroelectric phase transition temperature upon compressive strain and revealed c-domain structures in the ferroelectric phase. We experimentally clarified that the EO properties of compressively strained BST thin films are enhanced toward the phase transition temperature modified by the strain. The experimental results were compared with the theoretical prediction based on a phenomenological thermodynamic model. Although the measured EO coefficient rc was less than that theoretically predicted, the experimentally observed strain effect on the EO properties is in good qualitative agreement.

A Study of Energy Balance in Deformed Metals for Assessment of Damage Accumulation Stage

The work is devoted to study of energy balance in metals under plastic deformation and failure. Based on our previous experimental results we develop a phenomenological thermodynamic model of heat dissipation in metals. It allows us to simulate the energy balance under plastic deformation, to study the failure process of metals based on the stored energy criterion and the process of fatigue crack propagation. New internal thermodynamic variable is introduced as defect induced deformation and calculated based on the solution of statistical problem of mesodefect evolution. The developed model is adapted for using in standard final-elements numerical code (Abaqus) to simulate energy dissipation under quasi-static and cyclic loading in 3D geometries. The theoretical results were illustrated by computing of energy dissipation both under tensile test of Armco iron specimens and crack propagation under cyclic loading.

The metamagnetic transition behavior of DyCo2 predicted by a phenomenological thermodynamic model

Abstract Ferromagnetic MPB in the TbxDy1−xCo2 system was confirmed via both experimental and theoretical research, which demonstrates the simultaneous structural change with ferromagnetic phase transition. According to the ferromagnetic MPB theory, a phenomenological thermodynamic model of TbxDy1−xCo2 at Dy-rich side was constructed. The thermodynamic model predicts the behavior of DyCo2, which is consistent with the experimental value. The phenomenological thermodynamic model based on ferromagnetic MPB could be employed to make a quantitative analysis of magnetostrictive or magnetocaloric materials.

Computational study of nonlinear dielectric composites with field-induced antiferroelectric-ferroelectric phase transition

Electric field-induced antiferroelectric-ferroelectric phase transition and the associated nonlinear dielectric behavior in particulate composites are investigated for achieving a high dielectric capacity. A phenomenological thermodynamic model based on the Landau theory is first developed to discuss the generic phenomena of a temperature-electric field phase diagram, coexistence of antiferroelectric and ferroelectric phases, field-induced antiferroelectric-ferroelectric phase transition, and nonlinear dielectric behavior. The model is then used to carry out the phase field simulation of particulate nonlinear dielectric composites. It is found that the composites exhibit nonlinear dielectric behaviors, and the depolarization field in the composites helps reduce the dielectric hysteresis and enhance the reversibility of antiferroelectric-ferroelectric phase transitions, which are desired for energy storage applications. The simulations also reveal the underlying domain-level mechanisms for nucleation and growth processes of the phase transitions. It is shown that the macroscopic properties of the composites sensitively depend on the directional alignment of the antiferroelectric filler particles, and thus the filler morphology is an effective control variable in designing nonlinear dielectric composites.

Phase Diagram of the B–BN System at Pressures up to 24 GPa: Experimental Study and Thermodynamic Analysis

Phase relations in the B-BN system have been studied ex situ and in situ at pressures 2-20 GPa and temperatures up to 2800 K. The evolution of topology of the B-BN phase diagram has been investigated up to 24 GPa using models of phenomenological thermodynamics with interaction parameters derived from our experimental data on phase equilibria at high pressures and high temperatures. There are two thermodynamically stable boron subnitrides in the system i.e. B13N2 and B50N2. Above 16.5 GPa the B50N2 = L + B13N2 peritectic reaction transforms to the solid-phase reaction of B50N2 decomposition into tetragonal boron (t'-B52) and B13N2, while the incongruent type of B13N2 melting changes to the congruent type only above 23.5 GPa. The constructed phase diagram provides fundamentals for directed high-pressure synthesis of superhard phases in the B-BN system.

Thermodynamic Model for Quantum Dot Assemblies Formed Because of Charge Transfer

Two initially neutral semiconductor quantum dots with appropriate band offsets can participate in a ground state charge transfer process. The charge transfer manifests itself in the form of bleaching of optical transitions and also causes the quantum dots to precipitate from solution, giving rise to assemblies with unusual properties. As this represents a postsynthetic modification of the electronic structure of quantum dots, it holds tremendous potential for improving the characteristics of quantum dot devices. Here, we study the dependencies of the properties of these assemblies on the structure of the participating quantum dots. In particular, we find that for assemblies formed out of Cu:CdS and ZnTe/CdS quantum dots, the composition of the assembly varies from 1:1.26 to 1:0.23 ZnTe/CdS to Cu:CdS as the shell thickness of CdS in ZnTe/CdS is increased. In contrast, the composition changes from 1:1.1 to 1:15 for PbSe/CdSe and Cu:CdS quantum dots, as the size of the PbSe core is increased. These observations are explained on the basis of a phenomenological thermodynamic model. The applicability of thermodynamics to this example of self-assembly is verified empirically.

Kinetics modeling of nanoparticle growth on and evaporation off nanotubes

A kinetic Monte Carlo approach is developed for studying growth and evaporation of nanoparticles on/off nanotubes. This study has been motivated by the recent experimental advances in using nanoparticle evaporation (sublimation) off nanoparticle-decorated nanotubes for nanoscale “thermometry.” We demonstrate that the considered kinetic Monte Carlo approach can reproduce features of the process that are not included in the phenomenological thermodynamic modeling, as well as provide snapshots of the growth and evaporation process morphology.

Adsorption equilibrium of benzaldehyde and benzyl alcohol onto polymeric resin from supercritical CO2

A frontal chromatographic technique was used to measure the adsorption isotherms of benzaldehyde and benzyl alcohol onto a polymeric resin in supercritical CO2 (scCO2). The effect of temperature and pressure (density) on adsorption behavior was investigated. It was observed that benzyl alcohol has stronger adsorption than benzaldehyde. The desorption of benzaldehyde using scCO2 from the polymeric resin adsorbent was studied under the same temperature and pressure ranges. The local equilibrium theory was found to reasonably predict the desorption profiles. A phenomenological statistical thermodynamic model combined with classic Peng–Robinson equations of state was used to correlate the adsorption equilibrium isotherms of the solutes from scCO2. This theoretical model with three parameters is able to describe the adsorption behavior over wide temperature and pressure ranges.

Phase diagram of the B–B2O3 system at pressures to 24 GPa

The evolution of topology of the B-B2O3 phase diagram has been studied at pressures up to 24 GPa using models of phenomenological thermodynamics with interaction parameters derived from experimental data on phase equilibria at high pressures and high temperatures.

Interfacial charge-induced polarization switching in Al2O3/Pb(Zr,Ti)O3 bi-layer

Detailed polarization switching behavior of an Al2O3/Pb(Zr,Ti)O3 (AO/PZT) structure is examined by comparing the phenomenological thermodynamic model to the experimental polarization–voltage (P-V) results. Amorphous AO films with various thicknesses (2–10 nm) were deposited on the polycrystalline 150-nm-thick PZT film. The thermodynamic calculation showed that the transition from the ferroelectric-like state to the paraelectric-like state with increasing AO thickness occurs at ∼3 nm thickness. This paraelectric-like state should have exhibited a negative capacitance effect without permanent polarization switching if no other adverse effects are involved. However, experiments showed typical ferroelectric-like hysteresis loops where the coercive voltage increased with the increasing AO thickness, which could be explained by the carrier injection through the thin AO layer and trapping of the carriers at the AO/PZT interface. The fitting of the experimental P-V loops using the thermodynamic model considering the depolarization energy effect showed that trapped charge density was ∼±0.1 Cm−2 and critical electric field at the Pt electrode/AO interface, at which the carrier transport occurs, was ∼±10 MV/cm irrespective of the AO thickness. Energy band model at each electrostatic state along the P-V loop was provided to elucidate correlation between macroscopic polarization and internal charge state of the stacked films.

The giant electrocaloric effect in EuTiO3 nanowires near room temperature

A phenomenological thermodynamic model is employed to investigate electrocaloric effect in EuTiO3 nanowires, in which the effects of surface tension, gradient, external stress, nanowires radius and so on are considered. We are surprised that the decrease in size and the increase in external tensile stress can significantly enhance the electrocaloric effect of EuTiO3 nanowires under the same applied electric filed. Giant adiabatic temperature changes (ΔT = 15–20 K) are achieved near room temperature by controlling the radius of EuTiO3 nanowires and applied external electric fields, which is much higher than the previous results obtained in many other isomorphic electrocaloric materials. The large electrocaloric effects suggest the potential application for micro-nanodevice in refrigeration.

Thermodynamic calculation of the Al-B system at pressures to 8 GPa

Using models of phenomenological thermodynamics with interaction parameters derived from experimental data on phase equilibria at high pressures and high temperatures, the evolution of topology of the aluminum-boron phase diagram has been studied at pressures up to 8 GPa.

Thermodynamic calculation of the B-C system at pressures to 24 GPa

The evolution of topology of the B-C phase diagram has been studied at pressures up to 24 GPa using models of phenomenological thermodynamics with interaction parameters derived from experimental data on phase equilibria at high pressures and high temperatures.