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At least 19 records

Strain phase equilibria and phase‐field method of ferroelectric polydomain: A case study of monoclinic K x Na 1 − x NbO 3 thin films

Abstract Knowledge of the thermodynamic equilibria and domain structures of ferroelectrics is critical to establishing their structure–property relationships that underpin their applications from piezoelectric devices to nonlinear optics. Here, we establish the strain condition for strain phase separation and polydomain formation and analytically predict the corresponding domain volume fractions and wall orientations of, relatively low symmetry and theoretically more challenging, monoclinic ferroelectric thin films by integrating thermodynamics of ferroelectrics, strain phase equilibria theory, microelasticity, and phase‐field method. Using monoclinic K x Na 1 − x NbO 3 (0.5 < x < 1.0) thin films as a model system, we establish the polydomain strain–strain phase diagrams, from which we identify two types of monoclinic polydomain structures. The analytically predicted strain conditions of formation, domain volume fractions, and domain wall orientations for the two polydomain structures are consistent with phase‐field simulations and in good agreement with experimental results in the literature. The present study demonstrates a general, powerful analytical theoretical framework to predict the strain phase equilibria and domain wall orientations of polydomain structures applicable to both high‐ and low‐symmetry ferroelectrics and provide fundamental insights into the equilibrium domain structures of ferroelectric K x Na 1 − x NbO 3 thin films that are of technology relevance for lead‐free dielectric and piezoelectric applications.

36 MATERIALS SCIENCE↗

Theory of strain phase equilibria and diagrams

Chemical phase equilibria and phase diagrams are well established and have served as indispensable guides for designing materials through chemical tuning. However, a general thermodynamic theory for strain phase equilibria remains elusive despite extensive studies which have revealed dramatic impacts of mechanical strain on the stability of phases and domain states in solid-state materials. Here, we establish the thermodynamic theory of strain equilibria and a general framework for efficiently constructing multidomain and multiphase diagrams of arbitrarily strained solids under incoherent conditions. As examples, we obtain temperature-strain phase diagrams of ferroelectric PbTiO 3 , strongly correlated VO 2 , and unconventional ferroelectric Hf 0.5 Zr 0.5 O 2 . We reveal the analogs of the Gibbs phase rules, multiple- and multi-critical points, common-tangent construction, and level rule in strain equilibria to those in the familiar chemical phase equilibria. Finally, our strain equilibria theory offers a powerful framework for predicting the thermodynamic stability of structural phases and domains in strained solids and for guiding the strain engineering of their functional properties.

36 MATERIALS SCIENCE↗

From molecular to macroscopic: predicting liquid–liquid phase equilibria and small-angle scattering of mixtures of organic liquids from atomistic simulation using Kirkwood–Buff theory

Macroscopic phase equilibria between solutions define the functionality of many biological and industrial processes, yet they are challenging to predict due to the inherent complexity of liquids containing large molecules. This work introduces an approach for the purely predictive calculation of such phase equilibria in temperature-composition space from molecular dynamics (MD) simulations at one temperature in the single-phase region. We use an approach developed previously to obtain the entropic and enthalpic contributions to the free energy of mixing from the atomic-scale information given by MD simulations via Kirkwood–Buff theory. This allows us to accurately estimate the free energy of mixing as a function of temperature, and thus obtain liquid–liquid phase equilibria, including liquid–liquid critical points, associated binodal and spinodal lines, and composition fluctuations across a region of temperature and composition. Results for binary malonamide–alkane systems are validated by comparison to a direct experimental probe of the fluctuations: the small angle X-ray scattering intensity near zero wavenumber. The MDKB → Phase method demonstrated here provides a significant improvement in predicting liquid–liquid equilibria and free energy as a function of temperature for our systems of interest compared to conventional thermodynamic models. The accurate performance of this purely predictive approach lies in its preservation of atomistic details when determining thermodynamic properties. Furthermore, its inherent extensibility to multi-component systems will likely make the MDKB → Phase approach a valuable general tool for connecting molecular interactions to macroscopic phase equilibria and for the computational screening of materials for targeted thermodynamic behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Equilipy: a python package for calculating phase equilibria

The CALPHAD (CALculation of PHAse Diagram) approach (Nigel Saunders & Miodownik, 1998) provides predictions for thermodynamically stable phases in multicomponent-multiphase materials across a wide range of temperatures. Consequently, the CALPHAD calculations became an essential tool in materials and process design (Luo, 2015). Such design tasks frequently require navigating a high-dimensional space due to multiple components involved in the system. This increasing complexity demands high-throughput CALPHAD calculations, especially in the rapidly evolving field of alloy design. In response to the need, we developed Equilipy an open-source Python package designed for calculating phase equilibria of multicomponent-multiphase systems. Equilipy is specifically tailored for high-throughput CALPHAD calculations, offering parallel computations across multiple processors and nodes with the given NPT input conditions namely elemental compositions (N), pressure (P), and temperature (T). Equilipy utilizes the program structure and Gibbs energy functions from the Fortran-based program, Thermochimica (Piro et al., 2013), with incorporating a new Gibbs energy minimization algorithm. This algorithm, originally developed by Capitani and Brown in 1987 (Capitani & Brown, 1987), has been revised and implemented to enhance the stability and performance of calculations. The Fortran codes are precompiled and interfaced with Python via F2PY, ensuring high computation speed. Benchmark tests shown in Figure 1 demonstrate that Equilipy’s computation speed is comparable to those of established commercial software, TC-Python and PanPython. This result highlights its efficiency and potential applications in various scientific and industrial fields.

97 MATHEMATICS AND COMPUTING↗

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Abstract Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

36 MATERIALS SCIENCE↗

A critical analysis of U-Pu-Zr phase transitions using calorimetric, microstructural, and phase equilibria data

Metallic fuels consisting primarily of uranium, plutonium, and zirconium (U-Pu-Zr) are a leading material candidate for fast-spectrum nuclear reactors. Early demonstration programs proved the principle of safe and efficient fast reactor operation, however there is still considerable uncertainty regarding the phase equilibria and microstructural evolution across the ternary composition space. Quantitative phase formation and identification measurements are scarce and often incomplete, with studies reporting either phase transition temperatures or phase identification data, but not both from the same specimens. In this study, we critically compared experimental and calculated phase transition data and correlated with the microstructure and phase characterization data of as-cast and annealed U-Pu-Zr alloys. Differential scanning calorimetry (DSC) was used to measure phase transitions in the subsolidus regions (723−948 K) of three ternary U-Pu-Zr alloys with similar plutonium concentrations but various U/Zr ratios. Due to sluggish kinetics and narrow ranges of phase stability, complex peaks required the use of a Frazier-Suzuki peak fitting algorithm to deconvolute and calculate transition peak temperatures and enthalpies. We also identified trends of phase transition behavior by critically comparing our DSC data with previous phase transition measurements as well as historical and calculated phase equilibrium diagrams. In conclusion, this provides a critical approach for benchmarking and assessing the quality of new U-Pu-Zr phase equilibria data prior to its incorporation into nuclear material databases.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Phase equilibria and microstructure evolution in the Ni-rich region of binary Ni-Ce and ternary Ni-Ce-X (X=Al, Nb, Cr, Ti) systems at 900 °C

The equilibrium compositions of all phases in the Ni-rich region of binary Ni-Ce and ternary Ni-Ce-X (X=Al, Nb, Cr, Ti) systems at 900 °C were determined experimentally through isothermal annealing for up to 500 h and compared with currently available computational thermodynamic descriptions. Additionally, the study examined how adding a third element to the binary system affects the microstructure by analyzing changes in the volume fraction of the intermetallic phase in the eutectic region. It was observed that Nb and Ti addition lowered the intermetallic fraction in the eutectic region while Al and Cr addition did the opposite. The fraction of intermetallic phase in the eutectic region is very important because it contributes to extreme brittleness of these alloys. Also, Al, Nb and Ti addition promoted different precipitates upon annealing when added in sufficient amounts. The collected data on composition and phase equilibria provides crucial information for improving the thermodynamic assessments of the binary and ternary alloy systems.

energy dispersive spectrometry↗

Magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria: A DFT cluster expansion study

Magnetic contributions have the potential to significantly influence predicted phase stability within alloy and mineral mixing phase diagrams, yet have been historically challenging to incorporate due to a significant increase to phase space sampling. Here, in this work, we employ a computational protocol that includes spin orientation as an additional configurational component within multi-component cluster expansions between magnetic and non-magnetic metal oxide alloys [calculated using density functional theory (DFT) and the generalized gradient approximation]. This approach was used to determine the effect of magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria from first principles. Two-component cluster expansions of the magnetic components of eskolaite and hematite were first performed showing the ability of this method to properly calculate their respective magnetic properties. Two-component cluster expansions were then performed for non-magnetic Al(III) and ferromagnetic Cr(III) and Fe(III), and phase diagrams were calculated for later comparison. Finally, a non-magnetic Al(III) and “up” and “down” magnetic configurations for anti-ferromagnetic Cr(III) and Fe(III) were performed. Magnetic contributions to the calculated phase diagram for the corundumeskolaite system were shown to be inconsequential but are vital for accurate determination of the corundum-hematite solvus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The Ce-Fe-Ti System: Phase Equilibria in the Fe-rich Corner at 1000 °C

The rare earth–iron–transition metal systems are of increasing interest in the search for novel permanent magnet phases. This work reports on the solidification behavior, phase equilibria and stability range of solid phases in the ternary Ce-Fe-Ti system, focusing on the iron-rich region (> 65 at.% Fe) of the isothermal section at 1000 °C. Further, two ternary phases Ce 1.03 Fe 12-x Ti x (x = 0.87–1.02) with ThMn 12 structure type and Ce 3.06 Fe 27.6 Ti 1.4 with Nd 3 Fe 29 structure type were observed. Magnetic measurements of Ce 1.03 Fe 12-x Ti x and Ce 3.06 Fe 27.6 Ti 1.4 revealed ferromagnetic ordering with Curie temperatures of 550 K and 327 K, respectively.

36 MATERIALS SCIENCE↗

Re-investigation of high-temperature phase equilibria in Fe-rich Sm–Fe–Ti alloys

Recently renewed attempts to develop high-performance rare-earth-lean permanent magnets based on the Sm(Fe,Ti) 12 compound have drawn attention to the limited knowledge about the high-temperature phase equilibria in the Sm–Fe–Ti system. Experimental investigation of equilibrated alloys with electron probe microanalysis, X-ray diffraction and thermomagnetic analysis revealed several inaccuracies in the currently accepted phase relations at 1000°C and allowed for a revision of the Fe-rich corner of the Sm–Fe–Ti phase diagram. The Sm(Fe,Ti) 12 and Sm 3 (Fe,Ti) 29 phases were found to have more extended Ti ranges of 5.1–9.7 at% and 2.8–6.9 at%, respectively. With increasing of the Ti content, the Curie temperature of the Sm(Fe,Ti) 12 remains nearly constant at 306–312°C, whereas that of the Sm 3 (Fe,Ti) 29 increases from 188°C to 207°C. The low-titanium Sm 3 (Fe,Ti) 29 phase equilibrates not only with the Sm(Fe,Ti) 12 and Sm2(Fe,Ti) 17 phases, but also with (α-Fe) solid solution. Newly demonstrated equilibrium between Sm 2 (Fe,Ti) 17 and TiFe 2 phases makes impossible the earlier reported equilibrium between the Sm 3 (Fe,Ti) 29 and Sm(Fe,Ti) 11 phases. Because of an invariant reaction at 1000 °C, the revised phase diagram also features a class II four-phase equilibrium Sm 3 (Fe,Ti) 29 + TiFe 2 + Sm(Fe,Ti) 12 + Sm 2 (Fe,Ti) 17 . Peritectic decomposition of the Sm(Fe,Ti) 11 phase, which occurs either at 1075°C or at 1087°C, was found to have among its products the Sm(Fe,Ti) 12 phase. Although no such equilibration was attempted, it must be possible to obtain above 1087°C a two-phase state composed of the Sm(Fe,Ti) 12 phase and a liquid – which is important for manufacturing of the Sm(Fe,Ti) 12 - based permanent magnets via the liquid-phase sintering.

36 MATERIALS SCIENCE↗

Liquid and Gamma-BCC Phase Equilibria in the Uranium-Niobium System: A Simple Thermodynamic Model for Phase Diagram and Other Predictions

A simple thermodynamic model for the uranium-niobium (U-Nb) system was created using a Calphad-type approach, circa 2002. Only the liquid and gamma-BCC phases were modeled, with their subregular solution mixing terms optimized by trial and error. The custom (user-defined) database file (.tdb) and experimental data file (.exp) are listed, both of which are compatible with Thermo-Calc software. This model is used to calculate the solidus, liquidus, miscibility gap on the U-Nb phase diagram and also the enthalpy of melting in the U-6Nb alloy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Phase equilibria of advanced technology uranium silicide-based nuclear fuel

The phases in uranium-silicide binary system were evaluated in regards to their stabilities, phase boundaries, crystal structures, and phase transitions. The results from this study were used in combination with a well assessed literature to optimize the U-Si phase diagram using the CALPHAD method. A thermodynamic database was developed, which could be used to guide nuclear fuel fabrication, could be incorporated into other nuclear fuel thermodynamic databases, or could be used to generate data required by fuel performance codes to model fuel behavior in normal or off-normal reactor operations. The U 3 Si 2 and U 3 Si 5 phases were modeled using the Compound Energy Formalism model with 3 sublattices to account for the variation in composition. The crystal structure used for the USi phase was the tetragonal with an I4/mmm space. Above 450°C, the U 3 Si 5 phase was modeled. The composition of the USi 2 phase was adjusted to USi 1.84 . The calculated invariant reactions and the enthalpy of formation for the stoichiometric phases were in agreement with experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Phase equilibria in iron-rich Sm–Fe–Ti and Sm–(Fe,Co)–Ti alloys at 1100–1200 °C

Iron-rich corners of ternary Sm–Fe–Ti phase diagram at 1100 °C and quasi-ternary Sm–Fe 0.8 Co 0.2 –Ti phase diagrams at 1100 and 1200 °C are constructed based on experimental investigation of equilibrated alloys with electron probe microanalysis, X-ray diffraction and thermomagnetic analysis. In addition, the upper boundaries of the temperature ranges of Sm(Fe,[Co,]Ti) 12 and Sm 3 (Fe,[Co,]Ti) 29 phases are determined with differential thermal analysis to update earlier rough estimates. The existence of a high-temperature phase of the Th 2 Ni 17 type, originally reported by Ivanova et al. [J. Alloys Compd. 224 (1995) 29], is confirmed. In the Sm–Fe 0.8 Co 0.2 –Ti system, the composition and equilibria of this hexagonal phase are established for 1200 °C; it is Sm-depleted (≈9.8 at.% Sm) compared to the 2:17 stoichiometry and it coexists with the rhombohedral 2:17 phase. The magnetic anisotropy of the cobalt-substituted Th 2 Ni 17 -type phase is planar, with the easy magnetization direction parallel to [100]. Equilibrium between a Sm-rich liquid phase and the 1:12 phase, which is important for the development of new high-performance permanent magnets, is absent up to 1000 °C, but does exist at 1100 °C (for the 1:12 phase with at least 8.7–8.9 at.% Ti) and at 1200 °C (for the 1:12 phase with as little as 7.4 at.% Ti). The development of magnets may be complicated, however, by an observed tendency of the high-temperature liquid to solidify into ferromagnetic phases including the Th 2 Ni 17 -type phase. The Curie temperatures of the α-(Fe,Ti), Sm(Fe,Ti) 12 , Sm 3 (Fe,Ti) 29 and rhombohedral Sm 2 (Fe,Ti) 17 phases are not only increased by the partial Co substitution for Fe, but their dependence on the Ti concentration is changed by this Co substitution from positive (or, for the 1:12 phase, zero) to negative values.

36 MATERIALS SCIENCE↗

First-principles free energies by hybrid thermodynamic integration for phase equilibria and fission product solubility in molten salts

The overarching goal of this research project is quantitative microscopic modeling of phase diagrams and solubility of actinides and lanthanide-fission products in molten salts for molten salt reactors. Application of molten salts as coolants and liquid fuels for next-generation reactors requires quantitative understanding of phase diagrams, equations of state and transport properties of binary and ternary molten salt mixtures, as well as solubility of fuel, fission products and reactor-wall corrosion products, but these remain beyond the reach of current first-principles computational techniques. We will address this fundamental capability gap using a novel hybrid framework for thermodynamic integration to directly predict absolute free energies of solid and molten salts at any specified conditions of composition, temperature and pressure. This framework will combine a hierarchy of first-principles, molecular dynamics and continuum techniques to deliver first-principles-level accuracy at a fraction of the computational cost of conventional ab initio molecular dynamics approaches. In particular, this technique is expected to provide first-principles accuracy, while off-loading most of the computational work on much less expensive classical molecular dynamics and continuum techniques.

36 MATERIALS SCIENCE↗

Effect of Mn on eutectic phase equilibria in Al-rich Al-Ce-Ni alloys

Microstructural analysis of additively manufactured (AM) Al-Ce-Ni-Mn alloys has identified phases not predicted from existing ternary liquidus projections in the Al-Ce-Ni system. Because the rapid cooling rate of AM is orders of magnitude above that of traditional casting, it is unclear if these additional phases arose from the non-equilibrium processing conditions of AM, a drastic shift in phase stability in the system due to the addition of 1 wt% Mn, or some combination of these two influences. The phases and microstructure of cast samples of Al-Ce-Ni and Al-Ce-Ni-Mn alloys were characterized for several annealing conditions which revealed the equilibrium phases at different temperatures. Phase analysis confirmed that minute levels of Mn substituted for Ni in the system drastically shifts the liquidus projection in the Al-rich corner of the ternary phase diagram such that the eutectic Al 3 Ni phase is suppressed in favor of the Al 23 Ni 6 (Ce,Mn) 4 phase. Further addition of Mn promotes the formation of Al 20 Mn 2 Ce and Al 10 Mn 2 Ce phases. The phase analysis data was then used to improve the CALPHAD modeling of the liquidus projection and isothermal sections for the Al-rich Al-Ce-Ni-Mn quaternary system. Thermodynamic modeling and experimental analysis on phases in the AM sample of Al-Ce-Ni with Mn confirmed that the phases present are consistent with Mn-containing Al-Ce-Ni cast samples. Here, this investigation demonstrates the potential for using secondary alloying elements to drastically alter phase stability and microstructure in alloy systems.

36 MATERIALS SCIENCE↗

Computational Insights into Phase Equilibria Between Wide-Gap Semiconductors and Contact Materials

Novel wide-band-gap semiconductors are needed for next-generation power electronics, but there is a gap between a promising material and a functional device. Finding stable (metal) contacts is one of the major challenges that is currently dealt with mainly via trial and error. Herein, we computationally investigate the thermochemistry and phase coexistence at the junction between three wide-gap semiconductors, ..beta..-Ga2O3, GeO2, and GaN, and possible contact materials. The pool of possible contacts includes 47 elemental metals and a set of 4 common, n-type transparent conducting oxides (ZnO, TiO2, SnO2, and In2O3). We use first-principles thermodynamics to model the Gibbs free energies of chemical reactions as a function of gas pressure (pO2/pN2) and equilibrium temperature. We deduce whether a semiconductor/contact interface will be stable at relevant conditions or a chemical reaction between them is to be expected, possibly influencing the long-term reliability and performance of devices. We generally find that most elemental metals tend to oxidize or nitridize and form various interface oxide/nitride layers. Exceptions include select late- and post-transition metals and, in the case of GaN, also the alkali metals, which are predicted to exhibit stable coexistence, although in many cases at relatively low gas partial pressures. Similar is true for the transparent conducting oxides, for which, in most cases, we predict a preference toward forming ternary oxides when in contact with ..beta..-Ga2O3 and GeO2. The only exception is SnO2, which we find to form stable contacts with both oxides. Finally, we show how the same approach can be used to predict gas partial pressure vs temperature phase diagrams to help direct synthesis of ternary compounds. We believe these results provide a valuable guidance in selecting contact materials to wide-gap semiconductors and suitable growth conditions.

contact materials↗