Computed Phase Diagram Research Articles

Robust quantization of circular photogalvanic effect in multiplicative topological semimetals

Nonlinear response signatures are increasingly recognized as useful probes of condensed matter systems, in particular for the characterization of topologically nontrivial states. The circular photogalvanic effect (CPGE) is particularly useful in the study of topological semimetals, as the CPGE tensor quantizes for well-isolated topological degeneracies in strictly linearly dispersing band structures. Here, we study multiplicative Weyl semimetal band structures, and find that the multiplicative structure robustly protects the quantization of the CPGE even in the case of nonlinear dispersion. Computing phase diagrams as a function of Weyl node tilting, we find a variety of quantized values for the CPGE tensor, revealing that the CPGE is also a useful tool in detecting and characterizing the parent topology of multiplicative topological states. Published by the American Physical Society 2024

Design of eutectic high-entropy alloys in the Co-Cr-Ni-V-Ti-Al system using Scheil solidification path optimization

The design strategy for eutectic high-entropy alloys (EHEA) is still in need of further exploration. This paper explores a new design approach using data computation, combining the simple mixing enthalpy method with a computed phase diagram approach based on a high-entropy alloy database. By calculating the thermodynamic empirical parameters of existing FCC/BCC-type eutectic alloy systems, the proportion range of alloy elements for eutectic design was narrowed. Ultimately, by analyzing the solidification path through the Scheil model, six eutectic compositions were obtained for the Co-Cr-Ni-Ti-V-Al alloy system that satisfy theoretical concepts. Microscopic characterization revealed that the actual alloy’s microstructure has only minor differences from the theoretically calculated results, with the main phase compositions of the alloys being FCC and BCC phases, aside from minor metal precipitates and third phases. However, significant differences were observed in the microstructures and mechanical properties of the six alloys. The research results demonstrate that this new design theory shortens the EHEA design cycle, enhances design accuracy and provides guidance for the eutectic design of target alloy systems.

First-principles prediction of the Co–Al phase diagram including configurational, vibrational and magnetic contributions

Co-based superalloys have attracted attention to replace Ni-based superalloys in high temperature structural applications because of their higher melting temperature and corrosion resistance. Strengthening is provided by Co3(Al, X) (X = W, Cr, Mo, Ni) phases and optimization of their properties requires detailed information about the free energies of the different phases and of the phase diagram of the Co–Al system. This is achieved in this paper through first principles calculations in combination with statistical mechanics. Configurational entropic contributions to the free energy were included through Monte Carlo simulations using the cluster expansion formalism. The vibrational entropy of each phase was determined through the length-stiffness relationship while the magnetic entropy was also included through the Heisenberg Hamiltonian. The computed phase diagram is compared with the currently accepted experimental phase diagram and the different contributions to the stability of each phase are analyzed independently. The potential of this strategy to predict phase diagrams of magnetic systems is clearly established.

Phase equilibria of the Na2O‐TiO2‐SiO2 system between 900 and 1600°C in air

AbstractThe Na2O‐SiO2‐TiO2 system is important for the glass, ceramic, and metallurgical industries. Its features provide information on the composition and melting temperature to be utilized during the production of glass and ceramic and during the processing of TiO2‐bearing material in the metallurgical industry. The liquidus temperatures between 900 and 1600°C in the ternary system at saturation of solid SiO2, TiO2, Na2Ti6O13, Na2SiTiO5, and Na2Ti3O7 were measured using the equilibration‐quenching energy‐dispersive X‐ray spectroscopy/Electron Probe Microanalyzer technique. A wide range of liquidus compositions were obtained with Na2O between 0 and 41.7 mol% in the SiO2‐ and TiO2‐rich regions. The present study provides liquidus data at 1500 and 1600°C for the first time. Liquidus temperatures at various double saturations were also obtained in the present investigation to determine univariant lines in the phase diagram. The present experimental data were compared with previous investigations and computed phase diagrams. The data obtained in the present investigation can be employed to optimize the thermodynamic properties and phase diagrams of the Na2O‐SiO2‐TiO2 system.

Chiral Modulations in Non-Heisenberg Models of Non-Centrosymmetric Magnets Near the Ordering Temperatures

The structure of skyrmion and spiral solutions, investigated within the phenomenological Dzyaloshinskii model of chiral magnets near the ordering temperatures, is characterized by the strong interplay between longitudinal and angular order parameters, which may be responsible for experimentally observed precursor effects. Within the precursor regions, additional effects, such as pressure, electric fields, chemical doping, uniaxial strains and/or magnetocrystalline anisotropies, modify the energetic landscape and may even lead to the stability of such exotic phases as a square staggered lattice of half-skyrmions, the internal structure of which employs the concept of the “soft” modulus and contains points with zero modulus value. Here, we additionally alter the stiffness of the magnetization modulus to favor one- and two-dimensional modulated states with large modulations of the order parameter magnitude. The computed phase diagram, which omits any additional effects, exhibits stability pockets with a square half-skyrmion lattice, a hexagonal skyrmion lattice with the magnetization in the center of the cells parallel to the applied magnetic field, and helicoids with propagation transverse to the field, i.e., those phases in which the notion of localized defects is replaced by the picture of a smooth but more complex tiling of space. We note that the results can be adapted to metallic glasses, in which the energy contributions are the same and originate from the inherent frustration in the models, and chiral liquid crystals with a different ratio of elastic constants.

Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior.

The use of amorphous solid dispersions (ASDs) in commercial drug products has increased in recent years due to the large number of poorly soluble drugs in the pharmaceutical pipeline. However, the release behavior of ASDs is complex and remains not well understood. Often, the drug release from ASDs is rapid and complete at lower drug loadings (DLs) but becomes slow and incomplete at higher DLs. The DL where release becomes hindered is termed the limit of congruency (LoC). Currently, there are no approaches to predict the LoC. However, recent findings show that one potential cause leading to the LoC is a change in phase morphology after water-induced phase separation at the ASD/solution interface. In this study, the phase behavior of ASDs in contact with aqueous solutions was described thermodynamically by constructing experimental and computational ternary phase diagrams, and these were used to predict morphology changes and ultimately the LoC. Experimental ternary phase diagrams were obtained by equilibrating ASD/water mixtures over time. Computational ternary phase diagrams were obtained by Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT). The morphology of the hydrophobic phase was studied with fluorescence confocal microscopy. It was demonstrated that critical point (plait point) composition approximately corresponded to the ASD DL, where the hydrophobic phase, formed during phase separation, became interconnected and hindered ASD release. This work provides mechanistic insights into the ASD release behavior and highlights the potential of in silico ASD design using phase diagrams.

Flat band effects on the ground-state BCS-BEC crossover in atomic Fermi gases in a quasi-two-dimensional Lieb lattice

The ground-state superfluid behavior of ultracold atomic Fermi gases with a short-range attractive interaction in a quasi-two-dimensional Lieb lattice is studied using BCS mean-field theory, within the context of BCS-BEC crossover. We find that the flat band leads to nontrivial exotic effects. As the Fermi level enters the flat band, both the pairing gap and the in-plane superfluid density exhibit an unusual power law as a function of interaction, with strongly enhanced quantum geometric effects, in addition to a dramatic increase of compressibility as the interaction approaches the BCS limit. As the Fermi level crosses the van Hove singularities, the character of pairing changes from particle-like to hole-like or vice versa. We present the computed phase diagram, in which a pair density wave state emerges at high densities with relatively strong interaction strength.

Pair potential description on phase stability variations in close-packed polytypism

We report an extensive analysis on phase stability variations in close-packed (CP) polytypes, including hexagonal CP (hcp or 2H), face-centered cubic (fcc or 3C), and double hexagonal CP (dhcp or 4H) arrangements. This analysis involves the systematic development of interatomic pair potentials and the derivation of computational phase diagrams in the feature space of corresponding potential profiles. We focus on the following key components of interaction model: the reach distance of atomic interactions and perturbative long-range interactions reminiscent of Friedel oscillations which often lead to long-range interaction decay in crystalline materials. The computational experiments reveal that the perturbative interactions reflecting atomic local structures in CP polytypes, essentially diversify the polytypism in the phase diagrams. Using the pure La system with the 4H ground state, we also provide detailed procedures for creating practical pair potentials that approximately reproduce the energetics and physical properties deduced through the first-principles calculations.Graphical abstract

Phase Behavior of Hydrocarbon Fluids in Shale Reservoirs, Considering Pore Geometries, Adsorption, and Water Film.

Phase behavior of hydrocarbon fluids in nanopores is different from that observed in a PVT cell due to the confinement effect. While scholars have established various models for studying the phase behavior in nanopores, the authors often ignore the effect of pore geometries, which can significantly affect the critical fluid properties in shale nanopores. In this study, we extend the Soave-Redlich-Kwong equation of state (SRK EOS) using potential theory and establish models of critical property shift, considering pore geometries, adsorption, and water film. Our research shows that the critical property shifts, considering fluid adsorption, begin at rp ≤ 10 nm and are seriously strengthened with nanopore radius reduction. The extended SRK EOS is applied to compute phase diagrams of the 50% C1-50% nC10 mixture at different pore sizes and find that the thickness of adsorption and water film causes a depression in the P-T diagram and that the bubble point pressure is lower in cylindrical pores. At pressures above 6 MPa, the irreducible water saturation and pore geometries greatly impact the vapor-liquid ratio. This study is significant for evaluating residual oil distribution and studying fluid flow laws in shale reservoirs.

Effect of Ferrite/Austenite Phase Transformation on 475 °C Embrittlement in Duplex Stainless Steel Weld

The change in hardness due to 475°C embrittlement was investigated in the melt-run GTA welds of type 329J4L duplex stainless steel. A ferritic phase was hardened with ageing at 673-773K due to the phase decomposition into Fe-rich and Cr-rich phases, while an austenitic phase was barely hardened with ageing. Hardness in a ferritic phase was rapidly increased with ageing in the base metal (BM) region, and the hardening rate was reduced in the order of BM, weld metal (WM) and heat affected zone (HAZ). The ferrite/austenite fractions in HAZ and WM were higher than that in BM, furthermore, Cr content in a ferritic phase was lowered and Ni content in it was contrarily heightened in the same order of BM, WM and HAZ. A computed phase diagram suggested that the chemical composition of a ferritic phase in each region was located in the nucleation/growth region not spinodal decomposition region, which was situated between the spinodal and binodal lines. Computer simulation of phase decomposition phenomena in a ferritic phase using phase field model revealed that phase decomposition was accelerated with an increase in Cr content and a decrease in Ni content. It followed that Cr would enhance the 475°C embrittlement and Ni would inhibit it, because of the increased/decreased driving force of the phase decomposition. The difference in 475°C embrittlement behaviour at each region could be attributed to the difference in the chemical composition of a ferritic phase caused by the ferrite/austenite phase transformation during welding.

Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States.

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

Accurate prediction of the solid-state region of the Ni-Al phase diagram including configurational and vibrational entropy and magnetic effects

The solid-state region of the Ni-Al phase diagram is predicted from first-principles calculations and Monte Carlo simulations through the cluster expansion formalism. In addition to the formation enthalpy and to the configurational entropy, the vibrational entropy and the magnetic enthalpy are included to calculate the Gibbs free energy of each phase. The computed phase diagram is in excellent agreement with the experimentally accepted phase diagram and provides information about the phase boundary between AlNi3 and Ni below 300 K. These results demonstrate the potential of this methodology to determine accurately the phase diagram of alloys of technological interest. Finally, the contributions of vibrational entropy and magnetic effects to the overall stability and solubility of the different phases are analyzed independently.

Tips and tricks for computing phase diagrams

Phase diagrams are essential for understanding material properties, but computing them is not easy.

Stability and synthesis across barium tin sulfide material space

The underexplored Ba–Sn–S phase space is explored at various temperatures and cation ratios with combinatorial sputtering, crystallizing rocksalt-derived phases, Ba2SnS4, and Ba7Sn5S15. These findings are supported by DFT computed phase diagrams.

Experimental study and thermodynamic modelling of the ternary system Fe–Ni–Si with re-modelling of the constituent binary systems

The present paper reports on the thermodynamic modelling of the complete ternary Fe–Ni–Si system based on key experimental results and information reported in literature. The key experiments were performed to verify phases and phase fractions in selected ternary Fe–Ni–Si alloys using samples in the as-cast state as well as annealed samples. Chemical compositions of the samples were analysed by Energy Dispersive X-Ray Spectroscopy. Microstructure characterization was performed by Scanning Electron Microscopy and Electron Backscatter Diffraction techniques. Phase transformation temperatures were determined by Differential Scanning Calorimetry operated in the Differential Thermal Analysis mode. Calculations performed using proposed thermodynamic description reproduce experimental data well, including data from available literature. In particular, the Fe-rich corner of the Fe–Ni–Si system has been modelled in detail, with emphasis on the A2 and B2 phase fields. The developed ternary database was used to compute phase diagrams and thermodynamic properties of the constituent binary systems as well as selected isothermal and isopleth sections. Due comparison with commercially available and previously modelled thermodynamic descriptions is presented and discussed.

Mind the miscibility gap: Cation mixing and current density driven non-equilibrium phase transformations in spinel cathode materials

Cathode materials that exhibit phase transitions with large structural rearrangements during electrochemical cycling are generally seen as disadvantageous. Large volume changes and lattice mismatches between intermediate phases tend to lead to significant kinetic barriers, as well as strain and particle cracking. In this regard, solid solution reactions are more desirable as they provide lower energy barriers and no miscibility gap between co-existing phases. The high-voltage cathode material LiNi0.5Mn1.5O4 is an interesting candidate for high power and rate capability applications, however little is known on how its phase transitions occur on the particle level. In the presented work operando X-ray diffraction was utilized together with detailed peak profile analysis to elucidate the phase transition mechanism dependency on transition metal cation order and current density. When fully disordered, the material was found to undergo a bulk single-phase solid solution reaction between the intermediate phases LiNi0.44Mn1.56O4 and Li0.5Ni0.44Mn1.56O4 followed by a first order phase transition with a coherent interphase between the intermediates Li0.5Ni0.44Mn1.56O4 and Ni0.44Mn1.6O4. When fully ordered and slightly less ordered, two separate first order phase transitions with a coherent interphase between the same intermediate phases were observed. On discharge, the fast kinetics of the transition between Li0.5Ni0.44Mn1.56O4 and LiNi0.44Mn1.56O4 resulted in less strain on the former phase. For all samples the miscibility gap between the intermediate phases narrowed with increased current density, suggesting that the solid solution domain formed at the coherent interphase can be extended when the rate of (de)lithiation exceeds the movement speed of the interphase at the phase transition. This effect was found to be larger with increasing cation disorder. The influence of transition metal ordering on the ability to form solid solutions is in good agreement with computational phase diagrams of LiNi0.5Mn1.5O4, showing that disorder is important for promoting and stabilizing solid solutions. These results indicate that the degree of transition metal ordering within the material is of importance for obtaining a material with small lattice mismatches between the involved intermediate phases and for rational design of full solid solution materials.

Serpentinite dehydration at low pressures

Petrographic observations combined with mineral compositional analyses constrain the phase relations of prograde metamorphosed serpentinites in the Bergell contact aureole (Italy). In a 1500 m profile perpendicular to the north-eastern edge of the Bergell intrusion, seven dehydration reactions ran to completion. Three previously undocumented reactions have been identified within 70 m of the intrusive contact: olivine + anthophyllite = orthopyroxene + H2O, tremolite + Cr–Al-spinel = olivine + Mg-hornblende + H2O and chlorite = olivine + orthopyroxene + Cr-Al-spinel + H2O. Petrological analysis indicates that these reactions occur over a narrow range of pressure and temperature, 300 ± 30 MPa and 720 ± 10 °C respectively. Computed phase diagram sections reproduce the observed mineral parageneses with one notable exception. Due to the underestimation of aluminium and sodium contents in Ca-amphibole models, plagioclase is predicted above 700 °C instead of Mg-hornblende. In comparison with natural grains, the aluminium content of computed chlorite compositions is overestimated for low grade parageneses while it is underestimated near the upper thermal stability limit of chlorite. In the computed sections, Fe partitioning relative to Mg between olivine and other silicates, suggests a clear preference for Fe in olivine, that therefore shows lower Mg#s. In contrast, microprobe analyses of natural mineral pairs indicate that orthopyroxene, Mg-hornblende and anthophyllite have lower Mg#s than equilibrium olivine. The inferred thermal profile of the metamorphic aureole is not consistent with simple heat conduction models and indicates a contact temperature of ~ 800 °C, which is 120–230 °C higher than previously estimated. Petrography also reveals extensive retrograde overprint of the prograde parageneses within 200 m of the contact. Retrogression is related to metamorphic fluids that were released by dehydration reactions during contact metamorphism and magmatic fluids expelled from the tonalite intrusion. The thermal gradient between the intrusion and the country rocks induced hydrothermal circulation of these fluids throughout the contact aureole, which beyond peak metamorphic conditions caused retrograde overprint of the prograde parageneses. The proposed phase relations for low and high pressures, and in particular, the transition from tremolite to Mg-hornblende, provides a complete representation of hydration and dehydration processes in serpentinites in subduction zones, along deep oceanic transform faults, and at passive continental margins. The latter has new implications, specifically for subduction initiation.

On the stability and layered organization of protein-DNA condensates

Multi-component phase separation is emerging as a key mechanism for the formation of biological condensates that play essential roles in signal sensing and transcriptional regulation. The molecular factors that dictate these condensates’ stability and spatial organization are not fully understood, and it remains challenging to predict their microstructures. Using a near-atomistic, chemically accurate force field, we studied the phase behavior of chromatin regulators that are crucial for heterochromatin organization and their interactions with DNA. Our computed phase diagrams recapitulated previous experimental findings on different proteins. They revealed a strong dependence of condensate stability on the protein-DNA mixing ratio as a result of balancing protein-protein interactions and charge neutralization. Notably, a layered organization was observed in condensates formed by mixing HP1, histone H1, and DNA. This layered organization may be of biological relevance, as it enables cooperative DNA packaging between the two chromatin regulators: histone H1 softens the DNA to facilitate the compaction induced by HP1 droplets. Our study supports near-atomistic models as a valuable tool for characterizing the structure and stability of biological condensates.

Shear-induced migration of a viscous drop in a viscoelastic liquid near a wall at high viscosity ratio: Reverse migration

• A drop under shear migrates laterally away from a wall in shear. • Medium viscoelasticity and viscosity ratio affects the migration. • High viscosity ratio and high Deborah number leads to migration towards the wall. • The critical viscosity ratio varies inversely with the capillary number. • The critical Deborah number also varies inversely with the capillary number. Wall-induced migration of a viscous drop in a viscoelastic fluid subjected to a plane shear is numerically simulated to investigate the effects of drop/matrix viscosity ratio. In a Newtonian system, drop migration away from the wall is inhibited as the viscosity ratio is increased. Here, we show that the introduction of the matrix viscoelasticity further decreases the migration and can even reverse its direction ‘from away’ to ‘towards the wall’, a phenomenon not seen in Newtonian systems. The migration towards or away from the wall eventually settles in a quasi-steady state that only depends on the instantaneous wall separation independent of the initial position of the drop. Drops migrating towards the wall initially increase their velocity, but as they approach the wall, they decelerate, showing a non-monotonic variation. The migration direction depends on the viscosity ratio, viscoelasticity (Deborah number), and the capillary number. We compute phase diagrams in the parameter space showing boundaries where migration changes direction. The critical Deborah number (at a fixed viscosity ratio) and the critical viscosity ratio (at a fixed Deborah number) for direction reversal approximately scales with the inverse of the capillary number.

Vibrational anisotropy of <i>δ</i>-(Al,Fe)OOH single crystals as probed by nuclear resonant inelastic X-ray scattering

Abstract. The formation of high-pressure oxyhydroxide phases spanned by the components AlOOH–FeOOH–MgSiO2(OH)2 in experiments suggests their capability to retain hydrogen in Earth's lower mantle. Understanding the vibrational properties of high-pressure phases provides the basis for assessing their thermal properties, which are required to compute phase diagrams and physical properties. Vibrational properties can be highly anisotropic, in particular for materials with crystal structures of low symmetry that contain directed structural groups or components. We used nuclear resonant inelastic X-ray scattering (NRIXS) to probe lattice vibrations that involve motions of 57Fe atoms in δ-(Al0.87Fe0.13)OOH single crystals. From the recorded single-crystal NRIXS spectra, we calculated projections of the partial phonon density of states along different crystallographic directions. To describe the anisotropy of central vibrational properties, we define and derive tensors for the partial phonon density of states, the Lamb–Mössbauer factor, the mean kinetic energy per vibrational mode, and the mean force constant of 57Fe atoms. We further show how the anisotropy of the Lamb–Mössbauer factor can be translated into anisotropic displacement parameters for 57Fe atoms and relate our findings on vibrational anisotropy to the crystal structure of δ-(Al,Fe)OOH. As a potential application of single-crystal NRIXS at high pressures, we discuss the evaluation of anisotropic thermal stresses in the context of elastic geobarometry for mineral inclusions. Our results on single crystals of δ-(Al,Fe)OOH demonstrate the sensitivity of NRIXS to vibrational anisotropy and provide an in-depth description of the vibrational behavior of Fe3+ cations in a crystal structure that may motivate future applications of NRIXS to study anisotropic vibrational properties of minerals.