Phase Diagram Of System Research Articles

Distribution and Evaporation Characteristics of Rb and Cs in Complex Salt Brine Systems

The brine in salt lakes is rich in resources, including not only K, Mg, and B, but also valuable trace elements. During the enrichment and extraction of trace elements (Rb, Cs) from sodium sulfate subtype salt lake brines, the process is significantly influenced by the presence of other coexisting ions such as Li+, K+, and Mg2+.The physical and chemical properties of K+ are extremely similar to those of Rb+ and Cs+, and its impact on the extraction of Rb+ and Cs+ is particularly significant. When K+, Rb+, and Cs+ coexist, they can form solid solutions such as [(K, Rb)2SO4], [(K, Cs)2SO4], and [(Rb, Cs)2SO4]. The formation of these solid solutions can lead to severe losses of Rb and Cs during the evaporation process of the brine, resulting in low yield. In response to the aforementioned issues regarding the evaporation process of Rb and Cs, this paper uses the aqueous-salt system phase diagram as a guide and combines experimental research with simulation calculations to study the enrichment patterns of trace elements Rb and Cs in the Na+, K+//Cl-, CO32-, SO42--H2O aqueous-salt system, as well as the migration mechanism of Rb and Cs.

A Combined Experimental and Computational Study on the Effect of the Reactor Configuration and Operational Procedures on the Formation, Growth and Dissociation of Carbon Dioxide Hydrate

Clathrate hydrate-based technologies are considered promising and sustainable alternatives for the effective management of the climate change risks related to emissions of carbon dioxide produced by human activities. This work presents a combined experimental and computational investigation of the effects of the operational procedures and characteristics of the experimental configuration, on the phase diagrams of CO2-H2O systems and CO2 hydrates’ formation, growth and dissociation conditions. The operational modes involved (i) the incremental (step-wise) temperature cycling and (ii) the continuous temperature cycling processes, in the framework of an isochoric pressure search method. Also, two different high-pressure PVT configurations were used, of which one encompassed a stirred tank reactor and the other incorporated an autoclave of constant volume with magnetic agitation. The experimental results implied a dependence of the subcooling degree, (P, T) conditions for hydrate formation and dissociation, and thermal stability of the hydrate phase on the applied temperature cycling mode and the technical features of the utilized PVT configuration. The experimental findings were complemented by a thermodynamic simulation model and other calculation approaches, with the aim to resolve the phase diagrams including the CO2 dissolution over the entire range of the applied (P, T) conditions.

Nonlinear Ion Acoustic Waves in Multicomponent Plasmas with Nonthermal Electrons-positron and Bipolar Ions

Abstract This paper studied the propagating characteristics of (2+1) dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons, positrons and bipolar ions. The dispersion relations are initially explored by using the small amplitude wave's dispersion relation. Then, the Sagdeev potential method is employed to study large amplitude ion acoustic waves. The analysis involves examining the system's phase diagram, Sagdeev potential function, and solitary wave solutions through numerical solution of an analytical process in order to investigate the propagation properties of nonlinear ion acoustic waves under various parameters. It is found that the propagation of nonlinear ion acoustic waves is subject to the influence of various physical parameters, including the ratio of number densities between the unperturbed positrons, electrons to positive ions, nonthermal parameters, the masses ratio of positive ions to negative ions, and the charge numbers ratio of negative ions to positive ions, the ratio of the electrons’ temperature to positrons’ temperature. In addition, the multicomponent plasma system has a compressive solitary waves with amplitude greater than zero or a rarefactive solitary waves with amplitude less than zero, in the meantime, compressive and rarefactive ion acoustic wave characteristics depend on the charge numbers ratio of negative ions to positive ions.

Melting temperature and elastic constants of disordered nonstoichiometric cubic TiCy, ZrCy and HfCy carbides

Based on the analysis of phase diagrams of carbide-forming systems M–C (M = Ti, Zr, Hf), an empirical relationship is proposed between the elastic stiffness constants cij of nonstoichiometric cubic carbides of titanium, zirconium and hafnium and their melting temperature. The dependences of the melting temperatures of nonstoichiometric cubic carbides TiCy, ZrCy and HfCy on their composition in homogeneity regions are calculated using the elastic stiffness constants c11(y) and c44(y) of these carbides. The calculated maximum melting temperatures are observed for carbides ~TiC0.80, ~ZrC0.82 and ~ HfC0.94–0.95 and are equal to 3345, 3708 and 4192 K, respectively. There is a qualitative correlation between the concentration dependences of the melting temperatures Tm(y) of TiCy, ZrCy and HfCy carbides and the anisotropy of the elastic properties of these carbides.

Stabilization of gels and emulsions in the ternary water/eugenol/poloxamer 407-system: Physicochemical characterization and potential application as encapsulation platforms

The ternary system water/eugenol/poloxamer 407 can form a variety of phases that are strongly influenced by the mixture composition and the thermal history of the system. In this study, we investigated the stabilization of emulsion and gel-like systems in which eugenol is encapsulated in a poloxamer 407 matrix. Our results reveal the complex interplay between poloxamer 407 and eugenol compositions in the stabilization single-phase systems at 25ºC. Increasing concentrations of poloxamer were found to incorporate higher amounts of eugenol into emulsion-like dispersions, effectively preventing coalescence and Ostwald ripening. However, high concentrations of poloxamer 407 induced gelation of these dispersions, resulting in eugenol-loaded poloxamer 407 gels. The thermal annealing of the emulsions at 65°C for 1 h followed by equilibration at room temperature allows the extension of the compositional range for the formation of homogeneous single-phase systems providing a strategy to modulate the phase diagram of the ternary system. Additionally, the encapsulation of hydrophobic pesticides in gel-like matrices was investigated, showing uniform distribution and consistent loading capacity (approximately 0.70 % w/w) across different pesticides which may contribute to facilitate the environmental distribution and efficacy of the encapsulated molecules. This research highlights the potential of eugenol/poloxamer 407-based systems as an environmentally friendly platform for the encapsulation and delivery of hydrophobic active molecules, offering a versatile solution for various applications.

Solid-liquid phase equilibria in the aqueous system containing the chlorides of potassium, ammonium, and calcium at 298.2, 323.2, and 348.2 K

In order to obtain the crystalline forms of the salts of the potassium, ammonium, calcium coexisting chloride system, the phase equilibria relationship of quaternary system K+, NH4+, Ca2+//Cl–-H2O at 298.2, 323.2, and 348.2 K was studied by isothermal dissolution equilibrium method. The solubility and density of equilibrium liquid phases of the system were experimentally determined; X-ray powder diffractometer was used to determine the compositions of the equilibrium solid phase at the quaternary invariant point. It is found that the quaternary system is a complex system at these three temperatures. The phase diagram at 298.2 K consists of three invariant points, seven univariate curves and five crystalline phase regions, forming the solid solutions (NH4Cl)x(KCl)1–x and (KCl)x(NH4Cl)1–x; while at 323.2 and 348.2 K the phase diagram consists of five invariant points, eleven univariate curves and seven crystalline phase regions, the double salts (KCl·CaCl2) and (2NH4Cl·CaCl2·3H2O), solid solutions (KCl)x(NH4Cl)1–x and (NH4Cl)x(KCl)1–x were formed. Among them, the crystalline phase region of solid solution (KCl)x(NH4Cl)1–x is the largest at three temperatures, indicating that it is the easiest to crystallize in this system. Comparing the phase diagrams of the quaternary system at 298.2, 323.2, and 348.2 K, it can be seen that the crystalline form of CaCl2 changes with the increase of temperature: CaCl2·6H2O at 298.2 K, CaCl2·2H2O at 323.2 and 348.2 K. From 323 to 348 K, the crystalline phase regions of (KCl·CaCl2) and (2NH4Cl·CaCl2·3H2O) increased gradually.

Phase Diagrams of a Relativistic Self-Interacting Boson System

Within the Canonical Ensemble, we investigate a system of interacting relativistic bosons at finite temperatures and finite isospin densities in a mean-field approach. The mean field contains both attractive and repulsive terms. Temperature and isospin density dependences of thermodynamic quantities are obtained. It is shown that, in the case of attraction between particles in a bosonic system, a liquid-gas phase transition develops against the background of the Bose–Einstein condensate. The corresponding phase diagrams are given. We explain the reasons for why the presence of a Bose condensate significantly increases the critical temperature of the liquid-gas phase transition compared to that obtained for the same system within the framework of Boltzmann statistics. Our results may have implications for the interpretation of experimental data, in particular, how sensitive the critical point of the mixed phase is to the presence of the Bose–Einstein condensate.

Separation and extraction of NH4Br and (K,NH4)2SO4 from 1-Bromooctane production wastewater by crystallization method

This work provides a method for the separation and extraction of bromine salts from bromine-containing wastewater by crystallization. Wastewater from the production of 1-Bromooctane is rich in potassium and bromine salts. This will allow for the recycling of chemical resources in this aqueous salt system. Based on the need for the process design of the new method, the solubility phase equilibrium of the quaternary K+,NH4+//SO42-,Br-–H2O system at 298.15 K and 323.15 K was investigated in this paper by using the isothermal dissolution equilibrium method, and the dry basis phase diagrams were plotted using the experimental data. And the equilibrium solid phase composition was determined by X-ray diffraction. At 298.15 K, the dry phase diagram of the quaternary system K+,NH4+//SO42-,Br-–H2O consists of three invariant points and five crystalline regions (K2SO4, (NH4)2SO4, (K,NH4)2SO4, (K,NH4)Br, (NH4,K)Br). At 323.15 K, there is one invariant point in the phase diagram of this quaternary system and three crystalline regions((K,NH4)2SO4, (K,NH4)Br, (NH4,K)Br). The (K,NH4)Br crystallization zone grows while the (NH4,K)Br crystallization zone decreases with increasing temperature, according to comparisons of the dry basis phase diagrams of this quaternary system at different temperatures. Crystallization zones of solid solution (K,NH4)2SO4 replaced the K2SO4 and (NH4)2SO4 single salt crystallization zones at the same time. The Pitzer model was used to calculate the solubility of this quaternary system at 298.15 K. The results showed that the experimental values were in good agreement with the calculated values. Based on the theoretical analysis of the dry phase diagram of the quaternary system K+,NH4+//SO42-,Br-–H2O, a process route for salt extraction using bromine-containing wastewater generated from the production of 1-Bromooctane was proposed and designed. The new process was experimentally verified to be technically feasible to obtain NH4Br with 99.01 % purity and (K,NH4)2SO4. The process has significant advantages, such as production safety, low input costs and no three-waste emissions.

First principles study of the structure and superconductivity of La-Ge alloys under high pressure

High pressure is a fundamental approach for discovering and developing new materials, where adjusting the pressure can induce phase transitions and novel properties, such as superconductivity. In this study, we conduct a comprehensive investigation of the structural and electronic properties of La-Ge compounds within the pressure range of 0–30 GPa by using first-principles calculations. Three new stable compounds have been identified, namely I4/mmm_La2Ge, Fd3̅m_LaGe2, and P6/mmm_LaGe5. In combination with the known structures, the pressure-component phase diagram of the La-Ge binary system is constructed. The results of electronic structure calculations indicate that all structures represented in this diagram exhibit metallic properties. The new structure Fd3̅m_LaGe2 with C15 Laves phase is predicted to be stabilized dynamically from 23 GPa up to at least 30 GPa. The calculations of superconducting properties reveal that both Fd3̅m_LaGe2 and Immm_LaGe5 are superconductors with critical temperatures of 5.9 K at 23 GPa and 6.3 K at 0 GPa, respectively. Superconductivity observed in both Fd3̅m_LaGe2 and Immm_LaGe5 can be attributed primarily to the coupling between Ge-4p electrons and phonons situated in proximity to the Fermi level. Our results indicate that phases with elevated Tc are more prevalent in compounds with a higher proportion of Ge atoms in the total density of states. These findings are expected to provide theoretical guidance for future experimental investigations of La-Ge system, facilitating the exploration of C15-type superconductors in the form of AB2.

Impact of the Sr2+-Nd3+ heterovalent isomorphism on the luminescence of orthoborates in Sr3B2O6-NdBO3 system

The phase diagram of the Sr3B2O6-NdBO3 binary system was studied. The intermediate compound Sr3Nd2(BO3)4 can be synthesized over a wide range of compositions, from 27 to 70 mol.% NdBO3, at 1200°C. The maximum luminescence of Nd in this solid solution was measured for the highest content of Sr. The partial substitution of Nd by 3 mol.% Sr in NdBO3 does not significantly affect the presence of concentration quenching. The phase exhibiting the strongest luminescence within the system is neodymium doped Sr3B2O6.

Phase behavior of the carbon dioxide/toluene/poly(ethylene glycol) ternary system

The phase behavior of a carbon dioxide (CO2)/toluene (Tol)/poly(ethylene glycol) (PEG) ternary system was investigated in this study to consider the effect of the polymer species on the phase diagram. Measurements were performed using a synthetic method combined with laser displacement and turbidity measurements. Bubble points (vapor–liquid phase separation) were determined from changes in the piston displacement and cloud points (liquid–liquid (LL) phase separation) were determined from changes in the turbidity. The phase boundaries of the CO2 mass fractions ranging from 0.113 to 0.496 were measured by varying the Tol/PEG mass ratio. The homogeneous phase area decreased when the mass ratio of PEG to Tol increased and/or the temperature decreased. These changes in the LL phase-separation behavior were explained by referring to the free volume fraction and solubility parameter estimated using the Sanchez–Lacombe equation of state. The free volume integral fraction could explain the phase diagram, but not the solubility parameter; the effect of polymer species on the Px phase diagram of the ternary system was explained by considering specific interactions between dissimilar components. These results could promote a comprehensive understanding of the phase diagram of CO2/organic solvent/polymer systems and aid the prediction of phase behavior.

Phase diagram of strongly-coupled Rashba systems

Abstract Motivated by the recent discovery of a possible field-mediated parity switch within the superconducting state of CeRh2As2 [Khim et al., Science 373, 1012 (2021)], we thoroughly investigate the dependence of the superconducting state of a strongly-coupled Rashba mono- and bilayer on internal parameters and an applied magnetic field. The role of interlayer pairing, spin orbit coupling, doping rate and applied magnetic field and their interplay was examined numerically at low temperature within a t-J-like model, uncovering complex phase diagrams and transitions between superconducting states with different symmetry.

Primary alcohol-induced coacervation in alkyl polyglucoside micellar solution for supramolecular solvent-based microextraction and chromatographic determination of phthalates in baby food

This study reports for the first time the phenomenon of supramolecular solvent formation based on alkyl polyglucoside as an amphiphile and primary alcohol as a coacervation agent. The physical properties (density, kinematic viscosity, phase diagram for ternary system) of the supramolecular solvent were investigated, and a mechanism for its formation was proposed. A green and simple microextraction procedure for preconcentration and determination of phthalates in baby foods packaged in plastic packaging was developed as proof-of-concept example. The microextraction procedure assumed separation of analytes from solid phase sample in micellar solution of decyl glucoside and in situ formation of supramolecular solvent for analytes preconcentration after addition of n-heptanol. The determination of phthalates in obtained extracts was implemented by high-performance liquid chromatography with UV–Vis detection. The limits of detection, calculated from a blank test based on 3σ, were determined to be 10 μg kg−1 for dimethyl phthalate, diethyl phthalate, di-n-butyl phthalate, and di-n-octyl phthalate. The developed procedure did not require filtration of sample suspension, and assumed the use of green and biodegradable substances for the supramolecular solvent formation across a wide pH range.

Dynamics of pH Oscillators in Continuous Stirred Tanks in Series.

Complex reaction networks with positive and negative feedback can produce diverse nonlinear phenomena in open reactors, such as multistability and oscillations. pH oscillators driven by hydrogen or hydroxide autocatalytic processes show sustained oscillations in continuously stirred tank reactors (CSTR) but only a sharp pH switch in batch. Here, we present a numerical study on the dynamics of pH oscillators in a series of CSTRs. We show a critical residence time under which bistability and above which oscillations develop. The dynamics of the CSTR cascade show the cross-shaped phase diagram of nonlinear activatory inhibitory systems. In the domain of oscillations, one reactor starts to oscillate autonomously and induces forced complex oscillations in the following tanks with damped amplitudes. These results, with their practical implications, may contribute to understanding the recent experimental observations of nonlinear phenomena in the presence of a residence time ramp and inspire further research in this area.

Liquid-liquid equilibrium of the 1-butyl-3-methylimidazolium-based ionic liquids + sodium citrate + water systems at 298.15 K

Liquid-liquid extraction has long been the preferred option for process engineers to develop separation processes and it is used to separate and purify various biological products, metallic ions, colorants, pharmaceutical molecules, and small organic species. Ionic liquids (ILs) are special ecological solvents that can be used as possible substitutes for traditional organic solvents used for extraction and separation processes, becoming them more sustainable and safer. In combination with salts or inorganic polymers, they can form a liquid system of two phases, advantageous due to its wide polarity and viscosity. In this scenario, liquid–liquid equilibrium (LLE) data and phase diagrams for new aqueous two-phase systems containing ionic liquid ([BMIM][OH], [BMIM][Cl], [BMIM][Br]) (1) + sodium citrate (2) + water (3) were determined experimentally at 298.15 K. The ionic liquids were synthesized and characterized in the first part of the study. COSMO-RS was used as a tool to calculate polarity graphs of study molecules. In the second part, liquid–liquid equilibrium was studied using experimental measurements of the binodal curve and tie-lines, testing the quality of experimental data by mass balance, thermodynamic modeling using the NRTL model to correlate liquid–liquid equilibrium data and to do their phase stability. The accuracy of the model data results was verified by Gibbs energy topological mixing surface analysis and σ profiles. The experimental results indicated that the studied systems had type I liquid–liquid phase behavior. It was demonstrated that the ionic liquid [BMIM][OH] demonstrated better behavior to form Aqueous Two-Phase Systems mixed with sodium citrate and water. The results obtained by the thermodynamic modeling and stability with NRTL model weren’t satisfactory, because, besides the low deviations for the liquid phases compositions, the majority of calculated tie-lines was not tangent with the Gibbs surface, showing the limitations of the model for systems with electrolytes.

A Jacobian-free pseudo-arclength continuation method for phase transitions in inhomogeneous thermodynamic systems.

Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another.

Machine-Learning Prediction of Curie Temperature from Chemical Compositions of Ferromagnetic Materials.

Room-temperature ferromagnets are high-value targets for discovery given the ease by which they could be embedded within magnetic devices. However, the multitude of potential interactions among magnetic ions and their surrounding environments renders the prediction of thermally stable magnetic properties challenging. Therefore, it is vital to explore methods that can effectively screen potential candidates to expedite the discovery of novel ferromagnetic materials within highly intricate feature spaces. To this end, we explore machine-learning (ML) methods as a means to predict the Curie temperature (Tc) of ferromagnetic materials by discerning patterns within materials databases. This study emphasizes the importance of feature analysis and selection in ML modeling and demonstrates the efficacy of our gradient-boosted statistical feature-selection workflow for training predictive models. The models are fine-tuned through Bayesian optimization, using features derived solely from the chemical compositions of the materials data, before the model predictions are evaluated against literature values. We have collated ca. 35,000 Tc values and the performance of our workflow is benchmarked against state-of-the-art algorithms, the results of which demonstrate that our methodology is superior to the majority of alternative methods. In a 10-fold cross-validation, our regression model realized an R2 of (0.92 ± 0.01), an MAE of (40.8 ± 1.9) K, and an RMSE of (80.0 ± 5.0) K. We demonstrate the utility of our ML model through case studies that forecast Tc values for rare-earth intermetallic compounds and generate magnetic phase diagrams for various chemical systems. These case studies highlight the importance of a systematic approach to feature analysis and selection in enhancing both the predictive capability and interpretability of ML models, while being devoid of potential human bias. They demonstrate the advantages of such an approach over a mere reliance on algorithmic complexity and a black-box treatment in ML-based modeling within the domain of computational materials science.

Solid–Liquid Phase Equilibrium of the n-Nonane + n-Undecane System for Low-Temperature Thermal Energy Storage

The current article presents an exploration of the solid–liquid phase diagram for a binary system comprising n-alkanes with an odd number of carbon atoms, specifically n-nonane (n-C9) and n-undecane (n-C11). This binary system exhibits promising characteristics for application as a phase change material (PCM) in low-temperature thermal energy storage (TES), due to the fusion temperatures of the individual components, thereby motivating an in-depth investigation of the solid–liquid phase diagram of their mixtures. The n-nonane (n-C9) + n-undecane (n-C11) solid–liquid phase equilibrium study herein reported includes the construction of the phase diagram using Differential Scanning Calorimetry (DSC) data, complemented with Hot–Stage Microscopy (HSM) and low-temperature Raman Spectroscopy results. From the DSC analysis, both the temperature and the enthalpy of solid–solid and solid–liquid transitions were obtained. The binary system n-C9 + n-C11 has evidenced a congruent melting solid solution at low temperatures. In particular, the blend with a molar composition xundecane = 0.10 shows to be a congruent melting solid solution with a melting point at 215.84 K and an enthalpy of fusion of 13.6 kJ·mol–1. For this reason, this system has confirmed the initial signs to be a candidate with good potential to be applied as a PCM in low-temperature TES applications. This work aims not only to contribute to gather information on the solid–liquid phase equilibrium on the system n-C9 + n-C11, which presently are not available in the literature, but especially to obtain essential and practical information on the possibility to use this system as PCM at low temperatures. The solid–liquid phase diagram of the system n-C9 + n-C11 is being published for the first time, as far as the authors are aware.

Optimization of energy storage and electrocaloric performance in Pb(Zr,Ti)O3 via A-Site La and Bi Co-doping

Lead-based ferroelectrics are one of the most fascinating candidates in the field of state-of-the-art electronic technology. Their intriguing properties are further enriched via the realization of morphotropic phase boundaries. Moreover, the A-site chemical substitution provides insight into the emergence of various exotic phases. Here, we employ co-doping of La3+ and Bi3+ at the A-site of Pb(Zr,Ti)O3 (PZT) ferroelectric to broaden the practical perspective of relaxor systems. Here, we emphasize that the A-site co-doping approach introduces technologically appealing amendments in the well-established temperature composition phase diagram of the PZT system. La3+ and Bi3+ doping favors the evolution of a novel response to thermal and field fluctuations. The maximum values of −ΔS are found to be ∼0.157, 0.118 and 0.176 J (kg·K)−1 for x=0.01, 0.02 and 0.03 , respectively. We employ the electrocaloric characteristics and Arrott plot as probing tools. The observation of a negative electrocaloric effect and the systematic reversal of Arrott lines, followed by a poling effect on the dielectric constant, reveals the emergence of ergodic phase as a novel phase. This further reveals that the Bi doping approach leads to the emergence of exotic characteristics in the chemically modified PZT system. The maximum observed recoverable energy for the composition for x = 0.01 is 0.0479 J cm−3 at a temperature of 388 K.

Efficient determination of free energies of non-ideal solid solutions via hybrid Monte Carlo simulations

Predicting the phase diagram of solid solutions is crucial for understanding their physical behavior under various conditions and at different compositions. However, conventional sampling methods face challenges in efficiently addressing configurational and vibrational disorder for substitutional solid solutions. Additionally, a persistent obstacle has been the lack of a robust theoretical approach for determining the free energy of interstitial solid solutions characterized by the fluid-like diffusion of interstitial species. The method presented in this paper overcomes both hurdles by coupling thermodynamic integration with hybrid Monte Carlo algorithms. We validate the accuracy of the method by computing the free energies of iron alloys described by a Lennard-Jones potential. We also showcase its efficiency by determining the phase diagram of the MgO-CaO system, described by a machine-learning interatomic potential. The high efficiencies achieved with this method pave the way to the determination of the free energies of solid solutions with ab initio accuracy.