Temperature-composition Diagram Research Articles

Eutectic mixtures of nevirapine: Phase diagrams, solid-state characterization, and dissolution studies

Solid-state modifications can improve drug performance. Studies have shown that multicomponent crystals, such as cocrystals and eutectic compositions, have successfully improved the performance of certain drugs, including their solubility. Nevirapine (NEV) is an antiretroviral drug with low aqueous solubility, impacting its bioavailability. This work aimed to study different nevirapine/co-former solid eutectic systems, define their phase diagrams and evaluate their dissolution properties. Caffeine (CAF), Theobromine (TEOB), and Theophylline (THEO) were chosen as co-formers due to their functional groups that can interact with NEV. Aiming to determine both temperature and eutectic composition, phase and Tamman diagrams were obtained using the differential scanning calorimetry (DSC) analysis of the mixtures indifferent NEV-co-former compositions (%w/w). Powder X-ray diffraction (PXRD) and DSC were used to characterize the eutectic materials. To assess the influence of eutectic systems on dissolution properties, we determined the powder dissolution profiles and intrinsic dissolution rates of anhydrous NEV and eutectic systems NEV-CAF and NEV-THEO using different dissolution media (pH 1.2 and pH 6.8). The eutectic compositions were calculated through the phase diagrams, interpolating the curves obtained by linear regression. Thus, the eutectic composition of the NEV-CAF system was determined to be 36.55 % NEV and eutectic temperature at 201.1 °C, while in the NEV-THEO system, the eutectic was obtained in a composition of 71.04 % NEV and eutectic temperature at 217.8 °C. Tamman diagrams were generated using the enthalpy values obtained from the DSC curves, and eutectic compositions were calculated using linear regression. The analysis revealed a eutectic composition of 36.51 % of NEV for the NEV-CAF system, and a eutectic composition of 70.94 % of NEV for the NEV-THEO system. It was not possible to determine the eutectic mass fraction of NEV-TEOB. A comparison of dissolution profiles and intrinsic dissolution rates in different dissolution media showed a significant improvement in the NEV dissolution rate in both eutectic systems. In an acidic medium, NEV dissolved 16 times faster in the NEV-CAF sample and 4 times faster in the NEV-THEO sample compared to pure anhydrous NEV. In a neutral medium, the dissolution profile of NEV was even more favorable in the same eutectic systems, showing that the increase in dissolution is relevant in a wide range of pH. In addition, the intrinsic dissolution rate in the two eutectic systems was higher than that of anhydrous NEV in all employed dissolution mediums. These eutectic systems improve the dissolution rate compared to pure NEV, offering the potential for enhancing the dissolution of poorly water-soluble drugs in the future.

Roles of Refractory Solutes on the Stability of Carbide and Boride Phases in Nickel Superalloys

Nickel-base superalloys contain high amounts of solutes like Cr, Mo, W, Nb, Ti, etc. These solutes promote the formation of different types of carbide and boride phases that may contain multiple elements. Researchers have mostly discussed the roles of primary elements responsible for the formation of a given carbide/boride phase, often ignoring the role of other solutes on its stability. In the present work, thermodynamic stability of carbide and boride phases in seven commercial superalloys, namely, Alloy 625, Alloy 690, Alloy 718, MAR M246, Rene 100, Udimet 710 and Nimonic 80A, has been studied using the CALPHAD based Thermo-Calc software. The aim of the study was to understand the role of different alloying elements on temperature stability and chemical compositions of equilibrium phases in superalloys. As the accuracy of CALPHAD based predictions depends upon the database used, a detailed examination of its inadequacies has also been carried out to ascertain the limitations of the predicted data. From the calculated equilibrium chemical compositions, major and minor constituents promoting the formation of carbides and borides have been identified. The individual effect of a given solute as well as the synergistic effect of two solutes on the relative thermodynamic stability of carbide/boride phases has been identified using property diagrams and isothermal sections of the temperature-composition diagrams. Most of the simulated results have been found to be consistent with the experimental data available in the literature. From a comparison of the experimental literature and the simulated data of the stable carbide and boride phases in the studied alloys, the interplay of different solutes has been deduced to define conditions under which these phases form, within the limitations of the database used. This study has helped in better understanding of general tendencies of solutes to form different carbide and boride phases in nickel-based superalloys.

Coexistence of strain glass transition and martensitic transformation in highly nickel-rich ferroelastic alloy with large elastocaloric effect

Strain glass transition attracts increasing attention in ferroelastic alloys in the context that martensitic transformation serves as the dominant mechanism for shape memory alloys. However, observing the coexistence of strain glass transition and martensitic transformation has not been reported. In this work, we introduce the strain glass transition by doping element to form highly nickel-rich Ni55Ti45 at.% alloys and in the meantime attain the characteristics of martensitic transformation in the alloys. We confirm the existence of strain glass transition by 1) no exothermic/endothermic peaks in heat flow curves, 2) two deviations in electric resistivity curves, 3) two frequency-dependent dips of storage modulus, and 4) successive formation and constrained growth of nanodomains over a wide temperature range. We observe the martensitic transformation characterized by 1) two pronounced exothermic peaks upon cooling and one endothermic peak upon heating in heat flow curves, 2) thermal hysteresis in electric resistivity curves, and 3) macroscopic martensitic twins in transmission electron microscopy images. With these two phase transformations, the quasilinear superelasticity, high strength, and large elastocaloric ΔTad of up to 9.7 K are achieved. By designing the strain maps and microstructural evolution pathways, we have provided a temperature-composition transformation path diagram to offer mechanistic insights and tuning strategies for the development of advanced alloys.

Percolation in binary mixtures of linkers and particles: Chaining vs branching.

Equilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between colloids. A gel forming binary mixture whose linkers can self-assemble into linear chains while still promoting the aggregation of particles is considered in this work. The particles are patchy particles with fC patches of type C and the linkers are patchy particles with 2 patches of type A and fB patches of type B. The bonds between patches of type A (AA bonds) promote the formation of linear chains of linkers. Two different ways (model A and model B) of bonding the linkers to the particles-or inducing branching-are studied. In model A, there is a competition between chaining and branching, since the bonding between linkers and particles takes place through AC bonds only. In model B, the linkers aggregate to particles through bonds BC only, making chaining and branching independent. The percolation behavior of these two models is studied in detail, employing a generalized Flory-Stockmayer theory and Monte Carlo simulations. The self-assembly of linkers into chains reduces the fraction of particles needed for percolation to occur (models A and B) and induces percolation when the fraction of particles is high (model B). Percolation by heating and percolation loops in temperature-composition diagrams are obtained when the formation of chains is energetically favorable by increasing the entropic gain of branching (model A). Chaining and branching are found to follow a model dependent relation at percolation, which shows that, for the same composition, longer chains require less branching for percolation to occur.

Theoretical determination of distillation curves of gasoline, ethanol and ethyl tert-butyl ether ternary blends from the experimental distillation curve of gasoline

It is now environmentally desirable and legally mandatory to add renewable fuels such as ethanol or ethyl tert-butyl ether to gasoline. However, biofuels affect, among other properties, the distillation curve of gasoline, which is subject to strict regulations. This work presents a simple mathematical model capable of accurately predicting the influence that the addition of these oxygenates has on the distillation curve. In order to address this issue, it is essential to find a simple mathematical correlation between the boiling temperatures of the hydrocarbons present in gasoline and the properties (boiling temperature and volume or molar concentration of ethanol) of the corresponding azeotropic mixtures formed with ethanol. Power functions have been assumed to model the temperature composition diagrams of the vapour-liquid equilibrium. Experimental data previously published by these and other authors have been used to fit and validate the model. The results provided by the mathematical model can be of great interest to understand the process of fuel evaporation in spark-ignition engines or the adjustment of distillation cuts in refineries, in order to comply with the regulations, in terms of the distillation curve, after adding ethanol or ethyl tert-butyl ether.

Vapor–Liquid Equilibria of Mixtures Containing Ethanol, Oxygen, and Nitrogen at Elevated Pressure and Temperature, Measured with In Situ Raman Spectroscopy in Microcapillaries

Ethanol and oxygen containing gases are mixed in a T-junction at elevated pressure and then passed into a fused silica microcapillary, located in a heating block. Inside the microcapillary a Taylor flow of alternating liquid and vapor segments is formed. The thermodynamic equilibrium composition of the liquid and vapor segment depends on pressure and temperature. Their compositions are measured inside the microcapillary using in situ Raman spectroscopy. The main results obtained therefrom are temperature–composition (Tx) diagrams at conditions relevant for combustion engines [p = (3 to 8) MPa; T = (303 to 473) K]. Isothermal vapor–liquid equilibria (VLE) data are derived and given in pressure–composition (px) diagrams. The investigation of different gas mixtures containing oxygen and nitrogen allows furthermore the illustration of VLE data at constant pressure and temperature in ternary diagrams. The obtained results are compared to scarce literature data. An equation of state (Peng–Robinson EOS) is furthermore adjusted to the measured results.

Photoluminescence properties of Eu2+ activator ions in the SrS–Ga2S3 system

Various phosphors with activator Eu2+ ions in the host compositions of the SrS–Ga2S3 system were investigated on the basis of the temperature–composition diagram for the SrS–Ga2S3 system. The phosphors were prepared by solid-state reaction using stoichiometric amounts of SrS, EuS, and Ga2S3. The SrS:Eu2+, Sr2Ga2S5:Eu2+, and SrGa2S4:Eu2+ emitted red (610 nm), yellow-green (550 nm), and green (532 nm) light, respectively. For the SrS:Eu2+ phosphor, the host SrS had a cubic crystal structure and the Eu2+ activator ions were substituted at the Sr2+ sites of the host, surrounded by six sulfur anions (S2−) in Oh group symmetry. In the Sr2Ga2S5:Eu2+ phosphor, the Eu2+ cations occupied monocapped trigonal prism sites surrounded by seven S2– anions. In the SrGa2S4:Eu2+ phosphor, the Eu2+ cations occupied square anti-prismatic sites surrounded by eight S2– anions in D4d symmetry. The photoluminescence properties of the SrS:Eu2+, Sr2Ga2S5:Eu2+, and SrGa2S4:Eu2+ phosphors prepared at temperatures from 700 to 1000 °C were investigated.

Calculation of the Saturation Properties of a Model Octane-Water System Using Monte Carlo Simulation.

We use Monte Carlo simulation to compute the saturation properties of a model octane-water system. The system phase separates into water-rich liquid and vapor phases, octane-rich liquid and vapor phases, and water-rich liquid and octane-rich liquid phases at various conditions. We outline a strategy for determining the saturation properties of the mixture over a wide range of temperatures, pressures, and compositions. The approach begins with direct calculations that enable one to locate a single saturation point. A variety of expanded ensemble schemes are then used to trace saturation curves along paths of interest. We show how the overall strategy provides a means to construct pressure-composition diagrams at a fixed temperature and temperature-composition diagrams at a fixed pressure. In addition, we demonstrate how the approach is used to trace the liquid-liquid-vapor triple line over a wide range of temperatures. Simulation data are compared with experimental data, when available. Overall, our results show that the approach provides an efficient means to calculate the saturation properties of a binary system.

Thermodynamic assessment of the Mo-S system and its application in thermal decomposition of MoS2

The Mo-S system is crucial to extractive metallurgy, tribology, and various possible applications in design and fabrication of novel two-dimensional (2D) materials. First-principles calculations were utilized to compute the enthalpies of formation of molybdenum sulfides at 0 K and the heat capacity of Mo2S3 up to 960 K. A critical evaluation of the thermodynamic properties, phase equilibria, and phase diagram information in the literature was carried out to facilitate the thermodynamic optimization of the Mo-S system. The obtained thermodynamic description of the Mo-S system can satisfactorily represent most of the reliable thermodynamic and phase diagram information. Pressure-temperature (P-T), pressure-composition (P-x), and temperature-composition (T-x) diagrams of the Mo-S system were utilized to study the thermal decomposition of MoS2 for raw Mo production. Reduced pressure and high temperature are thermodynamically favorable conditions for the MoS2 reduction process.

Monte Carlo simulations of vapour–liquid phase equilibrium and microstructure for the system containing azeotropes

Phase equilibrium data of the mixtures including alcohols, esters and organic acids are of first interest particularly to design and optimise biodiesel production and reactive distillation processes. In this work, vapour–liquid phase equilibrium of these systems was simulated at low pressure using Gibbs ensemble Monte Carlo method. All Lennard–Jones parameters of pseudo-atoms involved in the systems were derived from previous parametrisations of TraPPE-UA force field. The Fourier coefficients of dihedrals encountered in ethyl acetate molecule have been obtained from the quantum calculations. Using this force field, temperature-composition diagrams are well reproduced for ethyl acetate + ethanol, ethyl acetate + methanol at 70.00 kPa and ethyl acetate + acetic acid mixtures at 77.33 kPa. The transferability of this force field to mixtures in these systems is noticeable. Analysis of the microstructure for the ethyl acetate + ethanol and ethyl acetate + acetic acid mixtures was presented. We found that the hydrogen bond networks consist of autoassociation and cross-association and autoassociation occupies the main position as compared with cross association in the ethyl acetate + ethanol mixture. OCHAc–HHAc and OCEtOAc–HHAc hydrogen bond interactions play a significant role in the phase behaviours or structures of ethyl acetate + acetic acid mixture.

(Vapor + Liquid) Equilibrium (VLE) for Binary Lead-Antimony System in Vacuum Distillation: New Data and Modeling Using Nonrandom Two-Liquid (NRTL) Model

In this work, new experimental vapor–liquid equilibrium (VLE) data of lead-antimony alloy (Pb-Sb alloy) in vacuum distillation are reported. The activity coefficients of components of Pb-Sb alloy were calculated by using the NRTL model. The calculated average relative deviations were ±0.1425 and ±0.2433 pct, and the average standard deviations were ±0.0009 and ±0.0007, respectively, for Pb and Sb. The VLE phase diagrams, such as the temperature composition (T-x) and pressure composition (P-x) diagrams of Pb-Sb alloy in vacuum distillation were predicted based on the NRTL model and VLE theory. The predicted results are consistent with the new experimental data indicating that VLE phase diagrams obtained by this method are reliable. The VLE phase diagrams of alloys will provide an effective and intuitive way for the technical design and realization of recycling and separation processes. The VLE data may be used in separation processes design, and the thermodynamic properties as the key parameters in specific applications.

Vapor–liquid phase equilibria of binary tin–antimony system in vacuum distillation: Experimental investigation and calculation

Vacuum distillation experiments were conducted for tin-antimony alloy (Sn–Sb alloy) under the system pressure of 5 Pa. The content of Sb (mole fraction) in crude Sn, viz., xSb was reduced from 0.5000 to 0.0619 in a single stage distillation process under the condition of residual pressure of 5–10 Pa, distillation temperature of 1373 K and distillation time of 60 min. The activity coefficients of components of Sn–Sb alloy were calculated by using the molecular interaction volume model (MIVM), and the calculated average relative deviation and the average standard deviation were ±0.00039 and ± 0.173%, respectively for both Sn and Sb. The vapor–liquid equilibrium (VLE) phase diagrams, including the temperature-composition (T-x) and pressure-composition (p-x) diagrams of Sn–Sb alloy in vacuum distillation were calculated based on VLE theory and the MIVM. A reasonable agreement between the calculated results and the experimental data indicates that VLE phase diagrams obtained by this method are reliable. The VLE phase diagrams of alloys will provide an effective and convenient way for the designing of the process parameters of industrial production of vacuum metallurgy, and for the prediction of the needed product component dependence of temperature and pressure during the process of vacuum distillation.

Composition Dependences of Entropy Change and Transformation Temperatures in Ni-rich Ti–Ni System

For Ni-rich Ti–Ni alloys, physical properties such as specific heat and electric resistance were systematically investigated. The B2/B19′ martensitic transformation temperatures ranging from 180 to 373 K were determined for Ni contents of 49.98–51.09 %, and a sudden disappearance of martensitic transformation was confirmed for Ni contents greater than 51.23 %, which has also been well reported in the literatures. The entropy change was also evaluated from differential scanning calorimeter measurement, and it was clarified that the entropy change plotted to T 0 temperature shows an S-shaped curve, starting to drastically decrease at about 300 K. Thermodynamic approaches were then carried out attempting to determine the reason for the disappearance of transformation. The entropy change estimated from direct measurements of specific heats for 51.75 Ni (B2) and 50.92 Ni (B19′) was found to be more consistent with the experimental data, rather than the calculated curve based on the Debye model for vibration specific heat. It was proposed that the equilibrium between the parent and martensite phases obeys the Clausius–Clapeyron relationship in the composition–temperature system. Using the constructed composition–temperature diagram, the disappearance of martensitic transformation in the Ti–Ni system can be well understood as being due to the drastic increase of hysteresis at low temperature.

Modeling the Dissociation Conditions of Carbon Dioxide + TBAB, TBAC, TBAF, and TBPB Semiclathrate Hydrates

The thermodynamic approach developed by Paricaud [J. Phys. Chem. B 2011, 115, 288–299] is applied to predict the dissociation conditions of semiclathrate hydrates made with tetra-n-butyl ammonium bromide (TBAB), tetra-n-butyl ammonium chloride (TBAC), tetra-n-butyl ammonium fluoride (TBAF), and tetra-n-butyl phosphonium bromide (TBPB). The SAFT-VRE equation of state is used to describe the properties of fluid phases, and a good description of osmotic and mean activity coefficients of electrolyte solution is obtained. The temperature–composition diagrams of water + tetra-n-alkylammonium/alkylphosphonium salt binary systems are well described by the model. Group contribution methods are proposed to predict the fusion enthalpies and the congruent melting points of semiclathrate hydrates. The van der Waals and Platteeuw theory is combined with the model to calculate the dissociation conditions of carbon dioxide semiclathrate hydrates. The liquid–vapor–hydrate three phase lines can be accurately described over...

Thermodynamics of Ferroelectric Solid Solutions with Morphotropic Phase Boundaries

A thermodynamic analysis is presented for the diffusionless phase diagrams of ferroelectric solid solutions that display a morphotropic phase boundary (MPB) separating adjacent tetragonal and rhombohedral phases. Equations are developed for the shape of the MPB, the locations of triple and tricritical points, and for the line along which the anisotropy of polarization vanishes. The appearance of lower symmetry orthorhombic and monoclinic phases is considered and the topologies of energy surfaces in the region of the phase diagram where these phases may stabilize are illustrated. The theory is applied to the solid solution of lead zirconate with lead titanate (PZT) and relationships between polar anisotropy and the transformation strain, dielectric susceptibility and piezoelectric properties, are discussed. The analysis is used to reproduce phase boundary lines for solid solutions of lead titanate with lead magnesium niobate (PMN‐PT) and lead zinc niobate (PZN‐PT) and composition–temperature diagrams along isopleths in the ternary system PMN‐PZT are estimated. The anisotropies of polarization in solid solutions based on lead titanate and barium titanate are contrasted. The results provide a thermodynamic framework useful for guiding experimental investigations of ferroelectric solid solutions and for generating energy functions used in constitutive modeling and phase field simulations of microstructure and properties.

Deconstructing Phase Diagram Calculations

Phase diagram calculations are an important topic in material science. They are usually carried out with limited-distribution software packages. This technology report is an introduction to software based phase diagram calculations. Three spreadsheets calculators are presented. The first one plots the Gibbs free energy versus composition for Al–Zn, Li–Mg, and Pelton’s fictional A–B alloy. The second one calculates equilibrium phase composition for A–B. The third one calculates the Li–Mg temperature–composition diagram. The coding is reduced to a minimum and calculations are directly accessible to the user. The programs aim to be practice tools to complement instructor’s lectures.

Phase equilibria in the system Sm–Rh–O and thermodynamic and thermal studies on SmRhO3

Using isothermal equilibration, phase relations are established in the system Sm-Rh-O at 1273 K. SmRhO3 with GdFeO3-type perovskite structure is found to be the only ternary phase. Solid-state electrochemical cells, containing calcia-stabilized zirconia as an electrolyte, are used to measure the thermodynamic properties of SmRhO3 formed from their binary component oxides Rh2O3 (ortho) and Sm2O3 (C-type and B-type) in two different temperature ranges. Results suggest that C-type Sm2O3 with cubic structure transforms to B-type Sm2O3 with monoclinic structure at 1110 K. The standard Gibbs energy of transformation is . Standard Gibbs energy of formation of SmRhO3 from binary component oxides Rh2O3 and Sm2O3 with B-type rare earth oxide structure can be expressed as . The decomposition temperature of SmRhO3 estimated from the extrapolation of electrochemical data is 1665 (+/- 2) K in air and 1773 (+/- 3) K in pure oxygen. Temperature-composition diagrams at constant oxygen pressures are constructed for the system Sm-Rh-O. Employing the thermodynamic data for SmRhO3 from emf measurement and auxiliary data for other phases from the literature, oxygen potential-composition phase diagram and 3-D chemical potential diagram for the system Sm-Rh-O at 1273 K are developed.

Geometrical study of the three-dimensional temperature–composition diagrams. An important aid to understand the behavior of the liquid–vapour equilibrium in ternary systems

In this work the usefulness of qualitatively studying and drawing three-dimensional temperature–composition diagrams for ternary systems is pointed out to understand and interpret the particular behavior of the liquid–vapour equilibrium of non-ideal ternary systems. Several examples have been used in order to highlight the interest and the possibilities of this tool, which should be an interesting support not only for lecturers, but also for researchers interested in experimental equilibrium data determination.

Decomposition mechanism of Al1−xSixNy solid solution and possible mechanism of the formation of covalent nanocrystalline AlN/Si3N4 nanocomposites

Using a combined ab initio density functional theory (DFT) and thermodynamic modeling, we study the stability of a variety of phases and the possible mechanism of the decomposition of the Al1−xSixNy solid solution and formation of nanocrystalline AlN/Si3N4 nanocomposites, which have been experimentally investigated in a number of recent publications. It is shown that the linear and exponential dependence of the interaction parameter on temperature yields reliable results. The hexagonal close-packed (hcp)(ZnS) to hcp(β) phase transition points occur at x∼0.36. The calculated temperature–composition diagrams show that spinodal decomposition mechanism is unlikely in this system because of too small de-mixing energy, which is comparable with the interfacial energy of semi-coherent interfaces. Thus, the decomposition should occur by nucleation and growth, accompanied by a phase transformation from the unstable hcp(ZnS)-SiN to stable hcp(β) or amorphous Si3N4, which probably limits the achievable hardness enhancement of the nanocomposites as compared with the nanocrystalline TiN/a-Si3N4 ones (where a indicates X-ray amorphous, and the stoichiometry Si3N4 symbolizes the fact that Si is fourfold coordinated to nitrogen, as in stoichiometric silicon nitride).

Phase chemistry of the system Nb–Rh–O

Abstract Phase relations in the system Nb–Rh–O at 1223 K were investigated by isothermal equilibration of eleven compositions and analysis of quenched samples using OM, XRD, SEM and EDS. The oxide phase in equilibrium with the alloy changes progressively from NbO to NbO2, NbO2.422 and Nb2O5−x with increasing Rh. Only one ternary oxide NbRhO4 with tetragonal structure (a=0.4708 nm and c=0.3017 nm) was detected. It coexists with Rh and Nb2O5. The standard Gibbs energy of formation of NbRhO4 from its component binary oxides measured using a solid-state electrochemical cell can be represented by the equation; Δ G f , ox o ( J / mol ) = − 38 , 350 + 5.818 × T ( ± 96 ) Constructed on the basis of thermodynamic information of the various alloy and oxide phases are oxygen potential diagram for the system Nb–Rh–O at 1223 K and temperature–composition diagrams at constant partial pressures of oxygen.