Regular Solution Approximation Research Articles

Substitution limits and thermodynamic stability of solid solutions in HTSC based on iron and yttrium oxyarsenides

The mixing energies (interaction parameters) and the critical decomposition (stability) temperatures of Y1–xLnxFeAsO0.6 solid solutions, where Ln = La–Er, 0 < x < 1.0, were determined within the framework of the V. S. Urusov crystal-energetic approach in the approximation of regular solid solutions. Diagram of thermodynamic stability and domes of the solid solution decomposition have been plotted, which make it possible to calculate the equilibrium isomorphous substitution limits of yttrium for rare earth elements x depending on the decomposition temperature Td, or the decomposition temperature depending on the substitution limit. The results of calculation do not contradict to the experimental data found earlier in the literature for La1–xYxFeAsO0.6 and related systems La1–yYvFeAsO, La0.8Y0.2FeAsO0.7, and Y0.95La0.05FeAsO1–vH0.15. The results of this work can be useful in choosing the components’ ratio in “mixed” matrices and the dopant content in high-temperature superconductors, effective magnetic and other materials.

Isotherm Theoretical Study of the AlxGa1-xAsySb1-y Quaternary Alloy Using the Regular Solution Approximation for Its Possible Growth via Liquid-Phase Epitaxy at Low Temperatures.

This work presents the theoretical calculation of isotherm diagrams for quaternary alloys of III-V semiconductor compounds with the form IIIxIII1-xVyV1-y. In particular, the isotherm diagrams for the AlxGa1-xAsySb1-y quaternary alloy at low temperatures were calculated (500 °C, 450 °C, 400 °C, and 350 °C). The AlxGa1-xAsySb1-y quaternary alloy was formed from four binary compounds such as GaAs, AlAs, AlSb, and GaSb, all with direct bandgaps. The regular solution approximation was used to find the quaternary isotherm diagrams, represented in four linearly independent equations, which were solved using Parametric Technology Corporation Mathcad 14.0 software for different arsenic and antimony atomic fractions. The results support the possible growth of layers via liquid-phase epitaxy in a range of temperatures from 500 °C to 350 °C, where the crystalline quality could be improved at low temperatures. These semiconductor layers could have applications for optoelectronic devices in photonic communications, thermophotovoltaic systems, and microwave devices with good crystalline quality.

Synergistic Interaction Between Cationic Novel Gemini Surfactant and Non-ionic Conventional Surfactants in Aqueous Medium

The interaction between novel gemini surfactant (alkane-α, ω-bis(dimethyl hexadecyl ammonium bromide) (G6)) and two different non-ionic surfactants (Triton X-114 (TX-114), Tween 20 (T-20)) has been investigated in the current study at temperature 298.15 K. The critical micelle concentration (cmc) values of mixed systems were computed by the conductometric titration in the aqueous medium. The results have been examined by utilizing numerous theoretical models (Clint, Rubingh, Motomura, Maeda, and Lange models). The experimentally determined cmc were lower than corresponding ideal values (cmc*) and decreased with the mixtures' stoichiometric mole fraction (α1) of G6. This shows non-ideal behavior between two employed components. The interaction parameter at mixed micelle (β) has been analyzed by using regular solution approximation. The attractive interaction or synergistic behavior in both mixed systems is confirmed by the negative values of β. The various energetics parameters were also evaluated and discussed.

Parameter dependent finite element analysis for ferronematics solutions

This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The first part of the article is devoted to the asymptotic analysis of global energy minimizers in the limit of vanishing elastic constant, ℓ→0 where the re-scaled elastic constant ℓ is inversely proportional to the domain area. The first results concern the strong H1-convergence and a ℓ-independent H2-bound for the global minimizers on smooth bounded 2D domains, with smooth boundary and topologically trivial Dirichlet conditions. The second part focuses on the discrete approximation of regular solutions of the corresponding non-linear system of partial differential equations with cubic non-linearity and non-homogeneous Dirichlet boundary conditions. We establish (i) the existence and local uniqueness of the discrete solutions using fixed point argument, (ii) a best approximation result in energy norm, (iii) error estimates in the energy and L2 norms with ℓ-discretization parameter dependency for the conforming finite element method. Finally, the theoretical results are complemented by numerical experiments on the discrete solution profiles, the numerical convergence rates that corroborates the theoretical estimates, followed by plots that illustrate the dependence of the discretization parameter on ℓ.

Mixed Micellization and Spectroscopic Studies of Anti-Allergic Drug and Non-Ionic Surfactant in the Presence of Ionic Liquid.

In drug delivery, surfactants are used to reduce side effects and to increase drug efficiency. The present work aimed to study the interaction of diphenhydramine hydrochloride (anti-allergic drug) with TX–45 (non-ionic surfactant) in the absence and presence of ionic liquid (1-hexyl-3-methylimidazolium chloride). The physicochemical parameters were estimated by the surface tension measurement. Various theoretical models (Clint, Rubingh, Motomura, and Maeda) were applied to determine the attractive behavior between drug and surfactant mixtures at the surface and in bulk. The drug and surfactant mixtures exhibit synergistic behavior in the absence and presence of ionic liquid. Several energetic parameters were also estimated with the assistance of regular solution approximation and pseudo phase separation model that indicate micelle formation and adsorption of surfactant at the surface is thermodynamically advantageous. The morphology of pure and mixture of amphiphiles has been estimated by the Tanford and Israelachvili theories. UV-visible spectroscopy was used to quantify the attractive behavior of the drug with surfactant with the help of a binding constant (K).

Determining the phase stability of luminescent materials based on the solid solutions of oxyorthosilicates (Lu<sub>1−x</sub>Ln<sub>x</sub>)[(SiO<sub>4</sub>)<sub>0.5</sub>O<sub>0.5</sub>], where Ln = La−Yb

Objectives. This study aimed to predict the limits of substitution and stability of luminescent materials based on low-temperature modifications of solid solutions (spatial group P21/c) with lutetium oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5], where Ln represents the rare-earth elements (REEs) of the La–Yb series.Methods. The V.S. Urusov’s crystal energy theory of isomorphous substitutions and a crystallochemical approach in the regular solid solution approximation were used to calculate the energies of the mixing (interaction parameters) of the solid solutions.Results. Using the V.S. Urusov’s theory, we calculated the energies of mixing (interaction parameters) in the systems under study. The dependences of the decomposition temperatures of solid solutions on the REE number and composition (x) were obtained and used to create a diagram of the thermodynamic stability of the solid solutions, allowing us to predict the substitution limits depending on the temperature or determine the decomposition temperature using the given substitution limits.Conclusions. The results of the study can be useful when choosing the ratio of components in matrices (host materials) and the amount of the activator (dopant) in the new luminescent, laser, and other materials based on low-temperature modifications of solid solutions of “mixed” REE oxyorthosilicates (Lu1−xLnx)[(SiO4)0.5O0.5].

Surface segregation in multicomponent high entropy alloys: Atomistic simulations versus a multilayer analytical model

This paper compares two approaches for investigating the near-surface composition profile that results from surface segregation in the so-called Cantor alloy, an equi-molar alloy of CoCrFeMnNi. One approach consists of atomistic computer simulations by a combination of Monte Carlo, molecular dynamics and molecular statics techniques, and the other is a nearest neighbor analytical calculation performed in the regular solution approximation with a multilayer model, developed here for the first time for a N-component system and tested for the 5-component Cantor alloy. This type of comparison is useful because a typical computer simulation requires the use of ~100 parallel processors for 2 to 3 h, whereas a similar calculation by means of the analytical model can be performed in a few seconds on a laptop machine. The results obtained show qualitatively good agreement between the two approaches. Thus, while the results of the computer simulations are presumably more reliable, and provide an atomic scale picture, if massive computations are required, for example, in order to optimize the composition of a multicomponent alloy, then an initial screening of the composition space by the analytical model could provide a highly useful means of narrowing the regions of interest, in the same way that the CALPHAD method allows rapid investigation of phase diagrams in complex multinary systems.

A phase-field approach for modeling equilibrium solute segregation at the interphase boundary in binary alloys

A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while also accounting for various mass transport mechanisms. Analytical equilibrium solutions of one-dimensional systems are presented, and excess IB quantities are evaluated independent of the Gibbs dividing surface convention. With the aid of the parallel tangent construction, IB segregation isotherms are established in terms of the alloy composition and the model parameters describing the free energy functions. Under the regular solution approximation, computational studies elucidating the dependence of the IB energy and segregation levels on temperature and free energy model parameters are presented. We show that the model is consistent with the Gibbs adsorption equation; therefore, it is possible to compare the adsorption behavior predicted by the model parameters with experiments and atomistic simulations. Future work on extending the model to ternary alloys, and incorporating the effect of elastic interactions on IB segregation is expected.

Solute drag and dynamic phase transformations in moving grain boundaries

A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain boundary and the solute drag force, and permits a broad exploration of the parameter space and different dynamic regimes. The grain boundary phases continue to exist in the moving grain boundary and show a dynamic hysteresis loop, a dynamic critical line, and other features that are similar to those for equilibrium phases. Grain boundary motion strongly affects the relative stability of the phases and can even stabilize phases that are absolutely unstable under equilibrium conditions. Grain boundary phase transformations are accompanied by drastic changes in the boundary mobility. The results are analyzed in the context of non-equilibrium thermodynamics. Unresolved problems and future work are discussed.

Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity

We study the initial-boundary value problem for 1D compressible magnetohydrodynamics equations of viscous nonresistive fluids in the Lagrangian mass coordinates. Based on the estimates of upper and lower bounds of the density, weak solutions are constructed by approximation of global regular solutions, the existence of which has recently been obtained by Jiang and Zhang [Nonlinearity 30, 3587–3612 (2017)]. The uniqueness of weak solutions is also proved as a consequence of Lipschitz continuous dependence on the initial data. Furthermore, long time behavior for global solutions is investigated. Specifically, based on the uniform-in-time bounds of the density from above and below away from zero, together with the structure of the equations, we show the exponential decay rate in L2- and H1-norm, respectively, with large initial data.

Solute Drag and Dynamic Phase Transformations in Moving Grain Boundaries

A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain boundary and the solute drag force, and permits a broad exploration of the parameter space and different dynamic regimes. The grain boundary phases continue to exist in the moving grain boundary and show a dynamic hysteresis loop, a dynamic critical line, and other features that are similar to those for equilibrium phases. Grain boundary motion strongly affects the relative stability of the phases and can even stabilize phases that are absolutely unstable under equilibrium conditions. Grain boundary phase transformations are accompanied by drastic changes in the boundary mobility. The results are analyzed in the context of non-equilibrium thermodynamics. Unresolved problems and future work are discussed.

Stress-controlled carbon diffusion channeling in bct-iron: A mean-field theory

Diffusion of interstitial carbon atoms in iron is the rate-limiting phenomenon of a number of phase transitions in body-centered (bcc) and body-centered tetragonal (bct) phases such as ferrite and martensite. These phases being rarely stress-free and undeformed, the influence of stress/strain on the diffusivity of carbon is essential, although scarcely documented. We developed a model of carbon elastodiffusion in bct-iron. We combined anisotropic linear elasticity theory of point defects, the dilute approximation of regular solutions and the multisite model of random walk into a coherent mean-field theory. The model allows predicting the effects of composition, temperature and mechanical loading on the anisotropy of carbon diffusion. Density functional theory calculations have provided most of the materials parameters. The predictions were successfully tested against kinetic Monte Carlo simulations. Our results show that compression of the crystal increases carbon diffusivity, while tension has the opposite effect. Axial straining is accompanied by a large anisotropy of diffusion. This effect could be exploited to produce stress-controlled diffusion channeling for the engineering of anisotropic microstructures during thermal ageing of martensitic Fe-C alloys.

Simulation of the first order phase transitions in binary alloys with variable mobility

The first order phase transitions in binary alloys were simulated basing on the Cahn–Hilliard equation for metastable states with mobility depending on the local composition. The simulation was carried out utilizing the semi-implicit Fourier spectral method for 3D fragment of a solid solution satisfying the regular solution approximation. We defined kinetics of the main characteristics of phase distribution: nucleation rate, average size, concentration of precipitates and autocorrelation function etc. Peculiarities of different stages of binary alloy decomposition (nucleation, diffusion growth and coarsening) were analyzed both for constant and variable mobility.

Mixing and electronic entropy contributions to thermal energy storage in low melting point alloys

Melting of crystalline solids is associated with an increase in entropy due to an increase in configurational, rotational, and other degrees of freedom of a system. However, the magnitude of chemical mixing and electronic degrees of freedom, two significant contributions to the entropy of fusion, remain poorly constrained, even in simple 2 and 3 component systems. Here, we present experimentally measured entropies of fusion in the Sn-Pb-Bi and In-Sn-Bi ternary systems, and decouple mixing and electronic contributions. We demonstrate that electronic effects remain the dominant contribution to the entropy of fusion in multi-component post-transition metal and metalloid systems, and that excess entropy of mixing terms can be equal in magnitude to ideal mixing terms, causing regular solution approximations to be inadequate in the general case. Finally, we explore binary eutectic systems using mature thermodynamic databases, identifying eutectics containing at least one semiconducting intermetallic phase as promising candidates to exceed the entropy of fusion of monatomic endmembers, while simultaneously maintaining low melting points. These results have significant implications for engineering high-thermal conductivity metallic phase change materials to store thermal energy.

A Thermodynamic Framework Bridging the Composition and Temperature Dependence of Bulk Modulus With Enthalpy of Mixing

The intrinsic thermodynamic links that exist between thermochemical and thermophysical quantities, especially their temperature, pressure, and composition dependence, have seldom been analyzed in sufficient detail in literature. In this connection, an attempt is made to establish a thermodynamic bridge, relating Δo H mix, the standard enthalpy of mixing with Δo B T , the change in isothermal bulk modulus as a result of alloying and its composition and temperature dependence. In essence, by adopting the standard regular and subregular solution approximations to the composition dependence of mixing enthalpy; and furthermore, incorporating separately the configurational (Δo S conf) and vibrational (Δo S Vib) entropy contributions to mixing Gibbs energy change (Δo G mix), simple models have been derived for the composition and temperature variations of excess bulk modulus ΔB T . In particular, a regular or subregular solution analog of the composition variation of ΔB T is shown to be possible if Δo H mix could be described likewise. The vibrational entropy contribution to ΔB T is found to be important only when the change in Gruneisen parameter during alloying turns to be significant. The practical utility of the theoretical framework developed in this study has been demonstrated by applying it to disordered fcc Cu1−x Ni x alloys, wherein it is shown that Δo H mix and Δo B T are linearly correlated, as predicted by the theory.

Simulation of the decomposition of binary alloys on the basis of the free energy density functional method

The simulation of the decomposition of a three-dimensional fragment of a solid solution satisfying the regular solution approximation has been carried out based on the Cahn–Hilliard equation taking into account the Gaussian fluctuations of the initial state of the alloy. The simulation has been performed for several temperatures and revealed the existence of four stages (nucleation, growth, coagulation, and coalescence) of the process. The influence of the temperature on the distribution of phases during the decomposition of binary alloys has been established, and the specific features in the change of stages of the decomposition process have been revealed.

Preferred nanocrystalline configurations in ternary and multicomponent alloys

In nanocrystalline alloys, a range of configurations can have low energies when solute atoms have favorable interactions with interfaces. Whereas binary nanostructured alloys have been well studied, here we lay groundwork for the computational thermodynamic exploration of alloy configurations in multicomponent nanocrystalline alloys. Multicomponent nanostructured systems are shown to occupy a vast space, with many topological possibilities not accessible in binary systems, and where the large majority of interesting configurations will be missed by a regular solution approximation. We explore one interesting ternary case in which the first alloying element stabilizes grain boundaries, and the second forms nano-sized precipitates.

Simulation of the early stage of binary alloy decomposition, based on the free energy density functional method

Based on the free energy density functional method, the early stage of decomposition of a onedimensional binary alloy corresponding to the approximation of regular solutions has been simulated. In the simulation, Gaussian composition fluctuations caused by the initial alloy state are taken into account. The calculation is performed using the block approach implying discretization of the extensive solution volume into independent fragments for each of which the decomposition process is calculated, and then a joint analysis of the formed second phase segregations is performed. It was possible to trace all stages of solid solution decomposition: nucleation, growth, and coalescence (initial stage). The time dependences of the main phase distribution characteristics are calculated: the average size and concentration of the second phase particles, their size distribution function, and the nucleation rate of the second phase particles (clusters). Cluster trajectories in the size–composition space are constructed for the cases of growth and dissolution.

Adsorption Effect on Wetting in a Copper/Lead System

Complex analysis of interfacial thermodynamics was performed for a lead–copper binary system. Contact angle on polycrystalline copper and surface tension was measured for saturated Pb–Cu alloys at 390–1000 and 390–800 °C temperature ranges correspondingly. Liquid–gas and interfacial solid–liquid energies were calculated for Pb–Cu binary system by statistical thermodynamics on the basis of regular solution approximation at 390–950 °C. Calculated values coincide well with measured ones and with literature data, except for the temperature region lower than 700 °C, where the reported values of interfacial energy seem to be overestimated. Analysis of literature data leads us to the conclusion that an adsorbed monolayer film of lead exists in equilibrium with Pb–Cu drop on copper/gas interface between 250 and 900 °C. The decrease of the solid/gas surface energy due to Pb adsorption was calculated on the basis of the Young equation and fitted with the Szyszkowski equation. An adsorption energy of 276 kJ/mol and ...

The Role of Interfaces in Nanomaterials Behavior at Extremes

The main statements of nanomaterials concept are shortly considered. Current developments in the metallic nanomaterials stability under thermal, irradiation, deformation and corrosion actions are generalized and discussed in detail. Special attention is paid to possible prediction of thermal grain growth characteristics using the regular solution approximation. The key role of nanotwinned interfaces in the stability increase at extremes is described and pointed out. The attention is paid to unresolved and insufficiently studied problems.