Regular Solution Model Research Articles

Successive strain hardening mechanisms induced by transformation induced plasticity in Fe60Mn20Co10Cr10 high entropy alloys

Transformation induced plasticity (TRIP) effect in high entropy alloys (HEAs) overcomes the strength–ductility “trade-off” and leads to the synchronous improvement of strength and ductility. In this work, we studied a TRIP Fe60Mn20Co10Cr10 HEA with a dual-phase structure consisting of face-centered cubic matrix and hexagonal close-packed (HCP) martensite. By warm-rolling and subsequent annealing, three samples with different recrystallization conditions and HCP phase volume fractions were obtained. The alloys exhibit a good combination of ultimate tensile strength (∼700–900 MPa) and elongation (∼45%–55%), representing sustainable strain hardening behavior over extended deformation regime. To reveal the deformation mechanism of the present TRIP HEA, the method to determine the stacking fault energy (SFE) via a regular solution model was discussed, and the SFE of Fe60Mn20Co10Cr10 alloys at 300 K was estimated as 15.3 mJ/m2. The low SFE promotes the formation and overlapping of stacking faults via dislocation interaction, which provides nucleation sites of HCP martensite and further contributes to the striking strain hardening capacity upon tension.

Regular solution theory applied to asphaltene related phase behaviour

AbstractAsphaltenes are the least soluble fraction of crude oil and they can phase separate from the oil upon a change in temperature, pressure, or composition. This phase separation, often described as precipitation, may be beneficial (eg, in a partial deasphalting process) or detrimental (eg, in pipeline and surface equipment fouling). A phase behaviour model that can predict the onset and amount of asphaltene precipitation and is compatible with process simulators is desirable for the design and operation of these processes. This brief review focuses on the regular solution modelling approach. The regular solution model is based on activity coefficients and therefore is well suited for liquid‐liquid phase separations such as asphaltene precipitation. The model and its internal correlations are presented and its performance on asphaltene phase separation from mixtures of heavy oils and solvent is demonstrated. Recent updates to this approach are presented and potential future applications are discussed. The strengths and limitations of this approach for oilfield applications are highlighted.

Equilibrium segregation in the stressed Ni(111)(Au) nano-films on inert substrate

Based on the network model and the regular solution model, the equilibrium surface and interface segregations are investigated for the Ni(111)2 at%(Au) nano-films under diffusion-induced stress and intrinsic stress. The size effect with respect to the film thickness, the interlayer interactions and the heteroepitaxial strain in the film are taken into account. The equilibrium layer concentration in the film with the lowest Gibbs free energy of the system is obtained according to the coordinate descent method. The influences of diffusion-induced stress and intrinsic compressive/tensile stress, temperature and bulk concentration on the equilibrium layer concentration of segregation in the film are quantitatively evaluated.

Determining the Interphase Boundary Parameters in Heterogeneous Binary Alloys on the Basis of the Hypothesis of Weak Nonlocality

Based on our earlier hypothesis of weak nonlocality, we developed a method for calculating the temperature dependences of the width and specific energy of the interphase boundary for binary substitutional alloys, using the concentration dependence of the internal energy or the equilibrium phase diagram of the alloy. Numerically calculated temperature dependences of the solubility limits, specific energy, and thickness of the interphase boundary are presented for three thermodynamic models: the regular solution model (Nb–Cu alloy), the quasi-regular solution model, and the general case (Fe–Cu alloy and A–B alloy that differs from Fe–Cu in the sign of excess entropy).

FORMAÇÃO DE AZEÓTROPOS DO PONTO DE VISTA DA TERMODINÂMICA DE SOLVATAÇÃO

FORMATION OF AZEOTROPES FROM THE STANDPOINT OF SOLVATION THERMODYNAMICS. The formation of azeotropes is related to the deviation of the ideality of liquid mixtures. This deviation is expressed by the activity coefficient of each component. However, the physical origin of this behavior is not well quantified in terms of molecular interactions. In this work, a regular solution model was used, relating the β parameter to the solvation free energy of pure liquids in themselves and in the other component. A mathematical expression was derived that indicates when an azeotrope is formed. This equation shows that the greater the difference in vapour pressure between components, the greater the solvation difference of each liquid in itself and in the other component is needed to form the azeotrope. A set of 10 mixtures were randomly chosen and investigated as a test, and the equation worked in all cases.

MODELING THE PHASE DIAGRAMS OF THE Tl9SmTe6–Tl4PbTe3 AND Tl9SmTe6–Tl9BiTe6 SYSTEMS

Using the multipurpose genetic algorithm, the analytical models of phase diagrams of the Tl9SmTe6–Tl8Pb2Te6 and Tl9SmTe6–Tl9BiTe6 systems as temperature dependencies of compositions of the equilibrium phases were obtained. The boundaries of the uncertainty band for the liquidus and solidus curves of solid solutions are determined. According to the model of regular solutions of non-molecular compounds, the thermodynamic functions of mixing solid solutions depending on the composition and temperature are determined. It was found that solid solutions based on the Tl9SmTe6, Tl8Pb2Te6 and Tl9BiTe6 compounds are thermodynamically stabile in the whole concentration range

Eutectic Mixing As a Knob for Next-Generation Flow Batteries

Flow batteries can offer scalability, long cycle-life, and power-to-energy tunability, however, they have low energy density. An under-explored “knob” for increasing the energy density of flow batteries is eutectic mixing for the depression of melting points. This knob could enable high energy-density flow batteries by achieving solvent-free electrolytes. We demonstrate the ability of eutectic mixing to decrease melting points in the case of n-component mixtures of benzoquinone derivatives, which are redox-active molecules. Predicting the properties of mixtures of more than two components is not commonly done, but we show that, in this case, a regular solution model has predictive power for finding the eutectic melting temperatures and compositions for mixtures of multiple components.

Atomic-Scale Coordination Effects on the Initial Stage of Passive Film Formation in Fe-Cr Alloys

The self-healing passivation behavior Fe-Cr alloys serve as a model for the development of corrosion resistant alloys and coatings. Both first principles-based calculations [1,2], neutron scattering [3] and Mössbauer spectroscopy [4] studies demonstrated that in FepCr1-p alloys, the atomic-scale distribution of Cr atoms in the BCC lattice depends on both composition and thermal history. These studies showed that there is an inversion in the Warren Cowley short range order (SRO) parameter [5] that occurs for 1-p ≅ 0.11 At. Cr compositions, less than this value, the alloys show a tendency toward ordering while at higher Cr compositions the alloys show a tendency for clustering. In terms of a simple regular solution model, this behavior is determined by the interaction parameter, ΔE = [EFe-Cr - 1/2(EFe-Fe + ECr-Cr)], where the E’s are nearest neighbor bond energies taken to be negative. Then for ΔE < 0 the system tends to short-range order, while for ΔE > 0, clustering behavior is expected. In order to study these atomic scale coordination effects on passivation, FepCr1-p alloys were heat-treated according to the protocols used in the neutron scattering and Mössbauer spectroscopy studies. The behaviors of these alloys were compared to that of their random solid solution counterparts. Linear sweep voltammetry and chronoamperometry were used to characterize the initial stage of passivation in these two sets of alloys. Our results reveal some subtle yet significant differences in their passivation behaviors [6]. These results are interpreted within the context of the percolation conjecture suggested by Sieradzki and Newman [7]. Klaver, T. P. C., Drautz, R. & Finnis, M. W. “Magnetism and Thermodynamics of Defect-Free Fe-Cr Alloys", Rev. B. 74, 94435 (2006).Olsson, P., Abrikosov, I. A., Wallenius, J. “Electronic Origin Of The Anomalous Stability of Fe-Rich Bcc Fe-Cr Alloys", Rev. B. 73, 104416 (2006).Mirebeau, I., Parette, G. “Neutron Study of The Short Range Order Inversion in Fe1− x Crx" Rev. B. 82, 104203 (2010).Dubiel, S. M., Cieslak, J.“ Short-Range Order in Iron-Rich Fe-Cr Alloys as Revealed by Mössbauer Spectroscopy", Rev. B. 83, 180202 (2011).Cowley, J.M. “Short-Range Order and Long-Range Order Parameters, Rev., 138, A1384 – 1389 (1965).Liu, M. Aiello, A., Xie, Y. Sieradzki, K., “The Effect of Short-Range Order on Passivation of Fe-Cr Alloys”, Electrochem. Soc., 165, C830-C834 (2018).Sieradzki, K., Newman, R. C.“ A. Percolation Model for Passivation in Stainless Steels", Electrochem. Soc. 133, pp. 1979–1980 (1986).

Effect of redox on Fe\u2013Mg\u2013Mn exchange between olivine and melt and an oxybarometer for basalts

The Fe–Mg exchange coefficient between olivine (ol) and melt (m), defined as {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} = (Feol/Fem)·(Mgm/Mgol), with all FeT expressed as Fe2+, is one of the most widely used parameters in petrology. We explore the effect of redox conditions on {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} using experimental, olivine-saturated basaltic glasses with variable H2O (≤ 7 wt%) over a wide range of fO2 (iron-wüstite buffer to air), pressure (≤ 1.7 GPa), temperature (1025–1425 °C) and melt composition. The ratio of Fe3+ to total Fe (Fe3+/∑Fe), as determined by Fe K-edge µXANES and/or Synchrotron Mössbauer Source (SMS) spectroscopy, lies in the range 0–0.84. Measured Fe3+/∑Fe is consistent (± 0.05) with published algorithms and appears insensitive to dissolved H2O. Combining our new data with published experimental data having measured glass Fe3+/∑Fe, we show that for Fo65–98 olivine in equilibrium with basaltic and basaltic andesite melts, {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} decreases linearly with Fe3+/∑Fe with a slope and intercept of 0.3135 ± 0.0011. After accounting for non-ideal mixing of forsterite and fayalite in olivine, using a symmetrical regular solution model, the slope and intercept become 0.3642 ± 0.0011. This is the value at Fo50 olivine; at higher and lower Fo the value will be reduced by an amount related to olivine non-ideality. Our approach provides a straightforward means to determine Fe3+/∑Fe in olivine-bearing experimental melts, from which fO2 can be calculated. In contrast to {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}}, the Mn–Mg exchange coefficient, {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}}, is relatively constant over a wide range of P–T–fO2 conditions. We present an expression for {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}} that incorporates the effects of temperature and olivine composition using the lattice strain model. By applying our experimentally-calibrated expressions for {text{Kd}}_{{{text{Fe}}^{T} {-} {text{Mg}}}} and {text{Kd}}_{{{text{Mn}} {-} {text{Mg}}}} to olivine-hosted melt inclusions analysed by electron microprobe it is possible to correct simultaneously for post-entrapment crystallisation (or dissolution) and calculate melt Fe3+/∑Fe to a precision of ≤ 0.04.

An Experimental-XANES Investigation of Cr Valence Systematics in Basaltic Liquids and Applications to Modeling Cr2+/ Σ Cr Evolution in Crystallizing Basaltic Magma Systems

Harvesting quantitative fO2 information from synchrotron μ-XANES measurements of Cr2+/ΣCr in olivine phenocrysts requires robust thermodynamic or empirical models that can accurately predict Cr2+/ΣCr in basaltic liquids as a function of fO2, temperature, and liquid chemistry. We present the results from a combined experimental-XANES study designed to illuminate how evolving liquid chemistry and decreasing temperature influence the equilibrium Cr2+/ΣCr ratios in crystallizing basaltic liquids. The Cr valence dataset produced from these experiments was fit with a symmetric regular solution model; this fitting generated a model equation that predicts the Cr2+/ΣCr in basaltic magmas. Using MELTS in conjunction with the newly calibrated Cr valence model, we calculated the Cr2+/ΣCr of a tholeiitic liquid undergoing isobaric equilibrium crystallization at 2.5 °C intervals. The modeling results indicate that Cr2+/ΣCr evolves dynamically in crystallizing liquids composition and may be partially decoupled from bona fide changes in magmatic fO2. These calculations suggest that the increasing iron content of the residual liquid is the most influential factor influencing the Cr2+/ΣCr of the residual liquid. Olivine normative tholeiitic liquids following a liquid line of descent parallel to an oxygen fugacity buffer curve experience significant decreases in the equilibrium Cr2+/ΣCr of their residual liquids. Our modeling also demonstrates that Cr2+/ΣCr values preserved in early olivine phenocrysts indeed reflect the magmatic fO2 conditions under which they grew; however, the effects of magmatic fO2 are also superimposed on the underlying influences of temperature and melt chemistry.

Heterostructural phase diagram of Ga2O3–based solid solution with Al2O3

Ga2O3, which is emerging as semiconductor material due to the ultra-wide bandgap, has tunability in bandgap and lattice constant by alloying Al. However, successful control of alloying phase is still challenging due to its heterostructural nature and rich polymorphs. Here, we identified the thermodynamic phase diagram of heterostructural (AlxGa1-x)2O3 alloy. Using density-functional theory (DFT) calculations and regular solution model, we calculated the Gibbs-free energy of mixing of heterostructural polymorphs. Based on the calculation, we show the phase diagram of (AlxGa1-x)2O3 alloy system with a markedly increased metastability than the isostructural alloy, which can make a vast phase space for homogeneous single-phase alloys. We also investigated the correlation between the bandgap and lattice constant within these systems using hybrid DFT calculations, which can guide the device design of Ga2O3 power electronics.

The Impact of the Next-Nearest Neighbor Dispersion Interactions on Spin Crossover Transition Enthalpy Evidenced by Experimental and Computational Analyses of Neutral π-Extended Heteroleptic Fe(III) Complexes.

A neutral heteroleptic Fe(III) complex 1 derived from a π-extension of the parent complex 2 was prepared and characterized. Complex 1 exhibited an abrupt spin crossover (SCO) transition exactly at room temperature (TSCO = 298 K). A crystal structure analysis of 1 revealed that the Fe(III) complex molecules formed a three-dimensional π-stacking interaction network. To thermodynamically clarify the mechanism of the SCO transition, the thermodynamic parameters of the SCO transitions for 1 and 2 were deduced from the temperature dependence of the magnetic susceptibility in the solid and solution states using the regular solution model. A comparison of the SCO enthalpy difference between the solid and molecule for 1 and 2 revealed that the lattice enthalpy difference would largely contribute to the SCO transition enthalpy difference. A computational evaluation of intermolecular interactions and lattice energies before and after the SCO transitions in 1 and 2 disclosed the significant contribution of the next-nearest neighbor dispersion interactions to the lattice enthalpy differences. This finding indicates that not only conventional nearest neighbor intermolecular interactions but also next-nearest neighbor dispersion interactions should be taken into account to understand the fundamental mechanism of a phase transition in molecular solids.

Application of the Modified Regular Solution Model to Crude Oils Characterized from a Distillation Assay

The modified regular solution model was developed to predict onset and amount (yield) of asphaltene precipitation from mixtures of crude oil and solvents. The most recent version of the model inclu...

Ab-initio study of ordered III–V antimony-based semiconductor alloys $$\mathbf{GaP }_{1-x}{} \mathbf{Sb} _{x} \mathbf{and} AlP _{1-x}{} \mathbf{Sb} _{x}$$

In this work, we have investigated the structural, electronic and thermodynamic properties of GaP $$_{1-x}$$ Sb $$_{x}$$ and AlP $$_{1-x}$$ Sb $$_{x}$$ ternary alloys for a number of ordered structures and compositions in a series of first-principles calculations within the density functional theory, using full potential-linearised augmented plane-wave (FP-LAPW) method, as implemented in the WIEN2k code. The exchange-correlation effect was treated within the generalised gradient approximation (GGA) in the form of GGA-PBEsol to optimise the structure and to compute the ground-state properties. In addition to the GGA, the modified Becke–Johnson (mBJ) potential coupled with the spin-orbit interaction (SOI) was also applied to obtain reliable results for the electronic properties. Our investigation on the effect of composition on lattice constant, bulk modulus and band gap showed almost nonlinear dependence on the composition. The GaP $$_{1-x}$$ Sb $$_{x}$$ and AlP $$_{1-x}$$ Sb $$_{x}$$ alloys are found to be semiconductors with a positive energy gap for the whole concentration range. The spin-orbit splitting $$\Delta _{\mathrm {SO}}$$ was found to increase with Sb composition with a marginal bowing parameter. Besides, a regular-solution model was used to investigate the thermodynamic stability of the alloys which mainly indicates a phase miscibility gap. In addition, the quasiharmonic Debye model was applied to analyse the effect of temperature and pressure on the Debye temperature and heat capacity.

AlGaInSbAs Solid Solutions Grown on InAs Substrates by Zone Recrystallization with a Temperature Gradient

The growth of AlGaInSbAs solid solutions on InAs substrates from the liquid phase in a temperature-gradient field is discussed. The calculation of parameters is performed, and the luminescence properties and spectral characteristics of AlGaInSbAs solid solutions isoperiodic to InAs substrates are investigated. The heterophase equilibria in the Al–Ga–In–Sb–As system are analyzed in the scope of the model of regular solutions. Regions of thermodynamic stability to the spinodal decomposition of AlGaInSbAs solid solutions and isoperiodicity ranges to the InAs substrate are revealed.

Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system

We present a new solid-state material phase which is a disordered solid solution but offers many ordered line-compound features. The emergent physical phenomena are rooted in the perfect short-range order which conserves the local octet rule. We model the dual-sublattice-mixed semiconductor alloy {mathrm{(ZnSnN}}_{mathrm{2}}{mathrm{)}}_{1 - x}{mathrm{(ZnO)}}_{2x} using first-principles calculations, Monte-Carlo simulations with a model Hamiltonian, and an extension of the regular solution model by incorporating short-range order. We demonstrate that this unique solid solution, occurring at a “magic” composition, can provide an electronically pristine character without disorder-induced charge localization and, therefore, a superior carrier transport similar to ordered phases. Interestingly, this phase shows singularities that are absent in the conventional solid-solution models, such as the regular solution and band-gap bowing model. Thermodynamically, this alloy phase has a sharply reduced enthalpy at its composition (like a line compound), but it still requires the entropy from long-range disorder to be stabilized at experimentally accessible temperatures.

A thermodynamic study on phase formation and thermal stability of AlSiTaTiZr high-entropy alloy thin films

Abstract The vast, unexplored chemical realm of multi-principal element alloys (MPEAs) has encouraged researchers to design and synthetize advanced materials based on refractory metals, metalloids, and deoxidizer elements, that are expected to follow single-phase, solid solution high-entropy alloys (HEAs)’ footsteps. In this paper, we have theoretically and experimentally studied the AlSiTaTiZr alloy in the thin film form, due to potential applications as a high-temperature oxidation-resistant coating. The MPEA film, synthetized by radio-frequency magnetron sputtering (RFMS), shows a considerable glass-forming ability. However, the metallic glass structure transits to several intermetallic compound phases by post-thermal annealing at ∼873 K, confirming that both thermodynamics and kinetics determine the formation of phases in sputtered MPEAs. Moreover, a strong tendency of Si and Al to form compounds with transition metals was revealed by X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), and thermodynamic investigations. Special focus is given to the role played by both entropy and enthalpy on the phase evolution, demonstrated by thermodynamic calculations using the regular solution model and the CALculation of PHAse Diagrams (CALPHAD) method. This methodology is presented as a useful approach for starting deeper thermodynamic investigations in the thin film literature of MPEAs and HEAs, currently focused on the ultimate properties of such alloys.

Modelling of short-range ordering kinetics in dilute multicomponent substitutional solid solutions

ABSTRACT Short-range ordering as the formation of couples and pairs between solutes is affected by their formation energies. This is not reflected in the standard regular solution model. Here, we present a new thermodynamic model which accounts for the dependence of the molar Gibbs energy on the concentrations of couples and pairs and their formation energies. The model treats kinetics of couples and pairs formation controlled by diffusion. This new model uses tracer diffusion coefficients of solutes and bond formation energies, which can be taken from ab initio calculations. Insofar, the current concept bridges the gap between ab initio methods and non-equilibrium thermodynamics. The reliability of the model is checked by comparison with kinetic Monte Carlo simulations. The model is applied to an Al-Mg-Si-Cu system. Finally, the configurational entropy for a binary system evaluated with the current model is compared with Bethe’s approximation, which allows estimating of applicability limits of the current model.

Injection of meteoric phosphorus into planetary atmospheres

This study explores the delivery of phosphorus to the upper atmospheres of Earth, Mars, and Venus via the ablation of cosmic dust particles. Micron-size meteoritic particles were flash heated to temperatures as high as 2900 ​K in a Meteor Ablation Simulator (MASI), and the ablation of PO and Ca recorded simultaneously by laser induced fluorescence. Apatite grains were also ablated as a reference. The speciation of P in anhydrous chondritic porous Interplanetary Dust Particles was made by K-edge X-ray absorption near edge structure (XANES) spectroscopy, demonstrating that P mainly occurs in phosphate-like domains. A thermodynamic model of P in a silicate melt was then developed for inclusion in the Leeds Chemical Ablation Model (CABMOD). A Regular Solution model used to describe the distribution of P between molten stainless steel and a multicomponent slag is shown to provide the most accurate solution for a chondritic-composition, and reproduces satisfactorily the PO ablation profiles observed in the MASI. Meteoritic P is moderately volatile and ablates before refractory metals such as Ca; its ablation efficiency in the upper atmosphere is similar to Ni and Fe. The speciation of evaporated P depends significantly on the oxygen fugacity, and P should mainly be injected into planetary upper atmospheres as PO2, which will then likely undergo dissociation to PO (and possibly P) through hyperthermal collisions with air molecules. The global P ablation rates are estimated to be 0.017 ​t ​d−1 (tonnes per Earth day), 1.15 ​× ​10−3 ​t ​d−1 and 0.024 ​t ​d−1 for Earth, Mars and Venus, respectively.

Estimation of Thermodynamic Equilibrium Constant for Binary and Ternary Cation Exchange Reactions Using Rothmund–Kornfeld and Regular Solution Models in Some Soils and Soil Clays

ABSTRACT Rothmund–Kornfeld selectivity coefficient (KRK) and regular solution model are rarely used to describe soil exchange data but it seems to be able to satisfactorily predict the true thermodynamic equilibrium constant (Kex). We tested the ability of Rothmund–Kornfeld and regular solution models to predict Kex in binary (K–NH4, Ca–Mg, and K–Ca) and ternary (Na–Ca–Mg) cation exchange systems in clays and soils with different dominant mineralogies. Applying the Rothmud–Kornfeld model to the exchange data indicated the preference of K over Ca and NH4, and Ca over Mg in binary, and Ca over Mg in ternary exchange systems. Similar results were obtained on the preference of cations by different exchangers when the regular solution model was applied to describe the exchange data. Despite the different assumptions of Rothmund–Kornfeld and regular solution models to approximate the activity coefficient of the ions on the exchange phase, similarity between the value of selectivity coefficients obtained by these two models was observed in homovalent cation exchange reactions. Also, a close agreement was observed between the value of selectivity coefficients obtained by these two models and Kex. However, in heterovalent cation exchange reactions, Rothmund–Kornfeld and regular solution models did not provide accurate estimation of the Kex. But these models can correctly indicate the overall preference of one ion to another as Kex. The results suggested Rothmund–Kornfeld and regular solution models can be applied satisfactorily in clay and soil systems as a rapid method to estimate Kex, especially in homovalent exchange reactions. Abbreviation KRK : Rothmund–Kornfeld selectivity coefficient; Kex: True thermodynamic equilibrium constant; ƒ: Exchange-phase activity coefficients; NP: Thermodynamic non-preference; E: Equivalent fractions of ion in exchange phases; Ẽ: Equivalent fractions of ion in solution phases; KRS: Regular solution selectivity coefficient; Kv: Vanselow selectivity coefficient; ∆Gex: Gibbs free energy change