Configurational Entropy Of Mixing Research Articles

Micro-scale tribological study of a Ni-Cr-Fe-Ti-Al-V high entropy alloy thin film by magnetron co-sputtering of Inconel-718 and Ti-6Al-4V

In this study, we fabricated high entropy alloy (HEA) thin films by RF magnetron co-sputtering of Inconel 718 and Ti-6Al-4V targets. Their coefficient of friction (CoF) and specific wear rate (K0) were investigated to evaluate their potential as a material for MEMS moving parts. By placing different number of Ti-6Al-4V pellets (samples abbreviated as IT2, IT4, IT6) on an Inconel 718 target (abbreviated as IT0), Ni-Cr-Fe-Ti-Al-V HEA thin films with configurational entropy of mixing (∆Sconf) >1.5R were successfully deposited. Electron microscopy and diffraction confirms that IT0 possessed a mixed nanocrysalline/amorphous structure, while the Ti-added IT2, IT4 and IT6 films were amorphous. They also have a significantly reduced root-mean-square roughness. In order to evaluate their micro-scale wear behavior, various tribological studies including indentation, scratch test and scanning wear test were conducted. From IT0 to IT6, film hardness H increases while reduced modulus Er remains similar. Plastic criterion Rw is also reduced, showing that the films IT2, IT4 and IT6 are more prone to elastic deformation. Scratch test also reveals that IT6 can afford the highest normal load before the transition of wear mode occurs. Lastly, a scanning wear test was conducted to evaluate the specific wear rate (K0) of each HEA film. It was found that IT6 had the lowest value of K0 = 2.26 × 10−4 mm3 N−1 m−1, which was also a lot lower than Si-to-Si (K0 = 0.0183 mm3 N−1 m−1) wear in other studies. The excellence of IT6 can be attributed to the fact that alloying of Ti effectively reduced the average interatomic distance in the HEA films, resulting in a densely packed, very elastic microstructure. Therefore, IT6 is expected to have longer service life than silicon if it were made into MEMS moving parts.

Phase formation capability and compositional design of β-phase multiple rare-earth principal component disilicates

A key strategy to design environmental barrier coatings focuses on doping multiple rare-earth principal components into β-type rare-earth disilicates (RE2Si2O7) to achieve versatile property optimization. However, controlling the phase formation capability of (nRExi)2Si2O7 remains a crucial challenge, due to the complex polymorphic phase competitions and evolutions led by different RE3+ combination. Herein, by fabricating twenty-one model (REI0.25REII0.25REIII0.25REIV0.25)2Si2O7 compounds, we find that their formation capability can be evaluated by the ability to accommodate configurational randomness of multiple RE3+ cations in β-type lattice while preventing the β-to-γ polymorphic transformation. The phase formation and stabilization are controlled by the average RE3+ radius and the deviations of different RE3+ combinations. Subsequently, based on high-throughput density-functional-theory calculations, we propose that the configurational entropy of mixing is a reliable descriptor to predict the phase formation of β-type (nRExi)2Si2O7. The results may accelerate the design of (nRExi)2Si2O7 materials with tailored compositions and controlled polymorphic phases.

DFT calculations of structural, magnetic, and stability of FeNiCo-based and FeNiCr-based quaternary alloys

As the Cantor-derived medium-entropy alloys (MEAs), FeNiCoMn and FeNiCrMn quaternaries in both equiatomic and non-equiatomic compositions were investigated by density functional theory combined with the quasiharmonic Debye–Grüneisen approximation using the special-quasirandom structure model. The structural properties, magnetic properties, and thermodynamics and phase stability were explored in detail. The temperature stabilization effect of lattice vibration, configurational mixing entropy, and thermal electronic excitation was discussed. Also FeNiCoPd and FeNiCrPd quaternaries, in which Mn was replaced by Pd, were considered in the same framework in order to highlight the similarities and differences between these Mn- and Pd-MEAs. The phase stability competition between homogeneous and inhomogeneous states in terms of both size and chemical ordering was revealed for four groups of FeNiCoMn, FeNiCoPd, FeNiCrMn, and FeNiCrPd MEAs.

The role of entropy and enthalpy in high entropy carbides

The thermodynamic stability of equiatomic mixed carbides, commonly referred to as high entropy carbides (HECs), is investigated via the CALculation of PHAse Diagrams (CALPHAD) approach for mixed carbides consisting of the group IVB and VB transition metal carbides as well as tungsten carbide. The Gibbs free energy of the B1-structured mixed carbides is computed using the compound energy formalism while that of the Bh-structured mixed carbides is evaluated using a point-defect model. The required thermodynamic data for the CALPHAD approach are obtained from density functional theory calculations and the Debye-Grüneisen model. The lower temperature limit at which the HECs mix in thermodynamic equilibrium is determined via numerical and analytical approaches. We find that enthalpy of mixing is at least as important as configurational mixing entropy in these mixed transition metal carbide compounds. The lower limit temperature where an equiatomic solid solution is present is largely independent of the number of components with the only exception being solutions containing tungsten carbide, where a weak temperature dependence is noted. Furthermore, the only equiatomic solid solutions that are thermodynamically stable below approximately 1000 K are those stabilized by enthalpy alone, indicating that many currently fabricated HECs are not at equilibrium at room temperature. Collectively, our results demonstrate that the formation of these carbides is controlled by the competition between entropy and enthalpy, or enthalpy alone, and thus these materials should be referred to as multi-principal component carbides since the former terminology can be misleading.

Estimation of the Grüneisen Parameter of High-Entropy Alloy-Type Functional Materials: The Cases of REO0.7F0.3BiS2 and MTe

In functional materials such as thermoelectric materials and superconductors, the interplay between functionality, electronic structure, and phonon characteristics is one of the key factors to improve functionality and to understand the underlying mechanisms. In the first part of this article, we briefly review investigations on lattice anharmonicity in functional materials on the basis of the Grüneisen parameter (γG). We show that γG can be a good index for large lattice anharmonicity and for detecting a change in anharmonicity amplitude in functional materials. Then, we show original results on the estimation of γG for recently developed high-entropy alloy-type (HEA-type) functional materials with a layered structure and a NaCl-type structure. As a common trend for those two systems with two- and three-dimensional structures, we found that γG increased with a slight increase in the configurational entropy of mixing (ΔSmix) and then decreased with increasing ΔSmix in the high-entropy region.

Measurement of Interdiffusion and Tracer Diffusion Coefficients in FCC Co-Cr-Fe-Ni Multi-Principal Element Alloy

Average effective interdiffusion coefficients of individual components and tracer diffusion coefficient of Ni were experimentally determined in FCC CoCrFeNi high entropy alloys. Average effective interdiffusion coefficients of individual elements in CoCrFeNi alloys were determined using the Dayananda-Sohn approach. Cr had the highest while Ni had the lowest magnitude of the average effective interdiffusion coefficient in the CoCrFeNi alloy. The tracer diffusion coefficient of Ni was determined without the application of radiotracers using the novel analytical method proposed by Belova et al. based on linear response theory coupled with the Boltzmann-Matano approach and Gaussian distribution function. Both average effective interdiffusion coefficients and tracer diffusion coefficients in CoCrFeNi were compared with the relevant high entropy alloys with varying entropy of mixing. The diffusion of individual elements in Al-containing high entropy alloys (e.g., Al-Co-Cr-Fe-Ni and Al-Co-Cr-Fe-Ni-Mn), with higher entropy of mixing, was higher than that in CoCrFeNi alloy, with relatively lower entropy of mixing. Therefore, diffusion cannot a priori consider to be sluggish in alloys with higher configurational entropy. Moreover, potential energy fluctuations determined in quinary and senary Al-containing high entropy alloys were higher than that in quaternary CoCrFeNi alloy. This also suggests that the diffusivity of a component may not be always lower in the alloys which possess higher fluctuations in potential energy or configurational entropy of mixing.

Modeling the Transport and Volumetric Properties of Solutions Containing Polymer and Electrolyte with New Model

A new theoretical model based on the local composition concept (TNRF-mNRTL model) was proposed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. This contribution of interaction along with the long-range contribution of interaction (Pitzer-Debye-Huckel equation), configurational entropy of mixing (Flory-Huggins relation) and Eyring absolute rate theory were used to fit the viscosity values of ternary aqueous solutions of polymer + electrolyte with considering temperature dependency. The local composition models which are available for correlating the thermodynamic properties of ternary polymer + electrolyte solutions (ternary-Wilson, ternary-modified NRTL, and ternary-modified Wilson) with Eyring absolute rate theory were also used for fitting the viscosity values of ternary solutions for the first time. THe fitting quality of Eyring-TNRF-mNRTL model was compared with these models. The equations of apparent molar volume were also derived from TNRF-mNRTL, ternary-Wilson, ternary-modified NRTL, and ternary-modified Wilson models. These equations were used for correlating the apparent molar volume and density values of ternary polymer + electrolyte solutions.

Modeling the Thermodynamic Properties of Solutions Containing Polymer and Electrolyte with New Local Composition Model

A new theory model based on the local composition concept (TNRF-modified NRTL (TNRF-mNRTL) model) was developed to express the short-range contribution of the excess Gibbs energy for the solutions containing polymer and electrolyte. An equation represented the activity coefficient of solvent was derived from the proposed excess Gibbs energy equation. The short-range contribution of interaction along with the long-range contribution of interaction and configurational entropy of mixing were used to correlate the activity coefficient of ternary polymer + electrolyte + water systems and also binary polymer + water and electrolyte + water systems. The long-range interaction and configurational entropy have been given by the Pitzer-Debye-Huckel equation and the Flory-Huggins relation, respectively. The performance of the proposed model in fitting the solvent activity of ternary polymer + electrolyte + water solutions has been compared with that obtained from the ternary NRTL, ternary Wilson, ternary modified NRTL and ternary modified Wilson models. Results comparison was demonstrated the validity of the proposed model for solvent activity of polymer + electrolyte + water solutions.

혼합엔트로피 제어에 따른 단일 FCC 고용체 합금의 물성변화 분석

혼합엔트로피 제어에 따른 단일 FCC 고용체 합금의 물성변화 분석

Compositional dependence of phase formation and mechanical properties in three CoCrFeNi-(Mn/Al/Cu) high entropy alloys

Starting from three typical equiatomic CoCrFeNiMn, CoCrFeNiAl and CoCrFeNiCu high entropy alloys (HEAs), we systematically investigated the compositional dependence of phase formation and mechanical properties of 78 alloys by varying the atomic ratio of the constituent elements. It was found that the simple phase structures, including a single face-centered cubic (FCC) or body-centered cubic (BCC) phase, duplex FCC phases, duplex BCC phases, instead of intermetallics, could form within a broad compositional landscape in 68 out of the 78 alloys not limited to the equiatomic composition where the configurational mixing entropy is maximum. This fact indicates that it may be the nature of the constituent elements that leads to simple phase structure formation. With compositional variation, the microstructure and mechanical properties including hardness and tensile properties show corresponding changes. It was found that the hardness variation of samples within the same structure is smaller for the FCC than that of the BCC. Tensile results indicated that the tensile elongation of (CoCrFeMn)(100−x)Nix (x = 0, 10 and 20) alloys increases with Ni addition due to the decreasing volume fraction of sigma phase. For the (CoCrFeAl)(100−x)Nix (x = 27.3, 33.3, 38.5, 42.9 and 50) alloys, the yield strength decreases and tensile elongation increases with Ni addition due to decreasing volume fraction of BCC phase which is hard yet brittle. The present results are important to understand the phase formation and relationship between microstructure and mechanical properties in HEAs.

Investigation of solubility in plasticised rubber systems for tire applications

Oligomer resins and process oils are indispensable for rubber technology in order to achieve high-performance tyres on wet roads and ultralow energy consumption with acceptable manufacturability. This study investigates the solubility of oligomer resins, oils and elastomers using differential scanning calorimetry and describes its implication on rubber compound hysteresis loss. Owing to the configurational entropy of mixing, resin molecular weight strongly influences miscibility within binary resin/oil, ternary resin/oil/elastomer and filled rubber compounds. Similarity of chemical structure plays a role in miscibility linked to enthalpic effects. Among Hansen solubility parameters, the polar component correctly ranks the compatibility of resins with oils and elastomers. It has been shown that increased solubility among the resin–oil–elastomer system provides better balance of predicted rolling resistance and wet grip of tread compounds. Therefore, optimisation of rubber properties relies on the adequate selective use of process oils and resins according to their chemical structure and molecular weight.

Towards the Development of a Universal Expression for the Configurational Entropy of Mixing

This work discusses the development of analytical expressions for the configurational entropy of different states of matter using a method based on the identification of the energy-independent complexes (clustering of atoms) in the system and the calculation of their corresponding probabilities. The example of short-range order (SRO) in Nb-H interstitial solid solution is used to illustrate the choice of the atomic complexes and their structural changes with H concentration, providing an alternative methodology to describe critical properties. The calculated critical composition of the miscibility gap is xc = 0.307, in remarkable agreement with the experimental value of xc ~ 0.31. The same methodology is applied to deduce the equation of state (EOS) of a hard sphere system. The EOS is suitable to describe the percolation thresholds and fulfills both the low and random close packing limits. The model, based on the partition of the space into Voronoi cells, can be applied to any off-lattice system, thus introducing the possibility of computing the configurational entropy of gases, liquids and glasses with the same level of accuracy.

Design of high entropy alloys: A single-parameter thermodynamic rule

Assuming random mixing of atoms, design of high entropy alloys (HEAs) was used to follow a simple route by maximizing their configurational entropy of mixing. Here we propose a single-parameter design paradigm taking into account formation enthalpy and the excessive entropy of mixing, which arises from dense atomic packing and atomic size misfit. The proposed paradigm is verified using the data hitherto reported and proven to be a physically accepted thermodynamic parameter for the design of HEAs.

The generalized thermodynamic rule for phase selection in multicomponent alloys

The design of modern multicomponent alloys (MCAs) appears complicated, which usually entails mixing multiple elements that have a variety of sizes and heat of mixing. As a result, different phases, such as single- and multi-phased solid-solution, intermetallic compounds and even metallic glasses, can be formed upon solidification of the corresponding metallic melts. To understand such diversities in the phase selection in MCAs, tremendous research efforts have been dedicated over the past decades, which, however, are empirically or semi-empirically based. In contrast, here we show that a simple thermodynamic rule can be derived from the hard sphere model, which predicts that the phases formed in cast MCAs only depend on two dimensionless thermodynamic parameters: one is related to the entropic departure of the alloy from the ideal solution and the other to the average heat of mixing scaled by the ‘ideal’ configurational entropy of mixing. Using this simple rule, we are able to unfold a general trend that guides phase selection in MCAs, including super-alloys, bulk metallic-glasses, high entropy alloys and many other engineering materials. The outcome of our current research sheds an important insight into the thermodynamic origin for phase stability and alloy design of MCAs

Thermodynamic properties of Th xU 1−xO 2 (0 < x < 1) based on quantum–mechanical calculations and Monte-Carlo simulations

Th x U 1− x O 2+ y binary compositions occur in nature, uranothorianite, and as a mixed oxide nuclear fuel. As a nuclear fuel, important properties, such as the melting point, thermal conductivity, and the thermal expansion coefficient change as a function of composition. Additionally, for direct disposal of Th x U 1− x O 2, the chemical durability changes as a function of composition, with the dissolution rate decreasing with increasing thoria content. UO 2 and ThO 2 have the same isometric structure, and the ionic radii of 8-fold coordinated U 4+ and Th 4+ are similar (1.14 nm and 1.19 nm, respectively). Thus, this binary is expected to form a complete solid solution. However, atomic-scale measurements or simulations of cation ordering and the associated thermodynamic properties of the Th x U 1− x O 2 system have yet to be determined. A combination of density-functional theory, Monte-Carlo methods, and thermodynamic integration are used to calculate thermodynamic properties of the Th x U 1− x O 2 binary (Δ H mix , Δ G mix , Δ S mix , phase diagram). The Gibbs free energy of mixing (Δ G mix ) shows a miscibility gap at equilibration temperatures below 1000 K (e.g., E exsoln = 0.13 kJ/(mol cations) at 750 K). Such a miscibility gap may indicate possible exsolution (i.e., phase separation upon cooling). A unique approach to evaluate the likelihood and kinetics of forming interfaces between U-rich and Th-rich has been chosen that compares the energy gain of forming separate phases with estimated energy losses of forming necessary interfaces. The result of such an approach is that the thermodynamic gain of phase separation does not overcome the increase in interface energy between exsolution lamellae for thin exsolution lamellae (10 Å). Lamella formation becomes energetically favorable with a reduction of the interface area and, thus, an increase in lamella thickness to >45 Å. However, this increase in lamellae thickness may be diffusion limited. Monte-Carlo simulations converge to an exsolved structure [lamellae || ( 2 1 1 ¯ ) ] only for very low equilibration temperatures (below room temperature). In addition to the weak tendency to exsolve, there is an ordered arrangement of Th and U in the solid solution [alternating U and Th layers || {1 0 0}] that is energetically favored for the homogeneously mixed 50% Th configurations. Still, this tendency to order is so weak that ordering is seldom reached due to kinetic hindrances. The configurational entropy of mixing (Δ S mix ) is approximately equal to the point entropy at all temperatures, indicating that the system is not ordered.

Thermodynamics of the Ceγ–αtransition: Density-functional study

We investigate the Cerium $\ensuremath{\gamma}\text{--}\ensuremath{\alpha}$ isostructural phase transition by explicitly incorporating finite temperature mixing of the Ce nonmagnetic and magnetic states. Unique to our approach is the calculation of vibrational properties from phonon theory. The critical behavior of the transition is shown to be controlled by the configurational mixing entropy between the magnetic and nonmagnetic states. Our theoretical framework leads to accurate predictions of the critical point and equation of state associated with the Ce $\ensuremath{\gamma}\text{--}\ensuremath{\alpha}$ phase transition.

Electronic theory of phase stability in substitutional alloys: application to the Au–Ni system

Abstract The total energies of formation of Au–Ni superstructures based on a fcc lattice have been calculated using the linear muffin-tin-orbital (LMTO) method in the full potential approach. Both unrelaxed and relaxed structures have been included in the calculations. The energy of formation is decomposed into three terms, a volume deformation contribution, a chemical contribution and a relaxation contribution. The enthalpy of mixing of the disordered solid solution has been calculated using an Ising-like cluster expansion for both the chemical and relaxation effects. In the Gibbs energy of mixing, a configurational entropy of mixing has been calculated with the cluster variation method (CVM) and the thermal excitations due to electronic and vibrational effects have been taken into account. The miscibility gap displayed in the Au–Ni system has been calculated. The results are discussed in comparison with the experimental data.

Some thermodynamic properties of the Berman and Brown model for CaO-Al2O3-SiO2

Abstract The Berman and Brown (1984) excess free energy model (B&B) is extremely convenient to use in modelling multicomponent solutions. However, spinodal calculations reveal that their calibration of this model for CaO-Al2O3-SiO2 produces liquation tielines that do not appear to be in agreement with experimental work. In addition, their calibration contains some strongly negative excess entropy parameters and these permit a most unusual inverted liquation field to start at approximately >2115°C, wt% (SiO2, Al2O3, CaO) = (70, 16, 14). This inverted field expands rapidly to cover most of the ternary for T > 2300°C and continues to expand at all higher temperatures. The Berman and Brown calibration for this system carries these negative excess entropies of mixing because the solution model is very strongly asymmetric as a result of the use of normal oxide mole weights in modelling the configurational entropy of mixing. A suggestion is made for a fairly natural restriction on the relative sizes of empirical models for excess versus configurational entropy. Expressions are presented for the general consolute condition (all solution models) and for the second and third partials of the B&B Gx model.

The Vapor-Pressure Equations of Solutions and the Osmotic Pressure of Rubber

Abstract 1. The laws which are obeyed by ideally dilute and by perfect solutions have been obtained by Guggenheim, and he has extended his analysis to obtain the properties of a class of solutions to which the name regular has been given. It is assumed that the solution consists of molecules of two types, α and β, of approximately the same size, and that each molecule, whether of type α or of type β, is surrounded by the same number z of other molecules, and the potential energy is regarded as the sum of contributions from each pair of molecules in direct contact. That is, the molecules are regarded as occupying sites on a regular lattice, and the potential energy arises from the interactions between molecules which occupy closest neighbor sites. Rushbrooke has examined the properties of such a solution, using the Bethe method to set up the partition function for the assembly. The properties of solutions in which the molecules of one type are of such a size and shape that they have to be regarded as occupying two lattice sites have been investigated by Fowler and Rushbrooke, who determined the limiting form of the vapor-pressure equations for extremely dilute and for extremely concentrated solutions. Chang has determined, for a two-dimensional lattice, the value of the combinatory factor, which can be written as g2,1(Nα,Nβ) for the case in which each molecule of type a occupies two closest neighbor sites and each molecule of type β occupies one site. Chang's determination of g2,1(Nα,Nβ) for a two-dimensional lattice is based on an analysis of the corresponding adsorption problem, in which he superimposes some arbitrary assumptions on the Bethe method. It has, however, been shown that the value which Chang obtained for g2,1(Nα,Nβ) is applicable to two- and to three-dimensional lattices in which no two closest neighbors of a given site are also closest neighbors of one another. Fowler and Guggenheim have shown how, once the combinatory factor has been evaluated, it can be used to determine the configurational entropy of mixing and thence the vapor-pressure equations when the energy of mixing is zero. Using Chang's value for g2,1(Nα,Nβ), they obtained for the vapor-pressure equations, when each solute molecule occupies two closest neighbor sites on the lattice and each solvent molecule occupies only one lattice site, the following equations: