Mixing Enthalpy ΔHmix Research Articles

Insights into the mechanical properties and thermal transport of Ti3(Al1-xAx)C2 solid solutions: A comprehensive theoretical study combined with experiment

The solid solution is a widely used and effective approach at a low cost to achieve desirable properties. Here, we performed theoretical investigation on a series of binary-A solid solution MAX (SS-MAX) phases, i.e., Ti3(Al1-xAx)C2 SS (A = Ga, In, Tl, Si, P, and S; x = 0–1 in 0.25 increments). Under the insight of the mixing enthalpy ΔHmix, Gibbs free energy ΔGmix, and formation enthalpy Hcp, S-alloyed MAX phases were evaluated to be unstable and are further corroborated by experiments. Interestingly, the bulk modulus of Ti3(Al0.75AGa0.25)C2 (Ti3(Al0.75In0.25)C2) unusually showed an approximate 12.8 % (11.1 %) enhancement than that of Ti3AlC2 and 11.0 % (17.1 %) enhancement than that of Ti3GaC2 (Ti3InC2). Moreover, the elastic moduli were exclusively enhanced by A elements capable of reducing triangular prism distortions. The anisotropic behavior was also revealed and interpreted as that the group IIIA elements (Ga, In, Tl) showed a pronouncedly strengthened effect on the intralayer bonding states, while Si and P acted on the interlayer interaction. Ti3(Al1-xSix)C2 presented strong resistance to phonon scattering, resulting in their similar lattice thermal conductivities. The phenomena and the underlying physics driven by the MX-A interlayer interaction will not only provide insights into manipulation on multi-site/lattice materials but also pave the way for accelerating the developments and applications of high-entropy MAX phases.

Modeling of the properties of the semiconductor solid solution Lu1-xVxNiSb in the presence of magnetic ordering

Modeling of the thermodynamic, structural, energetic and magnetic properties of the semiconductor solid solution Lu1-xVxNiSb was carried out under the condition of the presence of a magnetic moment on the V atoms and the occurrence of spontaneous magnetization. It is shown that the change in the unit cell parameter a(x) and the mixing enthalpy ΔHmix(х) depends little on the presence or absence of spontaneous magnetization. Modeling of the distribution of the density of electronic states DOS in the presence of a magnetic moment on V atoms revealed the splitting of energy states with spins up and down while preserving the band gap εg of Lu1-xVxNiSb. The relationship between the concentration of magnetic V atoms in Lu1-xVxNiSb and the Curie temperature ТС, when spontaneous magnetization is destroyed and the substance becomes paramagnetic, is established. The solid solution semiconductor Lu1-xVxNiSb, provided spontaneous magnetization is present, can be considered as a promising magnetocaloric.

Microstructure and mechanical properties of wedge-shaped CuZrAlNd metallic glass ingots

In this study, (Cu43Zr48Al9)100-xNdx (x = 1, 2, 3, or 4 at. %) bulk metallic glasses (BMGs) were successfully prepared by casting in wedge-shaped copper moulds. We studied the effect of rare-earth neodymium (Nd) addition on the glass forming ability (GFA) and mechanical properties of (Cu43Zr48Al9)100-xNdx. The enhancement of GFA in Cu–Zr–Al BMGs with Nd addition could be well explained by the atomic size difference δ, electronegativity difference Δx and negative mixing enthalpy ΔHmix. Of the alloys investigated, the (Cu43Zr48Al9)97Nd3 BMG exhibited the best GFA, with a high compressive strength of 2045 MPa. To prepare the wedge-shaped cast, the melt was subjected to a wide range of cooling rates that allow investigation of the transformed microstructure and dynamics. A U-shaped crystal-to-glass phase transition boundary was obtained. Based on the microstructural analysis of (Cu43Zr48Al9)97Nd3, we found that the equilibrium microstructure of this alloy consists of [CuZr + Cu10Zr7 + CuZr2].

Nanostructure and local polymorphism in “ideal-like” rare-earths-based high-entropy alloys

Rare-earths-based hexagonal high-entropy alloys (HEAs) composed of the elements from the heavy half of the lanthanide series (from Gd to Lu, with the exception of Yb) and yttrium are much closer to an ideal solid solution than HEAs composed of other elements from the entire periodic system. Using the method of high-frequency levitation melting, three candidates for a physical realization of an ideal HEA were synthesized, an Y-Gd-Tb-Dy-Ho, a Gd-Tb-Dy-Ho-Lu and a Tb-Dy-Ho-Er-Tm, and a study of their structure and composition was performed to see how close to ideal HEA samples can be prepared. We found that all three HEAs exhibit a nanostructure of a hexagonal close-packed (hcp) matrix and rod-like cubic close-packed (ccp) precipitates of the lengths 200–600 nm and widths 50–100 nm. EDS analysis has revealed a general trend that the precipitates are slightly enriched in the elements with larger atomic radii relative to the matrix. The origin of the nanostructure that represents a local hcp ↔ ccp polymorphism at zero external pressure appear to be lattice distortions (equivalent to a chemical pressure), occurring due to the minute differences of the elements' atomic radii. The volume per atom is slightly larger in the ccp precipitates that are enriched in larger atoms, so that the lattice distortions can be better accommodated and minimized, which reduces the lattice strain energy that contributes to the mixing enthalpy ΔHmix ≠ 0. The employed synthesis route, which is standard for the preparation of alloys of high structural quality, did not lead to a physical realization of an ideal HEA in the most promising theoretical candidates.

The Microalloying Effect of Ce on the Mechanical Properties of Medium Entropy Bulk Metallic Glass Composites

Novel ultra-strong medium entropy bulk metallic glasses composites (BMGCs) Fe65.4−xCexMn14.3Si9.4Cr10C0.9 and Ti40−xCexNi40Cu20 (x = 0, 1.0), through the martensite transformation induced plasticity (TRIP effect) to enhance both the ductility and work-hardening capability, were fabricated using magnetic levitation melting and copper mold suction via high frequency induction heating. Furthermore, the Ce microalloying effects on microstructure and mechanical behaviors were studied. The Fe-based BMGCs consisted of face-centered cubic (fcc) γ-Fe and body-centered cubic (bcc) α-Fe phase, as well as Ti-based BMGCs containing supercooled B2-Ti (Ni, Cu) and a thermally induced martensite phase B19’-Ti (Ni, Cu). As loading, the TRIP BMGCs exhibited work-hardening behavior, a high fracture strength, and large plasticity, which was attributed to the stress-induced transformation of ε-Fe martensite and B19’-Ti (Ni, Cu) martensite. Ce addition further improved the strengthening and toughening effects of TRIP BMGCs. Adding elemental Ce enhanced the mixing entropy ΔSmix and atomic size difference δ, while reducing the mixing enthalpy ΔHmix, thus improving the glass forming ability and delaying the phase transition process, and hence prolonging the work-hardening period before fracturing. The fracture strength σf and plastic stress εp of Ti39CeNi40Cu20 and Fe64.4CeMn14.3Si9.4Cr10C0.9 alloys were up to 2635 MPa and 13.8%, and 2905 MPa and 30.1%, respectively.

The anisotropy of three-component medium entropy alloys in AlCoCrFeNi system: First-principle studies

A theoretical investigation of the anisotropy of face-centered-cubic (FCC) and body-centered (BCC) medium entropy alloys (MEAs) based on the first-principle calculations has been implemented. The electronegativity difference Δχ, mixing enthalpy ΔHmix, range of electronegativity Rχ and total charge transfer have been considered. All elastic anisotropies of the selected MEAs change monotonously with the electronegativity difference Δχ, more specifically, the anisotropy decreases with decreasing electronegativity difference Δχ. A detailed investigation of electronic structure reveals that charges are mainly accumulated around the atom with minimal Pauling electronegativity (χ) and valence electron concentration (VEC), resulting in a high anisotropy of MEAs. For Al-containing MEAs, a substantial number of total charge transfer will lead to a great anisotropy. In addition, the range of electronegativity Rχ can be used to assist in identifying the anisotropy in the localized electron distribution.

Mixing enthalpy of Ag–Sn system at 1150 °C

This paper presents thermodynamic results of Ag–Sn alloys mixing at 1150 °C. The need for binary data on mixing enthalpy ΔH mix appeared obvious in the process of calorimetric study of the ternary system Ag–Cu–Sn known as the promising lead-free solder. The mixing enthalpies of Ag–Sn system were measured by drop calorimetry method using SETARAM MHTC thermal analyzer. All the tests were conducted in the dynamic protective atmosphere of argon. The calorimeter’s sensitivity calibration was performed with the use of pure metals (Ag, Sn) and standard leucosapphire samples and consisted of two stages. The use of two-stage calibration procedure improves significantly the convergence of two branches of ΔH mix isotherm plotted from the pure component toward each other. The experimental results were approximated with analytical function using quasi-chemical modification of subregular solutions model (quasi-chemical model of Sharkey et al.) postulating the presence of both pair and triple interactions in solution. The resultant equation is ΔH mix = N Ag·N Sn·(− 27.7075·N Ag − 0.9977·N Sn + 27.7079·N Ag·N Sn), kJ mol−1, where N is the component mole fraction. The measured compositional dependence of ΔH mix is substantially asymmetric like the previous results of the other authors, but, in contrast to those results, it does not change the sign and is entirely negative in the whole range of concentrations.

Prediction of structure and elastic properties of AlCrFeNiTi system high entropy alloys

The effect of alloy compositions on structure and elastic properties of single-phase AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Zn, Zr, Nb, Mo and La) high entropy alloys was investigated by calculating solid solution characteristics of alloys combining with the first principles method. The obtained formation enthalpy, cohesive energy and mechanical stability indicated AlCrFeNiTi and AlCrFeNiTiX (X = V, Mn, Co, Nb and Mo) HEAs adopt the body centered cubic structure instead of face centered cubic structure. There is a rather good agreement between theoretical structure predictions and the classic criteria of valence electron concentration VEC. A detailed investigation on electronic structure of AlCrFeNiTi and AlCrFeNiTiX alloys revealed the bonding behavior of alloys. In addition, the calculated results of polycrystalline elastic parameters confirmed the ductility of AlCrFeNiTiX alloys would weaken with increasing mixing enthalpy ΔHmix (or decreasing atomic size difference δ), and the increase in ΔHmix is predicted to decrease the elastic anisotropy. Furthermore, we predicted that the present high entropy alloys should be more elastically isotropic when the corresponding the mixing enthalpy ΔHmix has a larger value.

Formation rules of single phase solid solution in high entropy alloys

A new empirical rule to form single phase solid solution structured high entropy alloys was proposed by integrating three dependent parameters, i.e. atomic size difference δ, mixing enthalpy ΔHmix and valence electron concentration VEC. It was found that the single phase face centred cubic solid solution will form if δ < 4.27%, − 7.27 kJ mol− 1 < ΔHmix < 4 kJ mol− 1 and VEC>8, while the single phase body centred cubic solid solution will form in the case of δ < 4.27%, − 7.27 kJ mol− 1 < ΔHmix < 4 kJ mol− 1 and VEC < 6.87. This empirical rule was verified by typical high entropy alloys that have been reported.

A predictive model for thermodynamic stability of grain size in nanocrystalline ternary alloys

This work presents a model for evaluating thermodynamic stabilization of ternary nanocrystalline alloys. It is applicable to alloy systems containing strongly segregating size-misfit solutes with a significant enthalpy of elastic strain and/or immiscible solutes with a positive mixing enthalpy. On the basis of a regular solution model, the chemical and elastic strain energy contributions are incorporated into the mixing enthalpy ΔHmix, and the mixing entropy ΔSmix is obtained using the ideal solution approximation. The Gibbs mixing free energy ΔGmix is minimized with respect to simultaneous variations in grain size and solute segregation parameters. The Lagrange multiplier method is used to obtain numerical solutions for the minimum ΔGmix corresponding to an equilibrium grain size for given alloy compositions. The numerical solutions will serve as a guideline for choosing solutes and assessing the possibility of thermodynamic stabilization. The temperature dependence of the nanocrystalline grain size and interfacial solute excess can be evaluated for selected ternary systems. Model predictions are presented using available input data for a wide range of solvent-solute combinations. The model predictions are compared to experimental results for Cu-Zn-Zr, Fe-Cr-Zr, and Fe-Ni-Zr alloys where thermodynamic stabilization might be effective.

Thermodynamic stabilization of nanocrystalline binary alloys

The work presented here was motivated by the need to develop a predictive model for thermodynamic stabilization of binary alloys that is applicable to strongly segregating size-misfit solutes, and that can use available input data for a wide range of solvent-solute combinations. This will serve as a benchmark for selecting solutes and assessing the possible contribution of thermodynamic stabilization for development of high-temperature nanocrystalline alloys. Following a regular solution model that distinguishes the grain boundary and grain interior volume fractions by a transitional interface in a closed system, we include both the chemical and elastic strain energy contributions to the mixing enthalpy ΔHmix using an appropriately scaled linear superposition. The total Gibbs mixing free energy ΔGmix is minimized with respect to simultaneous variations in the grain-boundary volume fraction and the solute contents in the grain boundary and grain interior. The Lagrange multiplier method was used to obtain numerical solutions with the constraint of fixed total solute content. The model predictions are presented using a parametric variation of the required input parameters. Applications are then given for the dependence of the nanocrystalline grain size on temperature and total solute content for selected binary systems where experimental results suggest that thermodynamic stabilization could be effective.

First principles calculation of mixing enthalpy of β-Ti with transition elements

The mixing enthalpy ΔHmix(x) of body-centered cubic (BCC) β-Ti with transition elements was calculated using first-principles methods based on density functional theory (DFT). The solid solution effect was treated by two different approaches, viz. special quasi-random structures (SQS) and the parametric method. The SQS-N method uses direct DFT to calculate energy of structures containing N atoms which approximate the correlation of an ideal solid solution up to some distance, whereas the parametric method employs a polynomial representation for ΔHmix(x) and the coefficients are calculated using DFT. Comparison of the two methods shows fair agreement for most alloys though differences as high as 40% can also be seen among some of the alloys. The trends in ΔFmix(x), obtained by adding entropy contribution from ideal solution model to ΔHmix(x) for 3d-, 4d- and 5d-transition series were analyzed in terms of e/a, the ratio of number of valence electrons to atoms. The early transition elements, between Group 4–7, was found to have very small ΔFmix(x) over a wide range of concentration. Stability of the alloys is analyzed by combining ΔFmix(x) with Hume-Rothery rules.

Effect of Ti, Al and Cu Addition on Structural Evolution and Phase Constitution of FeCoNi System Equimolar Alloys

FeCoNi system equimolar alloys were fabricated by a vacuum arc melting. The phase constitution of FeCoNi system alloys was determined by XRD analysis and the microstructure was observed by OM. The comprehensive atomic radius δ, the mixing enthalpy ΔHmix and the mixing entropy ΔSmix of alloys were also calculated according to relevant equations. The results show that the addition of Ti, Al and Cu has an obvious influence on the microstructure and phase constitution of FeCoNi system equimolar alloys. Single Ti addition resulted in almost entire solid solution with a typical dendrite growth character and a little unknown phase. However, further addition of Al, Cu or Al+Cu into the FeCoNiTi equimolar alloys led to the occurrence of an entire solution phase with dendrite, coarse dendrite, and rosette dendrite respectively. Such a phenomena suggested that the mixing entropy caused by the increase of components number rather than the comprehensive atomic radius between the elements or the mixing enthalpy of the alloy systems might be responsible for the formation of almost entire solid solution in FeCoNi system equimolar alloys.

Structure and Microwave Dielectric Properties of Solid Solution in SrLaAlO4‐Sr2TiO4 System

Ceramics in (1−x)SrLaAlO4‐xSr2TiO4 system were synthesized in the entire range of 0 ≤ x ≤ 1 by a standard solid‐state reaction method. X‐ray diffraction patterns revealed a single solid solution phase Sr1+xLa1−xAl1−xTixO4 with K2NiF4‐type structure. The cell refinement showed the linear variation of lattice parameters a, c, and cell volume. With increasing x, εr increased from 17.6 to 31.0, whereas τf was tuned from −32 to 122 ppm/oC. The Qf value first increased and then decreased with increasing x due to the result of competition balance between the effect of layer mismatch and interlayer polarization. The degradation of Qf value in the vicinity of x = 0.2 could be attributed to the compositional fluctuation and inhomogeneity originated from the positive mixing enthalpy ΔHmix, which could be confirmed by TEM observation. The best combination of microwave dielectric characteristics was achieved at x = 0.4: εr = 18.5, Qf = 95 000 GHz, τf = −8.9 ppm/oC.

Thermodynamic characteristics of Ti-based glass-forming alloys

Abstract Based on thermodynamic characteristics of the stable metallic liquid at melting temperature and the supercooled liquid, the present work calculated the mixing enthalpy ΔHmix, the mixing entropy ΔSmix and the Gibbs free energy difference between the supercooled liquid and the resulting crystalline phases ΔG of typical Ti-based amorphous alloys. The results show that for the case of larger ΔSmix, moderate ΔHmix for the stable liquid and smaller ΔG for the supercooled liquid, Ti-based alloys tend to achieve high glass-forming ability (GFA). A new parameter, β, defined as (Tg − Tk)/(Tl − Tg), has been introduced to evaluate the GFA of Ti-based bulk amorphous alloys (wherein Tg, Tl, and Tk represent the glass transition temperature, the liquidus temperature, and the Kauzmann temperature, respectively). Experimental data imply that the larger the β, the better the GFA for Ti-based amorphous alloys.

Thermodynamic characteristics of metallic glass-forming liquids

On the basis of analyzing the thermodynamic model of regular melt, the mixing enthalpy ΔHmix and the mixing entropy ΔSmix of typical metallic glass melts were calculated. The distribution of ΔHmix vs. ΔSmix for typical metallic glasses was generalized, and a strategy for pinpointing metallic glass formers has been proposed by combining the critical cooling rate Rc based on the atomic intrinsic characteristics of the alloys including atom size, composition, and mixing enthalpy of binary systems among the components. On the condition of ΔSmix greater than 0.6 J·K-1mol-1 and ΔH less than -15 kJ·mol-1, the alloy tends to form a bulk metallic glass(BMG). It shows that Rc is intimately related with ΔSmix, and can be expressed as Rc=42.24×104 exp(-13.91 ΔSmix)+19.66. Two new glass formers, Zr40Al10Ni15Cu35, located far from the glass forming area of the existing Zr-Al-Ni-Cu BMGs with a content of 55at%—65at% zirconium, and Fe53Co5Nd12B30 of quaternary Fe-B-based BMG, were successfully prepared with this approach.