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Interpolation of compound semiconductor alloy parameters from those of their constituents

Several methods have been proposed for interpolation of the value of physical parameters of quaternary alloys from those of their constituent ternary and binary sub-alloys. These expressions agree when non-linear bowing terms are not required; they differ in how the bowing terms of the bounding ternaries should be utilized. Common interpolation expressions for quaternaries can be generalized into two groups: (1) those that use a linear interpolation of the nearest ternary parameter values and (2) those that interpolate over binary values with a bowing term derived from the bounding ternaries. The second group of methods is equivalent to a polynomial expansion over the alloy’s interpolation space. For compound semiconductor alloys, the geometry of the composition space is the direct sum of the group-III and group-V mixture sub-spaces. The mixture sub-spaces are best described using barycentric coordinates on a regular simplex. A general polynomial expansion of the value of an alloy parameter using barycentric coordinates for the group-III and group-V simplex spaces is described along with an algorithm to generate interpolation expressions for alloys with arbitrary numbers of elements, including quinary and senary alloys. It is shown that a polynomial expansion produces values in closer agreement with the direct gap of quaternaries lattice-matched to common substrates than do approaches using an interpolation of the ternary values, despite a prominent recommendation to the contrary. Finally, a quaternary correction term is described that improves the predicted direct bandgap energies of GaInAsSb for compositions near those lattice matched to InP, InAs, and GaSb.

Olesberg, Jonathon T. [Sandia National Laboratorie↗

Disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y alloys

This dataset contains input and output files from density functional theory (DFT) simulations used to study the disorder-induced magnetoelastic behaviors of MnTexSbyBi1-x-y (0 ≤ x + y ≤ 1) alloys and their binary end members MnTe, MnSb, and MnBi. The alloys adopt the hexagonal NiAs-type (nickeline) structure and span ternary (MnTexSb1-x, MnTexBi1-x, MnBixSb1-x), and quaternary compositions across the full MnTe–MnSb–MnBi composition triangle. For each alloy composition, the dataset provides DFT calculations in three magnetic configurations: A-type antiferromagnetic (AFM), C-type AFM, and ferromagnetic (FM). Every magnetic configuration folder contains the fully relaxed crystal structure (CONTCAR), VASP input parameters (INCAR), and the main VASP output file (OUTCAR), from which total electronic energies, Mn magnetic moments, lattice parameters, and percent volume changes between magnetic states are extracted. These data are used to construct compositional phase diagrams, evaluate thermodynamic stability (formability), and map magnetoelastic responses across the alloy space. For A-type AFM and FM configurations, additional data are provided as follows: (i) FORCE_CONSTANTS and thermal_properties.yaml files at the top level of A-type_AFM/ and FM/ folders — present only for compositions marked with an asterisk (*) in Table I of the main text. These are derived from Phonopy finite-displacement calculations on full disordered 128-atom supercells and provide vibrational free energy, entropy (Svib)contribution from explicit disorder calculations. (Table I of the associated main manuscript) (ii) A VCA/ subfolder within A-type_AFM/ and FM/, containing FORCE_CONSTANTS and thermal_properties.yaml from Virtual Crystal Approximation phonon calculations (without spin-orbit coupling). VCA data are available for all compositions and are used to estimate vibrational contributions to the Gibbs free energy across the full composition space. (iii) A SOC/ subfolder containing CONTCAR, INCAR, and OUTCAR from spin-orbit coupling calculations, providing relativistic corrections to electronic energies and lattice parameters (Tables S2–S3 of the SM, and Table I of the main manuscript). (iv) A SOC/VCA/ subfolder containing FORCE_CONSTANTS and thermal_properties.yaml from VCA phonon calculations performed within the SOC framework, combining relativistic and vibrational thermodynamic corrections. The computed properties are used to map the AFM–FM magnetic crossover near MnTe0.75Sb0.25, demonstrate disorder- and spin-induced phonon broadening, identify a semiconductor-to-metal crossover, and quantify the pronounced magnetoelastic volume response near the magnetic phase boundary.

36 MATERIALS SCIENCE↗

Critical cooling rates for amorphous-to-ordered complexion transitions in Cu-rich nanocrystalline alloys

Amorphous complexions in nanocrystalline metals have the potential to improve mechanical properties and radiation tolerance, as well as resistance to grain growth. In this study, the stability of amorphous complexions in binary and ternary Cu-based alloys is investigated by observing the effect of cooling rate from high temperature on the occurrence of amorphous-to-ordered complexion transitions. Bulk Cu-Zr and Cu-Zr-Hf alloy samples were annealed to induce boundary premelting and then quenched through a procedure that induces a gradient of local cooling rate through the sample height. Amorphous complexion thickness distributions were found to be invariant to local cooling rate in the Cu-Zr-Hf alloy, demonstrating enhanced stability of the amorphous complexion structure compared to the Cu-Zr alloy, which had thinner amorphous complexions in the regions that were slowly cooled. The experimental results are used to construct time-temperature-transformation diagrams for the amorphous-to-ordered complexion transition in both the binary and ternary alloys, enabling a deeper understanding of the influence of cooling rate and grain boundary chemistry on complexion transitions. In conclusion, the critical cooling rate necessary to avoid complexion transitions in the ternary alloy is found to be at least three orders of magnitude slower than that for the binary alloy.

36 MATERIALS SCIENCE↗

A map of single-phase high-entropy alloys

High-entropy alloys have exhibited unusual materials properties. The stability of equimolar single-phase solid solution of five or more elements is supposedly rare and identifying the existence of such alloys has been challenging because of the vast chemical space of possible combinations. Herein, based on high-throughput density-functional theory calculations, we construct a chemical map of single-phase equimolar high-entropy alloys by investigating over 658,000 equimolar quinary alloys through a binary regular solid-solution model. We identify 30,201 potential single-phase equimolar alloys (5% of the possible combinations) forming mainly in body-centered cubic structures. We unveil the chemistries that are likely to form high-entropy alloys, and identify the complex interplay among mixing enthalpy, intermetallics formation, and melting point that drives the formation of these solid solutions. We demonstrate the power of our method by predicting the existence of two new high-entropy alloys, i.e. the body-centered cubic AlCoMnNiV and the face-centered cubic CoFeMnNiZn, which are successfully synthesized.

36 MATERIALS SCIENCE↗

Deformation of binary and boron-doped Ni 3 Al alloys at high pressures studied with synchrotron x-ray diffraction

In situ x-ray synchrotron diffraction experiments were carried out on nickel-based high-strength superalloys under pressure to understand their deformation mechanism using a diamond anvil cell (DAC). Radial x-ray diffraction determines the room-temperature equations of state and yield strengths of binary Ni 3 Al alloy and 500 ppm boron-doped Ni 3 Al to pressures of 20 and 46 GPa, respectively. Crystallographic preferred orientations observed in these superalloys due to anisotropic stress field in DAC indicate the onset of plastic deformation. Inverse pole figure analysis reveals that the underlying deformation mechanisms change from an octahedral slip to a simultaneous activation of octahedral and cube slips upon doping with boron. The yield-strength values were found to increase with pressure and are comparable to those determined from axial diffraction experiments. The results indicate that the yield strength of Ni 3 Al:B is about 0.5 GPa higher (at pressures below 20 GPa) due to grain boundary strengthening by boron. It is shown that due to high elastic anisotropy of Ni 3 Al alloy, the yield-strength estimations from diffraction experiments strongly depend on the micromechanical model used to convert the measured elastic strains into stresses.

42 ENGINEERING↗

Machine Learning Vacancy Formation Energy in Nickel-Based Superalloys

Thermal vacancies play a critical role in high-temperature Ni-based superalloys and influence various properties such as creep resistance, oxidation, etc. This study systematically investigates the impact of commonly used transition metals (Cr, Co, Fe), refractory metals (Nb, Ta, Mo, W) and other elements (Al, Cu, Ti, Mn) on the thermodynamic stability of 36 binary, 20 ternary, 11 quaternary, 9 quinary, and 3 senary FCC Ni-based alloys covering various elemental combinations. Density functional theory-based studies on Ni-X binary alloys show that higher concentrations of Cr, Nb, Ta, Al, and Ti introduce significant lattice distortions and broaden the distribution of vacancy formation energies (standard deviation up to 0.15 eV). These elements partially donate electrons, reducing their self-consistent chemical potentials relative to single-element reference values and lowering vacancy formation energies, while Co, Fe, Mo, and W show lower charge localization. These trends extend from 3-6 element alloys, where Cr, Nb, and Ta-rich compositions have low-energy states (~0.5 eV) that increase vacancy concentrations. Finally, graph neural network models are developed to screen over 5000 virtual alloys. Eleven leading compositions are identified with mean vacancy formation energy higher than 1.75 eV and vacancy concentration ~2 orders of magnitude lower than pure Ni at 1000 K. These results provide valuable guidelines to achieve controlled defect engineering in structural alloys.

DFT↗

New insights on the effects of chemistry and temperature on α’ precipitation during aging of FeCrAl alloys

Here, the effect of Al on α' precipitation in FeCrAl alloys was studied through thermal aging of several model binary FeCr and FeCrAl alloys with Cr content of 13 wt.%, 17 wt.%, and 25 wt.% with and without 5.5 wt.% Al. Aging was performed up to 1,000h at varying temperatures from 400-500°C. At 400°C no age hardening was observed due to slow kinetics at this temperature. For both the 17Cr and 25Cr alloys, the addition of Al shows a lowering of the miscibility gap, consistent with other reports in literature. Interestingly, however, for the 25Cr alloys the addition of Al in the FeCrAl ternary alloy accelerated α' precipitation below the miscibility gap. Such enhanced precipitation has also been predicted by our atomistic kinetic Monte Carlo (AKMC) simulations. While previous literature has often focused on Al suppressing α', here we show that while Al can lower the miscibility gap in the Fe-Cr ferritic system thermodynamically, it may also enhance the kinetics of precipitation.

36 MATERIALS SCIENCE↗

Microstructural refinement of an Al-Ce-Mg alloy via Shear Assisted Processing and Extrusion

Al-Ce alloys have attracted recent interest because of their high thermal stability due to the low solubility of Ce in the Al matrix. The Al 11 Ce 3 eutectic phase gives excellent strain hardening behavior and moderate high-temperature strength in the as-cast state. However, its strengthening effect is limited by its coarse as-cast structure. Therefore, alternative manufacturing methods such as additive manufacturing or equal channel angular pressing have been applied to refine the Al 11 Ce 3 phase to good effect. However, these techniques are both expensive and time-consuming. Therefore, this study aims to use Shear Assisted Processing and Extrusion (ShAPE), an emerging solid phase processing technique that is more easily scalable than the previously mentioned methods. ShAPE can produce useful cross-sections of an Al-8Ce-4Mg alloy while refining the Al 11 Ce 3 phase to produce a higher strength material. It was found that a low temperature ShAPE process can improve the room temperature yield strength by ~60 % compared to a binary Al-4Mg alloy. Additionally, the high-temperature yield strength of the Al-Ce alloys increased by 20%, with a simultaneous 15% improvement in ductility compared to the binary Al-Mg alloy. Finally, these results highlight the potential for ShAPE as a processing technique for Al-Ce alloys.

36 MATERIALS SCIENCE↗

Wrought Aluminum-Cerium Alloys by Shear Assisted Processing and Extrusion

Al-Ce alloys have attracted recent interest because of their high thermal stability due to the very low solubility of Ce in the Al matrix. The Al 11 Ce 3 eutectic phase gives excellent strain hardening behavior and moderate high-temperature strength in the as-cast state. However, its strengthening effect is limited by its coarse as-cast structure. Therefore, alternative manufacturing methods such as additive manufacturing or equal channel angular pressing have been applied to refine the Al 11 Ce 3 phase to good effect. However, these techniques are both expensive and time-consuming. Therefore, this study aims to use Shear Assisted Processing and Extrusion (ShAPE), an emerging solid phase processing technique that is more easily scalable than the previously mentioned methods. ShAPE can produce useful cross-sections of an Al-8Ce-4Mg alloy while refining the Al 11 Ce 3 phase to produce a higher strength material. It was found that a low temperature ShAPE process can improve the room temperature yield strength by ~60% compared to a binary Al-4Mg alloy. Additionally, the high-temperature yield strength of the Al-Ce alloys increased by 20%, with a simultaneous 15% improvement in ductility compared to the binary Al-Mg alloy. These results highlight the potential for ShAPE as a processing technique for Al-Ce alloys.

36 MATERIALS SCIENCE↗

Interaction models and configurational entropies of binary MoTa and the MoNbTaW high entropy alloy

We introduce a simplified method to model the interatomic interactions of high entropy alloys based on a lookup table of cluster energies. Furthermore, these interactions are employed in replica exchange Monte Carlo simulations with histogram analysis to obtain thermodynamic properties across a broad temperature range. Kikuchi's cluster variation method entropy formalism is applied to directly calculate entropy from statistics on short- and long-range chemical order, and we discuss the convergence of the entropy as clusters of differing size are included. A high temperature series expansion aids in our understanding of the convergence. Computer codes implementing these methods, and supporting data, are freely available on the internet.

36 MATERIALS SCIENCE↗

Iron Bonding with Light Elements: Implications for Planetary Cores Beyond the Binary System

Light element alloying in iron is required to explain density deficit and seismic wave velocities in Earth’s core. However, the light element composition of the Earth’s core seems hard to constrain as nearly all light element alloying would reduce the density and sound velocity (elastic moduli). The alloying light elements include oxidizing elements like oxygen and sulfur and reducing elements like hydrogen and carbon, yet their chemical effects in the alloy system are less discussed. Moreover, Fe-X-ray Absorption Near Edge Structure (Fe-XANES) fingerprints have been studied for silicate materials with ferrous and ferric ions, while not many X-ray absorption spectroscopy (XAS) studies have focused on iron alloys, especially at high pressures. To investigate the bonding nature of iron alloys in planetary interiors, we presented X-ray absorption spectroscopy of iron–nitrogen and iron–carbon alloys at high pressures up to 50 GPa. Together with existing literature on iron–carbon, –hydrogen alloys, we analyzed their edge positions and found no significant difference in the degree of oxidation among these alloys. Pressure effects on edge positions were also found negligible. Our theoretical simulation of the valence state of iron, alloyed with S, C, O, N, and P also showed nearly unchanged behavior under pressures up to 300 GPa. This finding indicates that the high pressure bonding of iron alloyed with light elements closely resembles bonding at the ambient conditions. We suggest that the chemical properties of light elements constrain which ones can coexist within iron alloys.

Advanced Photon Source↗

Thermo4PFM: Facilitating Phase-field simulations of alloys with thermodynamic driving forces

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. Here we present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library.

36 MATERIALS SCIENCE↗

Alloying Effects on the Transport Properties of Refractory High-entropy Alloys

Additive Manufacturing (AM) has opened new frontiers for the design of refractory high-entropy alloys (HEAs) for high-temperature applications. The thermal conductivity of the AM feedstock is among the most important thermo-physical properties that control the melting and solidification process. Despite its significance, there remains a notable gap in both computational and experimental research concerning the thermal conductivity of HEAs. Here, we use density functional theory (DFT) to systematically investigate the alloying effects on the transport properties of Ti-Cr-Mo-W-V-Nb-Ta RHEAs, including electrical and thermal conductivities and Seebeck coefficient. The relaxation time of charge carriers is a key underlying parameter determining thermal conductivity that is exceedingly challenging to predict from first principles alone, and we thus follow the approach by Mukherjee, Satsangi, and Singh [Chem Mater 32, 6507 (2022)] to optimize the relaxation time for RHEAs. Here we validated thermal conductivity predictions on elemental solids, binary and ternary alloys, and RHEAs and compared them against thermodynamic (CALPHAD) predictions and our experiments with good correlations. To understand observed trends in thermal conductivity, we assessed the phase stability, electronic structure, phonon, and intrinsic- and tensile strength of down-selected RHEAs. Our electronic structure and phonon results connect well with the observed compositional trends for thermal transport in RHEAs. Our DFT assessment and CALPHAD predictions provide a unique design guide for RHEAs with tailored thermal conductivity, a critical consideration for AM and thermal-management applications.

36 MATERIALS SCIENCE↗

Ab initio free energies of liquid metal alloys: Application to the phase diagrams of Li-Na and K-Na

Comparison of free energies between different phases and different compositions underlies the prediction of alloy phase diagrams. To allow direct comparison, consistent reference points for the energies or enthalpies are required, and the entropy must be placed on an absolute scale, yielding absolute free energies. Here we derive absolute free energies of liquids from ab-initio molecular dynamics (AIMD) by combining the directly simulated enthalpies with an entropy derived from simulated densities and pair correlation functions. Additionally, as an example of the power of this method we calculate the phase diagrams of two binary alkali metal alloys, Li-Na and K-Na, revealing a critical point and liquid-liquid phase separation in the former case, and a deep eutectic in the latter. Good agreement with experimental data demonstrates the power of this simple method.

36 MATERIALS SCIENCE↗

Thermodynamic properties of Gd-Bi alloys determined by emf measurements in LiCl-KCl-GdCl 3 electrolyte

Thermodynamic properties of binary Gd-Bi alloys (mole fraction, x Gd = 0.02–0.35) were determined using electromotive force (emf) measurements in molten LiCl-KCl-GdCl 3 electrolyte in complement with structural, microstructural, and thermal characterization. X-ray diffractometry (XRD) and scanning electron microscopy (SEM) identified the phase constituents of Gd-Bi alloys (x Gd = 0.02–0.35) as Bi matrix and GdBi compound. According to differential scanning calorimetry (DSC) measurements up to 1250 K, a eutectic transition [L = Bi + GdBi] was observed at 543 K but the reported peritectic transition [L + GdBi = GdBi 2 ] was not detected, suggesting the absence of the GdBi 2 compound. Based on structural, microstructural, and thermal characterization of Gd-Bi alloys (x Gd = 0.02–0.35), the GdBi 2 compound was not detected, and its thermodynamic stability is questionable. The emf of Gd-Bi alloy (x Gd = 0.16) at 700–1048 K relative to Gd(s) was measured by electrodepositing pure Gd metal at 25 K increments. Further, the emf values of Gd-Bi alloys were determined via coulometric titration of Gd into liquid Bi using a two-phase [L + GdBi] alloy as a reference electrode at 773–973 K. The solubility of Gd in liquid Bi was also estimated to be 0.50 mol% (773 K), 0.99 mol% (873 K), and 2.21 mol% (973 K) and the excess partial molar Gibbs energy (Δ$\mathrm{\bar{G}^{ex}_{Gd}}$) of liquid Gd-Bi alloys was as low as 65 kJ mol –1 , indicating strong chemical interactions between Gd and Bi.

36 MATERIALS SCIENCE↗

Kinetics of amorphous defect phases measured through ultrafast nanocalorimetry

Recognition of the role of extended defects on local phase transitions has led to the conceptualization of the defect phase, localized thermodynamically stable interfacial states that have since been applied in a myriad of material systems to realize significant enhancements in material properties. Here, we explore the kinetics of grain boundary confined amorphous defect phases, utilizing the high temperature and scanning rates afforded by ultrafast differential scanning calorimetry to apply targeted annealing/quenching treatments at high rates capable of capturing the kinetic behavior. Four Al-based nanocrystalline alloys, including two binary systems, Al–Ni and Al–Y, and two ternary systems, Al–Mg–Y and Al–Ni–Y, are selected to probe the materials design space (enthalpy of mixing, enthalpy of segregation, chemical complexity) for amorphous defect phase formation and stability, with correlative transmission electron microscopy applied to link phase evolution and grain stability to nanocalorimetry signatures. A series of targeted isothermal annealing heat treatments is utilized to construct a Time–Temperature-Transformation curve for the Al–Ni system, from which a critical cooling rate of 2400 °C/s was determined for the grain boundary confined disordered-to-ordered transition. Finally, a thermal profile consisting of 1000 repeated annealing sequences was created to quantify the recovery of the amorphous defect phase following sequential annealing treatments, with results indicating remarkable microstructural stability after annealing at temperatures above 90% of the melting temperature. This work contributes to a deeper understanding of grain boundary localized thermodynamics and kinetics, with potential implications for the design and optimization of advanced materials with enhanced stability and performance.

Amorphous defect phases↗