Robust data-driven approach for predicting the configurational energy of high entropy alloys
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The Fe-Co-Cr-Ni quaternary system has been studied extensively in the past decade, not only because of the superior properties achieved like high tensile ductility and fracture toughness, but also it is the foundation for the development of FeCrCoNi-based HEAs. However, most of the investigations are mainly focusing on the equiatomic and semi-equiatomic compositions. The physical properties of non-equiatomic compositions are barely explored. In the current work, the ab initio approach is adopted to predict the lattice parameter, structure stabilities, elastic properties, and enthalpy of formations of fcc Fe-Cr-Co-Ni HEA single crystals with the special quasirandom structure (SQS) method. To expand the design of Fe-Co-Cr-Ni HEAs into a full composition range, the current simulations cover all the binaries, ternaries, and the whole quaternary system. The 2-D composition-property contour diagrams are created to show the physical properties in the ternary and quaternary systems. Furthermore, our investigation shows that the fcc alloys' lattice parameter increases with the addition of Fe and Cr and decreases with Ni and Co. In addition to the enthalpy of formation at o K, the shape distortion rate is proposed to be another essential parameter to evaluate crystal stability. The results show the addition of Cr would destabilize the fcc lattice and cause symmetry breaking. Finally, the result of Pugh’s ratio shows that most of the fcc alloys show ductile behavior (P > 1.75), especially for the alloys around Fe 3 Ni, FeCo, and Fe 2 NiCo (P > 2.5). The brittle behavior (P < 1.75) is located around Fe 3 Cr and Fe 2 CoCr. Meanwhile, Cr 2 NiCo and Cr 2 FeNiCo are considered promising compositions to be tried and verified experimentally because of the higher bulk modulus and moderate shear modulus.
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Laser beam directed energy deposition has become an increasingly popular advanced manufacturing technique for materials discovery as a result of the in situ alloying capability. In this study, we leverage an additive manufacturing enabled high throughput materials discovery approach to explore the composition space of a graded W x (CoCrFeMnNi) 100–x sample spanning 0 ≤ x ≤ 21 at%. In addition to microstructural and mechanical characterization, synchrotron high speed x-ray computer aided tomography was conducted on a W 20 (CoCrFeMnNi) 80 composition to visualize melting dynamics, powder-laser interactions, and remelting effects of previously consolidated material. Results reveal the formation of the Fe 7 W 6 intermetallic phase at W concentrations> 6 at%, despite the high configurational entropy. Unincorporated W particles also occurred at W concentrations> 10 at% accompanied by a dissolution band of Fe 7 W 6 at the W/matrix interface and hardness values greater than 400 HV. In this work, the primary strengthening mechanism is attributed to the reinforcement of the Fe 7 W 6 and W phases as a metal matrix composite. The in situ high speed x-ray imaging during remelting showed that an additional laser pass did not promote further mixing of the Fe 7 W 6 or W phases suggesting that, despite the dissolution of the W into the Fe 7 W 6 phase being thermodynamically favored, it is kinetically limited by the thickness/diffusivity of the intermetallic phase, and the rapid solidification of the laser-based process.
Interdiffusion experiments are usually time-consuming and tedious since diffusion couples must be annealed at several temperatures for a long time. The efforts required to study interdiffusion in multicomponent alloys increase dramatically as multiple diffusion couples are required to cover broad composition ranges and determine the diffusivities of individual elements in different chemical environments. To circumvent this challenge, we present a high-throughput approach applicable to single-phase and compositionally complex alloys, which are assumed to approximate ideal solid solutions. Here, a simple diffusion-multiple experiment combined with a physically based kinetic model is proposed to efficiently determine the diffusion coefficients of the constituent elements in quaternary CrFeCoNi alloys. Compared with tracer diffusivities reported in the literature, the results, thus, obtained do not differ by more than a factor of 2 and were obtained from a single interdiffusion experiment. In contrast, the diffusivities simulated with commercial mobility and thermodynamic databases are strongly overestimated by a factor ranging from 1 to 16. Therefore, our approach enables high-throughput determination of diffusivities and can help in the design of alloys for high-temperature applications where diffusion plays a key role.
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Powder X-ray diffraction data collected at the Advanced Photon Source 16-BM–D, confirms that the alloy with composition Mo 0.20 Nb 0.21 Ta 0.19 V 0.20 W 0.20 crystallizes in a simple body-centered cubic (bcc) structure with all five elements distributed over a single crystallographic site (Wyckoff position 2a of space group Im $\bar{3}$ m ).
Short-range order (SRO) in multicomponent concentrated alloys affects their mechanical response. Hence, is paramount to understand how composition modifies the chemical ordering in the system to design materials with optimal properties. Here, in this work, we present a methodology to predict the SRO and thermodynamic properties in chemically complex systems and apply it to the WTaCrVHf quinary alloy. We observe that the addition of Hf significantly modifies the SRO, mainly at intermediate to low temperatures, matching experimental observations.
Tailoring magnetic behavior by composition and annealing is an effective way. The phase transition from the face-centered-cubic (FCC) to B2 structure influenced by the Al content on the CoFeMnNiAl x alloys leads to the enhanced magnetization. However, the excessive Al addition in the B2-structured alloys impairs the magnetization. The phase transformation caused by annealing also indicates that the saturation magnetization of the alloy depends on the volume fraction of the B2 phase, and a higher content of the B2 phase is beneficial to the large saturation magnetization. Ab initio calculations are used to explain the magnetic behavior of the present HEAs and the effects of phase structures on magnetic characteristics. The phase stability of the CoFeMnNiAl x alloy is thoroughly studied by both the existing phase-formation empirical criteria and annealing. Here, the existing empirical criteria used to predict the phase formation are not universal. However, combining the ΔH mix -δ relation and the φ value, whether the single disordered solid-solution phase is formed can be preliminarily predicted.
On the one hand, multi-principal element alloys (MPEAs) have created a paradigm shift in alloy design due to large compositional space, whereas on the other, they have presented enormous computational challenges for theory-based materials design, especially density functional theory (DFT), which is inherently computationally expensive even for traditional dilute alloys. In this project, we developed a machine learning framework, namely PREDICT ( PR edict properties from E xisting D atabase I n C omplex alloys T erritory), that opens a pathway to predict elastic constants in large compositional space with little computational expense. The framework only relies on the DFT database of binary alloys and predicts Voigt–Reuss–Hill Young’s modulus, shear modulus, bulk modulus, elastic constants, and Poisson’s ratio in MPEAs. We show that the key descriptors of elastic constants are the A–B bond length and cohesive energy. The framework can predict elastic constants in hypothetical compositions as long as the constituent elements are present in the database, thereby enabling property exploration in multi-compositional systems. We illustrate predictions in a FCC Ni-Cu-Au-Pd-Pt system.
We report on the investigation of magnetic and structural properties of AlCoCrCuFeNi, which is known to crystallize in a dual phase solid solution: the face-centred cubic (FCC) or the body-centred cubic (BCC). The results of neutron (NPD) and synchrotron powder diffraction (SXRD) allow to partially resolve magnetic information coming from BCC and FCC phases, which is impossible in the bulk magnetic measurements. Electron diffraction (PED) revealed that AlCoCrCuFeNi forms dendritic microstructure with the Cu-rich FCC phase and the Ni-rich BCC phase. Lattice parameters obtained from PED method are in good agreement with parameters obtained after refinement on the basis of powder X-ray diffraction measurements. The local crystal and electronic structure around Co was studied using Co K X-ray Absorption Spectroscopy (XAS). The magnetic measurements show that AlCoCrCuFeNi reveal a ferromagnetic transition at about 330K and displays magnetic hysteresis loop at the room temperature. Results from NPD suggest that the magnetic moment is mostly located in the BCC subsystem. The alloy shows soft magnetic properties. Saturated magnetizations (M s ), remanence ratio (M r /M s ) and coercivity (H c ) of the cast are estimated to be 45.10emu/g, 5.1% and 56 Oe at 300K, respectively. Finally, the BCC-FCC phase transformation up to 673K (400°C) was investigated using temperature dependent NPD, where a possible second BCC phase was identified.
Corrosion behavior of a dual-phase Fe 50 Mn 30 Co 10 Cr 10 HEA subjected to supercritical water at different temperatures was investigated. Both weight gain and oxide film thickness increased with increasing temperatures. An outer layer with polyhedral MnFe 2 O 4 particles and an inner layer containing a mixture of CrMn 1.5 O 4 and Fe 3 O 4 were formed at 380 °C. Mn 2 O 3 outer and CrMn 1.5 O 4 inner layers developed at 550 and 650 °C, but the loose granular Mn 2 O 3 particles at 550 °C transformed into a compact oxide film at 650 °C. Besides, Cr 2 O 3 oxide particles were observed along the grain boundaries. Finally, the corrosion mechanism at different temperatures was also discussed.
Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 additively manufactured using laser powder bed fusion (LPBF) is among the toughest as-built alloys reported and is a promising candidate for use in extreme environments. However, its behavior under multi-megabar pressure regimes remains unexplored. We used femtosecond in situ X-ray diffraction to investigate the shock response of LPBF Ni40Co20Fe10Cr10Al18W2 under laser-driven shock compression and release. Our results reveal that the initial dual-phase face-centered + body-centered structure transforms to a single face-centered phase over a wide pressure range of 84±10 to 277±55 GPa, followed by a transition to a single body-centered phase at 431±48 GPa. We establish the Hugoniot equation-of-state of LPBF Ni 40 Co 20 Fe 10 Cr 10 Al 18 W 2 and compare it to the benchmark alloy AlCoCrFeNi 2.1 , demonstrating the effects of W-doping and increased Al content. High stacking fault probabilities, close to those measured in Au and Ag, are observed upon compression. A portion of the stacking faults are annihilated upon release to ambient pressure.
We report that obtaining surrogate models for various types of materials has long been a goal of computational material scientists and physicists, as they allow the calculation of thermodynamic quantities and properties of interest far more efficiently than DFT. Many surrogate models, including interatomic potentials generated by machine learning algorthims and cluster expansions, rely on incorporating many-body interactions such as three-body or four-body interactions. When utilizing machine learning algorithms for interatomic potentials, it is common to start with two-body interactions and systematically include three- and four-body clusters to improve the fit, stopping when including the additional clusters does not measurably change the predictive power of the model. In cluster expansions for FCC and related lattices, it is often enough to include mostly two-body interactions and a handful of three-body interactions. However, it remains to be seen whether those will be enough in the case of lattices with a lower packing fraction, such as BCC.
Significance This work serves to extend the fundamental ductile vs. brittle fracture theory, specifically the Rice–Thomson criterion, by introducing a grain boundary ahead of an initiating crack which propagates at an oblique angle to impinge the boundary. Atomistic fracture simulations on two refractory complex concentrated alloys, the brittle NbMoTaW and the ductile Nb 45 Ta 25 Ti 15 Hf 15 , demonstrate qualitative correspondence with the extended Rice–Thomson criterion and experimental observations. Abstract Understanding how grain boundaries mediate fracture remains a critical challenge in designing ductile, high-performance refractory alloys. Here, we extend the Rice–Thomson criterion to account for the angle between cracks and the impinging grain boundaries (GBs), capturing the competition between intergranular fracture and dislocation-mediated plasticity. Using machine learning interatomic potentials, we performed molecular statics simulations to probe fracture mechanisms in nanocrystalline NbMoTaW and Nb 45 Ta 25 Ti 15 Hf 15 , each with two different grain sizes, revealing trends consistent with experimental observations and the extended Rice model. Comparison with averaged R-curves for bulk samples demonstrates that GBs enhance ductility in Nb 45 Ta 25 Ti 15 Hf 15 in both grain sizes investigated. In contrast, GBs only locally improve fracture resistance in NbMoTaW when cracks are temporarily pinned at GBs inclined at high angles from the crack, but generally promote brittle intergranular fracture. These contrasting behaviors are attributed to differences in GB cohesion, reflecting clear alloying trends that align with ab-initio calculations and trends observed experimentally. Our results bridge classical fracture theory, atomistic simulations, and experimental observations, providing a comprehensive understanding of the fracture mechanisms in nanocrystalline refractory complex concentrated alloys.