journal article·2025-10-01Open access

Emergent B2 chemical orderings in the AlTiVNb and AlTiCrMo refractory high-entropy superalloys studied via first-principles theory and atomistic modelling

Christopher D Woodgate, Hubert J Naguszewski, David Redka, Ján Minár, David Quigley, Julie B Staunton

Journal of Physics: Materials· Volume 8· Issue 4

Abstract

Abstract We study the thermodynamics and phase stability of the AlTiVNb and AlTiCrMo refractory high-entropy superalloys using a combination of ab initio electronic structure theory—namely a concentration wave analysis—and atomistic Monte Carlo simulations. Our multiscale approach is suitable both for examining atomic short-range order in the solid solution, as well as for studying the emergence of long-range crystallographic order with decreasing temperature. In both alloys considered in this work, in alignment with experimental observations, we predict a B2 (CsCl) chemical ordering emerging at high temperatures, which is driven primarily by Al and Ti, with other elements expressing weaker site preferences. The predicted B2 ordering temperature for AlTiVNb is higher than that for AlTiCrMo. These chemical orderings are discussed in terms of the alloys’ electronic structure, with hybridisation between the sp states of Al and the d states of the transition metals understood to play an important role. Within our modelling, the chemically ordered B2 phases for both alloys have an increased predicted residual resistivity compared to the A2 (disordered bcc) phases. These increased resistivity values are understood to originate in a reduction in the electronic density of states at the Fermi level, in conjunction with qualitative changes to the alloys’ smeared-out Fermi surfaces. These results highlight the close connections between composition, structure, and physical properties in this technologically relevant class of materials.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: High Entropy Alloys Studies · High-Temperature Coating Behaviors · Intermetallics and Advanced Alloy Properties

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (100+)

Show source-provided references
1. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes10.1002/adem.200300567 ↗
2. Microstructural development in equiatomic multicomponent alloys10.1016/j.msea.2003.10.257 ↗
3. A critical review of high entropy alloys and related concepts10.1016/j.actamat.2016.08.081 ↗
4. High-entropy alloys10.1038/s41578-019-0121-4 ↗
5. Outstanding radiation resistance of tungsten-based high-entropy alloys10.1126/sciadv.aav2002 ↗
6. A quinary WTaCrVHf nanocrystalline refractory high-entropy alloy withholding extreme irradiation environments10.1038/s41467-023-38000-y ↗
7. A fracture-resistant high-entropy alloy for cryogenic applications10.1126/science.1254581 ↗
8. Exceptional fracture toughness of CrCoNi-based medium- and high-entropy alloys at 20 kelvin10.1126/science.abp8070 ↗
9. High-entropy alloys: potential candidates for high-temperature applications - an overview10.1002/adem.201700645 ↗
10. Discovery of a superconducting high-entropy alloy10.1103/PhysRevLett.113.107001 ↗
11. Quantum critical behavior in a concentrated ternary solid solution10.1038/srep26179 ↗
12. Extreme Fermi surface smearing in a maximally disordered concentrated solid solution10.1103/PhysRevLett.124.046402 ↗
13. Development and exploration of refractory high entropy alloys-a review10.1557/jmr.2018.153 ↗
14. Refractory high-entropy alloys10.1016/j.intermet.2010.05.014 ↗
15. Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys10.1016/j.intermet.2011.01.004 ↗
16. Lattice distortion in a strong and ductile refractory high-entropy alloy10.1016/j.actamat.2018.08.053 ↗
17. Mechanistic origin of high strength in refractory BCC high entropy alloys up to 1900K10.1016/j.actamat.2019.10.015 ↗
18. Effect of aluminum on the microstructure and properties of two refractory high-entropy alloys10.1016/j.actamat.2014.01.029 ↗
19. Microstructure and properties of aluminum-containing refractory high-entropy alloys10.1007/s11837-014-1066-0 ↗
20. Characterization of the microstructure of the compositionally complex alloy Al1Mo0.5Nb1Ta0.5Ti1Zr110.1016/j.scriptamat.2016.04.017 ↗
21. Refractory high entropy superalloys (RSAs)10.1016/j.scriptamat.2020.06.048 ↗
22. Three-dimensional atomic structure and local chemical order of medium- and high-entropy nanoalloys10.1038/s41586-023-06785-z ↗
23. Detection and impact of short-range order in medium/high-entropy alloys10.1016/j.isci.2023.106209 ↗
24. Structure and mechanical properties of the AlCr xNbTiV (x = 0, 0.5, 1, 1.5) high entropy alloys10.1016/j.jallcom.2015.08.224 ↗
25. Effect of Cr and Zr on phase stability of refractory Al-Cr-Nb-Ti-V-Zr high-entropy alloys10.1016/j.jallcom.2018.05.099 ↗
26. Crystallographic ordering in a series of Al-containing refractory high entropy alloys Ta-Nb-Mo-Cr-Ti-Al10.1016/j.actamat.2019.07.001 ↗
27. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data10.1107/S0021889811038970 ↗
28. Modeling the structure and thermodynamics of high-entropy alloys10.1557/jmr.2018.222 ↗
29. First-principles study of order-disorder transitions in multicomponent solid-solution alloys10.1088/1361-648X/ab13d8 ↗
30. Frontiers in atomistic simulations of high entropy alloys10.1063/5.0025310 ↗
31. Simulating short-range order in compositionally complex materials10.1038/s43588-023-00407-4 ↗
32. Hybrid Monte Carlo/molecular dynamics simulation of a refractory metal high entropy alloy10.1007/s11661-013-2000-8 ↗
33. Atomic-scale properties of Ni-based FCC ternary and quaternary alloys10.1016/j.actamat.2015.08.015 ↗
34. First-principles study of the order-disorder transition in the AlCrTiV high entropy alloy10.1103/PhysRevMaterials.8.093603 ↗
35. Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials10.1038/s41524-019-0195-y ↗
36. Machine-learned interatomic potentials for alloys and alloy phase diagrams10.1038/s41524-020-00477-2 ↗
37. B2 ordering in body-centered-cubic AlNbTiV refractory high-entropy alloys10.1103/PhysRevMaterials.5.053803 ↗
38. Thermodynamics up to the melting point in a TaVCrW high entropy alloy: systematic ab initio study aided by machine learning potentials10.1103/PhysRevB.105.214302 ↗
39. Roadmap for the development of machine learning-based interatomic potentials10.1088/1361-651X/ad9d63 ↗
40. Short-range order in high entropy alloys: theoretical formulation and application to Mo-Nb-Ta-V-W system10.1007/s11669-017-0582-3 ↗
41. Chemical short-range order in derivative Cr-Ta-Ti-V-W high entropy alloys from the first-principles thermodynamic study10.1039/D0CP03764H ↗
42. Interaction models and configurational entropies of binary MoTa and the MoNbTaW high entropy alloy10.1103/PhysRevMaterials.7.063803 ↗
43. Deciphering chemical ordering in high entropy materials: a machine learning-accelerated high-throughput cluster expansion approach10.1016/j.actamat.2024.120137 ↗
44. Atomic short-range order and incipient long-range order in high-entropy alloys10.1103/PhysRevB.91.224204 ↗
45. Long-ranged interactions in bcc NbMoTaW high-entropy alloys10.1080/21663831.2016.1198837 ↗
46. Ta-Nb-Mo-W refractory high-entropy alloys: anomalous ordering behavior and its intriguing electronic origin10.1103/PhysRevMaterials.2.055004 ↗
47. First-principles prediction of high-entropy-alloy stability10.1038/s41524-017-0049-4 ↗
48. CALPHAD-aided design for superior thermal stability and mechanical behavior in a TiZrHfNb refractory high-entropy alloy10.1016/j.actamat.2023.118728 ↗
49. Recent machine learning-driven investigations into high entropy alloys: a comprehensive review10.1016/j.jallcom.2024.177823 ↗
50. Statistical physics of multicomponent alloys using KKR-CPA10.1103/PhysRevB.93.054206 ↗
51. Compositional phase stability in medium-entropy and high-entropy Cantor-Wu alloys from an ab initio all-electron Landau-type theory and atomistic modeling10.1103/PhysRevB.105.115124 ↗
52. Short-range order and compositional phase stability in refractory high-entropy alloys via first-principles theory and atomistic modeling: NbMoTa, NbMoTaW and VNbMoTaW10.1103/PhysRevMaterials.7.013801 ↗
53. Woodgate · 2024 · vol 346
54. Coherent-potential model of substitutional disordered alloys10.1103/PhysRev.156.809 ↗
55. Coherent-potential approximation for a nonoverlapping-muffin-tin-potential model of random substitutional alloys10.1103/PhysRevB.5.2382 ↗
56. Complete solution of the Korringa-Kohn-Rostoker coherent-potential-approximation equations: Cu-Ni alloys10.1103/PhysRevLett.41.339 ↗
57. Total-energy and pressure calculations for random substitutional alloys10.1103/PhysRevB.41.9701 ↗
58. On the calculation of the energy of a Bloch wave in a metal10.1016/0031-8914(47)90013-X ↗
59. Solution of the Schrödinger equation in periodic lattices with an application to metallic lithium10.1103/PhysRev.94.1111 ↗
60. Calculating condensed matter properties using the KKR-Green’s function method-recent developments and applications10.1088/0034-4885/74/9/096501 ↗
61. Inhomogeneous electron gas10.1103/PhysRev.136.B864 ↗
62. Self-consistent equations including exchange and correlation effects10.1103/PhysRev.140.A1133 ↗
63. Local lattice distortion in high-entropy alloys10.1103/PhysRevMaterials.1.023404 ↗
64. Interplay between disorder and electronic correlations in compositionally complex alloys10.1038/s41467-024-52349-8 ↗
65. Bulk and element-specific magnetism of medium-entropy and high-entropy Cantor-Wu alloys10.1103/PhysRevB.102.174405 ↗
66. Fast ab initio design of high-entropy magnetic materials10.1103/PhysRevMaterials.9.L031401 ↗
67. Temperature dependent electronic transport in concentrated solid solutions of the 3 d -transition metals Ni, Fe, Co and Cr from first principles10.1103/PhysRevB.98.165141 ↗
68. Uncovering electron scattering mechanisms in NiFeCoCrMn derived concentrated solid solution and high entropy alloys10.1038/s41524-018-0138-z ↗
69. An investigation of high entropy alloy conductivity using first-principles calculations10.1063/5.0065239 ↗
70. Structural stability of NiCoFeCrAlx high-entropy alloy from ab initio theory10.1103/PhysRevB.88.085128 ↗
71. Impact of aluminum doping on the thermo-physical properties of refractory medium-entropy alloys10.1063/1.4973489 ↗
72. Elasticity of high-entropy alloys from ab initio theory10.1557/jmr.2018.237 ↗
73. Ordering in substitutional and interstitial solid solutions10.1016/0079-6425(78)90003-8 ↗
74. Concentration waves and Fermi surfaces in random metallic alloys10.1103/PhysRevLett.50.374 ↗
75. Compositional short-range ordering in metallic alloys: band-filling, charge-transfer and size effects from a first-principles all-electron Landau-type theory10.1103/PhysRevB.50.1450 ↗
76. First-principles all-electron theory of atomic short-range ordering in metallic alloys: D 0 22 - versus L 1 2 -like correlations10.1103/PhysRevB.50.1473 ↗
77. van hove singularity induced L11 ordering in CuPt10.1103/PhysRevLett.74.3225 ↗
78. The effect of thermal agitation on atomic arrangement in alloys10.1098/rspa.1934.0132 ↗
79. The effect of thermal agitation on atomic arrangement in alloys-II10.1098/rspa.1935.0165 ↗
80. History of the Lenz–Ising model10.1103/RevModPhys.39.883 ↗
81. Diffusion constants near the critical point for time-dependent ising models. I10.1103/PhysRev.145.224 ↗
82. Equation of state calculations by fast computing machines10.1063/1.1699114 ↗
83. Efficient, multiple-range random walk algorithm to calculate the density of states10.1103/PhysRevLett.86.2050 ↗
84. Landau · 2014
85. An approximate theory of order in alloys10.1103/PhysRev.77.669 ↗
86. X-ray measurement of short range order in Ag-Au10.1063/1.1699988 ↗
87. Short-range order and long-range order parameters10.1103/PhysRev.138.A1384 ↗
88. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems10.1143/JPSJ.12.570 ↗
89. The Boltzmann equation in the theory of electrical conduction in metals10.1088/0370-1328/71/4/306 ↗
90. Theory of electronic transport in random alloys: Korringa-Kohn-Rostoker coherent-potential approximation10.1103/PhysRevB.31.3260 ↗
91. The Munich SPR-KKR package
92. Linear methods in band theory10.1103/PhysRevB.12.3060 ↗
93. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis10.1139/p80-159 ↗
94. The “disordered local moment” picture of itinerant magnetism at finite temperatures10.1016/0304-8853(84)90367-6 ↗
95. Disordered local moment state of magnetic transition metals: a self-consistent KKR-CPA calculation10.1088/0305-4608/13/5/012 ↗
96. Data for “Emergent B2 chemical orderings in the AlTiVNb and AlTiCrMo refractory high-entropy superalloys studied via first principles theory and atomistic simulations”10.5281/zenodo.14849315 ↗
97. Energy and pressure versus volume: equations of state motivated by the stabilized jellium model10.1103/PhysRevB.63.224115 ↗
98. The atomic simulation environment-a Python library for working with atoms10.1088/1361-648X/aa680e ↗
99. Ab initio study of the thermodynamic properties of nonmagnetic elementary fcc metals: exchange-correlation-related error bars and chemical trends10.1103/PhysRevB.76.024309 ↗
100. Structure, short-range order and phase stability of the AlxCrFeCoNi high-entropy alloy: insights from a perturbative, DFT-based analysis10.1038/s41524-024-01445-w ↗