Short-range order can be developed in multi-principal element alloys and influences the point defect behavior due to the large variation of the local chemical environment. The effect of short-range order on vacancy and interstitial formation energy and migration behavior was studied in body-centered cubic multi-principal element alloy NbZrTi by first-principles calculations. Two short-range order structures created by density functional theory and Monte Carlo method at 500 and 800 K were compared with the structure of random solid solution. Both vacancy and interstitial formation energies increase with the degree of short-range order. Point defect formation energies tend to be higher in regions enriched in Nb and lower in regions enriched in Zr and Ti. Both vacancies and interstitials prefer to migrate toward Zr,Ti-rich regions and away from Nb-rich regions, suggesting that Zr,Ti-rich regions can potentially act as recombination centers for point defect annihilation. Compared to an ideal random solid solution, the short-range order increases the spatial inhomogeneity of point defect energy landscape. Tuning the degree of short-range order by different processing techniques can be a viable strategy to optimize the point defect behavior to achieve enhanced radiation resistance in multi-principal element alloys.
REFERENCES
1.
E. P.
George
, W.
Curtin
, and C. C.
Tasan
, “High entropy alloys: A focused review of mechanical properties and deformation mechanisms
,” Acta Mater.
188
, 435
–474
(2020
). 2.
W.
Li
, D.
Xie
, D.
Li
, Y.
Zhang
, Y.
Gao
, and P. K.
Liaw
, “Mechanical behavior of high-entropy alloys
,” Prog. Mater. Sci.
118
, 100777
(2021
). 3.
Y.
Ikeda
, B.
Grabowski
, and F.
Körmann
, “Ab initio phase stabilities and mechanical properties of multicomponent alloys: A comprehensive review for high entropy alloys and compositionally complex alloys
,” Mater. Charact.
147
, 464
–511
(2019
). 4.
Y.
Zhang
, Y. N.
Osetsky
, and W. J.
Weber
, “Tunable chemical disorder in concentrated alloys: Defect physics and radiation performance
,” Chem. Rev.
122
, 789
–829
(2021
). 5.
C.
Lu
, L.
Niu
, N.
Chen
, K.
Jin
, T.
Yang
, P.
Xiu
, Y.
Zhang
, F.
Gao
, H.
Bei
, S.
Shi
, M.-R.
He
, I. M.
Robertson
, W. J.
Weber
, and L.
Wang
, “Enhancing radiation tolerance by controlling defect mobility and migration pathways in multicomponent single-phase alloys
,” Nat. Commun.
7
, 13564
(2016
).6.
K.
Jin
, C.
Lu
, L.
Wang
, J.
Qu
, W.
Weber
, Y.
Zhang
, and H.
Bei
, “Effects of compositional complexity on the ion-irradiation induced swelling and hardening in Ni-containing equiatomic alloys
,” Scr. Mater.
119
, 65
–70
(2016
). 7.
T.-N.
Yang
, C.
Lu
, G.
Velisa
, K.
Jin
, P.
Xiu
, Y.
Zhang
, H.
Bei
, and L.
Wang
, “Influence of irradiation temperature on void swelling in NiCoFeCrMn and NiCoFeCrPd
,” Scr. Mater.
158
, 57
–61
(2019
). 8.
T.-N.
Yang
, C.
Lu
, G.
Velisa
, K.
Jin
, P.
Xiu
, M. L.
Crespillo
, Y.
Zhang
, H.
Bei
, and L.
Wang
, “Effect of alloying elements on defect evolution in Ni-20X binary alloys
,” Acta Mater.
151
, 159
–168
(2018
). 9.
X.
Chen
, Q.
Wang
, Z.
Cheng
, M.
Zhu
, H.
Zhou
, P.
Jiang
, L.
Zhou
, Q.
Xue
, F.
Yuan
, J.
Zhu
, X.
Wu
, and E.
Ma
, “Direct observation of chemical short-range order in a medium-entropy alloy
,” Nature
592
, 712
–716
(2021
). 10.
R.
Zhang
, S.
Zhao
, J.
Ding
, Y.
Chong
, T.
Jia
, C.
Ophus
, M.
Asta
, R. O.
Ritchie
, and A. M.
Minor
, “Short-range order and its impact on the CrCoNi medium-entropy alloy
,” Nature
581
, 283
–287
(2020
). 11.
D.
Liu
, Q.
Wang
, J.
Wang
, X.
Chen
, P.
Jiang
, F.
Yuan
, Z.
Cheng
, E.
Ma
, and X.
Wu
, “Chemical short-range order in Fe50Mn30Co10Cr10 high-entropy alloy
,” Mater. Today Nano
16
, 100139
(2021
). 12.
E.
Antillon
, C.
Woodward
, S.
Rao
, B.
Akdim
, and T.
Parthasarathy
, “Chemical short range order strengthening in a model FCC high entropy alloy
,” Acta Mater.
190
, 29
–42
(2020
). 13.
K.
Xun
, B.
Zhang
, Q.
Wang
, Z.
Zhang
, J.
Ding
, and E.
Ma
, “Local chemical inhomogeneities in TiZrNb-based refractory high-entropy alloys
,” J. Mater. Sci. Technol.
135
, 221
–230
(2023
). 14.
S.
Chen
, Z. H.
Aitken
, S.
Pattamatta
, Z.
Wu
, Z. G.
Yu
, D. J.
Srolovitz
, P. K.
Liaw
, and Y.-W.
Zhang
, “Simultaneously enhancing the ultimate strength and ductility of high-entropy alloys via short-range ordering
,” Nat. Commun.
12
, 4953
(2021
).15.
Z.
Lei
, X.
Liu
, Y.
Wu
, H.
Wang
, S.
Jiang
, S.
Wang
, X.
Hui
, Y.
Wu
, B.
Gault
, P.
Kontis
et al., “Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes
,” Nature
563
, 546
–550
(2018
). 16.
Z.
Su
, J.
Ding
, M.
Song
, L.
Jiang
, T.
Shi
, Z.
Li
, S.
Wang
, F.
Gao
, D.
Yun
, C.
Lu
, and E.
Ma
, “Radiation-tolerant high-entropy alloys via interstitial-solute-induced chemical heterogeneities,” Acta Materialia
245
, 118662 (2023
). 17.
J.
Ding
, Q.
Yu
, M.
Asta
, and R. O.
Ritchie
, “Tunable stacking fault energies by tailoring local chemical order in CrCoNi medium-entropy alloys
,” Proc. Natl. Acad. Sci. U.S.A.
115
, 8919
–8924
(2018
). 18.
S.
Wang
, X.
Liu
, Z.
Lei
, D.
Lin
, F.
Bian
, C.
Yang
, M.
Jiao
, Q.
Du
, H.
Wang
, Y.
Wu
, S. H.
Jiang
, and Z. P.
Lu
, “Chemical short-range ordering and its strengthening effect in refractory high-entropy alloys
,” Phys. Rev. B
103
, 104107
(2021
). 19.
Y.
Osetsky
, A. V.
Barashev
, L. K.
Béland
, Z.
Yao
, K.
Ferasat
, and Y.
Zhang
, “Tunable chemical complexity to control atomic diffusion in alloys
,” npj Comput. Mater.
6
, 1
–8
(2020
). 20.
Z.
Su
, J.
Ding
, M.
Song
, L.
Jiang
, T.
Shi
, Z.
Li
, and S.
Wang
, “Enhancing the radiation tolerance of high-entropy alloys via atomic-scale chemical heterogeneities
,” Acta Mater.
245
, 118662
(2023
). 21.
Z.
Su
, T.
Shi
, H.
Shen
, L.
Jiang
, L.
Wu
, M.
Song
, Z.
Li
, S.
Wang
, and C.
Lu
, “Radiation-assisted chemical short-range order formation in high-entropy alloys
,” Scr. Mater.
212
, 114547
(2022
). 22.
C.
Li
, X.
Hu
, T.
Yang
, N. K.
Kumar
, B. D.
Wirth
, and S. J.
Zinkle
, “Neutron irradiation response of a Co-free high entropy alloy
,” J. Nucl. Mater.
527
, 151838
(2019
). 23.
H.-S.
Do
and B.-J.
Lee
, “Origin of radiation resistance in multi-principal element alloys
,” Sci. Rep.
8
, 16015
(2018
).24.
Y.
Lin
, T.
Yang
, L.
Lang
, C.
Shan
, H.
Deng
, W.
Hu
, and F.
Gao
, “Enhanced radiation tolerance of the Ni-Co-Cr-Fe high-entropy alloy as revealed from primary damage
,” Acta Mater.
196
, 133
–143
(2020
). 25.
S.
Zhao
, G. M.
Stocks
, and Y.
Zhang
, “Defect energetics of concentrated solid-solution alloys from ab initio calculations: Ni0.5Co0.5, Ni0.5Fe0.5, Ni0.8Fe0.2 and Ni0.8Cr0.2
,” Phys. Chem. Chem. Phys.
18
, 24043
–24056
(2016
). 26.
S.
Zhao
, “Defect properties in a VTaCrW equiatomic high entropy alloy (HEA) with the body centered cubic (BCC) structure
,” J. Mater. Sci. Technol.
44
, 133
–139
(2020
). 27.
H.
Guan
, S.
Huang
, J.
Ding
, F.
Tian
, Q.
Xu
, and J.
Zhao
, “Chemical environment and magnetic moment effects on point defect formations in CoCrNi-based concentrated solid-solution alloys
,” Acta Mater.
187
, 122
–134
(2020
). 28.
Q.
Liu
, S.
Xia
, Y.
Su
, J.
Huang
, S.
Zhao
, F.
Luo
, H.
Liu
, W.
Ge
, J.
Xue
, C.
Wang
, and Y.
Wang
, “Enhanced recombination suppresses the void swelling in bcc multi-component alloys
,” Materialia
20
, 101234
(2021
). 29.
O.
Deluigi
, R.
Pasianot
, F.
Valencia
, A.
Caro
, D.
Farkas
, and E.
Bringa
, “Simulations of primary damage in a high entropy alloy: Probing enhanced radiation resistance
,” Acta Mater.
213
, 116951
(2021
). 30.
S.
Zhao
, “Role of chemical disorder and local ordering on defect evolution in high-entropy alloys
,” Phys. Rev. Mater.
5
, 103604
(2021
). 31.
B.
Xing
, X.
Wang
, W. J.
Bowman
, and P.
Cao
, “Short-range order localizing diffusion in multi-principal element alloys
,” Scr. Mater.
210
, 114450
(2022
). 32.
O. N.
Senkov
, D. B.
Miracle
, K. J.
Chaput
, and J.-P.
Couzinie
, “Development and exploration of refractory high entropy alloys a review
,” J. Mater. Res.
33
, 3092
–3128
(2018
). 33.
C.
Liu
, W.
Lu
, W.
Xia
, C.
Du
, Z.
Rao
, J. P.
Best
, S.
Brinckmann
, J.
Lu
, B.
Gault
, G.
Dehm
et al., “Massive interstitial solid solution alloys achieve near-theoretical strength
,” Nat. Commun.
13
, 1102
(2022
).34.
G.
Was
, D.
Petti
, S.
Ukai
, and S.
Zinkle
, “Materials for future nuclear energy systems
,” J. Nucl. Mater.
527
, 151837
(2019
). 35.
T.
Shi
, P.-H.
Lei
, X.
Yan
, J.
Li
, Y.-D.
Zhou
, Y.-P.
Wang
, Z.-X.
Su
, Y.-K.
Dou
, X.-F.
He
, D.
Yun
, W.
Yang
, and C.
Lu
, “Current development of body-centered cubic high-entropy alloys for nuclear applications
,” Tungsten
3
, 197
–217
(2021
). 36.
D.
King
, S.
Cheung
, S. A.
Humphry-Baker
, C.
Parkin
, A.
Couet
, M.
Cortie
, G.
Lumpkin
, S.
Middleburgh
, and A. J.
Knowles
, “High temperature, low neutron cross-section high-entropy alloys in the Nb-Ti-V-Zr system
,” Acta Mater.
166
, 435
–446
(2019
). 37.
T.
Shi
, Z.
Su
, J.
Li
, C.
Liu
, J.
Yang
, X.
He
, D.
Yun
, Q.
Peng
, and C.
Lu
, “Distinct point defect behaviours in body-centered cubic medium-entropy alloy NbZrTi induced by severe lattice distortion
,” Acta Mater.
229
, 117806
(2022
). 38.
O.
El-Atwani
, N.
Li
, M.
Li
, A.
Devaraj
, J.
Baldwin
, M. M.
Schneider
, D.
Sobieraj
, J. S.
Wróbel
, D.
Nguyen-Manh
, S. A.
Maloy
, and E.
Martinez
et al., “Outstanding radiation resistance of tungsten-based high-entropy alloys
,” Sci. Adv.
5
, eaav2002
(2019
). 39.
O.
Senkov
, S.
Rao
, K.
Chaput
, and C.
Woodward
, “Compositional effect on microstructure and properties of NbTiZr-based complex concentrated alloys
,” Acta Mater.
151
, 201
–215
(2018
). 40.
Y.
Wu
, Y.
Cai
, X.
Chen
, T.
Wang
, J.
Si
, L.
Wang
, Y.
Wang
, and X.
Hui
, “Phase composition and solid solution strengthening effect in TiZrNbMoV high-entropy alloys
,” Mater. Des.
83
, 651
–660
(2015
). 41.
P. E.
Blöchl
, “Projector augmented-wave method
,” Phys. Rev. B
50
, 17953
(1994
).42.
M.
Ernzerhof
and G. E.
Scuseria
, “Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional
,” J. Chem. Phys.
110
, 5029
–5036
(1999
). 43.
Z.
Su
, T.
Shi
, J.
Yang
, H.
Shen
, Z.
Li
, S.
Wang
, G.
Ran
, and C.
Lu
, “The effect of interstitial carbon atoms on defect evolution in high entropy alloys under helium irradiation
,” Acta Mater.
233
, 117955
(2022
). 44.
A.
Tamm
, A.
Aabloo
, M.
Klintenberg
, M.
Stocks
, and A.
Caro
, “Atomic-scale properties of Ni-based FCC ternary, and quaternary alloys
,” Acta Mater.
99
, 307
–312
(2015
). 45.
W. K.
Hastings
, “Monte carlo sampling methods using Markov chains and their applications
,” Biometrika
57
, 97
–109
(1970
).46.
S.
Zhao
, “Local ordering tendency in body-centered cubic (BCC) multi-principal element alloys
,” J. Phase Equilib. Diffus.
42
, 578
–591
(2021
).47.
B.
Widom
, “Some topics in the theory of fluids
,” J. Chem. Phys.
39
, 2808
–2812
(1963
). 48.
G.
Henkelman
, B. P.
Uberuaga
, and H.
Jónsson
, “A climbing image nudged elastic band method for finding saddle points and minimum energy paths
,” J. Chem. Phys.
113
, 9901
–9904
(2000
). 49.
A.
Zunger
, S.-H.
Wei
, L.
Ferreira
, and J. E.
Bernard
, “Special quasirandom structures
,” Phys. Rev. Lett.
65
, 353
(1990
). 50.
N.
Anento
, A.
Serra
, and Y. N.
Osetsky
, “Atomistic study of multimechanism diffusion by self-interstitial defects in -Fe
,” Modell. Simul. Mater. Sci. Eng.
18
, 025008
(2010
). 51.
W.
Tang
, E.
Sanville
, and G.
Henkelman
, “A grid-based Bader analysis algorithm without lattice bias
,” J. Phys.: Condens. Matter
21
, 084204
(2009
).52.
A.
Stukowski
, “Visualization and analysis of atomistic simulation data with OVITO—The open visualization tool
,” Modell. Simul. Mater. Sci. Eng.
18
, 015012
(2009
). 53.
S. P.
Ong
, W. D.
Richards
, A.
Jain
, G.
Hautier
, M.
Kocher
, S.
Cholia
, D.
Gunter
, V. L.
Chevrier
, K. A.
Persson
, and G.
Ceder
, “Python Materials Genomics (pymatgen): A robust, open-source Python library for materials analysis
,” Comput. Mater. Sci.
68
, 314
–319
(2013
). 54.
S.
Ishibashi
, Y.
Ikeda
, F.
Körmann
, B.
Grabowski
, and J.
Neugebauer
, “Correlation analysis of strongly fluctuating atomic volumes, charges, and stresses in body-centered cubic refractory high-entropy alloys
,” Phys. Rev. Mater.
4
, 023608
(2020
). 55.
Y.
Ikeda
, K.
Gubaev
, J.
Neugebauer
, B.
Grabowski
, and F.
Körmann
, “Chemically induced local lattice distortions versus structural phase transformations in compositionally complex alloys
,” npj Comput. Mater.
7
, 1
–8
(2021
). 56.
J.
Cowley
, “An approximate theory of order in alloys
,” Phys. Rev.
77
, 669
(1950
). 57.
A.
Takeuchi
and A.
Inoue
, “Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element
,” Mater. Trans.
46
, 2817
–2829
(2005
). 58.
Y.
Ikeda
, A.
Carreras
, A.
Seko
, A.
Togo
, and I.
Tanaka
, “Mode decomposition based on crystallographic symmetry in the band-unfolding method
,” Phys. Rev. B
95
, 024305
(2017
). 59.
F.
Körmann
, Y.
Ikeda
, B.
Grabowski
, and M. H.
Sluiter
, “Phonon broadening in high entropy alloys
,” npj Comput. Mater.
3
, 36
(2017
).60.
G. D.
Samolyuk
, Y.
Osetsky
, G. M.
Stocks
, and J.
Morris
, “Role of static displacements in stabilizing body centered cubic high entropy alloys
,” Phys. Rev. Lett.
126
, 025501
(2021
). 61.
H. S.
Oh
, S. J.
Kim
, K.
Odbadrakh
, W. H.
Ryu
, K. N.
Yoon
, S.
Mu
, F.
Körmann
, Y.
Ikeda
, C. C.
Tasan
, D.
Raabe
, T.
Egami
, and E. S.
Park
, “Engineering atomic-level complexity in high-entropy and complex concentrated alloys
,” Nat. Commun.
10
, 2090
(2019
).62.
J.
Hou
, Y.-W.
You
, X.-S.
Kong
, J.
Song
, and C.
Liu
, “Accurate prediction of vacancy cluster structures and energetics in BCC transition metals
,” Acta Mater.
211
, 116860
(2021
). 63.
T.
Shi
, X.
Qiu
, Y.
Zhou
, S.
Lyu
, J.
Li
, D.
Sun
, Q.
Peng
, Y.
Xin
, and C.
Lu
, “Unconventional energetics of small vacancy clusters in BCC high-entropy alloy Nb0.75ZrTiV0.5
,” J. Mater. Sci. Technol.
146
, 61
–71
(2023
). 64.
S.
Golubov
, B.
Singh
, and H.
Trinkaus
, “Defect accumulation in fcc and bcc metals and alloys under cascade damage conditions—Towards a generalisation of the production bias model
,” J. Nucl. Mater.
276
, 78
–89
(2000
). 65.
L.
Koch
, F.
Granberg
, T.
Brink
, D.
Utt
, K.
Albe
, F.
Djurabekova
, and K.
Nordlund
, “Local segregation versus irradiation effects in high-entropy alloys: Steady-state conditions in a driven system
,” J. Appl. Phys.
122
, 105106
(2017
). 66.
G. S.
Was
, Fundamentals of Radiation Materials Science: Metals and Alloys
(Springer
, 2016
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
