Abstract
Detailed comparative molecular dynamics simulations of the diffusion process in a model quinary equiatomic FeNiCrCoCu FCC alloy are presented. Vacancy-assisted diffusion is studied by a statistical technique obtaining distributions of vacancy formation and migration energy values. In addition, vacancy migration is simulated using molecular dynamics at high temperatures and monitoring mean square displacements over time. To assess the role of compositional complexity, the results are compared to corresponding simulations in each of the pure individual components of the alloy as well as the corresponding “average atom” potential, with similar properties to the alloy but no compositional randomness. The comparison shows that the diffusion kinetics in the random alloy is not slower than in the average atom material or the average of the components, indicating that compositional fluctuations do not always result in “sluggish” diffusion. The results are compared with experimental data for self-diffusion in similar high-entropy alloys.
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B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications. Science 345(6201), 1153–1158 (2014)
Y. Ye, Q. Wang, J. Lu, C. Liu, Y. Yang, High-entropy alloy: challenges and prospects. Mater. Today 19(6), 349–362 (2016)
E. Pickering, N. Jones, High-entropy alloys: a critical assessment of their founding principles and future prospects. Int. Mater. Rev. 61(3), 183–202 (2016)
G.D. Sathiaraj, P.P. Bhattacharjee, Effect of cold-rolling strain on the evolution of annealing texture of equiatomic CoCrFeMnNi high entropy alloy. Mater. Charact. 109, 189–197 (2015)
C.W. Tsai, Y.L. Chen, M.H. Tsai, J.W. Yeh, T.T. Shun, S.K. Chen, Deformation and annealing behaviors of high-entropy alloy Al05CoCrCuFeNi. J. Alloys Compd. 486(1–2), 427–435 (2009)
T. Butler, J. Alfano, R. Martens, M. Weaver, High-temperature oxidation behavior of Al–Co–Cr–Ni–(Fe or Si) multicomponent high-entropy alloys. JOM 67(1), 246–259 (2015)
D.H. Lee, M.Y. Seok, Y. Zhao, I.C. Choi, J. He, Z. Lu, J.Y. Suh, U. Ramamurty, M. Kawasaki, T.G. Langdon, Spherical nanoindentation creep behavior of nanocrystalline and coarse-grained CoCrFeMnNi high-entropy alloys. Acta Mater. 109, 314–322 (2016)
K.Y. Tsai, M.H. Tsai, J.W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys. Acta Mater. 61(13), 4887–4897 (2013)
S.V. Divinski, A.V. Pokoev, N. Esakkiraja, A. Paul, A mystery of" sluggish diffusion" in high-entropy alloys: the truth or a myth? (Trans Tech Publ, Diffusion Foundations, 2018), pp. 69–104
J. Dąbrowa, M. Danielewski, State-of-the-art diffusion studies in the high entropy alloys. Metals 10(3), 347 (2020)
J. Dąbrowa, M. Zajusz, W. Kucza, G. Cieślak, K. Berent, T. Czeppe, T. Kulik, M. Danielewski, Demystifying the sluggish diffusion effect in high entropy alloys. J. Alloy. Compd. 783, 193–207 (2019)
J. Dąbrowa, W. Kucza, G. Cieślak, T. Kulik, M. Danielewski, J.-W. Yeh, Interdiffusion in the FCC-structured Al–Co–Cr–Fe–Ni high entropy alloys: experimental studies and numerical simulations. J. Alloy. Compd. 674, 455–462 (2016)
M. Vaidya, S. Trubel, B. Murty, G. Wilde, S.V. Divinski, Ni tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Alloy. Compd. 688, 994–1001 (2016)
M. Vaidya, K. Pradeep, B. Murty, G. Wilde, S. Divinski, Radioactive isotopes reveal a non sluggish kinetics of grain boundary diffusion in high entropy alloys. Sci. Rep. 7(1), 1–11 (2017)
V. Verma, A. Tripathi, K.N. Kulkarni, On interdiffusion in FeNiCoCrMn high entropy alloy. J. Phase Equilib. Diffus. 38(4), 445–456 (2017)
C. Zhang, F. Zhang, K. Jin, H. Bei, S. Chen, W. Cao, J. Zhu, D. Lv, Understanding of the elemental diffusion behavior in concentrated solid solution alloys. J. Phase Equilib. Diffus. 38(4), 434–444 (2017)
M. Vaidya, K. Pradeep, B. Murty, G. Wilde, S. Divinski, Bulk tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. Acta Mater. 146, 211–224 (2018)
D. Gaertner, J. Kottke, G. Wilde, S.V. Divinski, Y. Chumlyakov, Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Mater. Res. 33(19), 3184–3191 (2018)
J. Kottke, M. Laurent-Brocq, A. Fareed, D. Gaertner, L. Perrière, Ł Rogal, S.V. Divinski, G. Wilde, Tracer diffusion in the Ni–CoCrFeMn system: Transition from a dilute solid solution to a high entropy alloy. Scripta Mater. 159, 94–98 (2019)
J. Kottke, D. Utt, M. Laurent Brocq, A. Fareed, D. Gaertner, L. Perrière, Ł Rogal, A. Stukowski, K. Albe, S.V. Divinski, Experimental and theoretical study of tracer diffusion in a series of (CoCrFeMn)100−xNix alloys. Acta Mater. 194, 236–248 (2020)
W. Chen, L. Zhang, High-throughput determination of interdiffusion coefficients for Co–Cr–Fe–Mn–Ni high-entropy alloys. J. Phase Equilib. Diffus. 38(4), 457–465 (2017)
Q. Li, W. Chen, J. Zhong, L. Zhang, Q. Chen, Z.-K. Liu, On sluggish diffusion in fcc Al–Co–Cr–Fe–Ni high-entropy alloys: an experimental and numerical study. Metals 8(1), 16 (2018)
R. Wang, W. Chen, J. Zhong, L. Zhang, Experimental and numerical studies on the sluggish diffusion in face centered cubic Co–Cr–Cu–Fe–Ni high-entropy alloys. J. Mater. Sci. Technol. 34(10), 1791–1798 (2018)
S.Y. Chen, Q. Li, J. Zhong, F.Z. Xing, L.J. Zhang, On diffusion behaviors in face centered cubic phase of Al–Co–Cr–Fe–Ni–Ti high-entropy superalloys. J. Alloy. Compd. 791, 255–264 (2019)
D. Beke, G. Erdélyi, On the diffusion in high-entropy alloys. Mater. Lett. 164, 111–113 (2016)
W. Kucza, J. Dabrowa, G. Cieslak, K. Berent, T. Kulik, M. Danielewski, Studies of “sluggish diffusion” effect in Co–Cr–Fe–Mn–Ni, Co–Cr–Fe–Ni and Co–Fe–Mn–Ni high entropy alloys; determination of tracer diffusivities by combinatorial approach. J. Alloy. Compd. 731, 920–928 (2018)
K. Jin, C. Zhang, F. Zhang, H.B. Bei, Influence of compositional complexity on interdiffusion in Ni-containing concentrated solid-solution alloys. Mater. Res. Lett. 6(5), 293–299 (2018)
A. Mehta, Y. Sohn, High entropy and sluggish diffusion “core” effects in senary FCC Al–Co–Cr–Fe–Ni–Mn alloys. ACS Comb. Sci. 22(12), 757–767 (2020)
A. Mehta, Y. Sohn, Investigation of sluggish diffusion in FCC Al0.25CoCrFeNi high-entropy alloy. Mater. Res. Lett. 9(5), 239–246 (2021)
J. Dabrowa, M. Danielewski, State-of-the-art diffusion studies in the high entropy alloys. Metals 10(3), 1–8 (2020)
Y.N. Osetsky, L.K. Beland, A.V. Barashev, Y.W. Zhang, On the existence and origin of sluggish diffusion in chemically disordered concentrated alloys. Curr. Opin. Solid State Mater. Sci. 22(3), 65–74 (2018)
M.S. Daw, M. Chandross, Sluggish diffusion in random equimolar FCC alloys. Phys. Rev. Mater. 5(4), 043603 (2021)
J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv. Eng. Mater. 6(5), 299–303 (2004)
C. Varvenne, A. Luque, W.A. Curtin, Average-atom interatomic potential for random alloys. Phys. Rev. B 93, 104201 (2016)
M.S. Daw, M.I. Baskes, Embedded-atom method - derivation and application to impurities surfaces, and other defects in metals. Phys. Rev. B 29(12), 6443–6453 (1984)
D. Farkas, A. Caro, Model interatomic potentials and lattice strain in a high-entropy alloy. J. Mater. Res. 33(19), 3218–3225 (2018)
S. Guo, Q. Hu, C. Ng, C.T. Liu, More than entropy in high-entropy alloys: Forming solid solutions or amorphous phase. Intermetallics 41, 96–103 (2013)
Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys. Rev. B 59(5), 3393–3407 (1999)
G.J. Ackland, V. Vitek, Many-body potentials and atomic-scale relaxations in noble-metal alloys. Phys. Rev. B 41(15), 10324–10333 (1990)
G. Bonny, R.C. Pasianot, L. Malerba, Fitting interatomic potentials consistent with thermodynamics: Fe Cu, Ni and their alloys. Philos. Mag. 89(34–36), 3451–3464 (2009)
D. Terentyev, G. Bonny, C. Domain, R.C. Pasianot, Interaction of a ½ <111> screw dislocation with Cr precipitates in bcc Fe studied by molecular dynamics. Phys. Rev. B 81(21), 1–8 (2010)
G. Bonny, R.C. Pasianot, Gauge transformations to combine multi-component many-body interatomic potentials. Philos. Mag. Lett. 90(8), 559–563 (2010)
G. Bonny, D. Terentyev, R.C. Pasianot, S. Ponce, A. Bakaev, Interatomic potential to study plasticity in stainless steels: the FeNiCr model alloy. Modell. Simul. Mater. Sci. Eng. 19(8), 085008 (2011)
W.G. Nöhring, W.A. Curtin, Thermodynamic properties of average-atom interatomic potentials for alloys. Modell. Simul. Mater. Sci. Eng. 24(4), 045017 (2016)
S. Plimpton, Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117(1), 1–19 (1995)
G. Henkelman, H. Jónsson, Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 113(22), 9978–9985 (2000)
W.G. Hoover, Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31(3), 1695–1697 (1985)
M.I. Mendelev, Y. Mishin, Molecular dynamics study of self-diffusion in bcc Fe. Phys. Rev. B 80(14), 144111 (2009)
G. Neumann, C. Tuijn, Self-diffusion and impurity diffusion in pure metals: handbook of experimental data (Elsevier, Amsterdam, 2011)
S. Rothman, L. Nowicki, G. Murch, Self-diffusion in austenitic Fe–Cr–Ni alloys. J. Phys. F 10(3), 383 (1980)
D.B. Butrymowicz, J.R. Manning, M.E. Read, Diffusion in copper and copper alloys. Part I. volume and surface self-diffusion in copper. J. Phys. Chem. Ref. Data 2(3), 643–656 (1973)
G.D. Lorenzi, F. Ercolessi, Multiple jumps and vacancy diffusion in a face-centered-cubic metal. Europhys. Lett. (EPL) 20(4), 349–355 (1992)
I. Belova, G. Murch, Computer simulation of solute-enhanced diffusion kinetics in dilute fcc alloys. Philos. Mag. 83, 377–392 (2003)
F. Faupel, D. Hentrich, J. Kluin, J. Wolff, A. Sager, T. Hehenkamp, Diffusion and vacancy impurity interaction in dilute fcc alloys, defect and diffusion. Forum 66–69, 573–580 (1990)
S. Divinski, O. Lukianova, G. Wilde, A. Dash, N. Esakkiraja, A. Paul, High-entropy alloys: diffusion. Encycl. Mater. (2020). https://doi.org/10.1016/B978-0-12-819726-4.11771-5
M.J. Mehl, D.A. Papaconstantopoulos, Applications of a tight-binding total-energy method for transition and noble metals: Elastic constants, vacancies, and surfaces of monatomic metals. Phys. Rev. B 54(7), 4519 (1996)
Y. Gong, B. Grabowski, A. Glensk, F. Körmann, J. Neugebauer, R.C. Reed, Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni. Phys. Rev. B 97(21), 214106 (2018)
W. Chen, X. Ding, Y. Feng, X. Liu, K. Liu, Z. Lu, D. Li, Y. Li, C. Liu, X.-Q. Chen, Vacancy formation enthalpies of high-entropy FeCoCrNi alloy via first-principles calculations and possible implications to its superior radiation tolerance. J. Mater. Sci. Technol. 34(2), 355–364 (2018)
T. Angsten, T. Mayeshiba, H. Wu, D. Morgan, Elemental vacancy diffusion database from high-throughput first-principles calculations for fcc and hcp structures. New J. Phys. 16(1), 015018 (2014)
A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Modell. Simul. Mater. Sci. Eng. 18(1), 015012 (2009)
Y. Osetsky, A.V. Barashev, Y. Zhang, Sluggish, chemical bias and percolation phenomena in atomic transport by vacancy and interstitial diffusion in NiFe alloys. Current Opin. Solid State Mater. Sci. 25(6), 100961 (2021)
Y.-Z. Wang, Y.-J. Wang, Disentangling diffusion heterogeneity in high-entropy alloys. Acta Mater. 224, 117527 (2022)
S.L. Thomas, S. Patala, Vacancy diffusion in multi-principal element alloys: The role of chemical disorder in the ordered lattice. Acta Mater. 196, 144–153 (2020)
Acknowledgments
The authors acknowledge Advanced Research Computing at Virginia Tech for providing computational resources and technical support that have contributed to the results reported within this paper. URL: https://arc.vt.edu/. AS acknowledges the support from Virginia Tech’s Institute of Critical Technologies and Applied Sciences Doctoral Scholars Program. DF acknowledges support from the National Science Foundation, Grant 1507846. XMB acknowledges the support from the National Science Foundation under Grant No. 1847780.
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Seoane, A., Farkas, D. & Bai, XM. Influence of compositional complexity on species diffusion behavior in high-entropy solid-solution alloys. Journal of Materials Research 37, 1403–1415 (2022). https://doi.org/10.1557/s43578-022-00545-x
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DOI: https://doi.org/10.1557/s43578-022-00545-x