Journal Home > Online First

Multi-edge extended X-ray absorption fine structure (EXAFS) spectroscopy combined with reverse Monte Carlo (RMC) simulations was used to probe the details of element-specific local coordinations and component-dependent structure relaxations in single crystalline equiatomic CrMnFeCoNi high-entropy alloy as a function of the annealing temperature. Two representative states, namely a high-temperature state, created by annealing at 1373 K, and a low-temperature state, produced by long-term annealing at 993 K, were compared in detail. Specific features identified in atomic configurations of particular principal components indicate variations in the local environment distortions connected to different degrees of compositional disorder at the chosen representative temperatures. The detected changes provide new atomistic insights and correlate with the existence of kinks previously observed in the Arrhenius dependencies of component diffusion rates in the CrMnFeCoNi high-entropy alloy.


menu
Abstract
Full text
Outline
About this article

Anomalies in the short-range local environment and atomic diffusion in single crystalline equiatomic CrMnFeCoNi high-entropy alloy

Show Author's information Alevtina Smekhova1( )Daniel Gaertner2Alexei Kuzmin3Ana Guilherme Buzanich4Goetz Schuck1Ivo Zizak1Gerhard Wilde2Kirill V. Yusenko4Sergiy Divinski2( )
Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), D-12489 Berlin, Germany
Institute of Materials Physics, University of Münster, D-48149 Münster, Germany
Institute of Solid State Physics, University of Latvia, LV-1063 Riga, Latvia
Bundesanstalt für Materialforschung und – prüfung (BAM), D-12489 Berlin, Germany

Abstract

Multi-edge extended X-ray absorption fine structure (EXAFS) spectroscopy combined with reverse Monte Carlo (RMC) simulations was used to probe the details of element-specific local coordinations and component-dependent structure relaxations in single crystalline equiatomic CrMnFeCoNi high-entropy alloy as a function of the annealing temperature. Two representative states, namely a high-temperature state, created by annealing at 1373 K, and a low-temperature state, produced by long-term annealing at 993 K, were compared in detail. Specific features identified in atomic configurations of particular principal components indicate variations in the local environment distortions connected to different degrees of compositional disorder at the chosen representative temperatures. The detected changes provide new atomistic insights and correlate with the existence of kinks previously observed in the Arrhenius dependencies of component diffusion rates in the CrMnFeCoNi high-entropy alloy.

Keywords: diffusion, high-entropy alloys, reverse Monte Carlo, extended X-ray absorption fine structure (EXAFS), short-range order

References(93)

[1]

Cantor, B.; Chang, I. T. H.; Knight, P.; Vincent, A. J. B. Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng. A 2004, 375–377, 213–218

[2]

Yeh, J. W.; Chen, S. K.; Lin, S. J.; Gan, J. Y.; Chin, T. S.; Shun, T. T.; Tsau, C. H.; Chang, S. Y. Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater. 2004, 6, 299–303.

[3]

Kao, Y. F.; Chen, S. K.; Sheu, J. H.; Lin, J. T.; Lin, W. E.; Yeh, J. W.; Lin, S. J.; Liou, T. H.; Wang, C. W. Hydrogen storage properties of multi-principal-component CoFeMnTi x V y Zr z alloys. Int. J. Hyd. Energy 2010, 35, 9046–9059.

[4]

Zaddach, A. J.; Niu, C.; Koch, C. C.; Irving, D. L. Mechanical properties and stacking fault energies of NiFeCrCoMn high-entropy alloy. JOM 2013, 65, 1780–1789.

[5]

Gludovatz, B.; Hohenwarter, A.; Catoor, D.; Chang, E. H.; George, E. P.; Ritchie, R. O. A fracture-resistant high-entropy alloy for cryogenic applications. Science 2014, 345, 1153–1158.

[6]

Schuh, B.; Mendez-Martin, F.; Völker, B.; George, E. P.; Clemens, H.; Pippan, R.; Hohenwarter, A. Mechanical properties, microstructure and thermal stability of a nanocrystalline CoCrFeMnNi high-entropy alloy after severe plastic deformation. Acta Mater. 2015, 96, 258–268.

[7]

Huang, S.; Li, W.; Lu, S.; Tian, F. Y.; Shen, J.; Holmström, E.; Vitos, L. Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy. Scr. Mater. 2015, 108, 44–47.

[8]

Varvenne, C.; Luque, A.; Curtin, W. A. Theory of strengthening in fcc high entropy alloys. Acta Mater. 2016, 118, 164–176.

[9]

Sahlberg, M.; Karlsson, D.; Zlotea, C.; Jansson, U. Superior hydrogen storage in high entropy alloys. Sci. Rep. 2016, 6, 36770.

[10]

Wang, B. F.; Fu, A.; Huang, X. X.; Liu, B.; Liu, Y.; Li, Z. Z.; Zan, X. Mechanical properties and microstructure of the CoCrFeMnNi high entropy alloy under high strain rate compression. J. Mater. Eng. Perform. 2016, 25, 2985–2992.

[11]

Zhang, Y. W.; Zhao, S. J.; Weber, W. J.; Nordlund, K.; Granberg, F.; Djurabekova, F. Atomic-level heterogeneity and defect dynamics in concentrated solid-solution alloys. Curr. Opin. Solid State Mater. Sci. 2017, 21, 221–237.

[12]

Ahmad, A. S.; Su, Y.; Liu, S. Y.; Ståhl, K.; Wu, Y. D.; Hui, X. D.; Ruett, U.; Gutowski, O.; Glazyrin, K.; Liermann, H. P. et al. Structural stability of high entropy alloys under pressure and temperature. J. Appl. Phys. 2017, 121, 235901.

[13]

Luo, H.; Li, Z. M.; Mingers, A. M.; Raabe, D. Corrosion behavior of an equiatomic CoCrFeMnNi high-entropy alloy compared with 304 stainless steel in sulfuric acid solution. Corros. Sci. 2018, 134, 131–139.

[14]

Shi, Y. Z.; Collins, L.; Feng, R.; Zhang, C.; Balke, N.; Liaw, P. K.; Yang, B. Homogenization of Al x CoCrFeNi high-entropy alloys with improved corrosion resistance. Corros. Sci. 2018, 133, 120–131.

[15]

Löffler, T.; Meyer, H.; Savan, A.; Wilde, P.; Garzón Manjón, A.; Chen, Y. T.; Ventosa, E.; Scheu, C.; Ludwig, A.; Schuhmann, W. Discovery of a multinary noble metal-free oxygen reduction catalyst. Adv. Energy Mater. 2018, 8, 1802269.

[16]

Kong, K.; Hyun, J.; Kim, Y.; Kim, W.; Kim, D. Nanoporous structure synthesized by selective phase dissolution of AlCoCrFeNi high entropy alloy and its electrochemical properties as supercapacitor electrode. J. Power Sources 2019, 437, 226927.

[17]

Xu, X.; Du, Y. K.; Wang, C. H.; Guo, Y.; Zou, J. W.; Zhou, K.; Zeng, Z.; Liu, Y. Y.; Li, L. Q. High-entropy alloy nanoparticles on aligned electronspun carbon nanofibers for supercapacitors. J. Alloys Compd. 2020, 822, 153642.

[18]

Fang, G.; Gao, J. J.; Lv, J.; Jia, H. L.; Li, H. L.; Liu, W. H.; Xie, G. Q.; Chen, Z. H.; Huang, Y.; Yuan, Q. H. et al. Multi-component nanoporous alloy/(oxy)hydroxide for bifunctional oxygen electrocatalysis and rechargeable Zn-air batteries. Appl. Catal. B: Environ. 2020, 268, 118431.

[19]

Pedersen, J. K.; Batchelor, T. A. A.; Bagger, A.; Rossmeisl, J. High-entropy alloys as catalysts for the CO2 and CO reduction reactions. ACS Catal. 2020, 10, 2169–2176.

[20]

Yao, Y. G.; Huang, Z. N.; Li, T. Y.; Wang, H.; Liu, Y. F.; Stein, H. S.; Mao, Y. M.; Gao, J. L.; Jiao, M. L.; Dong, Q. et al. High-throughput, combinatorial synthesis of multimetallic nanoclusters. Proc. Natl. Acad. Sci. USA 2020, 117, 6316–6322.

[21]

Pickering, E. J.; Carruthers, A. W.; Barron, P. J.; Middleburgh, S. C.; Armstrong, D. E. J.; Gandy, A. S. High-entropy alloys for advanced nuclear applications. Entropy 2021, 23, 98.

[22]

Zhu, M.; Zhao, B. Z.; Yuan, Y. F.; Guo, S. Y.; Wei, G. Y. Study on corrosion behavior and mechanism of CoCrFeMnNi HEA interfered by AC current in simulated alkaline soil environment. J. Electroanal. Chem. 2021, 882, 115026.

[23]

Ma, Y. J.; Ma, Y.; Wang, Q. S.; Schweidler, S.; Botros, M.; Fu, T. T.; Hahn, H.; Brezesinski, T.; Breitung, B. High-entropy energy materials: Challenges and new opportunities. Energy Environ. Sci. 2021, 14, 2883–2905.

[24]

Guo, S.; Ng, C.; Lu, J.; Liu, C. T. Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. J. Appl. Phys. 2011, 109, 103505.

[25]

Čižek, L.; Kratochvíl, P.; Smola, B. Solid solution hardening of copper crystals. J. Mater. Sci. 1974, 9, 1517–1520.

[26]

Gypen, L. A.; Deruyttere, A. Multi-component solid solution hardening. J. Mater. Sci. 1977, 12, 1028–1033.

[27]

Ma, D. C.; Grabowski, B.; Körmann, F.; Neugebauer, J.; Raabe, D. Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one. Acta Mater. 2015, 100, 90–97

[28]

Okamoto, N. L.; Yuge, K.; Tanaka, K.; Inui, H.; George, E. P. Atomic displacement in the CrMnFeCoNi high-entropy alloy-A scaling factor to predict solid solution strengthening. AIP Adv. 2016, 6, 125008.

[29]
Tong, Y.; Velisa, G.; Yang, T.; Jin, K.; Lu, C.; Bei, H.; Ko, J. Y. P.; Pagan, D. C.; Huang, R.; Zhang, Y. et al. Probing local lattice distortion in medium- and high-entropy alloys. 2017, arXiv: 1707.07745. arXiv.org e-Print archive. https://doi.org/10.48550/arXiv.1707.077459 (accessed Apr 1, 2022).
[30]

Zhang, F. X.; Tong, Y.; Jin, K.; Bei, H. B.; Weber, W. J.; Huq, A.; Lanzirotti, A.; Newville, M.; Pagan, D. C.; Ko, J. Y. P. et al. Chemical complexity induced local structural distortion in NiCoFeMnCr high-entropy alloy. Mater. Res. Lett. 2018, 6, 450–455.

[31]

Ding, Q. Q.; Zhang, Y.; Chen, X.; Fu, X. Q.; Chen, D. K.; Chen, S. J.; Gu, L.; Wei, F.; Bei, H. B.; Gao, Y. F. et al. Tuning element distribution, structure and properties by composition in high-entropy alloys. Nature 2019, 574, 223–227.

[32]

Cantor, B. Multicomponent high-entropy Cantor alloys. Prog. Mater. Sci. 2021, 120, 100754.

[33]

Oh, H. S.; Odbadrakh, K.; Ikeda, Y.; Mu, S.; Körmann, F.; Sun, C. J.; Ahn, H. S.; Yoon, K. N.; Ma, D. C.; Tasan, C. C. et al. Element-resolved local lattice distortion in complex concentrated alloys: An observable signature of electronic effects. Acta Mater. 2021, 216, 117135.

[34]

Billington, D.; James, A. D. N.; Harris-Lee, E. I.; Lagos, D. A.; O’Neill, D.; Tsuda, N.; Toyoki, K.; Kotani, Y.; Nakamura, T.; Bei, H. et al. Bulk and element-specific magnetism of medium-entropy and high-entropy Cantor–Wu alloys. Phys. Rev. B 2020, 102, 174405.

[35]

Smekhova, A.; Kuzmin, A.; Siemensmeyer, K.; Luo, C.; Chen, K.; Radu, F.; Weschke, E.; Reinholz, U.; Buzanich, A. G.; Yusenko, K. V. Al-driven peculiarities of local coordination and magnetic properties in single-phase Al x -CrFeCoNi high-entropy alloys. Nano Res. 2022, 15, 4845–4858.

[36]

Smekhova, A.; Kuzmin, A.; Siemensmeyer, K.; Luo, C.; Taylor, J.; Thakur, S.; Radu, F.; Weschke, E.; Buzanich, A. G.; Xiao, B. et al. Local structure and magnetic properties of a nanocrystalline Mn-rich Cantor alloy thin film down to the atomic scale. Nano Res. 2023, 16, 5626–5639.

[37]

Oh, H. S.; Ma, D. C.; Leyson, G. P.; Grabowski, B.; Park, E. S.; Körmann, F.; Raabe, D. Lattice distortions in the FeCoNiCrMn high entropy alloy studied by theory and experiment. Entropy 2016, 18, 321.

[38]

Smekhova, A.; Kuzmin, A.; Siemensmeyer, K.; Abrudan, R.; Reinholz, U.; Buzanich, A. G.; Schneider, M.; Laplanche, G.; Yusenko, K. V. Inner relaxations in equiatomic single-phase high-entropy Cantor alloy. J. Alloys Compd. 2022, 920, 165999.

[39]

Wilson, J. A.; Moore, C.; Goddard, D. T.; Middleburgh, S. C. Assessing the high concentration of vacancies in refractory high entropy alloys. Materialia 2023, 28, 101764.

[40]

Zhang, R. P.; Zhao, S. T.; Ding, J.; Chong, Y.; Jia, T.; Ophus, C.; Asta, M.; Ritchie, R. O.; Minor, A. M. Short-range order and its impact on the CrCoNi medium-entropy alloy. Nature 2020, 581, 283–287.

[41]

He, Q. F.; Tang, P. H.; Chen, H. A.; Lan, S.; Wang, J. G.; Luan, J. H.; Du, M.; Liu, Y.; Liu, C. T.; Pao, C. W. et al. Understanding chemical short-range ordering/demixing coupled with lattice distortion in solid solution high entropy alloys. Acta Mater. 2021, 216, 117140.

[42]

Bracq, G.; Laurent-Brocq, M.; Perrière, L.; Pirès, R.; Joubert, J. M.; Guillot, I. The fcc solid solution stability in the Co-Cr-Fe-Mn-Ni multi-component system. Acta Mater. 2017, 128, 327–336.

[43]

Otto, F.; Dlouhý, A.; Pradeep, K. G.; Kuběnová, M.; Raabe, D.; Eggeler, G.; George, E. P. Decomposition of the single-phase high-entropy alloy CrMnFeCoNi after prolonged anneals at intermediate temperatures. Acta Mater. 2016, 112, 40–52.

[44]

Tsai, K. Y.; Tsai, M. H.; Yeh, J. W. Sluggish diffusion in Co-Cr-Fe-Mn-Ni high-entropy alloys. Acta Mater. 2013, 61, 4887–4897.

[45]

Dash, A.; Paul, A.; Sen, S.; Divinski, S.; Kundin, J.; Steinbach, I.; Grabowski, B.; Zhang, X. Recent advances in understanding diffusion in multiprincipal element systems. Ann. Rev. Mater. Res. 2022, 52, 383–409.

[46]

Vaidya, M.; Trubel, S.; Murty, B. S.; Wilde, G.; Divinski, S. V. Ni tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Alloys Compd. 2016, 688, 994–1001.

[47]

Vaidya, M.; Pradeep, K. G.; Murty, B. S.; Wilde, G.; Divinski, S. V. Bulk tracer diffusion in CoCrFeNi and CoCrFeMnNi high entropy alloys. Acta Mater. 2018, 146, 211–224.

[48]

Chen, W. M.; Zhang, L. J. High-throughput determination of interdiffusion coefficients for Co-Cr-Fe-Mn-Ni high-entropy alloys. J. Phase Equilib. Diffus. 2017, 38, 457–465.

[49]

Kottke, J.; Utt, D.; Laurent-Brocq, M.; Fareed, A.; Gaertner, D.; Perrière, L.; Rogal, Ł.; Stukowski, A.; Albe, K.; Divinski, S. V. et al. Experimental and theoretical study of tracer diffusion in a series of (CoCrFeMn)100− x Ni x alloys. Acta Mater. 2020, 194, 236–248.

[50]

Zhang, J. F.; Gadelmeier, C.; Sen, S.; Wang, R.; Zhang, X.; Zhong, Y.; Glatzel, U.; Grabowski, B.; Wilde, G.; Divinski, S. V. Zr diffusion in BCC refractory high entropy alloys: A case of ‘non-sluggish’ diffusion behavior. Acta Mater. 2022, 233, 117970.

[51]

Sen, S.; Zhang, X.; Rogal, L.; Wilde, G.; Grabowski, B.; Divinski, S. V. “Anti-sluggish” Ti diffusion in HCP high-entropy alloys: Chemical complexity vs. lattice distortions. Scr. Mater. 2023, 224, 115117

[52]

Zhang, F.; Zhang, C.; Chen, S. L.; Zhu, J.; Cao, W. S.; Kattner, U. R. An understanding of high entropy alloys from phase diagram calculations. Calphad 2014, 45, 1–10.

[53]
Paul, A.; Laurila, T.; Vuorinen, V.; Divinski, S. V. Thermodynamics, Diffusion and the Kirkendall Effect in Solids; Springer: Cham, 2014.
DOI
[54]

Beke, D. L.; Erdélyi, G. On the diffusion in high-entropy alloys. Mater. Lett. 2016, 164, 111–113.

[55]

Kucza, W.; Dąbrowa, J.; Cieślak, G.; Berent, K.; Kulik, T.; Danielewski, M. 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. Alloys Compd. 2018, 731, 920–928.

[56]

Gaertner, D.; Kottke, J.; Wilde, G.; Divinski, S. V.; Chumlyakov, Y. Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high entropy alloys. J. Mater. Res. 2018, 33, 3184–3191.

[57]

Gaertner, D.; Kottke, J.; Chumlyakov, Y.; Hergemöller, F.; Wilde, G.; Divinski, S. V. Tracer diffusion in single crystalline CoCrFeNi and CoCrFeMnNi high-entropy alloys: Kinetic hints towards a low-temperature phase instability of the solid-solution. Scr. Mater. 2020, 187, 57–62.

[58]

Dąbrowa, J.; Danielewski, M. State-of-the-Art diffusion studies in the high entropy alloys. Metals 2020, 10, 347.

[59]

Ma, S. G.; Zhang, S. F.; Gao, M. C.; Liaw, P. K.; Zhang, Y. A successful synthesis of the CoCrFeNiAl0.3 single-crystal, high-entropy alloy by Bridgman solidification. JOM 2013, 65, 1751–1758.

[60]

Ma, S. G.; Zhang, S. F.; Qiao, J. W.; Wang, Z. H.; Gao, M. C.; Jiao, Z. M.; Yang, H. J.; Zhang, Y. Superior high tensile elongation of a single-crystal CoCrFeNiAl0.3 high-entropy alloy by Bridgman solidification. Intermetallics 2014, 54, 104–109.

[61]

Patriarca, L.; Ojha, A.; Sehitoglu, H.; Chumlyakov, Y. I. Slip nucleation in single crystal FeNiCoCrMn high entropy alloy. Scr. Mater. 2016, 112, 54–57.

[62]

Abuzaid, W.; Sehitoglu, H. Critical resolved shear stress for slip and twin nucleation in single crystalline FeNiCoCrMn high entropy alloy. Mater. Charact. 2017, 129, 288–299.

[63]

Moon, J.; Jang, M. J.; Bae, J. W.; Yim, D.; Park, J. M.; Lee, J.; Kim, H. S. Mechanical behavior and solid solution strengthening model for face-centered cubic single crystalline and polycrystalline high-entropy alloys. Intermetallics 2018, 98, 89–94.

[64]

Feuerbacher, M.; Würtz, E.; Kovács, A.; Thomas, C. Single-crystal growth of a FeCoCrMnAl high-entropy alloy. Mater. Res. Lett. 2017, 5, 128–134.

[65]

Chen, H. Q.; Yuan, X. T.; Ren, W. L.; Peng, J. C.; Ding, B.; Zheng, T. X.; Yu, J. B.; Liaw, P. K.; Zhong, Y. B. A new single crystal high entropy alloy with excellent high-temperature tensile property. Mater. Res. Express 2020, 7, 046507.

[66]

Liu, C. J.; Gadelmeier, C.; Lu, S. L.; Yeh, J. W.; Yen, H. W.; Gorsse, S.; Glatzel, U.; Yeh, A. C. Tensile creep behavior of HfNbTaTiZr refractory high entropy alloy at elevated temperatures. Acta Mater. 2022, 237, 118188.

[67]

Xiao, W. C.; Liu, S. F.; Zhao, Y. L.; Kai, J. J.; Liu, X. J.; Yang, T. A novel single-crystal L12-strengthened Co-rich high-entropy alloy with excellent high-temperature strength and antioxidant property. J. Mater. Res. Technol. 2023, 23, 2343–2350.

[68]

Gärtner, D.; Belkacemi, L.; Esin, V. A.; Jomard, F.; Fedotov, A. A.; Schell, J.; Osinskaya, Y. V.; Pokoev, A. V.; Duhamel, C.; Paul, A. et al. Techniques of tracer diffusion measurements in metals, alloys and compounds. Diffus. Found. 2021, 29, 31–73.

[69]
Mehrer, H. Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes; Springer: Berlin, 2007.
DOI
[70]

Riesemeier, H.; Ecker, K.; Görner, W.; Müller, B. R.; Radtke, M.; Krumrey, M. Layout and first XRF applications of the BAMline at BESSY II. X-Ray Spectrom. 2005, 34, 160–163.

[71]

Buzanich, A. G.; Radtke, M.; Yusenko, K. V.; Stawski, T.; Kulow, A.; Cakir, C. T.; Röder, B.; Naese, C.; Britzke, R.; Sintschuk, M. et al. BAMline—A real-life sample materials research beamline. J. Chem. Phys. 2023, 158, 244202.

[72]

Lutz, C.; Hampel, S.; Ke, X.; Beuermann, S.; Turek, T.; Kunz, U.; Guilherme Buzanich, A.; Radtke, M.; Fittschen, U. E. A. Evidence for redox reactions during vanadium crossover inside the nanoscopic water-body of Nafion 117 using X-ray absorption near edge structure spectroscopy. J. Power Sources 2021, 483, 229176.

[73]

Schuck, G.; Zisak, I. CryoEXAFS: X-ray absorption spectroscopy station with cryogenic or in-beam operando electrochemistry sample conditions at BESSY II. J. Large-Scale Res Facil. 2020, 6, A139.

[74]

Zizak, I.; Gaal, P. The KMC-3 XPP beamline at BESSY II. J. Large-Scale Res Facil. 2017, 3, A123.

[75]

Kuzmin, A.; Chaboy, J. EXAFS and XANES analysis of oxides at the nanoscale. IUCrJ 2014, 1, 571–589.

[76]
XAESA. xaesa v0.06; GitHub: 2022 [Online]. https://github.com/aklnk/xaesa (accessed Mar 1, 2022).
[77]

Timoshenko, J.; Kuzmin, A. Wavelet data analysis of EXAFS spectra. Comput. Phys. Commun. 2009, 180, 920–925.

[78]

Timoshenko, J.; Kuzmin, A.; Purans, J. Reverse Monte Carlo modeling of thermal disorder in crystalline materials from EXAFS spectra. Comput. Phys. Commun. 2012, 183, 1237–1245.

[79]

Timoshenko, J.; Kuzmin, A.; Purans, J. EXAFS study of hydrogen intercalation into ReO3 using the evolutionary algorithm. J. Phys. Condens. Matter 2014, 26, 055401.

[80]

Ankudinov, A. L.; Ravel, B.; Rehr, J. J.; Conradson, S. D. Real-space multiple-scattering calculation and interpretation of X-ray-absorption near-edge structure. Phys. Rev. B 1998, 58, 7565–7576.

[81]

Rehr, J. J.; Albers, R. C. Theoretical approaches to X-ray absorption fine structure. Rev. Mod. Phys. 2000, 72, 621–654.

[82]

Li, K. M.; Fu, C. C.; Nastar, M.; Soisson, F. Predicting atomic diffusion in concentrated magnetic alloys: The case of paramagnetic Fe-Ni. Phys. Rev. B 2023, 107, 094103.

[83]

Cowley, J. M. An approximate theory of order in alloys. Phys. Rev. 1950, 77, 669–675.

[84]

Cowley, J. M. Short-range order and long-range order parameters. Phys. Rev. 1965, 138, A1384–A1389.

[85]

Sugita, K.; Matsuoka, N.; Mizuno, M.; Araki, H. Vacancy formation enthalpy in CoCrFeMnNi high-entropy alloy. Scr. Mater. 2020, 176, 32–35.

[86]

Huang, E. W.; Chou, H. S.; Tu, K. N.; Hung, W. S.; Lam, T. N.; Tsai, C. W.; Chiang, C. Y.; Lin, B. H.; Yeh, A. C.; Chang, S. H. et al. Element effects on high-entropy alloy vacancy and heterogeneous lattice distortion subjected to quasi-equilibrium heating. Sci. Rep. 2019, 9, 14788.

[87]
Ravel, B. The Athena: A User’s Guide. https://bruceravel.github.io/demeter/aug/ (accessed Jun 1, 2023).
[88]

Hobbs, D.; Hafner, J.; Spišák, D. Understanding the complex metallic element Mn. I. Crystalline and noncollinear magnetic structure of α-Mn. Phys. Rev. B 2003, 68, 014407.

[89]

Oh, H. S.; Kim, S. J.; Odbadrakh, K.; Ryu, W. H.; Yoon, K. N.; Mu, S.; Körmann, F.; Ikeda, Y.; Tasan, C. C.; Raabe, D. et al. Engineering atomic-level complexity in high-entropy and complex concentrated alloys. Nat. Commun. 2019, 10, 2090.

[90]

Li, Q.; Chen, W. M.; Zhong, J.; Zhang, L. J.; Chen, Q.; Liu, Z. K. On sluggish diffusion in Fcc Al-Co-Cr-Fe-Ni high-entropy alloys: An experimental and numerical study. Metals 2018, 8, 16.

[91]

Jin, K.; Zhang, C.; Zhang, F.; Bei, H. B. Influence of compositional complexity on interdiffusion in Ni-containing concentrated solid-solution alloys. Mater. Res. Lett. 2018, 6, 293–299.

[92]

Park, N.; Lee, B. J.; Tsuji, N. The phase stability of equiatomic CoCrFeMnNi high-entropy alloy: Comparison between experiment and calculation results. J. Alloys Compd. 2017, 719, 189–193.

[93]

Ikeda, Y.; Grabowski, B.; Körmann, F. Ab initio phase stabilities and mechanical properties of multicomponent alloys: A comprehensive review for high entropy alloys and compositionally complex alloys. Mater. Charact. 2019, 147, 464–511

Publication history
Copyright
Acknowledgements
Rights and permissions

Publication history

Received: 27 September 2023
Revised: 27 November 2023
Accepted: 22 December 2023
Published: 27 February 2024

Copyright

© The Author(s) 2024

Acknowledgements

Acknowledgements

The authors thank the Helmholtz–Zentrum Berlin for the provision of access to synchrotron radiation facility and allocation of synchrotron radiation at the BAMline and KMC-3 (CryoEXAFS end-station) beamlines of BESSY II at HZB. Yu. Chumlyakov (Tomsk State University, Russia) is acknowledged for the growth of single crystals. A. S. also acknowledges personal funding from CALIPSOplus project (Grant Agreement No. 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020). A. K. is thankful for the financial support from the Latvian Council of Science project No. lzp-2023/1-0476. S. D. acknowledges financial support by the German Research Foundation (DFG), project DI 1419/24-1. G. W. acknowledges financial support by DFG via SPP2006, project WI 1899/32-2. Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the EU Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.

Rights and permissions

Copyright: © 2023 by the author(s). This article is an open access article distributed under Creative Commons Attribution License (CC BY 4.0), visit https://creativecommons.org/licenses/by/4.0/.

Return