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Quantifying local lattice distortions in refractory high-entropy alloys
Phys. Rev. Materials 8, 083602 – Published 2 August, 2024
DOI: https://doi.org/10.1103/PhysRevMaterials.8.083602
Abstract
Severe local lattice distortions (LLDs), originating from the size mismatch among atoms, have been proposed as one of the key mechanisms responsible for the excellent mechanical properties of bcc-structured high-entropy alloys (HEAs). They have also been connected to phase stability, as well as physical properties such as electrical conductivity. Experimental measurements of LLDs are, however, difficult and often ambiguous. Analysis of total scattering data in real space has been proposed to provide a uniquely suitable probe of LLDs, but its widespread application and validation are still limited. We conduct a thorough study of LLD measurements in refractory high-entropy alloys (RHEAs) using small-box pair distribution function (PDF) analysis. We start by reexamining existing literature data using a recently proposed coherent theoretical framework to demonstrate that LLDs in RHEAs can indeed be considered as severe and can be reliably measured even in the absence of known thermal components. We perform total scattering experiments of a typical RHEA (HfNbTaTiZr) using both x-rays and neutrons, and show that real-space PDF analysis of data from different types of radiation gives consistent values of LLDs. The results are also in good agreement with the values derived from reciprocal-space data. Finally, through simulation and analysis of theoretical two-phase PDFs, we demonstrate that the effect of the chemical segregation in the investigated RHEA on the measured LLDs is limited when dealing with comparatively large LLDs. The results show that PDF analysis using small-box modeling provides a fast and reliable tool for measuring LLDs in RHEAs, which makes it ideal for analysis of large data sets from time-resolved in situ measurements.
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References (80)
- E. P. George, D. Raabe, and R. O. Ritchie, High-entropy alloys, Nat. Rev. Mater. 4, 515 (2019).
- D. B. Miracle and O. N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater. 122, 448 (2017).
- J. W. Yeh, S. K. Chen, S. J. Lin, J. Y. Gan, T. S. Chin, T. T. Shun, C. H. Tsau, and S. Y. Chang, Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes, Adv. Eng. Mater. 6, 299 (2004).
- B. Cantor, I. T. Chang, P. Knight, and A. J. Vincent, Microstructural development in equiatomic multicomponent alloys, Mater. Sci. Eng. A 375–377, 213 (2004).
- J. W. Yeh, Alloy design strategies and future trends in high-entropy alloys, JOM 65, 1759 (2013).
- O. N. Senkov, G. B. Wilks, D. B. Miracle, C. P. Chuang, and P. K. Liaw, Refractory high-entropy alloys, Intermetallics 18, 1758 (2010).
- S. Sheikh, S. Shafeie, Q. Hu, J. Ahlström, C. Persson, J. Veselý, J. Zýka, U. Klement, and S. Guo, Alloy design for intrinsically ductile refractory high-entropy alloys, J. Appl. Phys. 120, 164902 (2016).
- 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 (2018).
- O. N. Senkov, G. B. Wilks, J. M. Scott, and D. B. Miracle, Mechanical properties of Nb25Mo25Ta 25W25 and V20Nb20Mo 20Ta20W20 refractory high entropy alloys, Intermetallics 19, 698 (2011).
- L. R. Owen and N. G. Jones, Lattice distortions in high-entropy alloys, J. Mater. Res. 33, 2954 (2018).
- L. R. Owen, E. J. Pickering, H. Y. Playford, H. J. Stone, M. G. Tucker, and N. G. Jones, An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy, Acta Mater. 122, 11 (2017).
- L. Owen, N. Jones, H. Stone, and H. Playford, Separation of static and dynamic displacements in the CrMnFeCoNi high entropy alloy, Acta Mater. 262, 119164 (2024).
- H. Song, F. Tian, Q. M. Hu, L. Vitos, Y. Wang, J. Shen, and N. Chen, Local lattice distortion in high-entropy alloys, Phys. Rev. Mater. 1, 023404 (2017).
- Y. Tong, S. Zhao, H. Bei, T. Egami, Y. Zhang, and F. Zhang, Severe local lattice distortion in Zr- and/or Hf-containing refractory multi-principal element alloys, Acta Mater. 183, 172 (2020).
- L. Casillas-Trujillo, B. Osinger, R. Lindblad, D. Karlsson, A. I. Abrikosov, S. Fritze, K. Von Fieandt, B. Alling, I. Hotz, U. Jansson, I. A. Abrikosov, and E. Lewin, Experimental and theoretical evidence of charge transfer in multi-component alloys-how chemical interactions reduce atomic size mismatch, Mater. Chem. Front. 5, 5746 (2021).
- F. Meng, W. Zhang, Z. Zhou, R. Sheng, A. C. Chuang, C. Wu, H. Huang, S. Zhang, H. Zhang, L. Zhu, L. Jiang, P. K. Liaw, S. Chen, and Y. Tong, Charge transfer effect on local lattice distortion in a HfNbTiZr high entropy alloy, Scr. Mater. 203, 114104 (2021).
- Z. Wang, Q. Fang, J. Li, B. Liu, and Y. Liu, Effect of lattice distortion on solid solution strengthening of BCC high-entropy alloys, J. Mater. Sci. Technol. 34, 349 (2018).
- P. Thirathipviwat, S. Sato, G. Song, J. Bednarcik, K. Nielsch, J. Jung, and J. Han, A role of atomic size misfit in lattice distortion and solid solution strengthening of TiNbHfTaZr high entropy alloy system, Scr. Mater. 210, 114470 (2022).
- S. I. Rao, C. Varvenne, C. Woodward, T. A. Parthasarathy, D. Miracle, O. N. Senkov, and W. A. Curtin, Atomistic simulations of dislocations in a model BCC multicomponent concentrated solid solution alloy, Acta Mater. 125, 311 (2017).
- Y. Y. Zhao, Z. F. Lei, Z. P. Lu, J. C. Huang, and T. G. Nieh, A simplified model connecting lattice distortion with friction stress of nb-based equiatomic high-entropy alloys, Mater. Res. Lett. 7, 340 (2019).
- C. Lee, G. Song, M. C. Gao, R. Feng, P. Chen, J. Brechtl, Y. Chen, K. An, W. Guo, J. D. Poplawsky, S. Li, A. T. Samaei, W. Chen, A. Hu, H. Choo, and P. K. Liaw, Lattice distortion in a strong and ductile refractory high-entropy alloy, Acta Mater. 160, 158 (2018).
- C. Lee, Y. Chou, G. Kim, M. C. Gao, K. An, J. Brechtl, C. Zhang, W. Chen, J. D. Poplawsky, G. Song, Y. Ren, Y. C. Chou, and P. K. Liaw, Lattice-distortion-enhanced yield strength in a refractory high-entropy alloy, Adv. Mater. 32, 2004029 (2020).
- B. Chen, S. Li, H. Zong, X. Ding, J. Sun, and E. Ma, Unusual activated processes controlling dislocation motion in body-centered-cubic high-entropy alloys, Proc. Natl. Acad. Sci. USA 117, 16199 (2020).
- C. Lee, F. Maresca, R. Feng, Y. C. Chou, T. Ungar, M. Widom, K. An, J. D. Poplawsky, Y. C. Chou, P. K. Liaw, and W. A. Curtin, Strength can be controlled by edge dislocations in refractory high-entropy alloys, Nat. Commun. 12, 5474 (2021).
- F. Wang, G. H. Balbus, S. Xu, Y. Su, J. Shin, P. F. Rottmann, K. E. Knipling, J.-C. Stinville, L. H. Mills, O. N. Senkov, I. J. Beyerlein, T. M. Pollock, and D. S. Gianola, Multiplicity of dislocation pathways in a refractory multiprincipal element alloy, Science 370, 95 (2020).
- B. Chen, S. Li, J. Ding, X. Ding, J. Sun, and E. Ma, Correlating dislocation mobility with local lattice distortion in refractory multi-principal element alloys, Scr. Mater. 222, 115048 (2023).
- G. D. Samolyuk, Y. N. Osetsky, G. M. Stocks, and J. R. Morris, Role of static displacements in stabilizing body centered cubic high entropy alloys, Phys. Rev. Lett. 126, 025501 (2021).
- S. Mu, S. Wimmer, S. Mankovsky, H. Ebert, and G. M. Stocks, Influence of local lattice distortions on electrical transport of refractory high entropy alloys, Scr. Mater. 170, 189 (2019).
- 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 (London) 581, 283 (2020).
- Q. He, P. Tang, H. Chen, S. Lan, J. Wang, J. Luan, M. Du, Y. Liu, C. Liu, C. Pao, and Y. Yang, Understanding chemical short-range ordering/demixing coupled with lattice distortion in solid solution high entropy alloys, Acta Mater. 216, 117140 (2021).
- X. Zhou, H. Song, C. Guo, Z. Yang, and F. Tian, Effect of short-range order on lattice distortion, stacking fault energy, and mechanical performance of Co-Fe-Ni-Ti high-entropy alloy at finite temperature, Phys. Rev. Mater. 8, 053602 (2024).
- Y. Zou, S. Maiti, W. Steurer, and R. Spolenak, Size-dependent plasticity in an refractory high-entropy alloy, Acta Mater. 65, 85 (2014).
- A. Béché, J. L. Rouvière, J. P. Barnes, and D. Cooper, Dark field electron holography for strain measurement, Ultramicroscopy 111, 227 (2011).
- J. W. Yeh, S. Y. Chang, Y. D. Hong, S. K. Chen, and S. J. Lin, Anomalous decrease in x-ray diffraction intensities of Cu-Ni-Al-Co-Cr-Fe-Si alloy systems with multi-principal elements, Mater. Chem. Phys. 103, 41 (2007).
- N. L. Okamoto, K. Yuge, K. Tanaka, H. Inui, and E. P. George, Atomic displacement in the CrMnFeCoNi high-entropy alloy—A scaling factor to predict solid solution strengthening, AIP Adv. 6, 125008 (2016).
- A. Fantin, A. M. Manzoni, H. Springer, R. D. Kamachali, and R. Maaß, Local lattice distortions and chemical short-range order in MoNbTaW, Mater. Res. Lett. 12, 346 (2024).
- Y. Y. Tan, T. Li, Y. Chen, Z. J. Chen, M. Y. Su, J. Zhang, Y. Gong, T. Wu, H. Y. Wang, and L. H. Dai, Uncovering heterogeneity of local lattice distortion in TiZrHfNbTa refractory high entropy alloy by SR-XRD and EXAFS, Scr. Mater. 223, 115079 (2023).
- L. R. Owen, H. J. Stone, and H. Y. Playford, The assessment of local lattice strains in alloys using total scattering, Acta Mater. 170, 38 (2019).
- M. M. Nygård, W. A. Sławiński, G. Ek, M. H. Sørby, M. Sahlberg, D. A. Keen, and B. C. Hauback, Local order in high-entropy alloys and associated deuterides—A total scattering and Reverse Monte Carlo study, Acta Mater. 199, 504 (2020).
- M. G. Tucker, D. A. Keen, M. T. Dove, A. L. Goodwin, and Q. Hui, RMCProfile: Reverse Monte Carlo for polycrystalline materials, J. Phys.: Condens. Matter 19, 335218 (2007).
- H. Y. Playford, L. R. Owen, I. Levin, and M. G. Tucker, New insights into complex materials using reverse Monte Carlo modeling, Annu. Rev. Mater. Res. 44, 429 (2014).
- H. Playford, D. Keen, and M. Tucker, Local structure of crystalline and amorphous materials using reverse Monte Carlo methods, Neutron News 27, 17 (2016).
- C. L. Farrow, P. Juhas, J. W. Liu, D. Bryndin, E. S. Boin, J. Bloch, T. Proffen, and S. J. Billinge, PDFfit2 and PDFgui: Computer programs for studying nanostructure in crystals, J. Phys.: Condens. Matter 19, 335219 (2007).
- S. J. L. Billinge, Real-space Rietveld: Full profile structural refinement of the atomic pair distribution function, in Local Structure from Diffraction, edited by S. J. L. Billinge and M. F. Thorpe, Fundamental Materials Research (Springer, Boston, MA, 2002), pp. 137–156.
- P. J. Chupas, X. Qiu, J. C. Hanson, P. L. Lee, C. P. Grey, and S. J. L. Billinge, Rapid-acquisition pair distribution function (RA-PDF) analysis, J. Appl. Cryst. 36, 1342 (2003).
- P. J. Chupas, K. W. Chapman, and P. L. Lee, Applications of an amorphous silicon-based area detector for high-resolution, high-sensitivity and fast time-resolved pair distribution function measurements, J. Appl. Cryst. 40, 463 (2007).
- L. R. Owen and N. G. Jones, Quantifying local lattice distortions in alloys, Scr. Mater. 187, 428 (2020).
- L. Y. Tian, G. Wang, J. S. Harris, D. L. Irving, J. Zhao, and L. Vitos, Alloying effect on the elastic properties of refractory high-entropy alloys, Mater. Des. 114, 243 (2017).
- H. Ge and F. Tian, A review of ab initio calculation on lattice distortion in high-entropy alloys, JOM 71, 4225 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevMaterials.8.083602 for correlation between different LLD metrics; determination of the relationship between melting temperatures derived from rule-of-mixture and CALPHAD; calculated thermal component of values for a range of RHEAs; tabulation of factors of pure elements; an extended discussion of the effect of reciprocal-space peak broadening on the PDF; calculations of average scattering lengths for dendrites and interdendritic regions; a list of parameters used in PDF simulations; calulations of volume fractions of dendrites and interdendritic regions from the lever rule; and description of two-phase small-box fitting procedure.
- X. T. Chen, L. Shao, T. W. Fan, N. Ding, J. Yang, and B. Y. Tang, Ab initio study of local lattice distortion of hexagonal closed-packed high-entropy () and the influence on thermodynamic property, J. Solid State Chem. 303, 122469 (2021).
- M. Widom, W. P. Huhn, S. Maiti, and W. Steurer, Hybrid Monte Carlo/molecular dynamics simulation of a refractory metal high entropy alloy, Metall. Mater. Trans. A 45, 196 (2014).
- O. N. Senkov, S. Gorsse, and D. B. Miracle, High temperature strength of refractory complex concentrated alloys, Acta Mater. 175, 394 (2019).
- Handbook of Physics, edited by W. Benenson, J. W. Harris, H. Stocker, and H. Lutz (Springer, New York, NY, 2002).
- L. M. Peng, G. Ren, S. L. Dudarev, and M. J. Whelan, Debye-Waller factors and absorptive scattering factors of elemental crystals, Acta Cryst. A 52, 456 (1996).
- M. S. Narayana, N. G. Krishna, and D. B. Sirdeshmukh, X-ray determination of Debye–Waller factors and Debye temperatures of h.c.p. elements Ti, Zr, Ru, Tm, Hf, Acta Cryst. A 57, 217 (2001).
- E. Purushotham and N. G. Krishna, Mean square amplitudes of vibration and associated Debye temperatures of rhenium, osmium and thallium, Phys. B: Condens. Matter 405, 3308 (2010).
- J. C. Slater, Atomic radii in crystals, J. Chem. Phys. 41, 3199 (1964).
- X. Yang and Y. Zhang, Prediction of high-entropy stabilized solid-solution in multi-component alloys, Mater. Chem. Phys. 132, 233 (2012).
- E. Takeshi and S. J. L. Billinge, Structure of complex materials, Pergamon Mater. Ser. 16, 1 (2012).
- F. Lukac, M. Dudr, R. Musalek, J. Klecka, J. Cinert, J. Cizek, T. Chraska, J. Cizek, O. Melikhova, J. Kuriplach, J. Zyka, and J. Malek, Spark plasma sintering of gas atomized high-entropy alloy HfNbTaTiZr, J. Mater. Res. 33, 3247 (2018).
- S. Y. Chen, Y. Tong, K. K. Tseng, J. W. Yeh, J. D. Poplawsky, J. G. Wen, M. C. Gao, G. Kim, W. Chen, Y. Ren, R. Feng, W. D. Li, and P. K. Liaw, Phase transformations of HfNbTaTiZr high-entropy alloy at intermediate temperatures, Scr. Mater. 158, 50 (2019).
- A. C. Dippel, H. P. Liermann, J. T. Delitz, P. Walter, H. Schulte-Schrepping, O. H. Seeck, and H. Franz, Beamline P02.1 at PETRA III for high-resolution and high-energy powder diffraction, J. Synchrotron Radiat. 22, 675 (2015).
- P. Juhás, T. Davis, C. L. Farrow, and S. J. L. Billinge, PDFgetX3: A rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions, J. Appl. Cryst. 46, 560 (2013).
- W. G. Williams, R. M. Ibberson, P. Day, and J. E. Enderby, GEM—General materials diffractometer at ISIS, Phys. B: Condens. Matter 241–243, 234 (1997).
- A. C. Hannon, Results on disordered materials from the General materials diffractometer, GEM, at ISIS, Nucl. Instrum. Methods Phys. Res. Sect. A 551, 88 (2005).
- A. K. Soper, GudrunN and GudrunX: Programs for correcting raw neutron and x-ray diffraction data to differential scattering cross section, RAL technical report RAL-TR-2011-013, 1 (2011).
- J. Kieffer, V. Valls, N. Blanc, and C. Hennig, New tools for calibrating diffraction setups, J. Synchrotron Radiat. 27, 558 (2020).
- B. H. Toby and R. B. Von Dreele, GSAS-II: The genesis of a modern open-source all purpose crystallography software package, J. Appl. Cryst. 46, 544 (2013).
- P. Juhás, C. L. Farrow, X. Yang, K. R. Knox, and S. J. Billinge, Complex modeling: A strategy and software program for combining multiple information sources to solve ill posed structure and nanostructure inverse problems, Acta Cryst. A 71, 562 (2015).
- I.-K. Jeong, R. H. Heffner, M. J. Graf, and S. J. L. Billinge, Lattice dynamics and correlated atomic motion from the atomic pair distribution function, Phys. Rev. B 67, 104301 (2003).
- D. Olds, C. N. Saunders, M. Peters, T. Proffen, J. Neuefeind, and K. Page, Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time- of-flight neutron diffractometers, Acta Cryst. A 74, 293 (2018).
- P. F. Peterson, D. Olds, M. T. McDonnell, and K. Page, Illustrated formalisms for total scattering data: A guide for new practitioners, J. Appl. Cryst. 54, 317 (2021).
- I. K. Jeong, M. J. Graf, and R. H. Heffner, Effects of Bragg peak profiles and nanoparticle sizes on the real-space pair distribution function, J. Appl. Cryst. 38, 55 (2005).
- V. F. Sears, Neutron scattering lengths and cross sections, Neutron News 3, 26 (1992).
- W. A. Sławiński, Calculation of pair distribution functions for multiphase systems, J. Appl. Cryst. 51, 919 (2018).
- X. Qiu, E. S. Božin, P. Juhas, T. Proffen, and S. J. Billinge, Reciprocal-space instrumental effects on the real-space neutron atomic pair distribution function, J. Appl. Cryst. 37, 110 (2004).
- J. Beyer, N. Roth, and B. Brummerstedt Iversen, Effects of Voigt diffraction peak profiles on the pair distribution function, Acta Cryst. A 78, 10 (2022).
- Y. Zhang, M. Eremenko, V. Krayzman, M. G. Tucker, and I. Levin, New capabilities for enhancement of RMCProfile: Instrumental profiles with arbitrary peak shapes for structural refinements using the reverse Monte Carlo method, J. Appl. Cryst. 53, 1509 (2020).
- https://doi.org/10.5286/ISIS.E.RB2000207