2000 character limit reached
Fractal structure, depinning, and hysteresis of dislocations in high-entropy alloys
Published 29 Oct 2024 in cond-mat.mtrl-sci | (2410.21838v1)
Abstract: High-entropy alloys (HEAs) are complex alloys containing multiple elements in high concentrations. Plasticity in HEAs is carried by dislocations, but the random nature of their composition pins dislocations, effectively hindering their motion. We investigate the resulting complex structure of the dislocation in terms of spatial correlation functions, which allow us to draw conclusions on the fractal geometry of the dislocation. At high temperature, where thermal fluctuations dominate, dislocations adopt the structure of a random walk with Hurst exponent $1/2$ or fractal dimension $3/2$. At low temperature we find larger Hurst exponents (lower dimensions), with a crossover to an uncorrelated structure beyond a correlation length. These changes in structure are accompanied by an emergence of hysteresis (and hence pinning) in the motion of the dislocation at low temperature. We use a modified Labusch/Edwards-Wilkinson-model to argue that this correlation length must be an intrinsic property of the HEA. This means dislocations in HEAs are an individual pinning limit, where segments of the dislocation are independently pinned by local distortions of the crystal lattice that are induced by chemical heterogeneity.
- C. Varvenne, A. Luque, and W. A. Curtin, Theory of strengthening in fcc high entropy alloys, Acta Mater. 118, 164 (2016a).
- R. Labusch, Statistische Theorien der Mischkristallhärtung, Acta Metall. 20, 917 (1972).
- R. Labusch, Physical aspects of precipitation- and solid solution-hardening, Czechoslov. J. Phys. 31, 165 (1981).
- S. F. Edwards and D. R. Wilkinson, The surface statistics of a granular aggregate, Proc. R. Soc. Lond. A 381, 17 (1982).
- Q.-J. Li, H. Sheng, and E. Ma, Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways, Nat. Commun. 10, 3563 (2019a).
- S. Zapperi and M. Zaiser, Depinning of a dislocation: The influence of long-range interactions, Mater. Sci. Eng. A 309-310, 348 (2001).
- A. I. Larkin, Effect of inhomogeneties on the structure of the mixed state of superconductors, J. Exp. Theor. Phys. 31, 784 (1970).
- R. Labusch, A statistical theory of solid solution hardening, Phys. Status Solidi B 41, 659 (1970).
- A. I. Larkin and Y. N. Ovchinnikov, Pinning in type II superconductors, J. Low Temp. Phys. 34, 409 (1979).
- H. E. Hurst, Long-Term Storage Capacity of Reservoirs, Trans. Am. Soc. Civil Eng. 116, 770 (1951).
- B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
- J. H. Zhai and M. Zaiser, Properties of dislocation lines in crystals with strong atomic-scale disorder, Mater. Sci. Eng. A 740-741, 285 (2019).
- M. Kardar, G. Parisi, and Y.-C. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56, 889 (1986).
- C. Campañá and M. H. Müser, Practical green’s function approach to the simulation of elastic semi-infinite solids, Phys. Rev. B 74, 075420 (2006).
- J. Coville, N. Dirr, and S. Luckhaus, Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients, Netw. Heterog. Media 5, 745 (2010).
- P. W. Dondl and M. Scheutzow, Ballistic and sub-ballistic motion of interfaces in a field of random obstacles, Ann. Appl. Probab. 27, 3189 (2017).
- P. Dondl, M. Jesenko, and M. Scheutzow, Infinite pinning, Bull. Lond. Math. Soc. 54, 760 (2022).
- A. Esfandiarpour, S. Papanikolaou, and M. Alava, Edge dislocations in multicomponent solid solution alloys: Beyond traditional elastic depinning, Phys. Rev. Res. 4, L022043 (2022).
- M. H. Müser, S. V. Sukhomlinov, and L. Pastewka, Interatomic potentials: achievements and challenges, Adv. Phys. X 8, 2093129 (2023).
- D. S. Fisher, Collective transport in random media: From superconductors to earthquakes, Phys. Rep. 301, 113 (1998).
- P. Chauve, T. Giamarchi, and P. L. Doussal, Creep and depinning in disordered media, Phys. Rev. B 62, 6241 (2000).
- A. Rosso, A. K. Hartmann, and W. Krauth, Depinning of elastic manifolds, Phys. Rev. B 67, 4 (2003).
- W. G. Nöhring and W. A. Curtin, Thermodynamic properties of average-atom interatomic potentials for alloys, Model. Simul. Mater. Sci. Eng. 24, 045017 (2016).
- X. W. Zhou, M. E. Foster, and R. B. Sills, An fe-ni-cr embedded atom method potential for austenitic and ferritic systems, J. Comput. Chem. 39, 2420 (2018).
- Q.-J. Li, H. Sheng, and E. Ma, Strengthening in multi-principal element alloys with local-chemical-order roughened dislocation pathways, Nat. Commun. 10 (2019b).
- F. H. Stillinger and T. A. Weber, Packing structures and transitions in liquids and solids, Science 225, 983 (1984).
- S. Nosé, A molecular dynamics method for simulations in the canonical ensemble, Mol. Phys. 52, 255 (1984).
- H. C. Andersen, Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys. 72, 2384 (1980).
- A. Stukowski and K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Model. Simul. Mater. Sci. Eng. 18, 085001 (2010).
- N. Wiener, Generalized harmonic analysis, Acta Math. 55, 117 (1930).
- A. Khintchine, Korrelationstheorie der stationären stochastischen Prozesse, Math. Ann. 109, 604 (1934).
- J. P. Hirth, J. Lothe, and T. Mura, Theory of Dislocations (2nd ed.) (Krieger Publishing Company, Malabar, 1983).
- D. Hull and D. J. Bacon, Introduction to Dislocations (Butterworth Heinemann, 2011).
- W. P. Kuykendall and W. Cai, Conditional convergence in two-dimensional dislocation dynamics, Model. Simul. Mater. Sc. 21, 055003 (2013).
- M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Oxford University Press, 1989).
- P. A. Geslin and D. Rodney, Thermal fluctuations of dislocations reveal the interplay between their core energy and long-range elasticity, Phys. Rev. B 98, 174115 (2018).
- M. Zaiser, Dislocation motion in a random solid solution, Philos. Mag. A 82, 2869 (2002).
- P. Meakin, Fractals, scaling and growth far from equilibrium (Cambridge University Press, 1998).
- M. O. Robbins and J. F. Joanny, Contact angle hysteresis on random surfaces, EPL 3, 729 (1987).
- P. A. Geslin and D. Rodney, Investigation of partial dislocations fluctuations yields dislocation core parameters, Model. Simul. Mater. Sci. Eng. 28, 055006 (2020).
- W. G. Nöhring and W. A. Curtin, Correlation of microdistortions with misfit volumes in high entropy alloys, Scr. Mater. 168, 119 (2019).
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