Correlation of grain boundary extra free volume with vacancy and solute segregation at grain boundaries: a case study for Al

References

• K.-D. Bauer, M. Todorova, K. Hingerl, and J. Neugebauer, A first principles investigation of zinc induced embrittlement at grain boundaries in bcc iron, Acta Mater. 90 (2015), pp. 69–76.10.1016/j.actamat.2015.02.018
   Web of Science ®Google Scholar
• G. Sha, R.K.W. Marceau, X. Gao, B.C. Muddle, and S.P. Ringer, Nanostructure of aluminium alloy 2024: Segregation, clustering and precipitation processes, Acta Mater. 59 (2011), pp. 1659–1670.10.1016/j.actamat.2010.11.033
   Web of Science ®Google Scholar
• N. Du, Y. Qi, P.E. Krajewski, and A.F. Bower, Aluminum Σ3 grain boundary sliding enhanced by vacancy diffusion, Acta Mater. 58 (2010), pp. 4245–4252.10.1016/j.actamat.2010.04.016
   Web of Science ®Google Scholar
• X. Sauvage, G. Wilde, S.V. Divinski, Z. Horita, and R.Z. Valiev, Grain boundaries in ultrafine grained materials processed by severe plastic deformation and related phenomena, Mater. Sci. Eng. A 540 (2012), pp. 1–12.10.1016/j.msea.2012.01.080
   Web of Science ®Google Scholar
• X. Sauvage, N. Enikeev, R. Valiev, Y. Nasedkina, and M. Murashkin, Atomic-scale analysis of the segregation and precipitation mechanisms in a severely deformed Al–Mg alloy, Acta Mater. 72 (2014), pp. 125–136.10.1016/j.actamat.2014.03.033
   Web of Science ®Google Scholar
• X. Sauvage, A. Ganeev, Y. Ivanisenko, N. Enikeev, M. Murashkin, and R. Valiev, Grain boundary segregation in UFG alloys processed by severe plastic deformation, Adv. Eng. Mater. 14 (2012), pp. 968–974.10.1002/adem.201200060
   Web of Science ®Google Scholar
• A. Suzuki and Y. Mishin, Atomistic modeling of point defects and diffusion in copper grain boundaries, Interface Sci. 11 (2003), pp. 131–148.
   Google Scholar
• A. Oudriss, J. Creus, J. Bouhattate, E. Conforto, C. Berziou, C. Savall, and X. Feaugas, Grain size and grain-boundary effects on diffusion and trapping of hydrogen in pure nickel, Acta Mater. 60 (2012), pp. 6814–6828.10.1016/j.actamat.2012.09.004
   Web of Science ®Google Scholar
• X.M. Bai, A.F. Voter, R.G. Hoagland, M. Nastasi, and B.P. Uberuaga, Efficient annealing of radiation damage near grain boundaries via interstitial emission, Science 327 (2010), pp. 1631–1634.10.1126/science.1183723
   PubMed Web of Science ®Google Scholar
• L.E. Karkina, I.N. Karkin, A.R. Kuznetsov, I.K. Razumov, P.A. Korzhavyi, and Y.N. Gornostyrev, Solute–grain boundary interaction and segregation formation in Al: First principles calculations and molecular dynamics modeling, Comput. Mater. Sci. 112 (2016), pp. 18–26.10.1016/j.commatsci.2015.10.007
   Web of Science ®Google Scholar
• H.B. Aaron and G.F. Bolling, Free volume as a criterion for grain boundary models, Surf. Sci. 31 (1972), pp. 27–49.10.1016/0039-6028(72)90252-X
   Web of Science ®Google Scholar
• H.B. Aaron and G.F. Bolling, Free volume as a guide to grain boundary phenomena, Scr. Metall. 6 (1972), pp. 553–562.10.1016/0036-9748(72)90089-0
   Google Scholar
• L.S. Shvindlerman, G. Gottstein, V.A. Ivanov, D.A. Molodov, D. Kolesnikov, and W. Łojkowski, Grain boundary excess free volume – direct thermodynamic measurement, J. Mater. Sci. 41 (2006), pp. 7725–7729.
   Web of Science ®Google Scholar
• H. Mehrer, Diffusion in solids, Springer Ser. Solid-State Sci. 87 (2011), pp. 841–845.
   Google Scholar
• Y.R. Kolobov, A.G. Lipnitskii, I.V. Nelasov, and G.P. Grabovetskaya, Investigations and computer simulations of the intergrain diffusion in submicro-and nanocrystalline metals, Russ. Phys. J. 51 (2008), pp. 385–399.
   Web of Science ®Google Scholar
• M. Rajagopalan, M.A. Bhatia, M.A. Tschopp, D.J. Srolovitz, and K.N. Solanki, Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries, Acta Mater. 73 (2014), pp. 312–325.10.1016/j.actamat.2014.04.011
   Web of Science ®Google Scholar
• M.A. Tschopp, G.J. Tucker, and D.L. McDowell, Structure and free volume of 〈1 1 0〉 symmetric tilt grain boundaries with the E structural unit, Acta Mater. 55 (2007), pp. 3959–3969.10.1016/j.actamat.2007.03.012
   Web of Science ®Google Scholar
• D. Wolf, Structure-energy correlation for grain boundaries in F.C.C. metals—III. Symmetrical tilt boundaries, Acta Metall. 38 (1990), pp. 781–790.10.1016/0956-7151(90)90030-K
   Google Scholar
• D. Wolf, Correlation between energy and volume expansion for grain boundaries in FCC metals, Scr. Metall. 23 (1989), pp. 1913–1918.10.1016/0036-9748(89)90482-1
   Google Scholar
• Y.H. Huang, J.M. Zhang, and K.W. Xu, Energy and volume expansion in Ag[–1 1 0]STGB, Appl. Surf. Sci. 253 (2006), pp. 698–702.10.1016/j.apsusc.2005.12.155
   Web of Science ®Google Scholar
• M.A. Tschopp and D.L. Mcdowell, Asymmetric tilt grain boundary structure and energy in copper and aluminium, Philos. Mag. 87 (2007), pp. 3871–3892.10.1080/14786430701455321
   Web of Science ®Google Scholar
• A. Hallil, A. Metsue, J. Bouhattate, and X. Feaugas, Correlation between vacancy formation and Σ3 grain boundary structures in nickel from atomistic simulations, Philos. Mag. 96 (2016), pp. 2088–2114.10.1080/14786435.2016.1189616
   Web of Science ®Google Scholar
• D.L. Olmsted, S.M. Foiles, and E.A. Holm, Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy, Acta Mater. 57 (2009), pp. 3694–3703.
   Web of Science ®Google Scholar
• T.D. Shen, J. Zhang, and Y. Zhao, What is the theoretical density of a nanocrystalline material?, Acta Mater. 56 (2008), pp. 3663–3671.10.1016/j.actamat.2008.04.003
   Web of Science ®Google Scholar
• T. Uesugi and K. Higashi, First-principles calculation of grain boundary energy and grain boundary excess free volume in aluminum: Role of grain boundary elastic energy, J. Mater. Sci. 46 (2011), pp. 4199–4205.
   Web of Science ®Google Scholar
• T. Uesugi and K. Higashi, First-principles calculation of grain boundary excess volume and free volume in nanocrystalline and ultrafine-grained aluminum, Mater. Trans. 54 (2013), pp. 1597–1604.10.2320/matertrans.L-M2013816
   Web of Science ®Google Scholar
• M.I. Buckett and K.L. Merkle, Determination of grain boundary volume expansion by HREM, Ultmi 56 (1994), pp. 71–78.
   Web of Science ®Google Scholar
• Y. Buranova, H. Rösner, S.V. Divinski, R. Imlau, and G. Wilde, Quantitative measurements of grain boundary excess volume from HAADF-STEM micrographs, Acta Mater. 106 (2016), pp. 367–373.10.1016/j.actamat.2016.01.033
   Web of Science ®Google Scholar
• E.M. Steyskal, B. Oberdorfer, W. Sprengel, M. Zehetbauer, R. Pippan, and R. Wurschum, Direct experimental determination of grain boundary excess volume in metals, Phys. Rev. Lett. 108 (2012), p. 055504.10.1103/PhysRevLett.108.055504
   PubMed Web of Science ®Google Scholar
• S.H. Na, M.S. Yang, and S.W. Nam, Effects of stress amplitude and internal stress on the grain boundary deformation behavior under high temperature creep in an Al-2.9%Mg alloy, Scr. Metall. Mater. 32 (1995), pp. 627–632.
   Google Scholar
• R.G. Song, M.K. Tseng, B.J. Zhang, J. Liu, Z.H. Jin, and K.S. Shin, Grain boundary segregation and hydrogen-induced fracture in 7050 aluminium alloy, Acta Mater. 44 (1996), pp. 3241–3248.10.1016/1359-6454(95)00406-8
   Web of Science ®Google Scholar
• R.G. Song, B.J. Zhang, and M.K. Tseng, Role of grain boundary segregation in corrosion fatigue process of high strength aluminium alloy, Mater. Chem. Phys. 45 (1996), pp. 84–87.10.1016/0254-0584(96)80054-X
   Web of Science ®Google Scholar
• G. Sha, L. Yao, X. Liao, S.P. Ringer, Z. Chao Duan and T.G. Langdon, Segregation of solute elements at grain boundaries in an ultrafine grained Al-Zn-Mg-Cu alloy, Ultmi 111 (2011), pp. 500–505.
   Web of Science ®Google Scholar
• G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996), pp. 11169–11186.10.1103/PhysRevB.54.11169
   PubMed Web of Science ®Google Scholar
• G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59 (1999), p. 1758.10.1103/PhysRevB.59.1758
   Web of Science ®Google Scholar
• P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994), pp. 17953–17979.10.1103/PhysRevB.50.17953
   PubMed Web of Science ®Google Scholar
• J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996), p. 3865.10.1103/PhysRevLett.77.3865
   PubMed Web of Science ®Google Scholar
• G. Simmons, Single crystal elastic constants and calculated aggregate properties, Southern Methodist University, Dallas, TX, 1965.
   Google Scholar
• Gang Lu , Nicholas Kioussis, Interaction of vacancies with a grain boundary in aluminum: A first-principles study, Phys. Rev B 64 (2001), pp. 167–173.
   Google Scholar
• Shengjun Zhang , Oleg Y. Kontsevoi , Arthur J. Freeman and Gregory B. Olson . Sodium-induced embrittlement of an aluminum grain boundary, Phys. Rev. B 22(2010), pp. 1755–1760.
   Google Scholar
• D.I. Thomson, V. Heine, M.C. Payne, N. Marzari, and M.W. Finnis, Insight into gallium behavior in aluminum grain boundaries from calculation on Σ = 11 (1 1 3) boundary, Acta Mater. 48 (2000), pp. 3623–3632.10.1016/S1359-6454(00)00175-0
   Web of Science ®Google Scholar
• R.W. Balluffi, A. Brokman, and A.H. King, CSL/DSC lattice model for general crystalcrystal boundaries and their line defects, Acta Metall. 30 (1982), pp. 1453–1470.10.1016/0001-6160(82)90166-3
   Google Scholar
• H. Gleiter, The structure and properties of high-angle grain boundaries in metals, Phys. Status Solidi B 45 (1971), pp. 9–38.10.1002/(ISSN)1521-3951
   Google Scholar
• S. Poulat, High-resolution transmission electron microscopy observations and atomic simulations of the structures of exact and near Σ = 11, 332 tilt grain boundaries in nickel, Philos. Mag. A 80 (2000), pp. 853–870.
   Google Scholar
• V. Vitek, Theoretical and experimental investigations of structures and energies of Σ = 3, [1 1 2] tilt grain boundaries in copper, Philos. Mag. A 77 (1998), pp. 1161–1184.
   Google Scholar
• J. Xu, Y. Jiang, L. Yang, and J. Li, Assessment of the CSL and SU models for bcc-Fe grain boundaries from first principles, Comput. Mater. Sci. 122 (2016), pp. 22–29.10.1016/j.commatsci.2016.05.009
   Web of Science ®Google Scholar
• J. Xu, J.B. Liu, S.N. Li, B.X. Liu, and Y. Jiang, Self-healing properties of nanocrystalline materials: a first-principles analysis of the role of grain boundaries, Phys. Chem. Chem. Phys. 18 (2016), pp. 17930–17940.10.1039/C6CP02505F
   PubMed Web of Science ®Google Scholar
• V. Yamakov, D. Wolf, S.R. Phillpot, A.K. Mukherjee, and H. Gleiter, Dislocation processes in the deformation of nanocrystalline aluminium by molecular-dynamics simulation, Nat. Mater. 1 (2002), p. 45.10.1038/nmat700
   PubMed Web of Science ®Google Scholar
• D.M. Saylor, B.S. El Dasher, A.D. Rollett, and G.S. Rohrer, Distribution of grain boundaries in aluminum as a function of five macroscopic parameters, Acta Mater. 52 (2004), pp. 3649–3655.10.1016/j.actamat.2004.04.018
   Web of Science ®Google Scholar
• M.A. Tschopp, S.P. Coleman, and D.L. McDowell, Symmetric and asymmetric tilt grain boundary structure and energy in Cu and Al (and transferability to other fcc metals), Integrating Mater. Manuf. Innov. 4 (2015), pp. 1–14.
   Web of Science ®Google Scholar
• R.-Z. Wang, M. Kohyama, S. Tanaka, T. Tamura, and S. Ishibashi, First-principles study of the stability and interfacial bonding of tilt and twist grain boundaries in Al and Cu, Mater. Trans. 50 (2009), pp. 11–18.10.2320/matertrans.MD200820
   Web of Science ®Google Scholar
• N. Chandra and P. Dang, Atomistic simulation of grain boundary sliding and migration, J. Mater. Sci. 34 (1999), pp. 655–666.
   Web of Science ®Google Scholar
• I. Adlakha, M.A. Bhatia, M.A. Tschopp, and K.N. Solanki, Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium, Philos. Mag. 94 (2014), pp. 3445–3466.10.1080/14786435.2014.961585
   Web of Science ®Google Scholar
• F. Sansoz and J.F. Molinari, Mechanical behavior of Σ tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study, Acta Mater. 53 (2005), pp. 1931–1944.10.1016/j.actamat.2005.01.007
   Web of Science ®Google Scholar
• J.J. Bean and K.P. McKenna, Origin of differences in the excess volume of copper and nickel grain boundaries, Acta Mater. 110 (2016), pp. 246–257.10.1016/j.actamat.2016.02.040
   Web of Science ®Google Scholar
• N. Hansen, Hall-Petch relation and boundary strengthening, Scr. Mater. 51 (2004), pp. 801–806.10.1016/j.scriptamat.2004.06.002
   Web of Science ®Google Scholar
• K. Edalati and Z. Horita, High-pressure torsion of pure metals: Influence of atomic bond parameters and stacking fault energy on grain size and correlation with hardness, Acta Mater. 59 (2011), pp. 6831–6836.10.1016/j.actamat.2011.07.046
   Web of Science ®Google Scholar
• R.W. Siegel, S.M. Chang, and R.W. Balluffi, Vacancy loss at grain boundaries in quenched polycrystalline gold Acta Metall. 28 (1980), pp. 249–257.
   Google Scholar
• P.A. Thorsen, J.B. Bilde-Sørensen, and B.N. Singh, Bubble formation at grain boundaries in helium implanted copper, Scr. Mater. 51 (2004), pp. 557–560.10.1016/j.scriptamat.2004.05.038
   Web of Science ®Google Scholar
• G. Duscher, M.F. Chisholm, U. Alber, and M. Rühle, Bismuth-induced embrittlement of copper grain boundaries, Nat. Mater. 3 (2004), pp. 621–626.10.1038/nmat1191
   PubMed Web of Science ®Google Scholar
• X.-M. Bai, L.J. Vernon, R.G. Hoagland, A.F. Voter, M. Nastasi, and B.P. Uberuaga, Role of atomic structure on grain boundary-defect interactions in Cu, Phys. Rev. B 85 (2012).
   Web of Science ®Google Scholar
• A. Suzuki and Y. Mishin, Interaction of point defects with grain boundaries in fcc metals, Interface Sci. 11 (2003), pp. 425–437.10.1023/A:1026195911339
   Google Scholar
• V.I. Razumovskiy, A.V. Ruban, I.M. Razumovskii, A.Y. Lozovoi, V.N. Butrim, and Y.K. Vekilov, The effect of alloying elements on grain boundary and bulk cohesion in aluminum alloys: An ab initio study, Scripta Mater. 65 (2011), pp. 926–929.10.1016/j.scriptamat.2011.08.014
   Web of Science ®Google Scholar
• X. Liu, X. Wang, J. Wang, and H. Zhang, First-principles investigation of Mg segregation at Σ = 11(113) grain boundaries in Al, J. Phys.: Condens. Matter 17 (2005), pp. 4301–4308.
   Web of Science ®Google Scholar
• S. Zhang, O.Y. Kontsevoi, A.J. Freeman, and G.B. Olson, Cohesion enhancing effect of magnesium in aluminum grain boundary: A first-principles determination, Appl. Phys. Lett. 100 (2012), p. 231904.10.1063/1.4725512
   Web of Science ®Google Scholar
• D. Scheiber, V.I. Razumovskiy, P. Puschnig, R. Pippan, and L. Romaner, Ab initio description of segregation and cohesion of grain boundaries in W–25at.% Re alloys, Acta Mater. 88 (2015), pp. 180–189.10.1016/j.actamat.2014.12.053
   Web of Science ®Google Scholar
• S. Zhang, O.Y. Kontsevoi, A.J. Freeman, and G.B. Olson, First principles investigation of zinc-induced embrittlement in an aluminum grain boundary, Acta Mater. 59 (2011), pp. 6155–6167.10.1016/j.actamat.2011.06.028
   Web of Science ®Google Scholar
• X.Y. Liu and J.B. Adams, Grain-boundary segregation in Al–10%Mg alloys at hot working temperatures, Acta Mater. 46 (1998), pp. 3467–3476.10.1016/S1359-6454(98)00038-X
   Web of Science ®Google Scholar
• R.Z. Valiev, N.A. Enikeev, M.Y. Murashkin, V.U. Kazykhanov, and X. Sauvage, On the origin of the extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation, Scr. Mater. 63 (2010), pp. 949–952.10.1016/j.scriptamat.2010.07.014
   Web of Science ®Google Scholar
• C. Wolverton, Solute–vacancy binding in aluminum, Acta Mater. 55 (2007), pp. 5867–5872.10.1016/j.actamat.2007.06.039
   Web of Science ®Google Scholar