Symmetric and asymmetric tilt grain boundary structure and energy in Cu and Al (and transferability to other fcc metals)
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Abstract
Symmetric and asymmetric tilt grain boundaries in Cu and Al were generated using molecular statics energy minimization in a classical molecular dynamics code with in-plane grain boundary translations and an atom deletion criterion. The following dataset (NIST repository, http://hdl.handle.net/11256/358) contains atomic coordinates for minimum energy grain boundaries in three-dimensional periodic simulation cells, facilitating their use in future simulations. This grain boundary dataset is used to show the relative transferability of grain boundary structures from one face-centered cubic system to another; in general, there is good agreement in terms of grain boundary energies (R2 > 0.99). Some potential applications and uses of this tilt grain boundary dataset in nanomechanics and materials science are discussed.
Keywords
Tilt grain boundaries Grain boundary structure Grain boundary energy fcc Molecular dynamics Copper Aluminum LAMMPS Face-centered cubicNotes
Acknowledgements
MT and SC would like to acknowledge the US Army Research Laboratory for funding this work. DLM is grateful for the support of the National Science Foundation (CMMI-1232878) and the Carter N. Paden, Jr. Distinguished Chair in Metals Processing.
References
- 1.Mishin Y, Asta M, Li J (2010) Atomistic modeling of interfaces and their impact on microstructure and properties. Acta Mater 58:1117–51CrossRefGoogle Scholar
- 2.Watanabe T (1984) An Approach to Grain-Boundary Design for Strong and Ductile Polycrystals. Res Mech 11:47–84Google Scholar
- 3.Watanabe T (1994) The Impact of Grain-Boundary-Character-Distribution on Fracture in Polycrystals. Mater Sci Eng A 176:39–49CrossRefGoogle Scholar
- 4.Randle V (1999) Mechanism of twinning-induced grain boundary engineering in low stacking-fault energy materials. Acta Mater 47:4187–96CrossRefGoogle Scholar
- 5.Sutton AP, Vitek V (1983) On the Structure of Tilt Grain-Boundaries in Cubic Metals: 1. Symmetrical Tilt Boundaries. Philos T R Soc A 309:1–68CrossRefGoogle Scholar
- 6.Wolf D (1990) Structure-Energy Correlation for Grain-Boundaries in Fcc Metals: 3. Symmetrical Tilt Boundaries. Acta Metall Mater 38:781–90CrossRefGoogle Scholar
- 7.Warner DH, Molinari JF. Effect of normal loading on grain boundary migration and sliding in copper. Model Simul Mater Sc. 2008;16:075007. Doi: 10.1088/0965-0393/16/7/075007 CrossRefGoogle Scholar
- 8.Sansoz F, Molinari JF (2005) Mechanical behavior of Sigma tilt grain boundaries in nanoscale Cu and Al: A quasicontinuum study. Acta Mater 53:1931–44CrossRefGoogle Scholar
- 9.Fensin SJ, Asta M, Hoagland RG (2012) Temperature dependence of the structure and shear response of a Sigma 11 asymmetric tilt grain boundary in copper from molecular-dynamics. Philos Mag 92:4320–33CrossRefGoogle Scholar
- 10.Peron-Luhrs V, Sansoz F, Noels L (2014) Quasicontinuum study of the shear behavior of defective tilt grain boundaries in Cu. Acta Mater 64:419–28CrossRefGoogle Scholar
- 11.de Koning M, Kurtz RJ, Bulatov VV, Henager CH, Hoagland RG, Cai W et al (2003) Modeling of dislocation-grain boundary interactions in FCC metals. J Nucl Mater 323:281–9CrossRefGoogle Scholar
- 12.Dewald M, Curtin WA. Multiscale modeling of dislocation/grain-boundary interactions: III. 60 degrees dislocations impinging on Sigma 3, Sigma 9 and Sigma 11 tilt boundaries in Al. Model Simul Mater Sc. 2011;19:055002. Doi: 10.1088/0965-0393/19/5/055002 CrossRefGoogle Scholar
- 13.Spearot DE, Sangid MD (2014) Insights on slip transmission at grain boundaries from atomistic simulations. Curr Opin Solid St M 18:188–95CrossRefGoogle Scholar
- 14.Adlakha I, Bhatia MA, Tschopp MA, Solanki KN (2014) Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium. Philos Mag 94:3445–66CrossRefGoogle Scholar
- 15.Adlakha I, Tschopp MA, Solanki KN (2014) The role of grain boundary structure and crystal orientation on crack growth asymmetry in aluminum. Mat Sci Eng A 618:345–54CrossRefGoogle Scholar
- 16.Cui CB, Beom HG (2014) Molecular statics simulations of intergranular fracture along Sigma 11 tilt grain boundaries in copper bicrystals. J Mater Sci 49:8355–64CrossRefGoogle Scholar
- 17.Luo SN, Germann TC, Tonks DL, An Q. Shock wave loading and spallation of copper bicrystals with asymmetric Sigma 3 <110> tilt grain boundaries. J Appl Phys. 2010;108:093526. Doi: 10.1063/1.3506707 CrossRefGoogle Scholar
- 18.Han WZ, An Q, Luo SN, Germann TC, Tonks DL, Goddard WA. Deformation and spallation of shocked Cu bicrystals with Sigma 3 coherent and symmetric incoherent twin boundaries. Phys Rev B. 2012;85:024107. Doi: 10.1103/Physrevb.85.024107
- 19.Fensin SJ, Valone SM, Cerreta EK, Escobedo-Diaz JP, Gray GT, Kang K, et al. Effect of grain boundary structure on plastic deformation during shock compression using molecular dynamics. Model Simul Mater Sc. 2013;21:015011. Doi: 10.1088/0965-0393/21/1/015011 CrossRefGoogle Scholar
- 20.Fensin SJ, Escobedo-Diaz JP, Brandl C, Cerreta EK, Gray GT, Germann TC et al (2014) Effect of loading direction on grain boundary failure under shock loading. Acta Mater 64:113–22CrossRefGoogle Scholar
- 21.Tschopp MA, Gao F, Solanki KN. Binding of HenV clusters to alpha-Fe grain boundaries. J Appl Phys. 2014;115:233501. Doi: 10.1063/1.4883357 CrossRefGoogle Scholar
- 22.Tschopp MA, Gao F, Yang L, Solanki KN. Binding energetics of substitutional and interstitial helium and di-helium defects with grain boundary structure in alpha-Fe. J Appl Phys. 2014;115:033503. Doi: 10.1063/1.4861719 CrossRefGoogle Scholar
- 23.Rajagopalan M, Tschopp MA, Solanki KN (2014) Grain Boundary Segregation of Interstitial and Substitutional Impurity Atoms in Alpha-Iron. JOM 66:129–38CrossRefGoogle Scholar
- 24.Frolov T, Olmsted DL, Asta M, Mishin Y. Structural phase transformations in metallic grain boundaries. Nat Commun. 2013;4:1899. Doi: 10.1038/Ncomms2919
- 25.Olmsted DL, Holm EA, Foiles SM (2009) Survey of computed grain boundary properties in face-centered cubic metals-II: Grain boundary mobility. Acta Mater 57:3704–13CrossRefGoogle Scholar
- 26.Janssens KGF, Olmsted D, Holm EA, Foiles SM, Plimpton SJ, Derlet PM (2006) Computing the mobility of grain boundaries. Nat Mater 5:124–7CrossRefGoogle Scholar
- 27.Tschopp MA, Coleman SP, McDowell DL. Al-Cu Symmetric/Asymmetric Tilt Grain Boundary Dataset. NIST Computational File Repository, 2015, http://hdl.handle.net/11256/358
- 28.Tschopp MA, McDowell DL (2007) Structural unit and faceting description of Sigma 3 asymmetric tilt grain boundaries. J Mater Sci 42:7806–11CrossRefGoogle Scholar
- 29.Tschopp MA, McDowell DL (2007) Structures and energies of Sigma 3 asymmetric tilt grain boundaries in copper and aluminium. Philos Mag 87:3147–73CrossRefGoogle Scholar
- 30.Tschopp MA, McDowell DL (2007) Asymmetric tilt grain boundary structure and energy in copper and aluminium. Philos Mag 87:3871–92CrossRefGoogle Scholar
- 31.van Beers PRM, Kouznetsova VG, Geers MGD, Tschopp MA, McDowell DL (2015) A multiscale model of grain boundary structure and energy: From atomistics to a continuum description. Acta Mater 82:513–29CrossRefGoogle Scholar
- 32.Tschopp MA, McDowell DL (2008) Grain boundary dislocation sources in nanocrystalline copper. Scr Mater 58:299–302CrossRefGoogle Scholar
- 33.Tschopp MA, McDowell DL (2008) Dislocation nucleation in Sigma 3 asymmetric tilt grain boundaries. Int J Plast 24:191–217CrossRefGoogle Scholar
- 34.Tschopp MA, Spearot DE, McDowell DL. Chapter 82 - Influence of Grain Boundary Structure on Dislocation Nucleation in FCC Metals. In: Hirth JP, editor. Dislocations in Solids: Elsevier; 2008. p. 43–139.Google Scholar
- 35.Tschopp MA, Tucker GJ, McDowell DL (2008) Atomistic simulations of tension-compression asymmetry in dislocation nucleation for copper grain boundaries. Comput Mater Sci 44:351–62CrossRefGoogle Scholar
- 36.Tschopp MA, Tucker GJ, McDowell DL (2007) Structure and free volume of <110> symmetric tilt grain boundaries with the E structural unit. Acta Mater 55:3959–69CrossRefGoogle Scholar
- 37.Tucker GJ, Tschopp MA, McDowell DL (2010) Evolution of structure and free volume in symmetric tilt grain boundaries during dislocation nucleation. Acta Mater 58:6464–73CrossRefGoogle Scholar
- 38.The Minerals, Metals & Materials Society (TMS), Modeling Across Scales: A Roadmapping Study for Connecting Materials Models and Simulations Across Length and Time Scales (Warrendale, PA 15086: TMS, 2015), http://www.tms.org/multiscalestudy/
- 39.Randle V (1996) The Role of the Coincidence Site Lattice in Grain Boundary Engineering: Institute of MaterialsGoogle Scholar
- 40.Plimpton S (1995) Fast Parallel Algorithms for Short-Range Molecular-Dynamics. J Comput Phys 117:1–19CrossRefGoogle Scholar
- 41.Rittner JD, Seidman DN, Merkle KL (1996) Grain-boundary dissociation by the emission of stacking faults. Phys Rev B 53:R4241–4CrossRefGoogle Scholar
- 42.Mishin Y, Mehl MJ, Papaconstantopoulos DA, Voter AF, Kress JD. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys Rev B. 2001;63.Google Scholar
- 43.Mishin Y, Farkas D, Mehl MJ, Papaconstantopoulos DA (1999) Interatomic potentials for monoatomic metals from experimental data and ab initio calculations. Phys Rev B 59:3393–407CrossRefGoogle Scholar
- 44.Hasson G, Herbeuva I, Boos JY, Biscondi M, Goux C (1972) Theoretical and Experimental Determinations of Grain-Boundary Structures and Energies - Correlation with Various Experimental Results. Surf Sci 31:115CrossRefGoogle Scholar
- 45.Ernst F, Finnis MW, Koch A, Schmidt C, Straumal B, Gust W (1996) Structure and energy of twin boundaries in copper. Zeitschrift Fur Metallkunde 87:911–22Google Scholar
- 46.Wolf U, Ernst F, Muschik T, Finnis MW, Fischmeister HF (1992) The Influence of Grain-Boundary Inclination on the Structure and Energy of Sigma=3 Grain-Boundaries in Copper. Philosophical Magazine A 66:991–1016CrossRefGoogle Scholar
- 47.Rittner JD, Seidman DN (1996) <110> symmetric tilt grain-boundary structures in fcc metals with low stacking-fault energies. Phys Rev B 54:6999–7015CrossRefGoogle Scholar
- 48.Spearot DE, Tschopp MA, Jacob KI, McDowell DL (2007) Tensile strength of <100> and <110> tilt bicrystal copper interfaces. Acta Mater 55:705–14CrossRefGoogle Scholar
- 49.Medlin DL, Mills MJ, Stobbs WM, Daw MS, Cosandey F (1993) Hrtem Observations of a Sigma=3 (112) Bicrystal Boundary in Aluminum. Atomic-Scale Imaging of Surface and Interfaces (MRS Symposium Proceedings, Volume 295). Materials Research Society, Pittsburgh, PA, pp 91–6Google Scholar
- 50.Ernst F, Finnis MW, Hofmann D, Muschik T, Schonberger U, Wolf U et al (1992) Theoretical Prediction and Direct Observation of the 9r Structure in Ag. Phys Rev Lett 69:620–3CrossRefGoogle Scholar
- 51.Hofmann D, Finnis MW (1994) Theoretical and Experimental-Analysis of near Sigma-3 (211) Boundaries in Silver. Acta Metallurgica Et Materialia 42:3555–67CrossRefGoogle Scholar
- 52.Campbell GH, Chan DK, Medlin DL, Angelo JE, Carter CB (1996) Dynamic observation of the FCC to 9R shear transformation in a copper Sigma=3 incoherent twin boundary. Scr Mater 35:837–42CrossRefGoogle Scholar
- 53.Holm EA, Olmsted DL, Foiles SM (2010) Comparing grain boundary energies in face-centered cubic metals: Al, Au, Cu and Ni. Scripta Materialia 63:905–8CrossRefGoogle Scholar
- 54.Warner DH, Molinari JF (2008) Deformation by grain boundary hinge-like behavior. Mater Lett 62:57–60CrossRefGoogle Scholar
- 55.Sansoz F, Molinari JF (2004) Incidence of atom shuffling on the shear and decohesion behavior of a symmetric tilt grain boundary in copper. Scr Mater 50:1283–8CrossRefGoogle Scholar
- 56.Cahn JW, Mishin Y (2009) Recrystallization initiated by low-temperature grain boundary motion coupled to stress. Int J Mater Res 100:510–5CrossRefGoogle Scholar
- 57.Cahn JW, Mishin Y, Suzuki A (2006) Coupling grain boundary motion to shear deformation. Acta Mater 54:4953–75CrossRefGoogle Scholar
- 58.Wan L, Li J. Shear responses of [110]-tilt {115}/{111} asymmetric tilt grain boundaries in fcc metals by atomistic simulations. Model Simul Mater Sc. 2013;21:055013. Doi: 10.1088/0965-0393/21/5/055013 CrossRefGoogle Scholar
- 59.de Koning M, Miller R, Bulatov VV, Abraham FF (2002) Modelling grain-boundary resistance in intergranular dislocation slip transmission. Philos Mag A 82:2511–27CrossRefGoogle Scholar
- 60.Dewald MP, Curtin WA (2007) Multiscale modelling of dislocation/grain-boundary interactions: I. Edge dislocations impinging on Sigma 11 (113) tilt boundary in Al. Model Simul Mater Sc 15:S193–215CrossRefGoogle Scholar
- 61.Dewald MP, Curtin WA (2007) Multiscale modelling of dislocation/grain boundary interactions. II. Screw dislocations impinging on tilt boundaries in Al. Philos Mag 87:4615–41CrossRefGoogle Scholar
- 62.Bulatov VV, Reed BW, Kumar M (2014) Grain boundary energy function for fcc metals. Acta Mater 65:161–75CrossRefGoogle Scholar
- 63.Marquis EA, Medlin DL (2005) Structural duality of 1/3 <111> twin-boundary disconnections. Phil Mag Lett 85:387–94CrossRefGoogle Scholar
- 64.Medlin DL, Campbell GH, Carter CB (1998) Stacking defects in the 9R phase at an incoherent twin boundary in copper. Acta Mater 46:5135–42CrossRefGoogle Scholar
- 65.Medlin DL, Carter CB, Angelo JE, Mills MJ (1997) Climb and glide of a/3<111> dislocations in an aluminium Sigma=3 boundary. Philosophical Magazine A 75:733–47CrossRefGoogle Scholar
- 66.Coleman SP, Sichani MM, Spearot DE (2014) A Computational Algorithm to Produce Virtual X-ray and Electron Diffraction Patterns from Atomistic Simulations. JOM 66:408–16CrossRefGoogle Scholar
- 67.Coleman SP, Spearot DE (2015) Atomistic simulation and virtual diffraction characterization of homophase and heterophase alumina interfaces. Acta Mater 82:403–13CrossRefGoogle Scholar
- 68.Coleman SP, Spearot DE, Capolungo L. Virtual diffraction analysis of Ni [010] symmetric tilt grain boundaries. Model Simul Mater Sc. 2013;21:055020. Doi: 10.1088/0965-0393/21/5/055020 CrossRefGoogle Scholar
- 69.Coleman S, Tschopp M, Weinberger C, Spearot D (2015) Bridging atomistic simulations and experiments via virtual diffraction: understanding homophase grain boundary and heterophase interface structures. J Mater Sci. doi: 10.1007/s10853-015-9087-9 CrossRefGoogle Scholar
- 70.Brown JA, Mishin Y. Dissociation and faceting of asymmetrical tilt grain boundaries: Molecular dynamics simulations of copper. Phys Rev B. 2007;76:134118. Doi: 10.1103/Physrevb.76.134118
- 71.Han WZ, Demkowicz MJ, Fu EG, Wang YQ, Misra A (2012) Effect of grain boundary character on sink efficiency. Acta Mater 60:6341–51CrossRefGoogle Scholar
- 72.Rajagopalan M, Bhatia MA, Tschopp MA, Srolovitz DJ, Solanki KN (2014) Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries. Acta Mater 73:312–25CrossRefGoogle Scholar
- 73.Suzuki A, Mishin Y (2003) Atomistic modeling of point defects and diffusion in copper grain boundaries. Interface Sci 11:131–48CrossRefGoogle Scholar
- 74.Tschopp MA, Solanki KN, Gao F, Sun X, Khaleel MA, Horstemeyer MF. Probing grain boundary sink strength at the nanoscale: Energetics and length scales of vacancy and interstitial absorption by grain boundaries in alpha-Fe. Phys Rev B. 2012;85:064108. Doi: 10.1103/Physrevb.85.064108
- 75.Bai XM, Voter AF, Hoagland RG, Nastasi M, Uberuaga BP (2010) Efficient Annealing of Radiation Damage Near Grain Boundaries via Interstitial Emission. Science 327:1631–4CrossRefGoogle Scholar
- 76.Bai XM, Vernon LJ, Hoagland RG, Voter AF, Nastasi M, Uberuaga BP. Role of atomic structure on grain boundary-defect interactions in Cu. Phys Rev B. 2012;85.Google Scholar
- 77.Tucker GJ, McDowell DL (2011) Non-equilibrium grain boundary structure and inelastic deformation using atomistic simulations. Int J Plasticity 27:841–57CrossRefGoogle Scholar
- 78.Vitek V, Sutton AP, Wang GJ, Schwartz D (1983) On the Multiplicity of Structures of Grain-Boundaries. Scripta Metall Mater 17:183–9CrossRefGoogle Scholar
- 79.Wang GJ, Sutton AP, Vitek V (1984) A Computer-Simulation Study of (001) and (111) Tilt Boundaries - the Multiplicity of Structures. Acta Metall 32:1093–104CrossRefGoogle Scholar
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