Nonplanar core structure of the screw dislocations in tantalum from the improved Peierls–Nabarro theory

References

• J. Christian, Some surprising features of the plastic deformation of body-centered cubic metals and alloys, Metall. Trans. A 14 (1983), pp. 1237–1256.
   Web of Science ®Google Scholar
• G. Taylor, Thermally-activated deformation of bcc metals and alloys, Prog. Mater. Sci. 36 (1992), pp. 29–61.
   Web of Science ®Google Scholar
• A. Seeger, The flow stress of high-purity refractory body-centred cubic metals and its modification by atomic defects, J. Phys. Paris IV 5 (1995), pp. C7–45.
   Google Scholar
• W. Pichl, Slip geometry and plastic anisotropy of body-centered cubic metals, Phys. Status Solidi A 189 (2002), pp. 5–25.
   Web of Science ®Google Scholar
• M.S. Duesbery and V. Vitek, Plastic anisotropy in bcc transition metals, Acta Mater. 46 (1998), pp. 1481–1492.
   Web of Science ®Google Scholar
• P.B. Hirsch, A. Howie, and M.J. Whelan, A kinematical theory of diffraction contrast of electron transmission microscope images of dislocations and other defects, Philos. Trans. A 252 (1960), pp. 499–529.
   Web of Science ®Google Scholar
• W. Sigle, High-resolution electron microscopy and molecular dynamics study of the (a/2)[111] screw dislocation in molybdenum, Philos. Mag. A 79 (1999), pp. 1009–1020.
   Google Scholar
• B. Mendis, Y. Mishin, C. Hartley, and K. Hemker, Use of the Nye tensor in analyzing HREM images of bcc screw dislocations, Philos. Mag. 86 (2006), pp. 4607–4640.
   Web of Science ®Google Scholar
• J.Y. Kim, D. Jang, and J.R. Greer, Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale, Acta Mater. 58 (2010), pp. 2355–2363.
   Web of Science ®Google Scholar
• P.D. Nellist, H. Yang, J.G. Lozano, T.J. Pennycook, and P.B. Hirsch, Stem optical sectioning for imaging screw displacements in dislocation core structures, Microsc. Microanal. 20 (2014), pp. 86–87.
   Google Scholar
• L. Yang, P. Söderlind, and J.A. Moriarty, Accurate atomistic simulation of 1/2a〈111〉 screw dislocations and other defects in bcc tantalum, Philos. Mag. A 81 (2001), pp. 1355–1385.
   Web of Science ®Google Scholar
• V. Vitek, R. Perrin, and D. Bowen, The core structure of 1/2 (1\,1\,1) screw dislocations in bcc crystals, Philos. Mag. 21 (1970), pp. 1049–1073.
   Web of Science ®Google Scholar
• V. Vitek, Theory of the core structures of dislocations in bcc metals, Cryst. Lattice Defects 5 (1974), pp. 1–34.
   Google Scholar
• Z. Basinski, M. Duesbery, and R. Taylor, Influence of shear stress on screw dislocations in a model sodium lattice, Can. J. Phys. 49 (1971), pp. 2160–2180.
   Web of Science ®Google Scholar
• A. Seeger and C. Wüthrich, Dislocation relaxation processes in body-centred cubic metals, Nuovo Cimento B (1971--1996). 33 (1976), pp. 38–75.
   Google Scholar
• G. Ackland and R. Thetford, An improved n-body semi-empirical model for body-centred cubic transition metals, Philos. Mag. A 56 (1987), pp. 15–30.
   Web of Science ®Google Scholar
• R. Johnson and D. Oh, Analytic embedded atom method model for bcc metals, J. Mater. Res. 4 (1989), pp. 1195–1201.
   Web of Science ®Google Scholar
• L. Yang and J. Moriarty, Kink-pair mechanisms for a/2〈111〉 screw dislocation motion in bcc tantalum, Mater. Sci. Eng., A 319 (2001), pp. 124–129.
   Web of Science ®Google Scholar
• K. Ito and V. Vitek, Atomistic study of non-schmid effects in the plastic yielding of bcc metals, Philos. Mag. A 81 (2001), pp. 1387–1407.
   Web of Science ®Google Scholar
• C. Woodward and S. Rao, Ab-initio simulation of isolated screw dislocations in bcc mo and ta, Philos. Mag. A 81 (2001), pp. 1305–1316.
   Web of Science ®Google Scholar
• C. Woodward and S. Rao, Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc mo and ta, Phys. Rev. Lett. 88 (2002), p. 216402.
   PubMed Web of Science ®Google Scholar
• C. Woodward, First-principles simulations of dislocation cores, Mater. Sci. Eng. A 400 (2005), pp. 59–67.
   Web of Science ®Google Scholar
• S. Ismail-Beigi and T. Arias, Ab initio study of screw dislocations in mo and ta: A new picture of plasticity in bcc transition metals, Phys. Rev. Lett. 84 (2000), p. 1499.
   PubMed Web of Science ®Google Scholar
• C.R. Weinberger, G.J. Tucker, and S.M. Foiles, Peierls potential of screw dislocations in bcc transition metals: Predictions from density functional theory, Phys. Rev. B. 87 (2013), p. 054114.
   Web of Science ®Google Scholar
• L. Dezerald, L. Ventelon, E. Clouet, C. Denoual, D. Rodney, and F. Willaime, Ab initio modeling of the two-dimensional energy landscape of screw dislocations in bcc transition metals, Phys. Rev. B 89 (2014), p. 024104.
   Web of Science ®Google Scholar
• L.M. Hale, J.A. Zimmerman, and C.R. Weinberger, Simulations of bcc tantalum screw dislocations: Why classical inter-atomic potentials predict {112} slip, Comput. Mater. Sci. 90 (2014), pp. 106–115.
   Web of Science ®Google Scholar
• J. Bassani, K. Ito, and V. Vitek, Complex macroscopic plastic flow arising from non-planar dislocation core structures, Mater. Sci. Eng., A 319 (2001), pp. 97–101.
   Web of Science ®Google Scholar
• G. Wang, A. Strachan, T. Cagin, and W.A. Goddard, Molecular dynamics simulations of 1/2a〈111〉 screw dislocation in ta, Mater. Sci. Eng., A 309 (2001), pp. 133–137.
   Web of Science ®Google Scholar
• G. Wang, A. Strachan, T. Çağın, and W.A. Goddard III, Atomistic simulations of kinks in 1/2a〈111〉 screw dislocations in bcc tantalum, Phys. Rev. B 68 (2003), p. 224101.
   Web of Science ®Google Scholar
• J. Li, C.Z. Wang, J.P. Chang, W. Cai, V.V. Bulatov, K.M. Ho, and S. Yip, Core energy and peierls stress of a screw dislocation in bcc molybdenum: A periodic-cell tight-binding study, Phys. Rev. B 70 (2004), p. 104113.
   Web of Science ®Google Scholar
• R. Gröger, A. Bailey, and V. Vitek, Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈111〉; screw dislocations at 0k, Acta Mater. 56 (2008), pp. 5401–5411.
   Web of Science ®Google Scholar
• R. Gröger, V. Racherla, J. Bassani, and V. Vitek, Multiscale modeling of plastic deformation of molybdenum and tungsten: Ii. Yield criterion for single crystals based on atomistic studies of glide of 1/2〈111〉 screw dislocations, Acta Mater. 56 (2008), pp. 5412–5425.
   Web of Science ®Google Scholar
• R. Gröger and V. Vitek, Multiscale modeling of plastic deformation of molybdenum and tungsten. III. Effects of temperature and plastic strain rate, Acta Mater. 56 (2008), pp. 5426–5439.
   Web of Science ®Google Scholar
• E. Clouet, L. Ventelon, and F. Willaime, Dislocation core energies and core fields from first principles, Phys. Rev. Lett. 102 (2009), p. 055502.
   PubMed Web of Science ®Google Scholar
• E. Clouet, Dislocation core field. I. modeling in anisotropic linear elasticity theory. Phys. Rev. B. 84 (2011), p. 224111.
   Web of Science ®Google Scholar
• E. Clouet, L. Ventelon, and F. Willaime, Dislocation core field. II. Screw dislocation in iron, Phys. Rev. B 84 (2011), p. 224107.
   Web of Science ®Google Scholar
• L. Ventelon, F. Willaime, E. Clouet, and D. Rodney, Ab initio investigation of the peierls potential of screw dislocations in bcc fe and w, Acta Mater. 61 (2013), pp. 3973–3985.
   Web of Science ®Google Scholar
• V. Vitek, Intrinsic stacking faults in body-centred cubic crystals, Philos. Mag. 18 (1968), pp. 773–786.
   Web of Science ®Google Scholar
• V. Vitek, Core structure of screw dislocations in body-centred cubic metals: Relation to symmetry and interatomic bonding, Philos. Mag. 84 (2004), pp. 415–428.
   Web of Science ®Google Scholar
• V. Vitek and V. Paidar, Non-planar dislocation cores: A ubiquitous phenomenon affecting mechanical properties of crystalline materials, Dislocations Solids 14 (2008), pp. 439–514.
   Google Scholar
• L. Lej\v{c}ek and F. Kroupa, Peierls nabarro model of nonplanar screw core, Czech. J. Phys. B 26 (1976), pp. 528–537.
   Google Scholar
• H. Zhang, E. Mann, and A. Seeger, Approximate solution of the peierls equation for screw dislocations with threefold symmetry, Phys. Stat. Sol. (b) 153 (1989), pp. 465–477.
   Web of Science ®Google Scholar
• A.H.W. Ngan, A generalized peierls-nabarro model for nonplanar screw dislocation cores, J. Mech. Phys. Solids 45 (1997), pp. 903–921.
   Web of Science ®Google Scholar
• J.A. Yan, C.Y. Wang, and S.Y. Wang, Generalized-stacking-fault energy and dislocation properties in bcc fe: A first-principles study, Phys. Rev. B 70 (2004), p. 174105.
   Web of Science ®Google Scholar
• E. Clouet, S. Garruchet, and H. Nguyen, Dislocation interaction with c in a-fe: A comparison between atomic simulations and elasticity theory. Acta Mater. 56 (2008), pp. 3450–3460.
   Web of Science ®Google Scholar
• R. Liu, S. Wang, and X. Wu, The peierls stress of the moving 1/2〈111〉{110} screw dislocation in ta, J. Phys.: Condens. Matter 21 (2009), p. 345401.
   PubMed Web of Science ®Google Scholar
• S. Wang, N. Jiang, R. Wang, and Y. Zhou, Structure of screw dislocation core in Ta at high pressure, J. Appl. Phys. 115 (2014), p. 093505.
   Web of Science ®Google Scholar
• G. Lu, V.V. Bulatov, and N. Kioussis*, A nonplanar peierls-nabarro model and its application to dislocation cross-slip, Philos. Mag. 83 (2003), pp. 3539–3548.
   Web of Science ®Google Scholar
• S. Bobylev, T. Ishizaki, S. Kuramoto, and I. Ovid’ko, Theory of the nonplanar splitting of screw dislocations in gum metal, Phys. Rev. B 77 (2008), p. 094115.
   Web of Science ®Google Scholar
• J.P. Hirth and J. Lothe, Theory of Dislocations, John Wiley & Sons, New York, 1982.
   Google Scholar
• J. Nye, Some geometrical relations in dislocated crystals, Acta Metall. 1 (1953), pp. 153–162.
   Google Scholar
• J. Eshelby, The continuum theory of lattice defects, Solid State Phys. 3 (1956), pp. 79–144.
   Web of Science ®Google Scholar
• E. Kröner, Continuum theory of defects, Phys. Defects 35 (1981), pp. 217–315.
   Google Scholar
• A. Kadic and D.G. Edelen, A Gauge theory of dislocations and disclinations, in Gauge Theory of Dislocations and Disclinations Vol. 174, 1983.
   Google Scholar
• F.R.N. Nabarro, Mathematical theory of stationary dislocations, Adv. Phys. 1 (1952), pp. 269–394.
   Web of Science ®Google Scholar
• G. Simmons and H. Wang, Single crystal elastic constants and calculated aggregate properties (1971).
   Google Scholar
• R. Wang, S. Wang, X. Wu, and Y. Yao, The third-order elastic moduli and pressure derivatives for alre (re = y, pr, nd, tb, dy, ce) intermetallics with b2-structure: A first-principles study, Solid State Commun. 151 (2011), pp. 996–1000.
   Web of Science ®Google Scholar
• J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996), pp. 3865–3868.
   PubMed Web of Science ®Google Scholar
• J.P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 78 (1996), pp. 1396–1396.
   Web of Science ®Google Scholar
• P.E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50 (1994), pp. 17953–17979.
   PubMed 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.
   PubMed Web of Science ®Google Scholar
• H.J. Monkhorst and J.D. Pack, Special points for brillouin-zone integrations, Phys. Rev. B 13 (1976), pp. 5188–5192.
   Web of Science ®Google Scholar
• W. Shaofeng, Lattice theory for structure of dislocations in a two-dimensional triangular crystal, Phys. Rev. B. 65 (2002), p. 094111.
   Web of Science ®Google Scholar
• S.F. Wang, A unified dislocation equation from lattice statics, J. Phys. A: Math. Theor. 42 (2008), p. 025208.
   Web of Science ®Google Scholar
• R. Peierls, The size of a dislocation, Proc. Phys. Soc. London 52 (1940), pp. 34–37.
   Google Scholar
• S. Wang, The dislocation equation as a generalization of peierls equation, Philos. Mag. 95 (2015), pp. 3768–3784.
   Web of Science ®Google Scholar
• J.W.V. Vítek, Dislocations and stacking faults, Rep. Prog. Phys. 33 (1970), pp. 307–411.
   Web of Science ®Google Scholar
• J. Hartford, B. Von Sydow, G. Wahnström, and B. Lundqvist, Peierls barriers and stresses for edge dislocations in pd and al calculated from first principles, Phys. Rev. B 58 (1998), pp. 2487–2496.
   Web of Science ®Google Scholar
• X. Wu, R. Wang, and S. Wang, Generalized-stacking-fault energy and surface properties for hcp metals: A first-principles study, Appl. Surf. Sci. 256 (2010), pp. 3409–3412.
   Web of Science ®Google Scholar
• X.Z. Wu, R. Wang, S.F. Wang, and Q.Y. Wei, Ab initio calculations of generalized-stacking-fault energy surfaces and surface energies for fcc metals, Appl. Surf. Sci. 256 (2010), pp. 6345–6349.
   Web of Science ®Google Scholar
• X. Wu and S. Wang, Application of parametric derivation method to the calculation of peierls energy and peierls stress in lattice theory, Acta Mech. Solida Sin. 20 (2007), pp. 363–368.
   Web of Science ®Google Scholar
• S.L. Frederiksen and K.W. Jacobsen, Density functional theory studies of screw dislocation core structures in bcc metals, Philos. Mag. 83 (2003), pp. 365–375.
   Web of Science ®Google Scholar
• Y.P. Pellegrini, Equation of motion and subsonic-transonic transitions of rectilinear edge dislocations: A collective-variable approach, Phys. Rev. B 90 (2014), p. 054120.
   Web of Science ®Google Scholar