A dislocation-dipole in one-dimensional lattice model

References

• U. Dehlinger, Zur Theorie der Rekristallisation reiner Metalle, Ann. Phys. 394(7) (1929), pp. 749–793.
   Google Scholar
• F.C. Frank and W.T. Read, Multiplication processes for slow moving dislocations, Phys. Rev. 79(4) (1950), pp. 722–723.
   Google Scholar
• F.R.N. Nabarro, The mathematical theory of stationary dislocations, Adv. Phys.1(3) (1952), pp. 269–394.
   Web of Science ®Google Scholar
• F.R.N. Nabarro, Dislocations in a simple cubic lattice, Proc. Phys. Soc. Lond. 59(332) (1947), pp. 256–272.
   Google Scholar
• R.E. Peierls, The size of a dislocation, Proc. Phys. Soc. Lond. 52 (1940), pp. 34–37.
   Google Scholar
• G. Schoeck, The energy of dislocation dipoles, Philos. Mag. 94(14) (2014), pp. 1542–1551.
   Web of Science ®Google Scholar
• F. Bormann, K. Mikes, O. Rokos, and R. Peerlings, The Peierls-Nabarro finite element model in two-phase microstructures – a comparison with atomistic, Mech. Mater. 150 (2020), p. 103555.
   Google Scholar
• J. Mianroodi, A. Hunter, I. Beyerlein, and B. Svendsen, Theoretical and computational comparison of models for dislocation dissociation and stacking fault/core formation in fcc crystals, J. Mech. Phys. Solids. 95 (2016), pp. 719–741.
   Web of Science ®Google Scholar
• S. Wang, Dislocation equation from the lattice dynamics, J. Phys. A Math. Theor. 41 (2008), pp. 015005.
   Google Scholar
• T. Luo, P. Ming, and Y. Xiang, From atomistic model to the Peierls-Nabarro model with γ-surface for dislocations, Arch. Ration. Mech. Anal. 230 (2018), pp. 735–781.
   Web of Science ®Google Scholar
• G. Liu, X. Cheng, J. Wang, K. Chen, and Y. Shen, Improvement of nonlocal Peierls-Nabarro models, Comput. Mater. Sci. 131 (2017), pp. 69–77.
   Web of Science ®Google Scholar
• M. Peach and J.S. Koehler, The forces exerted on dislocations and the stress fields produced by them. Phys. Rev. 80(3) (1950), pp. 436–439.
   Google Scholar
• J.D. Eshelby, The continuum theory of lattice defects, in Solid State Physics, Vol. 3, F. Seitz and D. Turnbull, eds., Academic Press, N.Y., 1956, pp. 79–144.
   Google Scholar
• J. Frenkel and T. Kontorova, On the theory of plastic deformation and twinning, Phys. z. Sowjetunion13 (1938), pp. 1–10.
   Google Scholar
• S.V. Dmitriev, L.V. Nauman, A.A. Ovcharov, and M.D. Starostenkov, Dislocation nucleation mechanism in a one-dimensional model of a Frenkel-Kontorova crystal, Russian Phys. J. 39(2) (1996), pp. 164–167.
   Google Scholar
• S.V. Dmitriev, L.V. Nauman, A.M. Wusatowska-Sarek, and M.D. Starostenkov, Generation and annihilation of dislocations in the discrete Frenkel-Kontorova model, Phys. Status Solidi (b) 89 (1997), pp. 89–96.
   Google Scholar
• N. Akhmediev and A. Ankiewicz, Solitons: Non-linear Pulses and Beams, Chapman and Hall, London, 1997.
   Google Scholar
• Y.N. Gornostyrev, M.I. Katsnelson, A.V. Kravtsov, and A.V. Trefilov, Kink nucleation in the two-dimensional Frenkel-Kontorova model, Phys. Rev. E. 66(2) (2002), p. 027201.
   Google Scholar
• A. Seeger and P. Schiller, Kinks in dislocation lines and their effects on the internal friction in crystals, in Physical Acoustics, Vol. IIIA, W. Mason, ed., Academic, New York, 1966, p. 361.
   Google Scholar
• J.P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968.
   Google Scholar
• A. Seeger, Solitons and statistical thermodynamics, in Trends in Applications of Pure Mathematics to Mechanics, E. Kröner, K. Kirchgässner, eds., Springer-Verlag, New York, 1986, pp. 114–155.
   Google Scholar
• W. Atkinson and N. Cabrera, Motion of a Frenkel-Kontorowa dislocation in a 1-dimensional crystal, Phys. Rev. 138(3A) (1965), pp. A763–766.
   Google Scholar
• O. Kresse and L. Truskinovsky, Mobility of lattice defects: discrete and continuum approaches, J. Mech. Phys. Solids. 51(7) (2003), pp. 1305–1332.
   Web of Science ®Google Scholar
• B.L. Sharma, On energy balance and the structure of radiated waves in kinetics of crystalline defects, J. Mech. Phys. Solids. 96 (2016), pp. 88–120.
   Web of Science ®Google Scholar
• J.H. Weiner and W.T. Sanders, Peierls stress and creep of linear chain, Phys. Rev. A-Gen. Phys.134(4A) (1964), pp. 1007–1015.
   Google Scholar
• T. Dumitrica, T. Belytschko, and B.I. Yakobson, Bond-breaking bifurcation states in carbon nanotube fracture, J. Chem. Phys. 118 (2003), pp. 9485.
   Web of Science ®Google Scholar
• Y. Kamimura, Experimental evaluation of the Peierls stresses in a variety of crystals and their relation to the crystal structure, Acta. Mater. 61(1) (2013), pp. 294–309.
   Web of Science ®Google Scholar
• R. Hobart, Peierls stress dependence on dislocation width, J. Appl. Phys.36(6) (1965), pp. 1944–1948.
   Web of Science ®Google Scholar
• B.L. Sharma, A family of solitary waves in Frenkel-Kontorova lattice, Oct (2019). Available at arXiv: 1910.06904.
   Google Scholar
• M. Bixon and R. Zwanzig, Brownian motion of a nonlinear oscillator, J. Stat. Phys. 3 (1971), pp. 245–260.
   Google Scholar
• M. Gitterman, The Noisy Oscillator, World Scientific, Singapore, 2005.
   Google Scholar
• J.A. Krumhansl and J.R. Schrieffer, Dynamics and statistical mechanics of a one-dimensional model Hamiltonian for structural phase transitions, Phys. Rev. B 11 (1975), pp. 3535.
   Web of Science ®Google Scholar
• T. Vegge, T. Rasmussen, T. Leffers, O.B. Pedersen, and K.W. Jacobsen, Determination of the of rate cross slip of screw dislocations, Phys. Rev. Lett. 85(18) (2000), p. 3866.
   PubMed Web of Science ®Google Scholar
• V. Celli and N. Flytzanis, Motion of a screw dislocation in a crystal, J. Appl. Phys. 41(11) (1970), pp. 4443–4447.
   Web of Science ®Google Scholar
• S. Ishioka, Uniform motion of a screw dislocation in a lattice, J. Phys. Soc. Jpn 30(2) (1971), pp. 323–327.
   Google Scholar
• A.A. Maradudin, Screw dislocations and discrete elastic theory, J. Phys. Chem. Solids 9(1) (1958), pp. 1–20.
   Web of Science ®Google Scholar
• W.T. Sanders, Peierls stress for an idealized crystal model, Phys. Rev. 128(4) (1962), pp. 1540–1549.
   Google Scholar
• J. Kratochvíl and V.L. Indenbom, The mobility of a dislocation in the Frenkel-Kontorova model, Czechoslov. J. Phys. B 13 (1963), pp. 814–821.
   Google Scholar
• H. Levy and F. Lessman, Finite Difference Equations, Dover, New York, 1992.
   Google Scholar
• B.L. Sharma, The kinetic relation of a Peierls dislocation in a higher-gradient dispersive continuum, Ph.D dissertation, Cornell University, Oct 2004.
   Google Scholar
• B.L. Sharma and A. Vainchtein, Quasistatic evolution of steps along a phase boundary, Contin. Mech. Thermodyn. 19(6) (2007), pp. 347–377.
   Web of Science ®Google Scholar
• P. Rosakis and A. Vainchtein, New solutions for slow moving kinks in a forced frenkel-Kontorova chain, J. Nonlinear Sci. 23 (2013), pp. 1089–1110.
   Web of Science ®Google Scholar
• J.L. Ericksen, Equilibrium of bars, J. Elast. 5 (1975), pp. 191–202.
   Web of Science ®Google Scholar
• L. Truskinovsky and A. Vainchtein, Peierls-Nabarro landscape for martensitic phase transitions, Phys. Rev. B. 67 (2003), pp. 172103.
   Google Scholar