October  2011, 4(5): 1057-1067. doi: 10.3934/dcdss.2011.4.1057

Interaction of moving discrete breathers with interstitial defects

1. 

Grupo de Física No Lineal. Departamento de Física Aplicada I., Escuela Politécnica Superior. Universidad de Sevilla, C/ Virgen de África, 7, 41011-Sevilla, Spain

2. 

Grupo de Física No Lineal. Departamento de Física Aplicada I., Escuela Politécnica Superior. Universidad de Sevilla, C/ Virgen de África, 7. 41011 Sevilla, Spain

3. 

Maxwell Institute and Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, United Kingdom

4. 

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, United Kingdom

Received  July 2009 Revised  October 2009 Published  December 2010

In this paper, interstitial migration generated by scattering with a mobile breather is investigated numerically in a Frenkel-Kontorova one-dimensional lattice. Consistent with experimental results, it is shown that interstitial diffusion is more likely and faster than vacancy diffusion. Our simulations support the hypothesis that a long-range energy transport mechanism involving moving nonlinear vibrational excitations may significantly enhance the mobility of point defects in a crystal lattice.
Citation: Jesús Cuevas, Bernardo Sánchez-Rey, J. C. Eilbeck, Francis Michael Russell. Interaction of moving discrete breathers with interstitial defects. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1057-1067. doi: 10.3934/dcdss.2011.4.1057
References:
[1]

G. Abrasonis, W. Möller and X. X. Ma, Anomalous ion accelerated bulk diffusion of interstitial nitrogen, Phys. Rev. Lett., 96 (2006), 065901. doi: 10.1103/PhysRevLett.96.065901.

[2]

G. Abrasonis, J. P. Rivière, C. Templier, A. Declémy, L. Pranevicius and X. Milhet, Ion beam nitriding of single and polycrystalline austenitic stainless steel, J. Appl. Phys., 97 (2005), 083531. doi: 10.1063/1.1863455.

[3]

A. Álvarez, J. F. R. Archilla, F. R. Romero, J. Cuevas and P. V. Larsen, Breather trapping and breather transmission in a DNA model with an interface, Eur. Phys. J. B, 51 (2006), 119-130.

[4]

S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Lattice dynamics (Paris, 1995), Physica D, 103 (1997), 201-250. doi: 10.1016/S0167-2789(96)00261-8.

[5]

S. Aubry and T. Cretegny, Mobility and reactivity of discrete breathers, Localization in nonlinear lattices (Dresden, 1997), Physica D, 119 (1998), 34-46. doi: 10.1016/S0167-2789(98)00062-1.

[6]

A. S. Barker and A. J. Sievers, Optical studies of the vibrational properties of disordered solids, Rev. Mod. Phys., 47 (1975), S1-S179. doi: 10.1103/RevModPhys.47.S1.2.

[7]

I. Bena, A. Saxena and J. M. Sancho, Interaction of a discrete breather with a lattice junction, Phys. Rev. E, 65 (2002), 036617. doi: 10.1103/PhysRevE.66.036617.

[8]

O. M. Braun and Yu. S. Kivshar, Nonlinear dynamics of the Frenkel-Kontorova model, Phys. Rep., 306 (1998), 1-108. doi: 10.1016/S0370-1573(98)00029-5.

[9]

O. M. Braun and Yu. S. Kivshar, "The Frenkel-Kontorova Model: Concepts, Methods and Applications," Texts and Monographs in Physics, Springer-Verlag, Berlin, 2004.

[10]

D. Chen, S. Aubry and G. P. Tsironis, Breather mobility in discrete $\phi^4$ nonlinear lattices, Phys. Rev. Lett., 77 (1996), 4776-4779. doi: 10.1103/PhysRevLett.77.4776.

[11]

J. Cuevas, J. F. R. Archilla, B. Sánchez-Rey and F. R. Romero, Interaction of moving discrete breathers with vacancies, Physica D, 216 (2006), 115-120. doi: 10.1016/j.physd.2005.12.022.

[12]

J. Cuevas, C. Katerji, J. F. R. Archilla, J. C. Eilbeck and F. M. Russell, Influence of moving breathers on vacancies migration, Phys. Lett. A, 315 (2003), 364-371. doi: 10.1016/S0375-9601(03)01097-1.

[13]

J. Cuevas and P. G. Kevrekidis, Breathers statics and dynamics in Klein-Gordon chains with a bend, Phys. Rev. E, 69 (2004), 056609. doi: 10.1103/PhysRevE.69.056609.

[14]

J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving discrete breathers in a Klein-Gordon chain with an impurity, J. Phys. A: Math. and Gen., 35 (2002), 10519-10530. doi: 10.1088/0305-4470/35/49/302.

[15]

T. Dauxois and M. Peyrard, "Physics of Solitons," Cambridge University Press, 2006.

[16]

S. V. Dmitriev, T. Miyauchi, K. Abe and T. Shigenari, Kink-breather solution in the weakly discrete Frenkel-Kontorova model, Phys. Rev. E, 61 (1998), 5880-5885. doi: 10.1103/PhysRevE.61.5880.

[17]

S. V. Dmitriev, T. Shigenari, A. A. Vasiliev and A. E. Miroshnichenko, Effect of discreteness on a sine-Gordon three-soliton solution, Phys. Lett. A, 246 (1998), 129. doi: 10.1016/S0375-9601(98)00459-9.

[18]

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon and H. C. Morris, "Solitons and Nonlinear Wave Equations," Academic Press, London, 1982.

[19]

J. C. Eilbeck, P. S. Lomdahl and A. C. Scott, Soliton structure in crystalline acetanilide, Phys. Rev. B, 30 (1984), 4703-4712. doi: 10.1103/PhysRevB.30.4703.

[20]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd and J. S. Aitchison, Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett., 81 (1998), 3383-3386.

[21]

S. Flach and A. Gorbach, Discrete breathers - Advances in theory and applications, Phys. Rep., 467 (2008), 1-116. doi: 10.1016/j.physrep.2008.05.002.

[22]

L. M. Floría and J. J. Mazo, Dissipative dynamics of the Frenkel-Kontorova model, Adv. Phys., 45 (1996), 505-598.

[23]

K. Forinash, M. Peyrard and B. A. Malomed, Interaction of discrete breathers with impurity modes, Phys. Rev. E, 49 (1994), 3400-3411. doi: 10.1103/PhysRevE.49.3400.

[24]

Ya. I. Frenkel and T. Kontorova, On the theory of plastic deformations and twinning, J. Phys., 1 (1939), 137-149.

[25]

M. V. Ivanchenko, O. I. Kanakov, V. D. Shalfeev and S. Flach, Discrete breathers in transient processes and thermal equilibrium, Physica D, 198 (2004), 120-135. doi: 10.1016/j.physd.2004.08.025.

[26]

P. V. Larsen, P. L. Christiansen, O. Bang, J. F. R. Archilla and Yu. B. Gaididei, Energy funneling in a bent chain of Morse oscillators with long-range coupling, Phys. Rev. E, 69 (2004), 026603. doi: 10.1103/PhysRevE.69.026603.

[27]

J. L. Marín and S. Aubry, Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit, Nonlinearity, 9 (1996), 1501-1528. doi: 10.1088/0951-7715/9/6/007.

[28]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2D hexagonal lattice, Phys. Lett. A, 248 (1998), 225-229.

[29]

F. M. Russell and D. R. Collins, Lattice-solitons in radiation damage, Nucl. Inst. Meth. Phys. Res. B, 105 (1995), 30-34. doi: 10.1016/0168-583X(95)00934-5.

[30]

F. M. Russell and J. C. Eilbeck, Evidence for moving breathers in a layered crystal insulator at 300K, Europhys. Lett., 78 (2007), 10004. doi: 10.1209/0295-5075/78/10004.

[31]

M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, D. A. Czaplewski and H. G. Craighead, Observation of locked intrinsic localized vibrational modes in micromechanical oscillator array, Phys. Rev. Lett., 90 (2003), 044102. doi: 10.1103/PhysRevLett.90.044102.

[32]

M. Sato, B. E. Hubbard and A. J. Sievers, Nonlinear energy localization and its manipulation in micromechanical ocillator arrays, Rev. Mod. Phys., 78 (2006), 137-157. doi: 10.1103/RevModPhys.78.137.

[33]

P. Sen, J. Akhtar and F. M. Russell, MeV ion-induced movement of lattice disorder in sigle crystalline silicon, Europhys. Lett., 51 (2000), 401-406. doi: 10.1209/epl/i2000-00508-7.

[34]

B. I. Swanson, J. A. Brozik, S. P. Love, G. O. Strouse, A. P. Shreve, A. R. Bishop, W. Z. Wang and M. I. Salkola, Observation of intrinsically localized modes in a discrete low-dimensional material, Phys. Rev. Lett., 82 (1999), 3288-3291. doi: 10.1103/PhysRevLett.82.3288.

[35]

E. Trías, J. J. Mazo and T. P. Orlando, Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array, Phys. Rev. Lett., 84 (2000), 741-744. doi: 10.1103/PhysRevLett.84.741.

[36]

G. P. Tsironis, J. M. Sancho, M. Ibañes, Localized energy transport in biopolymer models with rigidity, Europhys. Lett., 57 (2002), 697-703. doi: 10.1209/epl/i2002-00519-4.

[37]

D. L. Williamson, J. A. Davis, P. J. Wilbur, J. J. Vajo, R. Wei and J. N. Matossian, Relative roles of ion energy, ion flux, and sample temperature in low-energy nitrogen ion implantation of Fe--Cr--Ni stainless steel, Nucl. Inst. Meth. Phys. Res. B, 127 (1997), 930-934. doi: 10.1016/S0168-583X(97)00033-5.

[38]

M. Wuttig, D. Lüsebrink, D. Wamwangi, W. Wełnic, M. Gilleßen and R. Dronskowski, The role of vacancies and local distortions in the design of new phase-change materials, Nature Materials, 6 (2007), 122-128. doi: 10.1038/nmat1807.

show all references

References:
[1]

G. Abrasonis, W. Möller and X. X. Ma, Anomalous ion accelerated bulk diffusion of interstitial nitrogen, Phys. Rev. Lett., 96 (2006), 065901. doi: 10.1103/PhysRevLett.96.065901.

[2]

G. Abrasonis, J. P. Rivière, C. Templier, A. Declémy, L. Pranevicius and X. Milhet, Ion beam nitriding of single and polycrystalline austenitic stainless steel, J. Appl. Phys., 97 (2005), 083531. doi: 10.1063/1.1863455.

[3]

A. Álvarez, J. F. R. Archilla, F. R. Romero, J. Cuevas and P. V. Larsen, Breather trapping and breather transmission in a DNA model with an interface, Eur. Phys. J. B, 51 (2006), 119-130.

[4]

S. Aubry, Breathers in nonlinear lattices: Existence, linear stability and quantization, Lattice dynamics (Paris, 1995), Physica D, 103 (1997), 201-250. doi: 10.1016/S0167-2789(96)00261-8.

[5]

S. Aubry and T. Cretegny, Mobility and reactivity of discrete breathers, Localization in nonlinear lattices (Dresden, 1997), Physica D, 119 (1998), 34-46. doi: 10.1016/S0167-2789(98)00062-1.

[6]

A. S. Barker and A. J. Sievers, Optical studies of the vibrational properties of disordered solids, Rev. Mod. Phys., 47 (1975), S1-S179. doi: 10.1103/RevModPhys.47.S1.2.

[7]

I. Bena, A. Saxena and J. M. Sancho, Interaction of a discrete breather with a lattice junction, Phys. Rev. E, 65 (2002), 036617. doi: 10.1103/PhysRevE.66.036617.

[8]

O. M. Braun and Yu. S. Kivshar, Nonlinear dynamics of the Frenkel-Kontorova model, Phys. Rep., 306 (1998), 1-108. doi: 10.1016/S0370-1573(98)00029-5.

[9]

O. M. Braun and Yu. S. Kivshar, "The Frenkel-Kontorova Model: Concepts, Methods and Applications," Texts and Monographs in Physics, Springer-Verlag, Berlin, 2004.

[10]

D. Chen, S. Aubry and G. P. Tsironis, Breather mobility in discrete $\phi^4$ nonlinear lattices, Phys. Rev. Lett., 77 (1996), 4776-4779. doi: 10.1103/PhysRevLett.77.4776.

[11]

J. Cuevas, J. F. R. Archilla, B. Sánchez-Rey and F. R. Romero, Interaction of moving discrete breathers with vacancies, Physica D, 216 (2006), 115-120. doi: 10.1016/j.physd.2005.12.022.

[12]

J. Cuevas, C. Katerji, J. F. R. Archilla, J. C. Eilbeck and F. M. Russell, Influence of moving breathers on vacancies migration, Phys. Lett. A, 315 (2003), 364-371. doi: 10.1016/S0375-9601(03)01097-1.

[13]

J. Cuevas and P. G. Kevrekidis, Breathers statics and dynamics in Klein-Gordon chains with a bend, Phys. Rev. E, 69 (2004), 056609. doi: 10.1103/PhysRevE.69.056609.

[14]

J. Cuevas, F. Palmero, J. F. R. Archilla and F. R. Romero, Moving discrete breathers in a Klein-Gordon chain with an impurity, J. Phys. A: Math. and Gen., 35 (2002), 10519-10530. doi: 10.1088/0305-4470/35/49/302.

[15]

T. Dauxois and M. Peyrard, "Physics of Solitons," Cambridge University Press, 2006.

[16]

S. V. Dmitriev, T. Miyauchi, K. Abe and T. Shigenari, Kink-breather solution in the weakly discrete Frenkel-Kontorova model, Phys. Rev. E, 61 (1998), 5880-5885. doi: 10.1103/PhysRevE.61.5880.

[17]

S. V. Dmitriev, T. Shigenari, A. A. Vasiliev and A. E. Miroshnichenko, Effect of discreteness on a sine-Gordon three-soliton solution, Phys. Lett. A, 246 (1998), 129. doi: 10.1016/S0375-9601(98)00459-9.

[18]

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon and H. C. Morris, "Solitons and Nonlinear Wave Equations," Academic Press, London, 1982.

[19]

J. C. Eilbeck, P. S. Lomdahl and A. C. Scott, Soliton structure in crystalline acetanilide, Phys. Rev. B, 30 (1984), 4703-4712. doi: 10.1103/PhysRevB.30.4703.

[20]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd and J. S. Aitchison, Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett., 81 (1998), 3383-3386.

[21]

S. Flach and A. Gorbach, Discrete breathers - Advances in theory and applications, Phys. Rep., 467 (2008), 1-116. doi: 10.1016/j.physrep.2008.05.002.

[22]

L. M. Floría and J. J. Mazo, Dissipative dynamics of the Frenkel-Kontorova model, Adv. Phys., 45 (1996), 505-598.

[23]

K. Forinash, M. Peyrard and B. A. Malomed, Interaction of discrete breathers with impurity modes, Phys. Rev. E, 49 (1994), 3400-3411. doi: 10.1103/PhysRevE.49.3400.

[24]

Ya. I. Frenkel and T. Kontorova, On the theory of plastic deformations and twinning, J. Phys., 1 (1939), 137-149.

[25]

M. V. Ivanchenko, O. I. Kanakov, V. D. Shalfeev and S. Flach, Discrete breathers in transient processes and thermal equilibrium, Physica D, 198 (2004), 120-135. doi: 10.1016/j.physd.2004.08.025.

[26]

P. V. Larsen, P. L. Christiansen, O. Bang, J. F. R. Archilla and Yu. B. Gaididei, Energy funneling in a bent chain of Morse oscillators with long-range coupling, Phys. Rev. E, 69 (2004), 026603. doi: 10.1103/PhysRevE.69.026603.

[27]

J. L. Marín and S. Aubry, Breathers in nonlinear lattices: Numerical calculation from the anticontinuous limit, Nonlinearity, 9 (1996), 1501-1528. doi: 10.1088/0951-7715/9/6/007.

[28]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2D hexagonal lattice, Phys. Lett. A, 248 (1998), 225-229.

[29]

F. M. Russell and D. R. Collins, Lattice-solitons in radiation damage, Nucl. Inst. Meth. Phys. Res. B, 105 (1995), 30-34. doi: 10.1016/0168-583X(95)00934-5.

[30]

F. M. Russell and J. C. Eilbeck, Evidence for moving breathers in a layered crystal insulator at 300K, Europhys. Lett., 78 (2007), 10004. doi: 10.1209/0295-5075/78/10004.

[31]

M. Sato, B. E. Hubbard, A. J. Sievers, B. Ilic, D. A. Czaplewski and H. G. Craighead, Observation of locked intrinsic localized vibrational modes in micromechanical oscillator array, Phys. Rev. Lett., 90 (2003), 044102. doi: 10.1103/PhysRevLett.90.044102.

[32]

M. Sato, B. E. Hubbard and A. J. Sievers, Nonlinear energy localization and its manipulation in micromechanical ocillator arrays, Rev. Mod. Phys., 78 (2006), 137-157. doi: 10.1103/RevModPhys.78.137.

[33]

P. Sen, J. Akhtar and F. M. Russell, MeV ion-induced movement of lattice disorder in sigle crystalline silicon, Europhys. Lett., 51 (2000), 401-406. doi: 10.1209/epl/i2000-00508-7.

[34]

B. I. Swanson, J. A. Brozik, S. P. Love, G. O. Strouse, A. P. Shreve, A. R. Bishop, W. Z. Wang and M. I. Salkola, Observation of intrinsically localized modes in a discrete low-dimensional material, Phys. Rev. Lett., 82 (1999), 3288-3291. doi: 10.1103/PhysRevLett.82.3288.

[35]

E. Trías, J. J. Mazo and T. P. Orlando, Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array, Phys. Rev. Lett., 84 (2000), 741-744. doi: 10.1103/PhysRevLett.84.741.

[36]

G. P. Tsironis, J. M. Sancho, M. Ibañes, Localized energy transport in biopolymer models with rigidity, Europhys. Lett., 57 (2002), 697-703. doi: 10.1209/epl/i2002-00519-4.

[37]

D. L. Williamson, J. A. Davis, P. J. Wilbur, J. J. Vajo, R. Wei and J. N. Matossian, Relative roles of ion energy, ion flux, and sample temperature in low-energy nitrogen ion implantation of Fe--Cr--Ni stainless steel, Nucl. Inst. Meth. Phys. Res. B, 127 (1997), 930-934. doi: 10.1016/S0168-583X(97)00033-5.

[38]

M. Wuttig, D. Lüsebrink, D. Wamwangi, W. Wełnic, M. Gilleßen and R. Dronskowski, The role of vacancies and local distortions in the design of new phase-change materials, Nature Materials, 6 (2007), 122-128. doi: 10.1038/nmat1807.

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