American Institute of Mathematical Sciences

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October  2011, 4(5): 1267-1285. doi: 10.3934/dcdss.2011.4.1267

Persistent mobile lattice excitations in a crystalline insulator

Francis Michael Russell 1, and  J. C. Eilbeck 2,

1. 

Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, United Kingdom
2. 

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

Received  September 2009 Revised  November 2009 Published  December 2010

We examine tracks in crystals of muscovite of high energy charged particles, and of mobile lattice excitations created by kinetic atomic scattering. The mobile lattice excitations are interpreted as a type of breather, here called a quodon. The typical energy of a quodon can be found from the decay of potassium K40 atoms in the crystal and supports their interpretation as a type of breather. In turn, this establishes a unique signature for energetic quodons, the 'kinked-line' tracks, allowing discrimination against tracks formed by charged particles. The stability of quodons against crystal defects and thermal motion is considered. Measurements on energetic quodon tracks, with flight paths up to 530mm, show that they can propagate more than 109 unit cells with no evidence of energy loss. This suggests that quodons might persist indefinitely in certain crystals of high quality. Evidence is presented for a new type of mobile lattice excitation that is capable of creating energetic quodons, which also is stable against lattice defects. Possible practical applications of quodons are considered briefly. Although quodons can induce fusion in deuterium or tritium, present indications are that the rate is too low to be of practical use. Finally, a nonlinear lattice effect that might increase this rate is suggested.
Keywords: Annealing of defects, Heat transfer, Intrinsic localised modes, Condensed matter, Nuclear power..
Mathematics Subject Classification: Primary: 82-057; Secondary: 70Kxx, 70Fxx, 82Cx.
Citation: Francis Michael Russell, J. C. Eilbeck. Persistent mobile lattice excitations in a crystalline insulator. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1267-1285. doi: 10.3934/dcdss.2011.4.1267
References:
[1]

G. Abrasonis, W. Moller 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]

J. F. R. Archilla, J. Cuevas, M. D. Alba, M. Naranjo and J. M. Trillo, Discrete breathers for understanding reconstructive mineral processes at low temperatures, J. Phys. Chem. B, 110 (2006), 24112. doi: 10.1021/jp0631228.

[3]

E. Ben-Jacob and P. Garick, The formation of patterns in non-equilibrium growth, Nature, 343 (1990), 523-530. doi: 10.1038/343523a0.

[4]

I. P. Chernov, A. P. Mamontov, A. A. Botaki, P. A. Cherdantsev, B. V. Chakhlov, S. R. Sharov, Yu. A. Timoshnikov and L. A. Filipenko, Anomalous effect of small doses of ionizing radiation on metals and alloys, Radiation Effects, 97 (1986), 155-160. doi: 10.1080/00337578608208729.

[5]

D. R. Collins and F. M. Russell, Computer modelling studies of solitons in layered silicates, in "6th Int. Conf. Physics Computing, Lugano, Aug. 22-26," 1994.

[6]

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

[7]

V. Dubinko, Breather mechanism of void ordering in crystals under irradiation, to be published in: Nucl. Inst. and Meth. in Phys. Research B, (2009).

[8]

V. I. Dubinko, A. G. Guglya, E. Melnichenko and R. Vasilenko, Radiation-induced reduction in the void swelling, J. Nuclear Materials, 385 (2009), 228-230. doi: 10.1016/j.jnucmat.2008.11.028.

[9]

LANF was proposed in 2002 by F. M. Russell in private discussions with J. C. Eilbeck.,   Patent applications were filed on 2/05/2005 at the UK Pat. Office.

[10]

X. Z. Li, B. Liu, Q. M. Wei, S. X. Zheng and D. X. Cao, Chinese view on summary of condensed matter nuclear science, J. Fusion Energy, 23 (2004), 217-221. doi: 10.1007/s10894-005-5601-4.

[11]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2-D hexagonal lattice, Phys. Letts. A, 248 (1998), 225-229. doi: 10.1016/S0375-9601(98)00577-5.

[12]

J. L. Marín, J. C. Eilbeck and F. M. Russell, 2-D breathers and applications, in "Nonlinear Science at the Dawn of the 21th Century" (P. L. Christiansen and M. P. Soerensen, editors), Springer, Berlin, (2000), 293-306.

[13]

J. L. Marín, F. M. Russell and J. C. Eilbeck, Breathers in cuprate-like lattices, Phys. Letts. A, 281 (2001), 21-25. doi: 10.1016/S0375-9601(01)00092-5.

[14]

Yu. V. Martynenko and P. G. Moscovkin, Solitons in radiation physics of crystals, Rad. Eff. Def. Solids, 117, (1991), 321-328. doi: 10.1080/10420159108220750.

[15]

G. H. Miley, H. Towner and N. Ivich, "Fusion Cross Sections," Report COO-2218-17, Uni. of Illinois, Urbana, http://home.earthlink.net/ jimlux/nuc/sigma.htm.

[16]

D. M. Newns and C. C. Tsuei, Fluctuating Cu-O-Cu bond model of high-temperature superconductivity, Nature Physics, 3, (2007), 184-191. doi: 10.1038/nphys542.

[17]

F. M. Russell, Identification and selection criteria for charged lepton tracks in mica, Nucl. Tracks Radiat. Meas., 15 (1988), 41-44. doi: 10.1016/1359-0189(88)90098-2.

[18]

F. M. Russell and D. R. Collins, Lattice-solitons and non-linear phenomena in track formation, Radiation Measurements, 25 (1995), 67-70. doi: 10.1016/1350-4487(95)00034-C.

[19]

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

[20]

F. M. Russell and D. R. Collins, Anharmonic excitations in high Tc materials, Phys. Letts. A, 216 (1996), 197-202. doi: 10.1016/0375-9601(96)00251-4.

[21]

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

[22]

F. M. Russell, Y. Zolotaryuk, J. C. Eilbeck and T. Dauxois, Moving breathers in a chain of magnetic pendulums, Phys. Rev. B, 55 (1997), 6304-6308. doi: 10.1103/PhysRevB.55.6304.

[23]

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

[24]

R. H. Silbee, Focusing in collision problems in solids, J. Appl. Phys., 28 (1957), 1246. doi: 10.1063/1.1722626.

[25]

J. W. Steeds, F. M. Russell and W. J. Vine, Formation of epidote follil positron tracks in mica, Optik, 92 (1993), 149-154.

show all references

References:
[1]

G. Abrasonis, W. Moller 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]

J. F. R. Archilla, J. Cuevas, M. D. Alba, M. Naranjo and J. M. Trillo, Discrete breathers for understanding reconstructive mineral processes at low temperatures, J. Phys. Chem. B, 110 (2006), 24112. doi: 10.1021/jp0631228.

[3]

E. Ben-Jacob and P. Garick, The formation of patterns in non-equilibrium growth, Nature, 343 (1990), 523-530. doi: 10.1038/343523a0.

[4]

I. P. Chernov, A. P. Mamontov, A. A. Botaki, P. A. Cherdantsev, B. V. Chakhlov, S. R. Sharov, Yu. A. Timoshnikov and L. A. Filipenko, Anomalous effect of small doses of ionizing radiation on metals and alloys, Radiation Effects, 97 (1986), 155-160. doi: 10.1080/00337578608208729.

[5]

D. R. Collins and F. M. Russell, Computer modelling studies of solitons in layered silicates, in "6th Int. Conf. Physics Computing, Lugano, Aug. 22-26," 1994.

[6]

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

[7]

V. Dubinko, Breather mechanism of void ordering in crystals under irradiation, to be published in: Nucl. Inst. and Meth. in Phys. Research B, (2009).

[8]

V. I. Dubinko, A. G. Guglya, E. Melnichenko and R. Vasilenko, Radiation-induced reduction in the void swelling, J. Nuclear Materials, 385 (2009), 228-230. doi: 10.1016/j.jnucmat.2008.11.028.

[9]

LANF was proposed in 2002 by F. M. Russell in private discussions with J. C. Eilbeck.,   Patent applications were filed on 2/05/2005 at the UK Pat. Office.

[10]

X. Z. Li, B. Liu, Q. M. Wei, S. X. Zheng and D. X. Cao, Chinese view on summary of condensed matter nuclear science, J. Fusion Energy, 23 (2004), 217-221. doi: 10.1007/s10894-005-5601-4.

[11]

J. L. Marín, J. C. Eilbeck and F. M. Russell, Localized moving breathers in a 2-D hexagonal lattice, Phys. Letts. A, 248 (1998), 225-229. doi: 10.1016/S0375-9601(98)00577-5.

[12]

J. L. Marín, J. C. Eilbeck and F. M. Russell, 2-D breathers and applications, in "Nonlinear Science at the Dawn of the 21th Century" (P. L. Christiansen and M. P. Soerensen, editors), Springer, Berlin, (2000), 293-306.

[13]

J. L. Marín, F. M. Russell and J. C. Eilbeck, Breathers in cuprate-like lattices, Phys. Letts. A, 281 (2001), 21-25. doi: 10.1016/S0375-9601(01)00092-5.

[14]

Yu. V. Martynenko and P. G. Moscovkin, Solitons in radiation physics of crystals, Rad. Eff. Def. Solids, 117, (1991), 321-328. doi: 10.1080/10420159108220750.

[15]

G. H. Miley, H. Towner and N. Ivich, "Fusion Cross Sections," Report COO-2218-17, Uni. of Illinois, Urbana, http://home.earthlink.net/ jimlux/nuc/sigma.htm.

[16]

D. M. Newns and C. C. Tsuei, Fluctuating Cu-O-Cu bond model of high-temperature superconductivity, Nature Physics, 3, (2007), 184-191. doi: 10.1038/nphys542.

[17]

F. M. Russell, Identification and selection criteria for charged lepton tracks in mica, Nucl. Tracks Radiat. Meas., 15 (1988), 41-44. doi: 10.1016/1359-0189(88)90098-2.

[18]

F. M. Russell and D. R. Collins, Lattice-solitons and non-linear phenomena in track formation, Radiation Measurements, 25 (1995), 67-70. doi: 10.1016/1350-4487(95)00034-C.

[19]

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

[20]

F. M. Russell and D. R. Collins, Anharmonic excitations in high Tc materials, Phys. Letts. A, 216 (1996), 197-202. doi: 10.1016/0375-9601(96)00251-4.

[21]

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

[22]

F. M. Russell, Y. Zolotaryuk, J. C. Eilbeck and T. Dauxois, Moving breathers in a chain of magnetic pendulums, Phys. Rev. B, 55 (1997), 6304-6308. doi: 10.1103/PhysRevB.55.6304.

[23]

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

[24]

R. H. Silbee, Focusing in collision problems in solids, J. Appl. Phys., 28 (1957), 1246. doi: 10.1063/1.1722626.

[25]

J. W. Steeds, F. M. Russell and W. J. Vine, Formation of epidote follil positron tracks in mica, Optik, 92 (1993), 149-154.

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