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Kinetics of growth of nanowhiskers (nanowires and nanotubes)

Abstract

The kinetics of nanowhiskers growth is studied theoretically taking into account the adatom diffusion from the surface to the top of needle. An exponential growth with time is expected for the initial stages of the process, when the lengthl of the whisker is smaller than the average diffusion length λ of adatoms. It transforms to linear growth rate forl > λ. The formation of nanotubes with a hollow core dislocation is explained by accounting for the role of the stress in the middle of screw dislocations. When the magnitude of the Burgers vector exceeds a critical value, it is energetically more favorable to remove the highly strained material around the dislocation line and to create a tube with an additional free surface. Additionally, there is an important size effect, due to the small radiusR of the nanowhisker. The interplay, between the contributions from the size effects and from the diffusion, explains why for the very thin nanowhiskers the lengthl is proportional to the radiusR while, otherwise the length is inversely proportional to it, i.e.,l1/R.

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References

  1. 1.

    Givargizov E: J. Cryst. Growth. 1975, 31: 20. COI number [1:CAS:528:DyaE28Xot1KmtQ%3D%3D] 10.1016/0022-0248(75)90105-0

  2. 2.

    Duan X, Wang J, Lieber C: Appl. Phys. Lett.. 2000, 76: 1116. ; COI number [1:CAS:528:DC%2BD3cXhtlSgtb4%3D]; Bibcode number [2000ApPhL..76.1116D] 10.1063/1.125956

  3. 3.

    Lew K, Redwing J: J. Cryst. Growth. 2003, 254: 14.

  4. 4.

    Plante M, LaPierre R: J. Cryst. Growth. 2006, 286: 394. COI number [1:CAS:528:DC%2BD28XjsFan] 10.1016/j.jcrysgro.2005.10.024

  5. 5.

    Sears GW: Acta Metall.. 1955, 3: 367. COI number [1:CAS:528:DyaG2MXns1ajsQ%3D%3D] 10.1016/0001-6160(55)90042-0

  6. 6.

    Sears GW: J. Chem. Phys.. 1956, 25: 637. COI number [1:CAS:528:DyaG2sXotF2q] 10.1063/1.1743018

  7. 7.

    Gomer R: J. Chem. Phys.. 1958, 28: 457. COI number [1:CAS:528:DyaG1cXltl2htg%3D%3D] 10.1063/1.1744158

  8. 8.

    Dittmar W, Neumann K: Growth and Perfection of Crystals.. Edited by: Doremus R.H., Roberts B.W., Turnball D.. Wiley, New York; 1958.

  9. 9.

    Dittmar W, Neumann K: Z. Elektrochem.. 1960, 64: 297.

  10. 10.

    Frank FC: Acta Crystallogr.. 1951, 4: 497. COI number [1:CAS:528:DyaG38XivVymtg%3D%3D] 10.1107/S0365110X51001690

  11. 11.

    Heindl J, Dorsch W, Strunk HP, St. Müller G, Eckstein R, Hofmann D, Winnacker A: Phys. Rev. Lett.. 1998, 80: 740. ; COI number [1:CAS:528:DyaK1cXlsVyhug%3D%3D]; Bibcode number [1998PhRvL..80..740H] 10.1103/PhysRevLett.80.740

  12. 12.

    Scapski A: Acta Met.. 1956, 4: 576. 10.1016/0001-6160(56)90159-6

  13. 13.

    D. Turnbull, M. Cohen, in Modern Aspects of vitreous State ed. by S.D. Mackenzie (Butterworths, London, 1960) p. 38

  14. 14.

    Avramov I, Russel C, Avramova K: J. Non-Cryst. Sol.. 2004, 337: 220. COI number [1:CAS:528:DC%2BD2cXlsVehsbw%3D] 10.1016/j.jnoncrysol.2004.04.012

  15. 15.

    Budurov S, Stojcev N, Avramov I: Krist. Technik. 1972, 7: 387. COI number [1:CAS:528:DyaE38XlsFOhsLk%3D] 10.1002/crat.19720070403

  16. 16.

    Dubrovskii VG, Cirlin GE, Soshnikov IP, Tonkikh AA, Sibirev NV, Samsonenko YuB, Ustinov VM: Phys. Rev. B. 2005, 71: 205325. Bibcode number [2005PhRvB..71t5325D] Bibcode number [2005PhRvB..71t5325D] 10.1103/PhysRevB.71.205325

  17. 17.

    Ruth V, Hirth P: J. Chem. Phys.. 1964, 41: 3139. COI number [1:CAS:528:DyaF2cXkvVylsL8%3D] 10.1063/1.1725687

  18. 18.

    E.I. Givargizov, A.A. Chernov, Kristallografiya 18, 147 (1973)

  19. 19.

    Avramov I, Hoeche Th, Russel C: J. Chem. Phys.. 1999,110(17):8676. ; COI number [1:CAS:528:DyaK1MXisFCgsbg%3D]; Bibcode number [1999JChPh.110.8676A] 10.1063/1.478775

  20. 20.

    Soshnikov I: Lett. JTF. 2005, 31: 29. in Russian in Russian

  21. 21.

    V.G. Dubrovskii, G.E. Cirlin, I.P. Soshnikov, A.A. Tonkikh, N.V. Sibirev, Yu. B. Samsonenko, V.M. Ustinov, Phys. Rev. B 71, 205325 (2005)

  22. 22.

    Dubrovskii VG, Sibirev NV, Cirlin GE: Tech. Phys. Lett. 2004, 30: 682. COI number [1:CAS:528:DC%2BD2cXntVKrtLw%3D] 10.1134/1.1792313

  23. 23.

    Kashchiev D: Cryst. Growth Design. 2006, 6: 1154. COI number [1:CAS:528:DC%2BD28XjtlOis7o%3D] 10.1021/cg050619i

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Acknowledgment

The support of the EU Project INTERCONY, Contract no NMP4-CT-2006-033200 is appreciated.

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Correspondence to Isak Avramov.

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Keywords

  • Nanotubes
  • Nanowires
  • Nanowhiskers