Growth Kinetics on Nanoscale: Finite Diffusion Permeability of Interfaces

Article Preview

Abstract:

Growth kinetic is either diffusion or interface reaction controlled process, characterized by parabolic or linear relationships, respectively. The well known diffusion paradox, predicting infinitely fast diffusion kinetics at short times (distances) for diffusion control will be discussed and resolved, by showing that the diffusion permeability across the interface should be finite at the very beginning of the process. Thus one can arrive at an atomistic interpretation of the interface transfer coefficient, K, and at linear growth kinetics even if there is no extra potential barrier present at the interface, usually assumed in the interpretation of interface reaction control. It is also shown that this phenomenon is a typical nanoeffect: after a certain diffusion distance (lying between 0.01 and 300 nm, depending on the composition dependence of the diffusion coefficient) the finite permeability of the interface will not restrict the growth and normal diffusion control will be observed.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

1-12

Citation:

Online since:

September 2007

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2007 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] G. Martin, and P. Benoist, Scripta Met. 11, (1977) p.503.

Google Scholar

[2] J. Philibert: Atom Movements. Diffusion and Mass Transport in Solids (Les Ulis, France, Les Editions des Physique, Paris, 1991).

Google Scholar

[3] Z. Erdélyi, D.L. Beke, P. Nemes, G. A. Langer Phil. Mag. A, 79, (1999) p.1757.

Google Scholar

[4] J. Bernardini and D.L. Beke: Diffusion in Nanomaterials" in " Nanocrystalline Metals and Oxides: Selected Properties and Applications, (Eds. P. Knauth and J. Schoonman, Kluwer Publ. Boston, 2001).

Google Scholar

[5] D.L. Beke, C. Cserháti, Z. Erdélyi, I.A. Szabó, Segregation in Nanostructures" in "Advances in Nanophase Materials and Nanotechnology" Vol. "Nanoclusters and Nanocrystals, (Ed. H.S. Nalwa, American Scientific Publ. Califronia USA, 2003) p.211.

Google Scholar

[6] Z. Erdélyi and D.L. Beke, Phys. Rev. B. 68 (2003) p.092102.

Google Scholar

[7] D.L. Beke, G.A. Langer, A. Csik, Z. Erdélyi, M. Kis-Varga, I.A. Szabó and Z, Papp, Defect and Diffusion Forum, 194-199, (2001), p.1403.

DOI: 10.4028/www.scientific.net/ddf.194-199.1403

Google Scholar

[8] D.L. Beke, P. Nemes, Z. Erdélyi, I.A. Szabó, D.G. Langer, MRS Mat. Res. Soc. Symp. Proc. Vol. 527 (Eds. Y. Mishin, G. Vogl, N. Cowern, R. Catlow and D. Farkas) Warrendale, 1998, p.99.

DOI: 10.1557/proc-527-99

Google Scholar

[9] A. Csik, G. Langer, D.L. Beke, Z. Erdélyi, M., Menyhárd, and A. Sulyok, A. Journal of Appl. Phys. 89/1, (2001) pp.804-806.

Google Scholar

[10] Z. Erdélyi, CH, Girardeaux, ZS. Tıkei, D.L. Beke, C. Cserháti, C., Rolland, A. Surf. Sci., 496/1-2, (2002) p.129.

Google Scholar

[11] Z. Erdélyi, D.L. Beke and I.A. Szabó, Phys, Rev. Letters, 89 (2002) p.165901.

Google Scholar

[12] Z. Erdélyi, G. L. Katona, D.L. Beke, Phys. Rev. B69, 113407-1-4 (2004).

Google Scholar

[13] G.L. Katona, D.L. Beke, Z. Erdélyi, Ch. Dietrich, F. Weigl, H-G. Boyen, B. Koslowski, P. Ziemann. Phys. Rev. B. Vol. 71 (2005) p.115432.

DOI: 10.1103/physrevb.71.115432

Google Scholar

[14] Z. Erdélyi, M. Sladecek, L-M, Stadler, I. Zizak, G.A. Langer, M. Kis-Varga, D.L. Beke, B. Sepiol, Science, 306, 1913-1915 (2004).

DOI: 10.1126/science.1104400

Google Scholar

[15] D.L. Beke, Z. Erdélyi, Phys. Rev. B. Vol. 73 (2006) p.035426.

Google Scholar

[16] Ja.E. Geguzin, Ju.Y. Kaganovskii, Fizika Met. Metallov. (Russian) Vol. 39, (1975), p.553.

Google Scholar

[17] F.M. d'Heurle, P. Gas, J. Philibert, O. Thomas, Metals Materials and Processes Vol. 11, (1999), p.217.

Google Scholar

[18] U. Gössele, K.N. Tu, J. Appl. Phys. Vol. 53, (1982), p.3252.

Google Scholar

[19] P.J. Desre, A:R. Yavari, Phys. Rev. Lett. Vol. 64, (1990), p.1553.

Google Scholar

[20] A.M. Gusak, F. Hodaj, A.O. Bogatyev, J. Phys. -Condens. Mat., Vol. 13, (2001), p.2767.

Google Scholar

[21] H. Schmalzried, Chemical Kinetics of Solids, VCH Publ. New York (1995) p.422.

Google Scholar

[22] P. Maugis, G. Martin, Phys Rev. B 49, 11580-11587 (1994).

Google Scholar

[23] G. Martin, Phys. Rev. B41 (1990) p.2279.

Google Scholar

[24] D.L. Beke, Z. Erdélyi, I.A. Szabó, C. Cserháti, in Nanodiffusion, (Ed. D.L. Beke) special issue of Journal of Metastable and Nanocrystalline Materials, Vol. 19 (2004), p.107.

DOI: 10.4028/www.scientific.net/jmnm.19.107

Google Scholar

[25] C. Cserháti, H. Bakker and D.L. Beke, Surf. Sci. Vol. 290, (1993), p.345.

Google Scholar

[26] Z. Erdélyi, D.L. Beke, Phys. Rev. B Vol. 70, (2004), pp.245428-1.

Google Scholar

[27] A. Saúl, B. Legrand, G. Tréglia, Surf. Sci. Vol. 331-333, (1995), p.805.

Google Scholar

[28] S. Delage, B. Legrand, F. Soisson, A. Saúl, Phys. Rev. B Vol. 58, (1998), p.15810.

Google Scholar

[29] J. M. Roussel, A Saúl, G. Tréglia, B. Legrand, Phys. Rev. B Vol. 60, (1999), p.13890.

Google Scholar

[30] B. Pieraggi, R.A. Rapp, J.P. Hirth, Scripta Met. et Mat. Vol. 30, (1994), p.1491.

Google Scholar

[31] F.J.J. van Loo, B. Pieraggi, R.A. Rapp, Acta Metal. et Mater. Vol. 38, (1990), p.1769.

Google Scholar

[32] B. Pieraggi, R.A. Rapp, F.J.J. van Loo, J.P. Hirth, Acta Metal. et Mater. Vol. 38, (1990), p.1781.

Google Scholar

[33] M. Hillert, Metall. Mater. Trans. A Vol. 6, (1975), p.5.

Google Scholar