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Nanoscale volume diffusion

Diffusion in thin films, multilayers and nanoobjects (hollow nanoparticles)

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Abstract

Diffusion on the nano/atomic scales in multilayers, thin films has many challenging features even if the role of structural defects (grain-boundaries, dislocations, etc.) can be neglected and 'only' the effects related to the nano/atomic scale raise. This can be the case for diffusion in amorphous materials, in epitaxial, highly ideal thin films, or multilayers where diffusion along short circuits can be ignored and 'only' fundamental difficulties related to nanoscale effects are important. The objective of this article is to review some interesting fundamental experimental and theoretical results in the field of nanoscale volume diffusion in planar and spherical geometries.

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Notes

  1. This transformation can be done if both the initial and boundary conditions can also be expressed as the function of λ.

  2. Although usually it is not explicitly declared, zv is included in \(\Upgamma\) in Eqs. 9–12. From Eq. 13, zv is not included in \(\Upgamma\).

  3. It is worth mentioning that m′ = 2ZM/kBT log10e, where Z = zl + 2zv and e is the base of the natural logarithm. It also shows that M in Eq. 21 can be determined from diffusion experimental data.

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Acknowledgements

This study was supported by the OTKA Board of Hungary (Nos K67969, CK80126) and by TAMOP 4.2.1./B-09/1/KONV-2010-0007 project (implemented through the New Hungary Development Plan co-financed by the European Social Fund, and the European Regional Development Fund). One of the authors (Z. Erdélyi) of this article is a grantee of the ‘Bolyai János’ scholarship.

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  1. Department of Solid State Physics, University of Debrecen, P. O. Box. 2, Debrecen, 4010, Hungary

    Zoltán Erdélyi & Dezső L. Beke

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  1. Zoltán Erdélyi
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Correspondence to Zoltán Erdélyi.

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Erdélyi, Z., Beke, D.L. Nanoscale volume diffusion. J Mater Sci 46, 6465–6483 (2011). https://doi.org/10.1007/s10853-011-5720-4

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