Non-linear Non-linear Effects in Effects in Diffusion Diffusion on Nanoscale on Nanoscale Department of Solid State Physics Department of Solid State Physics University of Debrecen University of Debrecen D.L. D.L. Beke Beke Z. Erd Z. Erd élyi élyi , I.A. Szab , I.A. Szab ó ó , , Cs. Cserh Cs. Cserh á á ti ti
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Non-linear Effects in Diffusion on Nanoscale Department of Solid State Physics University of Debrecen D.L. Beke Z. Erdélyi, I.A. Szabó, Cs. Cserháti.
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Non-linearNon-linear Effects in Effects in DiffusionDiffusion
on Nanoscaleon Nanoscale
Department of Solid State PhysicsDepartment of Solid State PhysicsUniversity of DebrecenUniversity of Debrecen
D.L. D.L. BekeBeke Z. Erd Z. Erdélyiélyi, I.A. Szab, I.A. Szabóó,, Cs. CserhCs. Cserháátiti
Diffusion in nanomaterialsDiffusion in nanomaterials
Two important featuresTwo important features
a)a) High numbers of grain- orHigh numbers of grain- orphase boundaries (GB or PB) and phase boundaries (GB or PB) and dislocationsdislocations- fast diffusion and solid st. reactions, segregation, etc.- fast diffusion and solid st. reactions, segregation, etc.
b) Principal problems (very shortb) Principal problems (very shortdistances and preferably no structural distances and preferably no structural defects)defects)
Principal difficultiesPrincipal difficulties::
-Short diffusion distances LShort diffusion distances L d d(continuum description fails)(continuum description fails)
- Gradient energy correctionsGradient energy corrections
- Stress effectsStress effects
Discrete (MartinDiscrete (Martin‘‘s) models) model
-At short distances the continuum descriptions fails At short distances the continuum descriptions fails and this strongly depends on the concentration and this strongly depends on the concentration dependence of D (non-linearity)dependence of D (non-linearity)
- Non-linearity leads to - Non-linearity leads to shift of a sharpshift of a sharp interface interface-The non-linearity leads to The non-linearity leads to
a lineara linear shift of a sharp interface shift of a sharp interfacesharpening sharpening of an originally wide interfaceof an originally wide interface
-Gradient energy corrections are important not only in Gradient energy corrections are important not only in the currents but also in the mobilitiesthe currents but also in the mobilities
PapersPapers::
CSIK, A., LANGER, G., BEKE, D.L., ERDÉLYI, Z., MENYHÁRD, CSIK, A., LANGER, G., BEKE, D.L., ERDÉLYI, Z., MENYHÁRD, M. SULYOK, A. M. SULYOK, A. Journal of Appl. Phys. Journal of Appl. Phys. 89/189/1, 804-806 (2001), 804-806 (2001) BEKE, D.L., LANGER. G.A., CSIK, A., ERDÉLYI, Z., KIS-VARGA, BEKE, D.L., LANGER. G.A., CSIK, A., ERDÉLYI, Z., KIS-VARGA, M.,SZABÓ, I.A., PAPP, Z. M.,SZABÓ, I.A., PAPP, Z. Defect and Diff. Forum Defect and Diff. Forum 194-199194-199, 1403-1416 , 1403-1416 (2001) (2001) ERDÉLYI, Z., GIRARDEAUX., CH., BERNARDINI, J., BEKE, D.L, ERDÉLYI, Z., GIRARDEAUX., CH., BERNARDINI, J., BEKE, D.L, ROLLAND, A. ROLLAND, A. Defect and Diff. Forum Defect and Diff. Forum 194-199194-199, 1161-1166 (2001), 1161-1166 (2001)
ERDÉLYI, Z, ERDÉLYI, Z, SZABSZABÓ I.A., Ó I.A., BEKE, D.L. BEKE, D.L. Phys. Lev. LettersPhys. Lev. Letters,, in printin print
Chapters:Chapters:
BERNARDINI, J, BEKE, D.L., „Diffusion in Nanomaterials” BERNARDINI, J, BEKE, D.L., „Diffusion in Nanomaterials” in „Nanocrystalline materials: Properties and Applications” in „Nanocrystalline materials: Properties and Applications” (Eds. Knauth, P., Schoonman, J.) Kluwer Academic Publ., (Eds. Knauth, P., Schoonman, J.) Kluwer Academic Publ., Boston, 2001Boston, 2001
BEKE, D.L. CSERHÁTI, C.BEKE, D.L. CSERHÁTI, C.,, ERDÉLYI, Z. ERDÉLYI, Z.,, SZABÓ, I.A. SZABÓ, I.A.,, “Segregation in Nanostructures” in „Advances in Nanophase “Segregation in Nanostructures” in „Advances in Nanophase materials and nanotechnology” Volume: „Nanoclusters” (ed. materials and nanotechnology” Volume: „Nanoclusters” (ed. H.S. Nalwa) American Scientific Publ., 2002, in printH.S. Nalwa) American Scientific Publ., 2002, in print
SIDORENKO, S., BEKE. D.L., KIKINESHI, A., “Materials SIDORENKO, S., BEKE. D.L., KIKINESHI, A., “Materials Science of Nanosctutures, Naukova Dumka, Kiyv, 2002Science of Nanosctutures, Naukova Dumka, Kiyv, 2002