Ting-Yun Huang, 2012/11/15 Page 1 3.14/3.40J/22.71J Recap Diffusion Process & Surface Evolution...
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Transcript of Ting-Yun Huang, 2012/11/15 Page 1 3.14/3.40J/22.71J Recap Diffusion Process & Surface Evolution...
Ting-Yun Huang, 2012/11/15Page 1
3.14/3.40J/22.71J Recap
Diffusion Process & Surface Evolution
Ting-Yun Huang
2012 Nov. 15th
Outline• Diffusion of 1-2-v system: Interdiffusivity
• Kirkendall Effect
• Different diffusion mechanisms
• Fast diffusion path and lattice diffusion
• Capillary force/Surface energy
Ting-Yun Huang, 2012/11/15Page 2
Diffusion of 1-2-v system: Interdiffusivity
Ting-Yun Huang, 2012/11/15Page 3
• Crystal frame
• From crystal frame to lab frame (observed)
• Interdiffusivity:
– Note that D is usually concentration dependent, thus the here only
applies to small region
Kirkendall Effect
Ting-Yun Huang, 2012/11/15Page 4
Direct exchange mechanism
Ring mechanism Kirkendall’s experimental setup. Use Mo as fictitious marker.
JOM.49 (6) (1997), pp. 15-19.
Kirkendall Effect
• Vacancy Mechanism
• Criticism from Mehl
• The measured Zn concentration varies, and the diffusivity is different in Zn and Cu.
• Nanoparticle system.
Ting-Yun Huang, 2012/11/15Page 5
JOM.49 (6) (1997), pp. 15-19.
Kirkendall Effect- Nanoscale
Ting-Yun Huang, 2012/11/15Page 6
• Hollow nanocrystals
• Kirkendall effect forming the
nano porous materials
• Applications: due to large surface
area, can be applied to nano-
reactor and catalysts, etc.
Yin et al., 304 (5671): 711-714, Science
Diffusion of different mechanisms
•
– Di: diffusivity, controlled by migration energy.
– xi: molar fraction of sites
– i: denotes the species, can be vacancy, interstitials.
– : the migration energy of the species
– : the formation energy of the species
• Vacancy mechanism/Interstitial mechanism
Ting-Yun Huang, 2012/11/15Page 7
Fast diffusion path and lattice diffusion
• Dsurface(T)>>DGBs(T)~Dcores(T)>>Dlattice(T)
– for 0<T<Tmelt
• Mixed diffusion mechanism
• Lattice + Grain boundaries
• Lattice + Dislocation core
Ting-Yun Huang, 2012/11/15Page 8
Surface energy/Young-Laplace Pressure
• : n dependent. (n: unit normal)
• Wulff construction/Faceting of crystals
Ting-Yun Huang, 2012/11/15Page 9