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Unformatted text preview: MSE 803: N ANOMATERIALS AND N ANOTECHNOLOGY Professor Xudong Wang 213 MSE Building Spring 2010 Class 5: Fundamentals of Solid Surfaces Class Overview Surface to volume ratio Surface energy  dependence on nanoparticle (NP) size Physical properties resulting from size reduction Origin of surface energy Methods to reduce surface energy Shape/Size of nanoparticles Wullf plot Needs for Understanding Solid Surfaces Surface Energy!!! Size and morphology control. Property control Distribution of nanostructure What we should consider: Surface to volume ratio Surface energy Chemical potential Surface to Volume Ratio Calculation of Percentage of Surface Atoms The size and surface factors of NPs are closely related: For spherical particles, the surface to volume ratio is proportional to 1/R. Simple model used to calculate surface/volume ratio. Number of atoms/shell where n is sequence number of the shell. Total number of atoms in a cluster with n shells can be calculated as: Therefore, the surface/volume ratio is N s /N 2 10 2 n N s 3 / ) 3 11 15 10 ( 2 3 n n n N G. Schmid. In Nanoscale Materials in Chemistry ; K. J. Klabunde, Ed.; WileyInterscience: New York, 2001 ; Chapter 2, p15 Surface to Volume Ratio of QD as Function of Particle Radius For the smallest cluster with only one shell (n = 1), the surface/volume ratio is 12/13 = 92.3%. Assuming that the thickness per shell is 6 , the surface/volume ratio can be calculated a function of radius. Surface/volume ratio increases dramatically as radius of particle becomes smaller than 5 nm, which is on scale of quantum dots (QDs) C. Nutzenadel et al,, Eur. Phys. J. D8, 245 (2000) Percentage of Surface Atoms Nanomaterials process large fraction of surface atoms per unit volume Ratio of surface/interior atoms increases dramatically when subdivide macroscopic solid into smaller parts For iron: 1cm cube surface atoms 105 %, 10nm cube surface atoms 10% 1nm cube, every atom a surface atom This behavior leads to dramatic changes in physical and chemical properties The percentage of surface atoms changes with the palladium cluster diameter Variation of Surface Energy with Particle Diameter Total surface energy increases with overall surface area: which in turn is...
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 Spring '10
 Samuel

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