Lecture 22-23 Nano-1

# Lecture 22-23 Nano-1 - Nano There are many definitions in...

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Nano There are many definitions in the literature for “nano”, some of which are real and others are not, similar to the claims for what it can do. (Any materials science undergraduate has in fact come across nanoscale effects without much shouting. Much of what is described as “nano” is something that people have been working on for decades; it has just been “rediscovered” by a different community.) Within the context of this course one approach is to consider how a property scales as a function of the size of the system (R). In a generic sense one can write: P(R) = AR 3 + BR 2 + CR + D A => Bulk behavior B => Surface term, or at least what scales as a surface term C => Edge term D => Limit for atomic behavior A bulk system can be defined as one where the terms B, C & D are irrelevant; a “nano” as one where one has to include them. Another way to look at this which is sometimes useful is to look at the property as a function of volume as (with slightly different B, C and D) P(V)/V = A + BV -1/3 + CV -2/3 + DV -1 We can further break down the cases when this occurs 1) Simple “size” arguments, i.e. R is small 2) Fundamental changes due to, for instance, changes in the band-structure, quantum size effects. 3) Breakdown of the continuum approximation, i.e. the system is too small for this to be valid. 4) Counting – atoms are discrete; this is similar to but not quite the same as 3) 5) Changes in what forces are important. For instance, Van Der Waals forces scale as 1/ R 6 so are important at the nanoscale but relatively unimportant between macroscopic objects. Somewhat similarly, in air at room temperature many materials are covered in a monolayer or so of water. For a large system the effects of the surface tension of the liquid are minimal, but when the sizes are reduced (MEMS/NEMS) they can become important. 6) Boundary condition effects. Because of the presence of a boundary (e.g. image dislocation) there are changes. If a large fraction of the system is “close” (on the relevant scale of the decay of strain fields for instance) to the boundary things will change. Some of these you have already seen, and in fact many parts of “nano” are necessarily part of most undergraduate/graduate MSE courses without being defined as such – a classic example is anything associated with nucleation and growth (408) where one has to

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consider the surface terms. Some others are scaling arguments, for instance Hall-Petch effect. (This relies upon the fact that grain-boundaries impede the motion of the dislocations so if one increases the density of grain-boundaries the barriers per unit
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## This note was uploaded on 04/13/2010 for the course MAT SCI 404 taught by Professor Matsci during the Winter '10 term at Northwestern.

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Lecture 22-23 Nano-1 - Nano There are many definitions in...

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