Materials Science and Engineering 206 (196)
Prof. W.D. Nix
Imperfections in Crystalline Solids
Spring 2008
Homework Assignment #4
(due: May 1, 2008)
1.
A large crystal of FCC platinum is held at T=2000K, just below its melting
temperature, for a long period of time so that vacancy equilibrium is
established.
(a)
Write an expression for and calculate the equilibrium concentration of
vacancies,
c
o
, (in units of vacancies per m
3
) when no external
pressure is acting on the solid.
(b)
Now consider a tiny spherical particle of Pt of radius
R
(a
nanoparticle!) also held at T=2000K, near its melting temperature.
The
surface of this tiny particle exerts a pressure,
p
ext
=
2
±
/
R
, sometimes
called the Laplace pressure, where
±
is the surface free energy of Pt.
Write an expression for the vacancy concentration in such a small
particle, in terms of
c
o
.
(c)
For what nanoparticle size (radius) would one expect to find less than
one vacancy in the particle at 1000K?
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- Spring '08
- nix
- Thermodynamics, surface free energy
-
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