Hmwk_4+08 - Materials Science and Engineering 206(196...

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?