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

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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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This note was uploaded on 12/01/2011 for the course MS&E 206 taught by Professor Nix during the Spring '08 term at Stanford.

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

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