## Materials Science and Engineering: An Introduction

$\frac{N_{v}}{N} = 6.08 \times 10^{-16}$
Given: Copper with melting temperature of 1084°C (1357K) energy of vacancy formation is 0.90 eV/atom Required: fraction of atom sites that are vacant at room temperature (298K). Solution: Using Equation 4.1: $\frac{N_{v}}{N} = exp (-\frac{Q_{v}}{kT}) = exp (-\frac{0.90 eV/atom}{(8.62 \times 10^{-5} eV/atom-K)(298 K)} = 6.08 \times 10^{-16}$