Chapter 4, Problem 4.2P

Interpretation Introduction

Interpretation:

A number of vacancies per m³ for gold is to be determined at temperature 900ℾ. Taking 0.86eV/atom as the energy for vacancy formation.

Concept introduction:

Calculation of vacancies per m³ can be done using the following formulas-

Total number of atomic sites is given as follows-

  $N=\frac{N_A{\rho }_{Au}}{A_{Au}}$

Here,

N = total number of atomic sites

N_A = Avogadro number

theρ_Au= density of gold

A_Au = atomic mass of gold

Number of vacancies is given as follows-

  $\frac{N_v}{N}=\exp \left(\frac{-Q}{kT}\right)$

Here,

N= number of atomic sites

N_v = number of vacancies

Q = energy of energy formation

k = Boltzmann constant

T= temperature