Chapter 4, Problem 4.78CP

Interpretation Introduction

Interpretation:

A computer program to show the dependency of vacancy concentration on temperature is to be written. Also, graph of the calculated data to show the equilibrium vacancy concentration as s function of temperature is to be prepared.

Concept introduction:

The number of vacancies per ${\text{cm}}^3$ is calculated by the formula;

  $n_v=\frac{\text{number of vacancies in unit cell}}{V}$ ......... (1)

Volume of a unit cell $\left(V\right)$ is calculated using the lattice parameter $\left(a_0\right)$ as:

  $V={\left(a_0\right)}^3$ ......... (2)

The number of vacancies per ${\text{cm}}^3$ is calculated by the formula;

  $n_v=n\times \text{exp}\left(\frac{-Q_v}{RT}\right)$ ......... (3)

Here, $n$ is the number of atoms per ${\text{cm}}^3$, $Q_v$ is the energy required to deliver one mole of vacancy in $\text{cal/mol}$, $T$ is the temperature in Kelvin, and $R$ is the universal gas constant.

The relationship between the theoretical density $\left(\rho \right)$ of an element, number of atoms $\left(n\right)$ present in a unit cell and volume of a unit cell $\left(V\right)$ is:

  $\rho =\frac{n\times \left(\text{A}\text{.M}\right)}{V\times N_{\text{A}}}$ ......... (4)

Here, $\left(\text{A}\text{.M}\right)$ is the atomic mass of the element and $N_{\text{A}}$ is the Avogadro's number.