Chapter 4, Problem 4.6P

Interpretation Introduction

(a)

Interpretation:

The fraction of lattice points which are vacant in the sample of beryllium at the given conditions is to be determined.

Concept introduction:

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:

  $\rho =\frac{n\times \left(\text{A}\text{.M}\right)}{V\times N_{\text{A}}}$ ...... (1)

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

Volume of a unit cell $\left(V\right)$ for HCP crystal structure is calculated using the lattice parameter $\left(a_0\right)$ and $\left(c_0\right)$ as:

  $V={\left(a_0\right)}^2{c}_0\cos 30$ ...... (2)

Interpretation Introduction

(b)

Interpretation:

Total number of vacancies present in the cubic centimeter of beryllium is to be determined.

Concept introduction:

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

  $n_v=\frac{\text{number of vacancies in unit cell}}{V}$ ...... (3)