Chapter 4, Problem 4.15P

Interpretation Introduction

(a)

Interpretation:

The atomic fraction of the hydrogen atoms is to be determined.

Concept introduction:

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

  $\rho =\frac{{\displaystyle \sum n_i\times {\left(\text{A}\text{.M}\right)}_i}}{V\times N_{\text{A}}}$ ....... (1)

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

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)

Interpretation Introduction

(b)

Interpretation:

The number of unit cells that contains hydrogen atom is to be calculated for the given sample.

Concept introduction:

Number of cells containing $n$ atoms of a species is:

  $\text{Number of unit cells}=\frac{1}{n}$ ....... (3)