Chapter 15, Problem 15A.1ST

(a)

Interpretation Introduction

Interpretation:

The separation of the $\left\{133\right\}$ planes in an orthorhombic lattice has to be determined.

Concept Introduction:

The separation of planes in an orthorhombic lattice is given by

  $\frac{1}{d_{hkl}^2}=\frac{h^2}{a^2}+\frac{k^2}{b^2}+\frac{l^2}{c^2}$

Where,

$d_{hkl}=$ Separation between planes

a, b and c are unit cell parameters.

h, k and l are Miller indices.

Answer to Problem 15A.1ST

The separation between the given planes is found out to be $0.19nm.$

Explanation of Solution

Given data:

  $\begin{array}{l}a=0.82nm\\ \\ b=0.94nm\\ \\ c=0.75nm\\ \\ h=1,k=3andl=3\end{array}$

The separation of planes in an orthorhombic lattice is given by

  $\frac{1}{d_{hkl}^2}=\frac{h^2}{a^2}+\frac{k^2}{b^2}+\frac{l^2}{c^2}$

Now,

  $\begin{array}{l}\frac{1}{d_{133}^2}=\frac{1^2}{{\left(0.82nm\right)}^2}+\frac{3^2}{{\left(0.94nm\right)}^2}+\frac{3^2}{{\left(0.75nm\right)}^2}=27.6728n{m}^{-2}\\ \\ d_{133}=0.19nm.\end{array}$

Therefore, the separation between the given planes is found out to be $0.19nm.$

(b)

Interpretation Introduction

Interpretation:

The separation of the $\left\{399\right\}$ planes in an orthorhombic lattice has to be determined

Concept Introduction:

The separation of planes in an orthorhombic lattice is given by

  $\frac{1}{d_{hkl}^2}=\frac{h^2}{a^2}+\frac{k^2}{b^2}+\frac{l^2}{c^2}$

Where,

$d_{hkl}=$ Separation between planes

a, b and c are unit cell parameters.

h, k and l are Miller indices.

Answer to Problem 15A.1ST

The separation between the given planes is found out to be $0.19nm.$

Explanation of Solution

Given data:

  $\begin{array}{l}a=0.82nm\\ \\ b=0.94nm\\ \\ c=0.75nm\\ \\ h=3,k=9andl=9\end{array}$

The separation of planes in an orthorhombic lattice is given by

  $\frac{1}{d_{hkl}^2}=\frac{h^2}{a^2}+\frac{k^2}{b^2}+\frac{l^2}{c^2}$

Now,

  $\begin{array}{l}\frac{1}{d_{399}^2}=\frac{3^2}{{\left(0.82nm\right)}^2}+\frac{9^2}{{\left(0.94nm\right)}^2}+\frac{9^2}{{\left(0.75nm\right)}^2}=249.0552n{m}^{-2}\\ \\ d_{399}=0.063nm.\end{array}$

Therefore, the separation between the given planes is found out to be $0.063nm.$