Chapter 15, Problem 15A.1ST

Interpretation Introduction

Interpretation:

The Miller indices of the given set of planes in a crystal that intercepts the axes at 3a, 2b and 2c has to be given.

Concept Introduction:

Steps to find Miller indices:

Write the intercepts of the plane expressed in multiples of a, b and c.

Take reciprocal of all the numbers.

Clear the fractions to obtain the values of h, k and l.

Explanation of Solution

Given data:

A set of planes in a crystal intersects the axes at 3a, 2b and 2c.

Miller indices:

The intercepts of the crystal lattice are 3, 2 and 2.

On taking reciprocals we get,

  $\frac{1}{3},\frac{1}{2}\text{and }\frac{1}{2}$

Clear the above fractions to get the Miller indices.

  $\begin{array}{l}\frac{1}{3},\frac{1}{2},\frac{1}{2}\\ \text{Multiply to obtain 6 in denominator}\text{.}\\ \frac{2}{6},\frac{3}{6},\frac{3}{6}\\ \left\{2\text{, 3, 3}\right\}\end{array}$

Therefore, the Miller indices of the given set of plane is $\left\{2\text{, 3, 3}\right\}$.