Chapter 15, Problem 15A.2AE

Interpretation Introduction

Interpretation:

The Miller indices of the planes that intersect the crystallographic axes at given distances has to be determined.

Concept Introduction:

With the help of Miller indices, a plane in a space lattice can be described.

Notation used:

• $\left(h,k,l\right)$ represents a point.
• $\left[hkl\right]$ represents a direction.
• $\langle hkl\rangle$ represents a family of directions.
• $\left(hkl\right)$ represents a plane.
• $\left\{hkl\right\}$ represents a family of planes.
• Negative numbers/directions are denoted with a bar on the top of the number. Ex.-$\left(\overline{1}23\right)$.

Procedure:

• Identify the plane intercepts on the x, y and z-axes.
• Specify intercepts in fractional co-ordinates.
• Take the reciprocals of the fractional intercepts.
• If still a fraction is coming, then multiply with suitable number to get the final answer.