Question

a) Write down the procedure to determine directions in a unit cell (write only one algorithm). b) Find the Miller indices of the direction shown in the unit cell. Also draw [120], and [171] in the given empty unit cell. Show all the steps followed to draw the directions. Use the RH rule for XYZ axis notation.

Answer 1

THE PROCEDURE IS WRITTEN BELOW:

Step-by-step explanation:

Algorithm for determining the unit cell direction:

1. Determine the origin (start point) of the direction in the unit cell.

2. determines the end of the direction in the unit cell.

3. Determine the shortest translation vector from the start point to the endpoint.

4. Use the lattice parameters of the unit cell to express the vector.

If necessary, convert the vector to a number, making sure the results are proportional.

Enclose numbers in square brackets and use Miller exponents for expressions.

Use the right-hand rule (RH rule) to assign symbols to Miller indices based on the direction of the axes.

EXP.

(a) The direction [110] can be plotted as follows: starting from the origin (0, 0, 0) move along the positive x-axis until you reach (1 , 0, 0) and then move along the positive axis. It moves along the y-axis until it reaches (1, 1, 0) and finally along the positive z-axis until it reaches (1, 1, 1). (

b) Direction [120] can be drawn following the same steps but stopping at (1, 2, 0). Direction (

c) [171] can be drawn from the following steps, but stops at (1, 7, 1).