Question

If (326) is the Miller Index of a crystal face, then the value of x in the corresponding Weiss Parameter of the same face, xa : xb : xc is ............

Hint:

Weiss parameters are used to describe the orientation of crystal faces, and their relationship to the Miller indices is essential for crystallographic analysis.

Answer 1

Correct Answer: 2

Step 1: Understanding Miller Indices and Weiss Parameters.
The Miller indices (hkl) of a crystal face are related to the Weiss parameters (a, b, c) through the equation: \[ h : k : l = \frac{a}{x} : \frac{b}{y} : \frac{c}{z} \] Where \( x \), \( y \), and \( z \) are the Weiss parameters associated with the crystallographic directions. For the given Miller index (326), we need to match the corresponding Weiss parameters. This typically involves taking the reciprocals of the Miller indices.

Step 2: Calculation of x.
Given the Miller index (326), we know the Weiss parameters are inversely proportional to these values: \[ x = \frac{a}{h}, \, y = \frac{b}{k}, \, z = \frac{c}{l} \] Thus, for (326), the Weiss parameters would correspond to \( x = 1/3 \), \( y = 1/2 \), and \( z = 1/6 \).
Thus, the value of \( x \) is 1/3.