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

Given:

• Miller Index: (326)

Concept:

Miller indices and Weiss parameters are reciprocally related.

If Miller indices are (hkl), then the Weiss parameters are:

$$\frac{a}{h} : \frac{b}{k} : \frac{c}{l}$$

For Miller Index (326):

• h = 3
• k = 2
• l = 6

Weiss parameters:

$$\frac{a}{3} : \frac{b}{2} : \frac{c}{6}$$

To express in the form xa : xb : xc:

Find the least common multiple of the denominators (3, 2, 6) = 6

Multiply each term by 6:

$$\frac{a}{3} \times 6 : \frac{b}{2} \times 6 : \frac{c}{6} \times 6$$

$$= 2a : 3b : 1c$$

This can be written as:

$$2a : 3b : c$$

Comparing with xa : xb : xc, we have:

• Coefficient of a: x = 2
• Coefficient of b: 3
• Coefficient of c: 1

Answer: x = 2