Question

The Weiss symbol of a crystal face is 4a: 2b: c. The value of h in the corresponding Miller Index (hkl) is ...........

Hint:

In crystallography, the Miller indices are calculated by taking the reciprocals of the intercepts of the crystal face along the axes, and then simplifying the fractions.

Answer 1

Correct Answer: 1

Step 1: Understanding the Weiss symbol.
The Weiss symbol "4a: 2b: c" refers to a crystal face and gives the intercepts of the face along the crystallographic axes. These intercepts are measured as multiples of the unit cell dimensions (a, b, and c). In this case, the intercepts are 4a, 2b, and c. To convert this into Miller indices, we need to take the reciprocal of these intercepts.
Step 2: Converting to Miller indices.
The general formula for Miller indices is the reciprocal of the intercepts along the axes. So, for the given Weiss symbol (4a: 2b: c), we take the reciprocals of the intercepts:
- For 4a, the reciprocal is 1/4,
- For 2b, the reciprocal is 1/2,
- For c, the reciprocal is 1.
Thus, the corresponding Miller indices are (hkl) = (1/4, 1/2, 1).
Step 3: Simplification of Miller indices.
We simplify the Miller indices by clearing the fractions. To do this, we multiply each index by the least common multiple (LCM) of the denominators (4, 2, 1). The LCM of 4, 2, and 1 is 4. So, we multiply each index by 4:
- \( h = 1/4 \times 4 = 1 \),
- \( k = 1/2 \times 4 = 2 \),
- \( l = 1 \times 4 = 4 \).
This gives us the Miller index (1, 2, 4).
Step 4: Conclusion.
The value of h in the corresponding Miller Index (hkl) is 1.