Question

In a Triclinic crystal, a lattice plane makes intercepts at a length a, 2b and \( - \frac{{3c}}{2}\). The Miller indices of the plane are
1. 3 : 6 : 4
2. 6 : 3 : 4
3. 6 : 3 : - 4
4. 6 : 3 : -2

Answer 1

Correct Answer - Option 3 : 6 : 3 : - 4

Concept:

Miller Indices:

• Miler indices is a symbolic representation of vector for the orientation of an atomic plane in the crystal lattice.
• It is defined as the reciprocal of fractional intercept which the plane makes with the crystallographic axes.

Procedure to find Miller Indices:

1. Determine the intercept of the plane along each of three crystallographic directions.
2. Taking reciprocal of intercept.
3. Taking LCM of the fraction and multiply it by reciprocal of intercept.

Calculation:

Given,

Intercepts of plane = (a, 2b, \( - \frac{{3c}}{2}\))

Intercept = (1, 2, \( - \frac{{3}}{2}\))

Reciprocal of intercept = 1, \( \frac{{1}}{2}\), \( - \frac{{2}}{3}\))

LCM = 6

Miller indicates of the plane = LCM × Reciprocal of intercept

∴ Miller indicates of the plane = (6, 3, - 4)