Question

A plane in a unit cell is described by its miller indices a (632). The plane intersects x, y and z respectively at a point whose distances from origin are
1. 6, 3 and 2 units
2. \(\frac{{1}}{{6}}, \frac{{1}}{{3}}~and~\frac{{1}}{{2}}\) units
3. \(\frac{{2}}{{3}}, \frac{{1}}{{3}} ~and~ 1\)units
4. \(\frac{{1}}{{2}}, ~1 ~and~ \frac{{2}}{{3}}\)units

Answer 1

Correct Answer - Option 2 : \(\frac{{1}}{{6}}, \frac{{1}}{{3}}~and~\frac{{1}}{{2}}\) units

Concept:

• Miller indices are the styles to designate the planes and directions in the unit cells and crystals.
• Miller indices (hkl) are expressed as a reciprocal of intercepts p, q, and r made by the plane on the three rectangular axes x, y, and z respectively.
• These are the unit distances from the origin along the three axes. Thus

\(h=\frac{1}{p},~k=\frac{1}{q},~l=\frac{1}{r}\)

Where p = intercept of the plane on the x-axis, q = intercept of the plane on the y-axis, and r = intercept of the plane on the z-axis.

Calculation:

Given:

Miller indices of a plane = (632)

Since, Miller indices are obtained by reciprocal of intercept p, q, and r made by the plane on the three rectangular axes x, y, and z respectively. Hence the reciprocal of miller indices will give the intercepts.

Distances from the origin to points at which the plane intersects = \(\frac{{1}}{{6}}, \frac{{1}}{{3}}~and~\frac{{1}}{{2}}\) units