Question

A crystal has lattice parameters of \( a = 4.26\, \text{\AA}, \, b = 10.0\, \text{\AA} \) and \( c = 3.44\, \text{\AA} \), respectively. A plane intercepts on the \( a, b, c \) axes at 2.13 Å, 10 Å and 1.72 Å, respectively. The Miller Indices for the plane, written as an integer, is ________. (Answer in integer.)

Hint:

Miller Indices are always found by taking reciprocals of fractional intercepts of a plane with the crystallographic axes.

Answer 1

Correct Answer: 22

Step 1: Formula used.
Miller Indices (\(hkl\)) are obtained as reciprocals of intercepts (in units of lattice parameters).
Step 2: Find intercepts in units of lattice constants.
\[ \frac{x}{a} = \frac{2.13}{4.26} = 0.5, \quad \frac{y}{b} = \frac{10}{10} = 1, \quad \frac{z}{c} = \frac{1.72}{3.44} = 0.5 \] Step 3: Take reciprocals.
\[ h = \frac{1}{0.5} = 2, \quad k = \frac{1}{1} = 1, \quad l = \frac{1}{0.5} = 2 \] Step 4: Conclusion.
Miller indices = (2 1 2).