Question

Intercepts of a plane in crystal is given by a, b/2, 3c in a simple cubic unit cell, Miller indices are​

Answer 1

Explanation:

3 6 1)

Explanation:

Miller Indices are usually defined as a vector (symbolic vector) representation that is used for the arrangement of planes of atoms in a crystal lattice. It is commonly used in the field of geology as well as in solid physics.

In a simple cubic unit cell, the intercepts are given as:

a , \frac{b}{2}2b , 3c

( 1 , \frac{1}{2}21 , 3 )

( 1, 2 , \frac{1}{3}31 ) × 3

( 3 , 6 , 1 )

Thus, the correct answer is ( 3 , 6 , 1 )

Answer 2

Answer:

Miller indices for the given plane is calculated as$361.$

Explanation:

Hint: The notation system used in crystallography for planes in the crystal (Bravais) lattice is called Miller indices. Miller indices are needed to mention the directions and planes. The number of indices will match the dimension of the lattice of the crystal.

• -Miller indices were coined by the famous British mineralogist William Hallows Miller in the year 1839 and were known as the Millerian system from earlier times.
• -Miller indices are written (hkℓ) and denote the family of planes orthogonal to
• $hb_1+kb_2+lb_3$

where $b_1$ are the basis of the reciprocal lattice vectors (you must take here note that the plane is not always orthogonal to the linear combination of direct lattice vectors

$ha_1+ka_2+la_3$

because the lattice vectors need not be mutually orthogonal).

The rules for Miller indices are given below-

1. Start by deciding the intercepts of the face alongside the crystallographic axes, in terms of unit cell dimensions.
2. Take the reciprocals of the above values.
3. Clear the fractions by multiplying with a suitable number.
4. Reduce the digit to the lowest terms.

Following the above rules for solving the question,

We have the intercepts as a, b/2, and 3c.

Taking the reciprocal of the coefficients of the intercepts, we will get-

Here, $h=\frac{1}{1}, k=\frac{1}{\frac{1}{2}}=2, l=\frac{1}{3}$

So, $h k l=1: 2: \frac{1}{3}=3: 6: 1$

or $(361) \Rightarrow(h k l)=(361)$

Hence, the miller indices for the given plane is calculated as$361.$