Iron belongs to the BCC lattice. The Miller indices of the second allowed reflection in the powder diffraction pattern of iron would be

Concept:

• A lattice point is a point at the intersection of two or more grid lines in a regularly spaced array of points, which is a point lattice.
• The lattice is a 2D representation of a 3D crystal on the plane of a paper. It is constructed by using certain points known as lattice points and lattice lines.
• The unit cell is a smaller part of a crystal that is unique for a particular crystal substance.
• In crystallography, miller indices form a notation system for lattice planes in crystal lattices. In particular, a family of lattice planes of a given Bravais lattice is determined by three integers h, k, and ℓ, the Miller indices.

​Explanation:

• In crystallography, x-rays are allowed to be passed through a crystal in a series of parallel beams so that they diffract from different sets of parallel miller planes.
• The allowed cubic planes for a BCC (body-centered cubic) lattice in crystallography depend upon miller indices (h, k, ℓ) as, that the sum of h, k, and ℓ, must be even (\({\rm{h + k + l\; = \;even}}\)).
• Now, for the (100) plane, the value of h, k, and ℓ is 1, 0, and 0. The sum of h, k, and ℓ is an odd number and this cubic plane is not allowed for powder diffraction.

\({\rm{h + k + l = 1 + 0 + 0}}\)

\({\rm{ = 1}}\)

\({\rm{ = odd}}\)

• For the (111) plane, the value of h, k, and ℓ is 1, 1, and 1. The sum of h, k, and ℓ is an odd number and this cubic plane is not allowed for powder diffraction.

\({\rm{h + k + l = 1 + 1 + 1}}\)

\({\rm{ = 3}}\)

​\({\rm{ = odd}}\)

• For the (200) plane, the value of h, k, and ℓ is 2, 0, and 0. The sum of h, k, and ℓ is an even number and this cubic plane is allowed for powder diffraction.

\({\rm{h + k + l = 2 + 0 + 0}}\)

\({\rm{ = 2}}\)

\({\rm{ = even}}\)

• For the (210) plane, the value of h, k, and ℓ is 2, 1, and 0. The sum of h, k, and ℓ is an odd number and this cubic plane is not allowed for powder diffraction.

\({\rm{h + k + l = 2 + 1 + 0}}\)

\({\rm{ = 3}}\)

​\({\rm{ = odd}}\)

Conclusion:

• Hence, the Miller indices of the second allowed reflection in the powder diffraction pattern of iron would be (200)