A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below. The miller indices of peak A is 
To determine the Miller indices of peak A in the X-ray diffraction pattern of a single phase cubic polycrystal, let's consider the given information and apply relevant concepts from crystallography.
Step 1: Understanding X-Ray Diffraction and Miller Indices
The X-ray diffraction pattern of a polycrystal is marked by peaks at specific angles due to constructive interference of X-rays diffracted by various crystal planes. Each peak corresponds to a set of lattice planes indexed by Miller indices such as (hkl).
Step 2: Bragg's Law
Bragg's Law is given by:
\(n\lambda = 2d\sin\theta\)
where \(n\) is the order of diffraction (typically 1), \(\lambda\) is the wavelength of incident X-rays, \(d\) is the interplanar spacing, and \(\theta\) is the angle of diffraction.
Step 3: Finding the Miller Indices
For a cubic system, the interplanar spacing \((d_{hkl})\) is related to the Miller indices by:
\(\frac{1}{d_{hkl}^2} = \frac{h^2 + k^2 + l^2}{a^2}\)
where \(a\) is the lattice parameter.
Step 4: Reasoning from Given Peaks
Analyzing the pattern, we have peaks already labeled (110), (200), and (211). Given the nature of cubic systems, the next peak corresponds to the next permissible sum of squares of Miller indices for this arrangement.
- For (110), \(h^2 + k^2 + l^2 = 1^2 + 1^2 + 0^2 = 2\)
- For (200), \(h^2 + k^2 + l^2 = 2^2 + 0^2 + 0^2 = 4\)
- For (211), \(h^2 + k^2 + l^2 = 2^2 + 1^2 + 1^2 = 6\)
The next sequential peak corresponds to a sum of squares of 8, which is (220).
Conclusion:
Thus, the Miller indices of peak A is 220, which matches the correct option.
Important Questions from Crystallography Stereographic Projection
- Residual stress present in a material can be determined by which one of the following techniques:
In a powder diffraction experiment on BCC iron, the first peak occurs at $2\theta = 68.7^\circ$. The wavelength of X-rays is ________ (in nm to three decimal places).
Given: The lattice parameter of iron = $0.287 \text{ nm}$
- For an FCC metal, the ratio of interplanar spacing obtained from the first two peaks of the X-ray diffraction pattern is
X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle $\theta = 24.65^\circ$. The lattice parameter of this metal is ____________ nm.
Given, wavelength of the X-ray used is $0.1543$ nm.- If d is the inter-planar spacing of the planes {h k l}, the inter-planar spacing of the planes {nh nk nl}, n being an integer, is
