(110)
Simple Cubic Crystal: Peak Order Analysis
The position of diffraction peaks in an X-ray powder pattern depends on the interplanar spacing ($d_{hkl}$) via Bragg's Law. For cubic crystals, $d_{hkl}$ is related to the Miller indices ($hkl$) and lattice constant ($a$) by:
$d_{hkl} = \frac{a}{\sqrt{h^2 + k^2 + l^2}}$
Peaks appear in order of increasing $h^2 + k^2 + l^2$ values for simple cubic lattices, as this value dictates the spacing. We examine the lowest index planes:
- 1st Peak: Corresponds to the lowest possible value for $h^2 + k^2 + l^2$, which is 1. This is the (100) plane. ($1^2 + 0^2 + 0^2 = 1$)
- 2nd Peak: Corresponds to the second lowest value, $h^2 + k^2 + l^2 = 2$. This is the (110) plane. ($1^2 + 1^2 + 0^2 = 2$)
- Subsequent peaks follow the order of increasing $h^2 + k^2 + l^2$ (e.g., 3 for (111), 4 for (200)).
Thus, the 2nd peak in the X-ray powder pattern of a simple cubic crystal is associated with the (110) plane.
Important Questions from Crystallography Stereographic Projection
- Residual stress present in a material can be determined by which one of the following techniques:
A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below. The miller indices of peak A is
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.
