Experimental Determination of Crystal Structure & Properties

Abdulaziz July 26, 2020

Experimental Observation of Crystal Structure

The wavelength of X-rays is typically 1Å, comparable to interatomic spacing in solids.
This means that a crystal behaves as a three-dimensional diffraction grating for X-rays.
Bragg derived the condition for constructive interference
of the X-rays scattered from a set of parallel lattice planes.

X-ray diffraction results from an electromagnetic wave (Xray) impinging on a regular array of scatterers (the repeating arrangement of atoms within the crystal), producing a diffraction pattern.

Bragg’s Law

XRD set up

Example 2:

Calculate θ for λ=1.54 Å, cubic crystal, a = 5Å, 2d sin θ = nλ

2 different families of peaks

Example 3: Combining Bragg and d-spacing equation

X-rays with wavelength 1.54 Å are diffracted from the (1 1 0) planes of a cubic crystal with unit cell a= 6 Å. Calculate the Bragg angle, θ, for all orders of diffraction, n.

n = 1 :θ= 10.46° = (1 1 0)
n = 2 :θ= 21.30° = (2 2 0)
n = 3 :θ= 33.01° = (3 3 0)
n = 4 :θ= 46.59° = (4 4 0)
n = 5 :θ= 65.23° = (5 5 0)

In comparison: 1st order diffraction of (330) plane

1 family, different planes