# Experimental Determination of Crystal Structure & Properties

**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**