Peering Inside Crystals
Bragg's Law, formulated by Lawrence Bragg and his father William Henry Bragg in 1913, is the foundational equation for X-ray crystallography. It explains how electromagnetic radiation (like X-rays) scatters when it hits the regular, repeating planes of atoms inside a crystal lattice.
When X-rays hit a crystal, most of them pass through, but some bounce off the atomic planes. If the X-rays bouncing off the first plane line up perfectly (constructively interfere) with the X-rays bouncing off the second plane, a strong signal is detected.
The Conditions for Reflection
Constructive interference only happens when the extra distance traveled by the deeper X-ray is an exact multiple of the X-ray's wavelength ($\lambda$). This extra distance depends on:
- Lattice Spacing ($d$): The distance between the atomic planes.
- Diffraction Angle ($\theta$): The angle at which the X-rays strike the crystal.
The Formula
Example Calculation
You are studying a salt crystal with a known lattice spacing of $0.282 , \text{nm}$. You detect a strong first-order ($n=1$) reflection at an angle of $15^\circ$.
- Calculate Sine: $\sin(15^\circ) \approx 0.2588$.
- Multiply by 2d: $2 \times 0.282 \times 0.2588 \approx 0.146 , \text{nm}$.
The wavelength of the X-rays you are using is approximately $0.146 , \text{nm}$.