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# Diffraction

## Introduction

Diffraction is a wave property of electromagnetic radiation that causes the radiation to bend as it passes by an edge or through an aperture. Diffraction effects increase as the physical dimension of the aperture approaches the wavelength of the radiation. Diffraction of radiation results in interference that produces dark and bright rings, lines, or spots, depending on the geometry of the object causing the diffraction. Common interference effects for visible light are the rainbow pattern produced by an oil film on wet pavement and the diffraction of light from a narrow slit or a diffraction grating.

## Diffraction Methods

A certain wavelength of radiation will constructively interfere when partially reflected between surfaces that produce a path difference equal to an integral number of wavelengths. This condition is described by the Bragg law:
n = 2dsin
where n is an integer, lambda is the wavelength of the radiation, d is the spacing between surfaces, and theta is the angle between the radiation and the surfaces. This relation demonstrates that interference effects are observable only when radiation interacts with physical dimensions that are approximately the same size as the wavelength of the radiation.

Interference of radiation between atomic planes in a crystal

These interference effects are useful for determining dimensions in solid materials, and therefore crystal structures. Since the distances between atoms or ions is on the order of 10-10 m (1 Å), diffraction methods require radiation in the X-ray region of the electromagnetic spectrum, or beams of electrons or neutrons with a similar wavelength. Electrons and neutrons are commonly thought of as particles, but they have wave properties with the wavelength depending on the energy of the particles as described by the de Broglie equation. The three diffraction methods have different properties that are described in more detail in separate documents. For example, the penetration depths of the three types of beams are quite different:
neutrons > X-rays > electrons.

Schematic of crystal-structure determination by diffraction

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