MATTER Undergraduate web site
   
    MATTERDiffraction | Site Map | Help | Contact us | Glossary | About  
 
     

Previous ] Continue ]

Geometry

  Geometry of Diffraction: Braggs Law 1     2 of 18
 

Particles scatter incident rays in all directions. In some of these directions the scattered beams are in phase and reinforce each other to give diffracted beams i.e. constructive interference. The mathematical description of diffraction was first written down by von Laue in 1912 and his equations are still useful. However, a simpler way to describe the geometry (but not intensity) of diffraction is using Bragg's law.

Single layer of atoms

Rays on single row atoms image• Consider first a single plane of regularly spaced atoms:

• Imagine a beam of coherent light is incident on the atoms at an angle qIN. Some of the rays interact with the atoms and are scattered in all directions. (Most of the rays are transmitted.)  

• Consider the two scattered waves, A and B. They are in phase, reinforcing each other to give a diffracted beam, only when they travel the same distance, i.e. when x = y. This only occurs for scattered waves with an outgoing angle of:

qOUT = qIN

• Thus a diffracted beam from a single row of atoms is made up of all the waves which are scattered with an outgoing angle equal to the incoming angle of the incident waves. This is true for incident waves of any wavelength.

 

 
 

 Introduction  | Geometry | Intensity | X-ray Diffraction | Electron Diffraction 

 
 

© 2000 MATTER, The University of Liverpool. All rights reserved.
    contact us   Last updated: July 25, 2000 commercial information