Interference from Several Diffracting Sources

This applet was written to support an introductory course on X-ray Diffraction. It is also relevant to the simple optical case of interference from several sources.

The applet shows radiation (black lines) incident on a line of points (red circles: atoms in the X-ray case, slits or holes in the optical case) that diffract at a chosen angle '2theta', producing the diffracted waves shown in green . The angle of the diffracted waves is called '2 theta' in this applet, in keeping with the notation of X-ray diffraction. The extra path difference (in red) of the diffracted radiation between successive radiators is marked. On the right of the screen is a graph showing how the sum of all the diffracted waves varies with angle 2theta. The current angle is displayed using a red line on this graph. This line can be dragged vertically and the diffracted angle will change accordingly.

• Alternatively, alter this angle by entering a chosen value between -70 and +70 into the 2theta(°) box. In yet another option, the angle can be increased by pressing the left arrow key and decreased by pressing the right arrow key. Notice that the intensity is a maximum at angles where there is a whole number of wavelengths in the extra path difference between successive radiators.
• Alter the distance between neighbouring points, the d spacing, by entering a chosen value between 2 and 10 (Å) into the box entitled d-spacing. Alternatively, the spacing can be increased by pressing up arrow key and decreased by pressing the down arrow key. The angles at which the large maxima occur differ but the criterion for the maxima stays as before.
• The incident radiation isrepresented by the black waves on the left of the screen. The wavelength (lambda) of the radiation can be set as a number from 1 to 10. For X-rays, think in terms of Ångstroms (Å). The default wavelength is 1.54 (Å).
• A blue dotted line marks the end of the extra path length.
• Try values of 2theta, d and lambda corresponding to a real crystalline material and known x-rays.
• Beneath the atoms there is a schematic picture showing the resultant wave that will be produced by adding the diffracted waves together.
• The first box refers forward to Bragg's law by showing the value of 2dsin(theta)/lambda

Hidden feature

• Left click on the University Logo to increase the number of planes from 2 to 10. You will see the sharpness of the maxima increase substantially. This illustrates a very important point in both x-ray diffraction and in the use of diffraction gratings in optics.

 Applet produced and written by Gary Skinner.