X-Ray Diffraction from Atomic Planes

This applet was written as an extension to our applet showing interference from a set of diffracting sources. All atoms in a plane re-radiate in phase when the angle of the emitted waves to the plane is the same as the angle of the incident waves. This condition is always satisfied in the applet, which shows how the intensity of the waves diffracted from a set of planes depends on the phase relationship between diffraction from successive planes of atoms. This is embodied in Bragg's law, that gives the angles theta when the intensity is a maximum through the condition 2dsin theta = n lambda, where n is an integer. You can see in the applet that n represents the number of wavelengths in the path difference between the radiation from successive planes and that this must be an integer at the maxima of intensities.

• The incident x-rays are represented by the black waves on the left of the screen. The wavelength (lambda) of the radiation can be set as a chosen number from 1 to 10, taken as Ångstroms (Å). The default wavelength is 1.54Å. (Only a few waves incident on all the atoms are drawn, for clarity)
• When the radiation hits an atom (red circle) it is diffracted and is shown as a green wave. The extra path difference between the incident and diffracted waves is shown as a red wave.
• Blue dotted lines mark the regions where the extra path length occurs for neighbouring planes.
• To alter the spacing between the atomic planes, a chosen value between 1 and 3.5 Å can be entered into the box entitled d-spacing. The spacing can also be increased by pressing down arrow key and decreased by pressing the up arrow key, or by clicking and dragging the bottom filled atom with the mouse.
• The diffraction angle, measured from the atomic planes, can be altered by entering a value between 0.1 and 75 into the 2theta(°) box. Alternatively the angle can be increased by pressing the right arrow key and decreased by pressing the left arrow key.
• Beneath the atoms there is a graph showing how the intensity varies with angle. The current angle is displayed using a red line. This line can be dragged horizontally to change the diffraction angle. The atoms are assumed to diffract equally at all angles, which is not the case with real atoms but the principle of strong maxima in intensities when Brags's condition is satisfied remains true.

Hidden features

1. Left click on the University Logo to increase the number of planes from 10 to 50. This illustrates how the Bragg intensities are very sensitive to the number of planes illuminated.
2. Right click on the graph at the bottom to change the scaling criteria. The lighter the colour green the more intense the signal.
3. Right click on the University Logo to display the wave amplitude within the crystal that arises from the presence of both incident and diffracted waves. Note that the resulting standing wave pattern perpendicular to the planes just matches the interplanar spacing when the Bragg condition is satisfied.

This applet was produced and written by Gary Skinner.