6 Periodically modulated positions (a phonon)

From here you may load this preset , see the text of the next , or return to the preset list.

Here is a monatomic crystal with a periodic displacement of the atoms from their normal sites. The displacement of the nth atom is given by u_n = A*cos(qna). You see the effect of the displacements in the electron density plot; the diffraction pattern has been reduced to a mess.

Change the wave amplitude to 0.04 (giving displacements too small to see on the electron density graph) and calculate. Zoom the x-axis, by dragging with the cursor just below the axis, to cover the range delta k = 0 to about 10. The periodic distortion has added sidebands or satellites to the Bragg peaks. The satellites are separated from their associated Bragg peak by q or multiples of q. The intensities of the satellites increase with increasing amplitude of the disturbance (try it!) and with increasing order of the associated Bragg peak.