PHYS2006: Waves in One-dimensional Crystals

This is a collection of animations illustrating some properties of wave-like motions in a one-dimensional crystal.

One Type of Atom

First we have an infinite line of masses and springs, with all masses identical. The first image shows that a mode with wavevector k = Pi/6a and one with k = Pi/6a + 2 Pi/a give exactly the same displacements to the masses (indicated by the red dots).

Animation 1

The next image uses k = Pi/6a and k = Pi/6a - 2 Pi/a. Again the displacements of the masses are the same, even though the shorter wavelength background wave is propagating in the opposite direction.

Animation 2

Finally, we combine the above two pictures, to see that both the wavevectors from outside the Brillouin zone have identical physical effects to the original one from inside the zone.

Animation 3

Two Types of Atom

Here we have two different masses, alternating along the line. The following image shows the displacements in an optical mode with wavevector k = Pi/6a.

Animation 4


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Created: 12 May 1999
Last updated: 8 Oct 2004