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