Atomic vibrations in crystals

The first four simulations show the atomic vibrations for a one dimensional mass/spring chain (equal masses) for several phonon modes and a polaron mode. The next two simulations show the simplified motions for the vibrations of tungsten (W) and zirconium (Zr) in the negative thermal expansion material ZrW2O8. The last simulation shows dimeron motion at a temperature just above the ferromagnetic transition temperature, Tc.

NSF support: DMR007186, DMR0301971

Long Wavelength Acoustic Phonon
Short Wavelength Acoustic Phonon
&lambda approximately 31 atom spacings.
Very Short Wavelength Optical Phonon
&lambda = 2 atom spacings.
Polaron (static and motion of)
A polaron is a local lattice distortion that follows a mobile charge.
Negative Thermal Expansion
W is the green atom in the center of the triangle with Zr atoms at the vertices. Zn-W linkage is assumed to be relatively stiff in ZrW2O8.
Negative Thermal Expansion in 3-D
Shows the W vibrations along three (111) directions.
Dimeron Motion
Assumes electrons wave functions extend over two lattice sites and hop slowly through lattie.