Expt 9) Soft phonons at continuous structural phase transitions

That continuous structural phase transitions are associated with soft phonon modes was first put forth theoretically by Cochran in 1959-60. He posited that as an optical phonon branch reaches zero frequency the material must become structurally unstable. Qualitatively, when the phonon frequency goes to zero, that mode becomes macroscopically occupied, which ushers in a structural change. The symmetry of the phonon determines the new low temperature structure.

While this theory was tested soon thereafter by many, a soft phonon associated with a structural instability had already been observed by Raman and Nedungadi nineteen years prior. In 1940, they saw that the transition between -quartz and -quartz at 573C was associated with a soft phonon using (you guessed it!) Raman spectroscopy. However, it is important to note that the transition in quartz is a discontinuous phase transition. So while the phonon does soften considerably, it does not actually reach zero frequency before the structural transition takes place.

Below is the original image, showing the rather spectacular result, where the arrow indicates the phonon that softens significantly upon approaching the transition temperature (it starts out at at ~220 cm^-1). Both the Stokes and anti-Stokes softening can be observed due to the high temperature of the studies.

Phonon softening in quartz. As the temperature is raised, a phonon that starts out at the position of the arrow shifts toward lower frequency (i.e. towards the region of large intensity Rayleigh scattering). (The phonon mode, for some reason, is barely visible in the -192C spectrum.) At high temperatures, the phonon linewidth broadens considerably and is very difficult to see at 530C. It is actually easier to see the softening on the anti-Stokes side (towards the left of the Rayleigh scattering).