About soft phonon mode: is it simply of reduced energy

[zhanhai]

Can we simply understand a softened phonon mode as one having reduced energy/frequency?

Does "soft" indicate smaller value of the spring coefficient like the k in
f=kx,
where f is force and x is displacement of a spring, so a "soft" spring has a smaller k value?

Thanks for all help.

 

[Darwin123]

Can we simply understand a softened phonon mode as one having reduced energy/frequency?

Does "soft" indicate smaller value of the spring coefficient like the k in
f=kx,
where f is force and x is displacement of a spring, so a "soft" spring has a smaller k value?

Thanks for all help.

The "soft" indicates that the spring has "broken", not that its elasticity has changed. If the value of k merely changed, the spring could still vibrate as long as the vibrations are centered on the site of attachment of the spring. If the spring breaks, the bob can drift anywhere. The spring is softer because it has ceased to exist, not because its tension has changed.

The decrease in frequency does not come from a change in k, but from a loss of order. Changing the value of k does not change the degree of order in the system. Changing the value of k is like a change without a phase transition. The breaking of the spring is very much like a phase transition.

It is not complete to say that a soft phonon mode corresponds to a decrease in phonon frequency. I think it is more correct to say that the soft phonon mode corresponds to a decrease in crystal symmetry. The decrease in phonon frequency is a consequence of the decrease in crystal symmetry. The decrease in crystal symmetry is usually associated with a certain type of phase transition.

Soft phonons are usually associated with phase transitions in crystals that have more than one distinguishable lattice. There is a lattice associated with each atom of a unit cell which is distinguishable from the lattices associated with the other atoms of the unit cell. As long as all the lattices are intact, the crystal will have a band structure that includes several kinds of optical phonons. If one of the lattices becomes disordered, leaving the other lattices intact, the optical phonons associated with the disordered lattice become acoustical phonons. The optical phonon associated with the disordered phonon is referred to as a soft phonon.

Look at the phase transition as a type of partial melting. One of the lattices melts while the other lattices remain solid. While the crystal is entirely frozen, there will be transverse optical phonons associated with vibrations within each lattice. Each optical phonon has a finite frequency at zero wave vector. However, suppose one of the lattices melts. Liquids can’t support transverse waves, and neither can this melted lattice. Obviously, the vibrations associated with that transverse mode can no longer occur. So the zero wave vector frequency of this phonon has to become zero when that lattice “melts”.

Before the lattice melted, the crystal had a high degree of symmetry. The equilibrium point of every atom was restricted to a specific point on the unit cell and on the lattice. After a lattice melts, the atoms in that lattice can diffuse anywhere in the crystal. Thus, the crystal has a very low degree of symmetry after the transition. Therefore, the soft phonon mode is closely associated with the symmetry of the crystal before and after the phase transition.

Diffusion is one difference between what you are saying and the reality of soft phonons. In a crystal that isn’t undergoing a phase transition, the phonon could decrease in frequency without the associated atoms diffusing. One can heat or stress the crystal resulting in a lower phonon energy, and there will be no atoms diffusing. However, if one of the lattices becomes disordered, the atoms in that lattice can diffuse. So the decrease in frequency during this phase transition signals the onset of diffusion.

Here are some links concerning soft phonons and phase transition.


http://hal.archives-ouvertes.fr/docs/00/22/19/47/PDF/ajp-jphyscol198243C403.pdf
“The concept of "soft phonon" associated with a phase transition signifies a phenomenon in which a phonon mode, which coincides with a lower-symmetry structure, is very much amplified immediately before the onset of phase transition from a higher-symmetry structure.”

http://webspace.webring.com/people/ra/astrophys0msci/CrystalStructure_Handout10_0.pdf
“Zone-boundary phonons: When the distortion is driven by a zone-boundary phonon, the distorted structure will have a larger unit cell (the translational symmetry is broken). The 12 zone boundary point will then “fold” to the new zone center, and the soft phonon will harden below the phase transition to become a new zone center phonon.”


http://www.riken.jp/lab-www/library/publication/review/pdf/No_29/29_034.pdf
“The soft phonon phase transition is one of the best established mechanisms by which a crystal structure can change. In the pressure-induced case, the frequency of a given vibration in the lattice goes to zero as the transition is approached: zero frequency implies that the lattice structure is unstable, and will transform, typically to a lower symmetry phase.”

 

[zhanhai]

Darwin123:

I greatly appreciate your comprehensive explanation.

Actually, it is much beyond my interpretation. I am working on a model for interactions of superconducting electrons under the mediation of phonon modes. In the model, if the phonon frequency around the mediating phonon modes is lowered, desired interactions would be favored.

I remember I read somewhere that a dip in phonon dispersion curve would be an indication that the phonons were engaging in coupling with electrons.

It seems that I only look at k-space while phonon softening is more related to real space. Considerations of both spaces would of course make things better, but it is really difficult to me.

Thank you again.

 

[Darwin123]

Darwin123:

I greatly appreciate your comprehensive explanation.

Actually, it is much beyond my interpretation. I am working on a model for interactions of superconducting electrons under the mediation of phonon modes. In the model, if the phonon frequency around the mediating phonon modes is lowered, desired interactions would be favored.

I remember I read somewhere that a dip in phonon dispersion curve would be an indication that the phonons were engaging in coupling with electrons.

It seems that I only look at k-space while phonon softening is more related to real space. Considerations of both spaces would of course make things better, but it is really difficult to me.

Thank you again.

As a graduate student, I very briefly worked with soft phonon modes as associated with solid electrolytes. Solid electrolytes and superconductors are completely different materials. I don't know if soft phonon modes means the same thing in each material. However, it may be useful to understand them in solid electrolytes.

A phonon becomes soft during the phase transition from "solid insulator" to "solid electrolyte". As the temperature rises, the phase transition occurs when one of the sublattices in the crystal structure breaks down. This is a change in what you are calling "real space". The electronic structure is not changing significantly independent of the positions of the nuclei. The nuclei associated with a sublattice is breaking down.

The phonon changes during the phase transition in the following way. Long wavelength vibration turns into diffusion. The frequency at the band center goes to zero when diffusion of atoms replaces the vibration of atoms.

I wonder if a solid electrolyte can also be a superconductor? I know that metals don't become solid electrolytes. However, maybe ceramic superconductors can become solid electrolytes. If a ceramic superconductor can also become a solid electrolyte, then maybe you can tune the frequency of the phonon by inducing the phase transition. Perhaps you could look into the possibility.

There has been a lot of work on solid electrolytes. A lot of research has been done on soft phonons because of the possibility of solid electrolyte technology. The hope is that a safe car battery can be made with solid electrolytes instead of with the liquid electrolyte solutions.

Battery acid is very dangerous partly because it can slosh around. The high voltage batteries needed for electric cars will require even more corrosive chemicals. A corrosive solid may be safer then a corrosive liquid. Therefore, a solid car battery could be much safer than a liquid based car battery. To make such solid state batteries, one needs solid electrolytes.

 

[zhanhai]

Here is an exemplary paper in which "softening" of phonon mode is used for the other meaning:

http://www.esrf.eu/UsersAndScience/Publications/Highlights/2001/CAD/CAD1.html

It is said "Besides an overall renormalisation, an anomalous softening of the highest optical branch is clearly visible."

The highest optical branch does not go to zero at the long wave end, and the "anomalous softening" (dip?) does not occur at the long wave end; it happens at around [0.2,0,0].

BTW, what does it mean by "renormalisation"? Does it mean that the dispersion curve deviates from a standard dispersion curve?