Soft Mode Theory: Understanding & Implications for H.B

[Hyla Brook]

Dear all,

I have trouble in understanding the soft mode theory. It says the short range force constant (ks) corresponds to the force that pull the atom back to the equil. position and the long range force constant (kl) corresponds to the force that is reverse. When temperature is low, the ks is smaller thus the structure is not stable (e.g. BaTiO3), and when T is high, the ks will INCREASE because of NON-HARMONIC effect and thus the structure can be stable at temperature higher than the critical one Tc.

What I don't understand well is that, when non-harmonic effect is taking into consideration, the volume will increase during lifting T (normal matter.). The equation of state is something that like pair potential (Morse equation). The curve turns flat when volume increases. That means the ks is smaller when volume is larger, and I always understand it as the origin of thermal expansion. So how can I understand the soft mode theory? I guess I confused something but I cannot figure it out. Any idea is greatly appreciated. Thank you!

H.B

 

[eljose79]

.

Dear H.B.,

Thank you for sharing your thoughts and questions about the soft mode theory. This theory can be quite complex and can be difficult to fully understand at first. I will try to provide a simplified explanation that may help you better understand the concept.

Firstly, the short range force constant (ks) and long range force constant (kl) are both components of the interatomic force constant matrix. This matrix describes the interactions between atoms in a crystal lattice and is a key factor in determining the stability of the crystal structure. The short range force constant (ks) represents the interactions between atoms that are close to each other, while the long range force constant (kl) represents the interactions between atoms that are further apart.

At low temperatures, the ks value is smaller because the atoms are held together tightly, and the structure is stable. However, as temperature increases, the atoms start to vibrate more and the ks value increases due to non-harmonic effects. This means that the force pulling the atoms back to their equilibrium positions becomes stronger, making the structure more stable at higher temperatures. This is why some materials, like BaTiO3, can be stable at temperatures above their critical temperature (Tc).

Now, regarding your question about thermal expansion, it is important to note that the soft mode theory does not directly explain thermal expansion. Thermal expansion is a result of the increase in atomic vibrations at higher temperatures, which causes the atoms to take up more space and thus the material expands. However, the soft mode theory can help explain why some materials have a negative thermal expansion coefficient (i.e. they shrink when heated). This is due to the fact that as the ks value increases with temperature, the long range force constant (kl) decreases. This decrease in kl results in weaker interactions between atoms that are further apart, causing the material to contract instead of expand.

I hope this helps clarify some of your confusion about the soft mode theory. If you have any further questions or would like to discuss this topic in more detail, please do not hesitate to reach out. Keep up the curiosity and dedication to understanding complex scientific theories!