Atom Vibration in Solids: 3D Pattern

[nipiano93]

I just wantedhow the atoms vibrate in solids. I do not want to know the reason of their vibration (I know it). I just want to know their pattern of vibration. Some people say that they vibrate by undergoing a to and fro motion. But I do not think it is true because the objects are three dimensional. So, please give me a clear picture of their pattern of vibration (3 dimensional). Thanks :)

 

[Zacku]

I just wantedhow the atoms vibrate in solids. I do not want to know the reason of their vibration (I know it). I just want to know their pattern of vibration. Some people say that they vibrate by undergoing a to and fro motion. But I do not think it is true because the objects are three dimensional. So, please give me a clear picture of their pattern of vibration (3 dimensional). Thanks :)

Hi,

Well basically they go back and forth but in 3D .
If you consider a simple cubic lattice for instance, each particle will have 6 neighbours ( corresponding to the isostatic coordination number): one above, one below, one on the left, one on the right, one in the back and one on the front. If you imagine linking each one of these neighbours to the central particle with springs and then give some kick to it then you can have a pretty good of the motion of an atom or a molecule in a simple solid (if you can't imagine that then try to do the experiment with pen springs a small rubber ball and six friends holding one of the spring ).

 

[ZapperZ]

I just wantedhow the atoms vibrate in solids. I do not want to know the reason of their vibration (I know it). I just want to know their pattern of vibration. Some people say that they vibrate by undergoing a to and fro motion. But I do not think it is true because the objects are three dimensional. So, please give me a clear picture of their pattern of vibration (3 dimensional). Thanks :)

This actually isn't a simple question, and not as simple to answer. If you want a more technical detail, it is actually covered in a whole chapter in a Solid State Physics book (example: Chapters 22 and 23 in Ashcroft and Mermin text).

In just 1D alone, there are what we call "normal modes". The atoms on this 1D chain can vibrate "up and down" (transverse) or "left and right" (longitudinal). Even then, in each of those "modes", there are different variation, depending on what "basis" is attached to each of the solid's lattice points. This gives you what are known as acoustic modes and/or optical modes.

In 3D the fun multiplies exponentially. Note that the often used concept of "phonons", which are quantized lattice vibrations, would come into play here.

Zz.