How do compound objects maintain rigidity despite atomic vibrations?

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Hello,

as we all know, in compound solids atoms are always vibrating with some degree, depending on the temperature or the average kinetic energy they posses. My question is how do compound objects maintain their rigidity in those conditions, or to say it better how do atoms stay in fixed positions, or keep fixed distances inside a solid despite their vibrations. It seems as a straight-forward question, but I just wanted to know the details.
 
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They don't. The distance between atoms changes as they vibrate.
However it is not clear what you mean by "compound" solids. You mean composed by more than one type of atom?
 
Each atomic nucleus sits in a local minimum of potential energy. Therefore there is always a force that pushes it back to the equilibrium position when it moves away, e.g. due to thermal vibrations.

In a real solid, the atoms are not independent. Instead they are coupled, like a chain of balls with springs in between them. The result is that they all vibrate together. The phase between their oscillations leads to a wave-like motion. Because all this happens at the atomic level these motions are quantized - they are called phonons.

There are two basic types of phonons: with a small phase between the atoms they are called acoustic photons (because they are responsible for transmitting sound through the solid), and if they are nearly out of phase they are called optical phonons (because the frequencies are near those of visible light). Well, that's hand waving, the details are a bit more complicated.

http://en.wikipedia.org/wiki/Phonon

Bending and plastically deforming a material is yet another story. When you do that you introduce all kinds of defects into the crystal lattice that break the perfect translation symmetry.
 
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