How do atoms behave in a solid state?

[LogicalAcid]

This concept of when things have higher kinetic energy, their molecules and atoms move more never got to me. I don't get how something having more kinetic energy will make the atoms spread apart and liquify, if enough radiation gets to an object (infrared) in order to reach its melting point, I know it will liquify, but I never got how.

 

[Dr Lots-o'watts]

Do you agree that every atom in a solid vibrates about a mean position?