# What is Thermal expansion? [duplicate]

"Thermal expansion arises from the asymmetrical nature of potential energy curve for atoms in a solid. If oscillators were truly harmonic separation would not change regardless of the amplitude of vibration."

I don't understand how a temperature increase might not affect the volume of a solid substance if the oscillations were harmonic?

• You appear to be quoting. Please can you identify the source. – sammy gerbil May 11 '17 at 19:04
• Possible duplicate of Why solids expand on heating – sammy gerbil May 11 '17 at 19:07
• @DavidZ I would like to suggest that this question is not a duplicate as the OP is asking why one would get no expansion if the potential was symmetrical not why solids expand. That is the reason that I provided an answer. – Farcher May 12 '17 at 7:56
• @Farcher hm, maybe. I'd like to see this question edited by the OP to clarify that if that is really the case. – David Z May 12 '17 at 17:17

When the atom is not vibration the equilibrium separation between the atoms is $a_{\rm o}$.
As the temperature rises the kinetic energy, $E_!, E_2, E_3, E_4, E_5$, of the atoms increases and their amplitude of vibration increases.
For a potential that is symmetrical, as on the right, the average separation of the atoms, shown by the green blobs, stays the same at $a_{\rm o}$ and the material does not expand.
However for an asymmetrical potential graph, as shown on the left, the average separation of the atoms increases and progressively gets bigger than $a_{\rm o}$ and the material expands.