# Qualitative understanding on why solids expand

I'm trying to understand better why solids expand, and what I've been looking at to help guide my understanding is the following graphic from my lecture notes:

Now, to illustrate what I think is going on here I'm going to try and explain my thought process:

• Molecules of a solid at a temperature above absolute zero (so always) will be vibrating about their nominal positions
• As the temperature increases, it would make sense to believe the particles have more energy, and thus take longer to decrease their speed when moving around their nominal positions, so their displacements from the nominal positon increases with temperature.
• However, according to the graphic, for some reason the potential change isn't symmetrical, (e.g. going to the right some $x$ gives a different potential energy than going the same magnitude but to the left $x$) so the atom stays on a certain end of the particle's motion, but according to my lecture notes this explains why the average separation of the vibrating particles is longer.

Thus, I have two confusions with this:

Why isn't the potential change symmetrical?

Why does the particle being on one end of its motion around its nominal position explain why the average separation of the vibrating particles is longer?

• Ofcourse for a diatomic system ground state potential (typically the morse like potential) will not be symmetrical as it is plotted as a function of relative distance $|\vec{r}_1-\vec{r}_2|$. The figure you provided is meaningful, as when atoms approach, there is a strong repulsion hence steep increase of potential compared to the potential experienced by atoms when they are moving far apart. – Sunyam Oct 22 '17 at 2:31
• One of the search terms you want here is "van der Waals force", but none of the leading links on google have a really clear explanation of the functional form of the potential (could be a good question here or on Chemistry). However, several of the top search results offer the hint that the inner bound is set by Paul exclusion which implies a rapid rise as sketched in your text. – dmckee --- ex-moderator kitten Oct 22 '17 at 3:25