# Heating of solid - interatomic potential

## Main Question or Discussion Point

Hi!

In a book it said that it can be clearly seen from the interatomic potential (such as the Lennard Jones) that when a solid is heated it expands.

Please explain how is it exactly manifested by the interatomic potential graph?

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Mapes
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The interpretation is that the energy minimum in a plot of atomic spacing vs. energy (e.g., a Lennard Jones-type chart) corresponds to the equilibrium spacing at absolute zero. At nonzero temperatures, the energy will lie above this point, and there will be a distribution of interatomic distance values that corresponds to the width of the dip in the potential curve. The midpoint of the horizontal connecting line thus approximates the equilibrium spacing at nonzero temperatures. Since the potential curve is asymmetric and skewed towards the right (i.e., greater spacing), the equilibrium spacing increases with temperature and therefore solids expand when heated (ignoring entropic effects).

Does this make sense? It's easier shown graphically than explained verbally. Put another way, if interatomic potential vs. spacing were simply a parabola, then solids wouldn't expand when heated because even at increased energy levels the midpoint would always lie directly above the minima, and the average spacing would equal the spacing at absolute zero. This isn't the case with actual potential curves, however, where the midpoint moves to the right.

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Mapes