# Expansion of solids

1. May 20, 2006

### Amith2006

Sir,
Why does solid expand on heating?
The answer to this question given in my book is “The potential energy curve is asymmetric about the equilibrium distance between neighbouring atoms. Is it right?
I think solid expands due to increase in kinetic energy of atoms.

2. May 20, 2006

### Gokul43201

Staff Emeritus
Yes it is. The most eggregious flaw of the harmonic approximation to the treatment of solids is that it leads to zero thermal coefficient of expansion. Without anharmonicity (or asymmetry, or deviation from purely quadratic interaction terms), you can't solve this problem.
The classical oscillator turning points are separated by distances smaller than typical interatomic spacings. In the harmonic approximation, it's possible to make atoms oscillate much faster (irrespective of phase differences) about their mean positions, without having to change the distance between these mean positions. Alternatively, one can see that with a symmetric potential, no matter what the energy (and hence turning points), the mean position is always that of the minimum.

Now there are a few solids with virtually zero thermal expansion coefficient. These are solids where the interaction between atoms is almost exactly parabolic over a significant range of energies.

Edit : Look here for a picture - http://www.mse.uiuc.edu/info/mse182/t79.html

Last edited: May 20, 2006