Solids expand on heating because

The expansion of solids can be well understood by potential energy curve for two adjacent atoms in a crystalline solid as a function of their internuclear separation (r).At ordinary temperature : Each molecule of the solid vibrate about its equilibrium position P1 between A and B (r0 is the equilibrium distance of it from some other molecule)At high temperature : Amplitude of vibration increase (C D and E F). Due to asymmetry of the curve, the equilibrium positions (P2 and P3) of molecule displaced. Hence it's distance from other molecule increases (r2 > r1 > r0).Thus, on raising the temperature, the average equilibrium distance between the molecules increases and the solid as a whole expands