Solids expand on heating because
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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 it' s equilibrium position P 1 between A and B (r 0 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 (P 2 and P 3 ) of molecule displaced. Hence it's distance from other molecule increases (r 2 > r 1 > r 0 ).
Thus, on raising the temperature, the average equilibrium distance between the molecules increases and the solid as a whole expands.
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