Young's Moduli and thermal expansivities of various types of material

As shown in the figure, the Lennard-Jones potential is normally asymmetric, so that increases in temperature (ie in the amplitude of oscillation of atoms) lead to an increase in the average inter-atomic separation, and hence to (thermal) expansion. The stiffness (Young's modulus), on the other hand, depends on the restoring force when atoms are forced apart (or together), which is the gradient of the plot. Materials with strong inter-atomic forces (deep potential wells), such as ceramics, therefore tend to have low thermal expansion coefficients (expansivities) and high stiffness. In contrast, polymers, which in general have weak inter-atomic forces, tend to have high expansivities and low stiffness. Metals are usually intermediate between these two cases.