Honestly, I could think of at least 3 chemistry principles relating to this context. That would be the latent energy, intermolecular forces and melting point depression. They are actually related to each other. Pure solid melt at a very low range of melting point. The latent energy is the energy gained at a constant temperature to convert the solid into liquid form. Hence, an impure solid would have a wider range because of the varying type of intermolecular forces. This would lead to melting point depression where impure solid melt at lower temperatures than pure substances. However, they would still have a wide range. So, it is safe to say that pure solid have meting points, while impure solids have melting ranges.