why is the specific heat capacity of a solid lower than a liquid?

Answer 1

The atoms in the solid are packed more closely together and are able to transfer heat faster from atom to atom via conduction. But there is not enough room between molecules to allow the faster vibration rates as heat is applied.
The atoms in the liquid are farther apart and will allow faster vibration rates because there is more room for the atoms to move. The liquid can also expand at greater rates than the solid.

Answer 2

I don't believe it is a rule for all materials.

Have you checked?

Also, there is the strange phenomenon of those elements (or materials) that have no liquid state, these indicate that the liquid has such a low specific heat capacity that it immediately turns to gas. Hmm... like dry ice (solid CO2).

Iodine has no liquid state.

Answer 3

There are 3 states, solid, liquid, & gas.
For example; water only exists as water between the temperatures of 0 & 100 degrees C. Colder than that & it enters its solid state as ice; hotter & it becomes steam, which is a gas (not to be confused with what you see coming out of a boiling kettle, that is water vapour or steam which has cooled to the point where it is condensing back into water).