I've got a question regarding the microscopic difference between liquids and solids. I know that there exists a precise phase transition between solids and liquids, so some discrete parameter must change in the transition. I'm letting the molecules under examination be covalent, so we can't assume that a crystal lattice is formed in the solid case.
(1) Are different forces dominant in between solid and liquid molecules? By "forces" I mean ionic bonds, dipole-dipole interactions, London forces, etcetera.
(2) What is the difference in the geometric structure of the molecules' interactions? Solids are fixed and gases are mobile, but what precisely are liquids? Solid structures with enough degrees of freedom to pivot fluidly? Do liquids generally have the same structure (simple cubic, hexagonal, etcetera) as their solid counterparts when they do interact?
I guess my primary confusion is that the distance between molecules in a material (solid or liquid) should intuitively be a continuous parameter dependent on the density of particles and their temperature, not a discrete parameter taking the values present in the "solid" and "liquid" states. Why the discrete nature?