# Molecule vs Crystal

Feynman mentions in his lectures:

...the concept of a molecule of a substance is only approximate and exists only for a certain class of substances. It is clear in the case of water that the three atoms are actually stuck together. It is not so clear in the case of sodium chloride in the solid. There is just an arrangement of sodium and chlorine ions in a cubic pattern. There is no natural way to group them as "molecules of salt".

For me that's not clear. A molecule of water also is stuck in a pattern (at least when it's solid). I'd think of any molecule as 'atoms stuck in a pattern'. Thus why a crystal is not a special case of a molecule?

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In the case of ice, the hydrogen and oxygen atoms are actually sharing electrons. They are bonded "covalently". Each oxygen is bonded to two particular hydrogens, and so you can divide the atoms into separate groups: this oxygen is bonded to these hydrogens, and that one to those, and so on. That is not the case in NaCl, where really the different atoms are all attracted to each other electromagnetically. No sodium atoms are actually bonded to any particular single chlorine atom, so it makes no sense to speak of one of the molecules in a crystal.

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Covalency and ionicity are mixed in molecule. Like we may write the Full-CI wavefunction of hydrogen molecule under minimum basis as $$c_1 [\phi_1(r_1) \phi_1(r_2) + \phi_1(r_2) \phi_1(r_1)] + c_2 [\phi_1(r_1) \phi_2(r_2) + \phi_1(r_2) \phi_2(r_1)]$$ here $\phi_1(r)=e^{-\alpha r}$ and $\phi_2(r)=e^{-\alpha (r-R)}$. $R$ is the internuclear distance. This wavefunction corresponds to $\mathrm{H}^-\mathrm{H}^+$, $\mathrm{H}^+\mathrm{H}^-$, (ionic), and $\mathrm{H}-\mathrm{H}$ (covalent) resonance forms. –  user26143 Aug 2 '13 at 19:33

The difference between a liquid and a fluid is not well defined. Highly viscous fluids (like pitch in the famous pitch drop experiment) are solid at normal time scales but flow on very long time scales. Glasses are by definition amorphous, so show no long range spatial order (like a crystal); as a result they are not in their ground state and must have a finite but very long relaxation time. Amorphous solids have the highest degree of symmetry (isotropy); the transition from amorphous glass to crystalline (SiO2 say) involves a symmetry breaking.

So, first there is the issue of solid vs liquid (some finite but potentially very large viscosity). Then there is the issue of amorphous versus crystalline solids, a transition from continuous to discrete symmetry. Sodium Chloride FYI has a melting point of 800 C.

An interesting tangent is non-newtonian "fluids" like silly putty, which flow under gravity, but when struck with a hammer will crack. Also in the news recently scientists at Corning measure flow in an enormous block of Gorilla glass. But the thickening of mediaeval stain glass at the bottom is NOT the result of flow.

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$\mathrm{H}_2\mathrm{O}s$ in liquid water are weakly interacting. As a first-order approximation, it can be treated as isolated subsystem (molecule). NaCls are rather strongly interacting in a salt. It is not that good approximation to isolate a single "NaCl molecule" in a salt. Like in perturbation theory, $H=H_0 + H'$. If $H'$ is small, we can do perturbation expansion. $H_0$ is similar to the concept of molecule.