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• Helium won't freeze at any temperature: its ground state in the low-temperature limit at atmospheric pressure is a superfluid. The reason is that microscopically, matter does not behave like discrete magnets or something, but according to quantum mechanics.
• There is generally not just one solid state. In the magnet analogy, you can build completely different structures from the same components. Likewise, what we just call “ice” is actually just one possible crystal structure for solid water, more precisely called Ice I_h. There are quite a lot of other solid phases

##Liquid Now, if you increase temperature, that's like thoroughly vibrating you magnet sculpture. Because these bonds aren't infinitely strong, some of them will release every once in a while, allowing the whole to deform without actually falling apart. This is something like a liquid state.
###Actually though:

• Helium won't freeze at any temperature: its ground state in the low-temperature limit at atmospheric pressure is a superfluid. The reason is that microscopically, matter does not behave like discrete magnets or something, but according to quantum mechanics.
• There is generally not just one solid state. In the magnet analogy, you can build completely different structures from the same components. Likewise, what we just call “ice” is actually just one possible crystal structure for solid water, more precisely called Ice I_h. There are quite a lot of other solid phases.

##Liquid Now, if you increase temperature, that's like thoroughly vibrating your magnet sculpture. Because these bonds aren't infinitely strong, some of them will release every once in a while, allowing the whole to deform without actually falling apart. This is something like a liquid state.
###Actually though:

##Solid At very low temperatures, there is virtually no thermal motion that prevents the molecules sticking together. And they stick together because of various forces (the simplest: opposite-charged ions attract each other electrostatically). If you picture this with something like lots of small magnets, it's seems evident enough that you get a solid phase, i.e. a rigid structure where nothing moves.
###Actually though:

##Solid At very low temperatures, there is virtually no thermal motion that prevents the molecules sticking together. And they stick together because of various forces (the simplest: opposite-charged ions attract each other electrostatically). If you picture this with something like lots of small magnets, it's evident enough that you get a solid phase, i.e. a rigid structure where nothing moves.
###Actually though:

• Not all materials have a liquid phase. For instance, solid CO₂ (dry ice) sublimates if you increase the temperature, i.e. it goes immediately into the gas state (at atmospheric pressure).
• Many materials have huge molecules, i.e. the size of the chemical structure approaches the size of the physical structure. Now, that chemical structure can also be shaken loose by heat, but this isn't called melting but decomposition then. For instance, plastics decompose at some point between 200°C and 350°C. Some melt before i.e. they have two states; some stay solid all the way, they basically just have one state (solid).
  A decomposed material hasn't entered a new state of matter, it simply has ceased to be the original material.
• Furthermore, materials that aren't purely composed of one kind of molecule also generally don't have a simple fix melting point. There's a certain range in which two phases may coexist. (More generally, you can have all sorts of emulsions, dispersions, gels etc.)

• Not all materials have a liquid phase (at least not at all pressures). For instance, solid CO₂ (dry ice) sublimates at atmospheric pressure if you increase the temperature, i.e. it goes immediately into the gas state.
• Many materials have huge molecules, i.e. the size of the chemical structure approaches the size of the physical structure. Now, that chemical structure can also be shaken loose by heat, but this isn't called melting but decomposition then. For instance, plastics decompose at some point between 200°C and 350°C. Some melt before i.e. they have two states; some stay solid all the way, they basically just have one state (solid).
  A decomposed material hasn't entered a new state of matter, it simply has ceased to be the original material.
• Furthermore, materials that aren't purely composed of one kind of molecule also generally don't have a simple fix melting point. There's a certain range in which two phases may coexist. (More generally, you can have all sorts of emulsions, dispersions, gels etc.)