I have been informed that glass is a super-cooled liquid and is also considered to be an amorphous solid.
Can it be both and, if not, what category does it fall into?
Answer
I'll focus on the phase of the glass, since it seems there is some confusion in the comments (and the other answer). In glass forming systems, as you drop the temperature below the crystal phase melting temperature, one would expect to nucleate the crystal phase. For various reasons this does not happen. Instead, the liquid continues to cool, and the viscosity continues to increase as one might expect upon cooling. Below a critical point, the glass transition temperature, the viscosity rapidly increases by several orders of magnitude. Atomic mobilities are now so low that crystallization cannot occur. Furthermore, the viscosity is so high that the material is a 'solid' in common usage - all the atoms are frozen in place.
So, what is this 'solid'? Well, it isn't the stable crystal phase - you can tell that by x-ray diffraction. True, it is not 'liquid' in the common sense of flowing like water. But, two things point to it actually still being in the liquid phase.
First, in a disordered material if you do x-ray diffraction you measure a radial distribution function (rdf). This gives you the average spacings between atoms in the material. If you do x-ray diffraction from above the melt down to the glass formation, you will note that the rdf is not changing (well, the average spacing will change a bit with thermal contraction).
Second, the other indication of a phase change would be, of course, a signature of latent heat in calorimetry. Again, as you cool the liquid down to the glass formation temperature (and beyond), there is no latent heat measured. There is no first order phase transition. There is only the glass transition where the visocity increases.
Taken together, a glass is a configurationally (kinetically) frozen liquid. It has the structure of the liquid, and it does not have a first order phase transition to the liquid. I do not see how one could consider it anything but a super-cooled liquid.
To further emphasize - a super-cooled liquid is one below the melting point of the crystal phase that has not nucleated the stable crystal phase. Nothing says that the liquid viscosity can not get so high as to be considered 'solid'.
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