[math-fun] glasses are liquids?
But insofar as glass is amorphous there are arbitrarily small energy barriers against changes of configuration and so it is technically a liquid, even though in practical terms it's a solid.
Brent Meeker
--I deny this. I claim, it is at least in principle possible for an amorphous solid to exist in which any change requires at least a fixed energy change. One simple example would be usual periodic packing of bricks, but each brick is in one of 2 orientations ("upside down" or "rightside up") selected randomly, and any switch takes 1 electron volt to get you over the barrier.
Meeker: How is that amorphous? It seems to have a lot of periodic structure. --true. It is however, aperiodic. If you want an example apparently without periodic structure, then put point "atoms" in space, linked by "bonds" whenever the distance between any atom pair is in a certain subset of the positive real axis (e.g.: between 1 and 2). Each bond has energy 1. I suspect by choosing the distance-set right this will have amorphous ground state.
Also, re the claim glass is a "liquid with very high viscosity" how about solid crystalline metals? They can be deformed. In fact, they are a lot more deformable than glass. So are they liquids with high viscosity?
Meeker: The criterion isn't whether they can be deformed, it's whether they can be permanently deformed under arbitrarily small stresses. --that sounds like a good criterion for a "high viscosity liquid/." But a metal might obey this criterion. Thermal randomness (and quantum tunneling) will occasionally rearrange the metal atoms in funny ways that allow it to stretch. Due to this, I expect a chunk of metal under any permanent small tension, will gradually stretch. I actually think the whole notion that a metal rod has a "tensile strength" is a myth, there really is no such thing. I can also tell you it is an empirical fact that cables stretch, even though made of allegedly-crystalline materials. I had a plastic (nylon I think; nylon is regarded as crystalline) monofilament line hanging for a few years, and it stretched quite a lot, I had to retighten it several times. So... perhaps you could save your idea by arguing somehow that the stretching of crystals is somehow far more suppressed than for amorphous solids, in some mathematical sense like e.g. some exponential-style cutoff with temperature vs a power-law cutoff.
On 12/26/2012 5:27 PM, Warren Smith wrote:
But insofar as glass is amorphous there are arbitrarily small energy barriers against changes of configuration and so it is technically a liquid, even though in practical terms it's a solid.
Brent Meeker --I deny this. I claim, it is at least in principle possible for an amorphous solid to exist in which any change requires at least a fixed energy change. One simple example would be usual periodic packing of bricks, but each brick is in one of 2 orientations ("upside down" or "rightside up") selected randomly, and any switch takes 1 electron volt to get you over the barrier. Meeker: How is that amorphous? It seems to have a lot of periodic structure.
--true. It is however, aperiodic. If you want an example apparently without periodic structure, then put point "atoms" in space, linked by "bonds" whenever the distance between any atom pair is in a certain subset of the positive real axis (e.g.: between 1 and 2). Each bond has energy 1.
I suspect by choosing the distance-set right this will have amorphous ground state.
What's your definition of "amorphous"?
Also, re the claim glass is a "liquid with very high viscosity" how about solid crystalline metals? They can be deformed. In fact, they are a lot more deformable than glass. So are they liquids with high viscosity? Meeker: The criterion isn't whether they can be deformed, it's whether they can be permanently deformed under arbitrarily small stresses.
--that sounds like a good criterion for a "high viscosity liquid/."
But a metal might obey this criterion. Thermal randomness (and quantum tunneling) will occasionally rearrange the metal atoms in funny ways that allow it to stretch. Due to this, I expect a chunk of metal under any permanent small tension, will gradually stretch.
I actually think the whole notion that a metal rod has a "tensile strength" is a myth, there really is no such thing.
That will come as surprise to a lot of structural engineers.
I can also tell you it is an empirical fact that cables stretch, even though made of allegedly-crystalline materials.
Metals, as in cables, are made of many small crystal grains which can deform reversibly under stress by small amounts. Under higher stress they shift plastically. The irreversible 'stretch' of cables comes mainly from wear of the wires in the wire rope winding which allows them to compress in overall diameter thus changing the helical pitch.
I had a plastic (nylon I think; nylon is regarded as crystalline) monofilament line hanging for a few years, and it stretched quite a lot, I had to retighten it several times.
Nylon isn't really crystalline, it's a lot of polymer chains which can match up and form bonds between adjacent chains that make it more crystal like.
So... perhaps you could save your idea by arguing somehow that the stretching of crystals is somehow far more suppressed than for amorphous solids,
An amorphous solid is one that doesn't have crystalline structure. Of course it's a matter of degree, in a material may have some short range periodic structure and still be considered amorphous and a crystal may have some defects and still be considered crystalline.
in some mathematical sense like e.g. some exponential-style cutoff
Cutoff of what? Brent
with temperature vs a power-law cutoff.
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