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ElectroWin
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[*] posted on 12-9-2013 at 19:22
thinnest glass


i just saw this news from Cornell U. about glass:

http://www.news.cornell.edu/stories/2013/09/shattering-recor...

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[*] posted on 12-9-2013 at 19:53


This is one of my favorite parts of this forum&mdash;sharing interesting research. Thanks, <strong>ElectroWin</strong>!

<a href="viewthread.php?tid=25035&page=6#pid299592">[paper requested]</a>




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[*] posted on 12-9-2013 at 20:04


Fascinating! How strong is it, at only two atoms thick? (Also, wouldn't one atom thick be closer to the 2-dimensional mark?)



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[*] posted on 12-9-2013 at 20:22


Quote: Originally posted by elementcollector1  
Fascinating! How strong is it, at only two atoms thick? (Also, wouldn't one atom thick be closer to the 2-dimensional mark?)


Not really. It would need to be less than a Planck length thick to consider it close to 2 dimensional. An atom is gigantic in comparison.




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[*] posted on 13-9-2013 at 13:09


Not so; electrons are much "larger", and are quantized in peculiar (i.e., non-bulk) ways even at the surface of a bulk crystal (i.e., surface states). This is even more true of finite width crystals, where only several states (rather than a near-infinitude) in that dimension are available to electrons. Such a setup can be called two-dimensional.

2D electron gasses are very important in semiconductors. HEMT (high electron mobility transistors: field-effect transistors where the field "affects" a 2DEG) have some of the highest performance characteristics of any known physical device.

To put a chemical perspective on it, imagine the orbitals of the atoms in that film: only a few layers are present, so only as many states along that direction could possibly be occupied by electrons, and probably far fewer by errant electrons. Indeed, since none of the bonds have degenerate states, it will be an excellent insulator, and a conduction electron will have a hard time finding a place (no bound state). As a result, it's a very good insulator, but also, electrons tunnel through it no problem!

As for strength, I would like to know as well; also, how stretchy is it? Those irregular bonds ought to be much more "spongy" than, say, a rigid graphene sheet!

Tim




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[*] posted on 13-9-2013 at 14:07


I am going on the idea that an electron at rest has radius around 2.82 E-10 CM whereas a Planck length is around 10-33 CM, the overall 'size' of the atom being much greater than either. To say a dimension does not exist is to say the length is below the shortest possible length in space-time. When in motion (including orbitals) an electron has wave-like properties. Under these conditions one could see aspects such as your 2D gas, i.e. a suppressed dimension. Also I was considering His words "Also, wouldn't one atom thick be closer to the 2-dimensional mark?". I see this as asking does the one atom thick glass exist in 2 dimensions. So I see it as He is talking about the size of the atom not a single electron. Is the size of the smallest dimension (size of the atom) the diameter when looking at the atom (surface) bound by the ground state orbital? Quantum aspects aside it sounded to me like the question was looking at the atoms in the structure is one layer below physical dimension, leaving only area under consideration. I just do not see how looking at it in this way one can say a single layer of the glass can be 2 dimensional. To me the thickness of the layer would be much greater than the minimum length of dimension.

Occurs to me you could be replying to elementcollector1 and not my comment. Anyway this is how I was looking at the problem. I think one layer would have to be somewhat flexible in perpendicular direction to the plane although I do not think it would stretch in length much (fairly rigid).


[Edited on 9-14-2013 by IrC]




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[*] posted on 14-9-2013 at 10:25


I think it rather depends on the definition of "2d" you are using.
A mathematician would probably say that, while the Planck length is small, it's not zero so the structure would still be 3d.
From a crystallographic point of view it's 2d.
A much more interesting question is how does it behave and what can we do with it?
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[*] posted on 14-9-2013 at 11:32


Multilayer lenses for specialized applications?




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[*] posted on 14-9-2013 at 11:48


"2-dimensional" in math is obviously different from "2-dimensional" in applied science and... reality. ;)

It depends what science we're talking about. In biology, cellular membranes are considered effective examples of 2-dimensional fluids because any flowing is restricted to one plane.

Talking about 2-dimensional glass is pointless. It's 3-dimensional, but very thin.

[Edited on 14-9-2013 by Endimion17]




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[*] posted on 14-9-2013 at 13:03


Quote: Originally posted by Endimion17  
"2-dimensional" in math is obviously different from "2-dimensional" in applied science and... reality. ;)

It depends what science we're talking about. In biology, cellular membranes are considered effective examples of 2-dimensional fluids because any flowing is restricted to one plane.

Talking about 2-dimensional glass is pointless. It's 3-dimensional, but very thin.

[Edited on 14-9-2013 by Endimion17]


There could be 2-D glass in the sense that, at one atom thick, if it were any thinner it wouldn't be glass anymore.




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[*] posted on 14-9-2013 at 13:44


Endimion17 sees it like I do. If there is any length greater than below 10-33 CM (or whatever a 'Planck length' really is) in all of three perpendicular directions it absolutely cannot be less than three dimensional. 1,1,1 = xyz=ict; 1 = smallest unit possible. I read recently of an experiment measuring cosmic rays of very great energy as proving space is not bumpy, i.e. smooth as a .... Still I wonder, if the energy were high enough to have a Planck length wavelength I believe it would turn out to be bumpy after all, slowing down one of two widely varying energy level photons more than the other over intergalactic distances.

I will allow in my thinking a 'suppressed dimension' such as explaining the photon and how it can have momentum while at the same time being 2 dimensional. I cannot fathom how energy can exist in three dimensions simultaneously while being of zero mass.






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[*] posted on 14-9-2013 at 15:56


Quote: Originally posted by elementcollector1  
There could be 2-D glass in the sense that, at one atom thick, if it were any thinner it wouldn't be glass anymore.


"2D glass" and "glass which is 2D" are obviously not synonims. If we have a monolayer of molecules of X, we can call it effective examples of 2D X, but they aren't literally 2D.

2D doesn't have thickness. It's surface.
0D je point, a position. 1D is line, length. 2D is plane, surface. 3D is body, volume.
It's nonsensical to talk about the thickness of room's surface as much as it's nonsensical to talk about the volume of the distance between two cities.

Graphene monolayer sheets are effective 2D objects and atoms would be effective 0D in the crystalographic sense.

In true, literal sense, we only have 3D stuff around us, and 0D, 1D and 2D are the concepts.




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[*] posted on 14-9-2013 at 16:51


Which is why I emphasized the quantum aspect -- if the particle of interest (an electron) is confined to only one energy level in a given direction, it has no quantum measure in that dimension whatsoever.

The electron's wave function always has spacial extent -- to think or say otherwise would be absurd. It would take infinite energy to confine an electron to an infinitesimal plane! It matters very little indeed that the system exhibits "thickness" in our 3D space (using a suitable definition, like the 1/sqrt(2) surface of the probability density function). What does matter is what's interesting about the system, and if it quacks like a 2D plane, it's best to call it that.

Equally important to the number of dimensions is how they are measured. An atom might be zero-dimensional, in a reciprocal ("crystallographic") sense. But hydrogen, for example, has four quantum numbers associated with its electron: n, l, m_l and m_s. The measure of n is the positive integers [1]. The others are limited by n in turn, except for m_s, which is always 1/2 or -1/2 (a measure of 2). If one requires a dimension to have the measure of real numbers [2], then a hydrogen atom remains zero-dimensional, true; but if one instead uses the definition of "number of quantum parameters", it is four dimensional, in and of itself.

[1] It is fundamentally true that the measure of n is the positive integers, but being able to tell the difference between so many of them is highly unlikely. The energy difference between states n = 1000 and n = 1001 is smaller than the average thermal energy at STP, as is the amount of energy to completely ionize the atom (beyond n = infty). Therefore, the number of physically accessible or identifiable states is vastly smaller than the measure of the integers -- indeed, only a finite set is accessible.

[2] Physical systems cannot have this measure, of course, because the universe is finite. Since physicists are practical beings, they would be inclined to say "it looks like a real number if it's unfeasible to write out all the digits" (i.e., you'd write it in scientific notation instead).

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[*] posted on 15-9-2013 at 04:14


"Which is why I emphasized the quantum aspect -- if the particle of interest (an electron) is confined to only one energy level in a given direction, it has no quantum measure in that dimension whatsoever."

OK Tim maybe you can clarify something. I have read several papers in decades past concerning suppressed dimensions, usually related to momentum carried by a photon. While very convincing none have done a decent job on imparting a physical understanding to the underlying mechanism involved. Reading your posts for the better part of a decade I believe you have a better handle on this area of physics than most around here. Is the concept of a suppressed dimension purely quantum mechanical?

Reason I ask is quite honestly in the papers I have read either the authors did not understand the concept as well as they would like us to believe, or they all did really crappy jobs explaining the idea. Any thoughts?

Edit to add: I believe this question is very on topic for the reason that "thinnest glass" can only have meaning if one has a solid comprehension of what "thinness" is. Or put differently what is the mechanical explanation of what is the bottom end of 'thinness' while still existing in a material form in space-time.



[Edited on 9-15-2013 by IrC]




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[*] posted on 15-9-2013 at 06:30


Quote: Originally posted by elementcollector1  
[...] only two atoms thick? (Also, wouldn't one atom thick be closer to the 2-dimensional mark?)
Nope. Two atoms thick still qualifies it as substance made only of 2-D surfaces.

The answer is not essentially about quantum mechanics, although it gets involved later. When making a mathematical model of a substance, be that in continuum mechanics or solid state physics or material science, you have to basic kinds of physical quantities: bulk quantities defined as integrals over three spatial dimensions, and surface quantities defined as integrals over two. In very special cases, you can also get important behavior if your boundaries are degenerate: surfaces that intersect in curves, curves that intersect at points. For classical physics, you basically never need the lower dimension integrals. The surface integrals, however, model important phenomena such as surface tension. Perhaps the most accessible example of such 2D substances in classical physics are the film surfaces of soap bubbles. Even though there's an actual thickness to the soap film, it acts to first approximation as if there's no bulk interior.

So the colloquial meaning of a "2D substance" is that the mathematics which faithfully model its behavior only requires the surface integrals and not the bulk ones. In the case of this glass, it remains to be seen whether the right models require two such integrals (a "top" and "bottom" one) or whether a single one will suffice. The first case would be a bulk object with no interior, that is, just the two boundary surfaces. The second case would a surface object. Both are reasonably called 2D substances.
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[*] posted on 15-9-2013 at 06:42


Quote: Originally posted by IrC  
Is the concept of a suppressed dimension purely quantum mechanical?

Reason I ask is quite honestly in the papers I have read either the authors did not understand the concept as well as they would like us to believe, or they all did really crappy jobs explaining the idea.
Adding extra dimensions to explain physical phenomenon has mostly been associated with quantum mechanics, but that's largely a historical accident. The first such theory was the Kaluza-Klein theory, which was published in 1921, after the quantum era had begun but a few years before Schrodinger's equation. That theory was about electromagnetism and gravity only. These days, the main place where anybody talks about this is in string theory.

The important thing to realize is that no theory with compact dimensions (a more technically accurate way of saying "suppressed") has ever made a prediction that's been verified by experiment. In the case of string theory, it hasn't been able even to make a verifiable prediction at all. So the idea is almost a century old and the only fruit it has borne is a stuffing material for c.v.'s. It certainly looks at this point that it's one of many failed attempts to understand the physical world.
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[*] posted on 15-9-2013 at 06:48


Gosh. Stop being so incredibly narrow-minded. Dimensionality is not only a characteristic of Euclidean space. It is useful for a myriad of other concepts. In chemistry for example: connectivity and periodicity. A two dimensional coordination polymer vs. a one dimensional coordination polymer. A distinction that is perfectly sensible and useful. Or a perovskite slab periodic in two dimensions, a whole field of research devoted to that. If I say "a 2D-perovskite" every chemist will hopefully know what the 2D applies to and these are not even close to planar.

This has nothing to do with "effective". Looking at the connectivity network of a substance is just as valid as looking at the electron density of a point in Euclidean space. Or at the topology of a computer cluster. Or what ever. We need a rolls-eyes-smiley. :P
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[*] posted on 16-9-2013 at 17:53


Afraid I don't know what effect you're referring to, don't suppose you have an article offhand?

Articles reporting on QM are, of course, notoriously bad. Even Feynman said, "no one really understands QM", though I feel he was just saying that to play along. The science is often overblown and misreported, as are the advances ("quantum leap!") and implications ("may lead to improved nanobatteries in ten years!").

Visualizing dimensions isn't hard. Take a 2D image, for instance. Specifically, a computerized 2D raster image. 2D means spacial dimensions only here (as when written to a screen, where the data finally becomes a spacial image). A high-color image is stored with 24 bits of color information per pixel. But this is split into three channels, so it would be quite reasonable to say that the image space is five dimensional -- and with comparable measure between the dimensions, since a picture might be 800x600 pixels across, and each color permits 256 levels. These set measures are both finite, and much closer in value than, say, a hydrogen atom's m_s parameter (a set of two) is to its n parameter (positive integers), so it would be quite reasonable to call these independent dimensions.

But the dimensions don't stop there. We can add more. When transparency is needed, an alpha channel can be added (another 256-wide dimension). Typical 3D graphics employ further tricks: by adding directional information for each point on the surface, nearby lighting can be "cast" over the surface, giving the illusion of depth -- bump mapping. The vector map has 3 dimensions, of course. Congratulations, now you know your "2D" eyes can experience at least as many as nine dimensions!

As for hidden dimensions, well, how would you know that a surface is bump-mapped? A statically lit image could just as well be pre-rendered without implementing the bump map, so you couldn't know. If the illumination changes direction, however, you can infer the experience of depth, and after careful thought, come to the conclusion that the information is only available from an (otherwise hidden) vector space.

So it goes with physics; as we probe higher energy levels, more and more dimensions and parameters become evident. Quarks (and QCD) are governed by a large symmetry space, made up of many parameters of limited extent (e.g., a color charge of red/antired, etc.). Perhaps we will find something even below that.

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[*] posted on 16-9-2013 at 19:21


Quote: Originally posted by 12AX7  
Afraid I don't know what effect you're referring to, don't suppose you have an article offhand? Tim


So long ago. Worked at R&D lab in upstate NY with Ardent Sher of SRI (He was a paid consultant so not there every day), and Drs Kellog, Bentz. Both of Cornell, one was co worker with Sagan, Bentz I think but it was 1981 so memory faded. Lunchroom conversation one day the topic was the subject of photon suppressed dimension. Kellog had a couple papers He handed me which I read. Hard to follow as my math sucked then. Still does but not as bad at least. They made very convincing lunch break dissertations. Interesting enough to later read the papers. I know they were written at Cornell but I do not remember the author. Could have been one of them or a Dr Wu (or Woo) knew Him from work also but don't remember Spelling. He also worked there in another department so We usually only talked during lunch. When I have time I'll do some searching on the subject. Right now have differential on my Explorer completely apart and it is my first priority. Just came in to surf and get away from it for awhile.

Forgot to add but the crux of it was a physical explanation of how a photon of zero mass had momentum, one dimension being suppressed in flight but upon being annihilated (transferring photons energy to electron in metal), velocity of photon became zero as the zero dimension became unsuppressed as it transferred kinetic energy to the electron. I'm explaining it not very well but it was 32 years ago. Became more complex when considering event where all the photon energy was not given to a single electron. As example when an orbital electron was the target. Then IIRC He was talking about a photon of lower frequency being left as the orbital electron either changed orbitals or left (energy above electron work function of metal in question). Really a subject common in physics except for a brilliant mathematical treatise going into dimensionality. Actual real physical dimensional effects.

Around 17 years ago I read yet another paper at LANL trying to explain Bells inequality, and quantum connectedness. Giving an example of a photon greater than 1.22 Mev becoming an electron positron pair. The connection between them was being explained as one particle existing outside our normal space-time as it were, with what is seen as two opposite polarity particles going their separate ways as merely being the projection viewed within our normal space-time. In effect yet another explanation of physical entities we encounter using dimensional considerations.



[Edited on 9-17-2013 by IrC]




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[*] posted on 18-9-2013 at 00:55


Wow, that is really astounding! I haven't heard of something like this so far. Just a few moments in this forum and already found something interesting :)
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[*] posted on 19-9-2013 at 09:59


Tim on the subject of string theory and quantum mechanics:

http://www.youtube.com/watch?feature=player_embedded&v=2...

http://www.youtube.com/watch?v=VtItBX1l1VY

Attachment: A new quantization condition for parity-violating three-dimensional gravity - Tim Blais.pdf (754kB)
This file has been downloaded 496 times

I think it's on topic insofar as determining 'how thin can it be and to be or not be?'

OK stretching it I know but the paper is a good read and I thought the videos are well done.


[Edited on 9-19-2013 by IrC]




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