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An international group of researchers including Russian scientists from the Moscow State University has been studying the behaviour of the recently-discovered iron oxide Fe4O5 . The group has succeeded in describing its complex structure, and proposed an explanation for its very unusual properties. The article appeared in the current issue of the journal Nature Chemistry.
The scientists discovered that when Fe4O5 iron oxide is cooled to temperatures below 150K, it goes through an unusual phase transition related to a formation of charge-density waves—which lead to a "four-dimensional" crystal structure. Artem Abakumov, one of the paper's authors, said that the study of this material would contribute to the understanding of the interconnection between magnetic and crystal structures.
The origins of this research date back to 1939, when the German physicist E.J.W. Verwey first discovered that the iron oxide Fe3O4—commonly known as the mineral magnetite—had a strange phase transition. Magnetite in its normal state is a relatively good electrical conductor, but when cooled below 120K its conductivity markedly decreased, and the material practically became an insulator. Scientists discovered that below 120K, the iron atoms arrange themselves into a kind of ordered structure. In this structure, the electrons cannot move freely within the material and act as charge carriers, and the oxide even becomes a ferroelectric. But the scientists could not explain what exactly changes in the structure, which physicists have spent the last century studying. Researchers guessed that the phenomenon was related to the presence of iron atoms in two different oxidation states (valences)—two and three—and their consequent ability to form ordered structures.
[...] "We have found that here, just as in magnetite, when cooling to lower than 150K occurs, an unusual structure evolves. It's something of a mixture between standard charge density waves forming dimers," Artem Abakumov said. "And the situation with the trimerons that was observed in magnetite. This was very complicated in the case of Fe4O5—what's known as a 'incommensurately modulated structure', in which we can't identify three-dimensional periodicity. However, the periodicity can be observed in a higher-dimensional space—in this specific case, in the four-dimensional space. When we mention the four-dimensionality of such structures, we are not actually talking about the existence of these oxides in four dimensions, of course. This is just a technical construct for the mathematical description of such highly complex ordering."
Charge-ordering transition in iron oxide Fe4O5 involving competing dimer and trimer formation (DOI: 10.1038/NCHEM.2478)
(Score: 2) by bitstream on Saturday April 16 2016, @10:21PM
So when the temperature vibrations are of low enough amplitude the atoms come so close to eachother that a non-linear shift region temperature wise shows up and makes the substance take up a whole new type of inter-atom structure?
If the same phenomena can be had in the other direction where a substance instead becomes more conductive with higher temperature. Now that would be interesting. Perhaps the nature of Fe4O5 can give some insights to this?
(Score: 0) by Anonymous Coward on Sunday April 17 2016, @12:51AM
Superheated gas becomes plasma which is EM conductive...
(Score: 2) by bitstream on Sunday April 17 2016, @02:21AM
You'r right. I was thinking more along superconductors at room temperature or at least within -40 ⁰C to +50 ⁰C.
Those ceramic superconductors were interesting but it seems they couldn't be developed so far to work further up in temperature.
(Score: 0) by Anonymous Coward on Saturday April 16 2016, @10:36PM
So is this 4th dimension time, or not? Can't any periodic signal (eg a sine wave) be considered a crystal in the 4th dimension? So a crystal tied to a pendulum would be a four dimensional crystal?
(Score: 2) by rts008 on Saturday April 16 2016, @11:02PM
No, it is not time.
(Score: 0) by Anonymous Coward on Monday April 18 2016, @12:59AM
So wouldn't it be a 5th dimension, not 4th?
(Score: 2, Informative) by Anonymous Coward on Saturday April 16 2016, @11:38PM
No, nothing related to time, i.e. not some kind of motion but a static "ordered disorder" as you compare different locations in the crystal. The 4th dimensions is just a mathematical construct to describe the regular, but not matching ("incommensurate") periodic behaviour of some renegade atom or small molecule in the crystal.
If you think of it as a fly-through from one unit cell of the crystal through the neighboring ones, you would see that most everything looks the same, just one atom is shifted along in a channel formed by the others, or is switched between two equally likely positions as you go from one cell to the next. If the periodicity of that deviation is such that everything looks exactly the same after a small integral number of cells ("commensurate modulation"), say 3 or 4, you could just make the initial cell that much bigger in that direction and get a conventional description. If it is a more complex behaviour, you add e.g. a sine function to the coordinates of the atom to describe its deviation from the rest of the structure, and that is where the "fourth dimension" comes in. If there is deviation in more than one direction, this complexity can go to "six dimensional" or 3+3D as it would normally be written - 3+1D structure refinement is fairly straightforward with current crystallographic software, 3+2D is specialist material, I do not think I ever saw a practical example of 3+3D.
(Score: 4, Insightful) by devlux on Saturday April 16 2016, @11:47PM
No, but that's a damned good question!
It has to do with a convenience feature they added to the math to describe an observed property.
All crystals must obey certain specific laws of physics. Meaning, that given the composition and structure you can make predictions about the properties of any crystal and be reasonably certain that should you synthesize such a material, it's observed properties will match it's predicted properties.
In this case, we know the composition and we know it's properties.
There is no 3 dimensional description of this material which follows the relevant ruleset, that can be applied to this composition that yields a crystal with the correct properties. However if you add in a mathematical "4th dimension", then the numbers slot into place just fine.
If this were a real dimension it would be a "space like" dimension not a "time like" dimension because the effect described is not time dependent, such as nuclear decay rate.
The reality is that we like to describe things in general, but especially crystals as a regular lattice structure, and the math says that the properties emerge from the connections between lattice members.
Imagine putting 4 dots on a page in a square pattern, one dot to a corner.
You have a quantity dimension (4) and 2 positional dimensions, x & y. This is the minimum of information that can describe everything about those 4 dots.
Put another way, it is an array of of vectors containing x,y coordinates.
Now imagine connecting the 4 dots into a square.
You now have 1 square and you can toss the 1 from the math, because it's the only object being described,
You are in "square space" (which is right next door to hammerspace, and the home of cubical cows).
What you have is a scalar vector with 1 object described as two sets of x,y coordinates, vs an array of 4 objects described as single vectors of x,y
The properties of a crystal emerge from it's lines/sides of that square.
In this case to predict the observed properties, they had to add a diagonal line as well.
If you add a diagonal line to a square you no longer have 1 square, but 2 triangles. Yet you still have the original 4 dots.
Suddenly you are in triangle space, where the universe is described as an array of vectors (the array has 2 members), and each vector is contains 3 vertices (a,b,c).
You have added a new dimension. In the case of our square, the dimension is quantity which has been added back in. Then we transform the existing x,y points to poly vertices.
The dimension of quantity existed before, but once we entered square space, the quantity was implicit and therefore dimensionless and we just left it
off the math for simplicity sake. Now we have moved to triangle space, the math suddenly got more complex.
Yet you still only have 4 dots.
In the case of the "4 dimensional material", an observed property was only described/predicted by adding a new dimension to the calculation, in a similar fashion, but with cubes instead of squares.
(Score: 1, Insightful) by Anonymous Coward on Saturday April 16 2016, @11:59PM
So next time there is a crystal that doesn't fit the theory can't they just call it 5/6/n dimensional? At what point is it no longer a crystal?
(Score: 3, Informative) by devlux on Sunday April 17 2016, @12:59AM
A crystal by definition is a regular, ordered 3 dimensional lattice.
https://en.wikipedia.org/wiki/Crystal [wikipedia.org]
The properties of the nearly all crystals can be described with a series of laws and assumptions that describe the elements of the crystal.
Usually 3 dimensions is enough.
In this case we have a material where science failed to predict it's properties using the normal 3 dimensional matrix. However the same laws, extrapolated to 4 dimensions managed to predict the properties correctly. Ergo you have a 4 dimensional material and some new science saying "hey what other properties emerge if we take into account dimension n"
If 4 dimensions fail and 5 dimensions fail etc then the laws are failing to describe the observations. Ergo the material does not fit into the class of materials described by said laws. Either the laws need to be expanded, or we need new laws that can predict the observed behavior even if based on different principles.
That's the problem we have with super conductors right now too. We're using laws that describe existing super conductors just fine, then we stumble on a whole new family that should not be there and suddenly we find we need new laws. Laws that can predict all observed instances of a given class.
(Score: 2) by Gravis on Sunday April 17 2016, @12:30AM
no. time is not a dimension.
(Score: 4, Insightful) by devlux on Sunday April 17 2016, @12:45AM
A dimension, is just a way of measuring things in a quantifiable manner.
Time is a thing that can be measured in a quantifiable and meaningful way, ergo time is a dimension.
There are 4 consistent dimensions to the universe in which we exist, length, width, height and time.
Any point in the universe that ever was or ever will be can be described as a vector t,x,y,z
Furthermore time is inextricably linked to the spatial dimensions, but it is not as far as we can tell a "space like" dimension.
Yet the more mass/energy you put into a smaller sphere described by x,y,z the more x,y,z begin to warp and bend and this effect is observed as gravity which has known effects on time. So yes time is a dimension, just not a "space like" dimension and space is not a "time like" dimension. The point of interface between them appears to manifest as gravity.
Unrelated, but it opens with a good joke.
http://www.pbs.org/wgbh/nova/blogs/physics/2014/04/how-many-dimensions-does-the-universe-really-have/ [pbs.org]
Wish I could find the article now, but I remember reading a paper about a year or two back that was able to describe the accelerating expansion of the universe as an evolution of time into a space like dimension. Basically, time is hotspace just as energy is hot mass. It seemed well constructed and what I read was a pre-print before peer review, but I'm not able to find it on arxiv. If someone remembers it or can find it again, I'd be much obliged.
(Score: 2) by maxwell demon on Sunday April 17 2016, @11:38AM
Your explanation is actually of the worst type: Close enough to the truth that it cannot simply be done away as wrong, but still deviating enough from truth that it cannot be left alone.
You start with a possible definition of "dimension", which is not wrong but is not exactly the reason why we speak of time as the fourth dimension. According to that definition, you could also say temperature is a dimension (it's also a quantity we can measure in a quantifiable and meaningful way), and in a sufficiently abstract sense it's true. But time is the fourth dimension in a much more geometric sense.
This connection is related to relativity; however it already comes from special relativity, where there is no gravitation and no curvature of spacetime. The reason why time has to be considered to be unified with space in a four-dimensional spacetime that cannot be separated into space and time in an observer-independent way is the relativity of simultaneity, and the most direct manifestation of it is the constancy of the speed of light.
Also, gravitation doesn't just bend space, it bends spacetime. Gravitation cannot be described purely by the curvature of space (I think Gauss tried this for quite some time without success).
You are, however, correct that "spacelike" and "timelike" dimensions (or rather, directions in spacetime) are not completely equivalent. However that non-equivalence is smaller than you might think; basically it's a single sign that distinguishes space and time (and actually it's not even the sign itself that's relevant, but only the fact that it is different for spacelike and timelike directions).
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by devlux on Sunday April 17 2016, @11:06PM
The explanation is not wrong. Time, temperature, color etc are dimensions and can be quantized.
If it's quantifiable and measurable it can be a dimension mathematically.
You mention that time is basically a dimension with a sign to it.
It's still a dimension, but time is not the 4th dimension referenced by this article. ;)
(Score: 0) by Anonymous Coward on Monday April 18 2016, @05:44PM
guys guys it's all 1-dimensional strings vibrating [xkcd.com]
(Score: 2, Interesting) by Anonymous Coward on Sunday April 17 2016, @12:45AM
(Score: 3, Funny) by edIII on Sunday April 17 2016, @03:37AM
Sort of. You can read more about it by searching Google for "Time Cube"....
Technically, lunchtime is at any moment. It's just a wave function.
(Score: 0) by Anonymous Coward on Sunday April 17 2016, @04:12AM
Thanks. I'm not sure about the correlation between belly buttons and lying though. A baby could die yuoung and never get the chance to lie while still having a belly button.
(Score: 2) by maxwell demon on Sunday April 17 2016, @12:21PM
You are not up to date.. That theory was superseeded by the Time Cubicle! [wikia.com]
The Tao of math: The numbers you can count are not the real numbers.
(Score: 1) by gumby on Sunday April 17 2016, @11:29PM
Devlux's excellent reply [soylentnews.org] (with a wonderfully round ID number BTW) explains it well. But I thought I'd add another analogy from engineering: it's no different from using the imaginary components of a waveform even though they have no true physical component. Likewise these extradimensional components are not meaningfully physically observable, although their influence is.
(Score: 3, Informative) by inertnet on Sunday April 17 2016, @01:00AM
Verwey doesn't look like a German name to me, so I checked and he was indeed Dutch: https://en.wikipedia.org/wiki/Evert_Verwey [wikipedia.org]
(Score: 2) by fritsd on Sunday April 17 2016, @08:20AM
I found this topic particularly interesting because it ties in solid state chemistry (chemistry of crystals that are not reacting particularly much but why do they look how they look?) with abstract mathematics (symmetry, group theory).
You might want to read this article which discusses the "extra dimensions" a bit more clearly:
Quasicrystal [wikipedia.org]
It's fascinating stuff, just like a lot of solid state chemistry is. The Fourier transform of the positions of the atoms looks regular, but it is not just copies of unit cells; there's a wobble in its repetition pattern.
Oh and you might want to read up on group theory, particularly Space groups [wikipedia.org].