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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: 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.