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, 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.