Perfectly Disordered 'Anticrystals' Could Reveal the Secrets of Materials

A slight mess is much closer to random chaos than pure crystalline order.

Jul 8 2014, 10:50am
Image: Wikimedia/Rafał Chałgasiewicz

From diamonds storing quantum information to the semiconductors behind most all modern electronics, crystals are where the future is at. Metal was cool for a while, but now we have a whole range of new materials displaying baffling degrees of thermal and electrical conductivity, strength, and in some cases extreme flexibility, in both the literal sense of bending like a baseball card and in the sense of being easily manipulated in terms of conductivity.

A crystal (in semiconductor form) can be made to generate electricity directly from heat, dissipate electrical energy optically instead of thermally, and can transport electrons across distances unthinkable in metal conductors. 

This is all thanks to the relative perfection of the material's atomic arrangement. Rather than the amorphous jumble of a typical solid material, a crystal provides a repeating lattice structure of atoms or molecules connected by electrical bonds. There is, theoretically, no empty space in the material; every "hole" is filled in a pure crystal. The conceptual rub, however, is that this makes for the opposite of a conductor, as electrons have no pathways to follow. What actually makes the crystal a proper conductor is the introduction of defects through a process called doping.

So the desired properties of crystals need impurities to actually happen, and this brings us to the interesting conundrum of studying crystals and other materials: the most pure case is not the best case. According to a paper out today in Nature Physics, in our efforts to understand the behavior of materials, we might therefore be better off looking at theoretical "anticrystals" rather than crystals themselves. 

An anticrystal is just what it sounds—perfect disorder, no real structure; a stew of molecules and atoms. Its value in studying materials' properties has to do with the statistical implications: a material with even the slightest amount of disorder will have more in common with the anticrystal and its perfect disorder than the perfect order of an idealized crystal.

This diagram shows the spectrum from a perfectly disordered anticrystal (red) to a perfectly ordered crystal (blue). Image: Penn/Felice Macera

So to study most materials, a researcher would be better off starting from disorder and adding order, rather than the other way around. "If you keep adding disorder, the extrapolation from the perfect crystal fails badly. The mechanical properties can no longer be described well from the perfect crystal," said study co-author and Penn State grad student Carl Goodrich in a statement from the university. "That’s where the anticrystal comes in.”

This insight comes as the result of studying phase transitions in materials. The example given is of water freezing into ice, flopping from a disordered jumble, in which molecules are free to bounce around, into a crystalline solid, where the atomic constituents of the water are locked into place. By inducing this transition using pressure instead of temperature, the researchers were able to probe in great detail the prior conditions of the liquid jumble that led to the crystalline ice end-state.

What they found was that relatively orderly materials were often closer in nature to the jumble than they were to the idealized crystal. “Any time you have a critical point like a phase transition, studying the details really close to that transition tells you about how systems further away from the transition behave,” Goodrich explained.

The Penn State team gives another example that's perhaps a bit more intuitive. Think of a deck of cards arranged perfectly, and now give it a mental shuffle. Statistically speaking, it would take seven shuffles to get to a pure antideck, or a deck in a genuinely random state. "But suppose you just shuffle it once,” Goodrich said. “What we’re saying is that, when it comes to a materials’ mechanical behavior, even this deck is closer to being totally shuffled than totally ordered.” 

In particular, the authors point to materials like plastic and glass. "Glass, another ubiquitous form of rigid matter, cannot be described in any meaningful sense as a defected crystal," they write in the paper. Glass doesn't neccessarily have the long-range repetition of crystal, though it might share many of its properties. In this case, it makes more sense to look at its phase transitions into states of decreasing disorder, as sort of markers along a spectrum of entropy.

“Just as a perfect crystal has very well defined properties, the anticrystal has well defined properties, and we can think of real materials as being somewhere in between the two,"  said Andrea Liu, the paper's lead author, in the Penn State release. "What we’ve shown is that it doesn’t take much disorder before the anticrystal is a better starting point.”