Feature

Structures are a diamond's (and other crystal's) best friend!

CRYSTALS are objects of profound mystery. That's not because they channel occult energies, or hold misty hints of the future in their limpid depths. Their puzzle is much more prosaic: why are they as they are?

It is an incredibly basic question, yet physicists still struggle with it. Can we say why a given group of atoms prefers one particular arrangement over another? Can we predict how a crystal will be structured, and so deduce what properties it will have?

By and large, the answer is an embarrassing no. Or at least it used to be, if Chris Pickard of University College London is right. He has developed a surprisingly simple way of predicting crystal structures. His technique, along with another that has just emerged, might finally show us the way through the crystal maze.

There is more at stake here than the prettiness of some multifaceted amethyst. Crystals occur within most materials around us, be they metals, rocks or our own bones. Crystal structures determine crystal properties: the arrangement of atoms in a material makes it hard or soft, conducting or insulating. But theory alone has been unable to work out what those structures should be. "We have to rely on experiment," says Pickard. "That always bugged me."

With good reason. Sometimes X-rays and other probes just don't reveal how a crystal is built, and materials in extreme situations such as other planetary cores are simply beyond the reach of experiment. Besides, if you could cook up crystals in a theoretical simulation, you might be able to discover new materials with remarkable properties.

Pickard's idea for breaking the impasse took a while to crystallise. In 1994, when he was a novice PhD student at the University of Cambridge, his supervisor Mike Payne had written a computer program called CASTEP to simulate what electrons and nuclei do within solids. "He said, take it and calculate anything you like," recalls Pickard.

Pickard chose to tackle carbon, an element that typifies crystal mystery: depending on how its atoms team up, it can form ultrahard transparent diamond, or soft grey graphite. He started off by tossing carbon atoms randomly into a box large enough to fit the basic "unit cell" of the crystal, and worked out the energy of the resulting structure. Knowing that nature always favours the lowest-energy arrangement, CASTEP could work out how the atoms could move to reduce their energy. By repeating this process until the energy could be reduced no more, the final structure should by rights be nature's crystal.

In fact, it was an almighty mess. The carbon atoms did not arrange themselves into the regular tetrahedral cage of a diamond crystal, or into the flat, honeycomb sheets that make up graphite. The structure had no obvious symmetry to it at all.


Joining the dots

Pickard had hit the same snag as many before him. Although electrical forces between electrons and nuclei will naturally pull randomly arranged atoms into a more stable, low-energy arrangement, they won't necessarily find the stablest, lowest-energy arrangement. It is like dropping a ball onto a complex landscape of hills and valleys. The ball will roll to the bottom of the nearest dip, but in the gnarled and forbidding energy landscape that represents the interactions of even just a few atoms, the chance is slim that the dip is the very bottom of the deepest valley - the home of nature's crystals.

Deterred, Pickard turned to other projects. In 2004, though, he was helping his PhD student Rachel Strong use a different method, known as graph theory, to chip away at the structures of diamond and other similar crystals. The idea was first to draw a cartoon crystal with simple dots marking the atomic nuclei, and lines representing the electron bonds between them. Graph theory calculates which ways of joining the dots satisfy the constraints imposed by chemical bonding, and so radically reduces the number of configurations admissible in any simulation.

The join-the-dots tactic was showing some promise, but was also frustratingly imperfect. It only worked with some types of bond, and even then only if you made assumptions about how many bonds each atom could form. That's not always obvious. In graphite, each carbon atom forms bonds with three neighbours; in diamond, it is four.

On a whim, Pickard reran his calculations of 10 years before to compare them with the structures Strong was producing. Something remarkable happened. "I started to get sensible structures," he says.
When he reran his calculations of 10 years before, something remarkable happened: he started getting sensible results

What had changed? Computers had become faster, of course, and Pickard had helped to rewrite CASTEP to make it far easier to repeat simulations with atoms in different starting positions. That, it turned out, was the key. Most of the configurations that emerged were still random messes, but when Pickard ran the simulation many times some familiar-looking structures kept recurring - diamond and graphite. In mimicking nature, it seems that if at first you don't succeed, try and try again.

Pickard was initially sceptical that the result was more than a fluke, but when he showed his work to Richard Needs of the University of Cambridge, who studies the behaviour of electrons in solids, he got an enthusiastic response. The two soon unleashed the random structure search method on hydrogen.

Hydrogen is the simplest of atoms, consisting of just one proton circled by one electron, but in its solid state, it is a perplexing beast. Crude calculations suggest that solid hydrogen should become electrically conducting when squeezed to pressures of about 3 million atmospheres; in experiments, though, it remains insulating. Running the simulation with the pressure turned up, Pickard and Needs discovered a previously unsuspected form of solid hydrogen that was not only stable, but was indeed an insulator, with all its electrons bound to individual atoms rather than free to wander and carry an electrical current (Nature Physics, vol 3, p 473).

The duo weren't alone in their success. By the time they published the paper describing their method in 2006, other groups were starting to use rather different methods to predict crystal structures (see "Many ways through the crystal maze"). These predictive tools share the promise of revealing weird and wonderful new materials. Armed with such software, it should be possible to whip up any combination of atoms into a crystal and see what it's like. "You can see what the landscape gives you, then see what its properties are," says Pickard.

History cautions against excessive enthusiasm quite yet, however. A crystal prediction method must prove its worth on all sorts of structures - including, crucially, organic molecules, which Pickard has yet to take on. Nor is prediction the end of the story, as Pickard himself admits. "Say I stumble on a new crystal structure, and - wow! - it's the strongest material, it's a room-temperature superconductor, it cures cancer," he says. "Then the chemist says, 'But how do I make it?' I can't answer that yet."

Even discovering the possibility of some new ultrahard material or high-temperature superconductor would be a big step. Pickard and Needs are also looking for materials that efficiently pack a lot of hydrogen into a small space as a solid fuel for cars. They have already had one tantalising candidate: a mix of three hydrogen atoms to one aluminium atom that is solid at high pressures. Cranking the pressure in the simulation down, though, the structure did not survive.

A similar thing happens to mundane old nitrogen at very high pressures. At about 1 million atmospheres, it turns into a solid with a similar structure to diamond, but unlike diamond, it dissolves into a polymer mush when you take the pressure off. Even after it does so, it retains much of the energy stored in its bonds in the high-pressure state, potentially making it useful as a "green" explosive with no toxic residue, or as a fuel for stealth rockets that leave no chemical trace of their passage. Pickard is studying nitrogen right now, but he is a little cagey about why. "I can't say much about this," he says.

Together with his colleague Dominic Fortes, he is also looking into the properties of a mix of ammonia and water called ammonia monohydrate, whose behaviour could help answer whether there is a subsurface ocean on Jupiter's moon Ganymede and Saturn's moon Titan, and potentially explain the origin of watery volcanoes thought to exist on Titan. Here the appeal of simulations is obvious, given the difficulty of doing experiments in situ.

That said, experiments on Earth can at least match the pressures a few hundred kilometres under the crust of Titan, which reach several thousand atmospheres. Not so inside Jupiter, the solar system's weightiest planet, whose core pressure is thought to approach 100 million atmospheres. According to models of the solar system's formation, much of Jupiter's core is made of silicate rocks similar to those that make up the bulk of Earth. But is that a hard heart or a soft centre? At Jupiter's internal pressures no one knows whether silicates would be solid crystals or a liquid.

Experiments on Earth are unlikely to help. We can only create such extreme pressures in the lab for a split second, by sending shock waves through a sample - for example, using the lasers of the National Ignition Facility in Livermore, California. That's too brief to probe crystal structure. Researchers can compress matter less explosively using a device called a diamond anvil cell, but only up to about 3.5 million atmospheres - good enough to reproduce the heart of Earth, but not Jupiter.

Pickard's plan, now backed by a £1.3 million grant from a UK funding body, is that the simulations will boldly go there - and further. Beyond the solar system, planets even more massive than Jupiter are being discovered. What strange materials could lurk at their hearts? And what about some of the most extreme environments imaginable, the ultra-compressed crusts of neutron stars? Those would be some pretty far-out crystals. Unlocking their secrets, though, might not be so very far away.

Many ways through the crystal maze 
Chris Pickard's random structure search (see main story) is not the only path that might lead to the heart of the crystal mystery. One early approach, called simulated annealing, involves loading model atoms into a computer simulation, then repeatedly raising the temperature and lowering it again. Given enough of this thermal jiggling, the atoms should eventually find the most stable, lowest-energy configuration. In practice, though, this approach needs an unfeasible amount of computer time.

A more effective rival to Pickard's method emerged around 2006 in the form of genetic algorithms rooted in ideas of sex and death. Such simulations start with a small population of different crystal structures that then reproduce, with only the fittest crystals surviving (Journal of Chemical Physics, vol 124, p 244704).

Artem Oganov of Stony Brook University, New York, is a leading exponent of this approach. "We throw out the highest-energy stuctures, in a rather cruel way," he explains. "From the rest we create children." Some children are made from different pieces of two parent structures. Others are mutated offspring of a single parent, randomly distorted or with different atoms swapped around.

One problem with early genetic algorithms was that the population often turned into an unchanging set of clones before it reached the fittest, most stable structure. Oganov found that he could avoid this stagnation by making the mutations more extreme. With his algorithm, he has been able to reproduce some of the more familiar crystals of nature, such as diamond, and also many exotic new materials. He found, for example, that pure sodium, when compressed to about 3 million atmospheres, suddenly turns from being a red metal into an insulator that is clear as glass - and experiments have since confirmed this. He is now working on a project to find superhard materials.

Oganov and Pickard disagree on which of the two methods is the more efficient and powerful. It may just turn out that they are each better for different materials, says Pickard. "Maybe they will each find their niches and coexist."


 

 


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This was first published in October 2009

 

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