Before the discovery of quasicrystals, most scientists would have declared facets with five-fold symmetry were impossible because they violated the centuries-old rules established by Haüy and Bravais. Yet here is indisputable evidence that they exist.
It took some time to verify the results. But Paul Heiney and his student Peter Bancel were finally able to take an X-ray diffraction pattern for the new aluminum, copper, and iron sample, just as they had done for Shechtman’s Al6Mn. This time, Heiney and Bancel found something impressively different. The Bragg peaks in Tsai’s sample were sharp and pinpoint, not fuzzy, and the positions of those peaks perfectly aligned along straight lines, in agreement with our predictions for the icosahedral quasicrystal model.
At last, here was the first unambiguous, bona fide case of an icosahedral quasicrystal. Proponents of the icosahedral glass model graciously conceded, and quasicrystals were finally accepted as a true form of matter. Over the next few years, many more examples of perfect quasicrystals were found, in many cases by Tsai and his collaborators. When I finally had the chance to meet him in Japan many years later, I was pleased to be able to express in person how much I appreciated and admired his historic contributions.
Despite the new experimental proof, there remained a smattering of skeptics, including the venerable Linus Pauling, who maintained his staunch support of his multiple-twinning idea.
* * *
PHILADELPHIA, 1989: I invited Pauling to visit me at Penn in order to review the definitive measurements Heiney and Bancel had made of Tsai’s sample. It was a memorable occasion, and I was impressed by the number of hours Pauling spent meticulously combing through the data. He asked a lot of detailed questions as he reviewed the data, trying to identify potential problems with the new X-ray diffraction test.
By the end of the day, Pauling agreed that even a model with eight hundred atoms per repeating building block, which he had claimed could explain Shechtman’s Al6Mn data, would not explain the new quasicrystal. But that did not mean he was conceding defeat. It meant he would go back and substantially increase the number of atoms per building block in his theory until he could fit the new data, even though that would make his theory even more byzantine than before.
Pauling told us that he planned to write a new article in the Proceedings of the National Academy of Sciences in which he would describe his revised multiple-twinning model for Tsai’s perfect quasicrystal. In a gesture of professional respect, he invited us to write a companion piece explaining why the quasicrystal model explained the result more simply. With Pauling’s support, both articles appeared back to back in an issue later that year.
Pauling and I continued to correspond over the years as more and more combinations of elements producing perfect quasicrystals were found in the laboratory. As the years passed, he became increasingly familiar with the quasicrystal picture and seemed to acknowledge its advantages. I believe he understood that the quasicrystal theory would prevail, but he was not ready to give up his favorite idea. I could appreciate that. I enjoyed our ongoing friendly debate and was saddened to read the news in 1994 that he had passed away at the age of ninety-three.
By this time it was clear that there were no remaining roadblocks to synthesizing perfect, stable quasicrystals in the laboratory. The subject had achieved such wide acceptance that there were now annual international meetings on quasicrystals, with hundreds of people and creative contributions from a wide spectrum of experimentalists, theoreticians, and pure mathematicians.
I was proud to have been part of it. But I also felt that the subject was becoming too crowded and too mature for my tastes. In order for me to continue to work on quasicrystals, I needed to pursue a question that no one else was considering.
I reminded myself that growing perfect quasicrystals in the laboratory had proven to be easier than anyone had ever thought.
Might it be possible for perfect quasicrystals to develop on their own without any human intervention?
That idea was reminiscent of the question I had briefly explored in 1984, shortly after Dov and I had published our first paper: If synthetic quasicrystals were possible and so easy to create, what about natural quasicrystals?
Thus far, quasicrystals had only been synthesized in the laboratory under carefully controlled conditions that were too pristine to ever be duplicated in the natural world. So I was pretty sure that other scientists would consider natural quasicrystals to be absolute folly. Impossible. And that was a good enough reason for me to begin to pursue the idea.
PART II
* * *
THE QUEST BEGINS
SEVEN
* * *
DID NATURE BEAT US?
PRINCETON, 1999: “Has anyone ever discovered a natural quasicrystal?”
The jovial white-haired fellow rushed up to the lectern to ask the question the moment my lecture ended. I had just joined the faculty in the Department of Physics at Princeton and had decided to focus my debut talk on the history of quasicrystals. It had now been fifteen years since Dov Levine and I had first introduced the concept.
I did not recognize the man asking the question from any faculty meetings and soon understood why. He introduced himself as Ken Deffeyes from the Geosciences Department. I was surprised that he was attending the talk. Generally the only attendees at the weekly colloquiums were physicists and astrophysicists.
I appreciated Ken’s question because it meant that he understood the point of my lecture. I had presented a series of new theoretical arguments showing that quasicrystals can be as stable and as easy to grow as crystals. So it was only logical that, as a geologist, he would want to ask if they were known to exist in the natural world.
“No,” I answered. “I have spent time looking haphazardly in museum collections in the past without success. However,” I added with a smile, “I have an idea for a systematic way of searching for them.” Ken’s eyes grew wide, and he asked me to describe the idea.
I told him that it involved an automated search through a computer database containing tens of thousands of diffraction patterns. Some of the patterns were from synthetic materials. But nearly ten thousand of them were from natural minerals. Several years earlier, I had hired an undergraduate to search through the database pattern by pattern for potential quasicrystals. But he had run out of energy after a short period of time. Later, I realized that the screening process could probably be entirely automated. One could narrow the search with a computer program, obtain samples of the most promising candidates, and test them in the laboratory.
Ken thought that was a great idea and told me he knew just the person for the job, a bright undergraduate named Peter Lu. Peter had won national gold medals in the “Rocks, Minerals, and Fossils” event at four consecutive National Science Olympiad tournaments in high school. He was currently a junior in the Physics Department, Ken explained, which meant he would be looking for a senior thesis project the next year. Peter also had experience with an electron microscope, which would be an asset in case there were any potential quasicrystals identified during the search.
Ken also recommended that I contact Nan Yao, the director of Princeton’s Imaging and Analysis Center and a specialist in electron microscopy. Ken said that Nan was a gifted teacher who had trained Peter. Nan was also highly skilled in obtaining diffraction patterns from unusual materials.
The next day, Ken introduced me to Peter, who seemed to be perfectly suited for the project. Peter was an intense, ambitious student looking for a challenge. He was short and youthful, but spoke with enormous self-confidence and in an authoritative tone. He had not attended my lecture but felt that he had heard enough from Ken to speak assertively about the project and his qualifications.
Peter and Ken then took me to meet Nan at the Imaging Center and tour the facilities. The Center contained electron microscopes and an array of other expensive instruments for studying a variety of materials. It served scientists and students in departments throughout the university as well
as experts at nearby industrial laboratories. Nan was enthusiastic about our project and eager to help in any way possible, which included making sure we were allotted time to work with the Center’s electron microscope. I took note of his calm reserve and expertise as he showed us around the facilities. I knew he would be a valuable member of the team.
With Ken, Peter, and Nan on board, I found that I had the right combination of people, knowledge, and skills to move forward with a systematic search for natural quasicrystals. So my long-awaited quest began in earnest.
Although Peter’s talents were largely in mineralogy and experimental physics, he rapidly absorbed the basics of quasicrystal mathematics. We began working on a computer algorithm that would enable us to rank the likelihood that a given candidate mineral is a quasicrystal based on its diffraction pattern, as recorded by the International Centre for Diffraction Data (ICDD).
The ICDD is a nonprofit organization that collects information about materials and their X-ray powder-diffraction patterns from laboratories all over the world. The information is compiled in an encrypted database, and scientists and engineers purchase subscriptions to gain access to it. Experts commonly use the database to compare diffraction patterns they are examining with patterns from previously known materials.
The ICDD also provides software to extract information from the database, but their program turned out to be too cumbersome for our purposes. It could only provide access to one powder-diffraction pattern at a time, along with a lengthy amount of descriptive information that was superfluous for our purposes.
In order to conduct our statistical analysis, we only needed access to the powder-diffraction data. So we wrote to the ICDD, explained our project, and asked if they would allow us to work with a decrypted version of their database. We could then write our own software to extract the relevant information and compress it into one large file for our analysis. We were not sure what to expect, because we were asking for special access to their most valuable commodity. But they generously provided us with everything we needed at no cost.
The next hurdle for us to overcome was that we were limited to working with powder-diffraction patterns. If the ICDD had been able to offer single-grain diffraction patterns, it would have been an afternoon’s work to pick out the quasicrystal patterns (below left) from the crystal patterns (below right).
The ICDD does not collect single-grain diffraction patterns because they do not exist for most materials. One needs a sample of a certain size and thickness to make a high-quality single-grain diffraction pattern. For most of the minerals and materials that scientists study, those types of samples are too difficult or too time-consuming to find.
Instead, scientists collect many tiny individual grains oriented at random angles with respect to each other. A “powder” of grains like this might occur naturally, or it could be easily prepared by grinding one or more small samples into a fine powder.
Shining X-rays on the collection of grains produces what is called an “X-ray powder diffraction pattern,” which combines the diffraction patterns from all the grains. For example, if all the individual quasicrystals had a sharp, pinpoint diffraction pattern like the one shown on the left below, the powder-diffraction pattern would look like the one on the right.
The powder pattern is similar to what you might observe if the sharp pinpoint diffraction patterns were put on a turntable and spun rapidly so that each point became a circular blur. The left pattern shows points arranged with clear ten-fold symmetry. In the powder pattern on the right, all of the information about symmetry is lost. All that remains are rings with different radii and intensities.
Imagine that you only had the image on the right. Could you reconstruct the fact that it came from a powder of randomly oriented grains in which each individual grain produces a pattern like the one on the left? That was the question we were trying to answer. Amazingly enough, Peter and I were able to determine that there was enough information in the spacings and intensities of the rings on the right to identify potential quasicrystals and to infer the now-familiar snowflake pattern on the left.
The plot below summarizes our findings. The graph compares two different properties that we computed for each powder pattern in the ICDD catalog. The horizontal axis measures how close the powder-diffraction rings for the sample are to the ideal radii for a perfect icosahedral quasicrystal. The vertical axis measures how well the intensities match.
The two shaded squares in the lower left-hand side of the graph represent two of the known synthetic quasicrystals that were already in the ICDD catalogue. So in practice, those two squares were as close as one could get to perfection. If the powder pattern of a natural mineral had scored close to those squares, we could reasonably expect that it was a quasicrystal in which each grain had a pinpoint diffraction pattern.
The points on the graph represent the results for more than nine thousand minerals that lie too far from the shaded squares to be considered promising candidates. The circles represent the mineral powder patterns that came the closest to the squares and indicated potential quasicrystals.
The circles corresponded to the mineral samples that Peter and I now had to track down and bring to our lab in Princeton for further study. Once a sample arrived, it would be sliced into thin sections and examined under the electron microscope to determine if it was truly a quasicrystal.
When Peter’s final year at Princeton was finished, he presented the results of his work in his senior thesis defense. According to tradition, a team of faculty members grill the senior to test the student’s familiarity with the subject. But Peter opted for a bit of levity and decided that he was the one who was going to do the grilling. Literally.
So as part of the formal defense of his thesis, Peter amused the attendees by cooking a raw steak on a special frying pan made with a thin coating of quasicrystal metal. The use of synthetic quasicrystals for a nonstick coating was one of the first commercial applications of the new form of matter. The coating was conceived and patented by a French quasicrystal scientist, Jean-Marie Dubois, and his collaborators. A French manufacturer sold the pans under the trade name Cybernox.
The quasicrystal coating was slippery like Teflon, a popular nonstick coating, but much more durable. Peter was able to fry his steak without using any butter, demonstrating that nothing stuck to the quasicrystal surface. He capped off the demonstration by slicing into the steak with a sharp knife while it was still in the pan, something no one would ever attempt to do in a pan with a Teflon coating. Peter was able to show that there was no damage to the pan because of the hardness of the quasicrystal material. But the same could not be said for the steak knife, which left significant streaks of metal shavings on the pan’s surface.
Peter also presented the details of our search through the ICDD catalog. He explained the search algorithm we had developed and described the candidates we had managed to study. We had not succeeded in discovering a natural quasicrystal. But the process of trying to collect and test the minerals was a series of adventure stories, with the occasional funny mishap.
For example, after months of hard work, we had finally managed to obtain a sample of one of our topmost mineral candidates. The sample measured a few inches across. In order to study it under the electron microscope, though, we needed to obtain a slice as thin as a human hair.
The slicing procedure required a special facility that did not exist at Princeton. So we arranged to send the sample to a lab at UCLA. We expected to receive a thin slice from the lab, along with the remainder of the sample. If we succeeded in finding a quasicrystal in the slice, the rest of the sample would be extremely valuable for follow-up studies and would ultimately end up as a prize exhibit in a museum.
But when the package came back from UCLA, I opened the box and found that all it contained was a single ultrathin slice. What happened to the rest of the rare sample we had worked so hard to obtain?
I frantically called UCLA to find out when they would be sending
us the rest of our material. When I finally reached the technician involved, he cheerfully reported, “Oh, we assumed you only needed the one slice, so we threw out the rest of the sample.”
I was horrified. As far as we knew, this might turn out to be the only sample of that mineral in the world. If we examined the slice, and discovered it contained the first natural quasicrystal, we would have to live with the fact that 99.99 percent of the rare material had been tossed in the garbage can. The next few hours were nerve-wracking as we waited for Nan to check the wafer-thin slice. When he reported that the sample was a dud, Peter and I left the lab with a strange mixture of disappointment and relief.
Ultimately, all of the minerals that we identified, collected, and tested turned out to be duds, as well. A year after Peter passed his oral defense exam, we published a paper about our experiment in the Physical Review Letters, describing our computer search algorithm and our lengthy string of failures.
A weakness in our approach, we concluded, was that the quality of the data collected by the ICDD from diverse laboratories across the world was uneven. As a result, our automated search algorithm yielded a lot of false positives. I would have to accept the fact that there would continue to be many more failures before finding a true natural quasicrystal.
Peter graduated summa cum laude from Princeton, and headed off for Harvard Graduate School to study completely different topics. Although he was no longer involved in my search for natural quasicrystals, he remained intrigued by the beauty of quasicrystal tilings. When Peter was still an undergraduate, the two of us would sometimes discuss the fact that Penrose had managed to construct a quasicrystal tiling without being aware of its hidden quasiperiodic order. So perhaps, we speculated, it might be possible that quasiperiodic tilings had been unintentionally designed by someone prior to Penrose. A likely place to search for such a thing was among Islamic tilings because many Islamic cultures had an advanced knowledge of mathematics and an interest in geometric patterns.
The Second Kind of Impossible Page 10