The Second Kind of Impossible

by Paul Steinhardt

  Nan’s plan was to place a drop of acetone on the tip of the fiber, let the glue slowly soften, and then carefully remove the individual grains of material bit by bit, using a pair of tweezers. His explanation made it sound deceptively simple, but I knew it was excruciatingly detailed work that would require a great deal of skill.

  I sat alongside Nan as he brought the dropper to the glass fiber and carefully released a tiny droplet of acetone. I held my breath as the acetone hit the tip of the fiber. Right before our eyes, the entire speck suddenly vanished.

  We were both startled. The speck was supposed to contain metallic grains. Metallic grains cannot dissolve in acetone. What was going on? Neither of us said anything, but panic and confusion set in. Our eyes slowly shifted downward from the tip of the fiber. And then, seemingly simultaneously, we both let out a gasp.

  We had never imagined that the speck was attached to the tip with such a small amount of glue that the tiny drop of acetone Nan had applied would be enough to completely detach it from the mount.

  The speck could have fallen onto the floor, where it could have become contaminated. Worse yet, the barely visible speck might have been lost entirely. But as it turned out, about a foot below the glass tip was a table on which a tiny white crucible, about the size and shape of a doll’s teacup, had been placed. Nan had put it there to hold bits of material he planned to pick off the speck with his tweezers. Purely by chance, that crucible had been placed directly below the fiber tip.

  When Nan and I lowered our gaze, we saw that a droplet of acetone and the entire speck of metallic grains had landed safely right in the middle of the clean white crucible.

  The powdery speck of material, which had only been a tenth of a millimeter in size to begin with, had just been split into hundreds of minute grains that were all sitting in a little pool of acetone. We would have to wait for the acetone to evaporate before we could place the particles on a special gold grid, about the size of a small coin, which is commonly used to study powdery samples in a transmission electron microscope.

  The electron beam is so fine that only one part of one grain can be studied at a time. The ideal grain would be a pancake shape, wider along two directions but very thin along the direction the beam had to pass through.

  As Nan and I looked at the tiny grains in our sample, we realized it would be hopeless to try to slice any of them to the required thickness, which is a thousandth of a millimeter. Our only hope was to find a grain that, by chance, happened to be thin enough and oriented in the right direction for our purposes.

  Unfortunately, it would take some time before we could proceed. Princeton’s winter break was about to begin, and the Imaging Center would be closed for the holidays. After that, Nan said, the microscope needed for our test was booked solid for the next two months.

  I was not optimistic that the sample would prove to contain a quasicrystal. About a decade earlier, Peter Lu and I had studied several minerals with promising powder-diffraction patterns and every single one of them had failed the critical transmission electron microscope test. This sample would probably be no different, I thought. But even so, I did not like the idea of waiting around for months to find out.

  I asked Nan if there was any chance that we could check the sample any sooner. He pointed to the only open date on the calendar for the next two months: five o’clock in the morning on Friday, January 2nd.. What a surprise, I thought. No one was working the predawn hours the day after New Year’s.

  But the unfavorable time slot did not discourage me. “Fine!” I said. “See you then!” And, remarkably, Nan agreed.

  * * *

  PRINCETON, JANUARY 2, 2009: When the alarm clock went off at 4:30 a.m., the temperature in Princeton was a frigid 19o F. I bundled up in my warmest winter coat, hat, and gloves and headed off in the dark to meet Nan at the Imaging Lab.

  As I drove through town, it suddenly occurred to me that Nan and I had made the appointment weeks earlier, but had never confirmed the date. Perhaps he forgot? I wondered. Perhaps I had left my warm bed and was suffering through the freezing cold for no good reason.

  But once I arrived at the lab, there was Nan, the consummate professional, working away. I sat down next to him at the transmission electron microscope. He had already carefully placed our grains on a gold mesh sample holder, loaded the holder in the microscope, evacuated the chamber, and was beginning to search among the grains for a promising candidate to study. Nan would be looking directly through the microscope, and I would be able to watch what he was doing by studying the image projected on a nearby monitor.

  After a few minutes, he pointed out a grain that was two microns across, about one-thousandth the width of a human hair, seen in the enlarged image below. Under the microscope, the grain seemed to be roughly the shape of a tiny ax. Nan remarked that the part of the grain near the “handle” of the ax appeared thin enough for the electrons to pass through.

  He used the controls to slowly move the sample holder until the ax handle was directly in the line of fire of the electron beam. After a few checks, Nan announced he was ready to start the tests.

  The first step was to use the transmission electron microscope in “convergent beam mode,” which, for highly perfect crystal samples, produces a pattern of crisscrossing ribbons called a “Kikuchi pattern,” named for the Japanese physicist Seishi Kikuchi, who discovered the effect in 1928.

  To our surprise, the grain immediately produced a beautiful Kikuchi pattern. We did not expect to find such a perfect sample in the rock, and certainly not from the very first spot we tried.

  But what really caused our jaws to drop was that the pattern consisted of ten spokes arranged in a ten-fold symmetric pattern, as shown on the facing page. I stared intently at the monitor. A ten-fold symmetric Kikuchi pattern was impossible for ordinary crystals. Finding something like this was our first indication that the sample might actually be a natural quasicrystal.

  I felt myself straightening up in my chair. This could turn out to be quite a morning!

  The Kikuchi pattern makes it possible to align the electron beam so that it lies nearly perfectly along an axis of symmetry of the atomic arrangement. Nan fiddled with the controls to realign the sample and switch to diffraction mode.

  As soon as Nan pressed the switch, an image appeared on the screen that absolutely floored me. I saw a constellation of pinpoint diffraction spots arranged in a snowflake pattern composed of pentagons and decagons, the ideal signature pattern for an icosahedral quasicrystal. I felt a smile coming over my face. I could not believe what I was seeing. It was an electron diffraction pattern much more perfect than the one Shechtman had obtained in 1982. That sample was synthetic. This one was natural. I stared at the image on the screen in awe.

  Nan and I did not shout “Eureka!” or cheer or congratulate one another. In fact, we were dead silent, because no words were necessary. We both knew that we were witnessing a “second kind of impossible” moment. The first-ever discovery of a natural quasicrystal.

  Most scientists work for a lifetime hoping to have such a moment. As we sat shivering together in the still frozen lab, Nan and I were keenly aware of how lucky we were. It was a quietly overwhelming moment.

  It had been nearly twenty-five years since I first began my informal search for a natural quasicrystal in the mineral collections of natural history museums. And it had been ten years since Nan, Peter, Ken, and I had begun our systematic search of the worldwide database of minerals. Many people thought that laborious project was hopeless and perhaps even a bit silly. And just as the naysayers predicted, we had never once experienced an encouraging result. In fact, we had never even come close.

  But that unsuccessful search had led me to Luca Bindi and a long-forgotten sample in the storage room of his museum. And now, none of the decades of failure meant anything. Nothing made a whit of difference, except what I was looking at on the monitor. Below is a highly overexposed version of the first diffraction pattern we saw that morning
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  As Nan and I continued to admire the image, we finally began to exchange a few words. Our conversation was very businesslike as we calmly discussed the next steps.

  The first step was to set the sample on a mount that could tilt at certain precise angles in order to observe the different patterns along different directions. This test would be crucial in order to verify that the sample had all the symmetries of an icosahedron.

  As Nan explained it, the test could only be done by letting air back into the vacuum chamber in which the sample was held, and then resetting the mount. It was complicated, and would take time to accomplish. Despite the fact that the instrument was officially booked, the magnitude of our discovery prompted Nan to decide he would try to steal some time later in the week to perform the test. For now, it was time to go home.

  The freezing-cold streets of Princeton were still dark and deserted as I headed out of the laboratory. But I took no notice of the frigid temperature. I drove home almost in a dream state, replaying the morning over and over again in my mind. A natural quasicrystal. Impossible.

  A few hours later, after a brief nap, I sent an email to Luca with the subject line: Quasi-Happy New Year. My Italian colleague was the third person in the world to know that natural quasicrystals had just been discovered. Luca, though, would probably say that he was the first. The initial powder-diffraction tests at his Florence lab had been inconclusive. But Luca’s scientific intuition, which would prove to be remarkably accurate over the next few years, had given him complete confidence that the material he sent me contained a quasicrystal.

  A few days later, Nan was able to steal a bit more time on the transmission electron microscope, as promised. He rotated the sample at various angles and discovered a series of diffraction patterns with the symmetry of a rectangle (left image below) and a hexagon (right image below).

  The angles by which Nan needed to rotate the sample to go from the ten-fold pattern to the rectangular and then to the hexagonal, turned out to correspond to precisely the angles predicted for an icosahedron; for example, the angle between an imaginary line that passes between the center of an icosahedron and one of its corners and a line that passes between the center of the icosahedron and the center of one of its triangular faces. It was indisputable proof that our grain had perfect icosahedral symmetry.

  Luca’s preliminary test indicated that the grains contained aluminum, iron, and copper in roughly the same proportion that An-Pang Tsai and his collaborators had measured in the historic sample they discovered in 1987, which was the first bona fide example of a synthetic quasicrystal with pinpoint diffraction peaks. But we needed to make a more accurate measurement to be certain.

  I had a small sample of Tsai’s synthetic quasicrystal, which had been given to me as a memento in 1989. The nugget was a prized possession displayed in my office for more than twenty years, but I broke off a small chip for Nan so that he could make a quantitative comparison between the synthetic sample and the first known natural one.

  The match was nearly perfect: Al63Cu24Fe13 (63 percent aluminum, 24 percent copper, and 13 percent iron). Tsai’s beautifully faceted, dodecahedron-shaped synthetic quasicrystal and the tiny grains in the natural khatyrkite sample had precisely the same atomic arrangement and composition.

  These two substances had arrived in Princeton from opposite ends of the world. One of them was manufactured in a Japanese laboratory, the other created by nature and imported from Italy. And now, the two of them were discovered to be nearly a perfect match. Impossible.

  Luca and I drafted the paper, entitled “Discovery of Natural Quasicrystals,” with help from Nan Yao and Peter Lu, which we submitted to Science magazine, a leading journal for presenting new results. I knew we would have to wait several months to see if the article was accepted for publication.

  At this point, I should have been celebrating that we had finally succeeded in finding a natural quasicrystal, a goal that I had been pursuing for decades. But, instead, I felt strangely dissatisfied. I had a nagging sense that nature was still hiding something about the khatyrkite sample that had yet to be discovered.

  I could not put my finger on exactly what it was that made me feel that way, and I had no idea how long it would take before I would find out. There was just an overwhelming sense that the adventure was just beginning.

  TEN

  * * *

  WHEN YOU SAY IMPOSSIBLE

  PRINCETON, JANUARY 8, 2009: I knocked sharply on the tall oak door with a glass insert labeled “PROF. L. HOLLISTER.” It was to be the first of many meetings with the renowned geologist, and I had no idea what to expect.

  I knew Lincoln was an expert in petrology, the study of the origin and the composition of rocks. I also knew he was a hard-nosed scientist with a wide-ranging set of interests and was beloved on the Princeton campus. What I did not know was that he was about to become one of our strongest critics and would soon be questioning the validity of our entire project.

  Lincoln had made a career of challenging convention and ultimately proving his case. When he first entered the field in the 1960s, the standard view was that minerals in metamorphic rocks have uniform compositions because they formed at high temperatures and pressures. But Lincoln was able to explain why this is not the case. As one of the first geologists to receive rocks brought back from the moon, he showed that certain minerals in lunar lavas believed to have come from deep below the moon’s surface at high pressure had, in fact, developed in rapidly cooled lavas at the surface. He also significantly advanced our understanding of the continental crust with a series of explorations of remote regions of British Columbia, Alaska, and Bhutan.

  Throughout his career, Lincoln’s success relied on his survival skills in the wild and a tough, no-nonsense approach in the laboratory. I knew there was no better expert to help me figure out how our natural quasicrystal had formed.

  Man-made quasicrystals had now become commonplace all over the world, ever since An-Pang Tsai had fabricated the first perfect sample of Al63Cu24Fe13 in 1987. But Tsai had worked under carefully controlled laboratory conditions, beginning with just the right proportion of different metals and carefully regulating the rate at which he cooled the mixture. As a result, his team produced perfect man-made samples like the one on the left below. By contrast, the quasicrystals we discovered in the Florence sample were formed by nature in a totally uncontrolled environment and squeezed together with other minerals in a hodgepodge, as shown in the image on the right below. The white dots correspond to the locations of quasicrystals, but the other shaded dots correspond to various other crystalline minerals.

  Nature’s quasicrystal had the same atomic makeup as a synthetic quasicrystal, and they both had approximately the same defect-free structure. It was as if we were looking at identical twins born of different parents from distant parts of the world. How did that happen? I wanted to know.

  When Lincoln opened the door to welcome me, my first impression was: This fellow really looks the part of a geologist. Standing 5-foot-10 with a tanned complexion, silvery hair, and rugged good looks, Lincoln appeared ready to pick up a backpack and head off at a moment’s notice for another one of his outdoor adventures.

  In fact, he looked so physically fit that, had he not mentioned it, I would never have guessed that Lincoln was seventy years old and on the verge of retirement. He was packing up his office, he said, which explained why everything was in a state of disarray with maps, microscopes, and large rock samples strewn everywhere.

  Lincoln invited me into his inner office where there was more room to sit down, and I spent the next thirty minutes explaining my story. I told Lincoln about how we had first developed the theory of quasicrystals, the discoveries of synthetic versions in the lab, and my search for a natural sample that had begun in the 1980s and culminated less than a week earlier with the discovery at Princeton’s Imaging Center.

  And then I asked him a question that had been bugging me ever since: How had nature done it?
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  Lincoln narrowed his eyes and glared at me. I learned afterward that his students are all too familiar with that look. They call it the “Hollister gaze,” and it invariably means trouble.

  He must have felt sympathy for the fact that I was a theoretical physicist who obviously knew virtually nothing about geology. The Hollister gaze slowly softened as he began to break the bad news to me gently.

  “What you have there is . . .” he said, allowing a long, dramatic pause, “. . . impossible!”

  “Wait,” I quickly interrupted before he continued. I had been hearing that word for decades and wanted a chance to explain.

  “Quasicrystals are definitely possible,” I reminded him. “We have fabricated them in the laboratory, including ones with the very same composition as the natural sample that we have just discovered.”

  Clearly struggling to be patient with me, Lincoln raised his voice a notch or two. “I am not concerned about the quasicrystal part,” he said forcefully. “I never heard of them, but what you have explained sounds okay. What concerns me is that you said that the quasicrystal and the crystal khatyrkite both include metallic aluminum.

  “Aluminum has a very strong affinity for oxygen,” he stated. “There is plenty of aluminum on the Earth, but it is not metallic. It is all bonded to oxygen.” Once aluminum bonds to oxygen, it is no longer shiny and does not easily conduct electrons like metallic aluminum.

  “As far as I know, no sample of metallic aluminum or any alloy containing aluminum metal has ever been seen in nature. You think you have a natural rock. But, I am sorry to tell you, it is probably refuse from an aluminum smelter.” The metallic aluminum encountered in everyday life is all made synthetically by separating metallic aluminum from aluminum oxide.