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color:#990000;'><div style='float:right; padding:4px;'><a href='#' style='cursor:hand;' onclick='return floatingMenu.hide()'><img src='https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/close.gif' style='border:none;' /></a></div></div><a href='https://web.archive.org/web/20150930052107/http://www.magzter.com/IN/Delhi-Press/The-Caravan/News/' target='_blank' style='cursor:hand;'> <div style='height:190px;'></div></a></div>"); } </script> <div class="subhheading"><a href="/web/20150930052107/http://www.caravanmagazine.in/periscope/forbidden-symmetry">The quest for a radically new form of matter.</a></div><div class="authorndate">By <a href="/web/20150930052107/http://www.caravanmagazine.in/profile/573">VIRAT MARKANDEYA</a> | <span class="date-display-single">1 November 2013</span></div><div class="full-image-view"><div class="show-image" style="display:block"><div class="f-image"><a rel="lightbox[lightbox_full_image][<br /><br /><a class="lb-credit"> Courtesy Paul Steinhardt</a>]" title="" href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/opener-option-a-moonrise-350-dpi.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/opener-option-a-moonrise-350-dpi.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Courtesy Paul Steinhardt</div><div class="f-caption"></div></div><div class="show-image-6692" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][<br /><br /><a class="lb-credit"> Courtesy Paul Steinhardt</a>]" title="" href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/opener-option-a-moonrise-350-dpi.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/opener-option-a-moonrise-350-dpi.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Courtesy Paul Steinhardt</div><div class="f-caption"></div></div><div class="show-image-6694" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][Israeli scientist Dan Shechtman discovered the 5-fold symmetry (or ‘forbidden symmetry’) of crystal structures in 1982.<br /><br /><a class="lb-credit"> JINI/Xinhua Press/Corbis</a>]" title="Israeli scientist Dan Shechtman discovered the 5-fold symmetry (or ‘forbidden symmetry’) of crystal structures in 1982." href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/42-30012629.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/42-30012629.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">JINI/Xinhua Press/Corbis</div><div class="f-caption">Israeli scientist Dan Shechtman discovered the 5-fold symmetry (or ‘forbidden symmetry’) of crystal structures in 1982.</div></div><div class="show-image-6695" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][An example of a Penrose tiling. <br /><br /><a class="lb-credit"> Carol & Mike Werner/Visuals Unlimited/Corbis</a>]" title="An example of a Penrose tiling. " href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/42-33391986.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/42-33391986.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Carol & Mike Werner/Visuals Unlimited/Corbis</div><div class="f-caption">An example of a Penrose tiling. </div></div><div class="show-image-6696" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][The ornate tiling at the Darb-e-Imam mosque in Isfahan, Iran.<br /><br /><a class="lb-credit"> Arthur ThÈvenart/Corbis</a>]" title="The ornate tiling at the Darb-e-Imam mosque in Isfahan, Iran." href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/at002886.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/at002886.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Arthur ThÈvenart/Corbis</div><div class="f-caption">The ornate tiling at the Darb-e-Imam mosque in Isfahan, Iran.</div></div><div class="show-image-6697" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][From left to right: Luca Bindi, Valery Kryachko and Paul Steinhardt.<br /><br /><a class="lb-credit"> Courtesy Paul Steinhardt</a>]" title="From left to right: Luca Bindi, Valery Kryachko and Paul Steinhardt." href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/lucavalerypaul350dpi.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/lucavalerypaul350dpi.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Courtesy Paul Steinhardt</div><div class="f-caption">From left to right: Luca Bindi, Valery Kryachko and Paul Steinhardt.</div></div><div class="show-image-6698" style="display:none"><div class="f-image"><a rel="lightbox[lightbox_full_image][Field operations at the Listvenitovyi stream in the Koryak mountains, Siberia, Russia.<br /><br /><a class="lb-credit"> Courtesy Luca Bindi</a>]" title="Field operations at the Listvenitovyi stream in the Koryak mountains, Siberia, Russia." href="https://web.archive.org/web/20150930052107/http://www.caravanmagazine.in/sites/default/files/imagecache/lightbox_full_image/field-operations-at-the-listvenitovyi-stream.jpg"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/story_carousel/field-operations-at-the-listvenitovyi-stream.jpg" alt="" title="" width="680" height="435" class="imagecache imagecache-story_carousel"/></a></div><div class="f-credit">Courtesy Luca Bindi</div><div class="f-caption">Field operations at the Listvenitovyi stream in the Koryak mountains, Siberia, Russia.</div></div></div><div class="thumb-image-view thumbnail-list"><a href="javascript:loadmain(6692)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/opener-option-a-moonrise-350-dpi.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a><a href="javascript:loadmain(6694)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/42-30012629.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a><a href="javascript:loadmain(6695)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/42-33391986.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a><a href="javascript:loadmain(6696)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/at002886.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a><a href="javascript:loadmain(6697)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/lucavalerypaul350dpi.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a><a href="javascript:loadmain(6698)"><img src="https://web.archive.org/web/20150930052107im_/http://www.caravanmagazine.in/sites/default/files/imagecache/galleria_image_thumbnail/field-operations-at-the-listvenitovyi-stream.jpg" alt="" title="" width="65" height="44" class="imagecache imagecache-galleria_image_thumbnail"/></a></div> <div class="share-with"> <span class="st_facebook_hcount" displaytext="Facebook"></span> <span class="st_twitter_hcount" displaytext="Tweet"></span>  <script type="text/javascript" src="https://web.archive.org/web/20150930052107js_/https://apis.google.com/js/plusone.js"></script>  <g:plusone href="http://www.caravanmagazine.in/periscope/forbidden-symmetry"></g:plusone> <div class="print-email"><a href="/web/20150930052107/http://www.caravanmagazine.in/print/4008">Print</a>|<a href="/web/20150930052107/http://www.caravanmagazine.in/printmail/4008">E-Mail</a>|</div><a href="javascript:void(0);"><div class="single-page">Single Page</div><div class="multipage">Multiple Page</div></a></div> <script type="text/javascript">var switchTo5x=false;</script> <script type="text/javascript" src="https://web.archive.org/web/20150930052107js_/http://w.sharethis.com/button/buttons.js"></script> <script type="text/javascript">stLight.options({publisher:'8014eb0d-feae-4f08-9056-b8b78a153569'});</script> <div class="fullpage-body"><div class="detailBody"><div class="view view-story-page-views view-id-story_page_views view-display-id-block_1 view-dom-id-1"> <div class="view-content"> <div class="views-row views-row-1 views-row-odd views-row-first views-row-last"> <div class="views-field-body"> <div class="field-content"><div class="dropcap"> <p>Paul Steinhardt sat riveted to his seat as the driver, Victor, steered the double-track vehicle from side to side, dodging hazards every few feet. It was July 2011, and the 58-year-old physicist found himself in Chukotka, a region in Far Eastern Russia where the moon rises to white midnights framed against the smoky Koryak Mountains. He had never been camping, but was now leading a geological expedition deep into the Russian tundra, a land fractured from the Alaskan mass and inhabited by bears, against which the expedition team carried modified Kalashnikovs to defend themselves. There were no roads, and on occasion the vehicles, called snow-cats—rectangular boxes painted bright orange and blue-grey that trundled along at a top speed of 15 km per hour—would have to cross entire water bodies on a hope and a prayer.</p> </div> <p>Steinhardt was headed to a stream 230 km to the south-west of Anadyr, the capital of Chukotka, searching for fragments of a meteorite unlike any known before. Embedded in the rock could be a form of matter called quasicrystals that had never before been found in nature.</p> <p>Quasicrystals riff on something as basic as the way atoms (or molecules, or ions) are arranged in materials. When they were first synthesised in a lab in 1982, they overthrew 200 years of scientific dogma about the laws of matter. They form a bridge between ‘true’ crystals like salt and gold, and amorphous, disordered materials like glass, which were the only categories of solid material previously thought to exist.</p> <p>Quasicrystals changed the very definition of crystals and the assumptions of crystallography—the science used to study the arrangement of atoms in solids. Their discovery allowed materials researchers to play with an infinite new range of atomic structures. The internal structure, in turn, creates the solid’s unique properties. Practical applications for quasicrystals have already been found, such as in the strengthening of steel, and the unique way they interact with light has led to several patents.</p> <p>Steinhardt had been at the forefront of quasicrystal research—the word ‘quasicrystal’ itself came from a paper he co-authored in 1984. Initially met with scepticism and ridicule, hundreds of quasicrystals had since been found. (They are rather common in certain aluminium metallic phases.) But quasicrystals had only been artificially made in the laboratory, and were therefore thought not to be an important building blocks of the material universe. The primary goal of the Russian expedition was to show beyond a shred of doubt that quasicrystals could form in nature. This would move science one step closer to showing that quasicrystals were as robust (and perhaps as universal) a form of matter as crystals.</p> <p>After a “four-day rollercoaster ride”, as Steinhardt would later call it, the expedition arrived at the Listvenitovyi stream. The excavation team began panning for quasicrystal candidates, separating rock and other minerals from clay for a kilometre along the stream. An analysis team then sifted through the panned material, looking for minute grains in what had originally been a tonne of sediment. If indeed they found natural quasicrystals, it would rewrite mineralogy textbooks and open new directions for material science.</p> <p> </p> <p>BLAME THE OMNIVOROUS READING HABITS of an Italian geologist for starting it all. In 2007, Luca Bindi was a curator at the Università degli Studi di Firenze who was interested in incommensurate structures—in which, like quasicrystals, atomic clusters don’t repeat regularly or are aperiodic—in minerals.</p> <p>His curiosity led him to a 2001 paper in <em>Physical Review Letters</em>—not a staple journal for the earth sciences—by Peter J Lu at Harvard and Paul Steinhardt and Nan Yao at Princeton.</p> <p>It discussed a method to find and index new solids called “quasicrystals” based on their X-ray diffraction patterns. The analysis had found 50 promising mineral candidates, but no clincher.</p> <p>Bindi had never worked with this form of aperiodic structure before. Nevertheless, as he scanned the list of candidates, he saw three minerals he was familiar with: aktashite, gratonite, and tantalite.</p> <p>“I was shocked to see them in this list,” he recalled. “Could they exhibit a quasicrystalline structure?”</p> <p>Bindi knew quasicrystals were important. Finding a natural quasicrystal, for one, would revolutionize the way minerals were conventionally classified—because all known minerals were either crystalline or amorphous, rather than quasicrystalline in structure. At the end of the paper, a line caught his eye: “We are interested in collaborating in exploring the leading candidates, only some of which have been given in Table I. Those interested are encouraged to contact P. J. L. and P. J. S.”</p> <p>Bindi had a hunch that the minerals were among the collections of the Natural History Museum of the Università degli Studi di Firenze that he knew so well. Bindi ran to check out the database for the 50,000-specimen mineralogical collection at the museum. “They were there!” he later wrote to me in an e-mail. So he decided to contact Lu and Steinhardt.</p> <p>In October 2007, when Steinhardt received an e-mail from Bindi offering collaboration, the search for natural quasicrystals was in a slow phase. Steinhardt, who was known as a cosmologist for his work on inflationary models of the universe, tinkered around with several projects at once, including solid-state physics of which the quasicrystal hunt was a part. He had then been toying with the idea of compiling a catalogue for meteorites similar to the catalogue for terrestrial minerals compiled by the International Centre for Diffraction Data, which he had unsuccessfully used in the 2001 paper. Steinhardt had a hunch quasicrystals could be found in meteorites and a database would facilitate the search.</p> <p>Steinhardt didn’t know much about the Italian museum, but Bindi seemed enthusiastic, so the Princeton collaborators gave him a list of minerals that seemed promising but hadn’t yet been checked. Out of this list, Bindi thought he could procure about half a dozen.</p> <p>The laborious process of slicing the mineral, preparing the sample, and observing its powder pattern to check whether it was a good candidate or not took about a month. The researchers tested six samples in all. Nothing worked.</p> <p>“It was failure after failure after failure,” Steinhardt recalled. “We thought we’ll write a paper saying that we tried six more and they failed.”</p> <p>The idea was to update the 2001 paper, create some noise, and get more people interested. “Luca was pressing to write-write-write,” Steinhardt told me. “I was like, hmmnn, I don’t know.”</p> <p>The lull might have been fortuitous. Bindi decided to take a fresh approach to the problem. Rather than simply cross off the minerals he had been sent by Steinhardt, he put down a list of known synthetic quasicrystals and stared hard. Did these compounds show anything in common? The answer soon popped up: all the quasicrystals had metallic aluminium, and often copper, in their formula.</p>  <p>Bindi looked up mineralogical databases for natural aluminium-copper alloys. He found two—khatyrkite and cupalite. And then he made a second discovery: he had one of the minerals right under his nose. In a minor, but important, collection housed in the Florence Museum, he found a sample with the catalogue number “46407/G” labelled “Khatyrkite” and catalogued as sourced from the “Koryak Mts., Russia”.</p> <p>Bindi began careful single-ray X-ray diffraction and chemical analysis to see what the khatyrkite sample revealed. Soon, he was sure he had something. Excited, he emailed Steinhardt in early November 2008. Steinhardt was, in fact, in Genoa to give a talk at the Festival della Scienz on cosmology. (‘Beyond the Big Bang, The Universe Without End,’ it was titled.) Before the beginning of his presentation, Steinhardt responded on his BlackBerry: “I look forward to seeing the pptfile—it sounds much more exciting than what we had before (a null result).”</p> <p>After looking at the file, Steinhardt sent an effusive note saying that he agreed they actually might have a natural quasicrystal. The last overwhelming evidence would be a diffraction pattern taken with a transmission electron microscope. As Bindi did not have the equipment in Italy, he decided to send the samples to Princeton. Two 60-micron-sized grains were couriered there on November 11.</p> <p>The sample came FedEx-ed in a tiny plastic box labelled “khatyrkite”. The box contained two brass holders out of which glass rods stuck out, and on the glass rods were specks of matter.</p> <p>“If this turns out to be the quasicrystal, I’m going to be frustrated, because I can barely see this thing,” Steinhardt had joked. “I thought it would be something I could hold in my hand, like a rock.”</p> <p>Worse still, after waiting for close to a decade since his 2001 paper to find a sample of a natural quasicrystal, Steinhardt would have had to wait another few months to confirm that the sample was legitimate. It was going to be Christmas break in Princeton, and the only lab where a physicist could test the sample would be closed. Steinhardt was told he couldn’t have the lab for another three months because it was already booked. He decided he would slip in earlier.</p> <p>On New Year’s morning in 2009, when they knew no one would be there, Steinhardt and Nan Yao, head of the Princeton Institute for Science and Technology of Materials’ (PRISM) Imaging and Analysis Center, slinked into his lab at Princeton. Despite Bindi’s enthusiasm, Steinhardt thought they would spend a few minutes checking and failing—and then he could sleep again.</p> <p>Then, a small disaster almost struck. Before the scientists could proceed with their electron diffraction experiment, they had to take the samples off a needle. The sample had been described to them as being a grain: a single, solid thing. It actually was a tiny, micron-size powder of grains. “The moment the first drop of acetone fell on it, the whole thing fell off,” Steinhardt recalled. “If you had sneezed at that point, the entire sample would have been lost. Fortunately, just below the needle, we had a crucible where all the powder collected.”</p> <p>When they put the sample under the microscope, what they found was breathtaking. The grains yielded a beautiful pattern like the mosaic tiling on the ceiling of the Alhambra, but infused with light—the signature diffraction pattern of a quasicrystal.</p> <p>“That was just an incredible, incredible feeling,” Steinhardt told me. “I never believed that when I was looking at something in nature that it would be anything as good as that. I thought it might be something quite deceptive and poor, and that if you squint at it you might recognise it. Here it was, magnificent and perfect.”</p> <p>The next day, Bindi received an e-mail from Steinhardt. It was titled “Quasi-Happy New Year”. Bindi knew they had their sample. Less than two years later, in 2011, the Israeli researcher who discovered the first synthetic quasicrystal would win the Nobel Prize in Chemistry.</p> <p> </p> <p>“10 FOLD???” DAN SHECHTMAN SCRIBBLED in his notebook. It was April 1982 and Shechtman, a researcher who was visiting the U.S. National Institute of Standards and Technology (then called the National Bureau of Standards), had peered into his microscope and seen a pattern not unlike the one Steinhardt would later glimpse. What he saw were circles made of ten dots, each the same distance from one another.</p> <p>If what Shechtman was seeing was correct, then the crystal in front of him had a ten-fold symmetry. Turning the image by one-tenth—36 degrees—would yield the same picture. But this meant that the atoms inside the crystal were packed together in a way thought to be impossible. Further analysis by him showed that the crystal was actually based on 5-fold symmetry—a “forbidden symmetry”.</p> <p>Indeed, when Shechtman went back to Israel, the head of his laboratory handed him a textbook of crystallography to read. When Shechtman stubbornly persisted with his experimental results, he was asked to leave the research group. Even more powerful opposition came from two-time Nobel Prize winner Linus Pauling. In Shechtman's 2011 Nobel lecture, he recalled that Pauling, probably the most famous chemist of the 20th century, would go from conference to conference declaring that there was no such thing as quasi-crystals, just quasi-scientists.</p> <p>The tension between the younger and the older researcher arose because the arrangement of atoms in crystals, based on results since 1912, had always been found to be periodic—a regularly repeating arrangement. The very definition of a crystal furnished by the International Union of Crystallography in the 1980s was “a substance in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating three-dimensional pattern”.</p> <p>Shechtman’s work went against 70 years of experimental evidence but that wasn’t the worst of it. There was a reason why Pauling was more than sceptical, and that deeper argument had to do with mathematics—the way atoms can theoretically be packed together.</p> <p>Building the general argument up from a concrete example, consider the problem of tiling a two-dimensional surface—like a kitchen or bathroom floor—leaving no gaps, where different tile orientations are allowed. A quick examination will show that it is possible to do so with a triangular tile, a square tile, and a hexagonal tile.</p> <p>The general property underlying those specific shapes is rotational symmetry. Rotational symmetry refers to how an object or shape is indistinguishable from its original state when turning it to a certain degree.</p> <p>A triangular tile has a three-fold symmetry because if you turn it 120 degrees, the same pattern will appear. A square has four-fold symmetry because turning it 90 degrees gets you back to the same shape and so on. In fact, there are any number of shapes beyond the simple triangles and squares that can tile a floor without leaving gaps because they have this intrinsic property of three-fold or four-fold symmetry.</p> <p>But try tiling a floor with a five-fold symmetrical shape like a pentagon without leaving gaps, and the task is quite impossible. It is impossible for symmetries beyond six as well.</p>  <p>The same principle that applies to two dimensions applies to three-dimensional structures, including in the packing of atoms. Several proofs have shown that it is mathematically impossible to have regularly repeating structures of five-fold rotational symmetry and symmetries beyond six.</p> <p>But what about instances where the atomic arrangement does not repeat regularly?</p> <p>Here again the answer lies in mathematics. A British mathematician and cosmologist, Roger Penrose, trying to solve a long-standing problem in the field, had created the most elegant and simple form of aperiodic structures in the mid-1970s. Using just two tiles, a fat and a thin rhombus, and enforcing certain rules on how the two could fit together, he created a quasi-periodic mosaic in two dimensions.</p> <p>In 1982, a crystallographer at Birkbeck College in London, Alan Mackay, used the Penrose tiles to represent real-world crystallography. In his model, atoms lie at the intersection of three lines, or vertices, in the Penrose tiling. By this reasoning, he showed what kind of diffraction pattern a hypothetical crystal with five-fold symmetry would show.</p> <p>The five-fold symmetric Penrose tiling gives rise to a pattern that repeats at two different intervals—a long and a short interval that has an atomic equivalent. “Instead of atoms repeating throughout the structure at some regular interval, as in ordinary (periodic) crystals, atoms in quasicrystals are spaced at long or short intervals,” Steinhardt wrote in a 1996 PNAS (Proceedings of the National Academy of Science) paper.</p> <p>One particularly beautiful aspect is that the ratio between frequency of the long and the short intervals tends towards an irrational number—the famous golden ratio, which in turn is connected to the Fibonacci sequence (0, 0+1=1, 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13…).</p> <p>The interval that comes next comes of the enforced matching rules—but however much you zoom out to see the global structure, it is impossible to see it as a particular, even if spectacularly complex, repeating pattern. It is a kind of dissonance in space—just as you think a quasi-periodic sequence is settling down, it breaks its rhythm.</p> <p>Quasicrystal patterns often resemble other symmetric tilings, such the Islamic girih at Alhambra. But just as with the Penrose tiles, it is the enforced rules on how the tiles fit together that gives rise to a true quasi-periodic arrangement. Only the Darb-i-Imam in Iran seems to enforce similar rules to create a quasi-periodic tiling that could be extended infinitely, capturing that iterative property which allows quasi-periodicity.</p> <p>Meanwhile, Shechtman still had not found a journal to publish his results. He had been rebuffed by the <em>Journal of Applied Physics</em> in the summer of 1984. The editor had sent his manuscript back unread by return of post.</p> <p>It would be November 1984 before his findings, written up with collaborators Ilan Blech, Denis Gratias and John Cahn, were eventually published in <em>Physical Review Letters</em>. During the peer-review process, Steinhardt got the chance to see it.</p> <p>Steinhardt was approaching the quasicrystal debate from a theoretical point of view. Motivated by work he had done with David Nelson at Harvard on icosahedral bond orientational order in supercooled liquids, he was looking at forbidden symmetries in crystals with collaborator Dov Levine. By 1984, Steinhardt had shifted from the University of Pennsylvania to IBM in Yorktown Heights, NY, in order to encourage scientists to look for such materials in the laboratory.</p> <p>When Nelson visited him at IBM, Steinhardt saw a preprint of Shechtman’s work. “He did not know that Dov and I had been working on the quasicrystal idea. But when I turned to the page with the diffraction pattern, I jumped up, went over to the desk, and brought David back an image showing the diffraction pattern we had computed for an icosahedral quasicrystal. The two matched,” Steinhardt wrote in an e-mail.</p> <p>Publishing in the same journal as Shechtman that year on Christmas Eve, he and Levine also coined a word that stuck.</p> <p> </p> <p style="margin-left:14.15pt;">A quasicrystal is the natural extension of the notion of a crystal to structures with quasiperiodic, rather than periodic, translational order. We classify two- and three-dimensional quasicrystals by their symmetry under rotation and show that many disallowed crystal symmetries are allowed quasicrystal symmetries….</p> <p> </p> <p>Steinhardt has been championing quasicrystals ever since.</p> <p>In these three decades, hundreds of quasicrystals have been reported and confirmed. Researchers reinterpreted their past experimental results to find quasicrystals even before that date. They are no longer considered unique and are ubiquitous among certain metal alloys. But there was still one nagging issue: all the quasicrystal structures reported so far had been produced in the laboratory.</p> <p>Thinking in terms of principles, as is the wont of a theorist, Steinhardt could see no reason why quasicrystals would not exist, or even be abundant, in nature. “The theoretical view was that these were as robust as crystals,” he said. “Even being energetically favoured compared to crystals under some circumstances.”</p> <p>But when he put forward this idea, people would say, “Gee, so why hasn’t a natural quasicrystal been found?” and Steinhardt would respond that it hadn’t yet, “but I’m looking.” Therein lay the reason why he was so ecstatic that New Year’s morning in 2009. The elation, though, was short-lived.</p> <p> </p> <p>IT WAS CLEAR THAT THE FLORENCE SAMPLE was a quasicrystal, but was it a natural quasicrystal? What was its provenance? It was, after all, just a few micron-sized grains from a collection in Italy. Wasn’t it possible that it was an industrial by-product like slag?</p> <p>In fact, the grains were enveloped in carbonaceous chondrites, rock material that was thought to be from the very old, carbon-rich meteors. Steinhardt and Bindi took the sample to meteor expert Glenn McPherson at the Smithsonian.</p> <p>McPherson, who had been expecting them, met them at his door. He was deeply sceptical, and said if it was a meteorite, it was unlike any other he had seen.</p>  <p>Other experts were sceptical as well—it was merely a label that said the Florence sample was from a remote part of Siberia. Even if it had been found in Siberia, it wouldn’t be a clincher for geologists who had seen many false claims in the past.</p> <p>Such scepticism feeds into a shadowy market for meteorites that is both unregulated and rather lucrative. A cursory check on eBay on 29 April this year showed the bidding price for an “Apollo 11 meteorite” at $4.5 million. For fragments of the Chelyabinsk meteorite that crashed into Siberia in February, classifieds on a Russian website were asking for as much as $10,000, according to news reports.</p> <p>“When I first read this account I thought, wow, maybe this is a hoax,” said Ebel Denton, curator of the hall of meteorites at the American Museum of Natural History in New York, referring to Bindi’s original paper in 2009. “Maybe someone made this material in a lab and put it out in the middle of Siberia.”</p> <p>What Denton did agree with is that it is a strange rock indeed. Not only for the quasicrystal structure, but for the grains’ mineral composition: Al63Cu24Fe13. In other words, it contains 63 parts aluminium to every 24 parts copper and 13 parts iron: icosahedrite.</p> <p>Iron is about 2,000 times more abundant than copper, and yet there is more copper in this rock than iron. Copper and aluminium have also never been found combined together in a meteorite before, a fact that’s been explained by the very different geochemical behaviour of the two elements—that aluminium condenses at much higher temperatures than copper.</p> <p>Denton now seems convinced the Florence sample is a natural quasicrystal, but he still doesn’t know what to make of it. “I don’t know what the deal is with this rock,” he said. “It would be nice if there other rocks like it. There are probably in the order of 20,000 meteorites studied by humans over time, and no one has ever found anything like this.”</p> <p>In 2009, when the tests had whittled away the micron-sized quasicrystal grains, the urgency to get more of this material and to discover its provenance was even more palpable. But where would one look?</p> <p>Khatyrkite, the mineral in which the quasicrystal grain was embedded, got its name in 1985 from a paper by LV Razin, NS Rudashevskij, and LN Vyalsov. The <em>American Minerologist</em> has the Russian translation of the long title as, “New natural intermetallic compounds of aluminium, copper and zinc—khatyrkite CuAl, cupalite CuAl and zine aluminides—from hyperbasites of dunite-harzburgite formation.”</p> <p> </p> <p style="margin-left:14.15pt;">The minerals occur in black slick washed from greenish-gray cover weathering from serpentinite, Listvenitovij stream, Khatirskij Ultrabasic zone of the Koriakskho-Kamchatskaya fold area, eastern USSR (Koriakskhiye Mts.). They are intimately intergrown, forming small (up to 1.5 mm) irregular, angular, metallic, steel gray-yellow grains, similar to native Pt. Type material is preserved at the Mining Museum of the Leningrad Mining Institute, Leningrad, USSR.</p> <p style="margin-left:17.0pt;"> </p> <p>It was confirmation that the mineral associated with the Florence sample was also found in a stream in the Koryaks, but it was still only circumstantial proof—just as finding a sample of quartz certainly did not imply that it had to be from the same place where another sample of quartz had been discovered.</p> <p>Yet, there was the Koryak label. Steinhardt and Bindi needed to find this man LV Razin. With the help of friends in Russia, they did.</p> <p>Razin was in Israel, but was uncooperative. He asked for $15,000 just to speak to them. People said he had been a KGB agent, smuggling platinum out of the former U.S.S.R. In short, he was a man you couldn’t trust, and phone conversations, as Steinhardt soon found out, were futile.</p> <p>As the scientists looked into the original Razin paper, and followed many false leads, another mysterious figure emerged. His name was VV Kryachko, and it seemed he had found the original Khatyrkite sample. In the original paper “it is kind of an obscure sentence”, Steinhardt said. “There is this guy, VV Kryachko, and he is washing clay in the stream, and somehow he found this material. And it never mentions him again.”</p> <p>So they asked people in the Russian Academy of Sciences: who was this guy? According to Steinhardt, some thought he was a fictional character created by Razin to cover up his tracks while he was prospecting for platinum. But the team was desperate, so they asked again, and got the encouraging response that he was a real person but that he had died. Another time, the response was even more dramatic: he was a local Chukchi who had wandered off into the wilderness.</p> <p>After some scrounging, the researchers found a paper from the mid-1990s that carried the same name, VV Kryachko. On the phone with his co-author from Russia, Steinhardt was told that “Valery” was very much a real person. In fact, he was the doctoral student of the person on the other side of the call, Vadim Dissler. “And furthermore,” the voice on the other end said, “he is coming to town with me. Do you want to talk to him?”</p> <p> </p> <p>ON STEINHARDT'S WEBSITE there is a photograph of three men in khakhi. To the left is Luca Bindi, rugged and smiling, to the right, Paul Steinhardt, more restrained, and in the middle, a compact man with white stubble and knotted eyes.</p> <p>Valery Kryachko, who might have held the first known natural quasicrystal in his hands three years before Dan Shechtman peered into his microscope for a glimpse of one, works in the private mining sector in a town south of Moscow. Valery is over sixty and doesn’t speak English, only Russian. Steinhardt described him as warm, keenly interested in science, but not an academic in the usual sense.</p> <p>As Steinhardt exchanged e-mails with Valery, using Google to translate, it seemed to confirm that the sample was indeed natural. Meanwhile, the case against slag was also building. Around the summer of 2010, Bindi found stishovite inside their sample. Stishovite is silicon dioxide—quartz and sand. It needs extreme atmospheric pressure to form. Embedded inside the stishovite was the quasicrystal grain. It would be next to impossible to artificially recreate the conditions necessary to produce such a sample as such atmospheric pressures only exist deep within the Earth’s core or in cataclysmic processes in outer space.</p> <p>By the time of this second confirmation, Valery had already offered to guide a contingent to the source of the quasicrystals, which he fortuitously still remembered—a stream in the Koryaks. In October that year, Steinhardt decided to take him up on the offer.</p>  <p>Who would fund such a trip? It cost in the order of $150,000. Federal grants were out of the question and organisations like National Geographic and the American Museum of Natural History had their own agenda. To make matters worse, Princeton was in the middle of a fund-raising drive and forbade Steinhardt from approaching any donors associated with it. Steinhardt asked his contacts to ask their contacts and pass it forward. Finally, a donor, who Steinhardt preferred to remain anonymous, agreed to take care of the funding.</p> <p>After assembling a 15-person team including Italian, Russian, and American researchers, organising a meet-up in Princeton to see if the team clicked, wading through a morass of paperwork for a journey to the Autonomous Okrug of Chukotka, they were finally ready to hunt for quasicrystal grains.</p> <p> </p> <p>NEITHER STEINHARDT NOR BINDI know where to begin to describe their trip to the stream and back. They recall eating mushrooms and enormous salmons plucked from the stream, firing Kalashnikovs on vodka bottles, hearing tales of bears (“The claim was if you walked in groups of three or more they wouldn’t bother you”) dealing with regular engine trouble and working in an exotic land.</p> <p>Listening to Steinhardt at 1 a.m. with an undercurrent of thrill in his voice at the recollection, it doesn’t feel right to attempt to parse in data points what this journey meant to him or Bindi.</p> <p>But had they found the quasicrystal sample? When would they know?</p> <p>Bindi, who “has the best eyes” spotted what he thought was a quasicrystal grain the very first day at the stream. A few days later, they began to find grains with faces apparently the shape of a decahedron, which caused some excitement. The form suggested it was a quasicrystal with ten-fold symmetry, but as Steinhardt tells it, it turned out to be pyrite—Fool’s Gold.</p> <p>After gathering enough material, the expedition party moved back to Anadyr, the easternmost town in Russia and had a closeout scientific meeting to get everyone on the same page. At the end, only Bindi believed that they had more than a one per cent chance of finding something, because he had liked that grain on the first day.</p> <p>As it turns out, they did find grains that were quasicrystalline, but they didn’t know it until Bindi confirmed it in his lab weeks later in August.</p> <p>“That was an amazing moment,” Steinhardt said, “because this was a wild goose chase and suddenly we had the wild goose.”</p> <p>The 120 grains are dispersed among labs in Princeton, Caltech, the Smithsonian, Italy, and Russia. Of these, nine have been confirmed to be quasicrystalline. The story of those grains is both grand and mysterious.</p> <p>The grains were forged in our solar nebula 4.5 billion years ago, around the time the earth itself was new-born, through the process that is yet not known. They were attached to a meteorite that crashed to earth some 15,000 years ago.</p> <p>If this mineral with forbidden symmetry was present at the birth of the solar system, what else are we missing? How abundant are quasicrystals in the galaxy?</p> <p>Pulling on one loose end of solid-state physics had led to new geology and minerology, which led to meteorites and the formation of the solar system. It led to the first natural quasicrystal, icosahedrite, and the extra-terrestrial body hosting it—khatyrka. Now, in yet-to-be published results, the researchers are looking at other meteorites to understand how to look for related metallic phases (not necessarily quasicrystals) and the formation of planets.</p> <p> </p> <p>STEINHARDT WOULDN'T SAY MORE, but Bindi wrote me an email: “I am recently reading a lot about the possible mineralogy of other planets of our Solar System. Who knows? Maybe there could be a planet where quasicrystals are more common than ordinary crystals.”</p> <p> </p> <div> <strong><em>Corrections</em></strong></div> <div> <em>The following changes were made to the article after errors were pointed out by one of the scientists involved in the project.</em></div> <div>  </div> <div> <em>i) An earlier version of this article incorrectly identified Linus Pauling as the head of Shechtman’s laboratory. That has now been rectified.</em></div> <p><em>ii) An earlier version of this article omitted the names of Shechtman’s collaborators in his Physical Review Letters paper. The names Ilan Blech, Denis Gratias and John Cahn have now been added.</em></p></div> </div> <div class="views-field-phpcode"> <span class="field-content"><div class="shortbioview"></div></span> </div> </div> </div> </div> </div></div><div class="detail-body"><div class="detailBody"><div id="paging-pager-4008" class="paging-pager-contents"><div class="dropcap"> <p>Paul Steinhardt sat riveted to his seat as the driver, Victor, steered the double-track vehicle from side to side, dodging hazards every few feet. It was July 2011, and the 58-year-old physicist found himself in Chukotka, a region in Far Eastern Russia where the moon rises to white midnights framed against the smoky Koryak Mountains. He had never been camping, but was now leading a geological expedition deep into the Russian tundra, a land fractured from the Alaskan mass and inhabited by bears, against which the expedition team carried modified Kalashnikovs to defend themselves. There were no roads, and on occasion the vehicles, called snow-cats—rectangular boxes painted bright orange and blue-grey that trundled along at a top speed of 15 km per hour—would have to cross entire water bodies on a hope and a prayer.</p> </div> <p>Steinhardt was headed to a stream 230 km to the south-west of Anadyr, the capital of Chukotka, searching for fragments of a meteorite unlike any known before. Embedded in the rock could be a form of matter called quasicrystals that had never before been found in nature.</p> <p>Quasicrystals riff on something as basic as the way atoms (or molecules, or ions) are arranged in materials. When they were first synthesised in a lab in 1982, they overthrew 200 years of scientific dogma about the laws of matter. They form a bridge between ‘true’ crystals like salt and gold, and amorphous, disordered materials like glass, which were the only categories of solid material previously thought to exist.</p> <p>Quasicrystals changed the very definition of crystals and the assumptions of crystallography—the science used to study the arrangement of atoms in solids. Their discovery allowed materials researchers to play with an infinite new range of atomic structures. The internal structure, in turn, creates the solid’s unique properties. Practical applications for quasicrystals have already been found, such as in the strengthening of steel, and the unique way they interact with light has led to several patents.</p> <p>Steinhardt had been at the forefront of quasicrystal research—the word ‘quasicrystal’ itself came from a paper he co-authored in 1984. Initially met with scepticism and ridicule, hundreds of quasicrystals had since been found. (They are rather common in certain aluminium metallic phases.) But quasicrystals had only been artificially made in the laboratory, and were therefore thought not to be an important building blocks of the material universe. The primary goal of the Russian expedition was to show beyond a shred of doubt that quasicrystals could form in nature. This would move science one step closer to showing that quasicrystals were as robust (and perhaps as universal) a form of matter as crystals.</p> <p>After a “four-day rollercoaster ride”, as Steinhardt would later call it, the expedition arrived at the Listvenitovyi stream. The excavation team began panning for quasicrystal candidates, separating rock and other minerals from clay for a kilometre along the stream. An analysis team then sifted through the panned material, looking for minute grains in what had originally been a tonne of sediment. If indeed they found natural quasicrystals, it would rewrite mineralogy textbooks and open new directions for material science.</p> <p> </p> <p>BLAME THE OMNIVOROUS READING HABITS of an Italian geologist for starting it all. In 2007, Luca Bindi was a curator at the Università degli Studi di Firenze who was interested in incommensurate structures—in which, like quasicrystals, atomic clusters don’t repeat regularly or are aperiodic—in minerals.</p> <p>His curiosity led him to a 2001 paper in <em>Physical Review Letters</em>—not a staple journal for the earth sciences—by Peter J Lu at Harvard and Paul Steinhardt and Nan Yao at Princeton.</p> <p>It discussed a method to find and index new solids called “quasicrystals” based on their X-ray diffraction patterns. The analysis had found 50 promising mineral candidates, but no clincher.</p> <p>Bindi had never worked with this form of aperiodic structure before. Nevertheless, as he scanned the list of candidates, he saw three minerals he was familiar with: aktashite, gratonite, and tantalite.</p> <p>“I was shocked to see them in this list,” he recalled. “Could they exhibit a quasicrystalline structure?”</p> <p>Bindi knew quasicrystals were important. Finding a natural quasicrystal, for one, would revolutionize the way minerals were conventionally classified—because all known minerals were either crystalline or amorphous, rather than quasicrystalline in structure. At the end of the paper, a line caught his eye: “We are interested in collaborating in exploring the leading candidates, only some of which have been given in Table I. Those interested are encouraged to contact P. J. L. and P. J. S.”</p> <p>Bindi had a hunch that the minerals were among the collections of the Natural History Museum of the Università degli Studi di Firenze that he knew so well. Bindi ran to check out the database for the 50,000-specimen mineralogical collection at the museum. “They were there!” he later wrote to me in an e-mail. So he decided to contact Lu and Steinhardt.</p> <p>In October 2007, when Steinhardt received an e-mail from Bindi offering collaboration, the search for natural quasicrystals was in a slow phase. Steinhardt, who was known as a cosmologist for his work on inflationary models of the universe, tinkered around with several projects at once, including solid-state physics of which the quasicrystal hunt was a part. He had then been toying with the idea of compiling a catalogue for meteorites similar to the catalogue for terrestrial minerals compiled by the International Centre for Diffraction Data, which he had unsuccessfully used in the 2001 paper. Steinhardt had a hunch quasicrystals could be found in meteorites and a database would facilitate the search.</p> <p>Steinhardt didn’t know much about the Italian museum, but Bindi seemed enthusiastic, so the Princeton collaborators gave him a list of minerals that seemed promising but hadn’t yet been checked. Out of this list, Bindi thought he could procure about half a dozen.</p> <p>The laborious process of slicing the mineral, preparing the sample, and observing its powder pattern to check whether it was a good candidate or not took about a month. The researchers tested six samples in all. Nothing worked.</p> <p>“It was failure after failure after failure,” Steinhardt recalled. “We thought we’ll write a paper saying that we tried six more and they failed.”</p> <p>The idea was to update the 2001 paper, create some noise, and get more people interested. “Luca was pressing to write-write-write,” Steinhardt told me. “I was like, hmmnn, I don’t know.”</p> <p>The lull might have been fortuitous. Bindi decided to take a fresh approach to the problem. Rather than simply cross off the minerals he had been sent by Steinhardt, he put down a list of known synthetic quasicrystals and stared hard. Did these compounds show anything in common? The answer soon popped up: all the quasicrystals had metallic aluminium, and often copper, in their formula.</p> </div></div><div class="shortbioview"></div><div class="paging"><div class="links"><div class="go-to-page">Go to Page: </div><div class="item-list"><ul class="pager"><li class="pager-current first">1</li> <li class="pager-item"><a href="/web/20150930052107/http://www.caravanmagazine.in/periscope/forbidden-symmetry?page=0,1" title="Go to page 2" class="active">2</a></li> <li class="pager-item"><a href="/web/20150930052107/http://www.caravanmagazine.in/periscope/forbidden-symmetry?page=0,2" title="Go to page 3" class="active">3</a></li> <li class="pager-item"><a href="/web/20150930052107/http://www.caravanmagazine.in/periscope/forbidden-symmetry?page=0,3" title="Go to page 4" class="active">4</a></li> <li class="pager-next"><a href="/web/20150930052107/http://www.caravanmagazine.in/periscope/forbidden-symmetry?page=0,1" title="Go to next page" class="active">next ›</a></li> 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