In the early 1980s, physicists and crystallographers were astounded by the discovery of a new phase of matter. The term quasicrystal was coined by Paul Steinhardt and Dov Levine when they presented the first theoretical demonstration that the unusual symmetries of this phase could be realized in perfectly ordered atomic structures.
A quasicrystal is a material that exhibits internal symmetries incompatible with a regularly repeating pattern. The most interesting examples are metallic alloys that have the symmetry of a stack of regular decagons or an icosahedron. In both cases, the baffling nature of their atomic structure is revealed by X-ray diffraction experiments that show tenfold symmetric rings of bright spots with resolution-limited widths. The narrow peaks indicate that the atoms are arranged in a highly ordered way, but it is mathematically impossible to create a crystal that has an axis of tenfold symmetry. Crystallographers, mineralogists, and physicists long thought that real materials could never exhibit sharp peaks and a tenfold symmetry together.
That changed in the early 1980s. In experiments on a rapidly cooled metallic alloy, Dan Shechtman discovered the first material known to exhibit a diffraction pattern with icosahedral symmetry.1 At roughly the same time, Steinhardt and Levine showed theoretically that a certain pattern formed from two shapes could be a template for an icosahedral atomic structure.2 The pattern was inspired by the two-dimensional Penrose tiling discovered in the early 1970s by Roger Penrose.3 Considered an intriguing curiosity at the time, certain mathematical properties of Penrose tilings showed that a quasicrystalline arrangement of atoms is geometrically possible and could in principle be the lowest energy state of a system. Computer simulations undertaken by Levine and Steinhardt established the plausibility of a stable phase, and their diffraction pattern calculations closely matched the experimental images obtained by Shechtman.
In the late 1980s and throughout the 1990s, the unexpected fabrication of new quasicrystalline alloys set off an explosion of both experimental and theoretical research. These unusual alloys also had some practical applications, though none has yet provided a qualitative breakthrough on a critical engineering problem. A particularly important finding was the discovery of an icosahedral alloy of aluminum, copper, and iron that showed a degree of order comparable to that found in high-quality crystals.4 An intriguing lesson from this period was that quasicrystals may not be as difficult to produce as previously thought.
In the 2000s, much of the activity at conferences on quasicrystals turned toward other types of material. Computer simulations of collections of particles of various shapes or point particles with specially designed interactions showed that quasicrystal phases might spontaneously form in engineered systems with micron-scale constituents, and 3D printing techniques enabled the direct fabrication of quasicrystalline metamaterials with novel optical properties. At the same time, Steinhardt was pursuing a line of research with the goal of determining whether quasicrystals formed in nature, outside the lab.
In The Second Kind of Impossible, Steinhardt recounts a highly entertaining and personal tale of scientific discovery. The book tells the story of his first encounters with quasicrystals and a subsequent decades-long search for a naturally formed example. The science itself is explained in accessible terms, and the insights into the dreams, motivations, disappointments, hard choices, and perseverance required to support that science are welcome additions.
The book opens with an anecdote that explains the title. “Impossible!” turns out to be a term Richard Feynman used to express amazement rather than disbelief. To elicit an “Impossible!” from Feynman, one had to clearly and convincingly show that a commonly held belief or common-sense prediction is wrong. This is to be distinguished from the first kind of impossible, which applies to violations of such solidly established principles as the law of energy conservation. “[S]ometimes,” Steinhardt writes, “an idea is judged to be ‘impossible’ based on assumptions that could be violated under certain circumstances that have never been considered before. I call that the second kind of impossible.”5
Steinhardt begins the story of quasicrystals with an account of the emergence of ordinary crystallography as a scientific discipline in the nineteenth century. “Crystallography’s success,” he observes, “in explaining so many different properties of matter relevant to so many different disciplines has long been considered one of the great triumphs of nineteenth-century science.”6 While studying the way atoms arrange themselves as a liquid is cooled, Steinhardt becomes interested in the possibility that the icosahedral symmetry seen in small clusters of atoms might somehow be extended to larger-length scales. That starts him on a path that leads to a sequence of three wonderfully exciting discoveries. First comes the fundamental breakthrough with Levine that reveals the mathematical possibility of an icosahedral quasicrystal, along with the surprising news of Shechtman’s discovery of the first real sample. This is followed by a period of refinement and hard work to rule out more mundane explanations of various experimental results. Beyond the lesson in the science of quasicrystals, the reader will gain an appreciation for the fact that the excitement of the initial discovery is not quite enough; sound scientific conclusions require the subsequent exploration of a range of issues that simultaneously strengthen the original results and bring into focus the most fruitful lines of research.
The search for a natural quasicrystal brings in a new cast of characters from the world of mineralogy and geology. Guided by Steinhardt’s ideas about how to search through archived data sets, Luca Bindi, a central figure in the rest of the book, locates a micro-grain of metallic material on a mineral sample of unknown origin. This appears to be a real breakthrough, but Steinhardt insists on rock-solid support for such an extraordinary claim. The story of the work required to identify the geographic origin of the sample and confirm that it is natural makes for great reading. Steinhardt and Bindi grapple with characters one does not typically encounter while doing modern science, from mineral dealers to a recalcitrant museum curator in St. Petersburg to an unsavory Russian expat seeking money for questionable information. The sample’s origin in a riverbed in Kamchatka is eventually established, and this part of the narrative culminates in the official designation of icosahedrite as a new mineral in 2010. The grain of icosahedrite was created in a meteor millions of years before it crashed to earth, and the sample containing the micro-grain is shown to contain several other metallic phases that came as complete surprises to geologists. Steinhardt guides the reader through the arguments and counterarguments raised by geologists, deftly explaining aspects of mineralogy that are not common knowledge in the quasicrystal research or mainstream physics communities.
The discovery of a natural quasicrystal surprised quasicrystal researchers. This was not a case of a community pursuing multiple strategies to achieve a common goal. One group had pursued a long shot. The fact that icosahedrite was the same Al–Cu–Fe alloy that was fabricated in the late 1980s made the discovery plausible, though very few quasicrystal researchers would have understood the extent to which the find was baffling to geologists. The discovery established the stability of the material on a timescale of millions of years, while the mineral sample itself contained important clues to the physics of quasicrystal formation.
In describing an expedition to Kamchatka, the focus shifts from scientific issues to the managerial problems associated with fieldwork, with much about the rigors and dangers of travel in the Kamchatka Peninsula, as well as reflections on the personal qualities of his companions on the expedition. There is a happy ending. The samples are found, and there are new discoveries to be made both in quasicrystal physics and in geology and planetary science.
One of the most important aspects of the book concerns Steinhardt’s application and reflections on his own scientific method. He repeatedly emphasizes the importance of reaching out to collaborators with different areas of expertise and different skill sets, and the need to confront alternative explanations that challenge preconceptions. Steinhardt insisted, for example, that his research group include a red team of highly skeptical experts prepared to present the most compelling arguments against the hoped-for interpretations regarding the origins of Bindi’s micro-grain of icosahedrite.
Other elements essential to the story lie outside the typical repertoire of science books written for a general audience. While many authors strive to convey a sense of excitement about their work and may even mention the sense of euphoria that can be achieved, few include descriptions of the frustrating delays, the uncertainty and difficulty of challenging the experts, the fear of being proved wrong, or the unfulfilling prospect of jumping to a hasty conclusion that happens to be correct but is not truly justified. Steinhardt describes his emotional ups and downs as he faced all of these possibilities. “No one was less suited to take part in, much less lead, an expedition to the remote regions of Far Eastern Russia,” he recalls. “Yet here I was.”7 His most heartfelt writing is reserved for the friendship he developed with Bindi and the deepening of his relationship with his son. The writing is not florid or poetic, and there is the occasional awkward description of an imagined scene involving a historical figure, but there is something fitting about the consistency in tone of Steinhardt’s writing about human nature and his scientific explanations.
This is a highly readable book. Experts and nonexperts alike will delight in the twists and turns that take us from computer simulations and abstract ideas about icosahedral order to the wilds of the Kamchatka tundra. It is an amazing scientific path that would appear entirely implausible, but Steinhardt can describe it in a perfectly believable way—aided of course by the fact that it actually happened.
