Forbidden Matter - The Incredible Story of the Discovery of Quasicrystals
A New Addition to Wiser Tomorrow
Hello, my name is Tyler Gleckler, and welcome to the Wiser Tomorrow Podcast. Today I’m introducing a new narrative series covering a wide range of topics, from the history of science, to recent archeological discoveries. This won’t be replacing my regular conversations, but instead will allow me an avenue to cover more specific topics, in more detail, and in an organized fashion. I’ll also be posting this series in written form, which you can find here on the Wiser Tomorrow Substack. I’ve been very excited to introduce this format to the Wiser Tomorrow project, and look forward to hearing the response.
To kick off this series, I’m going to begin by sharing what I consider to be one of the most compelling stories of a groundbreaking scientific discovery in the last hundred years. This is the discovery of quasicrystals, for which the Nobel Prize in chemistry was awarded in 2011, and which fundamentally changed our most basic understanding of matter and the universe. This is a story that began centuries ago, and will likely continue on far into the future, and marks a significant advancement in the fields of chemistry and materials science. This is also a story of perseverance, highlighting the importance of thinking for yourself, and following evidence, not the crowd. So please, sit back, and let me take you through a fascinating part of scientific history, for which there are surely more surprises to come.
Unlike so many other great scientific discoveries which came about without one particular moment of revelation, the discovery of quasicrystals can be linked to a singular moment, like Archimedes in the bathtub. It begins with our main character, Dr. Dan Schedtman. Schechtman was born in Tel Aviv in 1941 and was interested in science from an early age, citing Jules Verne’s book “The Mysterious Island” as a key source of inspiration. He once stated, “The key figure in that book is Cyrus Smith - he’s an engineer and he could do everything, he could do anything, and I wanted to be like him”. His interest in science and engineering would continue into adulthood, leading him to study mechanical engineering at the Technion, the Israel Institute of Technology, in Haifa. His tenure in Haifa would continue through to this day, receiving his PhD in 1972, and beginning a long and fruitful career of research. And only after about 10 years following the completion of his doctorate, Schedtman would see the day of his most momentous discovery.
In 1982 Dr. Schedtman was on sabbatical in the United States at the National Bureau of Standards, now called the National Institute of Standards and Technology (NIST). Schedtman is a renowned expert in electron microscopy, a powerful scientific technique that uses a beam of accelerated electrons, rather than visible light, as a source of illumination. Because the wavelength of electrons can be several orders of magnitude shorter than that of visible light, electron microscopes allow scientists to resolve images of very small structures. Useful for many biological and inorganic samples, electron microscopes are among the most heavily employed tools by materials scientists, providing insight into the structure and composition of a wide range of different samples.
He was spending a rather routine morning working with one such electron microscope to study an alloy composed of Al and Mn, which had been rapidly cooled in an attempt to produce novel and potentially useful properties. With his extensive knowledge and keen eyes, Schedtman combed the images as he had so regularly done, but soon identified something that immediately struck him as strange. He came to view an area of the sample that displayed, to put it mildly, a rather unusual pattern.
As you’ve probably been told from an early age, matter can generally be categorized into three groups - solids, liquids, and gasses, leaving plasma aside. These three groups can be further subdivided to categorize specific types of each state of matter. In the case of solids, there are broadly two types: crystals and amorphous materials. The key difference between the two, is found in how the atoms are ordered. Amorphous materials have a randomly ordered molecular structure, with one of the best examples being plastic. The molecular structure of plastics have no repeating, predictable structure, and have an essentially random configuration. In contrast, crystals are materials with an ordered, periodic arrangement of atoms. The go-to example of a crystal is NaCl, or table salt, which is constructed of alternating ions of sodium and chlorine. Every NaCl crystal will follow the same pattern, and have a nearly identical structure.
These structural differences cause crystals and amorphous materials to generally have very different properties, making them useful for distinctly different applications. And these differences are not only between crystals and amorphous materials, but also between crystals with different crystal structures, or different ordered arrangements of atoms. Perhaps most interestingly, even between crystals composed of the same types of atoms, differences in crystal structures produce vastly different properties. One of the best examples of this are the allotropes of carbon, which is to say the different physical forms of carbon. Two familiar allotropes of carbon are graphite, which you’ll find at the tip of your pencil, and diamond, which you’ll find if you’re lucky. Graphite is soft and dark, while diamond is transparent and hard, and are therefore useful and valued for very different purposes. They are both made of carbon atoms, but have two completely different crystal structures, giving them two completely different sets of properties. To study, utilize, and engineer crystalline materials requires an understanding of the different types of crystal structures, and their basic properties.
One way to characterize crystalline materials, beloved by mathematicians, is to classify them by their different types of symmetries. For each pattern, you can find the transformations, including rotations, reflections, and translations, that will result in an identical structure, and there are simple geometric rules which govern the rules for compatible symmetries. Most important for our story, is a type of symmetry known as rotational symmetry. Rotational symmetry is the number of ways that the atoms in a solid can be rotated by a particular number of degrees, so that the resulting image is the same. Let’s take the example of 3-fold rotational symmetry. If something has 3-fold rotational symmetry, it can be rotated 3 times to produce an identical structure, and will then return to its original position. Think of rotating a triangle by 120 degrees; each time, the triangle will appear unchanged, and three rotations of 120 degrees will return the triangle to its starting position. There exists only a handful of rotational symmetries available for any arrangement, including one-, two-, three-, four-, or six-fold symmetry. For geometric reasons, five-fold symmetry was forbidden, as well as any symmetries above six.
What made the pattern identified by Schedtman appear so strange, is that it seemed to hold the forbidden 5-fold rotational symmetry, making it an impossible discovery. His response to what he saw was instant, and verbal: Eyn Chaya Kazo in Hebrew, or “there can be no such creature” in English. Schedtman himself couldn’t believe what he was seeing. As a seasoned scientist, he naturally proceeded to probe the sample further, taking it for another type of measurement using a technique called X-ray diffraction (XRD). XRD can be used to elucidate the crystallographic structure of a material, and is another critical tool in the belt of materials scientists, and one that could help him better understand what he was seeing. And similarly to his expertise with electron microscopy, Schedtman is also highly proficient with X-ray diffraction, giving him all the tools he needed to decipher this puzzle. Initially hoping to identify a simple mistake, or some form of illusion, the results of these measurements only caused more confusion.
The X-ray diffraction measurements still revealed the sample contained a pattern with 5-fold rotational symmetry. Dumbfounded, he continued to probe the sample to try and find an explanation for the impossible. To his increasing amazement, each experiment continued to suggest that this sample did in fact display 5-fold rotational symmetry, and that he had discovered something truly groundbreaking.
Schedtman’s analysis led him to conclude that his sample was not a regular crystal, but rather an entirely new type of material, now known as quasicrystals. As the name suggests, quasicrystals aren’t entirely different from ordinary crystalline materials, but do have several key differences. In quasicrystalline materials, the arrangement of atoms or molecules is ordered, but not periodic. This means that the atomic structures are arranged in a pattern where there are no gaps between the structures, but no pattern ever repeats. The constituent structures do repeat themselves throughout the larger pattern, but always in entirely different orientations.
Previously, it was assumed that all crystalline arrangements of atoms must have a pattern that repeats perfectly in all directions. Schedtman’s surprising symmetry appeared only in one direction, in which his X-ray diffraction data displayed spots arranged in concentric rings with 10 spots each. In other directions, the rings only contained 6 spots, typical of allowed six-fold symmetry. Overall, the symmetry of the pattern was exactly icosahedron, which was already well-known to researchers as a possible structure that readily occurs in tight-packed metal structures. However, it was also known that this symmetry was five-fold, which again was strictly forbidden for any periodic crystal.
While quasicrystalline materials were entirely unprecedented, quasiperiodic patterns were first developed centuries ago. The earliest known instance of quasiperiodic patterns are seen in the tile mosaics that are present at the Alhambra Palace in Spain, and the Darb–i Imam shrine in Iran. While it is unlikely that the people of the time were aware of the complex mathematics behind these patterns, they were likely aware that these patterns were different from the rest. Such techniques are estimated to have been developed between the 13th and 15th century, and were essentially forgotten by the world. These patterns are known as girih, consisting of polygon and star shapes, interlaced with zigzag lines. These girih were produced from permutations of only a handful of shapes ranging from pentagons to bow-ties, which has been confirmed by scrolls of the time that explain their methods, including such tiles that were likely used as conceptual building blocks.
From these early quasiperiodic patterns, the next major development in our understanding came through their rediscovery and elucidation of their underlying mathematics. This would happen in 1973, only about one decade before professor Schedtman’s discovery of quasicrystals, and is attributed to another scientific and intellectual giant: Sir Roger Penrose. Penrose identified what are now known as Penrose Tiles, which is a pattern that can be filled completely with only two types of rhombohedron. This is a whole story in itself, and there have been other science communicators who have done a wonderful job explaining this topic in more detail, and is beyond the scope of this episode. For the purposes of this story, what’s important to note is that Penrose’s work helped understand and express quasiperiodic patterns mathematically. However, there remained a question: could quasiperiodic patterns exist in the atomic structure of matter, either naturally or artificially? For many years, the consensus within the scientific community was a definitive no - until Dan Schedtman.
From the morning of Schedtman’s discovery, it would take another two years to fully decipher what he had just discovered, publishing his seminal paper in 1984. Five weeks later, another paper would be published by Levine and Steinhardt, who were the first to refer to this phenomenon as “quasicrystallinity”. And this delay was not only due to the difficulty of this work, but the enormous pushback that Schedtman received from the scientific community. For these two years, Schedtman found little solace with other researchers, many of which ridiculed him, and otherwise treated him like a fool for proposing something that was then considered so radical. Many scientists seemed to think that Schedtman had not been careful enough in his experiments, and one way or the other, he had made a mistake. And this didn’t just include the skeptical crystallographer from another corner of the globe, but the head of the very lab he then worked at.
Schedtman’s boss entered his office one day, and gently placed an X-ray diffraction textbook on his desk, stating “Danny, please read this book and you will understand that what you are saying cannot be.” Frustrated, Schedtman replied “I don’t need to read this book, I teach at the Technion, and I know this book, and I’m telling you my material is not in this book.”. After this initial gentle remark, only a few days later he would return to Schedtman, calling his presence in the group a disgrace, and expelling him.
Unbelievably, the criticism went beyond even the head of his own lab. One of the great chemists of the 20th century, Linus Pauling, one of the few people to ever win two Nobel Prizes, was among his biggest detractors. At a large scientific conference, Pauling claimed that Schedtman had indeed made a mistake, and proposed his own explanations for what he had reported. He even went as far as to state “Danny Schechtman is talking nonsense, there are no quasi-crystals, just quasi-scientists.” For a while, Pauling’s and others ideas were taken seriously as arguments against Schedtman’s discovery, but soon enough, scientists from around the world began to replicate Schedtman’s results, and Pauling's papers began to fail reaching the journals. Schedtman once said about Pauling, “...he was very insistent, was very sure of himself when he spoke; he was a flamboyant speaker.” Only a few years before his death, Pauling wrote a letter to Schedtman, saying “...may I propose to you to write the joint Schedtman-Pauling paper on quasi-periodic materials? And you will be first'', to which Schedtman responded, “...I’ll be delighted to write this paper with you, but before we even start we have to agree that quasi-periodic materials do exist”, to which Schedtman received a final letter saying “Well, that may be too early for that”, which would be their last correspondence.
In 1992, the International Union of Crystallography accepted that quasiperiodic materials must exist and altered the definition of what a crystal is from “a substance in which constituent atoms, molecules or ions are packed in a regularly ordered, repeating three-dimensional pattern” to “any solid having an essentially discrete diffraction diagram”. While finally vindicated and already receiving the fame and recognition for his discovery, it would be nearly two decades later that Schedtman would win the Nobel Prize.
In reference to Schedtman’s winning of the Nobel, the president of the Royal Society of Chemistry said that fundamental science is about breaking through boundaries of knowledge and sometimes that means pursuing an idea that others think is just too unbelievable to be true. “Dan Schedtman’s Nobel Prize celebrated not only a fascinating and beautiful scientific discovery, but also dogged determination against the close-minded ridicule of his peers, including leading scientists of the day. His prize didn’t just reward a difficult but worthy career in science; it put the huge importance and value of funding basic scientific research in the spotlight.”.
Today’s quasicrystals have found limited applications, with a few exceptions including as an additive to steel and in non-stick frying pans. But regardless of their minimal applications for the moment, the significance of their discovery, and the strangeness of their reality cannot be overstated. So much so, that scientists are still left with even the most fundamental of questions, including: how is it possible for quasicrystals to exist?
Schedtman’s discovery was one of great significance for our understanding of matter and the universe, and is an incredibly human story. However, this story begins far before Schedtman’s discovery in the lab, and continues on to this day. From the initial discovery of quasiperiodic patterns in the ancient Middle East, to their artificial creation in matter, our story has a final chapter that began only recently - the discovery of quasicrystals in nature.
Another giant of science, and major contributor towards the understanding of quasicrystals, is the aforementioned theoretical physicist, Paul Steinhardt. From as early as the 1970s, Steinhardt was developing a theory created with the help of a doctoral student named Dov Levine. Their theory predicted the possibility of quasicrystals, with symmetries that were determined to be theoretically possible, but extraordinarily unlikely. Steinhardt had imagined that crystals with five-fold symmetry might be possible, if on cooling, atoms were arranged into a network of icosahedra. Sound familiar? While Schedtman beat them to the punch, this was not the end of Steinhardt’s quest to better understand quasiperiodic materials. With artificial quasicrystals soon being discovered in many types of materials, Steinhardt shifted his focus to the possibility of naturally occurring quasicrystals.
Steinhardt and his team began by trying to identify quasicrystals in mineral samples across museums from around the world. For almost a decade, their search was without success, until yet another fateful day. Receiving what probably felt like their millionth mineral sample, this time from the Museum of Natural History in Florence, Italy, they again studied their sample. To their amazement, they had finally found their quasicrystal. The problem, however, was that the origins of this sample were unknown, starting an entirely new chapter of their quest. While another incredible story in itself, ultimately the team determined that the sample most likely came from the far East of Russia, on the volcanic Kamchatka Peninsula. With only one way to find out, the team embarked on a journey to this location in search of confirmation of their hypothesis. Professor Steinhardt published a book on this journey titled “The Second Kind of Impossible”, which I highly recommend, and hope to discuss with him at some point on the podcast. But for now, this is where our tale ends.
The story of the discovery of quasicrystals is one of overcoming challenges, connection through time, and exemplifies scientific principles and thinking. Beginning centuries ago, and continuing on even today, quasicrystals highlight the fact that science is a never-ending and constantly evolving process, with dogma plaguing even the best and brightest of humanity. Offering potential to change our world through new and revolutionary technologies, these discoveries also offer beauty by enriching our understanding of reality, and providing another avenue for thought and invention.
This has been the Wiser Tomorrow Podcast, I’m Tyler Gleckler, and thank you for reading.