With Shechtman’s encouragement, Blech proposed a model based on a series of assumptions. First, he assumed that the aluminum and manganese atoms would somehow group together in identical icosahedral clusters. Then, he assumed the icosahedral clusters were thrown together in a random arrangement as the aluminum-manganese liquid cooled and solidified. He further assumed that all the clusters would somehow arrange themselves with the same orientation throughout the solid. That idea was equivalent to assuming one could randomly throw dozens of icosahedron-shape dice from the Dungeons & Dragons game into a bowl and have them land miraculously such that their points are all aligned in the same directions. The model was based on a stack of assumptions, some of which seemed unlikely to occur in real matter.
The figures below summarize the idea. The figure on the top shows a pair of adjoining icosahedrons with their points aligned. The figure on the bottom is a rough representation of how the random structure would appear.
The drawing reveals the presence of large empty spaces between the icosahedrons when many are packed together according to Blech’s ideas. Dov and I had encountered the same problem when we had tried to build clusters out of Styrofoam balls and pipe cleaners. We already knew that empty gaps were a big problem because they would not remain empty. There would be no way to stop atoms from moving in to fill gaps as a liquid cooled. And once they did so, the atoms would exert enormous pressure on the icosahedral clusters and would break up their delicate arrangement. That was one of the reasons Dov and I eventually abandoned the idea of using icosahedral clusters as building blocks. Our quasicrystal model uses rhombohedrons, which can pack together without any gaps.
Blech then made another crude approximation. Since he had no specific idea about how atoms might fill the empty spaces, he could only approximate the diffraction pattern that would be created by atoms composing the icosahedral clusters. Without real justification, he did not include the contribution from any of the gap-filling atoms. Shechtman and Blech were impressed that the diffraction pattern was qualitatively similar to the one Shechtman had observed for Al6Mn under the electron microscope.
But there was a problem with that calculation, as well. Unlike our quasicrystal theory, the Shechtman-Blech model was not quasiperiodic. They assumed the arrangement of icosahedral clusters was random. But a random collection of icosahedron-shaped clusters could not possibly produce true pinpoint diffraction. It was unclear at the time whether the Al6Mn grains Shechtman had observed exhibited true pinpoint diffraction or not. So Shechtman and Blech chose to ignore that issue.
Instead, they wrote a paper describing Shechtman’s experimental results along with their explanation, the Shechtman-Blech model, and submitted it to the Journal of Applied Physics in the spring of 1984.
The paper was immediately rejected. The editor did not find either the experimental results or the theory compelling, and did not proceed with the next round of review, which would have involved circulating it among other scientists for comment.
Dov and I had not published anything yet. So Shechtman and Blech were completely unaware of our work. They had no idea that Dov and I had a fully developed theory that avoided all of the flaws of their model, or that our work could potentially explain the strange Al6Mn sample. Conversely, since Shechtman and Blech’s paper had been rejected before being circulated for peer review, Dov and I had no knowledge about the contents of Shechtman’s laboratory notebook.
If there had ever been any exchange between our two teams there is a good chance we would have joined forces and presented the theory and experiment together.
But history unfolded somewhat differently.
FIVE
* * *
SOMETHING EXCITING TO SHOW YOU
Most scientific breakthroughs are recognized slowly, like viewing a ship gradually emerging from a thick fog. But the discovery that quasicrystals are a reality, and not just a hypothetical idea, happened in a flash. I was fortunate enough to be there when it happened, and it was an unforgettable experience.
* * *
YORKTOWN HEIGHTS, NEW YORK, OCTOBER 10, 1984: It began as a fairly unremarkable autumn day. I was on a leave from the University of Pennsylvania and spending a few months at the IBM Thomas J. Watson Research Center, just north of New York City. I was hoping to work with other scientists at the lab to create the world’s first synthetic quasicrystal.
Harvard physicist David Nelson, my former collaborator, was giving a seminar at the Center that afternoon and planned to stop by my office for a brief visit. Dov would be there too, because we planned to surprise David. I was anxious to share our work on the wild idea for a new form of matter that had grown out of the earlier work we had done together on rapidly cooled liquids.
David and I had not seen each other for several years and greeted each other warmly. He had the same clean-cut, boyish looks set off by wire-rim glasses that I remembered. I had been looking forward to the meeting because I knew he would appreciate what Dov and I had to show him.
Dov and I had applied for a patent about our idea the previous year, but we had not distributed the disclosure to other scientists. Lawyers at the University of Pennsylvania had recently concluded that, although our idea was “an important discovery . . . novel and unobvious . . . the utility of the discovery is still speculative.” For similar reasons, we had not yet submitted our quasicrystal theory to a scientific journal. It was clear that we needed experimental proof to back up our “speculative” claims before we could publish our idea. So when David arrived and sat down to talk, he knew nothing about our work.
I began by telling him that Dov and I had something exciting to show him. But before I could say another word, David interrupted to say that he had something exciting to show me. We all laughed, and agreed the guest should be allowed to go first.
David reached into his briefcase and pulled out a “preprint,” which is a typed version of a scientific paper submitted to a professional journal for rigorous peer review before being accepted for publication. It was common practice then, as now, to share and discuss preprints. But circulation methods were much less efficient pre-Internet.
The paper had been submitted by the team of Dan Shechtman, Ilan Blech, Denis Gratias, and John Cahn.
I was immediately stunned by the title: “Metallic Phase with Long-Range Orientational Order and No Translational Symmetry.” Wait a minute, I thought. No Translational Symmetry? That suggested that the atoms in their material were randomly distributed. Orientational Order? That suggested the interatomic bonds were aligned.
The title, and the fact that David was showing it to me, led me to believe that the paper must be related to the computer simulations we had performed three years earlier while testing his “cubatic” idea.
That must be why he is showing me the preprint, I thought. It appears to be experimental verification of our earlier findings.
I quickly scanned the summary abstract to see if my first impression was correct and suddenly felt myself becoming alarmed. The scientists were studying a strange new alloy of aluminum and manganese when they found . . . Oh my God! . . . “sharp diffraction spots arranged with icosahedral symmetry.”
I felt my pulse quicken. This was definitely not what David and I had been working on. This was more like the concept of quasiperiodic crystals that Dov and I had invented but not yet published.
Has this other team scooped us? I thought.
I raced through the rest of the abstract and was relieved to see the answer was no. There was no theoretical model included because, as I would later learn, the Shechtman-Blech model had been judged unconvincing. The paper was merely the announcement of experimental data, with no attempt at theoretical explanation. The years of work Dov and I had performed had not been duplicated.
With my competitive instincts safely assuaged, I began flipping through the rest of the preprint for more details. I caught my breath when I got to page 8, because I suddenly found myself staring at a very familiar diffraction pattern.
It matched the pattern Dov and I had predicted for a quasicrystal, with the tell-tale symmetry of an icosahedron. Impossible.
I felt my chest starting to pound and fireworks going off in my head. I immediately recognized what this meant.
Quasicrystals exist! Here is proof that the crazy idea Dov and I were pursuing was actually not so crazy!
I knew it was a singular moment. For however brief a time, I was the only person who had seen both the experimental pattern and the theoretical one. I was the only person on earth who knew for a fact that quasicrystals had just become a scientific reality.
I did my best to keep a blank expression on my face in order to preserve the moment and have a bit more time to savor the experience. After another moment, I jumped up from my chair, still without saying a word, and stepped across the office to pick up a single sheet of paper from my desk that I had prepared for the meeting. I continued to try to suppress the smile on my face as I slowly walked back to where David and Dov were sitting.
“Here, David,” I said as calmly as possible, “is the exciting thing we wanted to show you.”
In my right hand was the sheet I had just picked up on my desk, which showed the pattern of diffraction peaks that Dov and I had predicted for a quasicrystal. In my left hand, I held the preprint, turned to the page with the experimentally measured diffraction pattern.
The two patterns were a match.
Dov, already familiar with our work, reacted immediately. “Oh my God!”
I was not sure what David was thinking. But Dov and I had no doubt about what had just happened. Two scientific groups, working in laboratories only 150 miles apart and totally unaware of each other’s efforts, had managed to make completely independent and yet totally complementary breakthroughs.
Dov and I had invented a theory of quasicrystals, but we had no experimental proof. Shechtman’s paper had an experiment, but no theoretical explanation. Each group had separate pieces of the same puzzle. Together, it was a radical, and yet fundamental, discovery about nature.
David began asking questions about how we had predicted the snowflake diffraction image. Dov and I tried to answer his questions and explain our research in detail. But in truth, we could barely contain ourselves and were both sputtering with nearly uncontrollable excitement throughout the rest of the meeting.
Dov and I were elated because our theory could explain the seemingly impossible experimental result. But unfortunately, it also meant we had no time to celebrate. I told Dov that we had to drop everything else we were doing, and pull together all the results we had accumulated over the last three years. We needed to identify the most important points and write a short announcement paper for Physics Review Letters. Then, we needed to prepare a much longer paper with the full results.
I knew all of this could be accomplished quickly because we had already completed an enormous amount of research. It was just a matter of prioritizing the material and choosing which parts to present and in what order.
We began the Letters paper by introducing the concept of quasicrystals. We explained that they were new forms of matter with a quasiperiodic arrangement of atoms and a symmetry that was long thought to be impossible. We showed that solids with this property have electron diffraction patterns comprised entirely of sharp Bragg peaks. There were no fuzzy peaks, and no diffuse cloud connecting them. We explained our atomic building blocks, the rhombohedrons, along with the proposed matching rules we had invented that enabled the atoms to fit together in a quasiperiodic pattern. We also presented illustrations of the predicted diffraction patterns, the culmination of three years’ worth of theoretical research.
Then, we turned our attention to the Shechtman team’s results. Since their paper had not yet been reviewed or published, there was still a chance that their alloy might turn out to be something other than a quasicrystal. So Dov and I were conservative and did not claim an exact match:
We show that the recently observed electron diffraction pattern of an aluminum-manganese alloy is closely related to that of an icosahedral quasicrystal.
Less than three weeks after our fateful meeting with David Nelson, Dov and I submitted our paper presenting the theoretical explanation for this bizarre new form of matter. We formally introduced its name to the scientific community in the title of our paper: “Quasicrystals: A New Class of Ordered Structures.”
At this point, Dov and I were ready to reach out to the experimental group to tell them our exciting news. As it turned out, though, David Nelson had already written to John Cahn at the National Bureau of Standards to let him know that Dov and I had already developed a theory that might be relevant. So there was not much need for me to introduce myself. We quickly arranged for John and his colleague and coauthor, French crystallographer Denis Gratias, to visit Dov and me in Yorktown Heights.
John Cahn was a large man with a kindly face. We had never met before, but unbeknownst to him, I had a strong professional connection to what I considered to be some of his most important work. John began our meeting by explaining his background, particularly his work on a little-known process called “spinodal decomposition,” a process that can occur during the solidification of metallic liquids.
John mentioned, almost as an aside, that he had heard there was a cosmologist who was using those ideas to develop a new theory of the early universe. I was a cosmologist. Did I know anything about that? he asked.
“Yes,” I said, “there is indeed a certain cosmologist I know who is using your experimental findings to help develop his theories. In fact,” I said with a smile, “that person just happens to be me.” John’s theory of spinodal decomposition was actually my key inspiration in developing a new inflationary theory of the universe, which introduced what is known as a “graceful exit” from the initial, explosive inflationary process. “It is an honor to finally meet you,” I told him.
After a brief discussion about our cosmic connection, we settled down to business and spent the next five hours excitedly comparing notes about quasicrystals. Each team explained their parallel histories, one experimental and one theoretical, which, to everyone’s amazement, had just crossed paths with fateful consequences.
John explained how his protégé, Dan Shechtman, had first discovered a ten-fold diffraction pattern in an alloy fabricated in 1982 at the National Bureau of Standards. When Dan had shown him the pattern, John prescribed a series of tests in order to exclude the most likely explanation, which was that the alloy was an ordinary multiply-twinned crystal.
John told us that he heard nothing more about the subject until two years later, in 1984. Dan returned to the lab with the results of the multiple-twinning test, along with a description of the model that he and Ilan Blech were proposing to explain the strange new alloy. Dan told him their paper had already been rejected by the Journal of Applied Physics.
John was greatly impressed by Dan’s improved data, especially the results that showed that the multiple-twinning idea was invalid. He was less impressed, though, by the Shechtman-Blech model, which he considered sketchy and flawed.
So instead of pursuing that theory, John had recommended that Dan focus solely on reporting the experimental results. He suggested that a short paper be submitted to the prestigious Physical Review Letters. Dan accepted the advice and invited John to join him as a collaborator and to help rewrite the paper. John, in turn, contacted Denis Gratias, a French crystallographer, to join their team and double-check the analysis. The end result was the preprint David had brought me, submitted for publication by the team of Shechtman, Blech, Gratias, and Cahn.
John told us he was already trying to duplicate the inexplicable experimental results. His lab group had begun further studies to strengthen their conclusions about the unusual alloy and to search for other materials that might have similar diffraction patterns.
Then it was our turn. Dov and I described in great detail how we had arrived at our ideas and recounted all the research we had performed in the last three years. Mo
st importantly, we showed them our predicted diffraction pattern for a quasicrystal with the symmetry of an icosahedron. All of us noted its close agreement with the measured diffraction pattern for the aluminum-manganese alloy reported in the preprint.
It was an intoxicating, exhausting, and exhilarating meeting.
A few weeks later, I made the first public presentation of the quasicrystal theory at a venue that held particular significance for me. I spoke at a specially arranged seminar at the Laboratory for Research on the Structure of Matter at the University of Pennsylvania. The lecture hall was packed. It was a homecoming of sorts for me, and our results were received enthusiastically. I was enormously grateful to the leaders and members of the Laboratory because they had steadfastly provided both encouragement and financial support throughout the prior three years, even when our quasicrystal idea seemed to have questionable scientific value.
John Cahn did me the honor of traveling more than two hours from Gaithersburg, Maryland, to attend the lecture. Once I had finished my presentation, he gave me yet another great honor by standing up and publicly endorsing our theory. John announced that in his view, our quasicrystal model correctly explained their team’s new material.
With our paper submitted and the first public presentation completed, I finally took some time to reflect on what we had just accomplished. The scientific fantasy I had secretly nursed since high school and floated practically on a whim in a university lecture was a scientific reality. I was struck by what seemed to be a logical extension of that new reality:
If quasicrystals are a fundamental new form of matter that truly exist, as the laboratory evidence shows, then surely they must exist in nature!
Perhaps they are hiding right under our noses, I thought. We just have to figure out where to look for them. There might even be quasicrystals on display right now in museums that have been misidentified as crystals.
The Second Kind of Impossible Page 7