I have just come from listening to a lecture by Dan Shechtman, this year’s Nobel Laureate in chemistry. The topic of his speech was his 1982 discovery of quasi crystals which has led, all these years later, to his achieving a Nobel Prize for his work.
He began his talk with an introduction to the science of Crystallography, which was founded in 1912 when Sir William Lawrence Bragg and his father Sir William Henry Bragg first starting using X-rays to study the diffraction pattern caused by crystals. (Prior to that breakthrough people studying crystals measured the angles between the faces of crystals, which had been done at least as far back as the 1600’s—Johannes Kepler published studies of snowflake crystals in 1611, and in 1669 Nicolaus Steno reported consistent sets of characteristic angles for quartz crystals, no matter where the crystals came from.)
During the next 70 years crystallographers studied 1000’s of crystals using X-ray diffraction, and they all conformed to a set of rules which became accepted as the definition of a crystal:
*They all had a periodicity; if you measure from the center of the diffraction pattern to the first spot, and then move out again that distance in the same direction you will encounter another spot, and another again each time you repeat the pattern.
*they all had a rotation of symmetry; this means that if you rotate a crystal around an axis you will get a repeat of the same pattern every certain number of degrees. The possible amounts of rotation were 2, 3, 4, and 6.
This means that a crystal with a 2-fold rotational symmetry can be rotated half way around (180 degrees) and will look exactly the same as before it was rotated. A crystal with a 3-fold rotational symmetry can be rotated to three different positions (each 120 degrees apart) which have the exact same pattern. 4-fold means that each rotation is 90 degrees apart, and 6 fold is 60 degrees apart.
As Professor Shechtman emphasized in the early portion of his talk, this list was it—crystallographers knew that no other rotation symmetry pattern was possible. There was no such thing as a 5-fold rotational symmetry, nor were there any crystals with rotational symmetry greater than 6. This was so well accepted that when he was a student he once had an exam question requiring that he prove that 5-fold rotational symmetry was impossible.
He shared with us his answer on the projector screen. It works better with images, but I will try it with words alone (see this page for more details). Start with a dot on the center of your page, then put five dots around it in a ring, each 66 degrees apart, all the same distance from the center dot and from one another. If 5-fold rotational symmetry is possible one could then take any pair of those encircling dots, rotate around them in five steps, plotting a new circle of dots around each, and the new dots around one would line up with the new dots around the other. However, as he showed us on the screen, this does not happen—if you colour one set in blue and the other in red they clearly fall near, but not upon, one another.
Therefore when he noticed a crystal which showed a 10-fold axis of rotation on a transmission electron microscope on the afternoon of 8 April 1982 is was more than a bit surprised, as one can see with the triple question marks he wrote in his notebook. His first thought was that it must be the result of crystal twinning, which had been known to cause the appearance of five-fold rotational symmetry but was really the result of having more than one crystal contributing to the diffraction pattern. So he zoomed in to the limits of the machine and took the diffraction pattern again, several more times, and each time he received the same result—a 10-fold rotational pattern, and from areas so tiny that the possibility of there being more than one crystal contributing to the pattern had been eliminated.
How was this possible? Well, the substance he was studying does have a rotational symmetry that had previously thought to be impossible, but it achieves it by lacking in periodicity—the pattern does not repeat if you jump a set distance in a given direction. As a result of his discovery the definition of a crystal has changed to say “any solid having an essentially discrete diffraction diagram”. These days we call substances such as the one he discovered “quasicrystals” and it turns out that they are reasonably common. But in the early days after the publication of his discovery he met with much resistance to his ideas—one scientist was even heard to declare that there are no quasi-crystals, only quasi-scientists”. However, as happens with science, other laboratories repeated is results, both with the compound he first noticed the phenomena in, and then with other compounds, and gradually the acceptance spread throughout the scientific community.
After he finished his speech there was time for a few questions from the audience. One of the University faculty members ask him a question—she pointed out that this university, like many others, has difficulties attracting students to the study of science, and she wondered if he had any advice in how we might better convince young people to study science. His reply included one of the best quotes I have heard in ages “Science is the ultimate game for adults”.
I believe that he is, in fact, correct with that description—studying science is fun, it requires us to use both our logical and creative parts of our brains, and to push both to their limits. It provides enough challenge to prevent us from ever being bored, and it comes with possibility of making discoveries which change the way we view our world. What could be more fun than that?