 Okay, should we start? Okay, very good. So welcome to everybody for this. I think this is the first colloquium of the year. And it's a good way to start with a special event because as you all know we have, this year it will be the international year of the periodic table. And so the subject fits very well with the year of the periodic table. So it's great to have the speaker, Mike Glaser here from the... Professor from the University of Oxford and visiting professor from Warwick University. And so let me say a few words about Professor Glaser before we start. His research between 65 and 68 was under the supervision of Kathleen Lonsdale at the University College London, working on the crystallography of organic mixed crystals. In 68 and 69, he was a fellow at Harvard University and then from 69 to 76, he was at the Cavendish lab in Cambridge. In 1976, he was appointed lecturer in physics at the Clarendon Laboratory of Oxford and as an official fellow and tutor at Jesus College Oxford until retirement. So he moved from Cambridge to Oxford, which we know is very hard for us to accept. Mike continues in academia as visiting professor at the University of Warwick, UK. Mike's research has mainly been in understanding the relationship between physical properties of crystals and their structures. He's perhaps best known for his classification system for tilted octahedra in perovskites. He's also one of the co-founders of Oxford Cryo Systems Limited, which supplies the world market in low-temperature apparatus for crystallographers. He's currently editor of the newsletter of the International Union of Crystallography. So before starting the seminar, as I told you, this is an event related to the International Union of the Periodic Table. We have here also Professor Oganov from the Skolkovo Institute of Science and Technology in Moscow, Russia. He has been one of the persons behind the proposal of this International Union of the Periodic Table because we are celebrating the 150th anniversary of Mendeleev's discovery. So I would like him to say a few words about the International Union of the Periodic Table. Thank you very much. We are all very proud of this year, which is the 150th anniversary of the discovery of the periodic law by Mendeleev, which is the most important, by construction, the most important law of chemical science. To chemistry, it has the same significance or maybe greater significance than Newton's laws for physics. The entire building of chemistry rests upon Mendeleev's law. And if you think 100 years, 150 years back, how brave one had to be to propose a law that at that time had gaps. And Mendeleev thought that these gaps correspond to elements that are yet to be discovered. If somebody proposes such a law today, most of us probably would laugh at that person. But Mendeleev was brave enough and visionary enough to understand that this is a fundamental law of nature, even though at that time nobody had the slightest idea why this would work and what is the relationship between atomic masses and chemistry of the elements. This was understood much, much later with the development of quantum mechanics. So you can see the great vision that he had decades before his law was understood and years before his law was confirmed. And now we know how true that law was and how right he was. Being a crystal chemist, I'm very happy looking at the history of such great human visions, great human breakthroughs in science. And being a Russian scientist, I am twice as happy. And I am three times as happy because I helped to shape the proposal which the United Nations has accepted. The proposal to name this year, 2019, the International Year of the Periodic Table. Well, this ties in very nicely with another celebration that we had just five years ago. The year 2014 was the International Year of Crystallography, which made me very happy because I'm a crystallographer by my training. At this workshop, we link crystallography, chemistry, periodic table, and principles for designing new materials. I think now we live in a very exciting time and we have seen in this workshop how new regularities, new rules, perhaps in the future even new laws of nature come from the data that we obtain using our computer codes, using our algorithms that we continually develop and improve. Actually, when we organized this workshop with Sandro and Alessandro, actually, can anyone explain to me what's the difference between Sandro and Alessandro? I thought it's the same name. So when we organized this workshop, we knew that this is going to be a very exciting event, but I must say that we probably underestimated, at least I underestimated, how actually exciting this is. I'm very proud that this event is not only scientifically high-caliber, but also this event, we run it. It is affiliated with the International Year of the Periodic Table, but we run it before the official inauguration of the International Year of the Periodic Table. So I thought we have the first event of this activity, but actually it turns out that some people in India run another event 10 days before us. So we are probably the second, we are at the second event of the International Year of the Periodic Table. Many of you have been presented the exciting lectures that were given here at our meeting. By the way, I know that there are some students. Just for your information, we will have a lot of exciting lectures tomorrow as well to some practical sessions in the following two days. So please come. And we also have in the program of this workshop a very special, a very exciting event that we planned from the very beginning. We wanted to invite one eminent scientist who could give a popular science lecture about the role of our science in general scientific context and in everyday life of humanity. And this scientist is present with us. It's Mike Laser from Oxford. And I'm very proud that he accepted our invitation and will give us his lecture right now. Let's do it. Thank you, Artem. And let me express my gratitude for the invitation to come and talk to you today about my favorite subject, the thing I've worked on for most of my life, it's crystallography. It gives me an opportunity to tell you something about this subject, where it came from, where it's been, what it's been doing recently. I hope in this talk to say a few words also about where this may be going in the future. So crystallography, what I want to do is to start off by considering where did it come from? Where did the interest in crystals start? How far back do we go to find any connection between human beings and crystallography? And the thing I'm going to start with is to do with a paper that I read just very recently and we published part of it in the Journal of the International Union of Crystallography, an article written by Juan Manuel Garcia Ruiz in Spain about ancient hominids, if I can have the slide. So he reported that it's been found when you look at the sites where these people lived, these ancient ape-like creatures lived, they find quartz crystals like this, perfect quartz crystals. And the interesting thing about that is they don't seem to have been used for anything. They've not been changed in any way, they've not been cut, they've not been used for tools. And so it raises the question, why would these ancient people, these ancient hominids, why did they have these quartz crystals? It seems that they were collecting them because they liked them. So the suggestion is that perhaps the collection of these crystals could be related to their later development, their brain development, started them thinking in a way that was different from before. And if you think about the world that these ancient hominids lived in, they saw trees, they saw rivers, they saw mountains and ground, they didn't see any straight lines. These things are probably the only things they saw which really were regular, had symmetry and straight lines. And it suggests that maybe it's that observation that changed something in their minds and started them to think in a way which has now led to us. And there's a connection with a funny connection here. Some of you will remember this film, 2001, A Space Odyssey. And for those of you who don't know this film, it starts off with these ape-like creatures living out in the wild and suddenly they come across a black slab here, being planted there probably by an alien civilization. And when they see this, it excites them so much, suddenly they start to develop new skills, new ideas, some aggression and so on. And this was taken originally from a book by Arthur C. Clarke called Sentinel of Eternity. Now originally this black slab here was actually a crystal. And what they did was that when they made the film they colored it black because when it was clear you couldn't see it. But it actually is a crystal. And this again in this film, it's science fiction, but again there was this idea that the aliens planted this straight-like object on the earth and it changed the mentality of these apes and that was the beginning of humanity. That was the idea. And yet that's what we find in these sites. Quite interesting. So here we are, perhaps the first crystallographer about a million years ago. Interesting. I don't know if it's true, but it's an interesting idea. Okay, moving on. So really over the centuries with crystals, most of the interesting crystals was really magical. The idea that crystals had some sort of magical powers because they were so strange with this regularity. Unfortunately, there are a lot of people around the world today still believe that. You've only got to go on the internet, go to Google, type the word crystalline and you get all kinds of rubbish. Well, the first really scientific endeavor to try to understand crystals is probably Johannes Kepler in 1611 who was interested in symmetry of snowflakes. And he wrote this famous pamphlet, Strenus suede nevus hexangular, in which he discussed the snowflakes and their symmetry. He said that where there is matter, there is geometry. The recognition that the crystal formation is related very much to geometrical construct. And another thing he did was he considered the close packing of spheres. Originally, the idea was to do with stacking of cannonballs on the deck of a ship to stop them rolling around. What was the best way to stack cannonballs? And this is the model that he came out. This is from his pamphlet here, which is an example of what we call cubic close packing. And he produced a conjecture that this would be the most stable arrangement. And that wasn't proved until I think about 1962. It took a long time, many centuries, to prove that that was the case, that this is the most stable packing arrangement of spheres. So this could be cannonballs, oranges, apples, or whatever. So that's really the beginning of trying to understand what crystals might be. But you see, it's already the idea that there are some things which are repeating in space in a regular fashion. And then in England, Robert Hook, in his book Micrographia, he considered various objects. For example, he looked at flint, broken flint, and he saw that he had regular faces, and he thought these were crystals. Actually, they're not crystalline. They're what we call amorphous materials. But he also looked at crystals grown from urea, and he could find some regularity. And in Micrographia, you see, he's already talking about packing of spheres to explain the shapes of these various objects. So this very early work to do this, he says, had I time and opportunity, I could make probable that all these regular figures arise only from three or four several positions of globular particles. Then later on, the study of crystals, after this, took place mainly in France and in Germany. There were the two countries where most of the ideas were generated. If you remember, this is a time when even the existence of atoms was not really known or believed. It's very, very fundamental in the kind of experiments they could do, not very sophisticated equipment. But one of the things that was noticed by Steino was what became known as the law of constancy of interfacial angles. So if you take a crystal, say a crystal of quartz, and look at it down a long axis, you see a hexagonal shape. But if you look carefully, you see that actually, they also grow like this, and the sides of these faces are all different. What is found was that if you take the perpendicularity of those faces, they all have the same angle. And so there was a constancy of this angle, which is characteristic of this particular type of crystal. The idea that the normals of the faces are the things you should look at. He applied this in particular to quartz, and Jean-Baptiste Gromy de Lille, he generalised this as being characteristic in general for particular crystalline substance. So that's the beginning of trying to understand the morphology of crystals, the external shapes of crystals. Let me come to this gentleman, René Jouiste Aoui, a Frenchman, a cleric, and there's a story. We don't know if the story is really true, but it's the one that everybody hears. He was visiting a friend of his who had a collection of crystals, and Aoui picked up one of the crystals and accidentally dropped it on the floor, and it smashed, and he noticed something. So he rushed back to his laboratory, got all these crystals and started smashing them up into bits, smaller and smaller pieces. And what he noticed was that the little tiny bits were the same shape as the big ones, and no matter how much he smashed these crystals up into smaller and smaller pieces, they always had this same sort of shape, with those angles between the faces still being preserved. And this led him to suggest that crystals must be made up of some set of repeating objects, and these are some of the diagrams from his treatment on this, different shapes of crystals, you see, just by stacking together little units of some kind. He didn't know what these units were. He called them molecular anti-grant in French, but he didn't know the eratoms, he didn't know what they were. He didn't think of these as what we call unit cells. Now the importance of this is twofold. First of all, crystals are made of regular repeating objects, molecules today, or atoms, we would think of that regularly. We call that translational symmetry. But the other thing was a more metaphysical question, because what it said was that matter, solid matter, is not continuous down to zero. It's broken up into pieces. And that means that there are interfaces between regions, interfaces between these blocks. This was a big problem in the 18th and 19th century, in the early part of the 19th century, because the question then was raised, well, what's in between these blocks? And the religious people would say, well, that must be where God is. And he got himself into trouble over this, and had quite a rough time with that problem. Anyway, so that's Haue. His name is on the Eiffel Tower, one of the great French scientists. Now, Haue was an interesting character. He pushed this argument too far sometimes, because it was soon found that there were other cases that didn't fit his theories, because he believed that these things were characters of each separate material, and that every solid would be different. But it was somebody called Mitchellich who showed that actually you could have different chemicals which have the same crystal shape. So there was arguments in the middle of the 19th century. Anyway, the important message, some sort of repeating object must make up a crystal at a microscopic level. And other scientists working at the time also were coming up with similar ideas. It was a time in France when people really were excited about these ideas. Again, in France, we come to August Bravais in 1848, who looked at another problem, actually directly nothing to do with crystals. What happens if you take a series of points, a series of points in three-dimensional space, such that you build in translational symmetry. You build in repetition of points. How many different ways, unique ways, can you do that? Well, he proved that actually there were 14, and here are the 14 original Bravais arrays. Now, just a little bit of the warning here, and this is a problem I'm afraid that I see all the time with my fellow physicists and chemists. I see this in publications all the time. A confusion between lattice points and atoms. These little black dots here are points. The only reason you can see them is because it's made them big enough so you can see them. They don't exist. A lattice does not have any physical existence. It's a mathematical device to tell you how to put molecules down in space. Please do not confuse lattice points with atoms. Unfortunately, the literature is full of these confusions. It's not simply a matter of terminology, but also if you don't understand that difference, it can lead you in your research down to regions which are actually wrong. I remember a student in Cambridge many years ago was trying to do the electronic band structure of something for a year and getting nowhere, and he was sent to me to see if I could help. I explained to him the difference between a lattice point and an atom. When he went to his programme, he put the right numbers in, out came the answer immediately. He wasted the year of his PhD, simply because he didn't understand that difference. Terminology has consequences. These are the four-team berylata, and they're grouped up into what we call crystal systems. We have triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, trigonal, cubic, and so on. The cubic ones, there are three different types of arrays that are cubic. The common feature amongst these is that they all have four three-fold axes of symmetry. That's what defines a cubic system. The reason why physicists in particular get confused is because if you look in the textbooks, they show very simple crystal structures where they replace each lattice point with an atom. This one here, for example, all face-centred, if I put a copper atom at each point, I get the copper crystal structure. But, of course, in reality, most crystals are much more complicated than that, even diamond is more complicated than that. So you see statements like the sodium chloride lattice, the copper lattice, the diamond lattice. They mean the diamond crystal structure, the copper crystal structure. They all have the same lattice type, face-centred cubic. Anyway, moving on. Structure prediction. Back in the, toward the end of the 19th century, there's a gentleman over here on the left called William Barlow, who's a very strange character. He was an amateur scientist. He had no proper scientific qualifications. His father was a surveyor, and then he got interested in crystals. In fact, he eventually became a fellow of the Royal Society for his work. And this is a paper in 1883. And look at this up here. He's playing around with alkali halides, trying to suggest what the arrangement of atoms would be. Members at a time when atoms were not completely accepted in the scientific world. They were still arguable about whether atoms existed. And it's also the time when we were building up the periodic table, this idea of a regularity in elements. Now, here we are. This is one of his models for sodium chloride, which in fact eventually turned out to be correct. He was predicting a likely crystal structure. There's another very odd one. Same time, Alexander Crumb Brown in Edinburgh, another very strange man. After he died, they found this. And these are balls of wool. And you see they alternate blue, red, blue, red. This is the structure of sodium chloride, like here. We don't know if Crumb Brown intended that. We don't know why he did that. But it's interesting, it's the same year. And I suspect that these two guys were in cahoots. They were talking to each other. And that's where it came from. But we don't really know. So that's the beginning of crystal structure prediction. In Germany, particularly, the accent was very much on symmetry. And we start to see the development of point group symmetry and then space group symmetry. And the two main individuals that were responsible for determination of the space groups, this is where you take point symmetry and you combine that with the Bravais lattices, you again get space groups. And you have to then add in some extra types of symmetry operations, so-called screw axes and glides. And then you get the so-called 230 space group types. This was achieved by Schoenfliess in Germany in 1892 and his notation is commonly used, particularly in spectroscopy. But at the more or less the same time, Yevdraf Fyodorov in Russia also developed the same things using a different route to get there. There was a little bit of argument about how many space group types they were originally, Fyodorov had seven extra ones, but he then eventually removed those and got the 230. So these two gentlemen were, at the same time, come up with this idea that all crystals should belong to one of the 230 space group types. That makes life easier because in all of the thousands of crystal structures out there, if you can limit them to individual space group types, you're putting them into compartments, it makes it easier then to go ahead and try to understand them. By the way, William Barlow again, he also is said to have generated the 230 space groups around the same time or just after this. Although I think there's quite a lot of doubt as to whether he really did that on his own. Okay, so that was the period to just over 100 years ago. That was about all we really knew about crystals. Everything was conjecture based on symmetry arguments, based on how his ideas and so on. And the big development happened in 1912 and it started in Munich. In 1895, Rentgen had discovered x-rays and the major problem was what are x-rays? What do they consist of? Are the rays that they got? Are they waves or are they particles? That was the big argument in theoretical physics at the time. In Munich, there was an institute of theoretical physics run on Sommerfeld and he had working for him at the time. This man here on the right, this is Max Lauer. It's a long story associated with how this was done and I haven't got the time to go through the whole story. But in a conversation with Paul Ewald, Lauer said to have had a sudden flash of inspiration because in the conversation they discussed whether crystals had regular units and if so, what would be the distances between the regular units of atoms? And Ewald said it would be of the order of Angstroms. And at that time there was suspicion that x-rays, although they were waves and there were a few experiments that seemed to demonstrate it, would have wavelengths similar to that. Lauer said to have realized that, well, why don't we just get some x-rays, shine them at a crystal, think of the crystal as a three-dimensional diffraction grating. We should get a diffraction pattern and that will prove whether x-rays are waves or particles. He went to Sommerfeld with this. Sommerfeld said, no, I'm not giving you any money for that. I'm not sparing any people to do this experiment. So Lauer approached two individuals, one called Knipping, the other one called Friedrich, one was a student of Lurentgen, another one was an assistant of Sommerfeld and they secretly did an experiment in probably March, April of 1912. And after some fiddling around, shining x-rays at a crystal of copper sulfate, they obtained this pattern here. And it's not a very good pattern, but you see that there are spots here. Clearly the x-rays have been deviated from the forward position. That same evening, they looked at another crystal zinc sulfide and they got this much nicer pattern and what you see is a series of spots and you see that there's a symmetry here. We're beginning to see the symmetry of the crystal in this pattern of spots. Notice the spots are slightly elliptical as well. Then the question is, well, how do we explain this? Now Lauer had the mistaken idea that the x-rays that we were seeing hitting the film here were coming from inside the crystal. They were generated, the incoming x-rays generated secondary x-rays in the crystal and the secondary x-rays went out to give the spots. That led him to think that the wavelength of the x-rays that he was using here were a single wavelength. But with that, he couldn't explain all these spots. So he later modified that and said, well, maybe we've got three or maybe five wavelengths in there. He still couldn't explain the pattern properly. Now in the summer of that year in Britain, William Henry Bragg received a letter from somebody who'd been to a lecture in Germany and that was Weigard. Weigard sent him a description of what he'd seen and that got William Bragg interested in this. William Bragg had a distinguished record in looking at radiation. He decided that, well, we can explain this not in terms of diffraction but of channeling of particles through the crystal. He believed in particles. He teamed up with his son. Here we have the two Braggs. So William Henry Bragg and William Lawrence Braggs. I'll call this William and Lawrence. This is Lawrence Bragg later on, by the way, in Manchester in 1936 and here he is in Cambridge in the Cavendish Laboratory in 1943 as an older man. And the two of them decided to do experiments to prove that x-rays were particles. The experiments failed. Lawrence Bragg, by this time, I should say that this was all done in Leeds in the north of England but Lawrence Bragg was a student in Cambridge, just qualified and he went back to Cambridge and suddenly had an idea. He realised that, while he was correct, these x-rays are waves. It is diffraction, they were saying, and he came up with a very simple way of explaining how the diffraction occurred and this is from his notebook at the time in 1912 and you see a formula up here, 2D cosine theta, which is related to the wavelength. Now, what young Lawrence, 22 years old, realised was that the beam of x-rays incident on the crystal in Lowell's experiment was a white beam. It was a continuum of wavelengths and this formula, which is got by thinking of the rays bouncing off planes in the crystal just like mirrors go in at a certain angle, come out with the same angle but you have interference between the rays going out, destructive and constructive interference and this gives rise to the spots and the reason this works is because you've got three parameters to satisfy. The interplanar spacing between the planes, the angle, theta and the wavelength and you have to have all three to fit that equation otherwise you don't get any intensity on the film, you don't get spots. Lowell originally didn't believe this, he thought that if you had a continuum of x-rays you'd just fog all the film. He didn't quite appreciate the significance of this. So in 1912, November the 11th, a paper was read to the Cambridge Philosophical Society by J.J. Thompson on behalf of Lawrence Bragg, paper was called The Diffraction of Short Electromagnetic Ways by a Crystal. He didn't mention diffraction in here deliberately because he didn't want to upset his father who believed in particles. But in this paper he explained exactly how it works. We've got the so-called Bragg's Law and here we have the formula that he derived originally in his notebook but later on, almost immediately, that angle theta was changed by 90 degrees. Instead of being the angle of incidence it was the angle of reflection and so it became 2D sine theta which is the famous equation that I'm sure everybody here has seen, so-called Bragg's Law and that's where it comes from. I'll explain in a moment why that was changed, why I believe that was changed. In this paper he showed that the beam was white, he showed that the Bragg's Law selected out only those spots corresponding to the Bragg's Law so when you look at those spots they come from different wavelengths on the film. Furthermore, he was able to explain all of the spots, why the spots were there and why some were missing which is something that Larry again couldn't do. So we have a white incident beam and he introduced the idea of a face-centered structure. Zinc sulfide, he didn't know where the atoms were but think of a zinc sulfide molecule, he put them not on the corners of a cube which is the way a typical theoretical physicist would do it, he put the molecule also on the centers of each face and when you do that you cancel out some of the intensities and you can explain the total pattern and that's another thing that Larry didn't appreciate. So what Lawrence Bragg had done, 22 years old he had obtained the first information about the lattice type of a crystal structure. So it's the beginning of crystal structure determination. So this is the beginning of modern crystallography, November the 11th, 1912. Now the father, W.H. Bragg, immediately saw the significance of what his son had done and they started to work together and William Bragg agreed X-rays must be waves but he also said there must be particles as well. So he was actually in 1912, 1913 already talking about the parity between particles and waves which was only really enunciated properly 15 or so years later. But he was so, he was ahead of his time. Okay, so this is the picture, some sort of units on the corners of the cube and on the face centers and this then was the clue to understanding how to derive information about the crystal structure from the diffraction pattern you get with X-rays. The father was a very good experimentalist and he had developed a thing called the ionization spectrometer and these are some examples. So these are where instead of using film you have a beam of X-rays, incident on a crystal and you have a telescope and you have a detector and you scan the crystal, you rotate the crystal and the detector and you find certain points where you get a peak. This then made it possible to measure the intensities of those spots which they couldn't do very well on those films and the two of them worked together on this and I think this is the reason why the angle was changed by 90 degrees because in a spectrometer you naturally measure the angle from the straight through position outwards going to higher and higher angle and that's the angle which then became two times the Bragg angle, two times theta. I think that's where it comes from. It appears mysteriously immediately in the first paper in 1913 that the formula has changed and that's the sign of the form that we know. And here we are, this is W.H. Father there with his spectrometer and here's Lawrence Bragg with another spectrometer. Now around the same time there were a lot of people also interested in Laue's experiment and we have Harry Mosley who was a student of Rutherford in Manchester at the time, later moved to Oxford. Here's a letter to his mother and he says I gave the first public explanation on Friday. He gave a talk around the same time that Bragg made his discovery and there is some suggestion he got the same answer, same result but it was never recorded so we don't know for sure. I knew privately however that Bragg and his son had worked out an explanation a few days before us and their explanation although approached from a different point of view turns out to be really the same as ours. We are therefore leaving the subject to them. The subject is very important and there will probably be an enormous amount of work done in the next few years. That's quite a prediction. And another letter here. So at this point Rutherford talks to W.H. Bragg. W.H. Bragg wanted to study X-rays, it's X-ray spectra rather than crystallography. That was his field. And Rutherford leaned on W.H. Bragg and said no, let Moseley do the X-ray spectra you concentrate on crystallography with your son. And William Bragg wasn't too happy about that at first but in the end he gave in and said okay you'll do that and in fact he invited Moseley to come to Leeds to learn the techniques of how to use the spectrometer and you can see this is a letter from Moseley back. There's nobody here who is an expert on the rays so I've had to find out details of modern X-ray practice from Bragg at Leeds. So there's the magnanimous W.H. Bragg showing a competitor how to do it. And of course Moseley made the very famous discovery namely that you can relate the square root of the frequency of the X-rays to the atomic number. And of course it's very important in the progress of the periodic table because it's this really that finally put the seal on the idea that there is a periodic table that it should make some sense. And it also suggested some other elements that hadn't been seen for example like hafnium. Moseley unfortunately was killed in 1915 during the First World War absolute tragedy had he lived he almost certainly would have had a Nobel Prize but they are that's what happens during wars. But the two Bragg in 1914 well rather Laue received the 1914 Nobel Prize in Physics and the two Braggs received the Nobel Prize in Physics in 1915 and that makes the two Braggs the youngest Nobel Prize winners in science even today and the only father and son team together Nobel Prize. This really began the whole story. So the first structure they did published in 1913 was on the alkali halides. So we had potassium chloride, sodium chloride and that was done by using Laue method with photographs and also the spectrometer together which he had from his father. And that was published by Lawrence Bragg and he also worked on the next paper on diamond the structure of diamond was a very important structure at the time and in 1913, 1914 until the beginning of the First World War the two of them worked all loads and loads of different crystal structures and they had like a minefield of different things that they could study. They had the whole field pretty well to themselves in that time. The sodium chloride structure alternating sodium chlorine sodium chlorine the chemists did not like this they wanted molecules of sodium chlorine not irregularly spaced atoms. The concept of ionic bonding didn't really exist at this time and Professor Smythals in Leeds even said to Lawrence Bragg please find that one sodium atom is just a tiny bit nearer to one chlorine than it was to the others. Lawrence Bragg resisted that one and then there's this very famous letter to nature as late as 1927 by Professor Armstrong I won't read the whole of it because I don't have time but he says here the equality in the number of sodium chlorine atoms is arrived at by a chessboard pattern of these atoms it is a result of geometry and not a pairing of the atoms remember Kepler the statement is more than repugnant to common sense it is absurd to the end's degree not chemical cricket so on well you know who won that argument younger Lawrence Bragg now it soon became obvious how to start to think about interpreting that because you can measure the intensities of these spots and in the old days and even when I first started as a student you measure the intensity spot by eye we didn't have many instruments that could measure those intensities and although in 1912, 13, 14 they were using this spectrometer after that it more or less died out nearly all data was collected on films so you had to measure the spot intensities by eye the formalism of this everybody has heard the so-called structure factor is given by a formula like that which contains the positions of the atoms and Hkl are the indices of the planes that are given rise to a particular spot or reflections we call it and this is really the amplitude of scattering and it involves an amplitude and a phase so if you want to now get the electron density because the scattering is by the electrons you want to find out where the atoms are and draw a picture of the structure you have a formula like this and this has the modulus of the amplitude which is related to the square root of the intensity so the square root of intensity gives us this thing here and then we have a phase angle and that's the problem we lose the phase information we don't have that but the problem was for a large part of the 20th century how do you get that phase information if you can't measure it it's called the phase problem W.H. Braggs had another suggestion he said that if you think of each spot coming from a wave arriving at that position in the detector then we can draw a set of plane waves and the orientation of those plane waves depends on the wave vector the plane has been diffracted so this is just an example of what you can do so this is a unit cell you have a plane wave travelling across this way you have the maxima going through the origin here minimum half way along that's a particular one I've just chosen at random here's another one and this time the wave is travelling in that direction it comes from a different plane and you notice the maxima is now here not at the origin you can just get something else and we start to see something disappearing here and something there and this is the idea of Fourier summation or Fourier synthesis W.H. Bragg had that idea first but it was never used until many years later by his son who then employed this to draw maps of crystal structures so you can see atoms and I think on my next slide I can demonstrate to you what that looks like here we go adding to loads of waves and the crystal structure suddenly comes out of the mist this was when the crystallographers saw this this was so exciting because you see how the crystal structure disappears like magic out of the mess that is there and here we are we are seeing the atoms and this is actually urea, this is a carbon atom those are two nitrogen atoms and that's an oxygen there and you see how they arrange in the crystal structure to do that you have to have the amplitudes and you have to know the phases come back to that in a minute but if you do know the amplitudes and the phases you can do this Fourier summation and you can plot it as a contour map which is the way it's usually done and in the old days if you look at the old publication on crystal structures this is very often you saw diagrams like this with contour diagrams and so on but today very often because today everything is done automatically by software they don't present that information normally they just give you the answers which is a pity really in many ways ok moving on another development about the phases Arthur Lindo Patterson in the United States had an idea that instead of using the amplitudes of the waves we use the square of the amplitudes and forget about the phases just put them all to zero and then you get essentially an auto correlation function and on the left here you see an order Fourier map of a crystal structure it's actually urea again looking down a different axis so this is carbon and oxygen on top of it and these are nitrogens and if you make a map with the square of the amplitudes put all the phases to zero and these peaks represent vectors between atoms so you see there is a lot of density at the origin because these are the zero vectors the vectors from one atom to itself and they all add together at the origin but the interesting ones are these and so these distances here from here to here from here to here are the vectors between the atoms in this crystal structure and the whole art of the crystallographer so let's start with that and get back to that but you can see there's only a limited set of models that are going to satisfy that it's not going to be an infinite set of models so this was a way for a long time, even today this is still used although it's disguised because the software does it all for you automatically a very important event so that got rid of the phase problems to a great extent W.H. Bragg was famous for encouraging women to crystallography out of 19 research students 11 were women and this was one of them, Kathleen Lonsdale I put her here because she was my Ph.D. supervisor and she working in the 1920s solved the structure of hexamethyl benzene and she showed that the benzene ring was flat which is something that the chemists wanted to know very important for aromatic chemistry and she solved that by very clever means she managed to solve it by looking at the intensities of the various peaks and using reasoning to say what is the most likely structure to do Fourier maps in the old days there were no computers so this was a box of tricks that was derived called beavers, lips and strips, strips of paper which all the trigonometric and cosine terms were printed and these boxes were made in Liverpool and Cambridge and they were exported all over the world around 700 were exported around the world to help crystallographers to add together all of those Fourier terms make it easier, it's still a small structure and I remember doing the hexamethyl benzene it could take a week to get one simple map out today it happens in a millisecond and much more complicated structures but this was a very important advance in its time then computers came along this one is the Farranti Pegasus Mark II, I put that there because this was the first computer I used in 1965 a monster of a machine, two huge units like this very high use, 8K a store on a drum my watch has about a thousand times the computing power of that machine there it was originally used for designing aircraft wings and we had that computer in our lab Kathleen Lonsdale was given that by the government of Norway so we used that input was in paper tape interestingly the box around the outside was all designed and built by Rolls-Royce that was an early computer and of course computers got developed very quickly there often and that's changed the whole thing, crystallographers were there pretty well at that time, the only scientists that had huge amounts of data and computers came along just at the right time huge amounts of data and a lot of the algorithms that we used today like least squares for example were designed for crystallographers for that reason phase problem, now the two gentlemen at the top is Jerry Carl and Herbert Hauptmann in the United States and they got the Nobel Prize in 1985 for inventing what's known as direct methods which looks at the statistics of the intensities of the diffraction spots in diffraction space and by using the statistical information there they could derive the likely phases for all the reflection and this then made the possibility of solving structures automatically without even trying to find the phase just does it behind the scenes with a bit of software and interestingly this picture is this one here because what this happened here is what we've done is the images, the photographs are made by a summary, a full re-assumption of amplitudes and phases so what we've done here is interchanged the phases that kept the amplitudes and you see they've changed rounds which shows you something the most important part of this are the phases not the amplitudes forget about the amplitudes, you can put all the amplitudes the same if you like provide you have the different phases you can solve it kind of interesting because we use the intensities as our way of getting at the phases yet we don't need them it's a puzzle, it really is anyway this emphasize the importance of phases during the 20th century when I started as a student we used to collect our data on films and a lot of different cameras were invented to do that this is an oscillation or rotation camera and you see the spots now lie on these lines here the spacing between the lines tells you about the repeat distances in the vertical direction and in principle you can measure the intensity of the spots by eye and make a list of those to do your structure analysis difficult because the spots tend to overlap each other a bit then this camera was invented the so called Weissenberg camera in which you have a it's usually horizontal you have a film cassette here and you can rotate the crystal around this axis here and at the same time you move the cassette backwards and forwards and you drag all the spots on one layer line out onto the film you get this strange pattern of spots but the nice thing about this is every spot is separate you use a chart to read off what all those spots are and you go around and you measure all these intensities I remember doing this as a student spending hours and hours and hours measuring the spot intensity on the Weissenberg film later on the so called procession camera was invented where the crystal is mounted on a point here and the the flat film is processed around as the crystal is oscillated it gives you an undistorted view of diffraction space or reciprocal space and that was the way everybody did their work until diffractometers appeared and here we are so these are a result of W.H. Bragg's original spectrometer which as I say disappeared for many years but as computers came along and techniques evolved so single crystal diffractometers like this one this uses a serial detector goes around and measures each spot separately and then later on with CCD technology you measure all the spots that one go and with the modern diffractometers like this you can collect data which used to take weeks before you can do it in about 10 minutes, 15 minutes sometimes collect all your data and you go straight into the computer use direct methods, pattern methods whatever and solve the structures and of course at the same time study of powder became more important and we have powder diffractometers as well so these are the the consequences of W.H. Bragg's original spectrometer and then we have rate discoveries this is Dorothy Hodgkin Nobel Prize in 1964 in Oxford she was working on two things, penicillin and on vitamin B12 and this is what she got the Nobel Prize for in 1964 she later worked on insulin in 1969, solved the structure of insulin as well and here's a stamp from British stamp from Dorothy Hodgkin and here's one of her Fourier maps, in those days to make a three-dimensional Fourier map you printed them out on transparent plastic sheets and you stacked the plastic sheets one above the other and then you could look through that and try and trace out where the molecules are these were done without computers this was done in 1940 no computers using those beaver's lips and strips and the Patterson method is how she derived the structures of these two and the penicillin was very important because there's a four fold ring in there which turns out to be critical for antibiotics of this sort and because of that structure solution we now have many more antibiotics of the penicillin type, it comes from that of course the wonderful British newspapers published this after she got the Nobel Prize Nobel Prize for British wife Nobel Prize for a wife from Oxford British woman wins Nobel Prize mother of three I'd like to think we don't do this anymore I would like to think we've grown up a bit more but that's how the British press presented it when she got the Nobel Prize I think that's shameful there you go another great discovery again this is in Cambridge in the department run by Lawrence Bragg Kendrew and Perutz Perutz worked with Lawrence Bragg a lot on this problem as well they solved the first protein structure which is myoglobin and hemoglobin rather complicated thing and these funny sort of rings represent alpha helices peptides helices and that was the first crystal structure the Patterson method principally and also heavy atom where you substitute a heavy atom which scatters more than the others and if you think about that Patterson method if you have one atom which is more dominant than the others then it's very easy to trace out heavy atom to light atom vectors and it helps to solve the structure so that's what they did Nobel Prize in 1962 and from the same department we have this famous one DNA, Crick and Watson working in the same department in Cambridge shared the Nobel Prize with Maurice Wilkins in 1962 same year both from the same department got Nobel Prize one in chemistry one in physiology and we all know about Rosalind Franklin with her famous photograph 51 and this cross like shape showed that you had a helix and we got the structure here because we all know that story by the way I can tell you that Rosalind Franklin wasn't the first to get this a year earlier in Leeds William Asprey had a student who got a photograph almost the same but William Asprey didn't realise the significance of it and he wasn't in touch with these guys either now had these people known what William Asprey was doing and seen in Leeds earlier you know who's working anyway, it's a long and interesting story diffractometer again another advance this is one that I'm partly responsible for this is why I'm showing it to you was the idea that you want to call a crystal and the only way you can do that sensibly and routinely is to have a cold stream of gas and in particular for the protein people it was discovered by Hock and Hopey there was a problem with proteins, they decay very quickly in the x-ray beam but if you flash cool the protein crystal keep it cold, they survive much longer and then it allows you to collect your data and we invented a device around this time when that discovery was made which is called the cryostream this is it here it's a device which pumps hydrogen over the crystal and allows you to do those experiments and we put that on sale in the 1980s and sales just took off all the protein crystallographers wanted to and today we are the only real distributors of low temperature equipment in crystallography as a result of that and here again you can see another diffractometer this is on a synchrotron and not just with ordinary x-rays in the lab but also with synchrotron and here's our cryostream again there Synchrotron radiation around the early 1970s started to be looked at before 1970 the radiation was just a spillover from high energy physics and a few of us started to play with synchrotrons and see what we could do in the early part and it became very apparent very carefully because the characteristics of the beam are very different than from a normal tube so the beam is very parallel in the vertical plane rather than divergent it's white radiation pure white radiation and you can see the spectra here very high brightness much brighter than from an ordinary x-ray tube so these are dangerous things and it's plane polarized in the horizontal plane the x-ray tube that's not polarized only slightly polarized and over the years as you all know new synchrotrons have come on the stream all over the world increasing the brightness and this is the logarithmic scale and this is the photon energy that you've got and you see that here is what you get with a tube and here is what you get with synchrotrons with so called wigglers and undulators and so on and pretty well every major country has a synchrotron these days and so now you go back to photographing techniques for example and you take an oscillation photograph of a protein crystal just oscillated a very small amount and look at all the spots you get just a huge amount of data that you get on a film and of course then you had automatic machines that can measure these intensities from the films but that's got superseded again by diffractometers which could handle all of this much better viruses this is from Dave Stewart foot and mouth disease virus in 1989 which he solved by calling a crystal of viruses a synchrotron got his data and was able to get the structure of the diamond here now one of the things I said to David was why is it that virus particles tend to crystallize in very simple cubic arrays why is that he said to me I don't know I don't care I'm not interested in what's holding the virus particles together I'm interested in the virus particle that set me thinking and worrying then we have another Nobel Prize here we are this one 2009 to Ramakrishnan Steitz and this is the ribosome this is the machine that creates proteins it's an enormous thing that happens in that molecule and they know not only the shape of this molecule but exactly how it works what goes in, what moves around inside it what comes out they can trace the whole of the history of the production of a protein through this and the ribosome of course we all have them in ourselves this is the thing we need to create the proteins which keeps us alive very very important discovery here's a few Nobel Prizes that we can relate to we have Laue Bragg and we keep going all the way through here and there's Ramakrishnan Steitz and then there was Dan Schechman discovered another form of crystals called quasi crystals and there's been two more Nobel Prizes since then which have relied on X-ray crystallography so the success rate in crystallography is unmatched in any other discipline I would say so in a hundred years we've gone from this which now looks very very simple despite its controversy and we've got the protein crystals we've got to the ribosome we've got to add this thing an adrenergic receptor Nobel Prize in 2012 and the question is what's going to happen in the next hundred years and I'll come back to that in a moment other things are of interest in crystallography because in addition to the sharp spots you often get diffuse patterns behind the scenes now we're now getting pretty good at interpreting these things because diffuse scattering comes from local short-range orders this is breakdown, remember we started with the idea of periodic arrays that's how crystals looked when I first started but it's become increasingly clear to me crystals really aren't like that they are disordered there's also interesting physics going on at the local level and one of the ways of studying that is by getting the diffuse scattering and then trying to use models to explain the diffuse scattering so this is crystallite it's a silicon dioxide and on the left you see the experimental pattern on a film and you can see spots but you can see streaks and this is a simulation using a model calculation these things originally to do this kind of work was extremely difficult but now with modern computer techniques a new theory this is now becoming much more routine and this then reveals when you look at the models that create this as to what's going on in crystallite at the local level how does the translational symmetry break down what's going on there what we call the local level then we have the so-called pair-radial distribution function which is now starting which has recently become popular and the whole idea is to look at radial distribution functions which is essentially all to do with if you take an atom and you move out what are the nearest neighbors atoms in a radial fashion and this actually is an old technique it goes back to the 1930s when people were looking at liquids they took the Fourier transform of the diffraction pattern which was just sort of a blur really you can do something like this this is liquid argon and you can see some peaks in here which tells you about the nearest neighbors when you see in a liquid it's not random there is a certain amount of short range order and today what we do now is we do this with powders powders consist of little tiny crystals so you get a powder pattern particularly with a synchrotron or maybe with neutrons similar sort of thing that the Fourier transform and you transform it back to a radial distribution function and you can get something like this with all these peaks to represent the nearest neighbors, the next nearest neighbors and so on and you can associate that with the local order in the structure so this is a very important technique now for looking not just the long range structure but also the local order in a crystal this is something that we did this is from a material called PZT it's a solid solution it is a piezoelectric material in fact it's the world's biggest ceramic piezoelectric material worth about 17 billion dollars a year it has a complicated phase diagram from zirconium rich to titanium rich and it's in the middle of that phase diagram that they make the piezoelectric that's where it's maximum the question is how does it work this is a problem that I've been working on for 45 years and I think I now know it and we use this pair distribution function analysis as part of the process of working out what was going on now what was found in the phase diagram is in the middle of the phase diagram there's a boundary on the titanium rich side is the tetragonal symmetry and on the zirconium rich side of that line it's rhombohedral trigonal three fold symmetry and that was always a problem how do you go from one to the other they were thermodynamically not allowed but then it was discovered by Beatrice Nojeda from Spain working in the states that actually there's a monoclinic region right in the middle of that and that acts as a bridging phase between the tetragonal and the rhombohedral but I notice that between that monoclinic phase and the rhombohedral phase there was no boundary you could find no boundary between those two phases even though the symmetries are different and so we started working on the zirconium rich part of the phase diagram and what we knew was in the structure the lead atom is displaced to make it polar if it were rhombohedral it would be displaced along the rhombohedral axis and actually we can see from what we call the anisotropic displacement parameters which are refined that actually it was slightly off and it was off in three positions so it averaged out to being along the rhombohedral axis but locally at the unit cell level it wasn't rhombohedral it was monoclinic and this started to give the clue as to what's going on in this system and so we did pair distribution function analysis experimental and the fit to the data and this is for the monoclinic component and this is using what we call RMC modeling where you make a box of atoms and you let them move around with certain conditions and comparing the Fourier transform with the observed data you make a fit and you can get pretty good fit from this and that combination allowed us to understand and produce this which is a cartoon of what we think goes on in PZT so the idea is that it's a mixture of ordered regions so we have blue, red and green those regions just looking down the rhombohedral axis these are ordered regions and these regions are monoclinic that's a monoclinic region that's a monoclinic region and in between you've got a random array of other unit cells and each of those unit cells is a monoclinic and the idea is that if you take the Fourier transform of that and look at the Bragg scattering that will suggest you that it's rhombohedral on average and the idea that we came up was supposing as you increase the titanium content go towards the middle of the phase diagram suppose that the monoclinic regions get larger and larger at the expense of these random regions until they're so large that they're bigger than the coherence length of the x-rays or neutrons and then you see a distinct monoclinic phase and that's how you can get from one to the other without a boundary and we published that and it caused quite a bit of excitement and we now think we understand exactly how this system works and it's this complicated thing now for the people here who are crystal structure predictors there's an interesting problem for you can you do this? can you show why this happens and furthermore can you show why it is that when you add titanium to this those monoclinic regions get larger because if you could do that you really would solve a problem about how this piezoelectric works okay moving on quickly now then we have the free electron laser appears on the scene and another technique just in recent times in which you take a powder of material proteins or whatever and you drop them through the beam the beam comes along its intensity is such that it kills each of the crystals in they explode before they explode they create a diffraction pattern and the technology now is such that they can collect 10,000 of these diffraction patterns as each of these little crystals goes through and then the computer technology is such it can source through all of those diffraction patterns work out the orientations of the crystal and get the crystal structure out all done in a fraction of a second this is a remarkable change that's happened if you're going to predict Nobel prizes this is one of them haven't got the year and then the latest thing is what we call cryoem this is using electron microscope electron microscope so it's advanced enormously since it was discovered in the 1930s particularly in terms of the the magnetic lenses are improved and more importantly the detectors have improved the detectors now using direct electron detectors and measure the intensities directly this is not diffraction this is actually imaging so what they do is they collect an image with lots and lots of little points of each of these are molecules and then they magnify them molecules looking which are very fuzzy not very well resolved but then they put them into bins according to the characteristics of these images and they combine them together and they approach so they can reconstruct the three dimensional picture of the molecule here this is not crystallography this is direct imaging of molecules and that is an important thing to understand and if you remember I talked about the problem of the viruses and molecules when I was at a meeting of the American Crystallographic Association several years ago I saw beautiful posters with all these lovely protein molecules on it and I went up and I asked people about it and I discovered none of them really knew anything about crystallography and these people are molecule people biologists are interested in the molecule they're not interested generally speaking in how the crystals pack together that's not relevant to them for them the crystallism is a necessary evil they have to contend with in order to get their information and if they could get rid of crystals they would and here we are there is a way not there yet but given enough time that could very well mean that the biologists will no longer be interested in crystallography they will disappear from our community the possibility and here this is the latest this just appeared last week so this is a virus done using the cryoem and it's a norovirus one of these creatures is sick and they found that it's actually in the action of sitting on a cell and it creates this little tunnel to feed into the cell and infect it brilliant piece of work going back to crystallography the latest technique which is causing a lot of excitement and in micro ED you have a powder and you put it in the electron microscope you choose a particular little crystal here and you get a diffraction pattern now in the past getting from this diffraction pattern to a structure was difficult because the intensity spots were not reliable because of what we call dynamical scattering that multiple scattering of the electron beam and if you have multiple scattering it's difficult to interpret those intensities but it turns out that if you're not down a particular strong axis in a crystal the amount of dynamical scattering is not so big and so you can start to measure these intensities to start to get the crystal structure so this is really being done for small molecule crystallography and the idea is you collect a diffraction pattern and you have a tilting stage that this crystal sits on it's very difficult because you need to have a tilting stage and you tilt it the crystal stays in the same position so the technology for this is not trivial it's quite difficult so you tilt the stage and you collect images at different tilt angles you build up a series of diffraction patterns at different angles one of the problems with it is when you measure the intensity of those spots you're not measuring the total intensity of those spots because you're cutting through some of those spots but what you can do you can tilt the electron and beam and make it process around the crystal at the same time and that gets you the actual intensities and so very quickly you can put a crystal this is progesterone and they manage to solve the structure to one angstrom resolution very quickly with this technique this means you can look at tiny tiny little crystals which you couldn't do with x-rays or neutrons or whatever and here you can see what happens when you rotate the crystal you see the diffraction pattern changing they get hundreds and hundreds of these images and then computerize that and from this can solve the structure small molecules this could be important in pharmaceuticals where they can't get crystals they can only get powders they want to know what sort of molecule they've got this is one of the ways that could be done and it's becoming routine and we can see this is going to advance we're going to see more of this in Monty Python what have the Romans ever done for us so my version of that is so what has crystallography ever done for us well drugs, pharmaceuticals, the design of those we didn't have crystallography we wouldn't have them most of us would be dead by now we wouldn't have antibiotics most of us would be dead for sure new organic compounds whatever you use plastic, whatever new alloys, new metals, new alloys they all rely on crystallographic information building materials, cements cements consist of lots of different crystals the design of modern cements is done using crystallography new materials in general with interesting physical properties elastic, thermal magnetic, optical piezoelectric as in my case these all require analysis by crystallographic techniques microelectronics our computers rely on this we have crystals in them your watches contain quartz crystals as well they vibrate to a certain frequency so crystallography again very important, losing crystals to to get at microelectronics and one of the latest things is photovoltaics as many of you will know there's an enormous amount of work going on in the perovskite field with what we call hybrid perovskites a colleague of mine in Oxford Henry Snaith one of the people who discovered this and he has set up a company which is next this year they will probably come out with the first device working at an efficiency of about 29% which competes very well with silicon and the advantage of silicon is you can make these things very cheaply and they don't you don't have to worry about defects in them with silicon you have to have it very clean very perfect but with the perovskites you don't need to have it that perfection and so there's a lot of work all over the world now every country, if everybody wants to work on these photovoltaics piezoelectric superconductors and so on the high teeth superconductors years ago they were based on perovskites the man who discovered it working on strontium titanate and other materials of that sort perovskites medicine, proteins and viruses we have to understand how proteins work in order to make the right sort of medicines and how to treat people the same with viruses and genetics of course the discovery of the structure the double helix of DNA is what launched the whole of the modern field of genetics so I think you can see that crystallography is a very strong pedigree in the future well as I mentioned the biological community is really only interested in molecules so suppose that there comes a time when the need to grow crystals becomes irrelevant they will no longer be interested in crystals and we have a community of crystallographers on our database in the international union we have something like one and a half thousand people's names and they are only a fraction of the crystallographers around the world and we have our international meetings where the biological field is a big part but we could lose all of that the question is then what would happen to crystallography as a subject and you can think about that in the inorganic field as far as I can see that will continue probably in the small molecule field also that will continue but we may lose the biological community in the world one of the impacts of that could be synchrotrons because the main financial justification for synchrotrons has always been the life sciences the biological community and if they don't want crystals and they can use electron microscope instead then they are not going to use synchrotrons and so the justification for synchrotrons becomes a problem I don't know whether that is what is going to happen but it gives you an idea of things to think about so developments of electron diffraction image that is certainly going to happen they are going to improve even more they are going to see great advances in there biological crystallography as I say will it continue there will be more emphasis on the local structure and disorder in crystals as opposed to these ideal crystals that we have played around with before because that is where a lot of the physical properties actually originate future synchrotrons I have mentioned there, the question mark will there be new neutron sources for sure to allow neutron diffraction to be done inorganic crystals materials minerals I think those will continue as they are now but obviously there will be new developments in how to study them predictions of crystal structures this is what most people here are on about will we need experiments maybe we will get to the point we don't need to experiment anymore you are so good at it you just put it to come out of a computer for 20-30 years with us to develop so the future in this area is very bright really it is very difficult to predict the future as you know but those are a few suggestions that I have and I am sure that many of you could think of some others that I haven't mentioned there so subject began a million years ago here we are today amazing advances going on thank you for your attention thank you very much Mike for the historical presentation and I am sure there will be some questions, comments Mike could you please detail about the role of crystallography in discovering antibiotics because Fleming discovered antibiotics without any use of crystallography at least penicillin would be available to us without our science what about other antibiotics the point about the crystallography is not the discovery of penicillin that was already done in the 30s and penicillin was first made available in 1942 mainly to a few people in the American army originally no the important thing was that studying the crystal structure of penicillin at that time by Dorothy Hodgkin meant that she could identify a particular group within that molecule and that four fold ring I mentioned the beta lactam would be very important if you want to make new penicillins today we have not just penicillin we have cousins of penicillin grandchildren of penicillin and so on and many of them contain this particular ring so to make the molecules you need to know what the molecular formula is and what the shape is to give you some idea of what you should do that's the reason why we have so many different antibiotics of that sort I mean there are different classes of antibiotics but they've all most of them have got crystal structures done with them so obviously crystals have many symmetries and I have been told that there are usage of group theory in the study of crystallography and I am asking about what role does group theory or mathematics in general play in the study of crystals it is the very center of crystallography started in Germany who looked at the symmetries I mentioned Schoenfleisch for example but we are dealing with objects which is in their ideal state so where we start from are symmetric objects and symmetries there the whole thing about crystals is symmetry ok so you can apply the standard group theoretical techniques in studying various things like the vibrations of atoms in a crystal you study them using group theory and for example if you are interested in phase transitions in crystals in many cases they follow group subgroup relationships and so you can go to a website now you can try it go to ISO distort and you can put in a crystal structure and you can generate all the phone on modes for a particular type of distortion of the structure it comes out of the structure thing about group theory the thing about symmetry let me shock you symmetry is boring crystals are boring they just sit there nothing happens they are static crystals and symmetry nothing happening you know these people who think that crystals can heal you and they have wet things coming out of them which affect you I have to say to these people I am sorry but crystals are the deadest objects in the universe nothing is coming out of a crystal nothing at all symmetry is boring think about music I am going to sing to you stand back here is my song da da da da da da da da da you bored yet? I will try it again da da da da da da did you notice something when I changed the pitch you woke up that is what makes music if you look at musical scores that is what composers do important thing is not the symmetry it is the breaking of symmetry that is important when you break symmetry things change and if we did not have breaking of symmetry and I gave you an example of disorder then we would not be here because we exist because of the breaking of symmetry because of phase transitions because of changes of state and so on and it is a very important concept although we study symmetry we do it to get at the breaking of symmetry in the end if you look at art work buildings, how they are constructed you will often see it is broken a bit to make it a bit more interesting breaking of symmetry is really the important thing not symmetry because that gives us the mathematical tools to do the study not just for Christians in general very good another question let me ask you something myself I think it is a beautiful perspective you gave us because it touches mathematics, physics chemistry, biology, all of them talk now music also is very good but in historically I think transition for people to study the materials then to move to study organic material it looks very smooth but somehow it attracted attention of biologists when they were supposed to be only for chemists and physicists it was smooth because to a crystallographer a crystal is a crystal it does not really matter whether it is a metal or an organic thing or whether it is organic the techniques are the same in a regular way so for a crystallographer there is not a lot of difference between them but in the case of the proteins of course there was a reason for doing that and it goes back to the 1930s mainly in the lab of Bernal with Dorothy Hodgkin was working actually and they began the first work on protein or biological material because they thought it should be possible using these techniques that they have been using for inorganics and metals it should be possible to apply that to crystals of biological material because a very, very tough problem and Bragg actually originally thought it would be impossible but when he moved to Cambridge to the Cavendish lab and Perutz joined him they started to look at the myoglobin hemoglobin problem gradually they began to realize they could apply the same techniques it was a transition, smooth transition it's interesting more personal go ahead when you think when you just sung so I get this idea do you see any time dependent experiment in the future because the X-ray and crystallography was static it's going to be dynamic there's a lot of time experiments going on for example there are groups who do things like take a crystal flash light on it create a transition state and collect the data because now you can collect the data so well so you can study the evolution of the transition state through a chemical reaction for example that's being done and then you've got things like people studying muscle so you want to see how does the muscle the muscle is crystalline how does that changing as it contracts the earliest work done on synchrotron radiation back in 1972 was underhacksily looking at muscles so even back then time resolved experiments were being done so it's another important area just going back to my question on a personal basis you made a comment which I think I liked is that you say that Bragg had a tradition to have female students and that Bragg had this tradition to have female students and that your own supervisor was a female at that time that was not very standard to have this top female scientist can you tell something about your experience on that well in crystallography we are very lucky we do have a very large number of female crystallographers quite often I go to meetings it's quite a large number of female crystallographers and the question of why that is has been a matter of debate for some time and there is a theory that it probably goes back to W.H. Bragg encouraging women into science we don't know whether that's really true some countries were better than others Germany was terrible no women Russia was wonderful a lot of women in crystallography because the Russian crystallographers encourage women into science Britain was good France was quite good Italy was okay but it was possible that it was William Bragg's open and also Lawrence Bragg also by the way were very open to have people in the lab and train them in an era when you had the gentlemen scientists who really didn't want women around a lot they were very forward thinking in many ways my PhD supervisor was Kathleen Lonsdale I was very fortunate that when I moved to Cambridge in 1969 I worked for another famous crystallographer female crystallographer Helen McGaw world famous for the work on perovskites I was very lucky to work for two fantastic women at that time in Cambridge there were not many colleges accepting women sorry at that time in Cambridge there were not many colleges accepting women so it was very strange crystallography has always been ahead of the game and you know the odd thing about crystallography is this it's almost unknown when did you last see a television program on crystallography eternal no television look at the science program what do you get cosmology, stars, particle physics medicine when did you see one on crystallography look at all our Nobel prizes look at that fantastic history look at these beautiful objects yet for some reason the only way it appears in the public mind is in crystal healing that annoys me can you comment on your last statement and your last statement that will we need experiments predicting crystal structures what to do you have to ask these guys here because these are the people who are predicting crystal structures and they're making extraordinary progress and what I've seen here they're going to the lectures they have very sophisticated algorithms and techniques for doing that and they are making distinct progress how far that will go for real crystals I don't know there are problems if you want to look at what I think is interesting which is the breakdowns in symmetry the short range order problems that I've mentioned here I think there's still a long way to go for the crystal prediction people but we're talking 50 years time who knows okay before we finish I think everybody who's invited to join us for some refreshments and as usual we have this tradition here that the students the diploma students are not allowed to go there because they will be asked to come and ask personal questions to the speaker and we guarantee that there will be some food and drinks afterwards so let's thank Mike again for the wonderful talk