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0:08
[APPLAUSE] On the 30th of April, 1852, Thomas Henry Huxley, one of my scientific heroes, walked through that door to give his first Friday evening discourse. His heart was beating like a sledgehammer, as is mine. [LAUGHTER] He wrote to his wife later, I now know what it feels like to be going to be hanged. [LAUGHTER] His nervousness, I think, was partly the fault of the audience. He continued, in his letter, "the audience is a most peculiar one-- at once the best and worst in London."
1:04
Such as tonight. "The best because you have all the first scientific men-- the worst because you have a great number of fashionable ladies. The only plan is to take a profound subject-- and play at battle and shuttle-cock with it-- so as to suit both." Well, Huxley's outrageous division of the sexes is, of course, of its time. We know now, thanks to quantum mechanics, that ladies can be fashionable and intelligent at the same time. [APPLAUSE] As can men. [LAUGHTER]
1:48
But where I agree with Huxley-- and I agree with him on many other topics, as well-- is in the choice of a profound subject. And I hope I have chosen a suitably deep subject for tonight. What I want to tell you about is the technique of x-ray crystallography, a technique that has a very famous and intimate relationship with this place. And it's a technique we are celebrating the 100th anniversary of the invention of this method, which has shown us the world in unprecedented detail.
2:17
And we're celebrating the centenary this year. Now, unfortunately, it doesn't really have the appeal in the public domain that I would like. It's hidden from us, and that's partly because the technique relies on a phenomenon that is not available to us in our everyday lives. We don't come across x-ray diffraction, which is the physical principle of which the method relies. But, it does speak to a broader subject, which is humankind's obsession with seeing things that are
2:51
normally too small to see. And that's something that, actually, has grabbed the human imagination for as long as we have been putting lenses together to make telescopes and microscopes. And one of the most famous publications from the 1600s-- it was 1665, and we have an original copy here-- is Micrographia, written by Robert Hooke, who was a pioneer of microscopy. And this was a very popular book in its day. It was a bestseller. Peeps tweeted about it.
3:24
It is the most ingenious book I have ever read. And the secret of Hooke's success, I think, was that he included images of things that were familiar-- such as his famous flea-- even if they were largely unseen to most people. And these astonishing detailed pictures of the horrific flea delighted and enthralled the people who bought his book. But, the trouble with microscopy is that it has got limits. It's fantastic in its own way, but there are limits in a number of ways.
3:59
One is, that when you're illuminating material with visible light, you, generally, only see the surface. You see the light that is reflected off the surface of the material, as with the flea here. You can't see inside. And also, you are limited in the size of the things that you can see. What if you want to see the molecules that the flea is made of? And what I want to tell you tonight is about the use of x-rays in order to solve both of those problems.
4:27
And I hope, in doing so, to sort of set the ball rolling in a popularisation of the technique. Because, now that we're celebrating the centenary, it is a method that has really transformed all of the sciences. It relies on a rather beautiful piece of physics and mathematics, but it has informed not only those subjects, but mineralogy, chemistry, and biology. It has really brought us an acquaintance with the world at the molecular and anatomic level, which was simply not
4:56
appreciated prior to the turn of the 20th century. So, I'm going to make you work a little bit hard a couple of times during this, as I go through the theory. But I am not going to delve into all the gory details-- I will spare you that, ladies and gentleman. But I do want to tell you about how you use x-rays, and how you use them in a very particular way. Now, from the very beginning, it was obvious that x-rays was a special kind of light, because it could see through matter.
5:25
And here you can see one of the very first-- it wasn't quite a medical x-ray. I think it was more an experiment that Rontgen, who discovered x-rays in 1895, did-- not on his own hand, smartly, but on that of his fashionable wife. And what you can see is that the skin and soft tissue is largely transparent, because matter is mostly transparent or semi-transparent to x-rays. But the bone is slightly denser. It's got calcium atoms in it, and so it casts a shadow. And the ring--
5:59
let's give Rontgen a bit of credit and assume that it's gold, which, with an atomic number of 79, is very electron-dense. And so it scatters x-rays and casts a darker shadow. So, what's happening here is that the electrons in the atoms and molecules of Anna Bertha's hand are scattering x-rays out of the beam, and so it attenuates the transmitted beam. And so you see the shadow. But rather than being a solid shadow, we see that it's semi-transparent because the x-rays are very penetrating.
6:34
So, let's think about the scattering that's happening and that explains that x-ray pattern-- that x-ray shadow. So, x-rays, we now know, is a special kind of light. It just has a very short wavelength, and it effectively consists of an oscillating electric and magnetic field. Here, we're just showing the electric field, and it's about to hit an electron. And when an electric field hits an electron-- a charged particle-- it causes that electron to oscillate up and down.
7:05
And an oscillating electron will, itself, emit radiation of the same wavelength, and so it emits x-rays. And, in fact, almost in all directions are x-rays emitted. And so, the transmitted beam is attenuated somewhat because of that. Most of the x-ray is unaffected, but a small part of the energy is re-radiated-- scattered, we say-- in all directions. And if we look at a more realistic representation of an atom, we can see that what happens is, the straight
7:39
through beam is attenuated as the x-ray is partially scattered by the electrons in the atom. So, what the x-ray is doing is penetrating and sampling all of that structure that's inside the atom. Now, when we take medical x-rays, we're only really looking at the transmitted beam, and we ignore the scattered radiation. But the technique of x-ray crystallography actually relies on the scattered radiation, because it, in itself, contains information about the object that's doing the scattering.
8:14
And that is the basis of the technique that I want to tell you about tonight. And what this technique can do-- because of the penetrating power of the x-rays, it shows us the interior structure of things. And it does so, not just at a fairly anatomical level-- we can actually begin to learn about the structures of molecules and of atoms. And that happens because of a very peculiar property of light-- of any kind of radiation-- when it interacts with matter which is of the similar size
8:43
to its own wavelength. And we can get an understanding of that-- that process, that phenomenon of diffraction. So what happens is, when light scatters from an object that is about the same size as the wavelength, it scatters in many directions. And we can get an idea of that by repeating classic optics experiments that were done in the early part of the 19th century by a polymath, Thomas Young. And I don't know how Young managed to do these, because I think he only had candles at his disposal.
9:13
But, fortunately, we have a laser. So, I would like to just show you the principle of diffraction that occurs in order to give you an idea of the strange property of light when it interacts with matter. So, if I just blank the slides and we could have the lights down a little bit, we'll be able to see what happens. So, this is a very cheap laser, and the beauty of laser light is that it gives us a very fine, very bright, and a very parallel beam. And that beam is travelling in a dead straight
9:51
line from the laser-- bouncing of the mirror, of course-- to the screen. So, we see a fine spot. But, if we then take an object, a very simple object-- and this is just a single slit, so there's a small gap here, which is of approximately the same size as the wavelength of light-- we can see-- let me see. Let me get that right. OK. So, you have to look a bit closely, but what you see is we no longer have a simple spot. And we don't have an image of the slit, either--
10:22
the slit is just a rectangular aperture. But, you see, what has happened is the light is spreading out at an angle. OK? Not necessarily very much here, but enough that you can see it. And you can see there's a bright band in the middle, and then flanking it on either side, if my laser holds up-- well, there we go-- then you can see that there are fainter bands on either side, as well. And what that tells us is two things. One is that the light is bent--
10:52
it's scattered at an angle by the small object-- and that there's a pattern here that appears to be related to the particular structure that's doing the scattering. And so, there's a relationship that, if you understand the rules of optics, we could work backward from that pattern to figure out that we had a single slit here. Now let's see what happens when we put two slits into the beam. So, these are just two slits, both the same width as the original slit in the first slide.
11:21
And now, we can see that there is a different pattern, although it is similar to the first one. So again, there's a central broad band, and its flanked by fainter bands on either side. But now, each of those bands is actually split into a series of dots. So, again, that tells us that we've changed the structure, here, that's doing the scattering, and that changes the diffraction pattern that we see on the wall. But, because the structure here is simply a duplicate of
11:48
the first structure, the overall pattern-- the envelope, as it were-- of the intensity variation changes. It's just that we see different points of light. And if we go from two slits, now, to six, then we see that, again, we get a similar overall pattern-- a, sort of, central bright than flanked by fainter bands on either side. And, again, now they are divided into dots. And the pattern of dots is exactly the same as with the two slits, because the spacing between the six slits is the
12:22
same as the spacing between the two slits. And that's a point I want you to keep in mind because we'll come back to talk about that when we talk about crystals and what crystals do. Because a crystal is, simply, a repeating form of matter. You have a structure that is repeated, and we will be using that to probe the structure of matter. But the optics shows us how that principle works. So, that's my diffraction, but-- so, I've mentioned crystals there, and I showed you that--
12:55
with a repeating pattern of the slits-- was important for getting an interesting diffraction pattern on the screen, that we could then start to think about it and interpreting. Although I haven't explained to you, yet, how you do that. But, before I do that, we want to, then, actually grow some crystals of our own. So, if Jayshan, my assistant, is going to come here. And so Jayshan-- he's a novice crystallographer. And so, what Jayshan is doing here is, we have a solution of a protein--
13:33
a purified protein-- called lysozyme, which some of you may be familiar with. OK, we have pre-filled these small wells with a solution that's got a high concentration of sodium chloride and an organic solvent, called polyethylene glycol, or PEG. And Jayshan is currently mixing some of that solution in with a drop of protein in this well, and he's then going to seal the chamber. And what's going to happen over the course of the lecture-- we hope--
14:03
is that, because we have a high concentration here, you have a lower vapour pressure above the reservoir. And so water gradually moves through the vapor phase, out of the drop and into the reservoir. And what that will do over a course of minutes, that will reduce the volume of the drop, and it will increase the concentration of protein inside the drop to a point where, we hope, it starts to precipitate out of solution. And when a protein precipitates out of solution,
14:31
what that means is that the molecules are starting to stick together. They interact with one another rather than interact with the water molecules. And what we hope is that they will aggregate together in a very regular array to give us a protein crystal. So, we are almost done with that. I did say he was a novice. I was going to do this myself. I thought I'd be too nervous, but my hand looks OK. The trouble is that's the hand I pipet with.
15:04
I believe that is a Tommy Cooper joke, just to give proper attribution. So, we are going to put that on one side. We want to take it out of the bright lights in case the temperature perturbs it, but we will come back to that experiment later in the lecture. But, I'm getting a little bit ahead of myself with crystals. I've told you about x-rays and diffraction. Let's think about how the two were finally brought together. So, as I said, x-rays were discovered in 1895 by Rontgen.
15:34
And they were quite a puzzle at the beginning, although we now know that they are a type of electromagnetic radiation, and so they are waves. At the time, there was a great debate-- are they waves or are they particles? It really wasn't known, and many people spent a lot of time trying to investigate their properties in order to work it out. And, in Germany then, a scientist called Max Von Laue thought that he would be able to crack the problem. Because he reasoned that inside crystals, and in a
16:07
crystal of copper sulphate-- this is a beautiful blue crystal here-- it was well understood, because of the regular faces that one sees in crystalline solids-- it was already presumed that the atoms or molecules within them would be lined up in regular arrays. And Laue figured that the wavelength of x-rays was probably about the same size as the spacing between the atoms in crystals like copper sulphate. And so, he persuaded to Walter Friedrich and Paul Knipping to do the experiment for him.
16:39
So, I guess they were the Jayshan's of their day. And, what he did was, he took a Crookes tube, which generates x-rays, and put it through fine slits in order to get a pencil beam, as they called it then. Placed a crystal here, in their experiment, and then placed a photographic plate at the far side. And they exposed that for several hours, and then developed it on tenterhooks in the dark room, and then produced one of the most remarkable images of the 20th century.
17:13
Now, I know it doesn't look like much, but it is a truly significant scientific result. It does look like a horrible smudge-- maybe it's a Rorschach diagram, I'm not quite sure-- but what you can see are two things. One, there is a diffraction pattern there. It's not a very regular diffraction pattern, not immediately apparent. But you can see that the beam has been split into different rays, and so it's scattering. So there's a ray here and a ray here, and these are spread out from the middle.
17:44
So the audience, here, is where the x-ray beam came from, and this is the pattern. So, Laue's hypothesis was supported, so it did suggest that x-rays are waves and that crystals could be used as a diffraction grating for them. But-- as well as showing that they were waves-- because you have a pattern here, what that tells you is that the structure within the crystal-- because the beam has passed straight through and been scattered off at angles--
18:13
the structure of the crystal has imprinted itself, somehow, on the pattern of scattering. And so, what you have in this pattern-- and when they moved the photographic plate back a bit, they got a slightly better resolved separation of the spots-- but there's information in here about the structure of the crystal that they were analysing. Now, this wasn't the most regular pattern. It turns out, there were good reasons, initially, for choosing copper sulphate, but--
18:39
although it is a nice, regular array-- the atoms are not arranged, in copper sulphate, in a very symmetric pattern. So they then chose a crystal of zinc blende, which is zinc sulphide. And from the appearance of these beautiful crystals, you can tell that it does look like the atoms are lined up in a cubic type of formation. And that certainly turns out to be the case. And if you take one of these crystals and you orient it properly in the beam, then you get a much nicer pattern.
19:08
And you can see, actually, that the pattern of scattering of the x-rays has a four-fold symmetry. You can see this makes a sort of square that is hinting at four-fold symmetry, which you would expect for a cube, inside the crystal. But, Laue tried to analyse this pattern and he was mostly able to solve it, but he wasn't quite able to get the whole way. And this is in 1912. So, it was a major breakthrough. It was big news in Europe, but Laue himself wasn't able to
19:44
solve the structure, wasn't able to figure out exactly how it is that you use x-ray diffraction information in order to work out structures. That fell to the father and son team of William and Lawrence Bragg. Now, William was already, at that time, a renowned physicist and had been working on the problem of x-rays up to that point for the past 10 or 15 years, and was a world expert on that. And so, a Norwegian colleague of his, Lars Vegard, wrote to him, because he'd been to Munich and
20:15
he'd talked to Laue. And he sent a letter saying, "Recently, however, certain new curious properties of x-rays have been discovered by Dr. Laue in Munich." And the letter was a long and detailed account of the experiments, and Laue was even kind enough to give Vegard a photograph, which he then knew he was going to send the Bragg's. So, this was a very nice example of scientific international co-operation. And this happened in the summer of 1912, and Lawrence,
20:44
William's son, had just completed his second degree-- a degree in physics-- in Cambridge. He'd earlier got a degree in mathematics when they were living in Adelaide in Australia. And it was Lawrence, really, who was able, ultimately, to crack the problem of figuring out how there is a relationship between the scattering pattern of the x-rays and the structure of inside the crystal. And it was fortunate for him, in a way. There was a sort of coming together of events.
21:16
He'd just finished his physics degree, so he had been learning about electromagnetic radiation, he'd been learning about the symmetry of crystals. And he also was blessed with a father who was a world expert in x-rays and who had, then, received this letter. They hadn't actually seen Laue's paper. And Lawrence realised that the key to the problem was realising that what's happening is that the x-rays are reflecting off planes of atoms in the crystal.
21:47
And so, I'm going to make you work hard here by explaining to you a little bit of the theory. So, we are all familiar-- at least those of us who wash regularly-- with the laws of reflection. So, you know that the angle of incidence equals the angle of reflection for light impinging on a silvered or polished surface. Now, that law of reflection applies equally-- although I won't explain the details-- even if that surface is discontinuous-- say, for example, it was made up of a set of atoms.
22:18
But remember, if we're now thinking about what x-rays do to atoms, matter is mostly transparent to x-rays. And so, a large fraction of the energy will actually pass through-- certainly the top layer of atoms. Only a small fraction of it will be reflected. Most of the energy-- more than 99%-- goes straight through. And so, that will interact, then, with the layers of atoms below that in the crystal. And we have regular arrays of atoms-- many, many of them.
22:47
And each layer will then, itself, reflect a tiny fraction of the incident x-rays. And what Lawrence realised was that what he needed to do was, to work out how much the beam is scattered in this direction, he needed to add up all of these rays. Now, this diagram is getting a little bit complicated, but Lawrence had a gift, I think, for simplifying things. So, let's just think about one of the rays going through, and you get a partial reflection of every single layer within
23:16
the crystal, from this law of reflection. Now, we also have to remember that what's happening here is an electromagnetic phenomenon, so the x-rays are waves. And so, we have to think about what the waves are doing. And to make it even simpler mathematically, we can boil that down to just two waves, although let me just tell you-- so here, the scattered rays are what we call in phase, and what that means is that the peaks are lined up. And so, all the peaks are lined up and all the troughs
23:47
are lined up. And when that happens, when you add those waves together, you get a very big wave-- a wave with a very big amplitude. It oscillates massively. So, that's called constructive interference. And so, that's the best way that waves can add up, although there are other relationships, too, as we'll see. But let's plough on and see how these relationships arise. So, if we just think about by what's happening in the reflections of adjacent rays-- so the top one and the one below.
24:19
So, we have the incident ray-- comes here and goes away. And then the lower ray hits the bottom layer and is reflected off the lower layer.
24:34
So let me just get that. So what you see is that the lower ray has to travel a bit further. OK? So it sort of falls out of step with the upper ray, because it has a shorter path to go around. It's like running in the outside lane on an athletics track, as it were. But, as long as this extra distance travelled-- which is indicated by the two black arrows on my diagram-- is equal to one wavelength, or two wavelengths, or three wavelengths, or any whole number of wavelengths, then
25:04
the waves will be back in step. And so, they will add up, and you will get appreciable scattering in this direction. So, Lawrence Bragg worked out, by simple trigonometry, that this extra distance from the spacing d, and when you're reflecting at an angle theta, the path difference is equal to 2d sine theta. And if that path difference-- 2d sine theta-- is equal to a whole number of wavelengths-- so, the wavelength is simply the distance between two adjacent peaks--
25:35
then you will get appreciable scattering in this direction. And that is Bragg's Law. Now, if you look at a slightly different angle-- and here we've just changed the angle of incidence-- and in this particular case-- the way that I've chosen it-- the path difference is such that the lower wavelength is out of step by half a wavelength, or a whole odd number of half wavelengths. So, in this case, the peak of the top ray lines up with the trough of the bottom ray.
26:07
And that means, in this case, that these two rays cancel one another out, so you get no scattering. Now, if you think about it, you'll have the same relationship for the next pair of layers down, and then the next pair after that, and so you get no scattering in that direction. And so, what Bragg's Law tells you is which directions you're going to get scattering in, depending on the angle that you're looking at and the spacing-- which is an indication of the structure-- within the crystal.
26:34
Now, you might think, well, OK, he's just shown us two particular special directions there. But, actually, Bragg's Law is a very severe law, and it only allows scattering if it is true. So, let me show you how that works out by a slightly more sophisticated example, and I'm going to come to the front so I can see this with you, as well. So, let's think about a case where it's coming in at an angle, and the difference between adjacent layers is
27:00
such that the path difference is only 1.01 wavelengths. It's a percent out. So, this ray-- this wave-- is almost exactly in phase with the lower one. Near as dammit. And if you, then, think about the next ray up, that is twice as far away from the first ray. And so, the path difference is doubled. And in this case, the path difference is 2.02 lambda, which is, again, almost in phase with the lower one. So you kind of think, well, this is going to add up--
27:30
there's going to be quite an appreciable amount. And the same for the third one-- it's only 3% out. It's not really too bad. But, by the time you get up to the 51st layer-- and remember that in any given crystal there will be thousands upon thousands of layers, if not millions upon millions-- when you get to the 51st, the path difference is 50.5 wavelengths. And so, this ray is half a wavelength out of step with the one from layer one, and so, those two will cancel out.
28:01
The diagram is a little bit misleading, but they are close enough in space that you do get interference here. And so, the 51st layer will cancel with the first one. What that means also, then, is that the scattering from 52 is going to be half a step out with the scattering from layer two. And so on, up the stack of layers in the crystal. So, unless Bragg's Law is satisfied-- and that is, bang on, one, two, three, or four wavelengths-- then you do not get any scattering.
28:37
And so, Bragg's Law places a severe restriction on the scattering of the planes. But it also tells you interesting information about the spacing between those planes. And also-- we've just looked at one horizontal set of planes in the crystal-- but there are many other ways of looking at crystals. These are the horizontal planes, but you can equally imagine that the atoms line up in a completely different way. And so, we have an angled set of planes here.
29:07
But you can look at the same thing again, and you have another set of angled planes, each with different spacings. And what Lawrence realised was the spots in a diffraction pattern are simply all the various different reflections that are allowed by his law coming off the interior of the crystal. And we can maybe get an idea of that just if we look in three dimensions. So, here is a atomic lattice, but if we sort of tilt it in three dimensions, you can see that we see a horizontal set
29:38
of planes, there, from the way that the atoms line up. But we can rotate it again, and here we have another set of planes which are sloping down from left to right. And then one final one-- rotate another direction, and here you can see there's another set of planes sloping from right to left. And so, all of those sets of planes are inside the crystal. And when x-rays come in to the crystal, they are bouncing off those sets of planes in all different directions.
30:08
And so, when he looked at a diffraction pattern-- oh, let me get back to the slides-- when he looked at a diffraction pattern, Lawrence realised that what he was seeing was each of these rays was one of the reflections off one set of planes. And so, it was telling him-- and the angle of the ray, which you could measure-- was telling him about the angle and the separation of the planes in the crystal. And he realised that by, if he could figure out where all the
30:33
angled planes were, then the atoms would be lying at the intersections of all those planes. And so, he would then be able to work out, once he'd solved that puzzle-- he would be able to work out where the atoms were. And so, he was the first, in that case then, to solve the structure of the atomic arrangement with inside a crystal. And this is from zinc blende, and this is Lawrence's interpretation of the pattern, or his prediction of what the diffraction would look like, once he had
31:01
figured out the structure. And as you can see, there's a very good correspondence. And he did this just in the few months after the summer of 1912, so this was by December of that year. And he'd gone back to Cambridge, because he was working with J.J. Thompson at the time. But, he was in regular correspondence with his father. "Dear Dad," he writes, and is, sort of, describing the experiment. And it's a nice, sort of, chatty letter. He's sending him some photographs, but some very bad
31:30
prints from the photos. They're not very good. But you can see there's a very, sort of, nice statement about his excitement at the achievement. So, if you can read the handwriting-- it's better than mine, I have to say-- "Larry's thing was equivalent to reflection but of course he didn't see it, and it's great fun getting it straight off, isn't it?" So, it's the young Bragg-- he was 22, 23 at this time, and you just get a real sense of his excitement.
32:01
And it was a real puzzle-solving exercise for him, and he was jolly pleased with the result, and quite right too. So, they went on. Soon, the Bragg's father and son team are working together analysing lots of crystal structures. This is one of their own early pictures. This is from a crystal of potassium chloride, which is a close relation of sodium chloride. And again, Lawrence was able to interpret the diffraction pattern, and this his own prediction from having worked out the structure.
32:35
You can see that he's annotated it, and here-- sorry if-- so, you can see that he has annotated it. And then, they also analysed sodium chloride, which actually has a similar atomic arrangement. But you can see that there are small differences in the pattern. You can see, you get many of the spots in the same places, but some of them change in intensity and darkness. And this was an early hint that it's not just the positions of the spots that are important, but the intensities are as well.
33:04
Now, initially they had mostly just been working on the positions of the spots, which told them about the angles of the planes. And it was by working out the angles of the planes that they could figure out where the atoms were. But this was an early indication of a more sophisticated analysis that was to follow it. So, this was a structure of sodium chloride that they worked out. They published it in 1913, and even then-- although they worked hard on it-- he wasn't entirely sure of himself.
33:32
It was on this rather slender and indirect evidence that I assigned the structure, in a paper read to the Royal Society in 1913. Fortunately, few further investigation established its correctness. Now, it was a major breakthrough. This was the first time that people had seen the interior of the matter, had seen the atomic arrangements inside a piece of crystalline matter. However, it didn't please everybody, and it took the chemists actually, in particular, a long time to get
34:00
on board with crystallography-- or some of them, at least. So, Bragg was writing, as late as 1927, "In sodium chloride there appears to be no molecules represented by sodium chloride." The chemists had expected to see molecules, of an atom of sodium and an atom of chloride stuck together. "The equality of number of sodium and chloride atoms is arrived at by a chessboard pattern of these atoms. It as a result of geometry and not a pairing of the atoms."
34:25
Now, a British chemist, by the name of Henry Armstrong, took exception to this. He got rather cross, and he wrote in the pages of Nature, "This statement is absurd to the nth degree, not chemical cricket. Chemistry is neither chess nor geometry, whatever x-ray physics may be." You can just hear the disdain in this voice. "It's time that chemists took charge of chemistry once more. " So, he was a little bit out of step, perhaps, with many of his colleagues, because many
34:55
chemists did adopt crystallography. But it didn't phase the Bragg's . They carried on at working with crystallography. An early structure that they solved the following year was the structure of diamond. And that was followed, and again, 10 years later, by the structure of graphite. Now, both of these are forms of carbon, and this shows how understanding the atomic structure helps us to understand the material properties of these. So, in diamond, carbon is bonded in a three-dimensional pattern.
35:23
We have a tetrahedral arrangement, and you have strong bonds in all three directions. Where as in graphite, again, a pure form of carbon, the atoms are arrayed two-dimensional hexagonal nets. And these nets can slide past one another, and that is why graphite is used as the lead in your pencil, and is very soft and leaves a smudge on a paper. So, understanding the intrinsic structure helps us to understand exactly what the material properties of these are.
35:52
So, we're getting new insights into material science from this. And the Bragg's kept going further and further into this. They solved more and more structures, mainly, initially, working on types of material that only naturally occur as crystal. So iron pyrite, calcite, and quartz. And, I agree with him when he wrote-- and, again, this is early June, 1914-- "we are scarcely guilty of over-statement if we say that Laue's experiment"-- and it was good of him to credit Laue--
36:20
"has led to the development of a new science." And I think that's absolutely true. Now, until that point, they had only been looking at relatively simple structures of types of matter that naturally occur as crystals, such as the beautiful crystal of rock salt that we have here. And, they had been largely relying simply on measuring the positions of the spots in the diffraction pattern, in order to, then, solve the puzzle of how to work out the internal structure. But again, early on--
36:54
1915, this is-- William Bragg give a lecture at the Royal Society and identified the opportunities for advancing the technique for improving it and applying it to more complicated structures. So, in this simple case, we'd be considering-- the consideration of the crystal symmetry-- though unable themselves to determine the crystal structure, comes so near to doing so that a few plain hints given by the new methods-- that is, the positions of the spot in the diffraction pattern--
37:22
have been sufficient for the completion of the task. The exact positions of the atoms are then known, so they could work it out. This is not the case with more complicated crystals, and he realised that a more sophisticated mathematical approach-- he realised, even early in 1915, that Fourier methods needed to be applied in order to bring in the information that was in the intensities of the spots in the diffraction pattern, so that they could start to analyse more complicated things.
37:48
Now, I'm not going to go through Fourier Theory with you here, tonight, in gory detail, but I do want to give you a type of graphical explanation for it. So, let's think about a more complicated molecule. So, this is a complicated molecule. I hope you'll agree it's a little bit more complicated than the two atoms of sodium chloride. This is in fact a protein-- doesn't really matter and what it is-- but you can see that it's a complex set of bonded atoms.
38:12
And what I'm showing here, in this blue mesh, is the electron density. So we see exactly where the electrons are. So, this is a representation. So, let's think about how x-rays interact with a molecule like this. So, an x-ray comes in from the side-- and here it comes-- and, as we saw before with the electron and with a single atom, the x-ray illuminates the whole of the molecule, and we get scattering in every direction from every part of the molecule. OK?
38:44
And what you'll notice here is that some of these scattered rays are beefier than others. So, this is quite a strong one, and it's coming off in this particular direction. We have quite a strong oscillation here. Whereas is this one is quite weedy, and what that means is that this is scattering from a point where there's quite high electron density-- strong electron density-- whereas here is a part of the structure which has weak electron density.
39:07
So, although the scattering is a bit of a mess because it's in all directions, what each scattering is doing-- it's carrying off a little bit of information about the electron density at the point where it was scattered from. Now, we can't do mathematical analysis on things like this. We like to break down the problem and take it step by step. So, let's simplify it, now, just by considering all the scattered rays in one particular direction. There will be thousands of them--I have only had
39:32
time to draw four. So, again, the amplitude-- so, the size of the oscillation-- varies according to position, and that will vary in different positions r, indicated by a vector in the structure. Now, each of these waves is heading off in a particular direction and can be represented mathematically by this function. Now, this function looks horrendous OK, I agree with you. But, it's actually not very difficult. So, as we said, the amplitude depends on the electron
40:05
density, and this function here-- rho of r-- tells you, what is the electron density at position r in the molecule. So, that's a measure of the electron density. If that's big-- that number-- then you'll get a big amplitude. And this dxdydz is just the little volume of electron density that we have at this point. This exponential function looks a bit odd, but that's just encoding the fact that this is a wave-- it tells us about the wavelength.
40:30
It also depends on s, which is a number that just varies with the angle at which we are thinking about. So, we're just thinking arbitrarily about this one angle, but we generate the mathematical methods just for that direction. But it also tells us about the phase, and the phase of the wave depends on r. And so, the phase has got information about the position of the electrons doing the scattering, as well. And the phase is simply, where is the position of the first
40:57
peak relative to some arbitrary origin. So, to calculate the total scattering in this direction, we have to add these up. And when we do addition of funny terms like this, we have to integrate-- so again, it looks horrible-- but all we're doing is just adding up the waves. OK? And when we add up the waves, we get one particular wave that travels in that direction. And we can think about the whole contribution from the whole molecule emerging from some arbitrarily chosen point
41:23
in the middle, and then we have a wave-- which we describe is this function, f of S. But this is just an expression. This means, a wave scattered in the direction associated with f, which we also know as theta. So, that's all the addition. So, that's that particular direction, but we would also then-- to calculate, we could sum up, then think about, all the waves scattered by all parts of the molecule in another direction. But, of course, we've got to think about all possible
41:48
directions because that will give us the most possible information. So, if we then were to, sort of, turn the detector around to face us and see what happens, then you would-- you might-- get something that looked a bit like this. So this doesn't look very regular. It looks a bit messy. But there's a pattern of, sort of, dark and light areas. We've got strong scattering here, medium strength scattering here, quite weak scattering here, quite weak scattering there.
42:14
But this is a very definite pattern, and this is the diffraction pattern-- it's just like the optical pattern that we saw from the laser at the beginning. And it's got information in it about the structure of the molecule because it's the x-rays that have come-- scattered from all points within the molecule, in its three-dimensional interior. And this mathematical formula, that we've worked out, is actually known as the Fourier transform, after the French
42:39
mathematician Jean Baptiste Joseph Fourier. What's interesting about Fourier is that he lived and died before the x-ray was even discovered, but his mathematical methods have turned out to have very general use in physics. He won a prize from the French Academy of Sciences, but they were a bit sniffy about it. They gave him the prize, but they did note in the citation, "the manner at which the author arrives at his equations is not without difficulties, and that his
43:05
analysis for integrating them still leaves something to be desired." But there you go, that's the French for you. Lord Kelvin, an Ulsterman, was right on the money when he said it is "one of the most beautiful results of modern analysis." Now, the beauty of Fourier's analysis when it's applied to x-ray crystallography is that we can work out what the scattering should look like from the electron density, but if you can calculate the Fourier transform mathematically, you can actually then, also,
43:35
simply do the inverse Fourier transform. So, we have, basically, rearranged the equation. You're allowed to do this, according to the mathematicians. So, if you measure all the scattering, you can work out from the maths what the electron density is. And this is basically a mathematical description of the shape of the molecule. And so, this is entire mathematical basis of x-ray crystallography that we use, and still use, in the modern era. It's just the maths is all now done inside a
44:01
computer, thank goodness.
44:05
This mathematical technique would allow us to work out the structure of a single molecule. However, we cannot work with single molecules. They are really small, so they're very hard to pick up. And even if you could pick it up and put in an x-ray beam, it was scatter so few photons-- so few x-rays-- that you wouldn't be able to measure it. So, the trick to get around that is to try and crystallise your molecule. And so, you take your protein, or whatever compound you're
44:34
interested in analysing, and you try to grow a crystal of it. It may not occur naturally, but chemistry has shown us that the final purification step is often crystallisation. So many compounds can crystallise, and we now know that even many proteins can crystallise, as well. And so, if you get a crystal, you'll see that it behaves exactly like a crystal of sodium chloride, or of salt. All you have is a regular ray-- not of atoms this time, but of molecules.
45:01
But you can identify planes, just in the same way as we did for sodium chloride in zinc blende. And so Bragg's Law still applies, and so there are only certain directions in which you will get diffraction. But, at least, as we saw with the slits when we put in six slits rather than two, we got much brighter diffraction because we were allowing more light through. And so, the crystal basically gives us an amplified signal that we can interpret.
45:28
So, I wonder, now, can we have a look and see how our crystals of lysozyme are doing? By the magic of-- oh, and it looks quite nice. So, this was a clear drop earlier, but you can see, here, there's a sort of grittiness to it. But this looks like a whole cluster of little jewels. And so, these are crystals of lysozyme-- a protein-- that have grown in the last 20 minutes, or so, that I've been talking. They're a little bit small. But, by modern standards, they're perfectly adequate,
46:00
perfectly serviceable for doing x-ray diffraction. So, as long as you can crystallise it, you can solve the structure of it. And that was what the Bragg's realised, back as early as 1915. So, the application of the Fourier methods allowed crystallographers-- allowed the Bragg's, initially-- to use the positional information, and the fact that the intensity of the spots varied in different directions, in order to calculate the electron density map.
46:29
So, they applied Fourier methods, and this is one of the very first, published by Lawrence Bragg. This is from 1929, from diopside-- still a fairly simple structure, but much more complicated than sodium chloride. And so, this is a section through the electron density map. You can see the contours. So, here's strong electron density here. This is kind of medium. And here is the structure that Bragg built into that electron density map and solved for diopside.
46:57
And so, through the '20s and '30s they showed that they could apply the technique to more and more complex molecules. And the chemists didn't all listen to Armstrong. And this is beautiful work done by one of Britain's, sort of, most celebrated female scientist, Dorothy Hodgkin-- or Crowfoot, as she was before her marriage. This is the structure of penicillin that was solved during World War II and published shortly afterwards. And this, she published in the late 1950s, is the structure
47:26
of vitamin B12-- a massive molecule. And it was the biggest molecule to have been solved at that time. So, a single molecule has over 100 atoms. And so, the technique moved on in power, thanks to the application of the Fourier method, which had been pioneered by the Bragg's. And crystallography is now, simply, an embedded part of chemistry. So, as well as telling us about material science, it's now a regular routine tool of chemistry. The database has over half a million crystal structures in
47:56
it, and 40,000 new structures are added every single year. So much for chemistry, which isn't really my subject. What about biology? So, again, this started relatively early-- so it was in the '20s and '30s that people started to think about how you could apply x-ray methods to look at biological problems. Biological proteins are much bigger, in general, and so it's much more challenging and demanding. But again, Bragg-- father and son, actually, were both very
48:26
instrumental in inspiring and guiding people to tackle these problems. One of the first to get involved was a chap called Bill Astbury, who worked here at the Royal Institution as part of William Bragg's group in the '20s and then moved to Leeds. And here we see the work of one of his Ph.D. Students from 1937 or '38, Florence Bell. And this is actually one of the very first x-ray diffraction patterns of DNA-- of nucleic acid. Now, you don't have a pattern of spots because this is not
48:54
exactly a crystal that they're analysing here. This is a fibre. But DNA has a very regular structure so it is crystal-like. And you can see, even in this early pattern-- this is 1938-- the typical, sort of, X pattern that is characteristic of the double helix that was eventually to emerge. Now, the whole story of the work on the structure of DNA in itself is convoluted and tortuous, and deserves a whole lecture in itself. What I want to focus on tonight is the crystal side of
49:27
biological crystallography. And that was kind of kicked off by this chap, J.D. Bernal, an Irishman from Tipperary, who worked-- one of his first students was Dorothy Hodgkin, or Dorothy Crowfoot. And Bernal-- he started off as a theorist. He wasn't very good with this hands, initially. But under William Bragg's tutelage, here at the Royal Institution, he eventually mastered the technique and became a crystallographer of some renown. And so, people would just send him crystals.
49:54
And so, a friend of his was travelling in Sweden in Svedberg's lab. They had accidentally grown crystals of pepsin, and their friend said, I know someone who would give his eyes for those crystals. And so, he was allowed to take them away-- carried them in his coat pocket back to London-- or, sorry, back to Cambridge, where Bernal was working at the time. And they put them into the beam, and they produced the very first x-ray diffraction pattern from a protein crystal.
50:23
It must have been quite a moment. Unfortunately, the photograph that they took is lost. It was probably destroyed in a bomb during World War II. However, it probably looked something like this. So, this is a diffraction pattern from a crystal of haemoglobin, which was taken by Max Perutz who was also a student of Bernal's, just a few years later. But, you see a fairly similar-- must have been very similar to the pattern from pepsin. And you can see many, many spots in here--
50:57
you get many more spots because the molecules are much bigger. Now, at that point, they couldn't really analyse the structure-- they couldn't work it out because it was too complicated. It was even beyond the Fourier methods that they had at the time. But they realised-- and this is 1934 that it was initially published by Crowfoot and Bernal, so Dorothy and-- well, Sage, as he was known, because he was such an intelligent and well-read person. Everybody called him Sage.
51:25
And there was two things they realised from this. One was that, because they had regular diffraction, it meant that the protein molecule is of a perfectly definite kind. That meant that the protein molecule had a definite structure. Before that, until that point, there had been a lot of debate on this point. It was thought that it was like a colloid-- a rather, sort of, loose association of peptides. But here they showed, because it diffracts, then it is a definite structure.
51:54
And they further realised that they now had, through this x-ray method, the means of really getting to grips with what proteins looked like and what they could do. And, although it was going to take quite some time before they could realise this, they knew-- and certainly, Astbury and Bernal knew-- that they were on the cusp of, I think, a major breakthrough. And there's a very nice quotation in a letter from Astbury to Bernal-- they wear pals--
52:23
where Astbury says, "If you and I do not make the most biological crystallography, we should have our respective bottoms kicked." While I don't think they deserve to have their bottoms kicked, they are, unfortunately, not as well-known in the scientific world as they deserve to be. Their names are well-known inside the crystallographic community. That's partly, I think, because they didn't, themselves, solve any landmark structures. But they both did early work and inspired other people to
52:52
go on to work on structures that were, themselves, landmark achievements. Astbury's initial work helped to inspire Maurice Wilkins to get involved in analysing DNA, and Wilkins was very instrumental in pursuing the project to fruition. Bernal-- he had mentored Hodgkin and, also, people like Max Perutz. But it took until 1959 before the very first protein structure was solved, and what a moment that must've been, when this model appeared. I won't offend the sensibilities of the find,
53:25
ladies and gentlemen of London, by telling you what I think it looks like this. But, the disappointment in Perutz's voice is palpable-- "Could the search for ultimate truth really have revealed so hideous and visceral an object?" Part of the disappointment was because the crystals they initially had weren't very good, and they didn't scatter to high angle. And so, that limited the information that they could get, and so the model really just shows the fold of the polypeptide chain--
53:51
that reveals the structure. But you don't really get any biological insight from a model like this. And it certainly-- this came six years after the structure of DNA had been solved-- well actually, DNA had been solved on the basis of much sparser information, but it produced this beautiful, double-helical molecule. It was just elegant in its simplicity, and it immediately suggested the mechanism for how genetic information is transmitted from copy to copy.
54:20
However, within a couple of years, the crystals improved and their analysis improved. And soon, they had a model of the protein structure that really did have all the atoms in it and was starting to give us real biological and mechanistic insights. So, this is myoglobin. This is a protein that comes from a sperm whale. It is an oxygen storage molecule, and so it is the molecule in the muscles of the sperm whale that allows this incredible beast to hold its breath for a very long time.
54:50
So, the initial myoglobin structure was solved by John Kendrew-- that was done in the Cavendish lab at Cambridge, again, under the watchful eye of Lawrence Bragg, who was director of it at the time. And Perutz himself, working in the same lab, produced the structure of haemoglobin a few years later-- this is in the early '60s. And this is a protein that's found in the blood of all mammals. It's the oxygen transporter, so it carries oxygen in your
55:14
blood from the lungs, all the way through your tissues, and back into the lungs. And immediately this was just the second molecule structure to be solved-- but what was remarkable about this was that when they overlaid the structure of myoglobin on it, they saw that it was almost the same as one of the chains of haemoglobin. And myoglobin from a sperm whale-- the haemoglobin here was from a horse-- but, it showed an evolutionary connection.
55:39
And this was the first time that people had seen evolution working at a structural level, at a molecular level. And this is a type of insight that we get from structural biology all the time now. Previously, it had really just been looking at morphological similarities in the external appearance of different animals, and different species of plants, and so on. Now, we can look at and study evolution at the molecular level. So, this is another benefit of the technique of crystallography.
56:08
So, a later structure, lysozyme, was solved here, in the Royal Institution, in a group involving David Phillips. And again, this was now the time when Lawrence Bragg was director. And this sketch of the protein molecule is actually done by Lawrence's own hand-- he was quite a talented artist. And what a pleasure it must have been for him-- and this is 1965, thereabouts-- 50 years after he and his father had first, sort of, worked on this technique and solved the structure of just
56:39
two atoms, here was the structure of lysozyme. This is an enzyme. This one is from chicken eggs-- it actually helps the chicken egg to fight off bacteria because it chews up the bacterial cell wall. This is a modern representation of it, and we can now see, in atomic detail-- the orange molecule is a small segment that looks like a bacterial cell wall-- and so, we can see how the enzyme works-- how it catalyses pulling apart this molecule. So, crystallography gives us incredible molecular,
57:11
atomic-level insights into the workings of biology. And it has just gone from strength to strength. That result was from the 1960s. These days, we have much better kit, but we're basically doing the same thing. We are still growing crystals, we are still collecting x-ray diffraction patterns, and we are still solving structures. The kit's a bit better. So rather than a Crookes tube, which is what the Bragg's started out with, we've got one of these. This is a particle accelerator.
57:39
It nestles in the Oxfordshire countryside near Didcot. This is the diamond light source. It is the most expensive scientific facility that Britain has built in the last 10 or 20 years, and it is something that we should be very proud of. It's an excellent, world-class facility. So now, we just grow our crystals, and we take them to diamond, and we fire x-rays at them. And instead of the, sort of, early patterns, like haemoglobin, this is now a modern-day diffraction pattern.
58:06
And as we illuminate the crystal, we can rotate it. And instead of collecting data on photographs, we now have electronic detectors that capture the diffraction almost in real time. And, from all of these different images, we can then work out structure after structure. And so, the technique really has matured, really has grown up. From sodium chloride, which was just two atoms in 1912, 1913, to lysozyme-- which is probably a couple of thousand atoms-- in the '60s.
58:37
We now have structures like this. This is actually a sodium potassium ATPase. So, this is --. This is salt. And this is a molecule-- a transporter-- that sits in your cell membranes and regulates the influx and efflux of the sodium and potassium ions to maintain a healthy salt balance within the living cell. So, this is a gigantic structure. However, it's not very big compared to this. Now, this is the ribosome. Now, the ribosome is a monster. So, this is the ribosome from a yeast, which is
59:12
a eukaryotic cell. It's a sophisticated type of cell, which has the same type of organism that we are. It's just we are a many-celled organism and yeast is only a single-celled organism. But, this is a truly gigantic structure. Bragg's first structure had two atoms. The ribosome has 404,714 atoms in this crystal structure. It's truly a monster. It might even be said to be akin to the monstrosity of Hooke's flea. I wish that it would capture the public imagination in
59:47
quite the same way, but it's worth bearing in mind that this flea contains many millions of copies of a molecule just like this. The ribosome is an enormous and powerful machine, which helps us to decode the genetic code and synthesises proteins. So, from all of those techniques, from x-ray crystallography applied to salt, we have moved to brand new territory. And so, we are learning all the time about life, and we are learning about it in ways that are brand new.
1:00:27
And so, if we now just, finally, look at the ribosome in the wild, so to speak, you can see where it takes its place inside the cell. And this is a beautiful painting from a book by David Goodsell-- if I show it up here to give him the credit for it-- this shows the molecular interior of a cell. This is bringing together all the knowledge we have about what molecules are present and what structures they are likely to have. We haven't yet solved all these structures, but thanks
1:00:54
to crystallography, we very soon will be able to do so. Finally, we are solving structures on Earth, but crystallography has moved beyond this planet. And on the Curiosity Rover that NASA sent to Mars last year, there is an instrument that does x-ray diffraction. And the robot arm can toss a sample of soil into this device, and it can take an x-ray diffraction pattern on Mars. And so, x-ray crystallography has moved off-world, so to speak, and is now telling us that the soil on Mars is a bit
1:01:27
like Hawaii. I don't think the climate is quite as nice. And this, again, is just a structure from this week's Nature, published on Wednesday-- another monster. This is a polymerase that actually makes the RNA that is used to build the ribosome. And so, we are making connection after connection at the atomic level. So, I hope you will now agree with me, that x-ray crystallography is one of the most powerful methods that science has produced in the 20th century, and has truly
1:02:01
allowed us to see the world in a completely different light. [APPLAUSE]
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