 
[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."
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]
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.
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
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.
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.
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.
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
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.
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--
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.
 
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.
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
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.
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
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.
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
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--
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--
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.
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
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
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--
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--
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--
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,
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.
 
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.
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
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.
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.
 
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.
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--
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--
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.
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
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
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,
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.
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.
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.
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.
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
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
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.
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.
 
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
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--
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.
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.
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
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--
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.
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.
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.
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
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.
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
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
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
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.
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.
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.
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.
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
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."
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
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.
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.
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--
"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--
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--
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.
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.
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?
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.
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
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
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.
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
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
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
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.
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
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
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,
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
computer, thank goodness.
 
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
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.
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.
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,
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.
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.
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
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
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
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
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
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.
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.
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--
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.
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.
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--
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
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,
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--
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.
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.
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
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.
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.
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
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,
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.
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.
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.
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
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
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.
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
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
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
allowed us to see the world in
a completely different light.
[APPLAUSE]
