Can you keep zooming in forever?

This is a tiny piece of metal  just three millimeters across. And here's what happens if  you just keep zooming in: 1,000 times, 100,000 times, 50 million times. Each of these blobs is an actual atom.

I saw this the other day at  the University of Sydney, and it kind of blew my mind  because up until just 30 years ago,   directly seeing atoms like this  was thought to be impossible. The rooms that you're going to see here are  perhaps the most shielded rooms on campus, or even in the whole of Sydney, I would say. And perhaps also the most expensive.

That's wild. So why is it so hard to see atoms? Well, you can't actually see  atoms with visible light.

That's because while light has wavelengths  between 380 and 750 nanometers, an atom is still over 3000 times  smaller, just 0. 1 nanometers. And if the wavelength of light is much  bigger than the thing you're trying to see, the light will just diffract or bend  around it so you won't be able to see it.

So if you want to see atoms, you need  something with a much, much smaller wavelength. The best candidate isn't even light. It's electrons.

In 1924, a French physicist named Louis de Broglie  worked out that everything was sort of wavelike. Not just light, but matter too. Atoms, molecules, even you  yourself have a wavelength.

And the formula for this  wavelength is Planck's constant,   divided by the object's momentum,  that is, mass times velocity. So here what you actually see,   that's the column of the microscope where  we accelerate the 300 kV electrons down. 300 kilovolts, these electrons?

So they are relativistic particles. How fast are they moving?  99% of the speed of light?

Around 80. 80% the speed of light? Yeah.

So what would be their wavelength? The wavelength is the Planck  constant over the momentum, right? So if we calculate that, we come to  around between 2 to 3 picometers.

Whoa! That's over 100,000 times  smaller than visible light. So theoretically, you get  100,000 times more resolution.

Shortly after de Broglie's discovery, a  group of scientists in Germany started   working on a microscope that would  use these high-speed electrons. The only problem is you can't  bend electrons using glass lenses. So how do you focus them?

Hans Busch, a German physicist, suggested that  an electromagnetic lens might do the trick. He published his results in 1926,  but never actually built one. Fortunately, a copy of his paper fell into the  hands of an eager young PhD student, Ernst Ruska.

Ruska built his first prototype by coiling up   some wire and surrounding it with iron —  taking care to leave a gap in the middle. Then, when he passed a current through the coil,   it induced a donut-shaped magnetic field  through the metal and across this gap. This was his lens.

To test it, Ruska first boiled  electrons off a tungsten filament,   the same kind of filament you'd  find in an incandescent light bulb. He accelerated these free electrons through a   positively charged anode down  to his electromagnetic lens. As an electron approaches the lens, the  magnetic field exerts a force on it.

So if an electron is traveling in the y direction  and the magnetic fields are in the x direction, this force, called the Lorentz  force, pushes it in the z direction. But as the electron moves this way, it encounters  other magnetic field lines along the donut shape, which constantly point its motion in a circle. But then this circular motion means  the Lorentz force starts pushing the   electron inwards as well, spiraling  it into the center of the lens.

Now, if you trace the path of  the whole beam of electrons,   you'll see they all get steered  into the center, focusing the beam. By 1931, Ruska and his colleague, Max Knoll, used this kind of design   to build the first working electron microscope. It was pretty basic, made of brass  roughly bolted together, but it worked.

The image itself was created once the focused   electron beam hit a sample  sitting at the focal point. The sample needed to be incredibly  thin, only around 100 nanometers thick. More electrons would make it through  the thinner parts of the sample than   the thicker parts, creating an  electron imprint of the sample.

Then a second electromagnetic lens magnified this   imprint down onto a fluorescent  detector, producing the final image. This was known as a transmission  electron microscope or TEM. Now, early versions of the  microscope barely magnified at all.

In fact, it wasn't even better  than an optical microscope. But Ruska was determined. Over the next few years, he experimented with   adding more lenses onto the microscope  to create bigger and bigger images.

By the mid-1930s, Ruska had gotten the  TEM way past 10,000 times magnification. It could produce close-ups of insects, bacteria,   and even viruses at a level far  surpassing the optical microscope. But right as Ruska's TEM was taking  off, a German physicist named Otto Scherzer   published a paper claiming that the  microscope was about to hit a brick wall.

There was a flaw in the electromagnetic lens,  he wrote, that was completely unavoidable. For an electron to make it  to the focus of the lens,   it needs to be deflected by a specific amount. If you simplify its trajectory, you can define  that ideal deflection with this angle theta.

This angle depends on the horizontal distance   of the electron from the optical  axis, and how far down the axis the focus is, also known as the focal  length. The shorter the focal length, the stronger the magnification. If you graph this angle as a function  of distance to the optical axis,   you'll see that it can be approximated as linear.

The problem is that the magnetic  field doesn't scale linearly. It's much stronger near the edges of the magnet. So if you plot the curve for the  actual deflection of the electrons,   you'll see that the magnetic field  overdeflects the electrons further out.

Their angles are bigger than they should be,   so they end up focusing  before the rays in the middle. And as a result, the focus is spread across the   optical axis instead of being  contained in a single point. The blur starts out around the edges of the image,  but it gets worse the higher the magnification.

This is called spherical aberration, and it  distorts every radially symmetric magnetic lens. In fact, it doesn't just affect magnetic lenses. Every spherical lens, from a camera to a telescope  to a magnifying glass also suffers from it.

But there is a surprisingly simple way to  minimize spherical aberration. Just add   a second lens, one that diverges  light instead of converging it. Now, a diverging lens also  suffers from spherical aberration.

But if it has the same amount of aberration  as your converging lens just in reverse, you can stack the two to essentially  cancel out their effects. And that removes the aberrations almost entirely. Almost all modern lens systems in cameras   and microscopes use some sort  of correcting divergent lens.

So you might imagine that the TEM  simply needs its own version of a   diverging spherical lens to magnify further. But with magnets, this is physically impossible. Every magnet has two poles, a North and a  South.

It's impossible to just have one. Even if you split a magnet down the middle,   it creates two smaller magnets,  both with a North and South. And all magnetic field lines have to start at one  pole and end at the other, forming a closed loop.

It's a direct result of the second  Maxwell equation because the field   that you create has field lines that  start and end at the same magnet. So the electrons will always  cross through two lines. The first time it passes through, by the Lorentz  force, it's brought into the spiraling motion.

And then the second time  from that spiraling motion,   which has then a slightly different  direction, it's pushed towards the axis. That's why all electromagnetic lenses by default  will converge that beam, and never diverge it. Even if you shot electrons in from the other  side of the lens, they would still get focused.

This is what Otto Scherzer's paper proved  in 1936, stopping progress on the TEM. It is impossible to produce a radially  symmetric magnetic lens that diverges. And this was, of course, a big roadblock  for the development of electron microscopy, because people saw, okay, we can  accelerate electrons as much as we want, the presence of spherical aberration  will always be in the way.

Because of this roadblock, advancements in the  microscope's resolution slowed significantly. By 1955, another microscope  beat the TEM to the punch and   took the first generally accepted image of atoms. This was called the field ion microscope,   and it worked by shooting helium or neon  atoms at an atomically sharp needle tip.

The tip was positively charged. So  when the gas atoms hit the needle,   they got ionized and were ejected  off perpendicular to the surface. And that could form an impression  of the atomic structure of the tip.

But this method was limited. You could only get a sense of the atomic  structure of the very tip of the needle. And the images weren't all that impressive.

Luckily, Ruska's electron microscope   wouldn't stay stuck in the realm  of insects and bacteria forever. Now, you might not be an insect getting  bombarded with relativistic electrons, but it can sometimes feel  like it when you're getting   bombarded with spam calls and targeted ads. It's a real problem when we're  researching for our videos.

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com/Veritasium. And now back to the electron microscope. Despite Scherzer's aberration limit  work on the transmission electron microscope continued.

During the next four decades. People tried boosting the resolution with  clever workarounds, and perhaps none more   so than British-American physicist Albert Crewe. His idea was to replace the tungsten filament,   which fired off electrons at  random, with a more directed source.

So instead of boiling electrons off the surface,   he tried pulling them off with  a stronger electric field. And, by sharpening the tungsten into a fine tip,   he was able to create a narrow beam which was  over a thousand times brighter than before. He paired his new narrow beam  with an unlikely technology.

The cathode ray tube TV. These TVs worked by scanning an  electron beam across a screen. The   screen was coated in a phosphor that  produced light when hit by electrons.

And by varying the intensity of the electron beam,   you could vary the brightness of the  screen, giving you a black-and-white image. Crewe was inspired to design a  similar electron beam for the TEM that would scan across the nanoscopic sample. So instead of creating an imprint  of the whole sample at once, Crewe's electron beam made smaller imprints,  mapping the sample out bit by bit.

This wasn't the first time someone had  tried to make a scanning version of the TEM. German researcher Manfred von Ardenne  built an early prototype in the 1930s,   but it was destroyed during WWII. When Crewe revived Ardenne's design,  he made several drastic improvements,   and by 1970 he had this.

The first image of single atoms  taken with the electron microscope. Researchers quickly jumped to employ his  tech, producing countless images of atoms. After nearly a century of improvements  from Ruska, Crewe, and many others,   the magnification upgrades on  the TEM had reached their peak.

But Scherzer's problem persisted. Spherical aberration set a hard  limit on how small you could see. Even Crewe himself gave up on trying to  get around it after over ten years of work.

"Unfortunately, we could never make it  work. After many heartbreaking attempts,   we were forced to admit defeat. " Around this time, other microscopes  emerged that could also image atoms.

These probe microscopes work by gliding an  incredibly small stylus across the sample. The stylus detects variations in quantum effects   or nanoscale forces to then map the  surface structure of the sample. These were easier to build, and  because they didn't use any lenses,   they weren't limited by spherical aberration.

Their images were even 3D. But the looming issue was that  these probes weren't really   seeing atoms. It was more like feeling atoms.

Throughout the 80s and 90s, this was all we had. But what if there was another way? Scherzer's theorem proof that a diverging,  radially symmetric lens isn't possible.

But if you're willing to give up on that  symmetry, well, the theorem no longer applies. The problem is that radial symmetry is  arguably the most important property of   any lens, because if you break the  symmetry, you also break the image. But three maverick scientists  thought there might be a way.

Knut Urban, Max Haider, and Harold Rose were known   in the electron microscope  community as troublemakers, and for years barely anyone had been  interested in their research or,   more importantly, in funding it. And for a good reason too.  Their idea was kind of crazy.

I mean, they purposely wanted to break the  image using a lens that wasn't symmetric. Their hope was that there would be a small part   of this distorted image that  would be slightly diverging. And maybe, just maybe, this  small part could correct the   spherical aberration of the original lens.

So they got to work To distort the image, they used a massive nest  of electromagnets with six,   eight, or even ten separate coils and  magnets with bumpy magnetic fields. These were known as the hexapole,  octopole, and decapole magnets. So as the electron beam passed through a hexapole,   it would twist and squeeze the flat  2D image into a triangular saddle.

And the circumference of the original beam  would be pushed into the three corners,   with the rest of the interior stretched out. But now the middle of the image  would have a slight concave bow,   giving the effect of a small divergence. Then Rose, Haider, and Urban forced the  beam through a second hexapole , one that worked   the opposite way, so it would unbend the  distorted image back into a circular shape.

But now they, calculated this  new image might have the remnants   of that tiny divergence still in its center, with  spherical aberration pointing in the opposite way. So if they got their maths and engineering  exactly right, they could feed an image with   spherical aberration through these two lenses  to almost completely counteract the effect. And I imagine a lot of people in the field thought  it was a crazy idea when it was proposed, right?

Not only the concept, but, that this is,  like, technically feasible, I believe.  It was thought that this is not possible. By May 1997, the group had just two months of   development time left before their  last sponsor withdrew their backing.

And to make matters worse, their latest lens  iteration was still just on the drawing board. But somehow, by the 23rd of July,   just a week before their funding ran  out, the new lens was ready to test. They gingerly placed it into the microscope,   but like every time before it,  the lens was unstable and failed.

So they decided to switch off the equipment  for 24 hours to allow the magnets to settle. And then at 2 a. m.

on the  24th, they turned it on again,   and almost magically, the  picture started to stabilize. Suddenly, there was no aberration.  Only beautiful, clear images of atoms.

After more than 60 years of failed attempts,   Urban, Rose, and Haider pulled  off the seemingly impossible. With this method, they cut the resolution  of the TEM down to only 0. 13 nanometers.

An average TEM image went from  looking like this to this. A few months after the group's breakthrough,   Knut Urban attended a microscopy  conference to share these results. But because of the group's reputation,   he was relegated to a small back  room that barely anyone noticed.

Soon, however, word spread that against all odds,   his pictures seemed real. Then  a crowd of hundreds formed. People were lining up outside, hoping to get  a glimpse of their stunningly sharp images.

So we're going to get a sample holder. Yeah, so we got a sample holder out. We put that under the optical microscope.

So the sample itself is a small lamella that  you can't see without the optical microscope. Yeah. Have a look through that.

Beautiful. On top of the B there's  a prong. Yeah.

And on the very top   of that on the left-hand side,  looks like a little bit of dust. That's our actual sample. Okay, now I simply go up with the magnification  and I do a very few, like, more basic alignments.  

In this electron microscope because it's  called transmission electron microscope, the electrons always transmit the sample. Here we  look through our entire sample at the same time. And that's why it's so important  that we align the sample.

If you imagine atoms in a high-symmetry  direction are lined up like pearls on a string. When we look down it, well, we can see an image. But if we are in, like, some random direction  that everything would be just blurred.

So that's why we have to do  some tilting in the edge. And this is where the actual sample  starts — the strontium titanate. And this is a thin region where we  hope to get atomic resolution.

So this is 5000 times? Yes Wow. And we see strontium, titanium.

We see  oxygen. We see carbon. That's contamination.

So most likely what we're looking  at is carbon contamination. When you do this focus, what  are you really looking for? I look for this edge to become sharp.

See atoms. What? Just like that.

That's wild.   Shortly after, the group successfully corrected    Orndrej Krivanek independently achieved   the same for Crewe’s version of  the microscope, the scanning TEM. And in 2020, all four were awarded  the prestigious Kavli Prize in   Nanoscience for accomplishing what  so many others thought impossible.

Through their persistence and ingenuity,  seeing atoms like this is, well, normal. How big of a difference does  aberration correction make? If you want to see atoms and if you want to,  for example, measure in atomic distances,   and if you want to learn what type of atoms  you have, you need aberration correction.

Any research that's material science.  Materials engineering, chemical engineering. .

. You need to see what's happening at the atomic  level because you want to relate  the properties to the structure. If you can't see the structure at the atomic  level, you only have half of the information.

So that was a game changer. That's why nowadays every university in  principle needs a microscope like that.