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. A thousand times, a hundred thousand 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 3,000 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 wave-like, 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. Yes. So they are relativistic particles. How fast are they moving? 99% the speed of light or? Well, around 80. 80% the speed of light. Yes. 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 two to three picometers. Whoa! Yeah. That's over a hundred thousand times smaller than visible light, so theoretically you get a hundred thousand 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 over-deflects 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 a 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 the 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 the 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, Resca'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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Make sure to use code VERITASIUM to get 60% off your annual subscription to take control of your data today. That's incogni.com slash 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 Arden built an early prototype in the 1930s. But it was destroyed during World War II. When Crewe revived Arden'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 aberrations set a hard limit on how small you could see. Even Crewe himself gave up on trying to get around it after over 10 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 proved that a diverging radially symmetric lens isn't possible. But if you're willing to give up on that symmetry, 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. Newt Urban, Max Hader, 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 purposefully 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 6, 8, or even 10 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, Hader, 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 technical 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 2am 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 Hayter 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, Newt Urban attended a microscopy conference to share these results. But because of the group's reputation, he was relegated to a small backroom 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. 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're in, like, some random direction, then everything would be just blurred. So that's why we have to do some tilting in the end. And this is where the actual sample starts, the strontium titanate. And this is a thin region where we hope to get atomic revolution. So this is 5,000 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 here 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 the aberrations in the TEM, Andrej Kravanek independently achieved the same for Kru'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 interatomic 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.