Therefore, at the same forces, electrons have a much faster response than atoms or molecules.
It turns out that just before the moment of separation, this droplet (here it is shown enlarged, this isthmus is also shown enlarged) behaves in a self-similar manner. That is, it means that this isthmus shape remains constant when approaching the separation point, but only its scale decreases, decreases, decreases. That is, here, of course, one can see like a dot, but if we could enlarge it, we would see the same shape – the same shape as here, only on a smaller scale.
And this is very interesting for theorists, because such self-similar behavior actually means something important about the properties of the equation in which it is described. Well, this is one of … not just mysteries – one of the properties of this isthmus. It turns out that it has many other interesting properties, and this is really actively being studied now in experiments.
About microseconds, I also want to tell you the following: that microseconds, in principle, can be studied in a school laboratory. This does not require buying any very expensive camera. To do this, you can use an ordinary camera, but you only need to illuminate the object with short microsecond pulses of light. And getting them is also not so difficult. This is done simply: take, for example, a laser pointer – well, or, if you don’t want to torment the laser, take a small mirror – install it on the motor and spin it in a horizontal plane. For example, 100 revolutions per second, in principle, is quite possible to get. You then get a ray of light that walks along the walls at great speed. Further: you put a screen at a distance, make a small hole in it (just on the trajectory of the ray), and then when this ray strikes along this hole, for example, a very short pulse of light passes into the next room. And you can make a rough estimate and see that pulses of just a few microseconds are readily available in the school lab. And then you just shoot it in a dark room with a camera. And you really see fast-moving phenomena.
Okay. Microseconds are also something more, as it were, mundane to our life.
Nanoseconds
Now let’s move on further, move on to the next range – this is nanoseconds. And it’s worth talking about nanoseconds in more detail. What are nanoseconds? This is, in fact, something that we do not encounter in ordinary life. If we take any typical phenomena that occur in ordinary life, with typical speeds – well, for example, sound, shock waves, or write an argumentative essay step by step just the movement of bodies – then they rarely exceed one kilometer per second. But one kilometer per second, if you recalculate it in nanoseconds, for 10-9 seconds, is literally a few microns. Even if we take the speed of light and multiply it by one nanosecond, the distance is also not that great, only 30 cm.And this all leads us to a very important conclusion: that when we study the nanosecond range and below, we no longer study bodies – we we study the substance. It doesn’t matter to us at all from which body this substance originated. Therefore, we turn to the study of matter, not bodies.
But how can all this be studied? In principle, of course, there are also video cameras that are a little bit in the nanosecond range. As far as I know, now the record is 6 million frames per second in the optical range, that is, one frame every 160 nanoseconds. Something, of course, can be seen here, but if you have an event that lasts, say, 10 nanoseconds, then, of course, you will not see any dynamics of it with the help of a video camera. Therefore, one way or another, we have to move from visual observation to some, perhaps more complex, but more perspicacious methods of research, which become more and more indirect when we go into ever smaller ranges of time.
In principle, there are many such methods. And my lecture, in fact, is dedicated to them. But before talking about them, I decided that it would be useful to illustrate here a slightly different idea: in order to study fast-paced processes, sometimes you do not need to keep track of them at all. Sometimes it is enough to somehow cleverly set up an experiment and look at its results – with a slow detector, with a slow technique. But then, looking at these results, it is already possible to reconstruct the dynamics of the event, which took place on a nanosecond scale. And so I found one of the works that was done not so long ago, which perfectly illustrates this idea.
This work belongs to a branch of physics called „surface physics“. Surface physics studies, roughly speaking, what happens on the surface of a solid – for example, a crystal. In fact, a lot of interesting things are happening there, there are thermodynamic, electrical, magnetic phenomena, mechanical phenomena. And they all proceed, as a rule, quite differently than in the thickness. Therefore, this area of condensed matter physics has its own mysteries, its own problems and its own research methods.
One of the specific questions, which is, of course, very important for this area, is the question of how an atomically smooth crystal surface lives at a finite temperature, that is, at ordinary room temperature. What does “atomic smoothness” mean? This means that he was raised atomically smoothly and then released into free swimming. He will not stand continuously like this, there are thermal fluctuations, and sometimes these fluctuations make an atom jump out and start walking on the surface. And in place of this atom, then a surface hole appears – it is called a „vacancy“ – which, it turns out, also has mobility: it begins to walk back and forth. How the vacancy walks, this is also understandable. It’s just that neighboring atoms jump into it, and as a result, the vacancy seems to move. So that’s it. These vacancies … This means that an atomically smooth surface can be thought of as a rarefied gas of two types of particles: surface atoms that jump from above, and vacancies that also somehow diffuse like this. This gas has its own concentration, it has its own typical diffusion coefficient, its typical hop times, and all this needs to be studied, since this is really how the surface lives.
So, the question arises: how to study the diffusion of surface vacancies? The first wish, of course, is to just take it and watch it with some kind of high-resolution method. For example, there is such a method – scanning tunneling microscopy – with which you can see individual atoms. Unfortunately, this method is very slow. It takes about a second to get a snapshot of even a small area of the surface. At the same time, theoretical estimates indicate that all these atomic vacancies move in times of the order of nanoseconds. You won’t get anything with this method. On the other hand, of course, there are also fast methods, which I will show later, but they, as a rule, have a very poor spatial resolution: they simply do not see an individual atom. As a result, a dilemma arises: how to look at these vacancies in order to see them. Some experimental trickery is required.
And such an experimental trick was implemented by scientists several years ago. They did such a thing: they decided to plant impurity atoms, that is, atoms of some other kind, on the surface of the grown crystal. These atoms are clearly visible in a scanning tunneling microscope, they just differ in their properties from the atoms of the substrate. These atoms, when they are first planted, are embedded in the upper surface layer and, as a rule, sit there motionless. They sit, sit, sit … You can take picture after picture – every, say, second – of some area, and it will be seen that the atoms are sitting there motionless. But at the moment when some vacancy comes running (it runs very fast), it comes running and interacts with these impurity atoms, moves them a few steps of the atomic lattice and runs away again. As a result, it turns out that in the next frame, these impurity atoms will be shifted. And by studying these jumps of atoms, which actually happen very rarely, one can also find out the dynamics, the diffusion of these vacancies.
Here is a picture from the experimental work (for more details about the work, see: Diffusion of impurity atoms on the surface of a single crystal). In fact, of course, there were a lot of pictures taken, and this is just a typical picture. Shown here is a small area of the copper surface on which the impurity indium atoms sit. The temperature was 320 Kelvin, which is quite room temperature. Naturally, no vacancies are visible, because this method is very slow. But sitting impurity atoms are visible. Here is a sequence of four frames. 160 seconds elapsed between the first two, that is, in 160 seconds they did not move anywhere. 20 seconds passed between the second and the third, and in 20 seconds, not only did they both jump somewhere, but some other atoms also got into the frame. This is quite consistent with the mechanism for moving through vacancies, about which I spoke. When the experimenters processed all the data, they were able to restore the dynamic properties of these vacancies. That is, it turned out that they really have very little concentration, among other things. And it turned out that the typical jump time is on the order of 10 nanoseconds. That is, this is an interesting illustration of the fact that a very slow instrument sometimes allows one to study the dynamics of much faster phenomena, if correctly, cleverly set up an experiment.
Picoseconds
Now we go from nanoseconds even deeper, to picoseconds. Picoseconds are an even shorter moment. And in picoseconds no bodies – and even light in general – have time to move any macroscopic distances. Here we are already moving into purely microscopic – well, or maybe mesoscopic – physics.
What typical processes occur at times of the order of picoseconds? These are, first of all, a variety of atomic, molecular phenomena. That is, phenomena associated with the movement of individual atoms or their groups. For example, synchronous vibrations of the crystal lattice, that is, phonons. That is, if you have, for example, sound, then … – you probably know that sound can be imagined as a stream of such quasiparticles that go through a crystal, that is, lattice vibrations, which are called phonons. Typical vibration times in these phonons are just units, tens, hundreds of picoseconds.
Further. For example, the behavior of biological molecules. For example, during the folding of proteins, you have a whole cascade of various processes. When your protein has just been transcribed … broadcast … so … and then it starts folding, then in the process of this folding you have phenomena that occur on a picosecond scale, on a nanosecond scale, down to seconds. But the fastest steps in the re-conformation of this protein occur on a picosecond scale. It is very important for biology to know how all this happens.
Here, there is such a thing as the kinetics of phase transitions. The word „kinetics“ means that we do not just look at the result of something, but we want to know in detail, preferably atomic, how this or that process occurs. That is, we say: „The ice is melting.“ Let’s say they shine a short flash of laser light onto the ice, and it melted. But we want to know how this process begins – atomic or through some vibrations, uniformly, non-uniformly? All this is studied on a picosecond scale.
Some electronic phenomena also fall into this category. I think you understand that in general there is a rather large gap in time between the movement of atoms and the movement of electrons, because electrons are several orders of magnitude lighter than atoms, nuclei. Therefore, at the same forces, electrons have a much faster response than atoms or molecules. Therefore, atoms and molecules and some rather slow electron motions fall on the picosecond scale. Well, for example, the kinetics of semiconductor charge carriers. That is, when a voltage was applied to your semiconductor, some current went, this current means that they shone light there, some processes began – for example, holes were born that flowed somewhere, began to recombine, and so on. All this takes place on a scale of the order of picoseconds. In chemical reactions too. It says: „A chemical reaction has taken place.“ In fact, it does not happen all at once, it is also a whole cascade of phenomena that start and follow each other. All this is accompanied by a rupture, overflow of electron clouds, rupture or creation of new chemical bonds. All this also applies to approximately the picosecond range.
I want to say two things about this picosecond range. First, we can say with complete confidence that this is real modern physics, that is, this is what is now being studied in thousands of laboratories around the world, published in hundreds of journals every day, this is really the most real modern physics. The second thing I want to tell you about the picosecond range is how to study such phenomena. And here, it turns out, there is an interesting thing, which I tentatively called the „nanosecond barrier“. This means this: a variety of ancient research methods, which, say, were used in the middle of the twentieth century or earlier, one way or another required the movement of something in space. For example, if you want to shoot with a fast camera, then you need to move the shutter, or if you want to get a short flash of light when a capacitor breaks through, then you have the movement of an electron flow from one plate to another plate. One way or another, you have some kind of mechanical movement at least millimeter distances. And as I said before, it all ends in nanoseconds. That is, nanoseconds are when at least some movement is still noticeable. On a picosecond scale, no movement of microscopic bodies is noticeable. Therefore, all these old research methods simply cannot study ranges of less than one nanosecond – in fact, even less than ten nanoseconds.
And here the real breakthrough was the invention of lasers. Well, or rather (I will show on the next slide) – a way with the help of lasers to obtain very short light pulses. In just a few years there has been a whole revolution, with the help of which the entire picosecond range has passed – from nanoseconds to a few picoseconds and even deeper. And it turned out that the laser is a completely unique research method. Because for fast-moving processes, it serves both as an initiator of the process and as a registering tool.
The standard technique, which is now often used in most, probably, experiments to study fast processes (in English it is called „pump-probe technique“ in Russian it is often translated as „pumping and probing“), looks like this: you have say, a pulse of light that you split into two short pulses of light, shift them relative to each other by a few picoseconds (this is all easy to do) and then send them to the sample under study.