What is x-ray diffraction?

This article describes a concept such as X-ray diffraction. The physical foundations of this phenomenon and its application are explained here.

Technologies for creating new materials

Innovation, nanotechnology is a trend in the modern world. News is full of reports of new revolutionary materials. But few people wonder what a huge research apparatus scientists need to create at least a small improvement in existing technologies. One of the fundamental phenomena that help people do this is x-ray diffraction.

Electromagnetic radiation

First you need to clarify what electromagnetic radiation is. Any moving charged body generates an electromagnetic field around itself. These fields pervade everything around, even the vacuum of deep space is not free from them. If periodic disturbances arise in such a field that can propagate in space, they are called electromagnetic radiation. Such concepts as wavelength, frequency and its energy are used to describe it. What is energy is intuitive, and the wavelength is the distance between the same phases (for example, between two adjacent maxima). The higher the wavelength (and, accordingly, the frequency), the lower its energy. Recall that these concepts are necessary to describe what X-ray diffraction is brief and succinct.

Electromagnetic spectrum

The whole variety of electromagnetic rays fits on a special scale. Depending on the wavelength, they distinguish (from the longest to the shortest):

• radio waves;
• terahertz waves;
• infrared waves;
• visible waves;
• ultraviolet waves;
• X-ray waves
• gamma radiation.

Thus, the radiation of interest to us has a very short wavelength and the highest energies (therefore it is sometimes called hard). Therefore, we are approaching a description of what X-ray diffraction is.

The origin of x-rays

The higher the radiation energy, the more difficult it is to get artificially. Having lit a fire, a person receives a lot of infrared radiation, because it transfers heat. But for x-ray diffraction to occur on spatial structures, a lot of work needs to be done. So, this type of electromagnetic radiation is released if an electron is knocked out of the shell of an atom, which is close to the nucleus. The electrons located above tend to fill the formed hole, their transitions and give x-ray photons. Also, during sharp braking of charged particles having a mass (for example, electrons), these high-energy rays are produced. Thus, the diffraction of x-rays on the crystal lattice is accompanied by the expenditure of a sufficiently large amount of energy.

On an industrial scale, this radiation is obtained as follows:

1. The cathode emits an electron with high energy.
2. An electron collides with anode matter.
3. The electron drastically slows down (while emitting an x-ray).
4. In another case, a decelerating particle knocks an electron from a low orbit of an atom out of the anode material, which also gives rise to an x-ray.

You must also understand that, like any other electromagnetic radiation, x-ray has its own spectrum. This radiation itself is used quite widely. Everyone knows that a broken bone or formation in the lungs is sought precisely by x-ray radiation.

The structure of crystalline matter

Now we have come close to what the method of x-ray diffraction is. For this, it is necessary to explain how a solid body is arranged. In science, a solid is called any substance in a crystalline state. Wood, clay or glass is solid, but they lack the main thing: a periodic structure. But crystals have this amazing property. The very name of this phenomenon contains its essence. First you need to understand that the atoms in the crystal are fixed rigidly. The bonds between them have a certain degree of elasticity, but they are too strong for atoms to move inside the lattice. Such episodes are possible, but with a very strong external impact. For example, if a metal crystal is bent, point defects of various types are formed in it: in some places the atom leaves its place, forming a vacancy, in others it moves to the wrong position, forming an interstitial defect. In the place of the bend, the crystal loses its harmonious crystalline structure, becomes very defective, loose. Therefore, it is better not to use a paper clip that was unbent once, since the metal has lost its properties.

If the atoms are fixed rigidly, they can no longer be randomly arranged relative to each other, as in liquids. They should be organized in such a way as to minimize the energy of their interaction. Thus, atoms line up in a lattice. In each lattice there is a minimal set of atoms located in a special way in space - this is a unit cell of a crystal. If you translate it entirely, that is, combine the edges with each other, shifting in any direction, we will get the whole crystal. However, it is worth remembering that this is a model. Any real crystal has defects, and it is almost impossible to achieve absolutely accurate translation. Modern silicon memory elements are close to ideal crystals. However, their production requires incredible amounts of energy and other resources. In laboratory conditions, scientists get perfect structures of different types, but, as a rule, the cost of their creation is too high. But we assume that all crystals are perfect: in any direction, the same atoms will be located at the same distances from each other. Such a structure is called a crystal lattice.

Crystal structure research

It is thanks to this fact that X-ray diffraction by crystals is possible. The periodic structure of crystals creates in them some planes in which there are more atoms than in other directions. Sometimes these planes are defined by the symmetry of the crystal lattice, sometimes by the mutual arrangement of atoms. Each plane is assigned its own designation. The distances between the planes are very small: on the order of several angstroms (recall, an angstrom is 10 ^-10 meters or 0.1 nanometers).

However, there are many planes of the same direction in any real crystal, even a very small one. X-ray diffraction as a method uses this fact: all waves that change direction on the planes of the same direction are added together, giving a sufficiently clear signal at the output. So scientists can understand in which directions these planes are located inside the crystal, and judge the internal structure of the crystal structure. However, only these data are not enough. In addition to the angle of inclination, you also need to know the distance between the planes. Without this, you can get thousands of different structure models, but don’t know the exact answer. How scientists learn about the distance between the planes will be discussed below.

Diffraction phenomenon

We have already given a physical justification for what X-ray diffraction on the spatial crystal lattice is. However, we have not yet explained the essence of the diffraction phenomenon. So, diffraction is the enveloping by waves (including electromagnetic) of obstacles. This phenomenon seems to violate the law of linear optics, but this is not so. It is closely related to the interference and wave properties of, for example, photons. If there is an obstacle in the path of light, then due to diffraction, photons can "peek" around the corner. How far the direction of light propagation deviates from the straight line depends on the size of the obstacle. The smaller the obstacle, the shorter the length of the electromagnetic wave. That is why X-ray diffraction on single crystals is carried out with the help of such short waves: the distance between the planes is very small, optical photons simply do not “crawl” between them, but only reflect off the surface.

Such a concept is true, but in modern science it is considered too narrow. To expand its definition, as well as for general erudition, we present methods for the manifestation of wave diffraction.

1. Changing the spatial structure of waves. For example, the expansion of the angle of propagation of a wave beam, the deviation of a wave or a series of waves in some selected direction. It is to this class of phenomena that the rounding by waves of obstacles belongs.
2. Wave decomposition into a spectrum.
3. Changing the polarization of the waves.
4. Transformation of the phase structure of waves.

The diffraction phenomenon, together with interference, is responsible for the fact that when a light beam is directed to a narrow gap behind it, we see not one, but several light maxima. The farther the maximum from the middle of the gap, the higher its order. In addition, when the experiment is set up correctly, the shadow from the usual sewing needle (naturally thin) is divided into several bands, and the light maximum, not the minimum, is observed exactly behind the needle.

Wolfe-Bragg Formula

We have already said above that the final signal is composed of all x-ray photons that are reflected from planes with the same slope inside the crystal. But to calculate the structure accurately allows one important relationship. Without it, X-ray diffraction would be useless. The Wulf-Bragg formula looks like this: 2dsinƟ = nλ. Here d is the distance between planes with the same angle of inclination, θ is the slip angle (Bragg angle), or the angle of incidence on the plane, n is the order of the diffraction maximum, λ is the wavelength. Since it is known in advance exactly which x-ray spectrum is used to obtain data and at what angle this radiation is incident, this formula allows us to calculate the value of d. We said a little higher that without this information it is impossible to obtain the structure of a substance precisely.

Current application of x-ray diffraction

The question arises: in what cases does this analysis need to be done, have the scientists really not studied everything in the world already, and when people receive fundamentally new substances, do they not guess what kind of result awaits them? There are four answers.

1. Yes, we have known our planet quite well. But every year new minerals are found. Sometimes their structure can not even be expected without x-rays.
2. Many scientists are trying to improve the properties of existing materials. These substances are subjected to various types of processing (pressure, temperature, lasers, etc.). Sometimes elements are added to or removed from their structure. To understand what kind of internal rearrangements occurred in this case, the diffraction of x-rays by crystals will help.
3. For some applications (for example, for active media of lasers, memory cards, optical elements of surveillance systems), crystals must very precisely meet the requirements. Therefore, their structure is checked using this method.
4. X-ray diffraction is the only way to find out how many and what phases were obtained during synthesis in multicomponent systems. An example of such systems is the ceramic elements of modern technology. The presence of unwanted phases can lead to serious consequences.

Space exploration

Many people ask: “Why do we need huge observatories in the orbit of the Earth, why do we need a rover, if humanity has not yet solved the problems of poverty and war?”

Each has its own pros and cons, but it is obvious that humanity must have a dream.

Therefore, looking at the stars, today we can say with confidence: we know more about them every day.

X-rays from the processes taking place in space do not reach the surface of our planet, they are absorbed by the atmosphere. But this part of the electromagnetic spectrum carries a lot of data on high-energy phenomena. Therefore, instruments that study x-rays should be carried out of the Earth, into orbit. Currently existing stations are studying the following objects:

• remnants of supernova explosions;
• centers of galaxies;
• neutron stars;
• black holes;
• collisions of massive objects (galaxies, groups of galaxies).

Surprisingly, for various projects, access to these stations is provided to students and even schoolchildren. They study the X-rays coming from deep space: diffraction, interference, spectrum become the subject of their interest. And some very young users of these space observatories make discoveries. A meticulous reader may, of course, argue that they just have time to examine and notice small details in high resolution. And of course, the importance of discoveries, as a rule, is understood only by serious astronomers. But such incidents inspire young people to devote their lives to space exploration. And this goal deserves to be followed.

Thus, the achievements of William Conrad Roentgen opened access to stellar knowledge and the ability to conquer other planets.