What is the difference between single crystals, polycrystals, amorphous materials, microcrystals, amorphous solids, and quasicrystals?

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To understand these concepts, one must first understand the concept of crystals and the concept of grains. Those who want to study solid-state physics or metal materials will surely be very familiar with these concepts! There are three states of matter in nature: gas, liquid, and solid. Solids can be further divided into two forms: crystals and amorphous solids. Crystals are solids that have a regular geometric shape, formed through the crystallization process ； In a crystal, atoms or molecules are arranged in space in a regular, periodic pattern. Common characteristics of crystals: Homogeneity: The macroscopic properties of all parts within a crystal are the same. Anisotropy: Crystals exhibit different physical properties in different directions. Fixed melting point: Crystals have a periodic structure, and for them to melt, the same temperature is required in all parts. Regular shape: Crystals grown under ideal conditions should be convex polygons. Symmetry: Both the ideal shape of a crystal and its internal structure possess specific symmetry. In their studies of crystals, solid physicists classify them from a structural perspective into ionic crystals, atomic crystals, molecular crystals, and metallic crystals. Microscopy, on the other hand, classifies crystals based on spatial geometry; there are seven crystal systems, fourteen Bravais lattices, and 230 space groups, which are studied and understood using concepts from topology and group theory. Reference can be made to the book *Symmetry Groups in Crystallography* (written by Guo Kexin and Wang Renhui). In contrast to crystals, solids in which atoms or molecules are arranged randomly, without any periodicity or symmetry, are called amorphous; examples include glass and amorphous carbon. Generally, amorphous means non-crystalline; in English it is called amorphous, and some also refer to it as glassy state. Grains are another concept, one that those working in materials science are most familiar with. The theory of solidification was the first to introduce this concept. The process of transitioning from a liquid state to a solid state begins with nucleation, followed by growth; this process is known as grain nucleation and growth. The molecules and atoms within a crystal grain are arranged in an orderly manner; therefore, a single crystal grain constitutes a single crystal. It consists of multiple grains; each grain has a different size and shape, and their orientations are random. It lacks a distinct shape and shows no anisotropy – it is polycrystalline. English grains are denoted as Grain; note the difference from Particle. With grains present, grain size (graininess), degree of uniformity, and the orientation relationship among the various grains are all important parameters related to the microstructure (which simply refers to the microscopic structural characteristics of a solid). For most metal materials, the finer the grain size, the better the material properties (mechanical properties). It’s similar to dough: dough with coarse particles is difficult to shape and tends to break easily. That is why many metallurgists and materials scientists have been developing grain refinement techniques. Science always favors extremes; a mirror that allows one to see further is called a telescope ； A mirror that allows for closer viewing is called a microscope. The grain size is the same; we prefer very small grain sizes, and we also like very large ones. Initially, when the magnification of the microscope wasn’t very high and objects could be seen at the micron scale, it seemed that the number of microns in a crystal grain was extremely small; moreover, the mechanical properties of the material were particularly good at that time. People *tend to refer to such small-scale grains as microparticles. However, science is always evolving. One day, people discovered that when the grain size is small, the properties of materials become incredible – quantum effects, tunneling effects, superductivity, and many other effects associated with small sizes emerge. This is what’s currently very popular these days: nanomaterials. Grains with a size between 1 nm and 100 nm are known as nanocrystals. Now let’s talk about amorphous materials. Amorphous materials have a random arrangement of atoms; they lack periodicity and symmetry. The atomic arrangement is disordered, and there is no fixed lattice constant. The only quantity that describes their structural characteristics is the radial distribution function, which is a statistical quantity. We don’t know the exact lattice constant, but we can always know the statistical distribution of the interplanar distances, right? Amorphous materials have many attractive properties, which is why there are many people who work on them all day long, especially on large-scale metallic amorphous materials. Because its stress-strain curve is very special. As mentioned earlier, there is a process of nucleation and growth from a liquid state to a solid state. If I prevent nucleation from occurring and go straight to the solid state, an amorphous material is obtained, which requires a very fast cooling rate. Therefore, various groups are striving to increase the cooling rate while simultaneously searching for new alloy formulations, as different alloy formulations have varying capabilities for forming amorphous structures; this is typically characterized by a Tg parameter, known as the glass transition temperature. Amorphous materials have no grains, and therefore no grain boundaries. Some people have also told me that amorphous materials can be considered to consist of grain boundaries. On the other hand, if I let it nucleate but prevent it from growing, then it becomes a nanocrystal. People say that forced sweetness does not exist; since nucleation and growth are both suppressed, thermodynamically many amorphous and nanocrystalline phases should not be stable states. So once you create amorphous or nanocrystalline materials, people naturally ask about their thermal stability. Later, there was another genius named Lu Ke. He specialized in amorphous materials, and even during his graduate studies he was determined to figure out the structure of amorphous substances (a true genius chooses such fascinating topics; to this day, the structure of amorphous materials is not yet fully understood). He thought that since I was able to create amorphous materials, why couldn’t I directly crystallize those amorphous materials into nanocrystals? Nanocrystals have high thermal properties; well, this is also a method, known as the amorphous-to-crystalline transformation method. Since grain boundaries are a type of defect, defects will naturally affect the properties of the material. Regardless of whether those effects are positive or negative, it’s difficult to control them anyway. What would happen if I turned an entire piece of material into a single crystal? It has been found that single crystals do indeed exhibit properties different from those of polycrystals and amorphous materials, namely anisotropy; this is something everyone knows. Of course, there are other features as well. So many people are also working hard every day to produce some single crystals. Now we have to talk about quasicrystals. The discovery of quasicrystals was a breakthrough in crystallographic research in the 1980s. This is the credit of us who work with electron microscopes. At the end of 1984, D. Shechtman and others announced that they had discovered alloy phases with five-fold rotational symmetry but without translational periodicity in rapidly solidified Al-Mn alloys, which caused a great stir in the fields of crystallography and related academic circles. Soon, such crystals with no translational periodicity but positional order were called quasicrystals. Later, when Mr. Guo took a look, he was amazed to see that there were so many such things here. He quickly began to analyze them and wrote articles right away. There were countless papers in APL and PRL dealing with those metal solid atom models – basically, all of the research focused on this topic. Quasicrystals are therefore also referred to by D. Shechtman as “Chinese images”. Banzhu also mentioned twinning, which is called twinning in English; twinning is actually an important concept in the plastic deformation of metals. Twinning and sliding are two basic deformation mechanisms. At the microscopic level, the crystal atoms are arranged in mirror symmetry along a specific plane. That noodle dish is called Luan Jing Noodles. Many textbooks cover it. In general, metal materials with a face-centered cubic structure have numerous slip systems and undergo sliding; however, twinning can also occur under certain conditions. Furthermore, the high stacking fault energy of the face-centered cubic structure makes twinning less likely to occur; once upon a time, it was possible to publish excellent papers on the discovery of twins in face-centered cubic structures. A couple of years ago, Maen published a paper in Science after discovering twins in aluminum. Last year, Lu Ke also published in Science for discovering many twins in nanocopper, which increased the strength of copper while preserving its good electrical conductivity (a combination that is usually contradictory). These days, being published in Science is really valuable. It’s like a poor, remote area, with nothing but a student from Tsinghua University. Now, from a microscopic perspective, there are single crystals, polycrystals, microcrystals, amorphous materials, quasicrystals, nanocrystals, plus twins. Single crystal and polycrystal: one grain constitutes a single crystal, multiple grains constitute a polycrystal, and the absence of grains results in an amorphous material. A single crystal has only one set of diffraction spots ； In the case of polycrystals, different orientations result in several sets of spots. During calibration, these sets are processed one by one; it’s possible for some spots to overlap. Calibration using polycrystalline diffraction allows it to be determined what the orientation relationship is between the grains or the two phases. If the grains are too small, polycrystalline diffraction rings may appear. Amorphous diffraction is an amorphous diffraction ring, which is uniform and continuous, differing from polycrystalline diffraction rings. Nanocrystals and microcrystals are terms used in relation to the size of crystal grains; larger grains are called coarse grains. From a diffraction perspective, it is generally difficult to perform single-crystal diffraction of nanocrystals, as the minimum objective aperture selection remains too large. Has anyone done NBED? I’m not sure if this is possible. The behavior of twins in diffraction is worth studying, and it also reflects one’s skill in calibrating diffraction patterns; readers may refer to Chapter 6 of the book \"Applications of Electron Diffraction in Materials Science\" authored by Guo Kexin and Ye Hengqiang. Quasicrystals; ordinary crystals do not possess five-fold symmetry – they only have 1, 2, 3, 4, or 6-fold rotational symmetry (this proof is often used as a question in doctoral entrance exams, hehe). So, seeing that the diffraction spots are five-fold symmetric, 10-fold symmetric, and so on, it’s likely a quasicrystal.