Crystalline and amorphous bodies melting and crystallization. Crystalline and amorphous substances. What is an ionic bond

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In solids, particles (molecules, atoms, and ions) are located so close to each other that the forces of interaction between them do not allow them to fly apart. These particles can only make oscillatory motions around the equilibrium position. Therefore, solid bodies retain their shape and volume.

According to their molecular structure, solids are divided into crystalline And amorphous .

The structure of crystalline bodies

Crystal cell

Such solids are called crystalline, in which molecules, atoms or ions are arranged in a strictly defined geometric order, forming a structure in space, which is called crystal lattice . This order is periodically repeated in all directions in three-dimensional space. It persists over long distances and is not limited in space. He is called long-range order .

Types of crystal lattices

The crystal lattice is mathematical model, with which you can imagine how the particles are arranged in the crystal. Mentally connecting in space with straight lines the points where these particles are located, we will get a crystal lattice.

The distance between atoms located at the nodes of this lattice is called lattice parameter .

Depending on which particles are located at the nodes, crystal lattices are molecular, atomic, ionic and metallic .

Such properties of crystalline bodies as melting point, elasticity, and strength depend on the type of crystal lattice.

When the temperature rises to a value at which the melting of the solid begins, the crystal lattice is destroyed. Molecules get more freedom, and the solid crystalline substance passes into the liquid stage. The stronger the bonds between molecules, the higher the melting point.

molecular lattice

In molecular lattices, bonds between molecules are not strong. Therefore, under normal conditions, such substances are in a liquid or gaseous state. The solid state for them is possible only at low temperatures. Their melting point (transition from solid to liquid) is also low. And under normal conditions, they are in a gaseous state. Examples are iodine (I 2), "dry ice" (carbon dioxide CO 2).

atomic lattice

In substances that have an atomic crystal lattice, the bonds between atoms are strong. Therefore, the substances themselves are very solid. They melt at high temperatures. Silicon, germanium, boron, quartz, oxides of some metals, and the hardest substance in nature, diamond, have a crystalline atomic lattice.

Ionic lattice

Substances with an ionic crystal lattice include alkalis, most salts, oxides of typical metals. Since the attractive force of ions is very high, these substances can only melt at very high temperatures. They are called refractory. They have high strength and hardness.

metal grate

At the nodes of the metal lattice, which all metals and their alloys have, both atoms and ions are located. Due to this structure, metals have good malleability and ductility, high thermal and electrical conductivity.

The most common form of a crystal is regular polyhedron. The faces and edges of such polyhedra always remain constant for a particular substance.

A single crystal is called single crystal . It has a regular geometric shape, a continuous crystal lattice.

Examples of natural single crystals are diamond, ruby, rock crystal, rock salt, Icelandic spar, quartz. Under artificial conditions, single crystals are obtained in the process of crystallization, when solutions or melts are cooled to a certain temperature and a solid substance in the form of crystals is isolated from them. With a slow crystallization rate, the faceting of such crystals has a natural shape. In this way, under special industrial conditions, for example, single crystals of semiconductors or dielectrics are obtained.

Small crystals, randomly fused with each other, are called polycrystals . The clearest example of a polycrystal is granite. All metals are also polycrystals.

Anisotropy of crystalline bodies

In crystals, particles are located with different densities in different directions. If we connect atoms in a straight line in one of the directions of the crystal lattice, then the distance between them will be the same in all this direction. In any other direction, the distance between the atoms is also constant, but its value may already differ from the distance in the previous case. This means that interaction forces of different magnitude act between atoms in different directions. Therefore, the physical properties of matter in these directions will also differ. This phenomenon is called anisotropy - the dependence of the properties of matter on direction.

Electrical conductivity, thermal conductivity, elasticity, refractive index and other properties crystalline substance vary depending on the direction in the crystal. Conducted differently in different directions electricity, the substance is heated differently, the light rays are refracted differently.

Anisotropy is not observed in polycrystals. The properties of matter remain the same in all directions.

There are several states of aggregation in which all bodies and substances are found. This:

liquid;
plasma;
hard.

If we consider the totality of the planet and space, then most of the substances and bodies are still in the state of gas and plasma. However, the content of solid particles is also significant on the Earth itself. Here we will talk about them, having found out what crystalline and amorphous solids are.

Crystalline and amorphous bodies: a general concept

All solids, bodies, objects are conventionally divided into:

crystalline;
amorphous.

The difference between them is huge, because the subdivision is based on signs of structure and properties. In short, solid crystalline are those substances and bodies that have a certain type of spatial crystal lattice, that is, they have the ability to change in a certain direction, but not in all (anisotropy).

If we characterize amorphous compounds, then their first sign is the ability to change physical characteristics in all directions simultaneously. This is called isotropy.

The structure and properties of crystalline and amorphous bodies are completely different. If the former have a clearly defined structure, consisting of ordered particles in space, then the latter do not have any order.

Properties of solids

Crystalline and amorphous bodies, however, belong to a single group of solids, which means they have all the characteristics of a given state of aggregation. That is, the common properties for them will be the following:

Mechanical - elasticity, hardness, ability to deform.
Thermal - boiling and melting points, coefficient of thermal expansion.
Electrical and magnetic - thermal and electrical conductivity.

Thus, the states we are considering have all these characteristics. Only they will manifest themselves in amorphous bodies somewhat differently than in crystalline ones.

Important properties for industrial purposes are mechanical and electrical. The ability to recover from deformation or, on the contrary, to crumble and grind - important feature. Also a big role is played by the fact whether a substance can conduct an electric current or is not capable of it.

The structure of crystals

If we describe the structure of crystalline and amorphous bodies, then first of all we should indicate the type of particles that compose them. In the case of crystals, these can be ions, atoms, atom-ions (in metals), molecules (rarely).

In general, these structures are characterized by the presence of a strictly ordered spatial lattice, which is formed as a result of the arrangement of the particles that form the substance. If we imagine the structure of a crystal figuratively, then we get something like this: atoms (or other particles) are arranged from each other at certain distances so that the result is an ideal unit cell of the future crystal lattice. Then this cell is repeated many times, and so the overall structure is formed.

The main feature is that the physical properties in such structures change in parallel, but not in all directions. This phenomenon is called anisotropy. That is, if you act on one part of the crystal, then the other side may not react to it. So, you can grind half a piece of table salt, but the second will remain intact.

Crystal types

It is customary to designate two variants of crystals. The first is single-crystal structures, that is, when the lattice itself is 1. Crystalline and amorphous bodies in this case are completely different in properties. After all, a single crystal is characterized by pure anisotropy. It is the smallest structure, elementary.

If single crystals are repeated many times and combined into one whole, then we are talking about a polycrystal. Then we are not talking about anisotropy, since the orientation of elementary cells violates the general ordered structure. In this regard, polycrystals and amorphous bodies are close to each other in terms of their physical properties.

Metals and their alloys

Crystalline and amorphous bodies are very close to each other. This can be easily verified by taking metals and their alloys as an example. By themselves, they are solids under normal conditions. However, at a certain temperature, they begin to melt and, until complete crystallization occurs, they will remain in a state of a stretching, thick, viscous mass. And this is already an amorphous state of the body.

Therefore, strictly speaking, almost every crystalline substance can become amorphous under certain conditions. Just like the latter, during crystallization it becomes solid with an ordered spatial structure.

Metals can have different types of spatial structures, the most famous and studied of which are the following:

Simple cubic.
face centered.
Volume centered.

The crystal structure can be based on a prism or a pyramid, and its main part is represented by:

triangle;
parallelogram;
square;
hexagon.

Ideal properties of isotropy have a substance that has a simple regular cubic lattice.

The concept of amorphism

Crystalline and amorphous bodies are quite easy to distinguish externally. After all, the latter can often be confused with viscous liquids. The structure of an amorphous substance is also based on ions, atoms, and molecules. However, they do not form an ordered strict structure, and therefore their properties change in all directions. That is, they are isotropic.

Particles are arranged randomly, randomly. Only sometimes they can form small loci, which still does not affect the overall properties exhibited.

Properties of similar bodies

They are identical to those of crystals. Differences are only in indicators for each specific body. For example, the following characteristic parameters of amorphous bodies can be distinguished:

elasticity;
density;
viscosity;
ductility;
conductivity and semiconductivity.

You can often meet the boundary states of connections. Crystalline and amorphous bodies can pass into a semi-amorphous state.

Also of interest is that feature of the state under consideration, which manifests itself under a sharp external impact. So, if an amorphous body is subjected to a sharp impact or deformation, then it is able to behave like a polycrystal and break into small pieces. However, if you give these parts time, they will soon join together again and go into a viscous fluid state.

This state of compounds does not have a specific temperature at which a phase transition occurs. This process is greatly extended, sometimes even for decades (for example, the decomposition of low-pressure polyethylene).

Examples of amorphous substances

Many examples of such substances can be cited. Let's outline some of the most obvious and frequently encountered.

Chocolate is a typical amorphous substance.
Resins, including phenol-formaldehyde, all plastics.
Amber.
Glass of any composition.
Bitumen.
Tar.
Wax and others.

An amorphous body is formed as a result of very slow crystallization, that is, an increase in the viscosity of the solution with a decrease in temperature. It is often difficult to call such substances solid, they are more likely to be referred to as viscous thick liquids.

A special state have those compounds that, when solidified, do not crystallize at all. They are called glasses, and the state is glassy.

glassy substances

The properties of crystalline and amorphous bodies are similar, as we found out, due to a common origin and a single internal nature. But sometimes a special state of substances, called glassy, is considered separately from them. This is a homogeneous mineral solution that crystallizes and hardens without the formation of spatial lattices. That is, it always remains isotropic in terms of changes in properties.

So, for example, ordinary window glass does not have an exact melting point. It's easy when you raise this indicator slowly melts, softens and turns into a liquid state. If the impact is stopped, then it will go reverse process and solidification will begin, but without crystallization.

Such substances are very much appreciated, glass today is one of the most common and sought after building materials worldwide.

Solid bodies retain their shape for a long time, and considerable effort is needed to change their volume.

In the definition solids we, as a rule, associate their properties with external signs - the preservation of shape and volume. However, solid bodies also differ in their internal structure. Some of them have crystalline structure- microparticles (atoms, ions, molecules), of which they are composed, are arranged in an orderly manner at considerable distances, that is, they retain long-range order. Such solids are called crystalline. These include metals, table salt, sugar, diamond, graphite, quartz, etc.

Other bodies do not have a certain ordered arrangement of atoms, ions or molecules, and in their internal structure they are more like liquids, since they are characterized by a short-range order of placement of microparticles. Such bodies are called amorphous. These are wax, glass, various resins, plastics, etc.

Crystalline and amorphous bodies can be distinguished visually: at a break, amorphous bodies form an irregularly shaped surface, and crystals have flat faces and a stepped surface.

The amorphous state is rather unstable, and over time amorphous bodies may become crystalline. For example, on sugar candies, amorphous in their properties, sugar crystals form after prolonged storage. Also, under certain conditions, crystalline bodies can become amorphous. For example, the rapid cooling of some metals leads to the formation of their amorphous (glassy) state.

Amorphous bodies have the same properties in different directions of intermolecular bonds. Therefore they say that they isotropic. As the temperature rises, they "become softer" and show fluidity, but, like crystalline bodies, they do not have a fixed melting point.

Word "isotropic" comes from gr.isos - even, the same;tropos - direction.

Crystalline bodies characterized by a certain internal order of placement of atoms and molecules, forming a variety of spatial lattices, which are called crystalline. Depending on their shape, different mono-crystals substances form certain geometric shapes. So, a mono-crystal of table salt has the shape of a cube, ice is a hexagonal prism, diamond is a regular hexagon (Fig. 3.12). As a rule, they are insignificant in size, but large single crystals are also found in nature, for example, a block of quartz was found as tall as a person.

Under natural conditions, most crystalline bodies consist of small single crystals that have grown together in disorder. They are called polycrystals. An example of such a polycrystal is a snowflake, which takes on various forms, but its wings always have a hexagonal direction. material from the site

Single crystals are different anisotropy properties, that is, their dependence on the direction of orientation of the crystal faces. For example, such a natural mineral as mica easily delaminates into plates under the action of force along one plane, but exhibits significant strength in the perpendicular direction. Polycrystals are isotropic in their properties. This is due to the random orientation of the single crystals of which they are composed.

Word "anisotropic" in translation from Greek means "not the same in direction."

Many crystalline bodies, identical in their own way chemical composition have different physical properties. Such a phenomenon is called polymorphism. For example, by chemical nature, diamond and graphite are carbon in two different modifications. They have crystal lattices of various shapes, and therefore the forces of interaction between atoms in them are different. This explains, in particular, their different hardness: graphite is soft, diamond is a hard mineral.

In laboratory conditions, about ten modifications of ice are obtained, although only one exists in nature.

On this page, material on the topics:

What properties are inherent in crystalline bodies
Crystalline bodies brief report
How can you visually distinguish crystalline from amorphous
Rigid bodyphysics briefly
Crystalline amorphous bodies briefly

Questions about this item:

Solids are either crystalline or amorphous.

Let's put experience

Examine through a magnifying glass crystals of table salt or sugar: they have even, as if cut edges. You can also grow a large crystal: in fig. 7.6, and such a crystal of table salt is depicted. Remarkably beautiful and at the same time always very “correct” snowflakes: these are ice crystals grown in heaven. Their pattern is always based on a regular hexagon (Fig. 7.6, b).

Rice. 7.6. Crystalline bodies: a - salt crystal, b - snowflake; crystal lattices: in - table salt, g - ice

Table salt, sugar, and ice are examples of crystalline solids. The correct shape of crystals is due to the fact that the atoms or molecules in the crystals are arranged in an orderly manner, forming a crystal lattice.

For example, in a crystal of table salt, the sodium and chlorine atoms strictly alternate, located at the tops of the cubes, which is why the salt crystals have the shape of a cube. And in an ice crystal, water molecules are located at the vertices of hexagons - that's why the pattern of any snowflake has a hexagonal "frame". On fig. 7.6, in schematically shows the crystal lattice of table salt, and in fig. 7.6, d - crystal lattice of ice.

amorphous bodies. Glass objects are examples of amorphous bodies (Fig. 7.7, a). Amorphous bodies have fluidity, although much less than liquids. As the temperature rises, the fluidity of amorphous bodies increases. Thanks to this, a glass vessel can be blown out of a drop of heated glass (Fig. 7.7, b) (just as a soap bubble is blown out of a drop of soapy water).

Rice. 7.7. Examples of amorphous bodies: a - glass vial; b - a drop of semi-liquid glass; c - schematic representation of the molecular structure amorphous body

On fig. 7.7c schematically depicts the molecular structure of an amorphous body. As you can see, the molecular structure of an amorphous body resembles the molecular structure of a liquid - this explains the fluidity of amorphous bodies. It is no coincidence that the word "amorphous" comes from the Greek. "amor-fos" - shapeless.

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Introduction

Chapter 1. Crystalline and amorphous bodies

1.1 Ideal crystals

1.2 Single crystals and crystalline aggregates

1.3 Polycrystals

Chapter 2. Elements of symmetry of crystals

Chapter 3. Types of defects in solids

3.1 Point defects

3.2 Line defects

3.3 Surface defects

3.4 Bulk defects

Chapter 4

Chapter 5

Conclusion

Bibliography

Introduction

Crystals are one of the most beautiful and mysterious creations of nature. Currently, the science of crystallography is engaged in the study of the diversity of crystals. It reveals signs of unity in this diversity, explores the properties and structure of both single crystals and crystalline aggregates. Crystallography is a science that comprehensively studies crystalline matter. this work also devoted to crystals and their properties.

Currently, crystals are widely used in science and technology, as they have special properties. Such applications of crystals as semiconductors, superconductors, quantum electronics, and many others require a deep understanding of the dependence of the physical properties of crystals on their chemical composition and structure.

Currently known methods of artificial growth of crystals. A crystal can be grown in an ordinary glass; this requires only a certain solution and the care with which it is necessary to take care of the growing crystal.

There are a great many crystals in nature, and there are also many different forms of crystals. In reality, it is almost impossible to give a definition that would fit all crystals. Here, the results of X-ray analysis of crystals can be used to help. X-rays make it possible, as it were, to feel the atoms inside the crystalline body, and determines their spatial arrangement. As a result, it was found that absolutely all crystals are built from elementary particles arranged in a strict order inside the crystalline body.

In all, without exception, crystalline constructions of atoms, one can single out many identical atoms arranged like nodes of a spatial lattice. To imagine such a lattice, let's mentally fill the space with a set of equal parallelepipeds, parallel oriented and touching along whole faces. The simplest example such a building is a masonry of identical bricks. If we select the corresponding points inside the bricks, for example, their centers or vertices, then we will get a model of the spatial lattice. For all, without exception, crystalline bodies are characterized by a lattice structure.

Crystals are called all solids in which the particles that make them up (atoms, ions, molecules) are arranged strictly regularly, like nodes of spatial lattices". This definition is as close as possible to the truth, it fits any homogeneous crystalline bodies: both boules (a form of a crystal that has neither faces, nor edges, nor protruding peaks), and grains, and flat-faced figures.

Chapter 1.Crystalline and amorphous bodies

According to their physical properties and molecular structure, solids are divided into two classes - amorphous and crystalline solids.

A characteristic feature of amorphous bodies is their isotropy, i.e. independence of all physical properties (mechanical, optical, etc.) from direction. Molecules and atoms in isotropic solids are arranged randomly, forming only small local groups containing several particles (short range order). In their structure, amorphous bodies are very close to liquids.

Examples of amorphous bodies are glass, various hardened resins (amber), plastics, etc. If an amorphous body is heated, then it gradually softens, and the transition to a liquid state occupies a significant temperature range.

In crystalline bodies, the particles are arranged in a strict order, forming spatial periodically repeating structures throughout the entire volume of the body. For a visual representation of such structures, spatial crystal lattices, at the nodes of which the centers of atoms or molecules of a given substance are located.

In each spatial lattice, one can single out a structural element of the minimum size, which is called unit cell.

Rice. 1. Types of crystal lattices: 1 - simple cubic lattice; 2 - face-centered cubic lattice; 3 - body-centered cubic lattice; 4 - hexagonal lattice

In a simple cubic lattice, the particles are located at the vertices of the cube. In a face-centered lattice, particles are located not only at the vertices of the cube, but also at the centers of each of its faces. In a body-centered cubic lattice, an additional particle is located at the center of each elementary cubic cell.

It should be remembered that the particles in crystals are densely packed, so that the distance between their centers is approximately equal to the size of the particles. In the image of crystal lattices, only the position of the particle centers is indicated.

1. 1 Perfect crystals

correct geometric shape crystals attracted the attention of researchers even at the early stages of the development of crystallography and gave rise to the creation of certain hypotheses about their internal structure.

If we consider an ideal crystal, we will not find violations in it, all identical particles are arranged in identical parallel rows. If we apply three elementary translations that do not lie in the same plane to an arbitrary point and repeat it infinitely in space, then we get a spatial lattice, i.e. three-dimensional system of equivalent nodes. Thus, in an ideal crystal, the arrangement of material particles is characterized by a strict three-dimensional periodicity. And in order to get a visual representation of the patterns associated with the geometrically regular internal structure of crystals, crystallography laboratory classes usually use models of ideally formed crystals in the form of convex polyhedra with flat faces and straight edges. In fact, the faces of real crystals are not perfectly flat, since during their growth they are covered with tubercles, roughness, grooves, growth pits, vicinals (faces deviated in whole or in part from their ideal position), growth or dissolution spirals, etc. .

Perfect Crystal- This is a physical model, which is an infinite single crystal that does not contain impurities or structural defects. The difference between real crystals and ideal ones is associated with the finiteness of their sizes and the presence of defects. The presence of some defects (for example, impurities, intergranular boundaries) in real crystals can be almost completely avoided using special methods of growth, annealing or purification. However, at a temperature T>0K, crystals always have a finite concentration of (thermoactivated) vacancies and interstitial atoms, the number of which in equilibrium decreases exponentially with decreasing temperature.

Crystalline substances can exist in the form of single crystals or polycrystalline samples.

A monocrystal is a solid body in which the regular structure covers the entire volume of the substance. Single crystals are found in nature (quartz, diamond, emerald) or artificially produced (ruby).

Polycrystalline samples are composed of a large number small, randomly oriented, different-sized crystals, which can be interconnected by certain interaction forces.

1. 2 monocrystalles and crystalline aggregates

Monocrystal- a separate homogeneous crystal having a continuous crystal lattice and sometimes having anisotropy of physical properties. External form single crystal is due to its atomic crystal lattice and conditions (mainly speed and uniformity) of crystallization. A slowly grown single crystal almost always acquires a well-pronounced natural faceting, under nonequilibrium conditions ( average speed growth) crystallization, the faceting is weak. At an even higher crystallization rate, instead of a single crystal, homogeneous polycrystals and polycrystalline aggregates are formed, consisting of many differently oriented small single crystals. Examples of faceted natural single crystals are single crystals of quartz, rock salt, Icelandic spar, diamond, and topaz. Single crystals of semiconductor and dielectric materials grown under special conditions are of great industrial importance. In particular, single crystals of silicon and artificial alloys of elements of group III (third) with elements of group V (fifth) of the periodic table (for example, GaAs gallium arsenide) are the basis of modern solid-state electronics. Single crystals of metals and their alloys do not have special properties and are practically not used. Single crystals of ultrapure substances have the same properties regardless of the method of their preparation. Crystallization occurs near the melting point (condensation) from gaseous (for example, frost and snowflakes), liquid (most often) and solid amorphous states with heat release. Crystallization from a gas or liquid has a powerful cleansing mechanism: the chemical composition of slowly grown single crystals is almost ideal. Almost all contaminants remain (accumulate) in the liquid or gas. This happens because during the growth of the crystal lattice, the necessary atoms (molecules for molecular crystals) are spontaneously selected not only by their chemical properties (valency), but also by size.

Modern technology is no longer enough of a poor set of properties of natural crystals (especially for the creation of semiconductor lasers), and scientists have come up with a method for creating crystal-like substances with intermediate properties by growing alternating ultra-thin layers of crystals with similar crystal lattice parameters.

Unlike other states of aggregation, the crystalline state is diverse. Molecules of the same composition can be packed in crystals in different ways. Physical and Chemical properties substances. Thus, substances with the same chemical composition often actually have different physical properties. For a liquid state, such a variety is not typical, but for a gaseous state it is impossible.

If we take, for example, ordinary table salt, then it is easy to see individual crystals even without a microscope.

If we want to emphasize that we are dealing with a single, separate crystal, then we call it single crystal, to emphasize that we are talking about an accumulation of many crystals, the term is used crystalline aggregate. If individual crystals in a crystalline aggregate are almost not faceted, this can be explained by the fact that crystallization began simultaneously at many points of the substance and its speed was quite high. Growing crystals are an obstacle to each other and interfere with the correct faceting of each of them.

In that work we will talk mainly about single crystals, and since they are constituents of crystalline aggregates, their properties will be similar to those of aggregates.

1. 3 Polycrystals

polycrystal- an aggregate of small crystals of a substance, sometimes called crystallites or crystalline grains because of their irregular shape. Many materials of natural and artificial origin (minerals, metals, alloys, ceramics, etc.) are polycrystals.

Properties and getting. The properties of polycrystals are determined by the properties of its constituent crystalline grains, their average size, which ranges from 1–2 microns to several millimeters (in some cases, up to several meters), the crystallographic orientation of grains, and the structure of grain boundaries. If the grains are randomly oriented and their sizes are small compared to the size of the polycrystal, then the anisotropy of physical properties characteristic of single crystals does not appear in the polycrystal. If a polycrystal has a predominant crystallographic grain orientation, then the polycrystal is textured and, in this case, has anisotropic properties. The presence of grain boundaries significantly affects the physical, especially mechanical, properties of polycrystals, since scattering of conduction electrons, phonons, dislocation deceleration, etc. occurs at the boundaries.

Polycrystals are formed during crystallization, polymorphic transformations, and as a result of sintering of crystalline powders. A polycrystal is less stable than a single crystal; therefore, during prolonged annealing of a polycrystal, recrystallization occurs (primary growth of individual grains at the expense of others), leading to the formation of large crystalline blocks.

Chapter 2. Elements of symmetry of crystals

The concepts of symmetry and asymmetry have appeared in science since ancient times rather as an aesthetic criterion than strictly scientific definitions. Before the appearance of the idea of symmetry, mathematics, physics, natural science as a whole resembled separate islands of hopelessly isolated from each other and even contradictory ideas, theories, laws. Symmetry characterizes and marks the era of synthesis, when disparate fragments of scientific knowledge merge into a single, integral picture of the world. One of the main trends of this process is the mathematization of scientific knowledge.

It is customary to consider symmetry not only as a fundamental picture of scientific knowledge, establishing internal connections between systems, theories, laws and concepts, but also to attribute it to attributes as fundamental as space and time, movement. In this sense, symmetry determines the structure of the material world, all its components. Symmetry has a multifaceted and multilevel character. For example, in the system of physical knowledge, symmetry is considered at the level of phenomena, the laws that describe these phenomena, and the principles underlying these laws, and in mathematics, when describing geometric objects. Symmetry can be classified as:

· structural;

· geometric;

dynamic, describing respectively the crystallographic,

mathematical and physical aspects of this concept.

The simplest symmetries are geometrically representable in our usual three-dimensional space and therefore visual. Such symmetries are associated with geometric operations that bring the body in question to coincide with itself. They say that symmetry manifests itself in the immutability (invariance) of a body or system with respect to a certain operation. For example, a sphere (without any marks on its surface) is invariant under any rotation. This shows its symmetry. A sphere with a mark, for example, in the form of a dot, coincides with itself only upon rotation, after which the mark on it falls into its original position. Our three-dimensional space is isotropic. This means that, like an unlabeled sphere, it coincides with itself in any rotation. Space is inextricably linked with matter. Therefore, our Universe is also isotropic. The space is also homogeneous. This means that it (and our Universe) has symmetry under the shift operation. Time has the same symmetry.

In addition to simple (geometric) symmetries in physics, very complex, so-called dynamic symmetries, that is, symmetries associated not with space and time, but with a certain type of interaction, are widely encountered. They are not visual, and even the simplest of them, for example, the so-called gauge symmetries, is difficult to explain without using a rather complex physical theory. Gauge symmetries in physics also correspond to some conservation laws. For example, the gauge symmetry of electromagnetic potentials leads to the law of conservation of electric charge.

In the course of social practice, humanity has accumulated many facts that testify both to strict orderliness, the balance between parts of the whole, and to violations of this orderliness. In this regard, the following five categories of symmetry can be distinguished:

· symmetry;

· asymmetry;

dissymmetry;

· antisymmetry;

supersymmetry.

Asymmetry . Asymmetry is asymmetry, i.e. a state where there is no symmetry. But even Kant said that negation is never a simple exception or absence of a corresponding positive content. For example, movement is a negation of its previous state, a change in an object. Movement denies rest, but rest is not the absence of movement, since there is very little information and this information is erroneous. There is no absence of rest, as well as movement, since these are two sides of the same essence. Stillness is another aspect of movement.

Complete lack of symmetry also does not happen. A figure that does not have an element of symmetry is called asymmetric. But, strictly speaking, this is not the case. In the case of asymmetric figures, the symmetry disorder is simply brought to an end, but not to a complete lack of symmetry, since these figures are still characterized by an infinite number of first-order axes, which are also elements of symmetry.

Asymmetry is associated with the absence of all symmetry elements in an object. Such an element is indivisible. An example is the human hand. Asymmetry is a category opposite to symmetry, which reflects the imbalance existing in the objective world, associated with change, development, restructuring of parts of the whole. Just as we talk about movement, meaning the unity of movement and rest, so symmetry and asymmetry are two polar opposites of the objective world. In real nature there is no pure symmetry and asymmetry. They are always in unity and continuous struggle.

At different levels of development of matter, there is either symmetry (relative order), or asymmetry (a tendency to disturb peace, movement, development), but these two tendencies are always the same and their struggle is absolute. Real, even the most perfect crystals are far in their structure from crystals of ideal shape and ideal symmetry considered in crystallography. They have significant deviations from ideal symmetry. They also have elements of asymmetry: dislocations, vacancies that affect their physical properties.

The definitions of symmetry and asymmetry indicate the universal, general nature of symmetry and asymmetry as properties of the material world. The analysis of the concept of symmetry in physics and mathematics (with rare exceptions) tends to absolutize symmetry and interpret asymmetry as the absence of symmetry and order. The antipode of symmetry acts as a purely negative concept, but deserving attention. Significant interest in asymmetry arose in the middle of the 19th century in connection with the experiments of L. Pasteur in the study and separation of stereoisomers.

Dissymmetry . Dissymmetry is called internal, or detuned, symmetry, i.e. the absence of some elements of symmetry in the object. For example, in rivers flowing along the earth's meridians, one bank is higher than the other (in the Northern Hemisphere, the right bank is higher than the left, and vice versa in the Southern). According to Pasteur, a dissymmetric figure is one that cannot be superimposed with its mirror image. The symmetry value of a dissymmetric object can be arbitrarily high. Dissymmetry in the broadest sense of its understanding could be defined as any form of approximation from an infinitely symmetrical object to an infinitely asymmetric one.

antisymmetry . Antisymmetry is called opposite symmetry, or symmetry of opposites. It is associated with a change in the sign of the figure: particles - antiparticles, convexity - concavity, black - white, stretching - compression, forward - backward, etc. This concept can be explained by the example of two pairs of black and white gloves. If two pairs of black and white gloves are sewn from a piece of leather, two sides of which are colored white and black, respectively, then they can be distinguished on the basis of rightness - leftism, on the basis of color - blackness and whiteness, in other words, on the basis of sign-informatism and some other sign. The operation of antisymmetry consists of ordinary symmetry operations, accompanied by a change in the second sign of the figure.

supersymmetry In the last decades of the 20th century, the model of supersymmetry began to develop, which was proposed by Russian theorists Gelfand and Lichtman. Simply put, their idea was that, just as there are ordinary dimensions of space and time, there should be extra dimensions that can be measured in so-called Grassmann numbers. As S. Hawking said, even science fiction writers did not think of something as strange as Grassmann's dimensions. In our usual arithmetic, if the number 4 times 6 is the same as 6 times 4. But the oddity of Grassmann numbers is that if X times Y, then this is equal to minus Y times X. Feel, how far is this from our classical ideas about nature and methods of describing it?

Symmetry can also be considered in terms of the forms of movement or the so-called symmetry operations. The following symmetry operations can be distinguished:

Reflection in the plane of symmetry (reflection in a mirror);

rotation around the axis of symmetry ( rotational symmetry);

reflection in the center of symmetry (inversion);

transfer ( broadcast) figures at a distance;

screw turns

permutation symmetry.

Reflection in the plane of symmetry . Reflection is the most well-known and most commonly occurring type of symmetry in nature. The mirror exactly reproduces what it "sees", but the order considered is reversed: your double's right hand will actually be left, since the fingers are placed on it in reverse order. Everyone, probably, has been familiar with the film "The Kingdom of Crooked Mirrors" since childhood, where the names of all the characters were read in reverse order. Mirror symmetry can be found everywhere: in the leaves and flowers of plants, architecture, ornaments. The human body, if we talk only about the external form, has a mirror symmetry, although not quite strict. Moreover, mirror symmetry is inherent in the bodies of almost all living beings, and such a coincidence is by no means accidental. The importance of the concept of mirror symmetry can hardly be overestimated.

Mirror symmetry has everything that can be divided into two mirror equal halves. Each of the halves serves as a mirror reflection of the other, and the plane separating them is called the plane of mirror reflection, or simply the mirror plane. This plane can be called an element of symmetry, and the corresponding operation - the symmetry operation . We encounter three-dimensional symmetrical patterns every day: these are many modern residential buildings, and sometimes entire blocks, boxes and boxes piled up in warehouses, atoms of matter in a crystalline state form a crystal lattice - an element of three-dimensional symmetry. In all these cases, the correct location allows economical use of space and ensures stability.

A remarkable example of mirror symmetry in the literature is the phrase "shifter": "And the rose fell on the paw of Azor" . In this line, the center of mirror symmetry is the letter "n", relative to which all other letters (not taking into account the gaps between words) are located in mutually opposite order.

Rotational symmetry . The appearance of the pattern will not change if it is rotated by some angle around the axis. The resulting symmetry is called rotational symmetry. . An example is the children's game "pinwheel" with rotational symmetry. In many dances, figures are based on rotational movements, often performed only in one direction (i.e., without reflection), for example, round dances.

The leaves and flowers of many plants exhibit radial symmetry. This is such a symmetry in which a leaf or flower, turning around the axis of symmetry, passes into itself. On cross sections of the tissues that form the root or stem of a plant, radial symmetry is clearly visible. The inflorescences of many flowers also have radial symmetry.

Reflection at the center of symmetry . An example of an object of the highest symmetry that characterizes this symmetry operation is a ball. Spherical shapes are widely distributed in nature. They are common in the atmosphere (fog drops, clouds), hydrosphere (various microorganisms), lithosphere and space. Spores and pollen of plants, drops of water released in a state of weightlessness have a spherical shape. spaceship. At the metagalactic level, the largest globular structures are globular galaxies. The denser the cluster of galaxies, the closer it is to a spherical shape. Star clusters are also globular shapes.

Broadcast, or transfer of a figure to a distance . Translation, or parallel transfer of a figure over a distance, is any unlimitedly repeating pattern. It can be one-dimensional, two-dimensional, three-dimensional. Translation in the same or opposite directions forms a one-dimensional pattern. Translation in two non-parallel directions forms a two-dimensional pattern. Parquet floors, wallpaper patterns, lace ribbons, paths paved with bricks or tiles, crystalline figures form patterns that have no natural boundaries. When studying the ornaments used in typography, the same elements of symmetry were found as in the pattern of tiled floors. Ornamental borders are associated with music. In music, the elements of a symmetrical design include the operations of repetition (translation) and reversal (reflection). It is these elements of symmetry that are found in the borders. Although in most cases music is not distinguished by strict symmetry, many musical works are based on symmetry operations. They are especially noticeable in children's songs, which, apparently, is why it is so easy to remember. Symmetry operations are found in the music of the Middle Ages and the Renaissance, in the music of the Baroque era (often in a very sophisticated form). At the time of I.S. Bach, when symmetry was an important principle of composition, a peculiar game of musical puzzles became widespread. One of them was to solve the mysterious "canons". Canon is a form of polyphonic music based on carrying out a theme led by one voice in other voices. The composer suggested a theme, and the listeners had to guess the symmetry operations that he intended to use when repeating the theme.

Nature sets up puzzles of the opposite type: we are offered a complete canon, and we must find the rules and motives underlying the existing patterns and symmetry, and vice versa, look for patterns that arise when repeating the motive according to different rules. The first approach leads to the study of the structure of matter, art, music, thinking. The second approach confronts us with the problem of design or plan, which has been exciting artists, architects, musicians, and scientists since ancient times.

Screw turns . Translation can be combined with reflection or rotation, and new symmetry operations arise. Rotation by a certain number of degrees, accompanied by translation to a distance along the axis of rotation, generates helical symmetry - the symmetry of a spiral staircase. An example of helical symmetry is the arrangement of leaves on the stem of many plants. The head of a sunflower has processes arranged in geometric spirals that unwind from the center outwards. The youngest members of the spiral are in the center. In such systems, one can notice two families of spirals unwinding in opposite sides and intersecting at angles close to right. But no matter how interesting and attractive the manifestations of symmetry in the world of plants are, there are still many secrets that control the development processes. Following Goethe, who spoke of the striving of nature towards a spiral, it can be assumed that this movement is carried out along a logarithmic spiral, starting each time from a central, fixed point and combining translational movement (stretching) with a turn of rotation.

Permutation symmetry . Further expansion of the number of physical symmetries is associated with the development quantum mechanics. One of the special types of symmetry in the microcosm is permutation symmetry. It is based on the fundamental indistinguishability of identical microparticles that do not move along certain trajectories, and their positions are estimated by probabilistic characteristics associated with the square of the modulus of the wave function. Permutation symmetry also lies in the fact that when quantum particles are "permuted", the probabilistic characteristics do not change, the square of the modulus of the wave function is a constant.

Similarity symmetry . Another type of symmetry is similarity symmetry, associated with the simultaneous increase or decrease of similar parts of the figure and the distances between them. Matryoshka is an example of this kind of symmetry. Such symmetry is very widespread in wildlife. It is demonstrated by all growing organisms.

Symmetry questions play a decisive role in modern physics. The dynamic laws of nature are characterized by certain types of symmetry. In a general sense, the symmetry of physical laws means their invariance with respect to certain transformations. It should also be noted that the considered types of symmetry have certain limits of applicability. For example, the symmetry of the right and left exists only in the region of strong electromagnetic interactions, but is violated in the case of weak ones. Isotopic invariance is valid only when electromagnetic forces are taken into account. To apply the concept of symmetry, you can introduce a certain structure that takes into account four factors:

the object or phenomenon that is being investigated;

the transformation with respect to which the symmetry is considered;

· Invariance of any properties of an object or phenomenon, expressing the considered symmetry. Connection of symmetry of physical laws with conservation laws;

limits of applicability various kinds symmetry.

The study of the symmetry properties of physical systems or laws requires the involvement of a special mathematical analysis, primarily the representations of group theory, which is currently the most developed in solid state physics and crystallography.

Chapter 3. Types of defects in solids

All real solids, both single-crystal and polycrystalline, contain so-called structural defects, types, concentration, the behavior of which is very diverse and depends on the nature, conditions for obtaining materials and the nature of external influences. Most of the defects created by an external action are thermodynamically unstable, and the state of the system in this case is excited (nonequilibrium). Such an external influence can be temperature, pressure, irradiation with particles and high-energy quanta, the introduction of impurities, phase hardening during polymorphic and other transformations, mechanical action, etc. The transition to an equilibrium state can occur in different ways and, as a rule, is realized through a series metastable states.

Defects of one type, interacting with defects of the same or another type, can annihilate or form new associations of defects. These processes are accompanied by a decrease in the energy of the system.

According to the number of directions N, in which the violation of the periodic arrangement of atoms in the crystal lattice, caused by this defect, extends, defects are distinguished:

Point (zero-dimensional, N=0);

· Linear (one-dimensional, N=1);

Surface (two-dimensional, N=2);

Volumetric (three-dimensional, N=3);

Now we will consider each defect in detail.

3.1 Point Defects

To zero-dimensional (or pinpoint) crystal defects include all defects that are associated with the displacement or replacement of a small group of atoms, as well as with impurities. They arise during heating, alloying, in the process of crystal growth and as a result of radiation exposure. Can also be made as a result of implantation. The properties of such defects and the mechanisms of their formation are the most studied, including motion, interaction, annihilation, and evaporation.

· A vacancy is a free, unoccupied atom, a node of the crystal lattice.

· Own interstitial atom - an atom of the main element, located in the interstitial position of the elementary cell.

· Impurity substitution atom - the replacement of an atom of one type by an atom of another type in a crystal lattice site. The substitution positions can contain atoms that differ relatively little from the atoms of the base in terms of their size and electronic properties.

· Interstitial impurity atom - the impurity atom is located in the interstices of the crystal lattice. In metals, interstitial impurities are usually hydrogen, carbon, nitrogen, and oxygen. In semiconductors, these are impurities that create deep energy levels in the bandgap, such as copper and gold in silicon.

Complexes consisting of several point defects are also often observed in crystals, for example, a Frenkel defect (vacancy + intrinsic interstitial atom), divacancy (vacancy + vacancy), A-center (vacancy + oxygen atom in silicon and germanium), etc.

Thermodynamics of point defects. Point defects increase the energy of the crystal, since a certain energy was spent on the formation of each defect. Elastic deformation causes a very small fraction of the vacancy formation energy, since the ion displacements do not exceed 1% and the corresponding deformation energy is tenths of an eV. During the formation of an interstitial atom, the displacements of neighboring ions can reach 20% of the interatomic distance, and the energy of elastic deformation of the lattice corresponding to them can reach several eV. The main part of the formation of a point defect is associated with a violation of the periodicity of the atomic structure and the bonding forces between atoms. A point defect in a metal interacts with the entire electron gas. Removing a positive ion from a node is tantamount to introducing a point negative charge; conduction electrons are repelled from this charge, which causes an increase in their energy. Theoretical calculations show that the energy of formation of a vacancy in the fcc copper lattice is about 1 eV, and that of an interstitial atom is from 2.5 to 3.5 eV.

Despite the increase in the energy of the crystal during the formation of its own point defects, they can be in thermodynamic equilibrium in the lattice, since their formation leads to an increase in entropy. At elevated temperatures, the increase in the entropy term TS of the free energy due to the formation of point defects compensates for the increase in the total energy of the crystal U, and the free energy turns out to be minimal.

Equilibrium concentration of vacancies:

Where E 0 is the energy of formation of one vacancy, k is the Boltzmann constant, T is the absolute temperature. The same formula is valid for interstitial atoms. The formula shows that the concentration of vacancies should strongly depend on temperature. The calculation formula is simple, but exact quantitative values can be obtained only by knowing the defect formation energy. It is very difficult to calculate this value theoretically, so one has to be content with only approximate estimates.

Since the defect formation energy is included in the exponent, this difference causes a huge difference in the concentration of vacancies and interstitial atoms. Thus, at 1000°C in copper, the concentration of interstitial atoms is only 10 −39, which is 35 orders of magnitude lower than the concentration of vacancies at this temperature. In close packings, which are typical for most metals, it is very difficult for interstitial atoms to form, and vacancies in such crystals are the main point defects (not counting impurity atoms).

Migration of point defects. Atoms oscillating in motion are constantly exchanging energy. Due to the randomness of thermal motion, energy is unevenly distributed between different atoms. At some point, an atom can receive such an excess of energy from its neighbors that it will occupy a neighboring position in the lattice. This is how the migration (movement) of point defects occurs in the volume of crystals.

If one of the atoms surrounding the vacancy moves to the vacant site, then the vacancy will correspondingly move to its place. Successive elementary acts of movement of a certain vacancy are carried out by different atoms. The figure shows that in a layer of close-packed balls (atoms), in order to move one of the balls to a vacant place, it must push balls 1 and 2 apart. is minimal, the atom must pass through a state with increased potential energy, overcome the energy barrier. For this, it is necessary for the atom to receive from its neighbors an excess of energy, which it loses, "squeezing" into a new position. The height of the energy barrier E m is called vacancy migration activation energy.

Sources and sinks of point defects. The main source and sink of point defects are linear and surface defects. In large, perfect single crystals, the decomposition of a supersaturated solid solution of intrinsic point defects is possible with the formation of the so-called. microdefects.

Complexes of point defects. The simplest complex of point defects is a divacancy (divacancy): two vacancies located at neighboring lattice sites. An important role in metals and semiconductors is played by complexes consisting of two or more impurity atoms, as well as impurity atoms and intrinsic point defects. In particular, such complexes can significantly affect the strength, electrical, and optical properties of solids.

3.2 Line defects

One-dimensional (linear) defects are crystal defects, the size of which in one direction is much larger than the lattice parameter, and in the other two - comparable with it. Linear defects include dislocations and disclinations. General definition: dislocation is the boundary of an area of incomplete shear in a crystal. Dislocations are characterized by a shear vector (Burgers vector) and an angle q between it and the dislocation line. When u=0, the dislocation is called a screw dislocation; at c=90° - marginal; at other angles - mixed and then can be decomposed into helical and edge components. Dislocations arise in the process of crystal growth; during its plastic deformation and in many other cases. Their distribution and behavior under external influences determine the most important mechanical properties, in particular, such as strength, plasticity, etc. A disclination is the boundary of an area of incomplete rotation in a crystal. It is characterized by a rotation vector.

3.3 Surface defects

The main defect representative of this class is the crystal surface. Other cases are material grain boundaries, including low-angle boundaries (representing associations of dislocations), twinning planes, phase separation surfaces, etc.

3.4 Volume defects

These include accumulations of vacancies that form pores and channels; particles settling on various defects (decorating), for example, gas bubbles, mother liquor bubbles; accumulations of impurities in the form of sectors (hourglasses) and growth zones. As a rule, these are pores or inclusions of impurity phases. They are a conglomerate of many defects. Origin - violation of crystal growth regimes, decomposition of a supersaturated solid solution, contamination of samples. In some cases (for example, during precipitation hardening), volumetric defects are deliberately introduced into the material in order to modify its physical properties.

Chapter 4no crystals

The development of science and technology has led to the fact that many precious stones or crystals that are simply rare in nature have become very necessary for the manufacture of parts for devices and machines, for scientific research. The need for many crystals has increased so much that it can be satisfied by expanding the production of old ones and the search for new ones. natural deposits turned out to be impossible.

In addition, for many branches of technology and especially for scientific research, single crystals of very high chemical purity with a perfect crystal structure are increasingly required. Crystals found in nature do not meet these requirements, since they grow in conditions that are very far from ideal.

Thus, the problem arose of developing a technology for the artificial production of single crystals of many elements and chemical compounds.

Development comparatively easy way making a "precious stone" causes it to cease to be precious. This is explained by the fact that most precious stones are crystals widely distributed in nature chemical elements and connections. So, diamond is a carbon crystal, ruby and sapphire are aluminum oxide crystals with various impurities.

Let us consider the main methods of growing single crystals. At first glance, it may seem that crystallization from a melt is very simple. It is enough to heat the substance above the melting point, obtain a melt, and then cool it. In principle, this is the right way, but if special measures are not taken, then at best a polycrystalline sample will be obtained. And if the experiment is carried out, for example, with quartz, sulfur, selenium, sugar, which, depending on the rate of cooling of their melts, can solidify in a crystalline or amorphous state, then there is no guarantee that an amorphous body will not be obtained.

In order to grow one single crystal, slow cooling is not enough. It is necessary first to cool one small section of the melt and obtain a "nucleus" of the crystal in it, and then, by successively cooling the melt surrounding the "nucleus", allow the crystal to grow throughout the entire volume of the melt. This process can be achieved by slowly lowering the crucible with the melt through the hole in the vertical tube furnace. The crystal originates at the bottom of the crucible, since it falls into the region of lower temperatures earlier, and then gradually grows over the entire volume of the melt. The bottom of the crucible is specially made narrow, pointed to a cone, so that only one crystalline nucleus can be located in it.

This method is often used to grow crystals of zinc, silver, aluminium, copper and other metals, as well as sodium chloride, potassium bromide, lithium fluoride and other salts used in the optical industry. For a day, you can grow a crystal of rock salt weighing about a kilogram.

The disadvantage of the described method is the contamination of the crystals with the material of the crucible. crystal defect symmetry property

The crucible-free method of growing crystals from a melt, which is used to grow, for example, corundum (rubies, sapphires), is deprived of this drawback. The finest powder of aluminum oxide from grains 2-100 microns in size is poured out in a thin stream from the bunker, passes through an oxygen-hydrogen flame, melts and, in the form of drops, falls on a rod of refractory material. The temperature of the rod is maintained slightly below the melting point of alumina (2030°C). Drops of aluminum oxide are cooled on it and form a crust of sintered mass of corundum. The clock mechanism slowly (10-20 mm / h) lowers the rod, and an uncut corundum crystal gradually grows on it, resembling an inverted pear in shape, the so-called boule.

As in nature, obtaining crystals from a solution comes down to two methods. The first of these consists in the slow evaporation of the solvent from the saturated solution, and the second in the slow decrease in the temperature of the solution. The second method is more commonly used. Water, alcohols, acids, molten salts and metals are used as solvents. A disadvantage of methods for growing crystals from a solution is the possibility of contamination of the crystals with solvent particles.

The crystal grows from those areas of the supersaturated solution that directly surround it. As a result, the solution is less supersaturated near the crystal than away from it. Since a supersaturated solution is heavier than a saturated solution, there is always an upward flow of "used" solution above the surface of a growing crystal. Without such agitation of the solution, crystal growth would quickly cease. Therefore, the solution is often additionally mixed or the crystal is fixed on a rotating holder. This allows you to grow more perfect crystals.

The slower the growth rate, the better the crystals. This rule is true for all growing methods. Crystals of sugar and table salt are easy to obtain from an aqueous solution at home. But, unfortunately, not all crystals can be grown so easily. For example, obtaining quartz crystals from a solution occurs at a temperature of 400°C and a pressure of 1000 at.

Chapter 5

Looking at various crystals, we see that they are all different in shape, but any of them represents a symmetrical body. Indeed, symmetry is one of the main properties of crystals. We call symmetrical bodies that consist of equal identical parts.

All crystals are symmetrical. This means that in each crystalline polyhedron one can find symmetry planes, symmetry axes, centers of symmetry and other symmetry elements so that the same parts of the polyhedron are aligned with each other. Let's introduce one more concept related to symmetry - polarity.

Each crystalline polyhedron has a certain set of symmetry elements. The complete set of all symmetry elements inherent in a given crystal is called a symmetry class. Their number is limited. Mathematically, it was proved that there are 32 types of symmetry in crystals.

Let us consider in more detail the types of symmetry in a crystal. First of all, in crystals there can be symmetry axes of only 1, 2, 3, 4 and 6 orders. Obviously, symmetry axes of the 5th, 7th and higher orders are not possible, because with such a structure, atomic rows and grids will not fill the space continuously, voids will appear, gaps between the equilibrium positions of atoms. The atoms will not be in the most stable positions, and the crystal structure will collapse.

In a crystalline polyhedron, you can find different combinations of symmetry elements - some have few, others have a lot. By symmetry, primarily along the axes of symmetry, crystals are divided into three categories.

TO the highest category the most symmetrical crystals belong, they can have several axes of symmetry of orders 2, 3 and 4, there are no axes of the 6th order, there can be planes and centers of symmetry. These forms include a cube, an octahedron, a tetrahedron, etc. They all have a common feature: they are approximately the same in all directions.

Crystals of the middle category can have axes of 3, 4 and 6 orders, but only one each. There can be several axes of the 2nd order; planes of symmetry and centers of symmetry are possible. The shapes of these crystals: prisms, pyramids, etc. Common feature: a sharp difference along and across the main axis of symmetry.

Of the crystals, the highest category includes: diamond, quartz, germanium, silicon, copper, aluminum, gold, silver, gray tin, tungsten, iron. To the middle category: graphite, ruby, quartz, zinc, magnesium, white tin, tourmaline, beryl. To the lowest: gypsum, mica, blue vitriol, Rochelle salt, etc. Of course, this list did not list all existing crystals, but only the most famous of them.

The categories, in turn, are divided into seven syngonies. Translated from Greek, "syngonia" means "similar coal". Crystals with the same axes of symmetry, and hence with similar angles of rotation in the structure, are combined into a syngony.

The physical properties of crystals most often depend on their structure and chemical structure.

First, it is worth mentioning two main properties of crystals. One of them is anisotropy. This term refers to the change in properties depending on the direction. At the same time, crystals are homogeneous bodies. The homogeneity of a crystalline substance lies in the fact that two of its sections of the same shape and the same orientation are the same in properties.

Let's talk about electrical properties first. In principle, the electrical properties of crystals can be considered using metals as an example, since metals, in one of the states, can be crystalline aggregates. Electrons, moving freely in the metal, cannot go outside, for this you need to expend energy. If radiant energy is expended in this case, then the effect of electron detachment causes the so-called photoelectric effect. A similar effect is also observed in single crystals. An electron pulled out of the molecular orbit, remaining inside the crystal, causes the latter to have metallic conductivity (internal photoelectric effect). Under normal conditions (without irradiation), such compounds are not conductors of electric current.

The behavior of light waves in crystals was studied by E. Bertolin, who was the first to notice that waves behave non-standardly when passing through a crystal. Bertalin once sketched dihedral angles Icelandic spar, then he put the crystal on the drawings, then the scientist saw for the first time that each line forks. He was convinced several times that all spar crystals bifurcate light, only then Bertalin wrote a treatise "Experiments with a birefringent Icelandic crystal, which led to the discovery of a wonderful and extraordinary refraction" (1669). The scientist sent the results of his experiments to several countries to individual scientists and academies. The work was accepted with complete disbelief. The English Academy of Sciences allocated a group of scientists to test this law (Newton, Boyle, Hooke, and others). This authoritative commission recognized the phenomenon as accidental, and the law as non-existent. The results of Bertalin's experiments were forgotten.

Only 20 years later, Christian Huygens confirmed the correctness of Bertalin's discovery and himself discovered birefringence in quartz. Many scientists who later studied this property confirmed that not only Icelandic spar, but also many other crystals bifurcate light.

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