Examples of crystalline bodies. Crystalline bodies
Solids.
V Unlike liquids, solids have elasticity of form .At any attempt to change the geometry of a solid body, elastic forces arise in it that prevent this effect. Based on the features of the internal structure solids, distinguish crystalline and amorphous solid bodies. Crystals and amorphous bodies differ significantly from each other in many physical properties.
Amorphous bodies in their internal structure, they are very similar to liquids, so they are often called supercooled liquids . Like liquids, amorphous bodies are structurally isotropic. Their properties do not depend on the considered direction. This is explained by the fact that in amorphous bodies, as well as in liquids, short range order (coordination number), and far (lengths and angles of bonds) is absent. This ensures complete uniformity of all macro physical properties amorphous body. Typical examples of amorphous bodies are glasses, resins, bitumen, and amber.
Crystalline bodies, in contrast to amorphous ones, have a clear ordered microstructure, which is preserved at the macro level and manifests itself externally in the form of small grains with flat faces and sharp edges, called crystals.
Crystalline bodies common in nature (metals and alloys, sugar and table salt, ice and sand, stone and clay, cement and ceramics, semiconductors, etc.) are usually polycrystals, consisting of randomly oriented, fused single crystals (crystallites), the sizes of which are about 1 micron (10 -6 m). However, single crystals of rather large sizes are sometimes found. For example, rock crystal single crystals reach human height B modern technology single crystals play an important role, so the technology of their artificial growth has been developed.
Inside a single crystal, atoms (ions) of a substance are placed in compliance with the long-range order, at the nodes of a geometric structure clearly oriented in space, called crystal lattice Each substance forms its own individual crystal lattice in the solid state. Its shape is determined by the structure of the molecules of the substance. In the lattice, one can always select elementary cell, preserving all its geometric features, but including the minimum possible number of nodes.
Single crystals of each particular substance can have different sizes. However, they all retain the same geometry, which manifests itself in maintaining constant angles between the corresponding crystal faces. If the shape of a single crystal is forcibly disturbed, then during subsequent growth from the melt or simply by heating, it necessarily restores its previous shape. The reason for such a restoration of the crystal shape is the well-known condition of thermodynamic stability - the tendency to a minimum of potential energy. For crystals, this condition was formulated independently by J. W. Gibbs, P. Curie and G. V. Wulff in the form of a principle: the surface energy of the crystal must be minimal.
One of the most characteristic features single crystals is anisotropy their many physical and mechanical properties. For example, the hardness, strength, brittleness, thermal expansion, elastic wave propagation velocity, electrical and thermal conductivity of many crystals can be affected by directions in the crystal. In polycrystals, anisotropy practically does not manifest itself only because of the chaotic mutual orientation of the small single crystals that form them. It is related to the fact that in the crystal lattice, the distances between nodes in different directions in the general case turn out to be significantly different.
Another important feature of crystals can be considered that they melt and crystallize at a constant temperature, in full accordance with the thermodynamic theory of first-order phase transitions. Amorphous solids do not have a clearly defined phase transition. When heated, they soften smoothly, over a wide range of temperature changes. This means that amorphous bodies do not have a definite regular structure and, when heated, it is destroyed in stages, while crystals, when heated, destroy a homogeneous crystal lattice (with its long-range order) strictly under fixed energy conditions, and hence also at a fixed temperature.
Some solids able to exist stably in both crystalline and amorphous states. Glass is a typical example. With sufficiently rapid cooling of the melt, the glass becomes very viscous and solidifies without having time to acquire a crystalline structure. However, upon very slow cooling, with holding at a certain temperature level, the same glass crystallizes and acquires specific properties (such glasses are called glass-ceramics ). Another typical example is quartz. In nature, it usually exists in the form of a crystal, and amorphous quartz is always formed from the melt (it is called fused quartz ). Experience shows that the more complex the molecules of a substance and the stronger their intermolecular bonds, the easier it is to obtain a solid amorphous modification upon cooling.
The rigid body is one of the four fundamental states matter other than liquid, gas and plasma. It is characterized by structural rigidity and resistance to changes in shape or volume. Unlike a liquid, a solid object does not flow or take on the shape of the container it is placed in. A solid does not expand to fill its available volume, as a gas does.
atoms in solid body are closely related to each other, are in an ordered state at the nodes of the crystal lattice (these are metals, ordinary ice, sugar, salt, diamond), or are arranged irregularly, do not have strict repeatability in the structure of the crystal lattice (these are amorphous bodies, such as window glass, rosin, mica or plastic).
Crystalline bodies
Crystalline solids or crystals have a distinctive internal feature - a structure in the form of a crystal lattice in which atoms, molecules or ions of a substance occupy a certain position.
The crystal lattice leads to the existence of special flat faces in crystals that distinguish one substance from another. When exposed to X-rays, each crystal lattice emits a characteristic pattern that can be used to identify a substance. The faces of crystals intersect at certain angles that distinguish one substance from another. If the crystal is split, then the new faces will intersect at the same angles as the original one.
They have two characteristic properties: isotropy and the absence of a specific melting point.
The isotropy of amorphous bodies is understood as the sameness of the physical properties of a substance in all directions.
In an amorphous solid, the distance to neighboring nodes of the crystal lattice and the number of neighboring nodes varies throughout the material. Therefore, in order to break intermolecular interactions, it is required different quantity thermal energy. Consequently, amorphous substances soften slowly over a wide temperature range and do not have a clear melting point.
A feature of amorphous solids is that at low temperatures they have the properties of solids, and with increasing temperature - the properties of liquids.
Crystalline and amorphous bodies
The purpose of the lesson:
To reveal the main properties of crystalline and amorphous bodies.
To introduce students to the correct shape of crystals and the property of anisotropy, a modeling method in the study of the properties of crystals.
Equipment:
A set of crystalline bodies; short focus lens.
Spirit lamp, glass rod.
Computer with multimedia projector; lesson plan, multimedia application for the lesson, made in Mikrosoft Point.
During the classes
Introduction: Most of the solids around us are substances in a crystalline state. These include building and construction materials: various grades of steel, various metal alloys, minerals, etc. A special area of physics - solid state physics - deals with the study of the structure and properties of solids. This area of physics is leading in all physical research. It is the foundation of modern technology.
In any branch of technology, the properties of a solid body are used: mechanical, thermal, electrical, optical, etc. Crystals are increasingly used in technology. You probably know about the merits of Soviet scientists - academicians, laureates of the Lenin and Nobel Prizes A. M. Prokhorova and N. G. Basova in the creation quantum generators. The action of modern optical quantum generators - lasers - is based on the use of the properties of single crystals (ruby, etc.) How is a crystal arranged? Why do many crystals have amazing properties? What are the structural features of crystals that distinguish them from amorphous bodies? You can answer these and similar questions at the end of the lesson. Let's write down the topic “Crystalline and amorphous bodies”.
Presentation of new material:
Let's go back to the material. What properties do solids have?
Student:
1) They retain their shape and volume.
2) In the structure they have a crystal lattice.
Teacher: All solids are divided into crystalline and amorphous. We will look at their similarities and differences.
What are crystals?
crystals - these are solid bodies, the atoms or molecules of which occupy certain, ordered positions in space. Crystals of the same substance have a variety of shapes. The angles between the individual faces of the crystals are the same. Some crystal shapes are symmetrical. The color of the crystals is different - obviously, it depends on the impurities.
For a visual representation of the internal structure of a crystal, its image is used with the help of a crystal lattice. There are several types of crystals:
1) ionic
2) atomic
3) metal
4) molecular.
The ideal shape of a crystal has the form of a polyhedron. Such a crystal is limited by flat faces, straight edges and has symmetry. In crystals, you can find various elements of symmetry. Crystalline bodies are divided into single crystals and polycrystals.
single crystals - single crystals (quartz, mica...) The ideal shape of a crystal is polyhedral. Such a crystal is limited by flat faces, straight edges and has symmetry. In crystals, you can find various elements of symmetry. Plane of symmetry, axis of symmetry, center of symmetry. At first glance, it seems that the number of types of symmetry can be infinitely large. In 1867, the Russian engineer A. V. Gadolin proved for the first time that crystals can have only 32 types of symmetry. Make sure the symmetry of the snow crystal - snowflakes
The symmetry of crystals and their other properties, which we will discuss below, led to an important guess about the regularities in the arrangement of particles that make up a crystal. Can any of you try to formulate it?
Student. Particles in a crystal are arranged in such a way that they form a certain regular shape, a lattice.
Teacher. Particles in a crystal form a regular spatial lattice. The spatial lattices of different crystals are different. Here is a model of the spatial lattice of table salt. (Demonstrates a model.) Balls of one color imitate sodium ions, balls of a different color imitate chlorine ions. If you connect these nodes with straight lines, then a spatial lattice is formed, similar to the presented model. In each spatial lattice, some repeating elements of its structure can be distinguished, in other words, an elementary cell.
The concept of a spatial lattice made it possible to explain the properties of crystals.
Let's consider their properties.
1) External regular geometric shape (models)
2) Constant melting temperature.
3) Anisotropy - the difference in physical properties from the direction chosen in the crystal (shows an example with mica, with a quartz crystal)
But single crystals are rare in nature. But such a crystal can be grown in artificial conditions.
Now let's get acquainted with polycrystals.
Polycrystals - these are solids consisting of a large number of crystals randomly oriented relative to each other (steel, cast iron ...)
Polycrystals also have a regular shape and even edges, their melting point has a constant value for each substance. But unlike single crystals, polycrystals are isotropic, i.e. physical properties are the same in all directions. This is explained by the fact that the crystals inside are arranged randomly, and each individually has anisotropy, while the crystal as a whole is isotropic.
In addition to crystalline bodies, there are amorphous bodies.
Amorphous bodies - these are solids where only short-range order in the arrangement of atoms is preserved. (Silica, resin, glass, rosin, sugar candy).
For example, quartz can be both in a crystalline state and in an amorphous state - silica. (See the pic in the textbook). They do not have a constant melting point and are fluid (indicates bending a glass rod over a spirit lamp). Amorphous bodies are isotropic, at low temperatures they behave like crystalline bodies, and at high temperatures they are like liquids.
Observation of crystalline and amorphous bodies
(make notes in notebook)
Examine salt crystals with a magnifying glass. - What shape do they have? (cube shape).
Consider the crystals of copper sulphate. – What is the peculiarity of these crystals? (some have flat edges).
Consider a fracture of zinc and find on it the faces of small crystals.
Consider amorphous bodies: glass, rosin or wax. Let's take a look at the broken glass. What is the difference from metal fracture? (smooth surface with sharp edges).
Tasks for independent work.
1. Why does snow creak underfoot in cold weather?
Answer : Hundreds of thousands of snowflakes - crystals break.
2. What is the origin of patterns on the surface of galvanized iron?
Answer : Patterns appear due to crystallization of zinc.
3. Final test.
Teacher: Open your diaries and write down your homework: § 75,76(1); § 24, 26,27. Task for those who wish: to grow crystals from a solution of copper sulphate or alum.
Literature:
1. Myakishev G.Ya., Bukhovtsev B.B., Sotsky N.N. Physics 10 cells. - M .: Education 1992.
2. Pinsky A.A. Physics 10 cells. - M. "Enlightenment" 1993.
3. Tarasov L. V. This amazingly symmetrical world. - M.: Enlightenment, 1982.
4. Schoolchildren about modern physics: physics of complex systems. - M.: Enlightenment, 1978.
5. Encyclopedic dictionary of a young physicist.
6. V.G. Razumovsky, L.S. Khizhnyakov. Modern physics lesson in high school. – M.: Enlightenment, 1983.
7. Methods of teaching physics in grades 8–10 of secondary school. Part 2 / Ed. V.P. Orekhova, A.V. Usova and others - M .: Education 1980.
8. V.A.Volkov. Pourochnye development in physics. M. "VAKO" 2006
Final test
1. Complete the sentence.
1) single crystals;
2) polycrystals.
a) single crystals;
1) a grain of salt;
3) a grain of sugar;
4) a piece of refined sugar
c) amorphous state.
1) crystalline bodies;
2) amorphous bodies.
Final test
1. Complete the sentence.
“The dependence of physical properties on the direction inside the crystal is called…”
2. Fill in the missing words.
"Solid bodies are subdivided into ... and ..."
3. Find a correspondence between solids and crystals.
1) single crystals;
2) polycrystals.
a) single crystals;
b) a large number of small crystals.
4. Find a correspondence between the substance and its state.
1) a grain of salt;
3) a grain of sugar;
4) a piece of refined sugar
a) polycrystalline state;
b) single-crystal state;
c) amorphous state.
5. Find a correspondence between the bodies and the melting point.
1) crystalline bodies;
2) amorphous bodies.
a) there is no specific melting point;
b) the melting temperature is constant.
Solid bodies retain their shape for a long time, and considerable effort is needed to change their volume.
In the definition of solids, we, as a rule, associate their properties with external features - the preservation of shape and volume. However, solid bodies differ from each other also 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 are characterized by a certain internal order placement of atoms and molecules that form various 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
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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 is 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 for the atoms inside a 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 is suitable for 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 distinguish structural element 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
The correct geometric shape of 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 size crystals that 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 growth rate) of crystallization, the faceting manifests itself weakly. 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 Group III (third) elements with Group V (fifth) elements of the Periodic Table (for example, GaAs Gallium Arsenide) form 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 there is a spontaneous selection of the necessary atoms (molecules for molecular crystals) 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 different ways. Physical and Chemical properties substances. Thus, substances with the same chemical composition often actually have different physical properties. For liquid state such a variety is not typical, and for a gaseous one 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 the 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 this paper, we will focus mainly on 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 scientific knowledge merge into a single, holistic picture of the world. One of the main trends of this process is the mathematization of scientific knowledge.
Symmetry is usually considered not only as a fundamental picture of scientific knowledge, establishing internal communications 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 isotropically. 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 an infinite number axes of the first order, 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. Human body, if we talk only about the external form, it has 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, the figures are based on rotational movements, often performed only in one direction (i.e. without reflection), for example, circle 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 spherical.
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 that underlie 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 that unwind in opposite directions and intersect 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 for a spiral, we can assume that this movement is carried out along a logarithmic spiral, starting each time from a central, fixed point and combining forward movement(stretch) with rotation 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. The isotopic invariance is valid only if we take into account electromagnetic forces. 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.
Exploring the properties of symmetry 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 of 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.
Vacancy - a free, unoccupied atom, node 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 vacancy, it must move 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 - the boundary of the region of incomplete shear in the 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 grown so much that it was impossible to satisfy it by expanding the scale of working out old and searching for new natural deposits.
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 gemstones 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 with a size of 2-100 microns 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, copper sulfate, 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. Basically electrical properties crystals can be considered on the example of metals, 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. Once Bertalin sketched the dihedral angles of Icelandic spar, then he put the crystal on the drawings, then the scientist saw for the first time that each line forked. 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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