What does "amorphous state" mean? School encyclopedia Solid amorphous state

amorphous state

a condensed state of matter characterized by isotropy of physical properties due to the disordered arrangement of atoms and molecules. Unlike the crystalline state, the transition from a solid amorphous to liquid occurs gradually. Various substances are in the amorphous state: glasses, resins, plastics, etc.

amorphous state

(from Greek a ≈ negative particle and morphē ≈ form), a solid state of matter with two features: its properties (mechanical, thermal, electrical, etc.) under natural conditions do not depend on the direction in the substance (isotropy); as the temperature rises, the substance, softening, passes into the liquid state gradually, i.e., into the atom. there is no definite melting point.

These features are due to the absence in A. s. long-range order ≈ strict repeatability characteristic of crystals in all directions of the same structural element (atom, group of atoms, molecule, etc.) over hundreds and thousands of periods. At the same time, the substance in A. s. there is a short-range order ≈ consistency in the arrangement of neighboring particles, i.e., an order observed at distances comparable to the sizes of molecules ( rice.). This consistency decreases with distance and disappears after 0.5≈1 nm (see Long-Range Order and Short-Range Order).

The short-range order is also characteristic of liquids, but in a liquid there is an intensive exchange of places between neighboring particles, which becomes more difficult as the viscosity increases; therefore, on the one hand, a solid body in A. s. It is customary to consider it as a supercooled liquid with a very high viscosity coefficient. On the other hand, the very concept of "A. with." include liquid.

The isotropy of properties is also characteristic of the polycrystalline state (see Polycrystals), but the latter is characterized by a strictly defined melting point, which makes it possible to distinguish it from A. s. Difference of structure And. from crystalline is easily detected using X-rays. Monochromatic x-rays, scattered by crystals, form a diffraction pattern in the form of distinct lines or spots (see X-ray diffraction). For A.S. this is not typical.

The stable solid state of matter at low temperatures is the crystalline state. However, depending on the properties of the molecules, crystallization may require more or less time - the molecules must have time to line up in a crystalline order when the substance is cooled. Sometimes this time is very long, so that the crystalline state is practically not realized. In other cases, A. s. obtained by speeding up the cooling process. For example, by melting crystalline quartz and then rapidly cooling the melt, amorphous quartz glass is obtained. Many silicates behave in the same way, which, when cooled, give ordinary glass. Therefore, A. s. often referred to as the glassy state. More often than not, however, even the most rapid cooling is not fast enough to prevent crystal formation. As a result of this, most substances are obtained in A. s. impossible. In nature, A. s. less common than crystalline. You. are: opal, obsidian, amber, natural resins, bitumen.

You. there can be not only substances consisting of individual atoms and ordinary molecules, like glasses and liquids (low molecular weight compounds), but also substances consisting of long-chain macromolecules - high molecular weight compounds, or polymers.

The structure of amorphous polymers is characterized by a short-range order in the arrangement of units or segments of macromolecules, which rapidly disappears as they move away from each other. Polymer molecules seem to form "swarms", the lifetime of which is very long due to the huge viscosity of polymers and large sizes of molecules. Therefore, in some cases, such swarms remain practically unchanged.

Amorphous polymers, depending on temperature, can be in three states that differ in the nature of thermal motion: glassy, highly elastic, and liquid (viscous-fluid). At low temperatures, segments of molecules are immobile, and the polymer behaves like an ordinary solid body in an A.S. At sufficiently high temperatures, the energy of thermal motion becomes sufficient to cause the movement of segments of the molecule, but still insufficient to set the molecule as a whole in motion. A highly elastic state arises, characterized by the ability of the polymer to easily stretch and shrink. The transition from a highly elastic state to a glassy state is called glass transition. In a viscous-fluid state, not only segments, but the entire macromolecule can move. Polymers acquire the ability to flow, but, unlike an ordinary liquid, their flow is always accompanied by the development of highly elastic deformation.

Lit .: Kitaigorodsky A.I., Order and disorder in the world of atoms, M., 1966; Kobeko P. P., Amorphous substances, M.≈ L., 1952; Kitaygorodsky AI, X-ray diffraction analysis of fine-crystalline and amorphous bodies, M.≈ L., 1952. See also lit. at Art. Polymers.

Solids are divided into amorphous and crystalline, depending on their molecular structure and physical properties.

Unlike crystals, molecules and atoms of amorphous solids do not form a lattice, and the distance between them varies within a certain range of possible distances. In other words, in crystals, atoms or molecules are mutually arranged in such a way that the formed structure can be repeated throughout the entire volume of the body, which is called long-range order. In the case of amorphous bodies, the structure of molecules is preserved only with respect to each one such molecule, a regularity is observed in the distribution of only neighboring molecules - short-range order. An illustrative example is shown below.

Amorphous bodies include glass and other substances in a glassy state, rosin, resins, amber, sealing wax, bitumen, wax, as well as organic substances: rubber, leather, cellulose, polyethylene, etc.

Properties of amorphous bodies

The peculiarity of the structure of amorphous solids gives them individual properties:

Weakly expressed fluidity is one of the most well-known properties of such bodies. An example would be glass streaks that have been standing in a window frame for a long time.
Amorphous solids do not have a specific melting point, since the transition to a liquid state during heating occurs gradually, by softening the body. For this reason, the so-called softening temperature range is applied to such bodies.

By virtue of their structure, such bodies are isotropic, that is, their physical properties do not depend on the choice of direction.
A substance in the amorphous state has more internal energy than in the crystalline state. For this reason, amorphous bodies are able to independently pass into a crystalline state. This phenomenon can be observed as a result of glass clouding over time.

glassy state

In nature, there are liquids that are practically impossible to convert to a crystalline state by cooling, since the complexity of the molecules of these substances does not allow them to form a regular crystal lattice. Molecules of some organic polymers belong to such liquids.

However, with the help of deep and rapid cooling, almost any substance can go into a glassy state. This is such an amorphous state that does not have a clear crystal lattice, but can partially crystallize, on the scale of small clusters. This state of matter is metastable, that is, it is preserved under certain required thermodynamic conditions.

With the help of cooling technology at a certain speed, the substance will not have time to crystallize, and will be converted into glass. That is, the higher the cooling rate of the material, the less likely it is to crystallize. So, for example, for the manufacture of metallic glasses, a cooling rate of 100,000 - 1,000,000 Kelvin per second is required.

In nature, matter exists in a glassy state and arises from liquid volcanic magma, which, interacting with cold water or air, cools rapidly. In this case, the substance is called volcanic glass. You can also observe the glass formed as a result of the melting of a falling meteorite interacting with the atmosphere - meteorite glass or moldavite.

amorphous state (from Greek a - negative particle and morphē - form)

a solid state of a substance that has two features: its properties (mechanical, thermal, electrical, etc.) under natural conditions do not depend on the direction in the substance (isotropy); as the temperature rises, the substance, softening, passes into the liquid state gradually, i.e., into the atom. there is no definite melting point.

These features are due to the absence in A. s. long-range order - characteristic of crystals (See Crystals) strict repetition in all directions of the same structural element (atom, group of atoms, molecule, etc.) over hundreds and thousands of periods. At the same time, the substance in A. s. there is a short-range order - consistency in the arrangement of neighboring particles, i.e., an order observed at distances comparable to the sizes of molecules ( rice. ). With distance, this consistency decreases and after 0.5-1 nm disappears (see Long-Range Order (See Long-Range Order and Short-Range Order) and close order).

The short-range order is also characteristic of liquids (See Liquid) , but in a liquid there is an intense exchange of places between neighboring particles, which becomes more difficult as the viscosity increases (See Viscosity) , therefore, on the one hand, a solid body in A. s. It is customary to consider it as a supercooled liquid with a very high viscosity coefficient. On the other hand, the very concept of "A. with." include liquid.

The isotropy of properties is also characteristic of the polycrystalline state (see Polycrystals) , but the latter is characterized by a strictly defined melting point, which makes it possible to distinguish it from A. s. Difference of structure And. from crystalline is easily detected using radiographs (See radiograph). Monochromatic x-rays, scattered by crystals, form a diffraction pattern in the form of distinct lines or spots (see X-ray diffraction). For A.S. this is not typical.

The stable solid state of matter at low temperatures is the crystalline state. However, depending on the properties of the molecules, crystallization may require more or less time - the molecules must have time to line up in a crystalline order when the substance is cooled. Sometimes this time is very long, so that the crystalline state is practically not realized. In other cases, A. s. obtained by speeding up the cooling process. For example, by melting crystalline Quartz and then rapidly cooling the melt, amorphous quartz glass is obtained. Many silicates behave in the same way, which, when cooled, give ordinary glass. Therefore, A. s. often called the glassy state (See Glassy state). More often than not, however, even the most rapid cooling is not fast enough to prevent crystal formation. As a result of this, most substances are obtained in A. s. impossible. In nature, A. s. less common than crystalline. You. are: Opal, Obsidian, Amber, Natural resins, Bitumens.

Lit.: Kitaygorodsky A.I., Order and disorder in the world of atoms, M., 1966; Kobeko P. P., Amorphous substances, M.-L., 1952; Kitaygorodsky A.I., X-ray diffraction analysis of fine-crystalline and amorphous bodies, M.-L., 1952. See also lit. at Art. Polymers.

The structure of quartz SiO 2: a - crystalline; b - amorphous; black circles are Si atoms, white circles are O atoms.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Amorphous state" is in other dictionaries:

- (from the Greek amorphos formless), a solid state in va, characterized by the isotropy of sv and the absence of a melting point. With an increase in temperature, amorphous water softens and gradually passes into a liquid state. These features are due to... Physical Encyclopedia

amorphous state- - the solid state of a substance, which has two features: its properties (mechanical, thermal, electrical, etc.) in natural conditions do not depend on the direction in the substance (isotropy); As the temperature rises, the substance... Encyclopedia of terms, definitions and explanations of building materials

AMORPHOUS STATE, the state of a solid body, characterized by the isotropy of physical properties due to the disordered arrangement of atoms and molecules. Unlike the crystalline state (see Crystals), the transition from the amorphous state ... Modern Encyclopedia

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The solid state of matter, characterized by the isotropy of physical properties due to the disordered arrangement of atoms and molecules. Unlike the crystalline state, the transition from a solid amorphous state to a liquid occurs ... ... encyclopedic Dictionary

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amorphous state- amorfinė būsena statusas T sritis chemija apibrėžtis Kondensuota, neturinti trimatės sandaros periodiškumo, medžiagos būsena. atitikmenys: engl. amorphous state amorphous state... Chemijos terminų aiskinamasis žodynas

amorphous state- amorfinė būsena statusas T sritis fizika atitikmenys: angl. amorphous state vok. amorpher Zustand, m rus. amorphous state, n pranc. état amorphe, m … Fizikos terminų žodynas

AMORPHOUS STATE- is the state of a solid that lacks the strict periodicity inherent in crystals (long-range order). Due to the lower orderliness, amorphous substances at the same R T have a larger volume and higher internal energy than crystals. ... ... Paleomagnetology, petromagnetology and geology. Dictionary reference.

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AMORPHOUS STATE(from the Greek. amorphos - shapeless) - solid non-crystalline. a state of matter characterized by isotropy of properties and the absence of a point. With an increase in temperature, an amorphous substance softens and gradually passes into a liquid state. These features are due to the absence in A. s., in contrast to crystalline. states, so-called. long-range order - strict periodic. repeatability in space of the same structural element (atom, group of atoms, molecules, etc.). At the same time, the substance in A. s. there is consistency in the arrangement of neighboring particles - the so-called. short-range order observed within the 1st coordinate. spheres (see coordination number) and gradually lost during the transition to the 2nd and 3rd spheres, i.e., observed at distances comparable to the particle sizes. Thus, the consistency decreases with distance and disappears after 0.5-1 nm (see Fig. Far and near order).

The short-range order is also characteristic of liquids, but in a liquid there is an intense exchange of places between neighboring particles, which becomes more difficult as the viscosity increases. Therefore, a solid in an amorphous state is usually considered as a supercooled liquid with a very high viscosity coefficient. Sometimes the very concept of "A. s." include liquid.

The thermodynamically stable solid state of matter at low temp-pax is crystalline. condition. However, depending on the properties of the particles crystallization may require more or less time - the molecules must have time to "line up" when the substance is cooled. Sometimes this time is so long that it is crystalline. state is almost non-existent. Usually A. s. formed upon rapid cooling of the melt. For example, melting crystalline. quartz and then rapidly cooling the melt, amorphous quartz glass is obtained (see Fig. glassy state).However, sometimes even the most rapid cooling is not fast enough to prevent the formation of crystals. In nature, A. s. (opal, obsidian, amber, resins) is less common than crystalline. You. there may be certain metals and alloys, including metallic. glass (see Amorphous metals), as well as (cf. Amorphous and glassy semiconductors) and polymers. The structure of amorphous polymers is characterized by a short-range order in the arrangement of units or segments of macromolecules, which rapidly disappears as they move away from each other. The polymer molecules seem to form "swarms", the lifetime of which is very long due to the enormous viscosity of the polymers and the large size of the molecules.

A natural difference in the structure of most solid materials (with the exception of single crystals), in comparison with liquid and especially gaseous (low molecular weight) substances, is their more complex multilevel organization (see Table 4.1 and Fig. 4.3). This is due to a decrease in covalence and an increase in the metallicity and ionicity of homo- and heteronuclear bonds of the elements of their microstructure (see Figs. 6.2 and 6.6 and Tables 6.1-6.7), which leads to an increase in the number of elements in the structure of matter and material and a corresponding change its aggregate state. When studying the structural hierarchy of solid materials, it is necessary to understand the unity and differences in the levels of structural organization of solid metallic and non-metallic materials, taking into account the degree of order in the volume of the material of the elements that form them. Of particular importance is the difference in the structure of solid crystalline and amorphous bodies, which consists in the ability of crystalline materials, unlike amorphous bodies, to form a number of more complex structures than the basic electron-nuclear chemical level of structures.

amorphous state. The specificity of the amorphous (translated from Greek - formless) state lies in the presence of a substance in condensed (liquid or solid) state with the absence in its structure of three-dimensional periodicity in the arrangement of elements (atomic cores or molecules) that make up this substance. As a result, the features of the amorphous state are due to the absence long-range order - strict repetition in all directions of the same structural element (nucleus or atomic core, group of atomic cores, molecules, etc.) over hundreds and thousands of periods. At the same time, the substance in the amorphous state has short range order- consistency in the arrangement of neighboring elements of the structure, i.e. an order observed at distances comparable to the size of the molecules. With distance, this consistency decreases and disappears after 0.5-1 nm. Amorphous substances differ from crystalline ones in isotropy, i.e. like a liquid, they have the same value of a given property when measured in any direction within a substance. The transition of an amorphous substance from a solid to a liquid state is not accompanied by an abrupt change in properties - this is the second important feature that distinguishes the amorphous state of a solid from the crystalline state. Unlike a crystalline substance, which has a certain melting point, at which an abrupt change in properties occurs, an amorphous substance is characterized by a softening interval and a continuous change in properties.

Amorphous substances are less stable than crystalline ones. Any amorphous substance should, in principle, crystallize over time, and this process should be exothermic. Often, amorphous and crystalline forms are different states of the same chemical substance or material in composition. So, amorphous forms of a number of homonuclear substances (sulfur, selenium, etc.), oxides (B 2 Oe, Si0 2, Ge0 2, etc.) are known.

However, many amorphous materials, in particular most organic polymers, cannot be crystallized. In practice, crystallization of amorphous, especially high-molecular, substances is observed very rarely, since structural changes are inhibited due to the high viscosity of these substances. Therefore, if you do not resort to special methods, such as long-term high-temperature exposure, the transition to the crystalline state proceeds at an extremely low rate. In such cases, we can assume that the substance in the amorphous state is almost completely stable.

Unlike the amorphous state inherent in substances that are both in liquid or molten form, and in solid condensed form, glassy state refers only to the solid state of matter. As a result, in liquid or molten substances can be in the amorphous state with any preferred type of connection(covalent, metallic and ionic) and, therefore, with molecular and non-molecular structure. However in solid amorphous, or more precisely, glassy state will primarily be HMC-based substances characterized predominantly covalent bond type elements in chains of macromolecules. This is due to the fact that the solid amorphous state of a substance is obtained as a result of supercooling of its liquid state, which prevents crystallization processes and leads to “freezing” of the structure with a short-range order of elements. Note that the presence of macromolecules in the structure of polymeric materials due to the influence of the steric-size factor (after all, it is easier to create a crystal from cations than from molecules) leads to an additional complication of the crystallization process. Therefore, organic (polymethyl methacrylate, etc.) and inorganic (oxides of silicon, phosphorus, boron, etc.) polymers are capable of forming glasses or realizing an amorphous state in solid materials. True, today metal melts at ultra-high cooling rates (>10 6 °C/s) are transferred to an amorphous state, obtaining amorphous metals or metal glass with a set of new valuable properties.

crystalline state. In a crystalline body, it is observed as near, and long range order arrangement of structural elements (atomic cores or particles in the form of individual molecules), i.e. elements of the structure are placed in space at a certain distance from each other in a geometrically correct order, forming crystals - solid bodies that have the natural shape of regular polyhedra. This shape is a consequence of the ordered arrangement of elements in the crystal, which form a three-dimensionally periodic spatial stacking in the form crystal lattice. A substance in a crystalline state is characterized by periodic repetition in three dimensions of the arrangement of atomic cores or molecules in its nodes. A crystal is an equilibrium state of solids. Each chemical substance that is under given thermodynamic conditions (temperature, pressure) in a crystalline state corresponds to a certain crystalline covalent or molecular, metallic and ionic structure. Crystals have one or another structural symmetry of atomic cores (cations in a metal or cations and anions in ionic crystals) or molecules, the corresponding macroscopic symmetry of the external form, as well as anisotropy of properties. Anisotropy - this is the dissimilarity of the properties (mechanical, physical, chemical) of a single crystal in different directions of its crystal lattice. Isotropy - This is the sameness of the properties of a substance in its various directions. Naturally, these patterns of change in the properties of a substance are determined by the specifics of the change or non-change in their structure. Real crystalline materials (including metals) are quasi-isotropic structures, those. they are isotropic at the mesostructural level (see Table 4.1) and their properties are the same in all directions. This is because most natural or artificial crystalline materials are polycrystalline substances, not single crystals

(like a diamond). They consist of a large number of so-called grains or crystallites, whose crystallographic planes are rotated relative to each other through a certain angle a. In this case, in any direction of the mesostructure of the material, there are approximately the same number of grains with different orientations of crystallographic planes, which leads to independence of its properties from the direction. Each grain consists of individual elements - blocks that are rotated relative to each other at angles of the order of several minutes, which also ensures the isotropy of the properties of the grain itself as a whole.

Crystalline states of the same substance can differ in structure and properties, and then they say that this substance exists in various modifications. The existence of several crystalline modifications in a given substance is called polymorphism, and the transition from one modification to another - polymorphic transformation. Unlike polymorphism, allotropy- this is the existence of an element in the form of various "simple" (or, more precisely, homonuclear) substances, regardless of their phase state. For example, oxygen 0 2 and ozone O e are allotropic forms of oxygen that exist in gaseous, liquid and crystalline states. At the same time, diamond and graphite - allotropic forms of carbon - are simultaneously its crystalline modifications, in this case the concepts of "allotropy" and "polymorphism" coincide for its crystalline forms.

Often there is also a phenomenon isomorphism, in which two substances of different nature form crystals of the same structure. Such substances can replace each other in the crystal lattice, forming mixed crystals. For the first time, the phenomenon of isomorphism was demonstrated by the German mineralogist E. Mitscherlich in 1819 using the example of KH 2 P0 4, KH 2 As0 4 and NH 4 H 2 P0 4. Mixed crystals are perfectly homogeneous mixtures of solids - these are substitutional solid solutions. Therefore, we can say that isomorphism is the ability to form substitutional solid solutions.

Traditionally, crystal structures are traditionally divided into homodesmic (coordination) and heterodesmic. homo-desmic structure have, for example, diamond, alkali metal halides. However, more often crystalline substances have heterodesmic structure; its characteristic feature is the presence of structural fragments, within which the atomic cores are connected by the strongest (usually covalent) bonds. These fragments can be finite groupings of elements, chains, layers, frames. Accordingly, island, chain, layered and frame structures are distinguished. Almost all organic compounds and inorganic substances such as halogens, 0 2, N 2, CO 2, N 2 0 4, etc. have island structures. Molecules play the role of islands, therefore such crystals are called molecular. Often polyatomic ions (for example, sulfates, nitrates, carbonates) act as islands. For example, crystals of one of the Se modifications (the atomic cores are connected in endless spirals) or PdCl 2 crystals, which contain endless ribbons, have a chain structure; layered structure - graphite, BN, MoS 2, etc.; the frame structure is CaTYu 3 (the atomic cores of Ti and O, united by covalent bonds, form an openwork frame, in the voids of which the atomic cores of Ca are located). Some of these structures are classified as inorganic (carbon-free) polymers.

According to the nature of the bond between atomic cores (in the case of homodesmic structures) or between structural fragments (in the case of heterodesmic structures), there are distinguished: covalent (for example, SiC, diamond), ionic, metallic (metals and intermetallic compounds) and molecular crystals. Crystals of the last group, in which the structural fragments are linked by intermolecular interaction, have the largest number of representatives.

For covalent single crystals such as diamond, carborundum, etc. are characterized by refractoriness, high hardness and wear resistance, which is a consequence of the strength and direction of the covalent bond in combination with their three-dimensional spatial structure (polymer bodies).

Ionic crystals are formations in which the adhesion of microstructure elements in the form of counterions is due mainly to ionic chemical bonds. An example of ionic crystals are the halides of alkali and alkaline earth metals, in the crystal lattice sites of which there are alternating positively charged metal cations and negatively charged halogen anions (Na + Cl -, Cs + Cl -, Ca + F^, Fig. 7.1).

Rice. 7.1.

AT metal crystals the adhesion of atomic cores in the form of metal cations is due predominantly to metallic non-directional chemical bonds. This type of crystals is characteristic of metals and their alloys. At the nodes of the crystal lattice there are atomic cores (cations) interconnected by OE (electron gas). The structure of metallic crystalline bodies will be discussed in more detail below.

molecular crystals are formed from molecules linked to each other by van der Waals forces or hydrogen bonds. A stronger covalent bond acts inside the molecules (C to prevails over C and and C m). Phase transformations of molecular crystals (melting, sublimation, polymorphic transitions) occur, as a rule, without the destruction of individual molecules. Most molecular crystals are crystals of organic compounds (eg naphthalene). Molecular crystals also form substances such as H 2, halogens of the type J 2, N 2, 0 2, S g, binary compounds of the type H 2 0, CO 2, N 2 0 4, organometallic compounds and some complex compounds. Molecular crystals also include crystals of such natural polymers as proteins (Fig. 7.2) and nucleic acids.

Polymers, as already mentioned above, as a rule, also refer to substances that form molecular crystals. However, in the case when the packing of macromolecules has a folded or fibrillar conformation, it would be more correct to speak of covalent molecular crystals(Fig. 7.3).

Rice. 7.2.

Rice. 7.3.

This is due to the fact that along one of the lattice periods (for example, the period with in the case of polyethylene, the macromolecules of which are in a folded conformation, forming a lamella), strong chemical (Fig. 7.3), mainly covalent, bonds act. At the same time, along two other lattice periods (for example, periods b and with in the same folded polyethylene crystals), already weaker forces of intermolecular interaction act.

The division of crystals into these groups is largely arbitrary, since there are gradual transitions from one group to another as the nature of the bond in the crystal changes. For example, among intermetallic compounds - compounds of metals with each other - one can distinguish a group of compounds in which a decrease in the metal component of a chemical bond and a corresponding increase in the covalent and ionic components lead to the formation of cholesterol in accordance with classical valences. Examples of such compounds are magnesium compounds with elements of the main subgroup IV and V of groups of the Periodic system, which are transitional between metals and non-metals (Mg 2 Si, Mg 2 Ge, Mg 2 Sn, Mg 2 Pb, Mg 3 As 2, Mg 3 Sb 7 , Mg 3 Bi 7), the main characteristic features of which usually include the following:

their heteronuclear crystal lattice differs from the homonuclear lattices of the parent compounds;
in their connection, a simple multiple ratio of components is usually preserved, which makes it possible to express their composition by a simple formula A sh B;? , where A and B are the corresponding elements; t and P - prime numbers;
heteronuclear compounds are characterized by a new quality of structure and properties, in contrast to the original compounds.

in crystal structural elements(ions, atomic cores, molecules) that form a crystal are arranged regularly in different directions (Fig. 7 La). Usually, a spatial image of the structure of crystals is presented schematically (Fig. 7.45), marking the centers of gravity of structural elements, including lattice characteristics, with dots.

Planes parallel to the coordinate planes that are at a distance a, b, c from each other, divide the crystal into many equal and parallel oriented parallelepipeds. The smallest of them is called elementary cell, their combination forms a spatial crystal lattice. The vertices of the parallelepiped are the nodes of the spatial lattice; the centers of gravity of the elements from which the crystal is built coincide with these nodes.

Spatial crystal lattices completely describe the structure of a crystal. To describe the elementary cell of the crystal lattice, six quantities are used: three segments equal to the distances to the nearest elementary particles along the coordinate axes a, b, c, and three angles between these segments a, (3, y.

The ratios between these quantities determine the shape of the cell, depending on which all crystals are divided into seven systems (Table 7.1).

The size of the unit cell of the crystal lattice is estimated by the segments a, b, s. They are called lattice periods. Knowing the lattice periods, it is possible to determine the radius of the atomic core of an element. This radius is equal to half of the smallest distance between particles in the lattice.

The degree of complexity of the lattice is judged by the number of structural elements, per one elementary cell. In a simple spatial lattice (see Fig. 7.4), there is always one element per cell. Each cell has eight vertices, but

Rice. 7.4. Arrangement of elements in a crystal: a- image with the placement of the volume of the atomic core of the element; b - spatial image of an elementary cell and its parameters

Table 7.1

Characteristics of crystalline systems

each element at the top refers, in turn, to eight cells. Thus, from the node to the share of each cell there is V 8 volume, and there are eight nodes in the cell, and, therefore, there is one structural element per cell.

In complex spatial lattices, there is always more than one structural element per cell, which are most common in the most important pure metal compounds (Fig. 7.5).

The following metals crystallize in the bcc lattice: Fe a, W, V, Cr, Li, Na, K, etc. Fe y, Ni, Co a, Cu, Pb, Pt, Au, Ag, etc. crystallize in the fcc lattice. Mg, Ti a, Co p, Cd, Zn, etc. crystallize in the hcp lattice.

System, period and number of structural elements, per unit cell make it possible to fully represent the location of the latter in the crystal. In some cases, additional characteristics of the crystal lattice are used, due to its geometry and reflecting the packing density of the element

Rice. 7.5. Types of complex elementary cells of crystal lattices: a - BCC; 6 - HCC; in- hcp of tare particles in a crystal. These characteristics are CF and compactness factor.

The number of nearest equidistant elementary particles determines coordination number. For example, for a simple cubic lattice, the CF will be 6 (Kb); in the lattice of a body-centered cube (bcc) for each atomic core, the number of such neighbors will be equal to eight (K8); for a face-centered cubic lattice (fcc), the CF number is 12 (K 12).

The ratio of the volume of all elementary particles per one elementary cell to the entire volume of the elementary cell determines compactness factor. For a simple cubic lattice, this coefficient is 0.52, for bcc - 0.68 and fcc - 0.74.

Sirotkin R.O. The effect of morphology on the yield behavior of solution crystallizedpolyethylenes: PhD thesis, University of North London. - London, 2001.