Summary: Crystals and their properties. The most important properties of crystals Physical properties of crystals

Most solids are in a crystalline state, which is characterized by a long-range order, that is, a three-dimensional periodicity of the structure throughout the volume of the solid (crystal lattice). Crystalline substances have a certain melting point, energy and crystal lattice constant and coordination number. The coordination number is the number of particles directly adjacent to a given particle in a crystal. The lattice constant characterizes the distance between the centers of particles occupying sites in the crystal. The energy of a crystal lattice is the energy required to destroy 1 mol of a crystal and remove particles beyond their interaction limits. According to the nature of the particles in the nodes of the crystal lattice and the nature of the chemical bonds between them, all crystals are divided into molecular, atomic-covalent, ionic and metallic. In addition, there are crystals with mixed chemical bonds.

molecular crystals. At the lattice sites there are molecules between which van der Waals forces or hydrogen bonds act. The energy of the crystal lattice is low (5-25 kJ/mol), molecular crystals have low melting and boiling points.
Atomic covalent crystals. At the nodes of crystals are atoms bound by covalent bonds. This determines the high energy of the lattice and the physical properties of substances. Due to the directionality of covalent bonds, the coordination numbers and packing density in atomic covalent crystals are usually low.

Ionic crystals. Structural units - ions, interconnected by the forces of electrostatic interaction. The energy of the crystal lattice is great.

Metal crystals and connection. Most of the elements in D.I. Mendeleev belong to metals that have common properties: high electrical conductivity (10 6 - 10 8 cm), thermal conductivity, malleability, ductility, metallic luster, high reflectivity with respect to light. The general properties of metals can be explained by a special type of chemical bond called metallic.

Many substances can exist in several crystalline modifications (phases) that differ in physical properties. This phenomenon is called polymorphism . The transition from one modification to another is called polymorphic transition. An interesting and important example of a polymorphic transition is the transformation of graphite into diamond. This transition in the production of artificial diamonds is carried out at pressures of 60–100 thousand atmospheres and temperatures of 1500–2000 K.

4) The concepts of "alloy", "phase". Phase types. solid solutions. intermediate phases. Intermediate bonds with a metallic bond, intercalation phases. Anisotropy.

metal alloy

Fusion;

electrolysis;

Sublimation (sublimation);

Plasma spraying, etc.

components.

phase

System

solid solutions called phases in which one of the alloy components retains its crystal lattice, and the atoms of the other or other components are located in the crystal lattice of the first component (solvent), changing its dimensions (periods).

Solid solutions have a metallic type of bonds. According to the nature of the distribution of atoms of the solute in the crystal lattice of the solvent, solid solutions are distinguished: substitutions, insertions, subtractions

intermediate phases

Implementation phases, which form transition group metals with metalloids having a small atomic radius.

Anisotropy is a characteristic property of single crystals and means that, in the general case, the properties of a crystal in different directions are different and only in particular cases can they be the same. The anisotropy of crystals is due to the different packing density of atoms and molecules in the crystal lattice in different directions. An important consequence of the existence of crystallographic anisotropy is the formation of texture, i.e., the predominant orientation of grains in polycrystalline materials. Its formation leads to the anisotropy of the functional properties of metal products subjected to thermomechanical processing (rolled, stamped, etc.), fibrous and film materials, and many composite materials. The formation of a complex of magnetic properties of substances and materials is greatly influenced by magnetocrystalline anisotropy. Anisotropy is also characteristic of liquid crystals and moving liquids.

5) The concepts of "alloy", "phase". Phase types. Defects in the crystal structure: point, linear, surface, volumetric.

metal alloy called a substance obtained by fusing two or more starting substances, mainly metallic, and having metallic properties.

Currently, alloys receive:

Fusion;

Sintering (powder metallurgy);

electrolysis;

Sublimation (sublimation);

Plasma spraying, etc.

Substances that form an alloy are called components.

In alloys, the components can interact with each other in different ways, forming certain phases.

phase is called a part of a heterogeneous thermodynamic system that is homogeneous in chemical composition, crystal structure, and physical properties, separated from its other parts by an interface, when passing through which the chemical composition or structure changes abruptly.

System is a set of phases that are in equilibrium and delimited by interfaces.

During the crystallization of alloys, the following main solid phases can form: solid solutions, chemical compounds, mechanical mixtures.

In addition to solid solutions in alloys, there are intermediate phases, which can be formed only by metals (intermetallic phases), as well as metals with non-metals. A feature of the intermediate phases is that they do not retain the crystal lattice of the solvent metal, but have their own lattice.

There are a large number of intermediate phases that differ in chemical composition and structure and have a significant effect on the mechanical and technological properties of alloys. There are intermetallic phases, these include electronic compounds, σ-phases, Lavss phases. In addition, intermediate phases include chemical compounds, intercalation and subtraction phases.

The structure of real crystals differs from ideal ones. Real crystals always contain imperfections (defects) of the crystal structure, which break bonds between atoms and affect the properties of metals.

Defects in crystals are usually classified according to the nature of their measurement in space:

1. Point . Point defects are violations of the periodicity of a crystal, the dimensions of which are comparable to the dimensions of an atom in all dimensions.

Point defects include vacancies, interstitial atoms, substitutional impurities, impurities of foreign interstitial atoms (Fig. 2.5).

Rice. 2.5. Point defects in the crystal lattice: a- vacancy;

b - interstitial atom; c- Frenkel's defect; d impurity atoms of substitution (large) and interstitial (small).

The arrows indicate the directions of displacements of atoms in the lattice.

Vacancies and interstitial atoms appear in crystals at any temperature above absolute zero due to thermal vibrations of atoms.

Supersaturation with point defects is achieved by rapid cooling after high-temperature heating, by plastic deformation, and by neutron irradiation. The higher the temperature, the greater the concentration of vacancies and the more often they move from site to site. Vacancies are the most important variety of point defects; they accelerate all processes associated with the movement of atoms: diffusion, sintering of powders, etc.

2. Linear . Linear defects in crystals are characterized by the fact that their transverse dimensions do not exceed several interatomic distances, and their length can reach the size of a crystal. Linear defects include dislocations - lines, along and near which the correct periodic arrangement of the atomic planes of the crystal is violated.

The most important types of linear imperfections are edge and screw dislocations

The edge dislocation in the cross section is the edge of the "extra" half-plane in the lattice (Fig. 2.7)

Rice. 2.7. Cross section of a simple cubic lattice: a - with an edge dislocation; b - without dislocation.

Around the dislocations, the lattice is elastically distorted. The scheme of formation of the Cottrell atmosphere in a crystal is shown in Figure 2.8.

Rice. 2.8. Formation of the Cottrell atmosphere: (a) substitution impurity atoms (shaded) and interstitials are randomly arranged in the lattice; b, c – impurity atoms moved to the dislocation, as a result of which the lattice energy decreased.

3. Surface (two-dimensional ). These defects are understood as violations that have a large extension in two dimensions and an extension of only a few interatomic distances in the third dimension.

Surface defects include stacking faults, twin boundaries, grain boundaries.

4.Volumetric (three-dimensional ). They are understood as violations, which in three dimensions have unlimited dimensions. Such violations include cracks, pores, shrinkage shells.

Crystals of substances have unique physical properties:
1. Anisotropy is the dependence of physical properties on the direction in which these properties are determined. Feature only single crystals.

This is explained by the fact that crystals have a crystal lattice, the shape of which causes a different degree of interaction in different directions.

Thanks to this property:

A. Mica delaminates into plates in only one direction.

B. Graphite is easily torn into layers, but one single layer is incredibly strong.

B. Gypsum conducts heat differently in different directions.

D. A ray of light hitting a tourmaline crystal at different angles gives it different colors.

Strictly speaking, it is anisotropy that determines the formation of a form by a crystal that is specific for a given substance. The fact is that due to the structure of the crystal lattice, the growth of the crystal occurs unevenly - in one place faster, in another much slower. As a result, the crystal takes shape. Without this property, the crystals would grow spherical or even completely of any shape.

This also explains the irregular shape of polycrystals - they do not have anisotropy, since they are an intergrowth of crystals.

2. Isotropy is a property of polycrystals, the opposite of anisotropy. Only polycrystals have it.

Since the volume of single crystals is much less than the volume of the entire polycrystal, all directions in it are equal.

For example, metals equally conduct heat and electric current in all directions, since they are polycrystals.

Without this property, we would not be able to build anything. Most building materials are polycrystals, so no matter how you turn them, they will withstand everything. Single crystals can be superhard in one position and very brittle in another.

3. Polymorphism - the property of identical atoms (ions, molecules) to form different crystal lattices. Due to different crystal lattices, such crystals can have completely different properties.

This property causes the formation of some allotropic modifications of simple substances, for example, carbon is diamond and graphite.

Diamond properties:

· High hardness .

· Does not conduct electricity.

· Burns in a stream of oxygen.

Graphite properties:

· soft mineral.

· Conducts electricity.

· It is used to make refractory clay.

Topic Symmetry of solids

1 Crystalline and amorphous bodies.

2 Elements of symmetry and their interactions

3 Symmetry of crystal polyhedra and crystal lattices.

4 Principles of constructing crystallographic classes

Lab #2

Studying the structure of crystal models

Instruments and accessories: cards indicating chemical elements with a crystalline structure;

The purpose of the work: to study crystalline and amorphous bodies, the symmetry elements of crystal lattices, the principles of constructing crystallographic classes, to calculate the period of the crystal lattice for the proposed chemical elements.

Basic concepts on the topic

Crystals are solid bodies with a three-dimensional periodic atomic structure. Under equilibrium conditions, formations have a natural form of regular symmetrical polyhedra. Crystals are the equilibrium state of solids.

Each chemical substance that is under given thermodynamic conditions (temperature, pressure) in a crystalline state corresponds to a certain atomic-crystalline structure.

A crystal that has grown under non-equilibrium conditions and does not have the correct cut or has lost it as a result of processing retains the main feature of the crystalline state - the lattice atomic structure (crystal lattice) and all the properties determined by it.

Crystalline and amorphous solids

Solids are extremely diverse in terms of their structure, the nature of the binding forces of particles (atoms, ions, molecules), and physical properties. The practical need for a thorough study of the physical properties of solids has led to the fact that about half of all physicists on Earth are engaged in the study of solids, the creation of new materials with predetermined properties and the development of their practical application. It is known that during the transition of substances from a liquid state to a solid state, two different types of solidification are possible.

Crystallization of matter

In a liquid cooled to a certain temperature, crystals appear (regions of ordered particles) - crystallization centers, which, with further heat removal from the substance, grow due to the addition of particles from the liquid phase to them and cover the entire volume of the substance.

Solidification due to the rapid increase in the viscosity of the liquid with decreasing temperature.

The solids formed during this solidification process are referred to as amorphous bodies. Among them, substances are distinguished in which crystallization is not observed at all (sealing wax, wax, resin), and substances that can crystallize, for example, glass. However, due to the fact that their viscosity increases rapidly with decreasing temperature, the movement of molecules necessary for the formation and growth of crystals is hindered, and the substance has time to solidify before crystallization occurs. Such substances are called glassy. The process of crystallization of these substances proceeds very slowly in the solid state, and more easily at high temperature. The well-known phenomenon of "devitrification" or "attenuation" of glass is due to the formation of small crystals inside the glass, at the boundaries of which light is reflected and scattered, as a result of which the glass becomes opaque. A similar picture occurs when "candied" transparent sugar candy.

Amorphous bodies can be considered as liquids with a very high viscosity coefficient. It is known that in amorphous bodies one can observe a weakly expressed property of fluidity. If you fill the funnel with pieces of wax or sealing wax, then after some time, different for different temperatures, the pieces of the amorphous body will gradually blur, taking the form of a funnel and flowing out of it in the form of a rod. Even glass has the property of fluidity. Measurements of the thickness of window panes in old buildings have shown that over several centuries the glass has had time to flow from top to bottom. The thickness of the bottom of the glass turned out to be slightly larger than the top.

Strictly speaking, only crystalline bodies should be called solids. Amorphous bodies in some properties, and most importantly in structure, are similar to liquids: they can be considered as highly supercooled liquids with a very high viscosity.

It is known that, in contrast to the long-range order in crystals (the ordered arrangement of particles is preserved throughout the volume of each crystal grain), in liquids and amorphous bodies, short-range order in the arrangement of particles is observed. This means that in relation to any particle, the arrangement of the nearest neighboring particles is ordered, although not as clearly expressed as in a crystal, but when struck from a given particle, the arrangement of other particles in relation to it becomes less and less ordered and at a distance 3 - 4 effective diameters of the molecule, the order in the arrangement of the particles completely disappears.

Comparative characteristics of various states of matter are given in Table 2.1.

Crystal cell

For the convenience of describing the correct internal structure of solids, the concept of a spatial or crystal lattice is usually used. It is a spatial grid, in the nodes of which there are particles - ions, atoms, molecules that form a crystal.

Figure 2.1 shows a spatial crystal lattice. Bold lines highlight the smallest parallelepiped, whose parallel movement along three coordinate axes coinciding with the direction of the edges of the parallelepiped, the entire crystal can be constructed. This parallelepiped is called the main or elementary cell of the lattice. The atoms are located in this case at the vertices of the parallelepiped.

For an unambiguous characteristic of an elementary cell, 6 values are specified: three edges a, b, c and three angles between the edges of the parallelepiped a, b, g. These quantities are called lattice parameters. Options a, b, c These are the interatomic distances in the crystal lattice. Their numerical values are about 10 -10 m.

The simplest type of lattices are cubic with parameters a=b=c And a = b = g = 90 0 .

Miller indices

For the symbolic designation of nodes, directions and planes in a crystal, the so-called Miller indices are used.

Node indexes

The position of any node in the lattice relative to the selected origin is determined by three coordinates X, Y, Z (Figure 2.2).

These coordinates can be expressed in terms of the lattice parameters as follows: X= ma, Y= nb, Z= pc, Where a, b, c lattice parameters, m, n, p whole numbers.

Thus, if we take not a meter as a unit of length along the lattice axis, but lattice parameters a, b, c (axial units of length), then the coordinates of the node will be the numbers m, n, p. These numbers are called knot indices and are denoted by .

For nodes lying in the area of negative coordinate directions, put a minus sign over the corresponding index. For example .

Direction indices

To set the direction in the crystal, a straight line is selected (Figure 2.2) passing through the origin. Its orientation is uniquely determined by the index m n p the first node it passes through. Therefore, the direction indices are determined by the three smallest integers characterizing the position of the nearest node from the origin, lying in this direction. Direction indices are written as follows.

Figure 2.3 Principal directions in a cubic lattice.

The family of equivalent directions is denoted by broken brackets.

For example, the family of equivalent directions includes the directions

Figure 2.3 shows the main directions in a cubic lattice.

Plane indices

The position of any in space is determined by setting three segments OA, OV, OS (Figure 2.4), which it cuts off on the axes of the selected coordinate system. In axial units of the length of the segments will be: ; ; .

three numbers m n p completely determine the position of the plane S. To obtain Miller indices with these numbers, some transformations need to be done.

Compose the ratio of the reciprocals of the axial segments and express it through the ratio of the three smallest numbers h, k, l so that the equality .

Numbers h, k, l are indices of the plane. To find the indices of the plane, the ratio is brought to the lowest common denominator and the denominator is discarded. The numerators of the fractions and give the indices of the plane. Let's explain this with an example: m = 1, n = 2, p = 3. Then . Thus, for the case under consideration h = 6, k = 3, l = 2. Miller plane indices are enclosed in parentheses (6 3 2). Segments m n p may be fractional, but the Miller indices in this case are expressed as integers.

Let m =1, n = , p = , then .

With a parallel orientation of the plane relative to any coordinate axis, the index corresponding to this axis is equal to zero.

If the segment cut off on the axis has a negative value, then the corresponding plane index will also have a negative sign. Let h = - 6 , k = 3, l = 2, then such a plane in the Miller indices of planes will be written .

It should be noted that the plane indices (h, k, l) do not specify the orientation of a particular plane, but a family of parallel planes, that is, in essence, determine the crystallographic orientation of the plane.

Figure 2.5 shows the main planes in a cubic lattice.

Some planes differing in Miller indices are

equivalent in the physical and crystallographic sense. In a cubic lattice, one example of equivalence is the faces of a cube. Physical equivalence consists in the fact that all these planes have the same structure in the arrangement of lattice nodes, and, consequently, the same physical properties. Their crystallographic equivalence lies in the fact that these planes coincide with each other when rotated around one of the coordinate axes by an angle that is a multiple of . The family of equivalent planes is given by curly brackets. For example, the symbol denotes the entire family of faces of a cube.

Miller's three-component symbolism is used for all lattice systems, except for the hexagonal one. In a hexagonal lattice (Figure 2.7 No. 8), nodes are located at the vertices of regular hexagonal prisms and at the centers of their hexagonal bases. The orientation of planes in crystals of the hexagonal system is described using four coordinate axes x 1, x 2, x 3, z, so-called Miller-Brave indices. axes x 1, x 2, x 3 diverge from the origin at an angle of 120 0 . Axis z perpendicular to them. The designation of directions according to the four-component symbolism is difficult and rarely used, therefore the directions in the hexagonal lattice are set according to Miller's three-component symbolism.

Basic properties of crystals

One of the main properties of crystals is anisotropy. This term refers to the change in physical properties depending on the direction in the crystal. So a crystal can have different strength, hardness, thermal conductivity, resistivity, refractive index, etc. for different directions. Anisotropy also manifests itself in the surface properties of crystals. The surface tension coefficient for dissimilar crystal faces has a different value. When a crystal grows from a melt or solution, this is the reason for the difference in the growth rates of different faces. The anisotropy of the growth rates determines the correct shape of the growing crystal. The anisotropy of surface properties also takes place in the difference in the adsorption capacity of the dissolution rates, the chemical activity of different faces of the same crystal. The anisotropy of physical properties is a consequence of the ordered structure of the crystal lattice. In such a structure, the packing density of plane atoms is different. Figure 2.6 explains what has been said.

Arranging the planes in descending order of the population density of their atoms, we obtain the following series: (0 1 0) (1 0 0) (1 1 0) (1 2 0) (3 2 0) . In the most densely filled planes, the atoms are more strongly bound to each other, since the distance between them is the smallest. On the other hand, the most densely filled planes, being separated from each other by relatively large distances than the sparsely populated planes, will be weaker connected with each other.

Based on the foregoing, we can say that our conditional crystal is easiest to split along the plane (0 1 0), than on other planes. This is where the anisotropy of mechanical strength manifests itself. Other physical properties of a crystal (thermal, electrical, magnetic, optical) can also be different in different directions. The most important property of crystals, crystal lattices and their elementary cells is symmetry with respect to certain directions (axes) and planes.

Crystal symmetry

Table 2.1

Crystal system	Unit cell edge ratio	The ratio of angles in the unit cell
Triclinic
Monoclinic
Rhombic
tetragonal
cubic
Trigonal (robohedral)
Hexagonal

Due to the periodic arrangement of particles in a crystal, it has symmetry. This property lies in the fact that as a result of some mental operations, the system of crystal particles is combined with itself, goes into a position that does not differ from the original one. Each operation can be associated with an element of symmetry. For crystals, there are four elements of symmetry. This - axis of symmetry, plane of symmetry, center of symmetry and mirror-rotary axis of symmetry.

In 1867, the Russian crystallographer A.V. Gadolin showed what could exist 32 possible combinations of symmetry elements. Each of these possible combinations of symmetry elements is called symmetry class. Experience has confirmed that in nature there are crystals belonging to one of the 32 symmetry classes. In crystallography, the indicated 32 symmetry classes, depending on the ratio of parameters a, b, c, a, b, g united in 7 systems (syngony), which bear the following names: Triclinic, monoclinic, rhombic, trigonal, hexagonal, tetragonal and cubic systems. Table 2.1 shows the parameter ratios for these systems.

As shown by the French crystallographer Bravais, there are 14 types of lattices belonging to different crystal systems.

If the nodes of the crystal lattice are located only at the vertices of the parallelepiped, which is a unit cell, then such a lattice is called primitive or simple (Figure 2.7 No. 1, 2, 4, 9, 10, 12), if, in addition, there are nodes in the center of the bases of the parallelepiped, then such a lattice is called base-centered (Figure 2.7 No. 3, 5), if there is a node at the intersection of spatial diagonals, then the lattice is called body-centered (Figure 2.7 No. 6, 11, 13), and if there are nodes in the center of all side faces - face-centered (drawing 2.7 Nos. 7, 14). Lattices whose elementary cells contain additional nodes inside the volume of the parallelepiped or on its faces are called complex.

The Bravais lattice is a collection of identical and equally located particles (atoms, ions) that can be combined with each other by parallel transfer. It should not be assumed that one Bravais lattice can exhaust all the atoms (ions) of a given crystal. The complex structure of crystals can be represented as a set of several solutions current Bravais, pushed one into the other. For example, the crystal lattice of table salt NaCl (Figure 2.8) consists of two cubic face-centered Bravais lattices formed by ions Na- And Cl + , offset relative to each other by half the edge of the cube.

Calculation of the grating period.

Knowing the chemical composition of a crystal and its spatial structure, one can calculate the lattice period of this crystal. The task is to determine the number of molecules (atoms, ions) in a unit cell, to express its volume in terms of the lattice period and, knowing the density of the crystal, to make an appropriate calculation. It is important to note that for many types of crystal lattice, most atoms do not belong to one unit cell, but are simultaneously included in several adjacent unit cells.

For example, let's determine the lattice period of sodium chloride, the lattice of which is shown in Figure 2.8.

The lattice period is equal to the distance between the nearest ions of the same name. This corresponds to the edge of the cube. Let us find the number of sodium and chlorine ions in an elementary cube, the volume of which is equal to d3, d- lattice period. There are 8 sodium ions along the vertices of the cube, but each of them is simultaneously the vertex of eight adjacent elementary cubes, therefore, only a part of the ion located at the vertex of the cube belongs to this volume. There are a total of 7 such sodium ions, which together make up the sodium ion. Six sodium ions are located in the centers of the faces of the cube, but each of them belongs to the considered cube only half. Together they make up the sodium ion. Thus, the elementary cube under consideration contains four sodium ions.

One chlorine ion is located at the intersection of the spatial diagonals of the cube. It belongs entirely to our elementary cube. Twelve chloride ions are located in the middle of the edges of the cube. Each of them belongs to the volume d3 by one quarter, since the edge of the cube is simultaneously common to four adjacent elementary cells. There are 12 such chlorine ions in the cube under consideration, which together make up chlorine ions. Total in elementary volume d3 contains 4 sodium ions and 4 chloride ions, i.e. 4 molecules of sodium chloride (n = 4).

If 4 molecules of sodium chloride occupy a volume d3, then one mole of the crystal will have a volume , where A is Avogadro's number, n is the number of molecules in a unit cell.

On the other hand, where is the mole mass, is the density of the crystal. Then where

(2.1)

When determining the number of atoms in one parallelepiped unit cell (calculating the content), one must be guided by the rule:

q if the center of the atomic sphere coincides with one of the vertices of the elementary cell, then from such an atom this cell belongs to, since at any vertex of the parallelepiped eight adjacent parallelepipeds simultaneously converge, to which the vertex atom equally belongs (Figure 2.9);

q from the atom located on the edge of the cell belongs to this cell, since the edge is common to four parallelepipeds (Figure 2.9);

q from an atom lying on the edge of the cell belongs to this cell, since the cell face is common to two parallelepipeds (Figure 2.9);

q an atom located inside a cell belongs to it entirely (Figure 2.9).

When using the specified rule, the shape of the parallelepiped cell is indifferent. The formulated rule can be extended to the cells of any systems.

Progress

For the obtained models of real crystals

1 Select an elementary cell.

2 Determine the type of Bravais grating.

3 Perform a "content count" for these elementary cells.

4 Determine the grating period.

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Are commoncrystal properties

Introduction

Crystals are solids that have a natural external shape of regular symmetrical polyhedra based on their internal structure, that is, on one of several defined regular arrangements of the particles that make up the substance.

Solid state physics is based on the idea of the crystallinity of matter. All theories of the physical properties of crystalline solids are based on the concept of perfect periodicity of crystal lattices. Using this idea and the statements about the symmetry and anisotropy of crystals that follow from it, physicists have developed a theory of the electronic structure of solids. This theory makes it possible to give a rigorous classification of solids, determining their type and macroscopic properties. However, it allows classifying only known, investigated substances and does not allow predetermining the composition and structure of new complex substances that would have a given set of properties. This last task is especially important for practice, since its solution would make it possible to create custom-made materials for each specific case. Under appropriate external conditions, the properties of crystalline substances are determined by their chemical composition and the type of crystal lattice. The study of the dependence of the properties of a substance on its chemical composition and crystal structure is usually divided into the following separate stages: 1) general study of crystals and the crystalline state of matter 2) construction of the theory of chemical bonds and its application to the study of various classes of crystalline substances 3) study of the general patterns of changes in the structure of crystalline substances when their chemical composition changes 4) the establishment of rules that make it possible to predetermine the chemical composition and structure of substances that have a certain set of physical properties.

Maincrystal properties- anisotropy, homogeneity, the ability to self-burning and the presence of a constant melting temperature.

1. Anisotropy

crystal anisotropy self-burning

Anisotropy - it is expressed in the fact that the physical properties of crystals are not the same in different directions. Physical quantities include such parameters as strength, hardness, thermal conductivity, speed of light propagation, and electrical conductivity. A characteristic example of a substance with pronounced anisotropy is mica. Crystalline plates of mica - easily split only along the planes. In transverse directions, it is much more difficult to split the plates of this mineral.

An example of anisotropy is a crystal of the mineral disthene. In the longitudinal direction, the hardness of disthene is 4.5, in the transverse direction - 6. The mineral disthene (Al 2 O), which is distinguished by sharply different hardness in unequal directions. Along the elongation, disthene crystals are easily scratched by a knife blade, in the direction perpendicular to the elongation, the knife does not leave any marks.

Rice. 1 Disthene Crystal

Mineral cordierite (Mg 2 Al 3). Mineral, aluminosilicate of magnesium and iron. The cordierite crystal appears differently colored in three different directions. If a cube with faces is cut out of such a crystal, then the following can be noticed. Perpendicular to these directions, then along the diagonal of the cube (from top to top, a grayish-blue color is observed, in the vertical direction - an indigo-blue color, and in the direction across the cube - yellow.

Rice. 2 Cube carved from cordierite.

A crystal of table salt, which has the shape of a cube. From such a crystal, rods can be cut in various directions. Three of them are perpendicular to the faces of the cube, parallel to the diagonal

Each of the examples is exceptional in its specificity. But through precise research, scientists have come to the conclusion that all crystals are anisotropic in one way or another. Also, solid amorphous formations can be homogeneous and even anisotropic (anisotropy, for example, can be observed when glass is stretched or squeezed), but amorphous bodies cannot by themselves take on a polyhedral shape, under any conditions.

Rice. 3 Detection of thermal conductivity anisotropy on quartz (a) and its absence on glass (b)

As an example (Fig. 1) of the anisotropic properties of crystalline substances, we should first of all mention the mechanical anisotropy, which consists in the following. All crystalline substances do not split in the same way along different directions (mica, gypsum, graphite, etc.). Amorphous substances, on the other hand, split in the same way in all directions, because amorphism is characterized by isotropy (equivalence) - physical properties in all directions are manifested equally.

The anisotropy of thermal conductivity can be easily observed in the following simple experiment. Apply a layer of colored wax to the face of a quartz crystal and bring a needle heated on a spirit lamp to the center of the face. The resulting melted circle of wax around the needle will take the form of an ellipse on the face of the prism or the shape of an irregular triangle on one of the facets of the crystal head. On an isotropic substance, for example, glass, the shape of melted wax will always be a regular circle.

Anisotropy is also manifested in the fact that when a solvent interacts with a crystal, the rate of chemical reactions is different in different directions. As a result, each crystal, when dissolved, eventually acquires its characteristic forms.

Ultimately, the reason for the anisotropy of crystals is that with an ordered arrangement of ions, molecules or atoms, the forces of interaction between them and interatomic distances (as well as some quantities not directly related to them, for example, electrical conductivity or polarizability) turn out to be unequal in different directions. The reason for the anisotropy of a molecular crystal can also be the asymmetry of its molecules, I would like to note that all amino acids, except for the simplest - glycine, are asymmetric.

Any particle of a crystal has a strictly defined chemical composition. This property of crystalline substances is used to obtain chemically pure substances. For example, when sea water is frozen, it becomes fresh and drinkable. Now guess if sea ice is fresh or salty?

2. Uniformity

Homogeneity - is expressed in the fact that any elementary volumes of a crystalline substance, equally oriented in space, are absolutely identical in all their properties: they have the same color, mass, hardness, etc. thus, every crystal is a homogeneous, but at the same time an anisotropic body. A body is considered to be homogeneous in which, at finite distances from any of its points, there are others that are equivalent to it not only physically, but also geometrically. In other words, they are in the same environment as the original ones, since the placement of material particles in the crystal space is “controlled” by the spatial lattice, we can assume that the face of the crystal is a materialized flat nodal lattice, and the edge is a materialized nodal row. As a rule, well-developed crystal faces are determined by nodal grids with the highest node density. The point where three or more faces converge is called the apex of the crystal.

Homogeneity is inherent not only in crystalline bodies. Solid amorphous formations can also be homogeneous. But amorphous bodies cannot by themselves take on a polyhedral shape.

Developments are underway that can increase the homogeneity factor of crystals.

This invention is patented by our Russian scientists. The invention relates to the sugar industry, in particular to the production of massecuite. The invention provides an increase in the coefficient of homogeneity of crystals in the massecuite, and also contributes to an increase in the growth rate of crystals at the final stage of growth due to a gradual increase in the supersaturation coefficient.

The disadvantages of the known method are the low coefficient of homogeneity of the crystals in the massecuite massecuite of the first crystallization, the significant duration of obtaining the massecuite.

The technical result of the invention is to increase the coefficient of homogeneity of the crystals in the massecuite massecuite of the first crystallization and the intensification of the process of obtaining the massecuite.

3. Ability for self-restraint

The ability to self-cutting is expressed in the fact that any fragment or a ball carved from a crystal in a medium suitable for its growth is covered over time with faces characteristic of a given crystal. This feature is related to the crystal structure. A glass ball, for example, does not have such a feature.

The mechanical properties of crystals include properties associated with such mechanical effects on them as impact, compression, tension, etc. - (cleavage, plastic deformation, fracture, hardness, brittleness).

The ability to self-cut, i.e. under certain conditions, take a natural multifaceted shape. This also shows its correct internal structure. It is this property that distinguishes a crystalline substance from an amorphous one. An example illustrates this. Two balls carved from quartz and glass are lowered into a silica solution. As a result, the quartz ball will be covered with facets, and the glass one will remain round.

Crystals of the same mineral can have a different shape, size and number of faces, but the angles between the corresponding faces will always be constant (Fig. 4 a-d) - this is the law of constancy of face angles in crystals. In this case, the size and shape of the faces in different crystals of the same substance, the distance between them and even their number may vary, but the angles between the corresponding faces in all crystals of the same substance remain constant under the same conditions of pressure and temperature. The angles between the faces of the crystals are measured using a goniometer (goniometer). The law of constancy of facet angles is explained by the fact that all crystals of one substance are identical in their internal structure, i.e. have the same structure.

According to this law, the crystals of a certain substance are characterized by their specific angles. Therefore, by measuring the angles, it is possible to prove that the crystal under study belongs to one or another substance.

Ideally formed crystals exhibit symmetry, which is extremely rare in natural crystals due to the advanced growth of faces (Fig. 4e).

Rice. 4 the law of constancy of facet angles in crystals (a-d) and the growth of leading faces 1,3 and 5 of a crystal growing on the cavity wall (e)

Cleavage is a property of crystals in which to split or split along certain crystallographic directions, as a result, even smooth planes are formed, called cleavage planes.

Cleavage planes are oriented parallel to actual or possible crystal faces. This property entirely depends on the internal structure of minerals and manifests itself in those directions in which the adhesion forces between the material particles of crystal lattices are the smallest.

Depending on the degree of perfection, several types of cleavage can be distinguished:

Very perfect - the mineral is easily split into separate thin plates or leaves, it is very difficult to split it in the other direction (mica, gypsum, talc, chlorite).

Rice. 5 Chlorite (Mg, Fe) 3 (Si, Al) 4 O 10 (OH) 2 (Mg, Fe) 3 (OH) 6)

Perfect - the mineral relatively easily splits mainly along the cleavage planes, and the broken pieces often resemble individual crystals (calcite, galena, halite, fluorite).

Rice. 6 Calcite

Medium - when splitting, both cleavage planes and uneven fractures in random directions (pyroxenes, feldspars) are formed.

Rice. 7 Feldspars ((K, Na, Ca, sometimes Ba) (Al 2 Si 2 or AlSi 3) O 8))

Imperfect - minerals split in arbitrary directions with the formation of uneven fracture surfaces, individual cleavage planes are found with difficulty (native sulfur, pyrite, apatite, olivine).

Rice. 8 Apatite crystals (Ca 5 3 (F, Cl, OH))

In some minerals, when splitting, only uneven surfaces are formed, in this case they speak of a very imperfect cleavage or its absence (quartz).

Rice. 9 Quartz (SiO 2)

Cleavage can manifest itself in one, two, three, rarely more directions. For a more detailed description of it, the direction in which the cleavage passes is indicated, for example, along the rhombohedron - in calcite, along the cube - in halite and galena, along the octahedron - in fluorite.

Cleavage planes must be distinguished from crystal faces: A plane, as a rule, has a stronger luster, forms a series of planes parallel to each other and, unlike crystal faces, on which we cannot observe shading.

Thus, cleavage can be traced along one (mica), two (feldspar), three (calcite, halite), four (fluorite), and six (sphalerite) directions. The degree of cleavage perfection depends on the structure of the crystal lattice of each mineral, since rupture along some planes (flat grids) of this lattice due to weaker bonds occurs much more easily than in other directions. In the case of identical adhesion forces between crystal particles, there is no cleavage (quartz).

Fracture - the ability of minerals to split not along cleavage planes, but along a complex uneven surface

Separation - the property of some minerals to split with the formation of parallel, although most often not quite even planes, not due to the structure of the crystal lattice, which is sometimes mistaken for cleavage. In contrast to cleavage, separateness is a property of only some individual specimens of a given mineral, and not of the mineral species as a whole. The main difference between separation and cleavage is that the resulting punches cannot be split further into smaller fragments with even parallel chips.

Symmetry- the most general pattern associated with the structure and properties of a crystalline substance. It is one of the generalizing fundamental concepts of physics and natural science in general. “Symmetry is the property of geometric figures to repeat their parts, or, to put it more precisely, their property in various positions to come into alignment with the original position.” For convenience of study, they use models of crystals that convey the forms of ideal crystals. To describe the symmetry of crystals, it is necessary to determine the symmetry elements. Thus, such an object is symmetrical, which can be combined with itself by certain transformations: rotations and (and) reflections (Figure 10).

1. The plane of symmetry is an imaginary plane that divides the crystal into two equal parts, and one of the parts is, as it were, a mirror image of the other. A crystal can have several planes of symmetry. The plane of symmetry is denoted by the Latin letter P.

2. The axis of symmetry is a line, during rotation around which by 360 ° the crystal repeats its initial position in space n-th number of times. It is denoted by the letter L. n - determines the order of the axis of symmetry, which in nature can only be 2, 3, 4 and 6th order, i.e. L2, L3, L4 and L6. There are no axes of the fifth and above the sixth order in crystals, and the axes of the first order are not taken into account.

3. Center of symmetry - an imaginary point located inside the crystal, at which the lines intersect and divide in half, connecting the corresponding points on the surface of the crystal1. The center of symmetry is indicated by the letter C.

The whole variety of crystalline forms found in nature is combined into seven syngonies (systems): 1) cubic; 2) hexagonal; 3) tetragonal (square); 4) trigonal; 5) rhombic; 6) monoclinal and 7) triclinic.

4. Constant melting point

Melting is the transition of a substance from a solid to a liquid state.

It is expressed in the fact that when a crystalline body is heated, the temperature rises to a certain limit; with further heating, the substance begins to melt, and the temperature remains constant for some time, since all the heat goes to the destruction of the crystal lattice. The reason for this phenomenon is believed to be that the main part of the energy of the heater, supplied to the solid, is used to reduce the bonds between the particles of the substance, i.e. to the destruction of the crystal lattice. In this case, the energy of interaction between particles increases. The molten substance has a greater store of internal energy than in the solid state. The remaining part of the heat of fusion is spent on doing work to change the volume of the body during its melting. The temperature at which melting begins is called the melting point.

During melting, the volume of most crystalline bodies increases (by 3-6%), and decreases during solidification. But, there are substances in which, when melted, the volume decreases, and when solidified, it increases.

These include, for example, water and cast iron, silicon and some others. That is why ice floats on the surface of the water, and solid cast iron - in its own melt.

Amorphous substances, unlike crystalline ones, do not have a clearly defined melting point (amber, resin, glass).

Rice. 12 Amber

The amount of heat required to melt a substance is equal to the product of the specific heat of fusion times the mass of the substance.

The specific heat of fusion shows how much heat is needed to completely convert 1 kg of a substance from a solid to a liquid state, taken at the melting rate.

The unit of specific heat of fusion in SI is 1J/kg.

During the melting process, the temperature of the crystal remains constant. This temperature is called the melting point. Each substance has its own melting point.

The melting point for a given substance depends on atmospheric pressure.

In crystalline bodies at the melting point, one can observe the substance simultaneously in the solid and liquid states. On the cooling (or heating) curves of crystalline and amorphous substances, one can see that in the first case there are two sharp inflections corresponding to the beginning and end of crystallization; in the case of cooling of an amorphous substance, we have a smooth curve. On this basis, it is easy to distinguish crystalline from amorphous substances.

Bibliography

1. Chemist's Handbook 21 "CHEMISTRY AND CHEMICAL ENGINEERING" p. 10 (http://chem21.info/info/1737099/)

2. Reference book on geology (http://www.geolib.net/crystallography/vazhneyshie-svoystva-kristallov.html)

3. UrFU named after the first President of Russia B.N. Yeltsin”, section Geometric Crystallography (http://media.ls.urfu.ru/154/489/1317/)

4. Chapter 1. Crystallography with the basics of crystal chemistry and mineralogy (http://kafgeo.igpu.ru/web-text-books/geology/r1-1.htm)

5. Application: 2008147470/13, 01.12.2008; IPC C13F1/02 (2006.01) C13F1/00 (2006.01). Patentee(s): State Educational Institution of Higher Professional Education Voronezh State Technological Academy (RU) (http://bd.patent.su/2371000-2371999/pat/servl/servlet939d.html)

6. Tula State Pedagogical University named after L.N. Tolstoy Department of Ecology Golynskaya F.A. "The concept of minerals as crystalline substances" (http://tsput.ru/res/geogr/geology/lec2.html)

7. Computer training course "General Geology" Course of lectures. Lecture 3 D0% B8% D0% B8/%D0% BB % D0% B5% D0% BA % D1% 86% D0% B8% D1% 8F_3.htm)

8. Physics class (http://class-fizika.narod.ru/8_11.htm)

Uniformity

It is expressed in the fact that any elementary volumes of a crystalline substance, equally oriented in space, are absolutely identical in all their properties: they have the same color, mass, hardness, etc. thus, every crystal is a homogeneous, but at the same time an anisotropic body.

Homogeneity is inherent not only in crystalline bodies. Solid amorphous formations can also be homogeneous. But amorphous bodies cannot by themselves take on a polyhedral shape.

Ability for self-restraint

Crystals of the same substance can differ from each other in their size, the number of faces, edges, and the shape of the faces. It depends on the conditions of crystal formation. With uneven growth, the crystals are flattened, elongated, etc. The angles between the corresponding faces of the growing crystal remain unchanged. This feature of crystals is known as law of constancy of facet angles. In this case, the size and shape of the faces in different crystals of the same substance, the distance between them and even their number may vary, but the angles between the corresponding faces in all crystals of the same substance remain constant under the same conditions of pressure and temperature.

The law of constancy of facet angles was established at the end of the 17th century by the Danish scientist Steno (1699) on crystals of iron luster and rock crystal; later this law was confirmed by M.V. Lomonosov (1749) and the French scientist Rome de Lille (1783). The law of constancy of facet angles is called the first law of crystallography.

The law of constancy of facet angles is explained by the fact that all crystals of one substance are identical in their internal structure, i.e. have the same structure.

To measure dihedral angles in crystals, special devices were invented - goniometers.

constant melting point

Amorphous substances, unlike crystalline ones, do not have a clearly defined melting point. On the cooling (or heating) curves of crystalline and amorphous substances, one can see that in the first case there are two sharp inflections corresponding to the beginning and end of crystallization; in the case of cooling of an amorphous substance, we have a smooth curve. On this basis, it is easy to distinguish crystalline from amorphous substances.

Summary: Crystals and their properties. The most important properties of crystals Physical properties of crystals

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4. Constant melting point

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