Properties of crystals, shape and syngony (crystallographic systems)

An important property of a crystal is a certain correspondence between different faces - the symmetry of the crystal. The following symmetry elements are distinguished:

1. Planes of symmetry: divide the crystal into two symmetrical halves, such planes are also called "mirrors" of symmetry.

2. Axes of symmetry: straight lines passing through the center of the crystal. The rotation of the crystal around this axis repeats the shape of the initial position of the crystal. There are axes of symmetry of the 3rd, 4th and 6th order, which corresponds to the number of such positions during the rotation of the crystal by 360 o .

3. Center of symmetry: the faces of the crystal corresponding to the parallel face change places when rotated 180 o around this center. The combination of these symmetry elements and orders gives 32 symmetry classes for all crystals. These classes, in accordance with their common properties, can be grouped into seven syngonies (crystallographic systems). Three-dimensional coordinate axes can be used to determine and evaluate the positions of crystal faces.

Each mineral belongs to one class of symmetry, since it has one type of crystal lattice, which characterizes it. On the contrary, minerals having the same chemical composition can form crystals of two or more symmetry classes. This phenomenon is called polymorphism. There are not isolated examples of polymorphism: diamond and graphite, calcite and aragonite, pyrite and marcasite, quartz, tridymite and cristobalite; rutile, anatase (aka octahedrite) and brookite.

SYNGONIES (CRYSTALLOGRAPHIC SYSTEMS). All forms of crystals form 7 syngonies (cubic, tetragonal, hexagonal, trigonal, rhombic, monoclinic, triclinic). The diagnostic signs of syngony are the crystallographic axes and the angles formed by these axes.

In the triclinic syngony there is a minimum number of symmetry elements. It is followed in order of complexity by the monoclinic, rhombic, tetragonal, trigonal, hexagonal, and cubic syngonies.

Cubic system. All three axes are of equal length and are perpendicular to each other. Typical crystal shapes: cube, octahedron, rhombic dodecahedron, pentagon dodecahedron, tetragon trioctahedron, hexaoctahedron.

Tetragonal system. Three axes are perpendicular to each other, two axes have the same length, the third (main axis) is either shorter or longer. Typical crystal shapes are prisms, pyramids, tetragons, trapezohedrons and bipyramids.

Hexagonal syngony. The third and fourth axes are inclined to the plane, have equal length and intersect at an angle of 120 o . The fourth axis, which differs from the others in size, is located perpendicular to the others. Both the axes and angles are similar in location to the previous syngony, but the symmetry elements are very diverse. Typical crystal shapes are trihedral prisms, pyramids, rhombohedrons and scalenohedra.

Rhombic system. Three axes are characteristic, perpendicular to each other. Typical crystalline forms are basal pinacoids, rhombic prisms, rhombic pyramids and bipyramids.

Monoclinic syngony. Three axes of different lengths, the second is perpendicular to the others, the third is at an acute angle to the first. Typical forms of crystals are pinacoids, prisms with obliquely cut edges.

Triclinic system. All three axes have different lengths and intersect at sharp angles. Typical shapes are monohedra and pinacoids.

Shape and growth of crystals. Crystals belonging to the same mineral species have a similar appearance. A crystal can therefore be characterized as a combination of external parameters (faces, angles, axes). But the relative size of these parameters is quite different. Consequently, a crystal can change its appearance (not to say appearance) depending on the degree of development of certain forms. For example, a pyramidal appearance, where all the faces converge, columnar (in a perfect prism), tabular, foliated or globular.

Two crystals with the same combination of external parameters may have a different appearance. This combination depends on the chemical composition of the crystallization medium and other conditions of formation, which include temperature, pressure, the rate of crystallization of a substance, etc. In nature, regular crystals are occasionally found that were formed under favorable conditions - for example, gypsum in a clay medium or minerals on the walls of the geode. The faces of such crystals are well developed. Conversely, crystals formed under changing or unfavorable conditions are often deformed.

UNITS. Often there are crystals that do not have enough space to grow. These crystals coalesced with others, forming irregular masses and aggregates. In free space among rocks, crystals developed together, forming druses, and in voids - geodes. In terms of their structure, such units are very diverse. In small fissures of limestone, there are formations resembling a petrified fern. They are called dendrites, formed as a result of the formation of oxides and hydroxides of manganese and iron under the influence of solutions circulating in these cracks. Therefore, dendrites never form at the same time as organic residues.

Doubles. During the formation of crystals, twins are often formed when two crystals of the same mineral species grow together with each other according to certain rules. Doubles are often individuals fused at an angle. Pseudosymmetry often manifests itself - several crystals belonging to the lowest class of symmetry grow together, forming individuals with a pseudosymmetry of a higher order. Thus, aragonite, which belongs to the rhombic system, often forms twin prisms with hexagonal pseudosymmetry. On the surface of such intergrowths, a thin hatching formed by twinning lines is observed.

SURFACE OF CRYSTALS. As already mentioned, flat surfaces are rarely smooth. Quite often, hatching, banding or striation is observed on them. These characteristic features help in the determination of many minerals - pyrite, quartz, gypsum, tourmaline.

PSEUDOMORPHOUSES. Pseudomorphoses are crystals that have the shape of another crystal. For example, limonite occurs in the form of pyrite crystals. Pseudomorphoses are formed when one mineral is completely chemically replaced by another while maintaining the shape of the previous one.

The forms of crystal aggregates can be very diverse. The photo shows a radiant aggregate of natrolite.
A sample of gypsum with twinned crystals in the form of a cross.

Physical and chemical properties. Not only the external shape and symmetry of a crystal are determined by the laws of crystallography and the arrangement of atoms - this also applies to the physical properties of the mineral, which can be different in different directions. For example, mica can separate into parallel plates in only one direction, so its crystals are anisotropic. Amorphous substances are the same in all directions, and therefore isotropic. Such qualities are also important for the diagnosis of these minerals.

Density. The density (specific gravity) of minerals is the ratio of their weight to the weight of the same volume of water. Specific gravity determination is an important diagnostic tool. Minerals with a density of 2-4 predominate. A simplified weight estimate will help with practical diagnostics: light minerals have a weight of 1 to 2, medium-density minerals - from 2 to 4, heavy minerals from 4 to 6, very heavy minerals - more than 6.

MECHANICAL PROPERTIES. These include hardness, cleavage, chip surface, toughness. These properties depend on the crystal structure and are used to select a diagnostic technique.

HARDNESS. It is quite easy to scratch a calcite crystal with the tip of a knife, but it is unlikely to be able to do this with a quartz crystal - the blade will slide over the stone without leaving a scratch. This means that the hardness of these two minerals is different.

Hardness in relation to scratching refers to the resistance of a crystal to an attempt at external deformation of the surface, in other words, the resistance to mechanical deformation from the outside. Friedrich Moos (1773-1839) proposed a relative scale of hardness from degrees, where each mineral has a higher scratch hardness than the previous one: 1. Talc. 2. Gypsum. 3. Calcite. 4. Fluorite. 5. Apatite. 6. Feldspar. 7. Quartz. 8. Topaz. 9. Corundum. 10. Diamond. All of these values ​​apply only to fresh, unweathered samples.

You can evaluate the hardness in a simplified way. Minerals with a hardness of 1 are easily scratched with a fingernail; while they are greasy to the touch. The surface of minerals with a hardness of 2 is also scratched with a fingernail. Copper wire or a piece of copper scratches minerals with a hardness of 3. The tip of a penknife scratches minerals up to a hardness of 5; good new file - quartz. Minerals with a hardness greater than 6 will scratch glass (hardness 5). From 6 to 8 does not take even a good file; sparks fly when you try. To determine hardness, test specimens with increasing hardness as long as they yield; then a sample is taken, which is apparently even harder. The opposite should be done if it is necessary to determine the hardness of a mineral surrounded by a rock whose hardness is lower than that of the mineral required for the sample.

Talc and diamond, two minerals at the extremes of the Mohs scale of hardness.

It is easy to draw a conclusion based on whether a mineral glides over the surface of another or scratches it with a slight squeak. The following cases may occur:
1. The hardness is the same if the sample and the mineral do not mutually scratch each other.
2. It is possible that both minerals scratch each other, since the tops and ledges of the crystal can be harder than the edges or cleavage planes. Therefore, it is possible to scratch the face of a gypsum crystal or its cleavage plane with the top of another gypsum crystal.
3. The mineral scratches the first sample, and a sample of a higher hardness class makes a scratch on it. Its hardness is in the middle between the samples used for comparison, and it can be estimated at half a class.

Despite the apparent simplicity of such a determination of hardness, many factors can lead to a false result. For example, let's take a mineral whose properties vary greatly in different directions, like disthene (kyanite): vertically the hardness is 4-4.5, and the tip of the knife leaves a clear mark, but in the perpendicular direction the hardness is 6-7 and the mineral is not scratched at all with a knife . The origin of the name of this mineral is associated with this feature and emphasizes it very expressively. Therefore, it is necessary to carry out hardness testing in different directions.

Some aggregates have a higher hardness than the components (crystals or grains) of which they are composed; it may turn out that a dense piece of gypsum is difficult to scratch with a fingernail. On the contrary, some porous aggregates are less solid, which is explained by the presence of voids between the granules. Therefore, chalk is scratched with a fingernail, although it consists of calcite crystals with a hardness of 3. Another source of errors is minerals that have experienced some kind of change. It is impossible to assess the hardness of powdered, weathered samples or aggregates of scaly and acicular structure by simple means. In such cases, it is better to use other methods.

Cleavage. By hitting a hammer or pressing a knife, the crystals along the cleavage planes can sometimes be divided into plates. Cleavage is manifested along planes with minimal adhesion. Many minerals have cleavage in several directions: halite and galena - parallel to the faces of the cube; fluorite - along the faces of the octahedron, calcite - rhombohedron. Muscovite mica crystal; cleavage planes are clearly visible (in the photo on the right).

Minerals such as mica and gypsum have perfect cleavage in one direction, but imperfect or no cleavage in other directions. With careful observation, one can notice the thinnest cleavage planes inside transparent crystals along well-defined crystallographic directions.

fracture surface. Many minerals, such as quartz and opal, do not cleave in either direction. Their bulk breaks into irregular pieces. The cleavage surface can be described as flat, uneven, conchoidal, semi-conchoidal, rough. Metals and hard minerals have a rough cleavage surface. This property can serve as a diagnostic feature.

Other mechanical properties. Some minerals (pyrite, quartz, opal) break into pieces under a hammer blow - they are brittle. Others, on the contrary, turn into powder without giving debris.

Malleable minerals can be flattened, as, for example, pure native metals. They do not form either powder or fragments. Thin plates of mica can be bent like plywood. After the cessation of exposure, they will return to their original state - this is the property of elasticity. Others, like gypsum and pyrite, can be bent but retain their deformed state - this is the property of being flexible. Such features make it possible to recognize similar minerals - for example, to distinguish elastic mica from flexible chlorite.

Coloring. Some minerals have such a pure and beautiful color that they are used as paints or varnishes. Often their names are used in everyday speech: emerald green, ruby ​​red, turquoise, amethyst, etc. The color of minerals, one of the main diagnostic features, is neither permanent nor eternal.

There are a number of minerals in which the color is constant - malachite is always green, graphite is black, native sulfur is yellow. Common minerals such as quartz (rock crystal), calcite, halite (common salt) are colorless when free of impurities. However, the presence of the latter causes coloration, and we know blue salt, yellow, pink, purple and brown quartz. Fluorite has a whole range of colors.

The presence of impurity elements in the chemical formula of the mineral leads to a very specific color. This photo shows green quartz (prase), in its pure form, it is completely colorless and transparent.

Tourmaline, apatite and beryl have different colors. Coloring is not an undoubted diagnostic sign of minerals with different shades. The color of the mineral also depends on the presence of impurity elements included in the crystal lattice, as well as various pigments, impurities, and inclusions in the host crystal. Sometimes it can be associated with radiation exposure. Some minerals change color depending on the light. So, alexandrite is green in daylight, and purple in artificial light.

For some minerals, the color intensity changes when the crystal faces are rotated relative to light. The color of the cordierite crystal during rotation changes from blue to yellow. The reason for this phenomenon is that such crystals, called pleochroic, absorb light differently depending on the direction of the beam.

The color of some minerals may also change in the presence of a film that has a different color. These minerals, as a result of oxidation, are covered with a coating, which, perhaps, somehow softens the effect of sunlight or artificial light. Some gemstones lose their color if exposed to sunlight for a period of time: emerald loses its deep green color, amethyst and rose quartz turn pale.

Many minerals containing silver (for example, pyrargyrite and proustite) are also sensitive to sunlight (insolation). Apatite under the influence of insolation is covered with a black veil. Collectors should protect such minerals from exposure to light. The red color of realgar in the sun turns into golden yellow. Such color changes occur very slowly in nature, but it is possible to artificially change the color of a mineral very quickly, accelerating the processes occurring in nature. For example, you can get yellow citrine from purple amethyst when heated; diamonds, rubies and sapphires are artificially "improved" with the help of radioactive irradiation and ultraviolet rays. Rock crystal, due to strong irradiation, turns into smoky quartz. Agate, if its gray color does not look very attractive, can be dyed by dipping ordinary aniline fabric dye into a boiling solution.

POWDER COLOR (DASH). The color of the line is determined by rubbing against the rough surface of unglazed porcelain. At the same time, one must not forget that porcelain has a hardness of 6-6.5 on the Mohs scale, and minerals with greater hardness will leave only a white powder of pounded porcelain. You can always get powder in a mortar. Colored minerals always give a lighter line, uncolored and white - white. Usually a white or gray line is observed in minerals that are artificially colored, or with impurities and pigment. Often it is, as it were, clouded, since in a diluted color its intensity is determined by the concentration of the coloring matter. The color of the trait of minerals with a metallic sheen differs from their own color. Yellow pyrite gives a greenish-black streak; black hematite is cherry red, black wolframite is brown, and cassiterite is an almost uncolored streak. A colored line allows you to quickly and easily identify a mineral by it than a diluted or colorless line.

SHINE. Like color, this is an effective method for identifying a mineral. Luster depends on how light is reflected and refracted on the surface of the crystal. There are minerals with metallic and non-metallic luster. If they cannot be distinguished, we can speak of a semi-metallic luster. Opaque metal minerals (pyrite, galena) are highly reflective and have a metallic sheen. For another important group of minerals (zinc blende, cassiterite, rutile, etc.), it is difficult to determine the luster. For minerals with non-metallic luster, the following categories are distinguished according to the intensity and properties of the luster:

1. Diamond shine, like a diamond.
2. Glass shine.
3. Oily sheen.
4. Dull luster (for minerals with poor reflectivity).

The luster may be associated with the structure of the aggregate and the direction of the dominant cleavage. Minerals, having a thin-layered structure, have a pearly luster.

TRANSPARENCY. The transparency of a mineral is a quality that is highly variable: an opaque mineral can easily be classified as transparent. The bulk of colorless crystals (rock crystal, halite, topaz) belong to this group. Transparency depends on the structure of the mineral - some aggregates and small grains of gypsum and mica appear opaque or translucent, while the crystals of these minerals are transparent. But if you look at small granules and aggregates with a magnifying glass, you can see that they are transparent.

REFRACTIVE INDEX. The refractive index is an important optical constant of a mineral. It is measured using special equipment. When a beam of light penetrates into an anisotropic crystal, the beam is refracted. Such birefringence gives the impression that there is a virtual second object parallel to the crystal under study. A similar phenomenon can be observed through a transparent calcite crystal.

LUMINESCENCE. Some minerals, such as scheelite and willemite, irradiated with ultraviolet rays, glow with a specific light, which in some cases may continue for some time. Fluorite glows when heated in a dark place - this phenomenon is called thermoluminescence. When some minerals are rubbed, another type of glow occurs - triboluminescence. These different types of luminescence are a characteristic that makes it easy to diagnose a number of minerals.

THERMAL CONDUCTIVITY. If you take a piece of amber and a piece of copper in your hand, it will seem that one of them is warmer than the other. This impression is due to the different thermal conductivity of these minerals. So you can distinguish glass imitations of precious stones; for this, you need to attach a pebble to your cheek, where the skin is more sensitive to heat.

The following properties can be determined by what feelings they cause in a person. Graphite and talc feel smooth to the touch, while gypsum and kaolin feel dry and rough. Minerals soluble in water, such as halite, sylvinite, epsomite, have a specific taste - salty, bitter, sour. Some minerals (sulphur, arsenopyrite and fluorite) have an easily recognizable odor that occurs immediately upon impact on the sample.

MAGNETISM. Fragments or powder of certain minerals, mainly those with a high iron content, can be distinguished from other similar minerals using a magnet. Magnetite and pyrrhotite are highly magnetic and attract iron filings. Some minerals, such as hematite, acquire magnetic properties when heated red-hot.

CHEMICAL PROPERTIES. Determining minerals based on their chemical properties requires, in addition to specialized equipment, extensive knowledge of analytical chemistry.

There is one simple method for determining carbonates, available to non-professionals - the action of a weak solution of hydrochloric acid (instead of it, you can take ordinary table vinegar - dilute acetic acid, which is in the kitchen). In this way, you can easily distinguish a colorless sample of calcite from white gypsum - you need to drop an acid on the sample. Gypsum does not react to this, and calcite "boils" when carbon dioxide is released.

The main properties of crystals - anisotropy, homogeneity, the ability to self-burning and the presence of a constant melting temperature - are determined by their internal structure.

Rice. 1. An example of anisotropy is a crystal of the mineral disthene. In the longitudinal direction, its hardness is 4.5, in the transverse direction it is 6. © Parent Géry

This property is also called disparity. It is expressed in the fact that the physical properties of crystals (hardness, strength, thermal conductivity, electrical conductivity, light propagation speed) are not the same in different directions. Particles forming a crystalline structure along non-parallel directions are separated from each other at different distances, as a result of which the properties of a crystalline substance along such directions should be different. A characteristic example of a substance with pronounced anisotropy is mica. The crystalline plates of this mineral are easily split only along planes parallel to its lamellarity. In transverse directions, it is much more difficult to split mica plates.

Anisotropy is also manifested in the fact that when a crystal is exposed to any solvent, the rate of chemical reactions is different in different directions. As a result, each crystal, when dissolved, acquires its own characteristic shapes, which are called etching figures.

Amorphous substances are characterized by isotropy (equivalence) - physical properties in all directions are manifested in the same way.

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

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.

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.

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. One of the methods for diagnosing crystals is based on this.

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

constant melting point

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 temperature at which melting begins is called the 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.

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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 edges, 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 R.

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)

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Lecture 16

Physical properties of crystals

Solid state physics deals with the study of the structure and physical properties of solids. It establishes the dependence of physical properties on the atomic structure of a substance, develops methods for obtaining and studying new crystalline materials with specified characteristics.

The physical properties of crystals are determined by:

1) the nature of the chemical elements that make up the crystals;

2) type of chemical bond;

3) the geometric nature of the structure, i.e., the mutual arrangement of atoms in the crystal structure;

4) imperfection of the structure, i.e., the presence of defects.

On the other hand, it is by the physical properties of crystals that we usually judge the type of chemical bond.

The strength of crystals can be most easily judged by their mechanical and thermal properties. The stronger the crystal, the greater its hardness and the higher its melting point. If we study the change in hardness with a change in composition in a series of substances of the same type and compare the data obtained with the corresponding values ​​for melting points, then we can notice "parallelism" in the change in these properties.

Let me remind you that the most characteristic feature of the physical properties of crystals is their symmetry and anisotropy. An anisotropic medium is characterized by the dependence of the measured property on the measurement direction.

We have already said that crystal chemistry is closely related to crystallography and physics. That's why, the main task of crystal physics(a section of crystallography that studies the physical properties of crystals) is the study of the regularities of the physical properties of crystals from their structure, as well as the dependence of these properties on external influences.

The physical properties of substances can be divided into two groups: structurally sensitive and structurally insensitive properties. The first depend on the atomic structure of the crystals, the second - mainly on the electronic structure and type of chemical bond. An example of the former is mechanical properties (mass, density, heat capacity, melting point, etc.), an example of the latter is thermal and electrical conductivity, optical and other properties.

Thus, good electrical conductivity of metals, due to the presence of free electrons, will be observed not only in crystals, but also in molten metals.

The ionic nature of the bond is manifested, in particular, in the fact that many salts, for example, alkali metal halides, dissolve in polar solvents, dissociating into ions. However, the fact that there is no solubility cannot yet serve as proof that the compound has a non-polar bond. Thus, the binding energy, for example, of oxides is so much greater than the binding energy of alkali halides that the dielectric constant of water is no longer sufficient to separate ions from the crystal.

In addition, some compounds, mainly with a homeopolar type of bond, under the influence of a large dielectric constant of a polar solvent, can dissociate into ions in solution, although they may not be ionic compounds in the crystalline state (for example, HCl, HBr).

In heterodesmic compounds, some properties, such as the mechanical strength of compounds, depend on only one (weakest) type of bond.

Therefore, a crystal can be considered, on the one hand, as a discontinuous (discrete) medium. On the other hand, a crystalline substance can be considered as a continuous anisotropic medium. In this case, the physical properties that manifest themselves in a certain direction do not depend on translations (transfers). This makes it possible to describe the symmetry of physical properties using point symmetry groups.

Describing the symmetry of a crystal, we take into account only the external form, that is, we consider the symmetry of geometric figures. P. Curie showed that the symmetry of material figures is described by an infinite number of point groups, which in the limit tend to the seven limit symmetry groups considered earlier (families of a rotating cone, a fixed cone, a rotating cylinder, a twisted cylinder, a fixed cylinder, a family of a ball with rotating points of the surface, families of the fixed ball).

Limiting point groups - Curie groups - point groups containing axes of infinite order are called. There are only seven limit groups: ¥, ¥mm, ¥/m, ¥22, ¥/mm, ¥/¥, ¥/¥mm.

The connection between the point symmetry group of a crystal and the symmetry of its physical properties was formulated by the German physicist F. Neumann: the material exhibits a symmetry of the same kind as its crystallographic form in regard to physical properties. This is known as the Neumann principle.

The German physicist W. Voigt, a student of F. Neman, significantly clarified this principle and formulated it as follows: the symmetry group of any physical property must include all elements of the point symmetry group of the crystal.

Let us consider some physical properties of crystals.

Density of crystals.

The density of a substance depends on the crystal structure of the substance, its chemical composition, the packing factor of atoms, the valencies and radii of the particles that make it up.

Density changes with changes in temperature and pressure, since these factors cause the expansion or contraction of a substance.

The dependence of density on the structure can be demonstrated using the example of three modifications of Al2SiO5:

andalusite (r = 3.14 - 3.16 g/cm3);

sillimanite (r = 3.23 - 3.27 g/cm3);

kyanite (r = 3.53 - 3.65 g/cm3).

With an increase in the packing factor of the crystal structure, the density of the substance increases. For example, during the polymorphic transition of graphite to diamond with a change in the coordination number of carbon atoms from 3 to 4, the density also increases accordingly from 2.2 to 3.5 g/cm3).

The density of real crystals is usually less than the calculated density (ideal crystals) due to the presence of defects in their structures. The density of diamond, for example, ranges from 2.7 to 3.7 g/cm3. Thus, by reducing the real density of crystals, one can judge the degree of their defectiveness.

The density also changes with a change in the chemical composition of the substance during isomorphic substitutions - when moving from one member of the isomorphic series to another. For example, in the olivine series (mg, Fe2+ )2[ SiO4 ] density increases as Mg2+ cations are replaced by Fe2+ from r = 3.22 g/cm3 for forsterite mg2 [ SiO4 ] up to r = 4.39 g/cm3 for fayalite.

Hardness.

Hardness refers to the degree of resistance of a crystal to external influences. Hardness is not a physical constant. Its value depends not only on the studied material, but also on the measurement conditions.

Hardness depends on:

the type of structure;

packing factor (specific gravity);

the charge of the ions forming the crystal.

For example, polymorphic modifications of CaCO3 - calcite and aragonite - have densities of 3 and 4, respectively, and differ in the different density of their structures:

· for the structure of calcite with CChSa = 6 - r = 2.72;

· for the structure of aragonite with CChSa = 9 - r = 2.94 g/cm3).

In a series of identically constructed crystals, the hardness increases with an increase in charges and a decrease in the size of cations. The presence in the structures of sufficiently large anions such as F-, OH-, H2O molecules reduces the hardness.

Facets of different forms of crystals have different reticular density and differ in their hardness. Thus, the greatest hardness in the diamond structure is possessed by the (111) octahedron faces, which have a higher reticular density compared to the (100) cube faces.

The ability to deform.

The ability of a crystal to undergo plastic deformation is determined primarily by the nature of the chemical bond between its structural elements.

covalent bond, which has a strict directionality, sharply weakens even at insignificant displacements of atoms relative to each other. Therefore, crystals with a covalent type of bond (Sb, Bi, As, se, etc.) do not show the ability to plastic deformation.

metal connection does not have a directed character and changes slightly when atoms are displaced relative to each other. This determines the high degree of plasticity of metals (ductility). The most malleable are those metals whose structures are built according to the law of cubic closest packing, which has four directions of close-packed layers. Less forging metals with hexagonal close packing - with one direction of the densest layers. So, among the polymorphic modifications of iron, a-Fe and b-Fe almost do not have malleability (type I lattice), while g-Fe with a cubic closest packing (face-centered cubic lattice) is a malleable metal like Cu, Pt, Au, Ag, etc. .

Ionic bond is not directional. Therefore, typical ionic crystals (NaCl, CaF2, CaTe, etc.) are as brittle as crystals with a covalent bond. But at the same time, they have a fairly high plasticity. Sliding in them proceeds along certain crystallographic directions. This is explained by the fact that (110) networks formed either by Na+ ions alone or by Cl– ions can be distinguished in the crystal structure. During plastic deformation, one flat mesh moves relative to the neighboring one in such a way that Na+ ions slide along Cl- ions. The difference in the charges of ions in neighboring networks prevents rupture, and they remain parallel to their original position. Sliding along these layers proceeds with minimal disturbance in the arrangement of atoms and is the easiest.

Thermal properties of crystals.

Thermal conductivity is closely related to symmetry. This can be most clearly demonstrated in the following experiment. Let's cover with a thin layer of paraffin the faces of three crystals: a cube, a hexagonal prism, a straight parallelepiped. With the tip of a thin hot needle, let's touch each of the faces of these crystals. From the outlines of the melting spots, one can judge the rate of heat propagation on the planes of the faces in different directions.

On a crystal of cubic syngony, the contours of melting spots on all faces will have the shape of a circle, which indicates the same speed of heat propagation in all directions from the point of contact with a hot needle. The shape of the spots in the idea of ​​circles on all faces of a cubic crystal is related to its symmetry.

The shape of the spots on the upper and lower faces of the hexagonal prism will also have the shape of a circle (the rate of heat propagation in the plane perpendicular to the main axis of the medium category crystal is the same in all directions). On the faces of a hexagonal prism, the melting spots will have the shape of ellipses, since the axes of the 2nd order pass perpendicular to these faces.

On all faces of a right parallelepiped (crystal of orthogonal syngony), the melting spots will have the shape of an ellipse, since the axes of the 2nd order pass perpendicular to these faces.

So, the rate of heat propagation through the crystal body is directly dependent on which linear symmetry element it propagates along. In cubic crystals the heat distribution surface will have the shape of a sphere. Consequently, with respect to thermal conductivity, cubic crystals are isotropic, i.e., they are equally characteristic in all directions. Thermal conduction surface crystals of the middle category expressed as an ellipsoid of revolution (parallel to the principal axis). IN crystals of the lowest category and all heat conduction surfaces are ellipsoidal.

The anisotropy of thermal conductivity is closely related to the structure of a crystalline substance. Thus, the densest atomic networks and rows correspond to high values ​​of thermal conductivity. Therefore, layered and chain crystals have large differences in the directions of thermal conductivity.

Thermal conductivity also depends on the degree of defectiveness of the crystal - for more defective crystals it is lower than for synthetic ones. A substance in the amorphous state has a lower thermal conductivity than crystals of the same composition. For example, the thermal conductivity of quartz glass is much lower than the thermal conductivity of quartz crystals. This property is the basis for the widespread use of quartz glassware.

Optical properties.

Each substance with a specific crystal structure is characterized by unique optical properties. Optical properties are closely related to the crystal structure of solids and its symmetry.

With regard to optical properties, all substances can be divided into optically isotropic and anisotropic. The former include amorphous bodies and crystals of the highest category, the latter - all the rest. In optically isotropic media, a light wave, which is a set of transverse harmonic oscillations of an electromagnetic nature, propagates with the same speed in all directions. In this case, the oscillations of the intensity vector of the electric and magnetic fields also occur in all possible directions, but in a plane perpendicular to the direction of the beam. Along its direction, light energy is transferred. This light is called natural or unpolarized(Figure a, b).

In optically anisotropic media, the wave propagation velocities in different directions can be different. Under certain conditions, the so-called polarized light, for which all oscillations of the vector of electric and magnetic fields pass in a strictly defined direction (figure c, d). The behavior of such polarized light in crystals is the basis for the method of crystal-optical studies using a polarizing microscope.

Birefringence of light in crystals.

linearly polarized with mutually perpendicular oscillation planes. The decomposition of light into two polarized beams is called birefringence or birefringence.

Birefringence of light is observed in crystals of all syngonies, with the exception of the cubic one. In crystals of the lowest and middle category, birefringence occurs in all directions, with the exception of one or two directions, called optical axes.

The phenomenon of birefringence is associated with the anisotropy of crystals. The optical anisotropy of crystals is expressed in the fact that the speed of light propagation in them is different in different directions.

IN crystals of the middle category among the many directions of optical anisotropy, there is one single direction - optical axis, coinciding with the main axis of symmetry of the 3rd, 4th, 6th orders. Along this direction, the light travels without splitting.

IN crystals of the lowest category There are two directions along which the light does not bifurcate. Cross sections of crystals perpendicular to these directions coincide with optically isotropic cross sections.

Influence of structural features on optical properties.

In crystal structures with layers of close-packed atoms, the distance between atoms inside the layer exceeds the distance between the nearest atoms located in neighboring layers. Such ordering leads to easier polarization if the electric field voltage vector of the light wave is parallel to the plane of the layers.

electrical properties.

All substances can be divided into conductors, semiconductors and dielectrics.

Some crystals (dielectrics) are polarized under the influence of external influences. The ability of dielectrics to polarize is one of their fundamental properties. Polarization is a process associated with the creation of electric dipoles in a dielectric under the action of an external electric field.

In crystallography and solid state physics, the phenomena piezoelectricity and pyroelectricity.

Piezoelectric effect - change in the polarization of some dielectric crystals during mechanical deformation. The magnitude of the resulting charges is proportional to the applied force. The charge sign depends on the type of crystal structure. The piezoelectric effect arises only in crystals devoid of an inversion center, i.e., having polar directions. For example, crystals of quartz SiO2, sphalerite (ZnS).

Pyroelectric effect - the appearance of electric charges on the surface of some crystals when they are heated or cooled. The pyroelectric effect occurs only in dielectric crystals with a single polar direction, the opposite ends of which cannot be combined by any operation of a given symmetry group. The appearance of electric charges can occur only according to certain, polar directions. Faces perpendicular to these directions receive charges of different signs: one is positive, and the other is negative. The pyroelectric effect can occur in crystals belonging to one of the polar symmetry classes: 1, 2, 3, 4, 6, m, mm2, 3m, 4mm, 6mm.

It follows from geometric crystallography that the directions passing through the center of symmetry cannot be polar. Directions perpendicular to the planes of symmetry or axes of even order cannot be polar either.

In the class of pyroelectrics, two subclasses are distinguished. The first group includes linear pyroelectrics, in which the electric polarization in an external field depends linearly on the electric field strength. For example, tourmaline NaMgAl3B3.Si6(O, OH)30.

Crystals of the second subclass are called ferroelectrics. For them, the dependence of the polarization on the strength of the external field is nonlinear, and the polarizability depends on the magnitude of the external field. The nonlinear dependence of the polarization on the electric field strength is characterized by a hysteresis loop. This feature of ferroelectrics suggests that they retain their electric polarization in the absence of an external field. Thanks to this, Rochelle salt crystals (hence the name of ferroelectrics) turned out to be reliable electrical energy custodians and electrical signal recorders, which allows them to be used in computer “memory cells”.

Magnetic properties.

This is the ability of bodies to interact with a magnetic field, that is, to become magnetized when placed in a magnetic field. Depending on the magnitude of the magnetic susceptibility, diamagnetic, paramagnetic, ferromagnetic and antiferromagnetic crystals are distinguished.

The magnetic properties of all substances depend not only on the features of their crystal structure, but also on the nature of the atoms (ions) that compose them, that is, magnetism is determined by the electronic structure of shells and nuclei, as well as by the orbital motion of electrons (spins) around them.

When an atom (ion) is introduced into a magnetic field, the angular velocity of electrons in orbit changes due to the fact that an additional rotational motion is superimposed on the initial rotational motion of electrons around the nucleus, as a result of which the atom receives an additional magnetic moment. Moreover, if all electrons with opposite spins in an atom are grouped in pairs (Figure A), then the magnetic moments of the electrons are compensated and their total magnetic moment will be equal to zero. Such atoms are called diamagnetic, and the substances consisting of them - diamagnets. For example, inert gases, B-subgroup metals - Cu, Ag, Au, Zn, Cd, most ionic crystals (NaCl, CaF2), as well as substances with a predominant covalent bond - Bi, Sb, Ga, graphite. In crystals with layered structures, the magnetic susceptibility for directions lying in a layer significantly exceeds that for perpendicular directions.

When filling electron shells in atoms, electrons tend to be unpaired. Therefore, there are a large number of substances, the magnetic moments of electrons, in the atoms of which, are located randomly and in the absence of an external magnetic field, spontaneous orientation of magnetic moments does not occur in them (Figure B). The total magnetic moment, due to electrons that are not bound in pairs and weakly interacting with each other, will be constant, positive or somewhat larger than that of dielectrics. Such atoms are called magnetic, and substances - paramagnets. When a paramagnet is introduced into a magnetic field, the misoriented spins acquire some orientation, as a result of which three types of ordering of uncompensated magnetic moments are observed - three types of phenomena: ferromagnetism (figure C), antiferromagnetism (figure D) and ferrimagnetism (figure D).

ferromagnetic properties possess substances whose magnetic moments of atoms (ions) are directed parallel to each other, as a result of which the external magnetic field can increase millions of times. The name of the group is associated with the presence in it of elements of the iron subgroup Fe, Ni, Co.

If the magnetic moments of individual atoms are antiparallel and equal, then the total magnetic moment of the atoms is zero. Such substances are called antiferromagnets. These include transition metal oxides - MnO, NiO, CoO, FeO, many fluorides, chlorides, sulfides, selenides, etc.

When the antiparallel moments of the atoms of the crystal structure are not equal, the total moment turns out to be different from zero, and such structures have spontaneous magnetization. Similar properties are ferrites(Fe3O4, garnet group minerals).

Solids are divided into amorphous bodies and crystals. The difference between the latter and the former is that the atoms of crystals are arranged according to a certain law, thereby forming a three-dimensional periodic stacking, which is called a crystal lattice.

It is noteworthy that the name of the crystals comes from the Greek words “harden” and “cold”, and in the time of Homer this word was called rock crystal, which was then considered “frozen ice”. At first, only faceted transparent formations were called this term. But later, opaque and uncut bodies of natural origin were also called crystals.

Crystal structure and lattice

An ideal crystal is presented in the form of periodically repeating identical structures - the so-called elementary cells of a crystal. In the general case, the shape of such a cell is an oblique parallelepiped.

It is necessary to distinguish between such concepts as a crystal lattice and a crystal structure. The first is a mathematical abstraction depicting a regular arrangement of certain points in space. While a crystal structure is a real physical object, a crystal in which a certain group of atoms or molecules is associated with each point of the crystal lattice.

Garnet crystal structure - rhombus and dodecahedron

The main factor determining the electromagnetic and mechanical properties of a crystal is the structure of the elementary cell and the atoms (molecules) associated with it.

Anisotropy of crystals

The main property of crystals that distinguishes them from amorphous bodies is anisotropy. This means that the properties of the crystal are different, depending on the direction. So, for example, inelastic (irreversible) deformation is carried out only along certain planes of the crystal, and in a certain direction. Due to anisotropy, crystals react differently to deformation depending on its direction.

However, there are crystals that do not have anisotropy.

Types of crystals

Crystals are divided into single crystals and polycrystals. Monocrystals are called substances, the crystal structure of which extends to the entire body. Such bodies are homogeneous and have a continuous crystal lattice. Usually, such a crystal has a pronounced cut. Examples of a natural single crystal are single crystals of rock salt, diamond and topaz, as well as quartz.

Many substances have a crystalline structure, although they usually do not have a characteristic shape for crystals. Such substances include, for example, metals. Studies show that such substances consist of a large number of very small single crystals - crystalline grains or crystallites. A substance consisting of many such differently oriented single crystals is called polycrystalline. Polycrystals often do not have faceting, and their properties depend on the average size of crystalline grains, their mutual arrangement, and also the structure of intergranular boundaries. Polycrystals include substances such as metals and alloys, ceramics and minerals, as well as others.