Any substance in nature, as is known, consists of smaller particles. They, in turn, are connected and form a certain structure, which determines the properties of a particular substance.

Atomic is characteristic and occurs at low temperatures and high pressure. Actually, it is precisely thanks to this that metals and a number of other materials acquire their characteristic strength.

The structure of such substances at the molecular level looks like a crystal lattice, each atom in which is connected to its neighbor by the strongest connection existing in nature - a covalent bond. All the smallest elements that form the structures are arranged in an orderly manner and with a certain periodicity. Representing a grid in the corners of which atoms are located, always surrounded by the same number of satellites, the atomic crystal lattice practically does not change its structure. It is well known that the structure of a pure metal or alloy can be changed only by heating it. In this case, the higher the temperature, the stronger the bonds in the lattice.

In other words, the atomic crystal lattice is the key to the strength and hardness of materials. However, it is worth considering that the arrangement of atoms in different substances may also differ, which, in turn, affects the degree of strength. So, for example, diamond and graphite, which contain the same carbon atom, are extremely different from each other in terms of strength: diamond is on Earth, but graphite can exfoliate and break. The fact is that in the crystal lattice of graphite, atoms are arranged in layers. Each layer resembles a honeycomb, in which the carbon atoms are joined rather loosely. This structure causes layered crumbling of pencil leads: when broken, parts of the graphite simply peel off. Another thing is diamond, the crystal lattice of which consists of excited carbon atoms, that is, those that are capable of forming 4 strong bonds. It is simply impossible to destroy such a joint.

Crystal lattices of metals, in addition, have certain characteristics:

1. Lattice period- a quantity that determines the distance between the centers of two adjacent atoms, measured along the edge of the lattice. The generally accepted designation does not differ from that in mathematics: a, b, c are the length, width, height of the lattice, respectively. Obviously, the dimensions of the figure are so small that the distance is measured in the smallest units of measurement - a tenth of a nanometer or angstroms.

2. K - coordination number. An indicator that determines the packing density of atoms within a single lattice. Accordingly, its density is greater, the higher the number K. In fact, this figure represents the number of atoms that are as close as possible and at an equal distance from the atom under study.

3. Lattice basis. Also a quantity characterizing the density of the lattice. Represents the total number of atoms that belong to the particular cell being studied.

4. Compactness factor measured by calculating the total volume of the lattice divided by the volume occupied by all the atoms in it. Like the previous two, this value reflects the density of the lattice being studied.

We have considered only a few substances that have an atomic crystal lattice. Meanwhile, there are a great many of them. Despite its great diversity, the crystalline atomic lattice includes units that are always connected by means (polar or non-polar). In addition, such substances are practically insoluble in water and are characterized by low thermal conductivity.

In nature, there are three types of crystal lattices: body-centered cubic, face-centered cubic, and close-packed hexagonal.

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Solids usually have a crystalline structure. It is characterized by the correct arrangement of particles at strictly defined points in space. When these points are mentally connected by intersecting straight lines, a spatial frame is formed, which is called crystal lattice.

The points at which particles are located are called crystal lattice nodes. The nodes of an imaginary lattice may contain ions, atoms or molecules. They make oscillatory movements. With increasing temperature, the amplitude of oscillations increases, which manifests itself in the thermal expansion of bodies.

Depending on the type of particles and the nature of the connection between them, four types of crystal lattices are distinguished: ionic, atomic, molecular and metallic.

Crystal lattices consisting of ions are called ionic. They are formed by substances with ionic bonds. An example is a sodium chloride crystal, in which, as already noted, each sodium ion is surrounded by six chloride ions, and each chloride ion by six sodium ions. This arrangement corresponds to the most dense packing if the ions are represented as spheres located in the crystal. Very often, crystal lattices are depicted as shown in Fig., where only the relative positions of the particles are indicated, but not their sizes.

The number of nearest neighboring particles closely adjacent to a given particle in a crystal or in an individual molecule is called coordination number.

In the sodium chloride lattice, the coordination numbers of both ions are 6. So, in a sodium chloride crystal it is impossible to isolate individual salt molecules. There is none of them. The entire crystal should be considered as a giant macromolecule consisting of an equal number of Na + and Cl - ions, Na n Cl n, where n is a large number. The bonds between ions in such a crystal are very strong. Therefore, substances with an ionic lattice have a relatively high hardness. They are refractory and low-flying.

Melting of ionic crystals leads to disruption of the geometrically correct orientation of the ions relative to each other and a decrease in the strength of the bond between them. Therefore, their melts conduct electric current. Ionic compounds generally dissolve easily in liquids consisting of polar molecules, such as water.

Crystal lattices, in the nodes of which there are individual atoms, are called atomic. The atoms in such lattices are connected to each other by strong covalent bonds. An example is diamond, one of the modifications of carbon. Diamond is made up of carbon atoms, each of which is bonded to four neighboring atoms. Coordination number of carbon in diamond is 4 . In the diamond lattice, as in the sodium chloride lattice, there are no molecules. The entire crystal should be considered as a giant molecule. The atomic crystal lattice is characteristic of solid boron, silicon, germanium and compounds of some elements with carbon and silicon.

Crystal lattices consisting of molecules (polar and non-polar) are called molecular.

Molecules in such lattices are connected to each other by relatively weak intermolecular forces. Therefore, substances with a molecular lattice have low hardness and low melting points, are insoluble or slightly soluble in water, and their solutions almost do not conduct electric current. The number of inorganic substances with a molecular lattice is small.

Examples of them are ice, solid carbon monoxide (IV) (“dry ice”), solid hydrogen halides, solid simple substances formed by one- (noble gases), two- (F 2, Cl 2, Br 2, I 2, H 2 , O 2 , N 2), three- (O 3), four- (P 4), eight- (S 8) atomic molecules. The molecular crystal lattice of iodine is shown in Fig. . Most crystalline organic compounds have a molecular lattice.

When carrying out many physical and chemical reactions, a substance passes into a solid state of aggregation. In this case, molecules and atoms tend to arrange themselves in such a spatial order in which the forces of interaction between particles of matter would be maximally balanced. This is how the strength of the solid substance is achieved. Atoms, once occupying a certain position, perform small oscillatory movements, the amplitude of which depends on temperature, but their position in space remains fixed. The forces of attraction and repulsion balance each other at a certain distance.

Modern ideas about the structure of matter

Modern science states that an atom consists of a charged nucleus, which carries a positive charge, and electrons, which carry negative charges. At a speed of several thousand trillion revolutions per second, electrons rotate in their orbits, creating an electron cloud around the nucleus. The positive charge of the nucleus is numerically equal to the negative charge of the electrons. Thus, the atom of the substance remains electrically neutral. Possible interactions with other atoms occur when electrons are detached from their parent atom, thereby disturbing the electrical balance. In one case, the atoms are arranged in a certain order, which is called a crystal lattice. In another, due to the complex interaction of nuclei and electrons, they are combined into molecules of various types and complexity.

Definition of crystal lattice

Taken together, various types of crystalline lattices of substances are networks with different spatial orientations, at the nodes of which ions, molecules or atoms are located. This stable geometric spatial position is called the crystal lattice of the substance. The distance between nodes of one crystal cell is called the identity period. The spatial angles at which the cell nodes are located are called parameters. According to the method of constructing bonds, crystal lattices can be simple, base-centered, face-centered, and body-centered. If the particles of matter are located only in the corners of the parallelepiped, such a lattice is called simple. An example of such a lattice is shown below:

If, in addition to the nodes, the particles of the substance are located in the middle of the spatial diagonals, then this arrangement of particles in the substance is called a body-centered crystal lattice. This type is clearly shown in the figure.

If, in addition to the nodes at the vertices of the lattice, there is a node at the place where the imaginary diagonals of the parallelepiped intersect, then you have a face-centered type of lattice.

Types of crystal lattices

The different microparticles that make up a substance determine the different types of crystal lattices. They can determine the principle of building connections between microparticles inside a crystal. Physical types of crystal lattices are ionic, atomic and molecular. This also includes various types of metal crystal lattices. Chemistry studies the principles of the internal structure of elements. The types of crystal lattices are presented in more detail below.

Ionic crystal lattices

These types of crystal lattices are present in compounds with an ionic type of bond. In this case, lattice sites contain ions with opposite electrical charges. Thanks to the electromagnetic field, the forces of interionic interaction are quite strong, and this determines the physical properties of the substance. Common characteristics are refractoriness, density, hardness and the ability to conduct electric current. Ionic types of crystal lattices are found in substances such as table salt, potassium nitrate and others.

Atomic crystal lattices

This type of structure of matter is inherent in elements whose structure is determined by covalent chemical bonds. Types of crystal lattices of this kind contain individual atoms at the nodes, connected to each other by strong covalent bonds. This type of bond occurs when two identical atoms “share” electrons, thereby forming a common pair of electrons for neighboring atoms. Thanks to this interaction, covalent bonds bind atoms evenly and strongly in a certain order. Chemical elements that contain atomic types of crystal lattices are hard, have a high melting point, are poor conductors of electricity, and are chemically inactive. Classic examples of elements with a similar internal structure include diamond, silicon, germanium, and boron.

Molecular crystal lattices

Substances that have a molecular type of crystal lattice are a system of stable, interacting, closely packed molecules that are located at the nodes of the crystal lattice. In such compounds, the molecules retain their spatial position in the gaseous, liquid and solid phases. At the nodes of the crystal, molecules are held together by weak van der Waals forces, which are tens of times weaker than the ionic interaction forces.

The molecules that form a crystal can be either polar or nonpolar. Due to the spontaneous movement of electrons and vibrations of nuclei in molecules, the electrical equilibrium can shift - this is how an instantaneous electric dipole moment arises. Appropriately oriented dipoles create attractive forces in the lattice. Carbon dioxide and paraffin are typical examples of elements with a molecular crystal lattice.

Metal crystal lattices

A metal bond is more flexible and ductile than an ionic bond, although it may seem that both are based on the same principle. The types of crystal lattices of metals explain their typical properties - such as mechanical strength, thermal and electrical conductivity, and fusibility.

A distinctive feature of a metal crystal lattice is the presence of positively charged metal ions (cations) at the sites of this lattice. Between the nodes there are electrons that are directly involved in creating an electric field around the lattice. The number of electrons moving around within this crystal lattice is called electron gas.

In the absence of an electric field, free electrons perform chaotic motion, randomly interacting with lattice ions. Each such interaction changes the momentum and direction of motion of the negatively charged particle. With their electric field, electrons attract cations to themselves, balancing their mutual repulsion. Although electrons are considered free, their energy is not enough to leave the crystal lattice, so these charged particles are constantly within its boundaries.

The presence of an electric field gives the electron gas additional energy. The connection with ions in the crystal lattice of metals is not strong, so electrons easily leave its boundaries. Electrons move along lines of force, leaving behind positively charged ions.

conclusions

Chemistry attaches great importance to the study of the internal structure of matter. The types of crystal lattices of various elements determine almost the entire range of their properties. By influencing crystals and changing their internal structure, it is possible to enhance the desired properties of a substance and remove undesirable ones and transform chemical elements. Thus, studying the internal structure of the surrounding world can help to understand the essence and principles of the structure of the universe.

Crystalline substances

Solid crystals- three-dimensional formations characterized by strict repeatability of the same structural element ( unit cell) in all directions. The unit cell is the smallest volume of a crystal in the form of a parallelepiped, repeated in the crystal an infinite number of times.

The geometrically correct shape of crystals is determined, first of all, by their strictly regular internal structure. If, instead of atoms, ions or molecules in a crystal, we depict points as the centers of gravity of these particles, we get a three-dimensional regular distribution of such points, called a crystal lattice. The points themselves are called nodes crystal lattice.

Types of crystal lattices

Depending on what particles the crystal lattice is made of and what the nature of the chemical bond between them is, different types of crystals are distinguished.

Ionic crystals are formed by cations and anions (for example, salts and hydroxides of most metals). In them there is an ionic bond between the particles.

Ionic crystals may consist of monatomic ions. This is how crystals are built sodium chloride, potassium iodide, calcium fluoride.
The formation of ionic crystals of many salts involves monoatomic metal cations and polyatomic anions, for example, the nitrate ion NO 3? , sulfate ion SO 4 2? , carbonate ion CO 3 2? .

It is impossible to isolate single molecules in an ionic crystal. Each cation is attracted to each anion and repelled by other cations. The entire crystal can be considered a huge molecule. The size of such a molecule is not limited, since it can grow by adding new cations and anions.

Most ionic compounds crystallize in one of the structural types, which differ from each other in the value of the coordination number, that is, the number of neighbors around a given ion (4, 6 or 8). For ionic compounds with an equal number of cations and anions, four main types of crystal lattices are known: sodium chloride (the coordination number of both ions is 6), cesium chloride (the coordination number of both ions is 8), sphalerite and wurtzite (both structural types are characterized by the coordination number of the cation and anion equal to 4). If the number of cations is half the number of anions, then the coordination number of cations must be twice the coordination number of anions. In this case, the structural types of fluorite (coordination numbers 8 and 4), rutile (coordination numbers 6 and 3), and cristobalite (coordination numbers 4 and 2) are realized.

Typically ionic crystals are hard but brittle. Their fragility is due to the fact that even with slight deformation of the crystal, cations and anions are displaced in such a way that the repulsive forces between like ions begin to prevail over the attractive forces between cations and anions, and the crystal is destroyed.

Ionic crystals have high melting points. In the molten state, the substances that form ionic crystals are electrically conductive. When dissolved in water, these substances dissociate into cations and anions, and the resulting solutions conduct electric current.

High solubility in polar solvents, accompanied by electrolytic dissociation, is due to the fact that in a solvent environment with a high dielectric constant, the energy of attraction between ions decreases. The dielectric constant of water is 82 times higher than that of vacuum (conditionally existing in an ionic crystal), and the attraction between ions in an aqueous solution decreases by the same amount. The effect is enhanced by solvation of ions.

Atomic crystals consist of individual atoms held together by covalent bonds. Of the simple substances, only boron and group IVA elements have such crystal lattices. Often, compounds of non-metals with each other (for example, silicon dioxide) also form atomic crystals.

Just like ionic crystals, atomic crystals can be considered giant molecules. They are very durable and hard, and do not conduct heat and electricity well. Substances that have atomic crystal lattices melt at high temperatures. They are practically insoluble in any solvents. They are characterized by low reactivity.

Molecular crystals are built from individual molecules, within which the atoms are connected by covalent bonds. Weaker intermolecular forces act between molecules. They are easily destroyed, so molecular crystals have low melting points, low hardness, and high volatility. Substances that form molecular crystal lattices do not have electrical conductivity, and their solutions and melts also do not conduct electric current.

Intermolecular forces arise due to the electrostatic interaction of the negatively charged electrons of one molecule with the positively charged nuclei of neighboring molecules. The strength of intermolecular interactions is influenced by many factors. The most important among them is the presence of polar bonds, that is, a shift in electron density from one atom to another. In addition, intermolecular interactions are stronger between molecules with a larger number of electrons.

Most nonmetals in the form of simple substances (for example, iodine I 2 , argon Ar, sulfur S 8) and compounds with each other (for example, water, carbon dioxide, hydrogen chloride), as well as almost all solid organic substances form molecular crystals.

Metals are characterized by a metallic crystal lattice. It contains a metallic bond between atoms. In metal crystals, the nuclei of atoms are arranged in such a way that their packing is as dense as possible. The bonding in such crystals is delocalized and extends throughout the entire crystal. Metal crystals have high electrical and thermal conductivity, metallic luster and opacity, and easy deformability.

The classification of crystal lattices corresponds to limiting cases. Most crystals of inorganic substances belong to intermediate types - covalent-ionic, molecular-covalent, etc. For example, in a crystal graphite Within each layer, the bonds are covalent-metallic, and between the layers they are intermolecular.

Isomorphism and polymorphism

Many crystalline substances have the same structures. At the same time, the same substance can form different crystal structures. This is reflected in the phenomena isomorphism And polymorphism.

Isomorphism lies in the ability of atoms, ions or molecules to replace each other in crystal structures. This term (from the Greek " isos" - equal and " morphe" - form) was proposed by E. Mitscherlich in 1819. The law of isomorphism was formulated by E. Mitscherlich in 1821 in this way: “The same numbers of atoms, connected in the same way, give the same crystalline forms; Moreover, the crystalline form does not depend on the chemical nature of the atoms, but is determined only by their number and relative position.”

Working in the chemical laboratory of the University of Berlin, Mitscherlich drew attention to the complete similarity of the crystals of lead, barium and strontium sulfates and the similarity of the crystalline forms of many other substances. His observations attracted the attention of the famous Swedish chemist J.-Ya. Berzelius, who suggested that Mitscherlich confirm the observed patterns using the example of compounds of phosphoric and arsenic acids. As a result of the study, it was concluded that “the two series of salts differ only in that one contains arsenic as an acid radical, and the other contains phosphorus.” Mitscherlich's discovery very soon attracted the attention of mineralogists, who began research on the problem of isomorphic substitution of elements in minerals.

During the joint crystallization of substances prone to isomorphism ( isomorphic substances), mixed crystals (isomorphic mixtures) are formed. This is only possible if the particles replacing each other differ little in size (no more than 15%). In addition, isomorphic substances must have a similar spatial arrangement of atoms or ions and, therefore, similar crystals in external shape. Such substances include, for example, alum. In crystals of potassium alum KAl(SO 4) 2. 12H 2 O potassium cations can be partially or completely replaced by rubidium or ammonium cations, and aluminum cations by chromium (III) or iron (III) cations.

Isomorphism is widespread in nature. Most minerals are isomorphic mixtures of complex, variable composition. For example, in the mineral sphalerite ZnS, up to 20% of zinc atoms can be replaced by iron atoms (while ZnS and FeS have different crystal structures). Isomorphism is associated with the geochemical behavior of rare and trace elements, their distribution in rocks and ores, where they are contained in the form of isomorphic impurities.

Isomorphic substitution determines many useful properties of artificial materials of modern technology - semiconductors, ferromagnets, laser materials.

Many substances can form crystalline forms that have different structures and properties, but the same composition ( polymorphic modifications). Polymorphism- the ability of solids and liquid crystals to exist in two or more forms with different crystal structures and properties with the same chemical composition. This word comes from the Greek " polymorphos"- diverse. The phenomenon of polymorphism was discovered by M. Klaproth, who in 1798 discovered that two different minerals - calcite and aragonite - have the same chemical composition CaCO 3.

Polymorphism of simple substances is usually called allotropy, while the concept of polymorphism does not apply to non-crystalline allotropic forms (for example, gaseous O 2 and O 3). A typical example of polymorphic forms is modifications of carbon (diamond, lonsdaleite, graphite, carbines and fullerenes), which differ sharply in properties. The most stable form of existence of carbon is graphite, however, its other modifications under normal conditions can persist indefinitely. At high temperatures they turn into graphite. In the case of diamond, this occurs when heated above 1000 o C in the absence of oxygen. The reverse transition is much more difficult to achieve. Not only high temperature is required (1200-1600 o C), but also enormous pressure - up to 100 thousand atmospheres. The transformation of graphite into diamond is easier in the presence of molten metals (iron, cobalt, chromium and others).

In the case of molecular crystals, polymorphism manifests itself in different packing of molecules in the crystal or in changes in the shape of molecules, and in ionic crystals - in different relative positions of cations and anions. Some simple and complex substances have more than two polymorphs. For example, silicon dioxide has ten modifications, calcium fluoride - six, ammonium nitrate - four. Polymorphic modifications are usually denoted by the Greek letters b, c, d, d, f, ... starting with modifications that are stable at low temperatures.

When crystallizing from steam, solution or melt a substance that has several polymorphic modifications, a modification that is less stable under given conditions is first formed, which then turns into a more stable one. For example, when phosphorus vapor condenses, white phosphorus is formed, which under normal conditions slowly, but when heated, quickly turns into red phosphorus. When lead hydroxide is dehydrated, at first (about 70 o C) yellow b-PbO, which is less stable at low temperatures, is formed; at about 100 o C it turns into red b-PbO, and at 540 o C it turns back into b-PbO.

The transition from one polymorph to another is called polymorphic transformation. These transitions occur when temperature or pressure changes and are accompanied by an abrupt change in properties.

The process of transition from one modification to another can be reversible or irreversible. Thus, when a white soft graphite-like substance of composition BN (boron nitride) is heated at 1500-1800 o C and a pressure of several tens of atmospheres, its high-temperature modification is formed - borazon, close to diamond in hardness. When the temperature and pressure are lowered to values ​​corresponding to normal conditions, borazone retains its structure. An example of a reversible transition is the mutual transformations of two modifications of sulfur (orthorhombic and monoclinic) at 95 o C.

Polymorphic transformations can occur without significant changes in structure. Sometimes there is no change in the crystal structure at all, for example, during the transition of b-Fe to c-Fe at 769 o C, the structure of iron does not change, but its ferromagnetic properties disappear.

Chemical-thermal treatment (CHT) is a heat treatment consisting of a combination of thermal and chemical effects in order to change the composition, structure and properties of the surface layer of steel.

Chemical-thermal treatment is one of the most common types of processing of materials in order to impart operational properties to them. The most widely used methods are saturation of the surface layer of steel with carbon and nitrogen, both separately and together. These are the processes of carburization (carburization) of the surface, nitriding - saturation of the steel surface with nitrogen, nitrocarburization and cyanidation - the joint introduction of carbon and nitrogen into the surface layers of steel. Saturation of the surface layers of steel with other elements (chrome - diffusion chrome plating, boron - boriding, silicon - silicon plating and aluminum - aluminizing) is used much less frequently. The process of diffusion saturation of the surface of a part with zinc is called galvanizing, and with titanium - titanation.

The chemical-thermal treatment process is a multi-stage process that includes three successive stages:

1. Formation of active atoms in a saturating environment near the surface or directly on the surface of the metal. The power of the diffusion flow, i.e. the number of active atoms formed per unit time depends on the composition and state of aggregation of the saturating medium, which can be solid, liquid or gaseous, the interaction of individual components with each other, temperature, pressure and chemical composition of the steel.

2. Adsorption (sorption) of the formed active atoms by the saturation surface. Adsorption is a complex process that occurs on the saturation surface in a non-stationary manner. A distinction is made between physical (reversible) adsorption and chemical adsorption (chemisorption). During chemical-thermal treatment, these types of adsorption overlap each other. Physical adsorption leads to the adhesion of adsorbed atoms of the saturating element (adsorbate) to the formed surface (adsorbent) due to the action of van der Waals forces of attraction, and it is characterized by easy reversibility of the adsorption process - desorption. During chemisorption, an interaction occurs between the atoms of the adsorbate and the adsorbent, which is close to chemical in nature and strength.

3. Diffusion - movement of adsorbed atoms in the lattice of the metal being processed. The diffusion process is possible only if there is solubility of the diffusing element in the material being processed and a sufficiently high temperature to provide the energy necessary for the process to proceed. The thickness of the diffusion layer, and therefore the thickness of the hardened layer of the surface of the product, is the most important characteristic of chemical-thermal treatment. The thickness of the layer is determined by a number of factors such as saturation temperature, duration of the saturation process, steel composition, i.e. the content of certain alloying elements in it, the concentration gradient of the saturated element between the surface of the product and in the depth of the saturated layer.

The cutting tool operates under conditions of prolonged contact and friction with the metal being processed. During operation, the configuration and properties of the cutting edge must remain unchanged. The material for the manufacture of cutting tools must have high hardness (IKS 60-62) and wear resistance, i.e. the ability to maintain the cutting properties of the edge for a long time under friction conditions.

The greater the hardness of the processed materials, the thicker the chips and the higher the cutting speed, the greater the energy spent on the cutting process. Mechanical energy turns into thermal energy. The generated heat heats the cutter, the workpiece, and the chips and is partially dissipated. Therefore, the main requirement for tool materials is high heat resistance, i.e. the ability to maintain hardness and cutting properties during prolonged heating during operation. Based on heat resistance, there are three groups of tool steels for cutting tools: non-heat-resistant, semi-heat-resistant and heat-resistant.

When non-heat-resistant steels are heated to 200-300°C during the cutting process, carbon is released from the hardening martensite and coagulation of cementite-type carbides begins. This leads to loss of hardness and wear resistance of the cutting tool. Non-heat-resistant steels include carbon and low-alloy steels. Semi-heat-resistant steels, which include some medium-alloy steels, for example 9Kh5VF, retain hardness up to temperatures of 300-500°C. Heat-resistant steels retain their hardness and wear resistance when heated to temperatures of 600°C.

Carbon and low-alloy steels have relatively low heat resistance and low hardenability, so they are used for easier working conditions at low cutting speeds. High-speed steels, which have higher heat resistance and hardenability, are used for more severe working conditions. Carbide and ceramic materials allow even higher cutting speeds. Of the existing materials, boron nitride, elbor, has the greatest heat resistance. Elbor allows the processing of high-hardness materials, such as hardened steel, at high speeds.