Magnetic permeability. Magnetic properties of substances

The magnetic moment is the main vector quantity that characterizes the magnetic properties of a substance. Since the source of magnetism is a closed current, the value of the magnetic moment M defined as the product of the current strength I to the area covered by the current circuit S:

M = I×S A × m 2 .

The electron shells of atoms and molecules have magnetic moments. Electrons and other elementary particles have a spin magnetic moment determined by the existence of their own mechanical moment - spin. The spin magnetic moment of an electron can be oriented in an external magnetic field in such a way that only two equal and oppositely directed projections of the moment on the direction of the magnetic field vector are possible, equal to Bohr magneton- 9.274 × 10 -24 A × m 2.

1. Define the concept of "magnetization" of a substance.

Magnetization - J- is the total magnetic moment per unit volume of the substance:

1. Define the term "magnetic susceptibility".

Magnetic susceptibility of a substance, א v- the ratio of the magnetization of a substance to the strength of the magnetic field, per unit volume:

אv = , dimensionless quantity.

Specific magnetic susceptibility, א – the ratio of magnetic susceptibility to the density of a substance, i.e. magnetic susceptibility per unit mass, measured in m 3 /kg.

1. Define the term "magnetic permeability".

Magnetic permeability, μ – this is a physical quantity that characterizes the change in magnetic induction when exposed to a magnetic field . For isotropic media, the magnetic permeability is equal to the ratio of induction in the medium AT to the strength of the external magnetic field H and to the magnetic constant μ 0 :

Magnetic permeability is a dimensionless quantity. Its value for a particular medium is 1 more than the magnetic susceptibility of the same medium:

μ = אv+1, since B \u003d μ 0 (H + J).

1. Give a classification of materials according to their magnetic properties.

According to the magnetic structure and the value of magnetic permeability (susceptibility), materials are divided into:

Diamagnets μ< 1 (the material "resists" the magnetic field);

Paramagnets µ > 1(the material weakly perceives the magnetic field);

ferromagnets µ >> 1(the magnetic field in the material is amplified);

Ferrimagnets µ >> 1(the magnetic field in the material increases, but the magnetic structure of the material differs from the structure of ferromagnets);

Antiferromagnets μ ≈ 1(the material reacts weakly to a magnetic field, although the magnetic structure is similar to ferrimagnets).

1. Describe the nature of diamagnetism.

Diamagnetism is the property of a substance to be magnetized towards the direction of an external magnetic field acting on it (in accordance with the law of electromagnetic induction and Lenz's rule). Diamagnetism is characteristic of all substances, but in its "pure form" it manifests itself in diamagnets. Diamagnets are substances whose molecules do not have their own magnetic moments (their total magnetic moment is zero), so they have no other properties besides diamagnetism. Examples of diamagnets:

Hydrogen, א = - 2×10 -9 m 3 /kg.

Water, א = - 0.7×10 -9 m 3 /kg.

Diamond, א = - 0.5×10 -9 m 3 /kg.

Graphite, א = - 3×10 -9 m 3 /kg.

Copper = - 0.09×10 -9 m 3 /kg.

Zinc, א = - 0.17×10 -9 m 3 /kg.

Silver = - 0.18×10 -9 m 3 /kg.

Gold, א = - 0.14×10 -9 m 3 /kg.

43. Describe the nature of paramagnetism.

Paramagnetism is a property of substances called paramagnets, which, when placed in an external magnetic field, acquire a magnetic moment that coincides with the direction of this field. Atoms and molecules of paramagnets, unlike diamagnets, have their own magnetic moments. In the absence of a field, the orientation of these moments is chaotic (due to thermal motion) and the total magnetic moment of the substance is zero. When an external field is applied, the partial orientation of the magnetic moments of the particles in the direction of the field occurs, and the magnetization J is added to the strength of the external field H: B = μ 0 (H+J). The induction in the substance is enhanced. Examples of paramagnets:

Oxygen, א = 108×10 -9 m 3 /kg.

Titanium = 3×10 -9 m 3 /kg.

Aluminium, א = 0.6×10 -9 m 3 /kg.

Platinum, א = 0.97×10 -9 m 3 /kg.

44. Describe the nature of ferromagnetism.

Ferromagnetism is a magnetically ordered state of matter, in which all the magnetic moments of atoms in a certain volume of matter (domain) are parallel, which causes the spontaneous magnetization of the domain. The appearance of magnetic order is associated with the exchange interaction of electrons, which is of an electrostatic nature (Coulomb's law). In the absence of an external magnetic field, the orientation of the magnetic moments of different domains can be arbitrary, and the volume of matter under consideration can generally have a weak or zero magnetization. When a magnetic field is applied, the magnetic moments of the domains are oriented along the field the more, the higher the field strength. In this case, the value of the magnetic permeability of the ferromagnet changes and the induction in the substance increases. Examples of ferromagnets:

Iron, nickel, cobalt, gadolinium

and alloys of these metals between themselves and other metals (Al, Au, Cr, Si, etc.). μ ≈ 100…100000.

45. Describe the nature of ferrimagnetism.

Ferrimagnetism is a magnetically ordered state of matter, in which the magnetic moments of atoms or ions form in a certain volume of matter (domain) magnetic sublattices of atoms or ions with total magnetic moments that are not equal to each other and directed antiparallel. Ferrimagnetism can be considered as the most general case of a magnetically ordered state, and ferromagnetism as a case with one sublattice. The composition of ferrimagnets necessarily includes atoms of ferromagnets. Examples of ferrimagnets:

Fe 3 O 4 ; MgFe2O4; CuFe 2 O 4 ; MnFe 2 O 4 ; NiFe 2 O 4 ; CoFe2O4 …

The magnetic permeability of ferrimagnets is of the same order as that of ferromagnets: μ ≈ 100…100000.

46. ​​Describe the nature of antiferromagnetism.

Antiferromagnetism is a magnetically ordered state of a substance, characterized by the fact that the magnetic moments of neighboring particles of the substance are oriented antiparallel, and in the absence of an external magnetic field, the total magnetization of the substance is zero. An antiferromagnet in relation to the magnetic structure can be considered as a special case of a ferrimagnet in which the magnetic moments of the sublattices are equal in absolute value and antiparallel. The magnetic permeability of antiferromagnets is close to 1. Examples of antiferromagnets:

Cr2O3; manganese; FeSi; Fe 2 O 3 ; NIO……… μ ≈ 1.

47. What is the value of the magnetic permeability of materials in the superconducting state?

Superconductors below the supertransition temperature are ideal diamagnets:

א= - 1; μ = 0.

Magnetics

All substances in a magnetic field are magnetized (an internal magnetic field arises in them). Depending on the magnitude and direction of the internal field, substances are divided into:

1) diamagnets,

2) paramagnets,

3) ferromagnets.

The magnetization of a substance is characterized by magnetic permeability,

Magnetic induction in matter,

Magnetic induction in vacuum.

Any atom can be characterized by a magnetic moment .

The current in the circuit, - the area of ​​the circuit, - the vector of the normal to the surface of the circuit.

The microcurrent of an atom is created by the movement of negative electrons along the orbit and around its own axis, as well as by the rotation of the positive nucleus around its own axis.

1. Diamagnets.

When there is no external field, in atoms diamagnets electron and nucleus currents are compensated. The total microcurrent of an atom and its magnetic moment are equal to zero.

In an external magnetic field, nonzero elementary currents are induced (induced) in atoms. In this case, the magnetic moments of the atoms are oriented oppositely.

A small own field is created, directed oppositely to the external one, and weakening it.

in diamagnets.

Because< , то для диамагнетиков 1.

2. Paramagnets

AT paramagnets microcurrents of atoms and their magnetic moments are not equal to zero.

Without an external field, these microcurrents are located randomly.

In an external magnetic field, the microcurrents of paramagnetic atoms are oriented along the field, amplifying it.

In a paramagnet, the magnetic induction = + slightly exceeds .

For paramagnets, 1. For dia- and paramagnets, you can count 1.

Table 1. Magnetic permeability of para- and diamagnets.

The magnetization of paramagnets depends on temperature, because. the thermal motion of atoms prevents the ordered arrangement of microcurrents.

Most substances in nature are paramagnetic.

The intrinsic magnetic field in dia- and paramagnets is insignificant and is destroyed if the substance is removed from the external field (the atoms return to their original state, the substance is demagnetized).

3. Ferromagnets

Magnetic permeability ferromagnets reaches hundreds of thousands and depends on the magnitude of the magnetizing field ( highly magnetic substances).

Ferromagnets: iron, steel, nickel, cobalt, their alloys and compounds.

In ferromagnets, there are regions of spontaneous magnetization ("domains"), in which all microcurrents of atoms are oriented in the same way. The domain size reaches 0.1 mm.

In the absence of an external field, the magnetic moments of individual domains are randomly oriented and compensate. In the external field, those domains in which microcurrents enhance the external field increase their size at the expense of neighboring ones. The resulting magnetic field = + in ferromagnets is much stronger than in para- and diamagnets.

Domains containing billions of atoms have inertia and do not quickly return to their original disordered state. Therefore, if a ferromagnet is removed from the external field, then its own field is preserved for a long time.

The magnet demagnetizes during long-term storage (over time, the domains return to a chaotic state).

Another method of demagnetization is heating. For each ferromagnet, there is a temperature (it is called the “Curie point”) at which bonds between atoms are destroyed in the domains. In this case, the ferromagnet turns into a paramagnet and demagnetization occurs. For example, the Curie point for iron is 770°C.

called magnetic permeability . Absolute magneticpermeability environment is the ratio of B to H. According to the International System of Units, it is measured in units called 1 henry per meter.

Its numerical value is expressed by the ratio of its value to the value of the magnetic permeability of the vacuum and is denoted by µ. This value is called relative magneticpermeability(or simply magnetic permeability) of the medium. As a relative quantity, it has no unit of measure.

Therefore, the relative magnetic permeability µ is a value showing how many times the field induction of a given medium is less (or more) than the vacuum magnetic field induction.

When a substance is exposed to an external magnetic field, it becomes magnetized. How does this happen? According to Ampere's hypothesis, microscopic electric currents constantly circulate in every substance, caused by the movement of electrons in their orbits and the presence of their own. Under normal conditions, this movement is disordered, and the fields “quench” (compensate) each other. When a body is placed in an external field, the currents are ordered, and the body becomes magnetized (that is, it has its own field).

The magnetic permeability of all substances is different. Based on its size, substances are subject to division into three large groups.

At diamagnets the value of the magnetic permeability µ is slightly less than unity. For example, bismuth has µ = 0.9998. Diamagnets include zinc, lead, quartz, copper, glass, hydrogen, benzene, and water.

Magnetic permeability paramagnets slightly more than unity (for aluminum, µ = 1.000023). Examples of paramagnets are nickel, oxygen, tungsten, ebonite, platinum, nitrogen, air.

Finally, the third group includes a number of substances (mainly metals and alloys), whose magnetic permeability significantly (by several orders of magnitude) exceeds unity. These substances are ferromagnets. These mainly include nickel, iron, cobalt and their alloys. For steel µ = 8∙10^3, for nickel-iron alloy µ=2.5∙10^5. Ferromagnets have properties that distinguish them from other substances. First, they have residual magnetism. Secondly, their magnetic permeability depends on the magnitude of the induction of the external field. Thirdly, for each of them there is a certain temperature threshold, called Curie point, at which it loses its ferromagnetic properties and becomes a paramagnet. For nickel the Curie point is 360°C, for iron it is 770°C.

The properties of ferromagnets are determined not only by the magnetic permeability, but also by the value of I, called magnetization of this substance. This is a complex nonlinear function of magnetic induction, the growth of magnetization is described by a line called magnetization curve. In this case, having reached a certain point, the magnetization practically stops growing (there comes magnetic saturation). The lagging of the value of the magnetization of a ferromagnet from the growing value of the induction of the external field is called magnetic hysteresis. In this case, there is a dependence of the magnetic characteristics of a ferromagnet not only on its current state, but also on its previous magnetization. The graphic representation of the curve of this dependence is called hysteresis loop.

Due to their properties, ferromagnets are widely used in engineering. They are used in the rotors of generators and electric motors, in the manufacture of transformer cores and in the production of parts for electronic computers. ferromagnets are used in tape recorders, telephones, magnetic tapes and other media.

6. MAGNETIC MATERIALS

All substances are magnetic and are magnetized in an external magnetic field.

According to their magnetic properties, materials are subdivided into weakly magnetic ( diamagnets and paramagnets) and strongly magnetic ( ferromagnets and ferrimagnets).

Diamagnetsμ r < 1, значение которой не зависит от напряженности внешнего магнитного поля. Диамагнетиками являются вещества, атомы (молекулы) которых в отсутствие намагничивающего поля имеют магнитный момент равный нулю: водород, инертные газы, большинство органических соединений и некоторые металлы ( Cu , Zn , Ag , Au , Hg ) and also AT i, Ga, Sb.

Paramagnets- substances with magnetic permeabilityμ r> 1, which in weak fields does not depend on the strength of the external magnetic field. Paramagnets include substances whose atoms (molecules) in the absence of a magnetizing field have a magnetic moment other than zero: oxygen, nitric oxide, salts of iron, cobalt, nickel and rare earth elements, alkali metals, aluminum, platinum.

For diamagnets and paramagnets, the magnetic permeabilityμ rclose to unity. Application in engineering as magnetic materials is limited.

In highly magnetic materials, the magnetic permeability is much greater than unity (μ r >> 1) and depends on the strength of the magnetic field. These include: iron, nickel, cobalt and their alloys, as well as chromium and manganese alloys, gadolinium, ferrites of various compositions.

6.1. Magnetic characteristics of materials

The magnetic properties of materials are evaluated by physical quantities called magnetic characteristics.

Magnetic permeability

Distinguish relative and absolute magnetic permeability substances (material) that are interconnected by the ratio

μ a = μ o μ, H/m

μois the magnetic constant,μo = 4π 10 -7 Gn/m;

μ – relative magnetic permeability (dimensionless value).

To describe the properties of magnetic materials, relative magnetic permeability is usedμ (more commonly referred to as magnetic permeability), and for practical calculations use the absolute magnetic permeabilityμ a, calculated by the equation

μ a = AT /H,H/m

H– strength of the magnetizing (external) magnetic field, A/m

AT – magnetic field induction in a magnet.

Big valueμ shows that the material is easily magnetized in weak and strong magnetic fields. The magnetic permeability of most magnets depends on the strength of the magnetizing magnetic field.

To characterize the magnetic properties, a dimensionless quantity is widely used, called magnetic susceptibility χ .

μ = 1 + χ

Temperature coefficient of magnetic permeability

The magnetic properties of matter depend on temperatureμ = μ (T) .

To describe the nature of the changemagnetic properties with temperatureuse the temperature coefficient of magnetic permeability.

Dependence of the magnetic susceptibility of paramagnets on temperatureTdescribed by the Curie law

where C - Curie constant .

Magnetic characteristics of ferromagnets

The dependence of the magnetic properties of ferromagnets has a more complex character, shown in the figure, and reaches a maximum at a temperature close toQ to.

The temperature at which the magnetic susceptibility decreases sharply, almost to zero, is called the Curie temperature -Q to. At temperatures aboveQ to the process of magnetization of a ferromagnet is disturbed due to the intense thermal motion of atoms and molecules, and the material ceases to be ferromagnetic and becomes a paramagnet.

For iron Q k = 768 ° C , for nickel Q k = 358 ° C , for cobalt Q k = 1131 ° C.

Above the Curie temperature, the dependence of the magnetic susceptibility of a ferromagnet on temperatureTdescribed by the Curie-Weiss law

The process of magnetization of highly magnetic materials (ferromagnets) has hysteresis. If a demagnetized ferromagnet is magnetized in an external field, then it is magnetized along magnetization curve B = B(H) . If then, starting from some valueHstart to reduce the field strength, then inductionBwill decrease with some delay ( hysteresis) with respect to the magnetization curve. With an increase in the field of the opposite direction, the ferromagnet is demagnetized, then remagnetizes, and with a new change in the direction of the magnetic field, it can return to the starting point, from where the demagnetization process began. The resulting loop shown in the figure is called hysteresis loop.

At some maximum tensionH m magnetizing field, the substance is magnetized to a state of saturation, in which the induction reaches the valueAT H , which is calledsaturation induction.

Residual magnetic induction AT O – observed in a ferromagnetic material, magnetized to saturation, when it is demagnetized, when the magnetic field strength is zero. To demagnetize a material sample, it is necessary that the magnetic field strength reverses its direction (-H). Field strengthH To , for which the induction is zero, is called coercive force(holding force) .

The magnetization reversal of a ferromagnet in alternating magnetic fields is always accompanied by thermal energy losses, which are due to hysteresis loss and dynamic losses. Dynamic losses are related to the eddy currents induced in the volume of the material and depend on the electrical resistance of the material, decreasing with increasing resistance. Hysteresis lossW in one cycle of magnetization reversal determined by the area of ​​the hysteresis loop

and can be calculated for a unit volume of a substance by the empirical formula

J / m 3

where η - coefficient depending on the material,B H is the maximum induction achieved during the cycle,n- exponent equal to 1.6 depending on the material¸ 2.

Specific energy losses due to hysteresis R G – losses spent on the magnetization reversal of a unit mass in a unit volume of material per second.

where f – AC frequency,Tis the period of oscillation.

Magnetostriction

Magnetostriction - the phenomenon of changing the geometric dimensions and shape of a ferromagnet with a change in the magnitude of the magnetic field, i.e. during magnetization. Relative change in material dimensionsΔ l/ lcan be positive and negative. For nickel, the magnetostriction is less than zero and reaches a value of 0.004%.

In accordance with Le Chatelier's principle on the system's resistance to the influence of external factors that tend to change this state, the mechanical deformation of a ferromagnet, leading to a change in its size, should affect the magnetization of these materials.

If, during magnetization, the body experiences a reduction in its size in a given direction, then the application of mechanical compressive stress in this direction contributes to magnetization, and tension makes it difficult to magnetize.

6.2. Classification of ferromagnetic materials

All ferromagnetic materials can be divided into two groups according to their behavior in a magnetic field.

Soft magnetic – with high magnetic permeabilityμ and small coercive forceH To< 10A / m. They are easily magnetized and demagnetized. They have low hysteresis losses, i.е. narrow hysteresis loop.

The magnetic characteristics depend on the chemical purity and the degree of distortion of the crystal structure. The less impurities(FROM, R, S, O, N ) , the higher the level of characteristics of the material, therefore, it is necessary to remove them and oxides in the production of a ferromagnet, and try not to distort the crystal structure of the material.

Hard magnetic materials - have greatH K > 0.5 MA/m and residual induction (AT O ≥ 0.1T). They correspond to a wide hysteresis loop. They are magnetized with great difficulty, but they can store magnetic energy for several years, i.e. serve as a source of a constant magnetic field. Therefore, permanent magnets are made from them.

By composition, all magnetic materials are divided into:

· metal;

· non-metallic;

· magnetodielectrics.

Metal magnetic materials - these are pure metals (iron, cobalt, nickel) and magnetic alloys of some metals.

to non-metallic materials include ferrites, obtained from powders of iron oxides and other metals. They are pressed and fired at 1300 - 1500 ° C and they turn into solid monolithic magnetic parts. Ferrites, like metallic magnetic materials, can be magnetically soft and magnetically hard.

Magnetodielectrics – these are composite materials from 60 - 80% magnetic material powder and 40 - 20% organic dielectric. Ferrites and magnetodielectrics have a great value of electrical resistivity (ρ \u003d 10 ÷ 10 8 Ohm m), The high resistance of these materials ensures low dynamic energy losses in alternating electromagnetic fields and allows them to be widely used in high-frequency technology.

6.3. Metal magnetic materials

6.3.1. metal soft magnetic materials

Metallic soft magnetic materials include carbonyl iron, permalloys, alsifers, and low-carbon silicon steels.

carbonyl iron – obtained by thermal decomposition of liquid iron pentacarbonylF e( CO ) 5 to obtain particles of pure powdered iron:

F e( CO ) 5 → Fe+ 5 CO,

at a temperature of about 200°Сand a pressure of 15 MPa. Iron particles are spherical, 1–10 µm in size. To get rid of carbon particles, iron powder is subjected to heat treatment in an environment H 2 .

The magnetic permeability of carbonyl iron reaches 20000, the coercive force is 4.5¸ 6,2A / m. Iron powder is used to make high-frequency magnetodielectric cores, as a filler in magnetic tapes.

Permalloys -ductile iron-nickel alloys. To improve the properties, enter Mo, FROM r, Cu, obtaining doped permalloys. They have high plasticity, they are easily rolled into sheets and strips up to 1 micron.

If the nickel content in permalloy is 40 - 50%, then it is called low-nickel, if 60 - 80% - high-nickel.

Permalloys have a high level of magnetic characteristics, which is ensured not only by the composition and high chemical purity of the alloy, but also by special thermal vacuum treatment. Permalloys have a very high level of initial magnetic permeability from 2000 to 30000 (depending on the composition) in the region of weak fields, which is due to the low value of magnetostriction and the isotropy of magnetic properties. Supermalloy has especially high characteristics, the initial magnetic permeability of which is 100,000, and the maximum reaches 1.5 10 6 at B= 0.3 T

Permalloys are supplied in the form of strips, sheets and rods. Low-nickel permalloys are used for the manufacture of inductor cores, small-sized transformers and magnetic amplifiers, high-nickel permalloys – for parts of equipment operating at sonic and supersonic frequencies. The magnetic characteristics of permalloys are stable at –60 +60°C.

alsifera – non malleable brittle alloys of composition Al – Si– Fe , consisting of 5.5 - 13%Al, 9 – 10 % Si, the rest is iron. Alsifer is close in properties to permalloy, but cheaper. Cast cores are made from it, magnetic screens and other hollow parts with a wall thickness of at least 2–3 mm are cast. The fragility of alsifer limits the scope of its application. Using the brittleness of alsifer, it is ground into powder, which is used as a ferromagnetic filler in pressed high-frequency magnetodielectrics(cores, rings).

Silicon low carbon steel (electrical steel) – alloy of iron and silicon (0.8 - 4.8%Si). The main magnetically soft material of mass application. It is easily rolled into sheets and strips of 0.05 - 1 mm and is a cheap material. Silicon, which is in the steel in a dissolved state, performs two functions.

· By increasing the resistivity of steel, silicon causes a decrease in dynamic losses associated with eddy currents. The resistance is increased by silica formation SiO 2 as a result of the reaction

2 FeO + Si→ 2Fe+ SiO 2 .

· The presence of silicon dissolved in steel contributes to the decomposition of cementite Fe 3 C - a harmful impurity that reduces the magnetic characteristics, and the release of carbon in the form of graphite. In this case, pure iron is formed, the growth of crystals of which increases the level of magnetic characteristics of steel.

The introduction of silicon into steel in an amount exceeding 4.8% is not recommended, since, by improving the magnetic characteristics, silicon sharply increases the brittleness of the steel and reduces its mechanical properties.

6.3.2. Metallic hard magnetic materials

Hard magnetic materials - these are ferromagnets with a high coercive force (more than 1 kA / m) and a large value of residual magnetic inductionAT O. They are used to make permanent magnets.

They are divided depending on the composition, condition and method of obtaining into:

· alloyed martensitic steels;

· cast hard magnetic alloys.

Alloy martensitic steels – this is about carbon steels and steels, alloyedCr, W, Co, Mo . carbonaceous become aging quickly and change their properties, so they are rarely used for the manufacture of permanent magnets. For the manufacture of permanent magnets, alloyed steels are used - tungsten and chromium (HС ≈ 4800 A / m,AT About ≈ 1 T), which are made in the form of bars with various cross-sectional shapes. Cobalt steel has a higher coercive force (HС ≈ 12000 A / m,AT About ≈ 1 T) compared with tungsten and chromium. Coercive force H FROM cobalt steel increases with increasing content FROM about .

Cast hard magnetic alloys. The improved magnetic properties of the alloys are due to a specially selected composition and special processing - cooling the magnets after casting in a strong magnetic field, as well as a special multi-stage heat treatment in the form of quenching and tempering in combination with magnetic treatment, called precipitation hardening.

For the manufacture of permanent magnets, three main groups of alloys are used:

· Iron - cobalt - molybdenum alloy type remalloy with coercive forceH K \u003d 12 - 18 kA / m.

· Alloy group:

§ copper - nickel - iron;

§ copper - nickel - cobalt;

§ iron - manganese, dopedaluminum or titanium;

§ iron - cobalt - vanadium (F e- Co - V).

An alloy of copper-nickel-iron is called kunife (FROM u– Ni - Fe). Alloy F e– Co – V (iron - cobalt - vanadium) is called wicala . The alloys of this group have a coercive force H To = 24 – 40 kA/m. Are issued in the form of a wire and in sheets.

· System Alloys iron - nickel - aluminum(F e – Ni– Al), formerly known as alloy alni. The alloy contains 20 - 33% Ni + 11 - 17% Al, the rest is iron. The addition of cobalt, copper, titanium, silicon, niobium to alloys improves their magnetic properties, facilitates manufacturing technology, ensures the repeatability of parameters, and improves mechanical properties. The modern marking of the brand contains letters indicating the added metals (Yu - aluminum, N - nickel, D - copper, K - cobalt, T - titanium, B - niobium, C - silicon), numbers - the content of the element, the letter of which comes before the number, for example, UNDK15.

Alloys have a high value of coercive force H To = 40 - 140 kA/m and a large stored magnetic energy.

6.4. Non-metallic magnetic materials. Ferrites

Ferrites are ceramic ferromagnetic materials with low electronic electrical conductivity. Low electrical conductivity combined with high magnetic characteristics allows ferrites to be widely used at high frequencies.

Ferrites are made from a powder mixture consisting of iron oxide and specially selected oxides of other metals. They are pressed and then sintered at high temperatures. The general chemical formula is:

Meo Fe 2 O 3 or MeFe 2 O 4,

where Medivalent metal symbol.

For example,

ZnO Fe 2 O 3 or

NiO Fe 2 O 3 or NiFe 2 O 4

Ferrites have a cubic spinel-type latticeMgOAl 2O3 - magnesium aluminate.Not all ferrites are magnetic. The presence of magnetic properties is associated with the arrangement of metal ions in the cubic spinel lattice. So systemZnFe 2 O 4 does not have ferromagnetic properties.

Ferrites are made using ceramic technology. The initial powdered metal oxides are crushed in ball mills, pressed and fired in furnaces. The sintered briquettes are ground into a fine powder, a plasticizer is added, for example, a solution of polyvinyl alcohol. From the resulting mass, ferrite products are pressed - cores, rings, which are fired in air at 1000 - 1400 ° C. The resulting hard, brittle products, mostly black, can only be processed by grinding and polishing.

Soft magnetic ferrites

Soft magneticferrites are widely used in the field of high frequencies of electronic engineering and instrumentation for the manufacture of filters, transformers for low and high frequency amplifiers, antennas for radio transmitting and radio receiving devices, pulse transformers, and magnetic modulators. The industry produces the following types of soft magnetic ferrites with a wide range of magnetic and electrical properties: nickel - zinc, manganese - zinc and lithium - zinc. The upper limiting frequency of the use of ferrite depends on their composition and varies for different grades of ferrites from 100 kHz to 600 MHz, the coercive force is about 16 A / m.

The advantage of ferrites is the stability of magnetic characteristics, the relative ease of manufacture of radio components. Like all ferromagnetic materials, ferrites retain their magnetic properties only up to the Curie temperature, which depends on the composition of the ferrites and ranges from 45° to 950°C.

Hard magnetic ferrites

For the manufacture of permanent magnets, hard magnetic ferrites are used; barium ferrites (VAO 6 Fe 2 O 3 ). They have a hexagonal crystal structure with a largeH To . Barium ferrites are a polycrystalline material. They can be isotropic - the similarity of the properties of ferrite in all directions is due to the fact that the crystalline particles are arbitrarily oriented. If, during the pressing of magnets, the powdery mass is exposed to an external magnetic field of high intensity, then the crystalline ferrite particles will be oriented in one direction, and the magnet will be anisotropic.

Barium ferrites are distinguished by good stability of their characteristics, but are sensitive to temperature changes and mechanical stress. Barium ferrite magnets are cheap.

6.5. Magnetodielectrics

Magnetodielectrics - these are composite materials consisting of finely dispersed particles of a magnetically soft material connected to each other by an organic or inorganic dielectric. Carbonyl iron, alsifer, and some grades of permalloy, crushed to a powder state, are used as soft magnetic materials.

Polystyrene, bakelite resins, liquid glass, etc. are used as dielectrics.

The purpose of the dielectric is not only to connect the particles of the magnetic material, but also to isolate them from each other, and, consequently, to sharply increase the electrical resistivity magnetodielectric. Specific electrical resistancermagnetodielectricsis 10 3 – 10 4 ohm× m

Magnetodielectricsused for the manufacture of cores of high-frequency components of radio equipment. The production process of products is simpler than from ferrites, because. they do not require high temperature heat treatment. Products from magnetodielectrics are characterized by high stability of magnetic properties, high class of surface finish and dimensional accuracy.

The highest magnetic characteristics are possessed by magnetodielectrics filled with molybdenum permalloy or carbonyl iron.

The total magnetic flux penetrating all the turns is called the flux linkage of the circuit.

If all the turns are the same, then the total magnetic flux, i.e. flux linkage:

where
- magnetic flux through one turn; - number of turns. Therefore, the flux linkage of the solenoid, for example, during induction AT=0,2 T, number of turns of the solenoid
and section of the solenoid window
dm 2 will be Wb.

Absolute magnetic permeability measured in units "henry per meter"
.

Magnetic permeability vacuum in the SI system of units is taken equal to
H/m

Attitude
absolute magnetic permeability to the magnetic permeability of vacuum is called the relative magnetic permeability .

According to the value  All materials are divided into three groups:

If dia- and paramagnetic substances are placed in a uniform magnetic field, then in a diamagnetic one the field will be weakened, and in a paramagnetic one it will be amplified. This is explained by the fact that in a diamagnetic substance the fields of elementary currents are directed towards the external field, and in a paramagnetic substance - according to it.

In table. 1 shows the values ​​of the relative magnetic permeability of some materials. It can be seen that the values ​​of the relative magnetic permeability of diamagnetic and paramagnetic materials differ very little from unity, therefore, for practice, their magnetic permeability is assumed to be unity.

Field strength dimension H(Table 2):

.

1 car - is the intensity of such a magnetic field, the induction of which in vacuum is equal to
Tl.

Table 1. Relative magnetic permeability of some materials

Sometimes the field strength is also measured in

"oerstedach" (E),

"amps per centimeter" (A / cm),

"kiloamperes per meter" (kA/m).

The relationship between these values ​​is as follows:

1 A/cm = 100 A/m; 1 E \u003d 0.796 A / cm; 1 kA/m = 10 A/cm;

1 A/cm = 0.1 kA/m; 1 E \u003d 79.6 A / cm; 1 kA/m = 12.56 Oe;

1 A/cm = 1.256 Oe; 1 E \u003d 0.0796 kA / cm; 1 kA/m = 1000 A/m.

It is interesting to know the strengths of some magnetic fields.

The intensity of the Earth's field in the Moscow region is 0.358 A/cm.

The field strength for magnetization of structural steel parts is 100...200 A/cm,

on the poles of a permanent magnet - 1000 ... 2000 A / cm.

Sometimes they use the so-called magnetic moment
circuits with current . It is equal to the product of the current To the square , bounded by a contour
(Fig. 4).

When a magnet is divided into parts, each of them is a magnet with two poles. This can be seen from fig. 5. According to the table. 2 it can be determined that one unit of magnetic moment is equal to 1
m 2 \u003d 1
. This unit is called "ampere-square meter". An ampersquare meter is the magnetic moment of a circuit through which a current of 1 A flows and which limits an area equal to 1 m 2.

Rice. 4. Circuit (1) with current ; Rice. 5. Division of a permanent magnet into parts.

2 - current source:

- magnetic moment;

- field strength.

Table 2. Basic and derived units of measurement of the SI system used in non-destructive testing

Electron magnetic moment equals

, because
, a
,
.

Relatively recently, the interaction of the poles of magnets was explained by the presence of a special substance - magnetism. With the development of science, it was shown that no substance exists. The source of magnetic fields are electric currents. Therefore, when a permanent magnet is divided in each piece, electron currents create a magnetic field (Fig. 5). The magnetic charge is considered only assome mathematical quantity that does not have a physicalcal content.

The unit of magnetic charge can be obtained by the formula:

,
,

where - work on bypassing the magnetic pole around the conductor with current .

One conventional unit of magnetic charge will be
.

In the Gaussian system, a unit of magnetic charge is taken to be such a value that acts on an equal magnetic charge at a distance of 1 cm in vacuum with a force equal to 1 dyne.

The ability of materials to be magnetized is explained by the existence of currents in them:

the rotation of an electron around the nucleus in an atom,

around its own axes (electron spin) and

rotation of electron orbits (precession of electron orbits) (Fig. 6).

The ferromagnetic material consists of small regions (with linear dimensions of about 0.001 mm) in which elementary currents are directed spontaneously. These areas of spontaneous magnetization are called domains. In each domain, a resulting field of elementary currents is formed.

In a demagnetized material, the magnetic fields of the domains are chaotically directed and compensate each other so that the resulting field in the part is almost zero.

As a result of external action, the fields of individual regions (domains) are set in the direction of the external field, and thus a strong field of the magnetized part is formed.

Consequently, magnetization - is the degree oflaced orientation magnetic fields of domains in a metal, or otherwise, this is an induction created by elementary currents.

Since elementary currents have magnetic moments, magnetization is also defined as the ratio of the total magnetic moment of the body to its volume, i.e.:

.

Magnetization measured in "amps per meter" (A/m).

Sign-variable loading of the metal structure, for example, in continuously operating turbine blades, in bolts, etc. parts leads to a certain ordering of the internal magnetic field in the loading zone, to the appearance of traces of this field on the surface of the part. This phenomenon is used to estimate the residual life, to determine mechanical stresses.

Magnetization part to be tested depends on the field strength
, acting on this part. The ferromagnetic properties of the material also depend on temperature. For each ferromagnetic material, there is a temperature at which regions of spontaneous magnetization are destroyed by thermal motion and the ferromagnetic material becomes paramagnetic. This temperature is called the Curie point. The Curie point for iron is 753 0 C. When this temperature drops below this point, the magnetic properties are restored.

Rice. 6. Types of elementary currents:

a - the movement of electron 1 around the nucleus 4;

b - rotation of an electron around its axis;

c - precession of the electron orbit;

5 - electronic orbit;

6 - plane of the electron orbit;

8 - trajectory of the precessional motion of the electron orbit.

Induction the resulting field of the part can be determined by the well-known formula:

,

where - magnetization, i.e. induction created by molecular currents;
is the strength of the external field. From the above formula, it can be seen that the induction in the part is the sum of two components:
- determined by the external field
and - magnetization, which also depends on
.

On fig. 7 shows dependencies
, and
ferromagnetic material from the strength of the external field.

Rice. 7. Dependence of magnetic induction and magnetization from the magnetizing field
.

Curve
shows that at relatively weak fields, the magnetization grows very quickly (section a-b) . Then growth slows down (section b-c) . Further growth decreasing, curve
goes into a straight line , having a slight inclination to the horizontal axis
. At the same time, the value
gradually approaching its limit
. Component
varies in proportion to the field strength
. On fig. 7 this dependence is shown by a straight line o-e .

To get the magnetic induction curve on the strength of the external field, it is necessary to add the corresponding ordinates of the curves
and
. This dependence is represented by a curve
, called the initial magnetization curve. Unlike magnetization, magnetic induction grows as long as the value
, since after the growth of the magnetization stops, the quantity
continues to increase proportionately
.

The remagnetization of the part occurs by an alternating or periodically changing in direction constant field.

On fig. 8 shows the complete magnetic response of the sample - the hystresis loop. In the initial state, the sample is demagnetized. The current in the winding is increased in a straight line 0-8 . The strength of the field created by this current changes in a straight line 0-1. At the same time, the induction and magnetization in the sample will increase along the curves of the initial magnetization 16 and 17 to points 16 "and 17", corresponding to magnetic saturation, in which all magnetic fields of domains are directed along the external field.

With a decrease in current in a straight line 8-9 the field strength decreases by 1-0 (Fig. 8, a). At the same time, the induction and magnetization change to value .

As the current increases in the negative direction by 9-10, the field strength also increases in the negative direction by 0-2 , remapping the sample.

At point 6 induction
, because
, those.
. Field strength corresponding to point 6 , called the coercive force
by induction.

At the point 4 magnetization
, a
.

The field strength corresponding to point 4, called the coercive force H si by magnetization. With magnetic control, the coercive force is calculated
.

With a further increase in the field strength to point 2, the induction and magnetization reach the greatest negative values
and
(points 16" and 17") corresponding to magnetic saturation
sample. With decreasing current in a straight line 10-11 induction and magnetization will take values ​​corresponding to
.

Thus, as a result of changing the external field
along 0-1, 1-0, 0-2, 2-0 (Fig. 8), and the magnetic state of the sample changes along a closed curve - a magnetic hysteresis loop.

Rice. 8. Induction dependence and magnetization from tension
(a), change in current in the magnetization winding (b).

The magnetic hysteresis loop determines the following characteristics used in magnetic testing:

H t - the maximum magnetic field strength at which the saturation state of the sample is reached;

AT r - residual induction in the sample after removing the field;

H With - coercive force is the strength of the magnetic field that must be applied opposite to the magnetization of the sample in order to completely demagnetize it;

AT t - technical saturation induction. It is considered to be AT t = 0,95 B max, where B max- theoretically possible saturation induction of the initial magnetization.

If a ferromagnetic body is exposed to fields of the same sign, then the hysteresis loop, which in this case is asymmetric about the origin, is called private (Fig. 9).

There are static and dynamic hysteresis loops.

Static hysteresis loop is called a loop obtained by slowly changing H, at which the effect of eddy currents can be neglected.

Dynamic hysteresis loop called a loop obtained by periodically changing H with some finite speed at which the influence of eddy currents becomes significant. This results in a dynamic loop having a much larger width than a static loop. With an increase in the amplitude of the applied voltage, the width of the dynamic hysteresis loop increases.

On fig. 10 shows the dependency
. At H=0 the magnetic permeability is equal to its initial value.

Rice. 9. Asymmetric hysteresis loops 1-3 - intermediate loops; 4 - limit loop; 5 - initial magnetization curve.

Along the magnetization curve H(H) absolute magnetic permeability in a given field H defined as
, and relative as
.

The differential magnetic permeability is often mentioned:

.

The first of them is equal to the tangent of the slope of the line 1, and the second is equal to the tangent of the slope of the tangent 2.

The magnetomotive force (mfs) is equal to F = Iw, current product I in the winding for its number of turns.

The magnetic flux is:

where F - MDS, measured in ampere-turns; l Wed- length of the center line of the magnetic circuit, m; S - cross section of the magnetic circuit, m 2.

Value
determines the magnetic resistance R m .

Rice. 10. Magnetic permeability , and induction AT field strength
:
,
;
.

Magnetic flux is directly proportional to current I and inversely proportional to the magnetic resistance R m . Suppose we need to determine the current strength in a toroidal winding of 10 turns of cable to magnetize a bearing ring with an induction of 1 T.

Using the formula Ф = F/ R m , find:

The field pattern around the conductor is a concentric circle centered on the axis of the conductor (Fig. 11).

Rice. 11. Powder distribution pattern (a) and induction around a conductor with current (b)

The direction of the field around a conductor or a solenoid created by coils of cable can be determined by the gimlet rule.

If you place the corkscrew along the axis of the conductor and rotate it clockwise so that its translational movement coincides with the direction of the current in the conductor, then the direction of rotation of the corkscrew handle will indicate the direction of the field.

Change in field strength H inside and outside conductor 3 when a direct current passes through it from a distance from the measuring point to the axis of the conductor with a radius shown in fig. 12.

Fig.12. The distribution of the field strength H inside (1) and outside (2) of the current-carrying conductor.

From where it can be seen that the field on the axis of the conductor is zero, and inside the conductor (at > ) it changes linearly:

,

and outside of it (with > ) by hyperbole
, where - distance from the conductor axis to the measurement point, m; - current in the conductor, A.

If the field strength is given H at a point located at a distance from the axis of the wire, then to obtain this intensity, the current strength is determined using the formula:

,

where H[A/m], [m].

If a current carrying conductor passes through a hollow part, for example, a bearing ring, then, unlike the previous case, the induction sharply increases in the zone of the ferromagnetic part (Fig. 13).

Rice. 13- Induction during magnetization of the part when current is passed through the central conductor.

The field changes in areas: 0-1 in law H =0 ; 1-2 by law
; 2-3 by law
.

Magnetic induction B changes: in section 0-2 according to the law
; in sections 2-3; 6-7 by law
.

Induction jumps AT in sections 3-4; 5-6 due to the ferromagnetism of the part 8 (- conductor radius; - distance from the center of the conductor).

Let us assume that a cylindrical hollow part is magnetized by a central conductor. Determine the current strength in the conductor to obtain induction AT= 12.56 mT on the inner surface of a part with a diameter of 80 mm.

The strength of the current in the conductor is determined by the formula:

Field distribution inside and outside the hollow part 4, magnetized by passing a current through it, shown in Fig. 14. It can be seen that the field inside the part with a radius R 1 equals zero. Field in plot 1-2 (inside the part material) varies according to the law

and in section 2-3 - in law
. This formula determines the field strength on the outer surface of the part or at some distance from it.

Rice. 14. Field distribution H inside and outside the part.

If a current of 200.0 A is passed through a cylindrical part with a diameter of 50 mm and it is necessary to determine the field strength at points located at a distance of 100 mm from the surface of the part. The field strength at a distance of 100 mm from the surface of the part is determined by the formula:

.

The field strength on the surface of the part will be:

.

On fig. 15 shows a diagram of the magnetic field around and inside the solenoid. The figure also shows that the magnetic lines of force inside the solenoid are directed along its longitudinal axis. At the output windows of the solenoid, magnetic poles are formed N and S.

The field strength in the center on the axis at the edge of the solenoid is determined by the above formulas.

The field strength at the center of the coil with radius R determined by the formula H = I/ R, A / m, where I- current in the coil of the conductor, A.

If it is necessary to determine the field strength in the center of the attached solenoid with a current of 200 A, and at the same time the number of turns w = = -6, length 210 mm, diameter 100 mm, then the field strength will be:

.

If the current in the solenoid is 200 A, and the length of the solenoid is 400 mm, the diameter is 100 mm, the number of turns is 8,
,
(see Fig. 15), then it is possible to calculate the strength at individual points of the solenoid.

The field strength distribution inside the solenoid is:

a - in the center of the solenoid:

,

where H - field strength in center of the solenoid, A/cm; l, With- length and radius of the solenoid, cm; w- number of turns;

b - on the axis of the solenoid:

,

where l- solenoid length, cm;

in - at the edge of the solenoid:

,

where l , With - length and radius of the solenoid, cm; w- number of turns.

The field strength created by the current in the toroidal winding:
, A/cm; I- current, A; l- length of the middle line of the winding, cm; w - number of turns. In this example:

a) tension H 1 , in the center on the axis of the solenoid:

b) field strength at a point A - H 2 :

c) field strength at the edge of the solenoid - H 3:

If the coil diameter is 160 mm with a total current of 180.0 A, then the field strength at the center of the coil will be:

Rice. 15. The magnetic field of the solenoid and the distribution of strength in its center (a), on the axis (b) and at the edge (c).