Determination of the magnetic permeability of a substance. Its role in describing the magnetic field

If you conduct an experiment with a solenoid that is connected to a ballistic galvanometer, then when the current in the solenoid is turned on, you can determine the value of the magnetic flux F, which will be proportional to the deflection of the galvanometer needle. Let's carry out the experiment twice, and set the current (I) in the galvanometer to be the same, but in the first experiment the solenoid will be without a core, and in the second experiment, before turning on the current, we will introduce an iron core into the solenoid. It is discovered that in the second experiment the magnetic flux is significantly greater than in the first (without a core). When repeating the experiment with cores of different thicknesses, it turns out that the maximum flow is obtained in the case when the entire solenoid is filled with iron, that is, the winding is tightly wound around the iron core. You can conduct an experiment with different cores. The result is that:

where $Ф$ is the magnetic flux in a coil with a core, $Ф_0$ is the magnetic flux in a coil without a core. The increase in magnetic flux when a core is introduced into the solenoid is explained by the fact that to the magnetic flux that creates the current in the solenoid winding, a magnetic flux created by a set of oriented ampere molecular currents was added. Under the influence of a magnetic field, molecular currents are oriented, and their total magnetic moment ceases to be equal to zero, and an additional magnetic field arises.

Definition

The quantity $\mu $, which characterizes the magnetic properties of the medium, is called magnetic permeability (or relative magnetic permeability).

This is a dimensionless characteristic of a substance. An increase in the flux Ф by $\mu $ times (1) means that the magnetic induction $\overrightarrow(B)$ in the core is the same number of times greater than in vacuum with the same current in the solenoid. Therefore, we can write that:

\[\overrightarrow(B)=\mu (\overrightarrow(B))_0\left(2\right),\]

where $(\overrightarrow(B))_0$ is the magnetic field induction in vacuum.

Along with magnetic induction, which is the main force characteristic of the field, an auxiliary vector quantity is used as magnetic field strength ($\overrightarrow(H)$), which is related to $\overrightarrow(B)$ by the following relation:

\[\overrightarrow(B)=\mu \overrightarrow(H)\left(3\right).\]

If formula (3) is applied to the experiment with a core, we obtain that in the absence of a core:

\[(\overrightarrow(B))_0=(\mu )_0\overrightarrow(H_0)\left(4\right),\]

where $\mu $=1. If there is a core, we get:

\[\overrightarrow(B)=\mu (\mu )_0\overrightarrow(H)\left(5\right).\]

But since (2) is satisfied, it turns out that:

\[\mu (\mu )_0\overrightarrow(H)=(\mu m)_0\overrightarrow(H_0)\to \overrightarrow(H)=\overrightarrow(H_0)\left(6\right).\]

We found that the magnetic field strength does not depend on what kind of homogeneous substance the space is filled with. The magnetic permeability of most substances is about unity, with the exception of ferromagnets.

Magnetic susceptibility of a substance

Usually the magnetization vector ($\overrightarrow(J)$) is associated with the intensity vector at each point of the magnet:

\[\overrightarrow(J)=\varkappa \overrightarrow(H)\left(7\right),\]

where $\varkappa $ is magnetic susceptibility, a dimensionless quantity. For non-ferromagnetic substances and in small fields $\varkappa $ does not depend on the strength and is a scalar quantity. In anisotropic media, $\varkappa $ is a tensor and the directions $\overrightarrow(J)$ and $\overrightarrow(H)$ do not coincide.

Relationship between magnetic susceptibility and magnetic permeability

Let us substitute the expression for the magnetization vector (7) into (8), and obtain:

\[\overrightarrow(H)=\frac(\overrightarrow(B))((\mu )_0)-\overrightarrow(H)\left(9\right).\]

Expressing the tension, we get:

\[\overrightarrow(H)=\frac(\overrightarrow(B))((\mu )_0\left(1+\varkappa \right))\to \overrightarrow(B)=(\mu )_0\left( 1+\varkappa \right)\overrightarrow(H)\left(10\right).\]

Comparing expressions (5) and (10), we get:

\[\mu =1+\varkappa \left(11\right).\]

Magnetic susceptibility can be either positive or negative. From (11) it follows that the magnetic permeability can be either greater than unity or less than it.

Example 1

Task: Calculate the magnetization in the center of a circular coil of radius R=0.1 m with a current of strength I=2A, if it is immersed in liquid oxygen. The magnetic susceptibility of liquid oxygen is equal to $\varkappa =3.4\cdot (10)^(-3).$

As a basis for solving the problem, we will take an expression that reflects the relationship between magnetic field strength and magnetization:

\[\overrightarrow(J)=\varkappa \overrightarrow(H)\left(1.1\right).\]

Let's find the field in the center of the coil with current, since we need to calculate the magnetization at this point.

Let us select an elementary section on the current-carrying conductor (Fig. 1); as a basis for solving the problem, we use the formula for the strength of the current-carrying coil element:

where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is specified by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. Based on Fig. 1 $\vartheta=90()^\circ $, therefore (1.1) will be simplified, in addition, the distance from the center of the circle (the point where we are looking for the magnetic field) of the conductor element with current is constant and equal to the radius of the turn (R), therefore we have:

The resulting magnetic field strength vector is directed along the X axis, it can be found as the sum of individual vectors $\ \ \overrightarrow(dH),$ since all current elements create magnetic fields in the center of the turn, directed along the normal of the turn. Then, according to the principle of superposition, the total magnetic field strength can be obtained by passing to the integral:

Substituting (1.3) into (1.4), we get:

Let's find the magnetization if we substitute the intensity from (1.5) into (1.1), we get:

All units are given in the SI system, let’s carry out the calculations:

Answer: $J=3.4\cdot (10)^(-2)\frac(A)(m).$

Example 2

Task: Calculate the fraction of the total magnetic field in a tungsten rod that is in an external uniform magnetic field, which is determined by molecular currents. The magnetic permeability of tungsten is $\mu =1.0176.$

The magnetic field induction ($B"$), which accounts for the molecular currents, can be found as:

where $J$ is magnetization. It is related to the magnetic field strength by the expression:

where the magnetic susceptibility of a substance can be found as:

\[\varkappa =\mu -1\ \left(2.3\right).\]

Therefore, we find the magnetic field of molecular currents as:

The total field in the rod is calculated according to the formula:

We use expressions (2.4) and (2.5) to find the required relationship:

\[\frac(B")(B)=\frac((\mu )_0\left(\mu -1\right)H)(\mu (\mu )_0H)=\frac(\mu -1) (\mu).\]

Let's do the calculations:

\[\frac(B")(B)=\frac(1.0176-1)(1.0176)=0.0173.\]

Answer:$\frac(B")(B)=0.0173.$

If in the experiments described above, instead of an iron core, we take cores from other materials, then a change in the magnetic flux can also be detected. It is most natural to expect that the most noticeable effect will be produced by materials similar in their magnetic properties to iron, i.e. nickel, cobalt and some magnetic alloys. Indeed, when a core made of these materials is introduced into the coil, the increase in magnetic flux turns out to be quite significant. In other words, we can say that their magnetic permeability is high; for nickel, for example, it can reach a value of 50, for cobalt 100. All these materials with large values ​​are combined into one group of ferromagnetic materials.

However, all other “non-magnetic” materials also have some effect on the magnetic flux, although this effect is much less than that of ferromagnetic materials. With very careful measurements, this change can be detected and the magnetic permeability of various materials can be determined. However, it must be borne in mind that in the experiment described above, we compared the magnetic flux in a coil whose cavity is filled with iron with the flux in a coil with air inside. As long as we were talking about such highly magnetic materials as iron, nickel, cobalt, this did not matter, since the presence of air has very little effect on the magnetic flux. But when studying the magnetic properties of other substances, in particular air itself, we must, of course, make a comparison with a coil inside which there is no air (vacuum). Thus, for magnetic permeability we take the ratio of magnetic fluxes in the substance under study and in vacuum. In other words, we take the magnetic permeability for vacuum as one (if , then ).

Measurements show that the magnetic permeability of all substances is different from unity, although in most cases this difference is very small. But what is especially remarkable is the fact that for some substances the magnetic permeability is greater than one, while for others it is less than one, i.e., filling the coil with some substances increases the magnetic flux, and filling the coil with other substances reduces this flux. The first of these substances are called paramagnetic (), and the second - diamagnetic (). As the table shows. 7, the difference in permeability from unity for both paramagnetic and diamagnetic substances is small.

It should be especially emphasized that for paramagnetic and diamagnetic bodies, magnetic permeability does not depend on the magnetic induction of an external, magnetizing field, i.e., it is a constant value characterizing a given substance. As we will see in § 149, this is not the case for iron and other similar (ferromagnetic) bodies.

Table 7. Magnetic permeability for some paramagnetic and diamagnetic substances

The influence of paramagnetic and diamagnetic substances on the magnetic flux is explained, just like the influence of ferromagnetic substances, by the fact that the magnetic flux created by the current in the coil winding is joined by the flux emanating from elementary ampere currents. Paramagnetic substances increase the magnetic flux of the coil. This increase in flux when the coil is filled with a paramagnetic substance indicates that in paramagnetic substances, under the influence of an external magnetic field, elementary currents are oriented so that their direction coincides with the direction of the winding current (Fig. 276). A slight difference from unity only indicates that in the case of paramagnetic substances this additional magnetic flux is very small, i.e., that paramagnetic substances are magnetized very weakly.

A decrease in the magnetic flux when filling the coil with a diamagnetic substance means that in this case the magnetic flux from elementary ampere currents is directed opposite to the magnetic flux of the coil, i.e., that in diamagnetic substances, under the influence of an external magnetic field, elementary currents arise, directed opposite to the winding currents (Fig. 277). The smallness of deviations from unity in this case also indicates that the additional flow of these elementary currents is small.

Rice. 277. Diamagnetic substances inside the coil weaken the magnetic field of the solenoid. The elementary currents in them are directed opposite to the current in the solenoid

Magnetics

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

1) diamagnetic materials,

2) paramagnetic materials,

3) ferromagnets.

The magnetization of a substance is characterized by magnetic permeability,

Magnetic induction in matter,

Magnetic induction in a vacuum.

Any atom can be characterized by a magnetic moment .

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

The microcurrent of an atom is created by the movement of negative electrons in 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 diamagnetic materials the currents of electrons and nuclei are compensated. The total microcurrent of an atom and its magnetic moment are equal to zero.

In an external magnetic field, non-zero elementary currents are induced (induced) in atoms. The magnetic moments of the atoms are oriented in the opposite direction.

A small field of its own is created, directed opposite to the external one, weakening it.

In diamagnetic materials.

Because< , то для диамагнетиков 1.

2. Paramagnetic materials

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

Without an external field, these microcurrents are located chaotically.

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

In a paramagnetic material, magnetic induction = + slightly exceeds .

For paramagnets, 1. For dia- and paramagnets, we can assume 1.

Table 1. Magnetic permeability of para- and diamagnetic materials.

The magnetization of paramagnetic materials depends on temperature, because The thermal movement 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 atomic microcurrents 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 compensated. In an 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 compared to para- and diamagnetic materials.

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 remains 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 the bonds between atoms in the domains are destroyed. In this case, the ferromagnet turns into a paramagnet and demagnetization occurs. For example, the Curie point for iron is 770°C.

4. Magnetic materials

Magnetic materials play as important a role in electrical and radio communications as conductive and dielectric materials. In electrical machines, transformers, chokes, electrical radio equipment and measuring instruments, magnetic materials are always used in one form or another: as a magnetic circuit, in the form of permanent magnets or for shielding magnetic fields.

Any substance, when placed in a magnetic field, acquires a certain magnetic moment M. The magnetic moment per unit volume is called magnetization J m:

J m =M/V. (4.1)

Magnetization is related to the magnetic field strength:

J m =k m H, (4.2)

where k m is a dimensionless quantity characterizing the ability of a given substance to be magnetized in a magnetic field and is called magnetic susceptibility .

The root cause of the magnetic properties of matter is the internal hidden forms of movement of electric charges, which are elementary circular currents with magnetic moments. Such currents are orbital spins and orbital rotation of electrons in an atom. The magnetic moments of protons and neutrons are approximately 1000 times smaller than the magnetic moment of an electron, therefore the magnetic properties of an atom are entirely determined by electrons; the magnetic moment of the nucleus can be neglected.

4.1. Classification of substances by magnetic properties

According to the reaction to an external magnetic field and the nature of the internal magnetic ordering, all substances in nature can be divided into five groups:

• diamagnetic materials;
• paramagnetic materials;
• ferromagnets;
• antiferromagnets;
• ferrimagnets.

Diamagnets – magnetic permeability m is less than unity and does not depend on the strength of the external magnetic field.

Diamagnetism is caused by a slight change in the angular velocity of the orbital rotation of the electron when the atom is introduced into a magnetic field.

The diamagnetic effect is universal, inherent in all substances. However, in most cases it is masked by stronger magnetic effects.

Diamagnets include inert gases, hydrogen, nitrogen, many liquids (water, oil), a number of metals (copper, silver, gold, zinc, mercury, etc.), most semiconductors and organic compounds. Diamagnets are all substances with a covalent chemical bond and substances in a superconducting state.

The external manifestation of diamagnetism is the expulsion of diamagnets from a non-uniform magnetic field.

Paramagnets – substances with m greater than unity, independent of the strength of the external magnetic field.

An external magnetic field causes the preferential orientation of the magnetic moments of atoms in one direction.

Paramagnetic substances placed in a magnetic field are drawn into it.

Paramagnetic materials include: oxygen, nitrogen oxide, alkali and alkaline earth metals, salts of iron, cobalt, nickel and rare earth elements.

The paramagnetic effect is in many ways similar in physical nature to the dipole-relaxation polarization of dielectrics.

TO ferromagnets include substances with high magnetic permeability (up to 10 6), which strongly depends on the strength of the external magnetic field and temperature.

Ferromagnets are characterized by internal magnetic order, expressed in the existence of macroscopic regions with parallel oriented magnetic moments of atoms. The most important feature of ferromagnets is their ability to be magnetized to saturation in weak magnetic fields.

Antiferromagnets are substances in which, below a certain temperature T°, an antiparallel orientation of the magnetic moments of identical atoms or ions of the crystal lattice spontaneously arises

When heated, an antiferromagnet transforms into a paramagnetic state. Antiferromagnetism was found in chromium, manganese and a number of rare earth elements (Ce, Nd, Sm, Tm, etc.)

TO ferrimagnets include substances whose magnetic properties are due to uncompensated antiferromagnetism. Their magnetic permeability is high and strongly depends on the magnetic field strength and temperature.

Some ordered metal alloys have ferrimagnetic properties, but mainly various oxide compounds, and ferrites are of main interest.

Dia-, para- and antiferromagnets can be combined into a group weakly magnetic substances, while ferro- and ferrimagnets are highly magnetic materials are of greatest interest.

4.2. Magnetic characteristics of materials

The behavior of a ferromagnetic material in a magnetic field is characterized by the initial magnetization curve:

Rice. 4.1. Initial magnetization curve.

Showing the dependence of magnetic induction B in a material on magnetic field strength H.

The properties of magnetic materials are assessed by magnetic characteristics. Let's look at the main ones.

4.2.1. Absolute magnetic permeability

The absolute magnetic permeability m a of a material is the ratio of the magnetic induction B to the magnetic field strength H at a given point on the magnetization curve for a given material and is expressed in H/m:

m a = B/N (4.3)

The relative magnetic permeability of a material m is the ratio of the absolute magnetic permeability to the magnetic constant:

m =m a /m o (4.4)

μ 0 – characterizes the magnetic field in vacuum (m 0 =1.256637·10 -6 H/m).

Absolute magnetic permeability is used for calculation purposes only. To evaluate the properties of magnetic materials, m is used, which does not depend on the chosen system of units. It is called magnetic permeability. Magnetic permeability depends on the magnetic field strength:

Rice. 4.2. Dependence of magnetic permeability on magnetic field strength.

There are initial m n and maximum magnetic permeability m m. The initial one is measured at magnetic field strengths close to zero.

Large values ​​of m n and m m indicate that this material is easily magnetized in weak and strong magnetic fields.

4.2.2. Temperature coefficient of magnetic permeability

The temperature coefficient of magnetic permeability TKm allows us to estimate the nature of the change in m depending on

TK μ = (μ 2 - μ 1)/ μ 1 (T 2 – T 1)

A typical dependence of μ on T° is shown in Fig. 4.3.

Fig.4.3. Typical dependence of the magnetic permeability of ferromagnetic materials on temperature

T° at which μ drops almost to zero is called Curie temperature Tk. At T > Tk, the magnetization process is disrupted due to the intense thermal movement of atoms and molecules of the material, therefore, the material ceases to be ferromagnetic.

So, for pure iron Tc = 768°C
for nickel Tk = 358°C
for cobalt Tc = 1131°C

4.2.3. Saturation induction

Induction B s, characteristic of all magnetic materials, is called saturation induction (see Fig. 4.4). The greater the B s for a given H, the better the magnetic material.

If a sample of a magnetic material is magnetized by continuously increasing the magnetic field strength H, the magnetic induction B will also continuously increase along the initial magnetization curve 1:

Fig.4.4. Hysteresis loop of magnetic material

This curve ends at the point corresponding to the saturation induction B s. As H decreases, the induction will also decrease, but starting from the value of B m, the values ​​of B will not coincide with the initial magnetization curve.

4.2.4. Residual magnetic induction

Residual magnetic induction B r is observed in ferromagnetic material when H = 0. To demagnetize a sample, the magnetic field strength must change its direction to the opposite direction - N. The field strength at which the induction becomes zero is called the coercive force N c. The higher Hc, the less the material is able to demagnetize.

If, after demagnetizing a material, it is magnetized in the opposite direction, a closed loop is formed, which is called limit hysteresis loop – a loop taken with a smooth change in the magnetic field strength from +H to –H, when the magnetic induction becomes equal to the saturation induction B s.

4.2.5. Specific losses due to hysteresis

This is the loss Pg spent on reversing the magnetization of a unit mass of material in one cycle [W/kg]. Their value depends on the frequency of magnetization reversal and the value of the maximum induction. They are determined (for one cycle) by the area of ​​the hysteresis loop.

4.2.6. Dynamic hysteresis loop

It is formed when the material is remagnetized by an alternating magnetic field and has a larger area than the static one, because Under the action of an alternating magnetic field, in addition to losses due to hysteresis, losses due to eddy currents and a magnetic aftereffect (time lag of parameters from H) occur, which is determined by the magnetic viscosity of the material.

4.2.7. Energy losses due to eddy currents

Energy losses due to eddy currents P in depend on the electrical resistivity of the material ρ. The larger ρ, the smaller the losses. P in also depend on the density of the material and its thickness. They are proportional to the square of the amplitude of magnetic induction B m and the frequency f of the alternating field.

4.2.8. Hysteresis loop squareness coefficient

To estimate the shape of the hysteresis loop, use the squareness coefficient of the hysteresis loop:

K p = V r / V m (4.6)

The larger K p, the more rectangular the loop. For magnetic materials used in automation and computer storage, K p = 0.7-0.9.

4.2.9. Specific volumetric energy

This characteristic, the applied portion of the assessment of the properties of magnetically hard materials, is expressed by the formula:

W m = 1/2(B d H d), (4.7)

where B d and H d are the induction and magnetic field strength, respectively, corresponding to the maximum value of the specific volumetric energy (Fig. 4.5).

Fig.4.5. Demagnetization and magnetic energy curves

The greater the volumetric energy, the better the magnetic material and the permanent magnet made from it.

4.3. Classification of magnetic materials

According to their behavior in a magnetic field, all magnetic materials are divided into two main groups - soft magnetic (MM) and hard magnetic (HMM). MMMs are characterized by large values ​​of initial and maximum magnetic permeability and low values ​​of coercive force (less than 4000 A/m). They are easily magnetized and demagnetized and have low hysteresis losses.

The purer the MMM, the better its magnetic characteristics.

MTMs have a high coercive force (more than 4000 A/m) and residual induction (more than 0.1 T). They are magnetized with great difficulty, but they can retain magnetic energy for a long time, i.e. serve as sources of constant magnetic field.

Based on their composition, all magnetic materials are divided into

1. metal
2. non-metallic
3. magnetodielectrics.

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

Non-metallic magnetic materials are ferrites obtained from a powdered mixture of iron oxides and oxides of other metals. Pressed ferrite products are annealed, as a result of which they turn into solid monolithic parts.

Magnetodielectrics are composite materials consisting of 60-80% powdered magnetic material and 40-20% dielectric.

Ferrites and magnetodielectrics differ from metallic magnetic materials by their large ρ (10 2 -10 8 Ohm m), which makes eddy current losses small. This allows them to be used in high-frequency technology. In addition, ferrites have great stability of magnetic parameters in a wide range of frequencies (including microwave frequencies).

4.4. Metallic soft magnetic materials

The main soft magnetic materials used in electronic equipment are carbonyl iron, permalloy, alsifer and low-carbon silicon steel.

4.4.1. Carbonyl iron

It is a fine powder consisting of spherical particles with a diameter of 1–8 microns.

μ n = 2500 – 3000
μ m = 20000 – 21000
N s = 4.5 – 6.2 A/m

It is used in the manufacture of high-frequency magnetodielectric cores.

4.4.2. Permalloy

Ductile iron-nickel alloys with a nickel content of 45–80% are easily rolled into thin sheets and strips up to 1 micron thick. With a nickel content of 45–50%, they are called low-nickel, 60–80% are called high-nickel.

μ n = 2000 – 14000
μ m = 50000 – 270000
N s = 2 – 10 A/m
ρ = 0.25 – 0.45 µOhm m

To improve the magnetic characteristics, molybdenum, chromium, silicon or copper is introduced into permalloy and annealed in hydrogen or vacuum using turbomolecular pumps.

Alloyed permalloys are used for equipment parts operating at frequencies of 1–5 MHz. Permalloys with a rectangular hysteresis loop are used in magnetic amplifiers.

4.4.3. Alsifera

They are non-malleable, brittle alloys consisting of 5.5–13% aluminum, 9–10% silicon, and the rest iron.

μ n = 6000 – 7000
μ m = 30000 – 35000
N s = 2.2 A/m
ρ = 0.8 µOhm m

Cast cores are made from it, operating in the range up to 50 kHz.

4.4.4. Low carbon silicon steels

They are alloys of iron with 0.8–4.8% silicon, carbon content no more than 0.08%. This is a relatively cheap material. The introduction of a large amount of silicon improves the magnetic properties of the material, but increases its fragility (therefore, silicon is no more than 4.8%).

Silicon steel sheets are produced by rolling blanks in heated and unheated states, therefore a distinction is made between hot-rolled and cold-rolled steel.

Improved magnetic characteristics of cold-rolled steels are observed only when the direction of the magnetic flux coincides with the rolling direction. Otherwise, the properties of hot-rolled steels are higher.

Table 4.1. Steels are used in less critical components of electronic equipment.

4.5. Metallic magnetic hard materials

Based on their composition, condition and method of production, magnetically hard materials are divided into:

1. alloy steels hardened to martensite;
2. cast magnetic hard alloys;
3. powder magnets;
4. magnetically hard ferrites;
5. plastically deformable alloys and magnetic tapes.

The characteristics of materials for permanent magnets are coercive force, residual induction and the maximum energy given off by the magnet to the external space. The magnetic permeability of materials for permanent magnets is lower than MMM, and the higher the coercive force, the lower the magnetic permeability.

4.5.1. Alloy steels hardened to martensite

These steels are the simplest and most accessible material for permanent magnets. They are alloyed with tungsten, chromium, molybdenum and cobalt. The value of W m ​​for martensitic steels is 1–4 kJ/m 3. Currently, martensitic steels have limited use due to their low magnetic properties, but they are not completely abandoned because they are cheap and can be machined on metal-cutting machines.

4.5.2. Cast magnetic hard alloys

Al-Ni-Fe ternary alloys, which were previously called alloys, have greater magnetic energy alni . By adding cobalt or silicon to these alloys, their magnetic properties increase. The disadvantage of these alloys is the difficulty of manufacturing products of precise dimensions from them due to their fragility and hardness, which can only be processed by grinding.

4.5.3. Powder magnets

The need to obtain especially small products with strictly maintained dimensions led to the use of powder metallurgy methods to produce permanent magnets. In this case, a distinction is made between metal-ceramic magnets and magnets made from powder grains held together by one or another binder (metal-plastic magnets).

4.5.4. Plastically deformable alloys and magnetic tapes

Such alloys include vicalloy, kunife, kuniko and some others. Basic ideas about these alloys are given in Table 4.2.

Table 4.2.

4.6. Ferrites

These are compounds of iron oxide Fe 2 O 3 with oxides of other metals: ZnO, NiO. Ferrites are made from a powdered mixture of oxides of these metals.

The name of ferrites is determined by the name of the mono-, divalent metal, the oxide of which is part of the ferrite:

If ZnO is zinc ferrite

NiO – nickel ferrite.

Ferrites have a cubic crystal lattice similar to the spinel lattice found in nature: MgO Al 2 O 3 . Most compounds of this type, like natural magnetic iron ore FeO·Fe 2 O 3, have magnetic properties. However, zinc ferrite and cadmium ferrite are non-magnetic. Research has shown that the presence or absence of magnetic properties is determined by the crystal structure of these materials, and in particular by the arrangement of divalent metal and iron ions between oxygen ions. In the case of the structure of ordinary spinel, when Zn ++ or Cd ++ ions are located in the center of oxygen tetrahedra, there are no magnetic properties. With the structure of the so-called inverted spinel, when Fe +++ ions are located in the center of oxygen tetrahedra, the material has magnetic properties. Ferrites, which contain only one oxide in addition to iron oxide, are called simple. Chemical formula of simple ferrite:

MeO x Fe 2 O 3 or MeFe 2 O 4

Zinc ferrite – ZnFe 2 O 4, nickel ferrite – NiFe 2 O 4.

Not all simple ferrites are magnetic. So CdFe 2 O 4 is a non-magnetic substance.

The best magnetic characteristics are possessed by complex or mixed ferrites, which are solid solutions of one in the other. In this case, non-magnetic ferrites are used in combination with simple magnetic ferrites. The general formula of widespread nickel-zinc ferrites is as follows:

mNiO Fe 2 O 3 + nZnO Fe 2 O 3 + pFeO Fe 2 O 3, (4.8)

where the coefficients m, n and p determine the quantitative relationships between the components. The percentage composition of the components plays a significant role in obtaining certain magnetic properties of the material.

The most widely used in REA are mixed soft magnetic ferrites: nickel-zinc, manganese-zinc and lithium-zinc.

Advantages of ferrites– stability of magnetic characteristics in a wide frequency range, low eddy current losses, low magnetic wave attenuation coefficient, as well as ease of manufacturing of ferrite parts.

Disadvantages of all ferrites– fragility and a pronounced dependence of magnetic properties on temperature and mechanical influences.

4.7. Magnetodielectrics

These are composite materials consisting of fine particles of soft magnetic material connected by some organic or inorganic dielectric. Carbonyl iron, alsifers and some varieties of permalloy are used as finely dispersed MMMs. As a dielectric - epoxy or bakelite resins, polystyrene, liquid glass, etc.

The purpose of dielectrics is not only to connect particles of magnetic material, but also to create electrical insulating layers between them and thereby increase the electrical resistance of the magnetodielectric. This dramatically reduces eddy current losses and makes it possible to operate at frequencies of 10–100 MHz (depending on composition).

The magnetic characteristics of magnetodielectrics are somewhat lower than the original ferromagnetic fillers. Despite this, magnetodielectrics are used for the manufacture of cores of RF electronic components. This is due to the great stability of magnetic characteristics and the possibility of manufacturing cores of complex shapes from them. In addition, products made from dielectrics are characterized by high surface cleanliness and dimensional accuracy.

The best magnetodielectrics are filled with fillers: molybdenum permalloy or carbonyl iron.

Magnetic permeability. Magnetic properties of substances

Magnetic properties of substances

Just as the electrical properties of a substance are characterized by dielectric constant, the magnetic properties of a substance are characterized by magnetic permeability.

Due to the fact that all substances located in a magnetic field create their own magnetic field, the magnetic induction vector in a homogeneous medium differs from the vector at the same point in space in the absence of a medium, i.e. in a vacuum.

The relationship is called magnetic permeability of the medium.

So, in a homogeneous medium, the magnetic induction is equal to:

The value of m for iron is very large. This can be verified by experience. If you insert an iron core into a long coil, then the magnetic induction, according to formula (12.1), will increase m times. Consequently, the flux of magnetic induction will increase by the same amount. When the circuit feeding the magnetizing coil with direct current is opened, an induction current appears in the second, small coil wound on top of the main one, which is recorded by a galvanometer (Fig. 12.1).

If an iron core is inserted into the coil, then the deflection of the galvanometer needle when the circuit is opened will be m times greater. Measurements show that the magnetic flux when an iron core is introduced into the coil can increase thousands of times. Consequently, the magnetic permeability of iron is enormous.

There are three main classes of substances with sharply different magnetic properties: ferromagnets, paramagnets and diamagnetic materials.

Ferromagnets

Substances for which, like iron, m >> 1, are called ferromagnets. In addition to iron, cobalt and nickel are ferromagnetic, as well as a number of rare earth elements and many alloys. The most important property of ferromagnets is the existence of residual magnetism. A ferromagnetic substance can be in a magnetized state without an external magnetizing field.

An iron object (for example, a rod), as is known, is drawn into a magnetic field, that is, it moves to an area where the magnetic induction is greater. Accordingly, it is attracted to a magnet or electromagnet. This happens because the elementary currents in the iron are oriented so that the direction of the magnetic induction of their field coincides with the direction of the induction of the magnetizing field. As a result, the iron rod turns into a magnet, the nearest pole of which is opposite to the pole of the electromagnet. Opposite poles of magnets attract (Fig. 12.2).

Rice. 12.2

STOP! Decide for yourself: A1–A3, B1, B3.

Paramagnets

There are substances that behave like iron, that is, they are drawn into a magnetic field. These substances are called paramagnetic. These include some metals (aluminum, sodium, potassium, manganese, platinum, etc.), oxygen and many other elements, as well as various electrolyte solutions.

Since paramagnets are drawn into the field, the induction lines of the own magnetic field they create and the magnetizing field are directed in the same way, so the field is enhanced. Thus, they have m > 1. But m differs from unity extremely slightly, only by an amount of the order of 10 –5 ...10 –6. Therefore, powerful magnetic fields are required to observe paramagnetic phenomena.

Diamagnets

A special class of substances are diamagnetic materials, discovered by Faraday. They are pushed out of the magnetic field. If you hang a diamagnetic rod near the pole of a strong electromagnet, it will be repelled from it. Consequently, the induction lines of the field created by it are directed opposite to the induction lines of the magnetizing field, i.e., the field is weakened (Fig. 12.3). Accordingly, for diamagnetic materials m< 1, причем отличается от единицы на вели­чину порядка 10 –6 . Магнитные свойства у диамагнетиков вы­ражены слабее, чем у парамагнетиков.