Electrical permeability

Permeability is a quantity that characterizes the capacitance of a dielectric placed between the plates of a capacitor. As you know, the capacitance of a flat capacitor depends on the size of the area of ​​the plates (than larger area plates, the greater the capacitance), the distance between the plates or the thickness of the dielectric (the thicker the dielectric, the lower the capacitance), as well as from the material of the dielectric, the characteristic of which is the electric permeability.

Numerically, the electric permeability is equal to the ratio of the capacitance of a capacitor with some dielectric of the same air condenser... To create compact capacitors, it is necessary to use dielectrics with high electrical permeability. The electrical permeability of most dielectrics is several units.

Dielectrics with high and ultrahigh electrical permeability have been obtained in technology. Most of them are rutile (titanium dioxide).

Figure 1. Electrical permeability of the medium

Dielectric loss angle

In the article "Dielectrics" we examined examples of the inclusion of a dielectric in a DC and AC circuit. It turned out that when a real dielectric works in an electric field formed by an alternating voltage, thermal energy is released. The power absorbed in this case is called dielectric loss. The article "AC Circuit Containing Capacitance" will prove that in an ideal dielectric, the capacitive current leads the voltage by an angle less than 90 °. In a real dielectric, the capacitive current leads the voltage by an angle less than 90 °. The decrease in the angle is influenced by the leakage current, otherwise called the conduction current.

The difference between 90 ° and the shear angle between voltage and current flowing in a circuit with a real dielectric is called the dielectric loss angle or loss angle and is denoted δ (delta). More often, not the angle itself is determined, but the tangent of this angle -tg δ.

It was found that dielectric losses are proportional to the square of the voltage, the frequency of the alternating current, the capacitance of the capacitor and the tangent of the angle of dielectric losses.

Consequently, the larger the dielectric loss tangent, tan δ, the greater the energy loss in the dielectric, the worse the dielectric material. Materials with a relatively high tan δ (of the order of 0.08 - 0.1 and more) are poor insulators. Materials with relatively low tan δ (of the order of 0.0001) are good insulators.

The capacity of a capacitor depends, as experience shows, not only on the size, shape and relative position of its constituent conductors, but also on the properties of the dielectric filling the space between these conductors. The influence of the dielectric can be established using the following experiment. Let's charge the flat capacitor and observe the readings of the electrometer, which measures the voltage across the capacitor. Let us then push an uncharged ebonite plate into the capacitor (Fig. 63). We will see that the potential difference between the plates will noticeably decrease. If ebonite is removed, then the electrometer readings remain the same. This shows that when replacing air with ebonite, the capacitance of the condenser increases. Taking some other dielectric instead of ebonite, we get a similar result, but only the change in the capacitance of the capacitor will be different. If is the capacitance of a capacitor, between the plates of which there is a vacuum, and is the capacitance of the same capacitor, when all the space between the plates is filled, without air gaps, with some kind of dielectric, then the capacitance will be several times larger than the capacitance, where it depends only on the nature of the dielectric. So one can write

Rice. 63. The capacitance of the capacitor increases when the ebonite plate is pushed in between its plates. The electrometer leaves fall off, although the charge remains the same

The quantity is called the relative dielectric constant or simply the dielectric constant of the medium that fills the space between the capacitor plates. Table 1 shows the values ​​of the dielectric constant of some substances.

Table 1. Dielectric constant of some substances

Substance
Water (clean)
Ceramics (radio engineering)

The foregoing is true not only for a flat capacitor, but also for a capacitor of any shape: replacing the air with some kind of dielectric, we increase the capacitance of the capacitor by times.

Strictly speaking, the capacitance of a capacitor increases several times only if all the field lines going from one plate to another pass through the given dielectric. This will be, for example, for a capacitor that is completely immersed in some kind of dielectric liquid poured into a large vessel. However, if the distance between the plates is small in comparison with their dimensions, then we can assume that it is enough to fill only the space between the plates, since it is here that the electric field of the capacitor is practically concentrated. So, for a flat capacitor, it is enough to fill only the space between the plates with a dielectric.

By placing a substance with a high dielectric constant between the plates, the capacitance of the capacitor can be greatly increased. This is used in practice, and usually not air is chosen as a dielectric for a capacitor, but glass, paraffin, mica and other substances. In fig. 64 shows a technical capacitor in which the dielectric is a paraffin-impregnated paper tape. Its covers are sheet metal, pressed on both sides to waxed paper. The capacity of such capacitors often reaches several microfarads. So, for example, an amateur radio capacitor the size of matchbox has a capacitance of 2 μF.

Rice. 64. Technical flat capacitor: a) assembled; b) partially disassembled: 1 and 1 "- staniole tapes, between which tapes of waxed thin paper are laid 2. All tapes are folded together" like an accordion "and put into a metal box. Contacts 3 and 3" are soldered to the ends of tapes 1 and 1 " to include a capacitor in the circuit

It is clear that only dielectrics with very good insulating properties are suitable for the manufacture of a capacitor. Otherwise, the charges will flow through the dielectric. Therefore, water, despite its high dielectric constant, is not at all suitable for the manufacture of capacitors, because only extremely thoroughly purified water is a sufficiently good dielectric.

If the space between the plates of a flat capacitor is filled with a medium with a dielectric constant, then formula (34.1) for a flat capacitor takes the form

The fact that the capacitance of a capacitor is dependent on the environment indicates that the electric field inside dielectrics changes. We have seen that when a capacitor is filled with a dielectric with a dielectric constant, the capacitance increases by a factor. This means that with the same charges on the plates, the potential difference between them decreases by a factor. But the potential difference and the field strength are related to each other by the relation (30.1). Therefore, a decrease in the potential difference means that the field strength in the capacitor when it is filled with a dielectric is reduced by a factor. This is the reason for the increase in the capacitance of the capacitor. times less than in a vacuum. Hence, we conclude that Coulomb's law (10.1) for point charges placed in a dielectric has the form

VIRTUAL LABORATORY WORK No. 3 SOFTWARE

SOLID BODY PHYSICS

Methodical instructions for implementation laboratory work No. 3 on the section of physics "Solid state" for students of technical specialties of all forms of education

Krasnoyarsk 2012

Reviewer

Candidate of Physical and Mathematical Sciences, Associate Professor O. N. Bandurina

(Siberian State Aerospace University

named after academician M.F. Reshetnev)

Published by the decision of the ICT Methodological Commission

Determination of the dielectric constant of semiconductors. Virtual laboratory work No. 3 on solid state physics: Methodical instructions for the implementation of laboratory work No. 3 on the section of physics "Solid state" for students of tech. specialist. all forms of education / comp .: A.M. Kharkov; Sib. state aerospace un-t. - Krasnoyarsk, 2012 .-- 21 p.

Siberian State Aerospace

University named after academician M.F. Reshetnev, 2012

Introduction …………………………………………………………………………… ... 4

Admission to laboratory work ………………………………………………… ... 4

Registration of laboratory work for protection …………………………………… ... 4

Determination of the dielectric constant of semiconductors ………… ........ 5

Method theory …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………… 5

Dielectric constant measurement technique ………………… .. …… ..11

Processing of measurement results ……………………… .. ……………………… 16

Test questions ………… .. ……………………………………………… .17

Test ……………………………………………………………………………… .17

References ……………………………………………………………… 20

Appendix ………………………………………………………………………… 21

INTRODUCTION

Data guidelines contain descriptions for laboratory works that use virtual models from the course "Solid State Physics".

Laboratory work permit:

Conducted by the teacher in groups with a personal survey of each student. For admission:

1) Each student prepares in advance his personal summary of this laboratory work;

2) The teacher individually checks the design of the abstract and asks questions about the theory, measurement technique, installation and processing of results;

3) The student answers questions asked;

4) The teacher allows the student to work and puts his signature in the student's synopsis.

Registration of laboratory work for protection:

A fully completed and prepared for defense work must meet the following requirements:

Fulfillment of all points: all calculations of the required values, all tables are filled with ink, all graphs are built, etc.

Schedules must meet all the requirements of the teacher.

For all values ​​in the tables, the corresponding unit of measurement must be recorded.

Conclusions for each graph are recorded.

An answer has been written out in the prescribed form.

The conclusions of the answer are recorded.

DETERMINATION OF THE DIELECTRIC PERMEABILITY OF SEMICONDUCTORS

Method theory

Polarization Is the ability of a dielectric to polarize under the influence of an electric field, i.e. change in space the arrangement of bound charged dielectric particles.

The most important property dielectrics is their ability to polarize electrically, i.e. under the influence of an electric field, a directed displacement of charged particles or molecules occurs over a limited distance. Under the action of an electric field, charges are displaced, both in polar and non-polar molecules.

There are over a dozen different types polarization. Let's consider some of them:

1. Electronic polarization Is the displacement of electron orbits relative to the positively charged nucleus. It occurs in all atoms of any substance, i.e. in all dielectrics. Electronic polarization is established in a time of 10 -15 -10 -14 s.

2. Ionic polarization- displacement relative to each other of oppositely charged ions in substances with ionic bonds. The time of its establishment is 10 -13 -10 -12 s. Electronic and ionic polarization are among the instantaneous or deformation types of polarization.

3. Dipole or orientation polarization due to the orientation of the dipoles in the direction of the electric field. Polar dielectrics have dipole polarization. The time of its establishment is 10 -10 -10 -6 s. Dipole polarization is a slow or relaxation type of polarization.

4. Migration polarization observed in inhomogeneous dielectrics, in which electric charges are accumulated at the boundary of the section of inhomogeneities. The processes of establishing migratory polarization are very slow and can last for minutes or even hours.

5. Ion relaxation polarization is caused by an excessive transfer of weakly bound ions under the action of an electric field over distances exceeding the lattice constant. Ion relaxation polarization manifests itself in some crystalline substances in the presence of impurities in the form of ions or loose packing of the crystal lattice. The time of its establishment is 10 -8 -10 -4 s.

6. Electronic relaxation polarization arises due to the excess "defective" electrons or "holes" excited by thermal energy. This type of polarization usually results in a high dielectric constant.

7. Spontaneous polarization- spontaneous polarization that occurs in some substances (for example, Rochelle salt) in a certain temperature range.

8. Elasto-dipole polarization associated with the elastic rotation of the dipoles through small angles.

9. Residual polarization- polarization, which remains in some substances (electrets) for a long time after the removal of the electric field.

10. Resonant polarization... If the frequency of the electric field is close to the natural frequency of the vibrations of the dipoles, then the vibrations of the molecules can increase, which will lead to the appearance of resonant polarization in the dipole dielectric. Resonant polarization is observed at frequencies in the infrared region. A real dielectric can simultaneously possess several types of polarization. The appearance of a particular type of polarization is determined by physicochemical properties substances and the range of frequencies used.

Main parameters:

ε - dielectric constant- a measure of the material's ability to polarize; it is a value that shows how many times the force of interaction of electric charges in a given material is less than in a vacuum. Inside the dielectric, a field appears that is directed opposite to the external one.

The strength of the external field weakens in comparison with the field of the same charges in vacuum by a factor of ε, where ε is the relative permittivity.

If the vacuum between the plates of the capacitor is replaced by a dielectric, then as a result of polarization, the capacitance increases. A simple definition of dielectric constant is based on this:

where C 0 is the capacitance of the capacitor, between the plates of which there is a vacuum.

C d is the capacitance of the same capacitor with a dielectric.

The dielectric constantε of an isotropic medium is determined by the ratio:

(2)

where χ is the dielectric susceptibility.

D = tan δ - dielectric loss tangent

Dielectric loss - losses electrical energy caused by the flow of currents in dielectrics. Distinguish between current through conduction I sk.pr, caused by the presence in dielectrics of a small amount of readily mobile ions, and polarization currents. With electronic and ionic polarization, the polarization current is called the displacement current I cm, it is very short-lived and is not recorded by instruments. Currents associated with delayed (relaxation) types of polarization are called absorption currents I abs. V general case the total current in the dielectric is defined as: I = I abs + I sk.pr. After establishing polarization, the total current will be equal to: I = I sk.pr. If in a constant field polarization currents arise at the time of switching on and off the voltage, and the total current is determined in accordance with the equation: I = I sk.pr, then in an alternating field polarization currents arise at the moment of voltage polarity reversal. As a consequence, the losses in the dielectric in an alternating field can be significant, especially if the half-period of the applied voltage approaches the time for establishing polarization.

In fig. 1 (a) shows a circuit equivalent to a capacitor with a dielectric in an alternating voltage circuit. In this circuit, a capacitor with a real dielectric, which has losses, is replaced by an ideal capacitor C with an active resistance R connected in parallel. 1 (b) shows a vector diagram of currents and voltages for the considered circuit, where U is the voltage in the circuit; I ak - active current; I p - reactive current, which is ahead of the active component in phase by 90 °; I ∑ - total current. In this case: I a = I R = U / R and I p = I C = ωCU, where ω is the circular frequency of the alternating field.

Rice. 1. (a) - diagram; (b) - vector diagram of currents and voltages

The angle of dielectric loss is called the angle δ, which complements the phase shift angle φ between the current I ∑ and the voltage U in the capacitive circuit to 90 °. Losses in dielectrics in an alternating field are characterized by the tangent of the dielectric loss angle: tan δ = I a / I p.

The limiting values ​​of the dielectric loss tangent for high-frequency dielectrics should not exceed (0.0001 - 0.0004), and for low-frequency - (0.01 - 0.02).

Dependences of ε and tan δ on temperature T and frequency ω

Dielectric parameters of materials in varying degrees depend on temperature and frequency. A large number of dielectric materials does not allow to cover the features of all dependences on these factors.

Therefore, in Fig. 2 (a, b) show general trends, typical for some major groups i.e. the typical dependences of the dielectric constant ε on the temperature T (a) and on the frequency ω (b) are shown.

Rice. 2. Frequency dependence of the real (εʹ) and imaginary (εʺ) parts of the dielectric constant in the presence of an orientation relaxation mechanism

Complex dielectric constant. In the presence of relaxation processes, it is convenient to write the dielectric constant in a complex form. If the Debye formula is valid for polarizability:

(3)

where, τ is the relaxation time, α 0 is the statistical orientational polarizability. Then, assuming the local field equal to the external one, we obtain (in the CGS):

Graphs of εʹ and εʺ dependence on the product ωτ are shown in Fig. 2. Note that a decrease in εʹ (real part of ε) takes place near the maximum of εʺ (imaginary part of ε).

Such a course of variation of εʹ and εʺ with frequency serves as frequent example a more general result, according to which εʹ (ω) on frequency entails also the dependence of εʺ (ω) on frequency. In the SI system, 4π should be replaced by 1 / ε 0.

Under the action of an applied field, molecules in a nonpolar dielectric are polarized, becoming dipoles with an induced dipole moment μ and proportional to the field strength:

(5)

In a polar dielectric, the dipole moment of a polar molecule μ in the general case is equal to the vector sum of the intrinsic μ 0 and the induced μ and moments:

(6)

The strengths of the field created by these dipoles are proportional to the dipole moment and inversely proportional to the cube of the distance.

For non-polar materials, usually ε = 2 - 2.5 and does not depend on frequency up to ω ≈10 12 Hz. The dependence of ε on temperature is due to the fact that when it changes, the linear dimensions of solids and the volumes of liquid and gaseous dielectrics change, which changes the number of molecules n per unit volume

and the distance between them. Using the relations known from the theory of dielectrics F = n \μ and and F =ε 0 (ε - 1) E, where F- polarization of the material, for non-polar dielectrics we have:

(7)

For E = const also μ and= const and the temperature change in ε is due only to the change in n, which is linear function temperature Θ, the dependence ε = ε (Θ) is also linear. There are no analytical dependences for polar dielectrics, and empirical ones are usually used.

1) With increasing temperature, the volume of the dielectric increases and the dielectric constant decreases slightly. The decrease in ε is especially noticeable during the period of softening and melting of nonpolar dielectrics, when their volume significantly increases. Due to the high frequency of revolution of electrons in orbits (of the order of 10 15 –10 16 Hz), the time for establishing an equilibrium state of electronic polarization is very short and the permittivity ε of nonpolar dielectrics does not depend on the field frequency in the commonly used frequency range (up to 10 12 Hz).

2) With an increase in temperature, the bonds between individual ions weaken, which facilitates their interaction under the action of an external field and this leads to an increase in ionic polarization and dielectric constant ε. Due to the shortness of the time required for the establishment of the ionic polarization state (of the order of 10 13 Hz, which corresponds to the natural frequency of ion vibration in crystal lattice) a change in the frequency of the external field in the usual operating ranges has practically no effect on the value of ε in ionic materials.

3) The dielectric constant of polar dielectrics strongly depends on the temperature and frequency of the external field. With increasing temperature, the mobility of particles increases and the energy of interaction between them decreases, i.e. their orientation becomes easier under the action of an external field - the dipole polarization and dielectric constant increase. However, this process continues only up to a certain temperature. With a further increase in temperature, the permeability ε decreases. Since the orientation of the dipoles in the direction of the field is carried out in the process thermal motion and by thermal motion, the establishment of polarization is time consuming. This time is so long that in variable fields high frequency dipoles do not have time to orient themselves along the field, and the permittivity ε decreases.

Dielectric constant measurement technique

Capacitor capacity. Capacitor Is a system of two conductors (plates) separated by a dielectric, the thickness of which is small compared to the linear dimensions of the conductors. So, for example, two flat metal plates, located in parallel and separated by a dielectric layer, form a capacitor (Fig. 3).

If the plates of a flat capacitor are given charges of the opposite sign of equal magnitude, then the electric field strength between the plates will be twice as high as the field strength of one plate:

(8)

where ε is the dielectric constant of the dielectric filling the space between the plates.

Physical quantity determined by the charge ratio q one of the capacitor plates to the potential difference Δφ between the capacitor plates is called electrical capacity of the capacitor:

(9)

Unit of electrical capacity SI - Farad(F). A capacitor of 1 F is possessed by such a capacitor, the potential difference between the plates of which is equal to 1 V when the plates are supplied with opposite charges of 1 C: 1 F = 1 C / 1 V.

Capacity of a flat capacitor. The formula for calculating the electrical capacity of a flat capacitor can be obtained using expression (8). Indeed, the field strength is: E= φ / εε 0 = q / εε 0 S, where S Is the area of ​​the plate. Since the field is uniform, the potential difference between the capacitor plates is: φ 1 - φ 2 = Ed = qd/εε 0 S, where d Is the distance between the plates. Substituting into formula (9), we obtain an expression for the electrical capacity of a flat capacitor:

(10)

where ε 0 - dielectric constant of air; S- the area of ​​the capacitor plate, S = hl, where h- plate width, l- its length; d- the distance between the plates of the capacitor.

Expression (10) shows that the electrical capacity of a capacitor can be increased by increasing the area S its plates, decreasing the distance d between them and the use of dielectrics with large values dielectric constant ε.

Rice. 3. Capacitor with a dielectric placed in it

If a dielectric plate is placed between the plates of the capacitor, the capacitance of the capacitor will change. Consideration should be given to the location of the dielectric plate between the plates of the capacitor.

Let's denote: d c - the thickness of the air gap, d m - the thickness of the dielectric plate, l B is the length of the air part of the condenser, l m is the length of the part of the capacitor filled with a dielectric, ε m is the dielectric constant of the material. Considering that l = l in + l m and d = d in + d m, then these options can be considered for cases:

When l b = 0, d at = 0 we have a capacitor with a solid dielectric:

(11)

From the equations of classical macroscopic electrodynamics, based on Maxwell's equations, it follows that when a dielectric is placed in a weak alternating field that changes harmonically with a frequency ω, the complex dielectric constant tensor takes the form:

(12)

where σ is the optical conductivity of the substance, εʹ is the dielectric constant of the substance associated with the polarization of the dielectric. Expression (12) can be reduced to the following kind:

(13)

where the imaginary term is responsible for the dielectric loss.

In practice, C is measured - the capacitance of a sample in the form of a flat capacitor. This capacitor is characterized by the dielectric loss tangent:

tgδ = ωCR c (14)

or quality factor:

Q c = 1 / tgδ (15)

where R c - resistance, depending mainly on dielectric losses. There are a number of methods for measuring these characteristics: various bridge methods, measurements with conversion of the measured parameter into a time interval, etc. ...

When measuring the capacitance C and the dielectric loss tangent D = tgδ in this work, we used the technique developed by the GOOD WILL INSTRUMENT Co. Ltd. The measurements were carried out on a precision immittance meter - LCR-819-RLC. The device allows you to measure capacitance in the range of 20 pF – 2.083 mF, loss tangent in the range 0.0001-9999 and apply a displacement field. Internal offset up to 2 V, external offset up to 30 V. The measurement accuracy is 0.05%. Test signal frequency 12 Hz -100 kHz.

In this work, measurements were carried out at a frequency of 1 kHz in a temperature range of 77 K< T < 270 К в нулевом магнитном поле и в поле 5 kOe. Образцы для измерений имели форму параллелепипеда с размерами 2*3*4 мм (х=0.1), где d = 2 мм – толщина образца, площадь грани S = 3*4 мм 2 .

In order to obtain temperature dependences, the cell with the sample is placed in a coolant (nitrogen) stream passed through a heat exchanger, the temperature of which is set by the heater. The heater temperature is controlled by a thermostat. Feedback from the temperature meter to the thermostat allows you to set the rate of temperature measurement, or to stabilize it. A thermocouple is used to control the temperature. In this work, the temperature was changed at a rate of 1 deg / min. This method allows you to measure temperature with an error of 0.1 degrees.

The measuring cell with the sample fixed on it is placed in a flow-through cryostat. The cell is connected to the LCR meter by shielded wires through a connector in the cryostat cap. The cryostat is placed between the poles of the FL-1 electromagnet. The magnet power supply unit allows obtaining magnetic fields up to 15 kOe. To measure the magnitude of the tension magnetic field H uses a thermally stabilized Hall sensor with an electronics unit. To stabilize the magnetic field, there is a feedback between the power supply and the magnetic field meter.

The measured values ​​of the capacitance C and the tangent of the loss angle D = tan δ are related to the values ​​of the sought physical quantities εʹ and εʺ by the following relationships:

(16)

(17)

№	C (pF)	Re (ε ')	T (° C)	tg δ	Q c	Im (ε ")	ω (Hz)	σ (ω)
	3,805	71,66		0,075	13,33	5,375	10 3
	3,838			0,093
	3,86			0,088
	3,849			0,094
	3,893			0,106
	3,917			0,092
	3,951			0,103
	3,824			0,088
	3,873			0,105
	3,907			0,108
	3,977			0,102
	4,031			0,105
	4,062			0,132
	4,144			0,109
	4,24			0,136
	4,435			0,175
	4,553			0,197
	4,698			0,233
	4,868			0,292
	4,973			0,361
	5,056			0,417
	5,164			0,491
	5,246			0,552
	5,362			0,624
	5,453			0,703
	5,556			0,783
	5,637			0,867
	5,738			0,955
	5,826			1,04
	5,902			1,136

Table # 1. Gd x Mn 1-x S, (x = 0.1).

The dielectric constant

The phenomenon of polarization is judged by the value of the dielectric constant ε. The parameter ε, which characterizes the ability of a material to form a capacitance, is called the relative permittivity.

The word "relative" is usually omitted. It should be taken into account that the electrical capacity of the insulation section with electrodes, i.e. capacitor depends on the geometric dimensions, configuration of the electrodes and on the structure of the material that forms the dielectric of this capacitor.

In vacuum ε = 1, and any dielectric is always greater than 1. If C0 - em-

bone, between the plates of which there is a vacuum, of arbitrary shape and size, and C is the capacitance of a capacitor of the same size and shape, but filled with a dielectric with a dielectric constant ε, then

Denoting through C0 the electrical constant (F / m) equal to

C0 = 8.854.10-12,

find the absolute dielectric constant

ε’ = ε0 .ε.

Let us determine the capacitance values ​​for some forms of dielectrics.

For flat capacitor

С = ε0 ε S / h = 8.854 1О-12 ε S / h.

where S is the cross-sectional area of ​​the electrode, m2;

h is the distance between the electrodes, m.

Practical value dielectric constant is very high. It determines not only the ability of the material to form a capacity, but also enters into a number of basic equations that characterize physical processes flowing in the dielectric.

The dielectric constant of gases, due to their low density (due to large distances between molecules), is insignificant and close to unity. Usually gas polarization is electronic or dipole if the molecules are polar. ε of a gas is the higher, the larger the radius of the molecule. A change in the number of gas molecules per unit volume of gas (n) with a change in temperature and pressure causes a change in the dielectric constant of the gas. The number of molecules N is proportional to pressure and inversely proportional to absolute temperature.

With a change in humidity, the dielectric constant of air changes slightly in direct proportion to the change in humidity (at room temperature). At elevated temperatures, the effect of humidity increases significantly. The temperature dependence of the dielectric constant is characterized by the expression

T K ε = 1 / ε (dε / dT).

Using this expression, you can calculate the relative change in the dielectric constant when the temperature changes by 1 0 K - the so-called temperature coefficient TK of the dielectric constant.

The TC value of a non-polar gas is found by the formula

T K ε = (ε -1) / dT.

where T is the temperature. TO.

The dielectric constant of liquids is highly dependent on their structure. The ε values ​​of non-polar liquids are small and close to the square of the refractive index of light n 2. The dielectric constant of polar liquids, which are used as technical dielectrics, ranges from 3.5 to 5, which is noticeably higher than that of non-polar liquids.

Thus, the polarization of liquids containing dipole molecules is determined simultaneously by the electron and dipole relaxation polarizations.

Strongly polar liquids are characterized by a high ε value due to their high conductivity. The temperature dependence of ε in dipole liquids is more complex than neutral liquids.

Therefore, ε at a frequency of 50 Hz for chlorinated biphenyl (Savol) rapidly increases due to a sharp drop in the viscosity of the liquid, and the dipole

the molecules have time to orient themselves following the change in temperature.

The decrease in ε occurs due to the intensification of the thermal motion of the molecules, which prevents their orientation in the direction of the electric field.

Dielectrics are divided into four groups according to the type of polarization:

The first group - single-composition, homogeneous, pure without additives, dielectrics, in which mainly electronic polarization or close packing of ions. These include non-polar and weakly polar solid dielectrics in the crystalline or amorphous state, as well as non-polar and weakly polar liquids and gases.

The second group - technical dielectrics with electronic, ionic and simultaneously with dipole relaxation polarizations. These include polar (dipole) organic semi-liquids and solids, such as oil rosin compounds, cellulose, epoxy resins, and composites composed of these substances.

The third group - technical dielectrics with ionic and electronic polarizations; dielectrics with electronic, ionic relaxation polarizations are divided into two subgroups. The first subgroup includes mainly crystalline substances with close packing of ions ε< 3,0.

The second subgroup includes inorganic glasses and materials containing a glassy phase, as well as crystalline substances with loose ion packing.

The fourth group consists of ferroelectrics with spontaneous, electronic, ionic, electron-ionic relaxation polarizations, as well as migration or high-voltage polarizations for composite, complex and layered materials.

4. Dielectric losses of electrical insulating materials. Types of dielectric losses.

Dielectric loss is the power dissipated in a dielectric when an electric field is applied to it and causing the dielectric to heat up.

Losses in dielectrics are observed both at alternating voltage and at constant voltage, since a through current due to conduction is found in the material. At constant voltage, when there is no periodic polarization, the quality of the material is characterized, as indicated above, by the values ​​of specific volume and surface resistance. With alternating voltage, it is necessary to use some other characteristic of the quality of the material, since in this case, in addition to the through current, additional causes arise that cause losses in the dielectric.

Dielectric losses in an electrical insulating material can be characterized by the power dissipated per unit volume, or specific losses; more often, to assess the ability of a dielectric to dissipate power in an electric field, they use the angle of dielectric loss, as well as the tangent of this angle.

Rice. 3-1. Charge versus voltage for a linear dielectric without losses (a), with losses (b)

The angle of dielectric loss is the angle that complements the phase shift angle between current and voltage in a capacitive circuit to 90 °. For an ideal dielectric, the current vector in such a circuit will advance the voltage vector by 90 °, while the dielectric loss angle will be zero. The more power dissipated in the dielectric, which turns into heat, the smaller the phase shift angle and the larger the angle and its function tg.

It is known from the theory of alternating currents that the active power

Pa = UI cos (3-1)

Let us express the powers for series and parallel circuits in terms of the capacitances Cs and Cp and the angle, which is the complement of the angle up to 90 °.

For a sequential circuit, using expression (3-1) and the corresponding vector diagram, we have

P a = (3-2)

tg = C s r s (3-3)

For parallel circuit

P a = UI a = U 2 C p tg (3-4)

tg = (3-5)

Equating expressions (3-2) and (3-4), as well as (3-3) and (3-5), we find the relationship between Сp and Cs and between rp and rs

C p = C s / 1 + tg 2 (3-6)

r p = r s (1+ 1 / tg 2 ) (3-7)

For high-quality dielectrics, the value of tan2 can be neglected in comparison with unity in formula (3-8) and Cp Cs C can be considered. Expressions for the power dissipated in the dielectric, in this case, will be the same for both circuits:

P a U 2 C tg (3-8)

where Ra is active power, W; U - voltage, V; - angular frequency, s-1; C - capacity, F.

Resistance rр in parallel circuit, as follows from expression (3-7), is many times greater than the resistance rs. The expression for the specific dielectric losses, i.e., the power dissipated per unit volume of the dielectric, has the form:

(3-9)

where p - specific losses, W / m3; = 2 - angular frequency, s-1, E - electric field strength, V / m.

Indeed, the capacity between the opposite sides of a cube with a side of 1 m will be

C1 = 0 r, reactive conductivity

(3-10)

a active component

Having determined by some method at a certain frequency the parameters of the equivalent circuit of the investigated dielectric (Cp and rp or Cs and rs), in the general case, the obtained values ​​of capacitance and resistance cannot be considered inherent in this capacitor and use these data to calculate the loss angle at a different frequency. Such a calculation can only be made if equivalent circuit has a certain physical basis. So, for example, if it is known for a given dielectric that losses in it are determined only by losses from through electrical conductivity in a wide frequency range, then the loss angle of a capacitor with such a dielectric can be calculated for any frequency lying in this range

tg = 1 / Crp (3-12)

where C and rp are constant capacitance and resistance measured at the given frequency.

Losses in such a capacitor, as is easy to see, do not depend on the frequency:

Pa = U2 / rp (3-13)

on the contrary, if the losses in the capacitor are mainly due to the resistance of the lead wires, as well as the resistance of the electrodes themselves (for example, a thin layer of silver), then the power dissipated in such a capacitor will increase in proportion to the square of the frequency:

Pa = U2 C tg = U2 C Crs = U2 2C2rs (3-14)

From last expression a very important practical conclusion can be drawn: capacitors intended for operation at high frequency should have as low as possible the resistance of both electrodes and connecting wires and transition contacts.

Dielectric losses, according to their characteristics and physical nature, can be divided into four main types:

1) dielectric losses due to polarization;

2) dielectric losses due to through electrical conductivity;

ionization dielectric losses;

dielectric losses due to structure inhomogeneity.

Dielectric losses due to polarization are especially clearly observed in substances with relaxation polarization: in dielectrics of a dipole structure and in dielectrics of an ionic structure with a loose packing of ions.

Relaxation dielectric losses are caused by the violation of the thermal motion of particles under the influence of electric field forces.

Dielectric losses observed in ferroelectrics are associated with the phenomenon of spontaneous polarization. Therefore, losses in ferroelectrics are significant at temperatures below the Curie point, when spontaneous polarization is observed. At temperatures above the Curie point, losses in ferroelectrics decrease. The electrical aging of a ferroelectric with time is accompanied by a slight decrease in losses.

Dielectric losses due to polarization also include the so-called resonance losses, which manifest themselves in dielectrics at high frequencies. This type of loss is observed with particular clarity in some gases at a strictly defined frequency and is expressed in the intense absorption of the energy of the electric field.

Resonant losses are also possible in solids if the frequency of forced vibrations caused by the electric field coincides with the frequency of natural vibrations of the particles of the solid. The presence of a maximum in the frequency dependence of tan is also characteristic of the resonant loss mechanism, however, in in this case temperature does not affect the position of the maximum.

Dielectric losses due to through electrical conductivity are found in dielectrics with noticeable bulk or surface conductivity.

The tangent of the dielectric loss angle in this case can be calculated by the formula

Dielectric losses of this type do not depend on the field frequency; tg decreases with frequency according to the hyperbolic law.

Dielectric losses due to electrical conductivity increase exponentially with temperature

PaT = Aexp (-b / T) (3-16)

where A, b are material constants. Formula (3-16) can be roughly rewritten as follows:

PaT = Pa0exp (t) (3-17)

where PaT - losses at temperature t, ° С; Pa0 - losses at a temperature of 0 ° C; - constant material.

The tangent of dielectric losses depending on temperature changes according to the same law that was used to approximate the temperature dependence of Pa, since the temperature change in capacitance can be neglected.

Ionization dielectric losses are inherent in dielectrics and gaseous state; Ionization losses are manifested in inhomogeneous electric fields at intensities exceeding the value corresponding to the onset of ionization of a given gas. Ionization losses can be calculated by the formula

Pa. U = A1f (U-Ui) 3 (3-18)

where A1 is a constant coefficient; f is the field frequency; U is the applied voltage; Ui is the voltage corresponding to the onset of ionization.

Formula (3-18) is valid at U> Ui and a linear dependence of tan on E. The ionization voltage Ui depends on the pressure at which the gas is located, since the development of impact ionization of molecules is associated with the mean free path of charge carriers.

Dielectric losses due to structural inhomogeneity are observed in layered dielectrics, made of impregnated paper and cloth, in plastics with a filler, in porous ceramics in micanites, micalex, etc.

Due to the diversity of the structure of inhomogeneous dielectrics and the features of the components they contain, there is no general formula for calculating dielectric losses of this type.

Dielectricś permeabilitý capacity environment - a physical quantity characterizing the properties of an insulating (dielectric) medium and showing the dependence of electrical induction on the strength of the electric field.

It is determined by the effect of polarization of dielectrics under the action of an electric field (and with the value of the dielectric susceptibility of the medium characterizing this effect).

Distinguish between relative and absolute permittivity.

The relative permittivity ε is dimensionless and shows how many times the force of interaction of two electric charges in a medium is less than in a vacuum. This value for air and most other gases under normal conditions is close to unity (due to their low density). For most solid or liquid dielectrics, the relative permittivity ranges from 2 to 8 (for a static field). The dielectric constant of water in a static field is quite high - about 80. Its values ​​are great for substances with molecules that have a large electric dipole moment. The relative dielectric constant of ferroelectrics is tens and hundreds of thousands.

The absolute dielectric constant in the foreign literature is denoted by the letter ε, in the domestic one the combination is predominantly used, where is the electric constant. Absolute dielectric constant is used only in the International System of Units (SI), in which induction and electric field strength are measured in different units. In the CGS system, there is no need to introduce an absolute dielectric constant. The absolute dielectric constant (like the electric constant) has the dimension L −3 M −1 T 4 I². In units of the International System of Units (SI): = F / m.

It should be noted that the dielectric constant is highly dependent on the frequency electromagnetic field... This should always be taken into account, since the tables of the handbooks usually contain data for a static field or low frequencies up to several kHz units without specifying this fact... At the same time, there are optical methods for obtaining the relative permittivity from the refractive index using ellipsometers and refractometers. The value obtained by the optical method (frequency 10 14 Hz) will differ significantly from the data in the tables.

Consider, for example, the case of water. In the case of a static field (frequency is zero), the relative permittivity under normal conditions is approximately 80. This is the case up to infrared frequencies. From about 2 GHz ε r starts to fall. In the optical range ε r is approximately 1.8. This is quite consistent with the fact that in the optical range, the refractive index of water is 1.33. In a narrow frequency range, called optical, dielectric absorption drops to zero, which actually provides a person with the mechanism of vision [ source not specified 1252 days] in the earth's atmosphere saturated with water vapor. WITH further growth the frequencies of the properties of the medium change again. The behavior of the relative permittivity of water in the frequency range from 0 to 10 12 (infrared) can be read in (eng.)

The dielectric constant of dielectrics is one of the main parameters in the design of electrical capacitors. The use of materials with a high dielectric constant can significantly reduce the physical dimensions of the capacitors.

The capacitance of the capacitors is determined by:

where ε r- dielectric constant of the substance between the plates, ε O- electric constant, S- area of ​​capacitor plates, d is the distance between the plates.

The dielectric constant is taken into account when designing printed circuit boards. The value of the dielectric constant of the substance between the layers, in combination with its thickness, affects the value of the natural static capacitance of the power supply layers, and also significantly affects the characteristic impedance of the conductors on the board.

SPECIFIC RESISTANCE electrical, physical quantity equal to electrical resistance ( cm. ELECTRICAL RESISTANCE) R of a cylindrical conductor of unit length (l = 1m) and unit cross-sectional area (S = 1 m 2) .. r = R S / l. In Xi, the unit of resistivity is Ohm. m. Resistivity can also be expressed in ohms. see Resistivity is a characteristic of the material through which the current flows, and depends on the material from which it is made. Specific resistance equal to r = 1 Ohm. m means that a cylindrical conductor made of of this material, length l = 1 m and with a cross-sectional area S = 1 m 2 has a resistance R = 1 Ohm. m. The value of the resistivity of metals ( cm. METALS), which are good guides (cm. CONDUCTORS), can have values ​​of the order of 10 - 8 - 10 - 6 Ohm. m (for example, copper, silver, iron, etc.). The resistivity of some solid dielectrics ( cm. DIELECTRICS) can reach a value of 10 16 -10 18 Ohm.m (for example, quartz glass, polyethylene, electroporcelain, etc.). The resistivity of many materials (especially semiconductor materials ( cm. SEMICONDUCTOR MATERIALS)) significantly depends on the degree of their purification, the presence of alloying additives, thermal and mechanical treatments, etc. cm. SIEMENS (unit of conductivity)) per meter S / m. Electrical resistivity (conductivity) is a scalar quantity for an isotropic substance; and tensor - for anisotropic matter. In anisotropic single crystals, the anisotropy of electrical conductivity is a consequence of the anisotropy of the inverse effective mass ( cm. EFFECTIVE MASS) electrons and holes.

1-6. ELECTRICAL CONDUCTIVITY OF INSULATION

When the insulation of a cable or wire is turned on to a constant voltage U, a current i passes through it, changing over time (Fig. 1-3). This current has constant components - the conduction current (i ∞) and the absorption current, where γ is the conductivity corresponding to the absorption current; T is the time during which the current i abs falls to 1 / e of its initial value. For an infinitely long time, i abs → 0 and i = i ∞. The electrical conductivity of dielectrics is explained by the presence in them of a certain amount of free charged particles: ions and electrons.

The most characteristic for most of electrical insulating materials is ionic conductivity, which is possible due to the inevitably present in the insulation of impurities (impurities of moisture, salts, alkalis, etc.). In a dielectric with an ionic character of electrical conductivity, Faraday's law is strictly observed - the proportionality between the amount of electricity passed through the insulation and the amount of substance released during electrolysis.

As the temperature rises, the resistivity of electrical insulating materials decreases and is characterized by the formula

where_ρ o, A and B are constants for a given material; T- temperature, ° K.

A large dependence of the insulation resistance on moisture occurs in hygroscopic insulating materials, mainly fibrous (paper, cotton yarn, etc.). Therefore, fibrous materials are dried and impregnated, as well as protected by moisture-resistant casings.

The insulation resistance can decrease with increasing voltage due to the formation of space charges in the insulating materials. The additional electronic conductivity created in this case leads to an increase in electrical conductivity. There is a dependence of conductivity on voltage in very strong fields (the law of Ya.I. Frenkel):

where γ about - conductivity in weak fields; a - constant. All electrical insulating materials are characterized by certain values ​​of the insulation conductivity G. Ideally, the conductivity of insulating materials is zero. In real insulating materials, the conductivity per unit length of the cable is determined by the formula

In cables with an insulation resistance of more than 3-10 11 ohm-m and communication cables, where dielectric polarization losses are much greater than heat losses, conductivity is determined by the formula

Insulation conductivity in communication engineering is an electrical parameter of a line that characterizes energy losses in the insulation of cable cores. The frequency dependence of the conductivity is shown in Fig. 1-1. The inverse of conductivity, the insulation resistance, is the ratio of the DC voltage applied to the insulation (in volts) to the leakage current (in amperes), i.e.

where R V is the volumetric insulation resistance, which numerically determines the obstacle created by the passage of current through the thickness of the insulation; R S - surface resistance, which determines the obstacle to the passage of current along the surface of the insulation.

A practical assessment of the quality of the used insulating materials is the specific volume resistivity ρ V expressed in ohm-centimeters (ohm * cm). Numerically, ρ V is equal to the resistance (in ohms) of a cube with an edge of 1 cm from a given material, if the current passes through two opposite faces of the cube. The specific surface resistance ρ S is numerically equal to the surface resistance of the square (in ohms) if the current is applied to the electrodes bounding two opposite sides of this square.

The insulation resistance of a single-core cable or wire is determined by the formula

Moisture properties of dielectrics

Moisture resistance - it is the reliability of the operation of the insulation when it is in an atmosphere of water vapor close to saturation. Moisture resistance is assessed by the change in electrical, mechanical and other physical properties after finding the material in an atmosphere with high and high humidity; by moisture and water permeability; by moisture and water absorption.

Moisture permeability - the ability of the material to pass moisture vapor in the presence of a difference in the relative humidity of the air on both sides of the material.

Moisture absorption - the ability of the material to absorb water during prolonged stay in a humid atmosphere close to the saturation state.

Water absorption - the ability of a material to absorb water during prolonged immersion in water.

Tropic resistance and tropicalization equipment – protection of electrical equipment from moisture, mold, rodents.

Thermal properties of dielectrics

The following quantities are used to characterize the thermal properties of dielectrics.

Heat resistance- the ability of electrical insulating materials and products to withstand high temperatures and sudden temperature changes without harm to them. Determined by the temperature at which a significant change in mechanical and electrical properties is observed, for example, tensile or bending deformation under load begins in organic dielectrics.

Thermal conductivity- the process of transferring heat in the material. It is characterized by an experimentally determined coefficient of thermal conductivity λ t. Λ t is the amount of heat transferred in one second through a layer of material 1 m thick and a surface area of ​​1 m 2 at a temperature difference of the layer surfaces of 1 ° K. The thermal conductivity coefficient of dielectrics varies within wide limits. The most low valuesλ t have gases, porous dielectrics and liquids (for air λ t = 0.025 W / (m K), for water λ t = 0.58 W / (m K)), crystalline dielectrics have high values ​​(for crystalline quartz λ t = 12.5 W / (m K)). The thermal conductivity coefficient of dielectrics depends on their structure (for fused quartz λ t = 1.25 W / (m · K)) and temperature.

Thermal expansion dielectrics are estimated by the temperature coefficient of linear expansion: ... Materials with low thermal expansion, as a rule, have a higher heat resistance and vice versa. Thermal expansion organic dielectrics significantly (tens and hundreds of times) exceeds the expansion of inorganic dielectrics. Therefore, the dimensional stability of parts made of inorganic dielectrics with temperature fluctuations is much higher compared to organic ones.

1. Absorption currents

Displacement currents of various types of delayed polarization are called absorption currents. Absorption currents at constant voltage flow in the dielectric until an equilibrium state is established, changing their direction when the voltage is turned on and off. With an alternating voltage, absorption currents flow during the entire time the dielectric is in the electric field.

In general electricity j in the dielectric is the sum of the through current j sc and absorption current j ab

j = j ck + j ab.

The absorption current can be determined through the bias current j cm - the rate of change of the electric induction vector D

The through current is determined by the transfer (movement) in the electric field of various charge carriers.

2. Electronic electrical conductivity is characterized by the movement of electrons under the action of a field. In addition to metals, it is present in carbon, metal oxides, sulfides, and other substances, as well as in many semiconductors.

3. Ionic - due to the movement of ions. It is observed in solutions and melts of electrolytes - salts, acids, alkalis, as well as in many dielectrics. It is subdivided into intrinsic and impurity conductivity. Intrinsic conductivity is due to the movement of ions obtained during dissociation molecules. The movement of ions in an electric field is accompanied by electrolysis - transfer of a substance between the electrodes and its release on the electrodes. Polar liquids are more dissociated and have higher electrical conductivity than non-polar ones.

In non-polar and weakly polar liquid dielectrics (mineral oils, organosilicon liquids), electrical conductivity is determined by impurities.

4. Molecular conductivity - caused by the movement of charged particles called molions... Observe it in colloidal systems, emulsions , suspensions ... The movement of molions under the action of an electric field is called electrophoresis... During electrophoresis, unlike electrolysis, new substances are not formed; the relative concentration of the dispersed phase in different layers of the liquid changes. Electrophoretic conductivity is observed, for example, in oils containing emulsified water.