THE DIELECTRIC CONSTANT

Dielectric constant of the mediumε c is a quantity that characterizes the influence of the medium on the forces of interaction of electric fields. Various environments have different values ​​of ε c .

Absolute the dielectric constant vacuum is called the electric constant ε 0 =8.85 10 -12 f/m.

The ratio of the absolute permittivity of the medium to the electrical constant is called the relative permittivity

those. relative permittivity ε is a value showing how many times the absolute permittivity of the medium is greater than the electrical constant. The value ε has no dimension.

Table 1

Relative permittivity of insulating materials

As can be seen from the table, most dielectrics ε = 1-10 and little depends on electrical conditions and ambient temperature .

There is a group of dielectrics called ferroelectrics, in which ε can reach values ​​up to 10,000, and ε strongly depends on the external field and temperature. Ferroelectrics include barium titanate, lead titanate, Rochelle salt, etc.

Control questions

1. What is the structure of an atom of aluminum, copper?

2. In what units are the sizes of atoms and their particles measured?

3. What electric charge do electrons have?

4. Why are substances electrically neutral in their normal state?

5. What is called an electric field and how is it conventionally depicted?

6. What determines the strength of interaction between electric charges?

7. Why are some materials conductors and others insulators?

8. What materials are conductors and which are insulators?

9. How can the body be charged with positive electricity?

10. What is called the relative permittivity?

Did you know, what's happened thought experiment, gedanken experiment?
It is a non-existent practice, an otherworldly experience, the imagination of what is not really there. Thought experiments are like daydreams. They give birth to monsters. Unlike a physical experiment, which is an experimental test of hypotheses, a “thought experiment” magically replaces an experimental test with the desired, untested conclusions, manipulating logical constructions that actually violate logic itself by using unproved premises as proven ones, that is, by substitution. Thus, the main task of the applicants of "thought experiments" is to deceive the listener or reader by replacing a real physical experiment with his "doll" - fictitious reasoning on parole without physical verification itself.
Filling physics with imaginary, "thought experiments" has led to an absurd, surreal, confusing picture of the world. A real researcher must distinguish such "wrappers" from real values.

Relativists and positivists argue that the "thought experiment" is a very useful tool for testing theories (also arising in our minds) for consistency. In this they deceive people, since any verification can only be carried out by a source independent of the object of verification. The applicant of the hypothesis himself cannot be a test of his own statement, since the reason for this statement itself is the absence of contradictions visible to the applicant in the statement.

We see this in the example of SRT and GR, which have turned into a kind of religion that governs science and public opinion. No amount of facts that contradict them can overcome Einstein's formula: "If the fact does not correspond to the theory, change the fact" (In another version, "Does the fact not correspond to the theory? - So much the worse for the fact").

The maximum that a "thought experiment" can claim is only the internal consistency of the hypothesis within the framework of the applicant's own, often by no means true, logic. Compliance with practice does not check this. A real test can only take place in a real physical experiment.

An experiment is an experiment, because it is not a refinement of thought, but a test of thought. Thought that is consistent within itself cannot test itself. This has been proven by Kurt Gödel.

Electrical Permeability

Electrical permittivity is a value 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 area of ​​​​the plates (than more 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, whose characteristic is the electrical permeability.

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

In technology, dielectrics with high and ultrahigh electrical permeability have been obtained. Their main part is rutile (titanium dioxide).

Figure 1. Electrical permeability of the medium

Dielectric loss angle

In the article "Dielectrics" we analyzed examples of the inclusion of a dielectric in a circuit of constant and alternating current. It turned out that a real dielectric when working in electric field formed by an alternating voltage, thermal energy is released. The power absorbed in this case is called dielectric losses. In the article "An AC circuit containing a capacitance", it will be proved 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 shift 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 has been established that dielectric losses are proportional to the square of voltage, AC frequency, capacitor capacitance and dielectric loss tangent.

Therefore, 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 large tg δ (on the order of 0.08 - 0.1 or more) are poor insulators. Materials with relatively small tg δ (on the order of 0.0001) are good insulators.

The dielectric constant

The phenomenon of polarization is judged by the value of the permittivity 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 capacitance of the insulation section with electrodes, i.e. capacitor, depends on geometric dimensions, the configuration of the electrodes, and the structure of the material that forms the dielectric of this capacitor.

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

a 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 permittivity ε, then

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

C0 = 8.854.10-12,

find the absolute permittivity

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 capacitance, but also enters into a number of basic equations that characterize the physical processes occurring 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. Typically, the polarization of a gas is electronic or dipole if the molecules are polar. ε of the gas is 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.

When humidity changes, the dielectric constant of air changes slightly in direct proportion to the change in humidity (at room temperature). At elevated temperature the influence of humidity is greatly enhanced. The temperature dependence of the permittivity is characterized by the expression

T K ε = 1 / ε (dε / dT).

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

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

T K ε \u003d (ε -1) / dT.

where T is temperature. TO.

The dielectric constant of liquids is highly dependent on their structure. The values ​​of ε 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.

So the polarization of liquids containing dipole molecules, is determined simultaneously by the electronic and dipole-relaxation polarizations.

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

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

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

The decrease in ε occurs due to an increase in the thermal motion of 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 is single-composition, homogeneous, pure, without additives, dielectrics, which mainly have electronic polarization or dense 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 is technical dielectrics with electronic, ionic and simultaneously with dipole-relaxation polarizations. These include polar (dipole) organic semi-liquid and solid substances, such as oil-rosin compounds, cellulose, epoxy resins and composite materials made up of these substances.

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

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

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

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

Dielectric losses are the power dissipated in a dielectric when exposed to an electric field and causing heating of the dielectric.

Losses in dielectrics are observed both at alternating voltage and at constant voltage, since a through current is detected in the material due to conductivity. At a constant voltage, when there is no periodic polarization, the quality of the material is characterized, as mentioned above, by the values ​​of the specific volume and surface resistances. With an 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, there are additional causes that cause losses in the dielectric.

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

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

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

From the theory of alternating currents, it is known that the active power

Ra = UI cos (3-1)

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

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

Pa = (3-2)

tg = C s r s (3-3)

For parallel circuit

P a \u003d Ui a \u003d 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) to each other, we find the relationship between Сp and Cs and between rp and rs

C p \u003d C s /1 + tg 2 (3-6)

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

For high-quality dielectrics, you can neglect the value of tg2 compared to unity in formula (3-8) and calculate Ср Cs С. The expressions for the power dissipated in the dielectric, in this case, will be the same for both circuits:

P a U 2 Ctg (3-8)

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

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

(3-9)

where р - specific losses, W/m3; \u003d 2 - angular frequency, s-1, E - electric field strength, V / m.

Indeed, the capacitance between opposite faces of a cube with a side of 1 m will be

С1 = 0 r , reactive component of conductivity

(3-10)

a active component

Having determined by some method at a certain frequency the parameters of the equivalent circuit of the dielectric under study (Ср and rр or Cs and rs), in the general case, it is impossible to consider the obtained values ​​of capacitance and resistance as 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 the equivalent circuit has a certain physical justification. So, for example, if it is known for a given dielectric that the losses in it are determined only by losses from through conduction 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 a given frequency.

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

Pa=U2/rp (3-13)

on the contrary, if the losses in the capacitor are mainly due to the resistance of the supply 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 the last expression, a very important practical conclusion can be drawn: capacitors designed to operate at high frequency should have the lowest possible resistance of both the electrodes and the connecting wires and transitional contacts.

According to their features and physical nature, dielectric losses can be divided into four main types:

1) dielectric losses due to polarization;

2) dielectric losses due to through conduction;

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 loose packing of ions.

Relaxation dielectric losses are caused by 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 some decrease in losses.

Dielectric losses due to polarization should also include the so-called resonant 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.

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

Dielectric losses due to through conduction are found in dielectrics that have a noticeable volume or surface conductivity.

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

Dielectric losses of this kind do not depend on the frequency of the field; 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. Approximately formula (3-16) can be rewritten as follows:

PaT=Pa0exp( t) (3-17)

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

The dielectric loss tangent varies with temperature according to the same law that is 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 in the gaseous state; Ionization losses appear in non-uniform electric fields at strengths exceeding the value corresponding to the beginning of the ionization of a given gas. Ionization losses can be calculated by the formula

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

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

Formula (3-18) is valid for U > Ui and a linear dependence of tg 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, from impregnated paper and fabric, in filled plastics, in porous ceramics in micanites, mycalex, etc.

Due to the diversity of the structure of inhomogeneous dielectrics and the features of the components contained in them, there are no general formula calculation of dielectric losses of this type.

VIRTUAL LABORATORY WORK #3 ON

PHYSICS OF THE SOLID STATE

Methodical instructions for implementation laboratory work No. 3 in the section of physics " solid body" for students technical specialties 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 decision of the methodological commission of the ICT

Determination of the dielectric constant of semiconductors. Virtual laboratory work No. 3 in solid state physics: Guidelines 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. Reshetneva, 2012

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

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

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

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

Theory of the method……………………………………………………………………......5

Method for measuring the dielectric constant…………………..……..11

Processing measurement results…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

Control questions…………..………………………………………………….17

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

References…………………………………………………………………20

Application……………………………………………………………………………21

INTRODUCTION

These guidelines contain descriptions for laboratory work that uses virtual models from the Solid State Physics course.

Access to laboratory work:

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

1) Each student preliminarily draws up his personal summary of this laboratory work;

2) The teacher individually checks the design of the abstract and asks questions about the theory, measurement methods, 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 abstract.

Registration of laboratory work for protection:

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

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

Graphs must meet all the requirements of the teacher.

For all quantities in the tables, the appropriate unit of measure must be recorded.

Recorded conclusions for each graph.

The answer is written in the prescribed form.

Recorded conclusions on the answer.

DETERMINATION OF THE DIELECTRIC RESISTANCE OF SEMICONDUCTORS

Method theory

Polarization is the ability of a dielectric to polarize under the action of an electric field, i.e. change in space the location of the bound charged particles of the dielectric.

The most important property dielectrics is their ability to electrical polarization, 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 various kinds 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. The electronic polarization is established in 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 orientational polarization due to the orientation of the dipoles in the direction of the electric field. Dipole polarization is possessed by polar dielectrics. Its establishment time is 10 -10 -10 -6 s. Dipole polarization is one of the slow or relaxation types of polarization.

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

5. Ion relaxation polarization due to the excess 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. Its establishment time is 10 -8 -10 -4 s.

6. Electronic relaxation polarization arises due to excess “defective” electrons or “holes” excited by thermal energy. This type of polarization usually causes high value permittivity.

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

8. Elastic-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 dipole oscillations, then the oscillations of molecules can increase, which will lead to the appearance of resonant polarization in the dipole dielectric. Resonant polarization is observed at frequencies lying in the infrared light region. A real dielectric can simultaneously have several types of polarization. The occurrence of one or another type of polarization is determined by the physicochemical properties of the substance and the range of frequencies used.

Main settings:

ε is the permittivity is a measure of the ability of a material to polarize; is a value showing how many times the force of interaction electric charges v this material less than in vacuum. Inside the dielectric there is a field 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 ε times, 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. This is the basis for a simple definition of the permittivity:

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 permittivity ε of an isotropic medium is determined by the relation:

(2)

where χ is the dielectric susceptibility.

D = tg δ is the dielectric loss tangent

Dielectric losses - losses of electrical energy due to the flow of currents in dielectrics. Distinguish between the through conduction current I sk.pr, caused by the presence of a small number of easily mobile ions in dielectrics, and polarization currents. With electronic and ionic polarization, the polarization current is called the displacement current I cm, it is very short-term and is not recorded by instruments. The currents associated with slow (relaxation) types of polarization are called absorption currents I abs. In the general case, the total current in the dielectric is defined as: I = I abs + I rms. After establishing the polarization, the total current will be equal to: I=I rms. If in a constant field polarization currents occur at the moment of switching on and off the voltage, and the total current is determined in accordance with the equation: I \u003d I sk.pr, then in an alternating field polarization currents arise at the moment of changing the voltage polarity. As a result, losses in the dielectric in an alternating field can be significant, especially if the half-cycle of the applied voltage approaches the polarization settling time.

On fig. 1(a) shows a circuit equivalent to a dielectric capacitor in an AC 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 circuit under consideration, where U are the voltages in the circuit; I ak - active current; I p - reactive current, which is 90 ° ahead of the active component in phase; 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) scheme; (b) - vector diagram of currents and voltages

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

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

Therefore, in fig. 2 (a, b) are shown general trends, characteristic of some main groups i.e. Typical dependences of the permittivity ε on the temperature T (a) and on the frequency ω (b) are shown.

Rice. 2. Frequency dependence of the real (ε') and imaginary (ε') parts of the permittivity in the presence of the orientational relaxation mechanism

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

(3)

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

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

This behavior of εʹ and εʺ with frequency is a frequent example of a more general result, according to which εʹ(ω) on frequency also entails 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 is generally equal to the vector sum of its own μ 0 and induced μ and moments:

(6)

The field strengths created by these dipoles are proportional to dipole moment and are 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 solid 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 is the polarization of the material, for nonpolar 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 increases significantly. Due to the high frequency of electrons in orbits (on the order of 1015–1016 Hz), the time for establishing the equilibrium state of electron polarization is very short and the permeability ε of nonpolar dielectrics does not depend on the field frequency in the commonly used frequency range (up to 1012 Hz).

2) As the temperature rises, 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 permittivity ε. In view of the smallness of the time of establishing the state of ion polarization (on the order of 10 13 Hz, which corresponds to the natural frequency of ion oscillations in crystal lattice) the 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 permittivity of polar dielectrics strongly depends on the temperature and frequency of the external field. As the temperature increases, the mobility of particles increases and the energy of interaction between them decreases, i.e. their orientation is facilitated under the action of an external field - the dipole polarization and permittivity 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 of thermal motion and by means of thermal motion, the establishment of polarization requires a considerable time. This time is so long that in alternating high-frequency fields, the dipoles do not have time to orient themselves along the field, and the permeability ε drops.

Method for measuring the permittivity

Capacitor capacitance. Capacitor- this 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 equal charges of the opposite sign, then the electric field strength between the plates will be twice as large as the field strength of one plate:

(8)

where ε is the permittivity 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 capacitance:

(9)

SI unit of electrical capacity - Farad(F). Such a capacitor has a capacity of 1 F, the potential difference between the plates of which is 1 V when the plates are given opposite charges of 1 C each: 1 F = 1 C / 1 V.

Capacitance of a flat capacitor. The formula for calculating the electric capacitance of a flat capacitor can be obtained using expression (8). Indeed, the field strength: 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- distance between plates. Substituting into formula (9), we obtain an expression for the electric capacitance of a flat capacitor:

(10)

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

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

Rice. 3. Capacitor with a dielectric placed in it

If a dielectric plate is placed between the plates of a 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.

Denote: d c - the thickness of the air gap, d m is 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, a d = d in + d m, then these options can be considered for cases:

When l at = 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 according to a harmonic law with a frequency ω, the complex permittivity tensor takes the form:

(12)

where σ is the optical conductivity of the substance, εʹ is the permittivity of the substance related to the polarization of the dielectric. Expression (12) can be reduced to the following form:

where the imaginary term is responsible for the dielectric losses .

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 goodness:

Q c =1/tanδ (15)

where R c is the resistance, which depends mainly on dielectric losses. To measure these characteristics, there are a number of methods: various bridge methods, measurements with the 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 campaign. The measurements were carried out on a precision immitance meter - LCR-819-RLC. The device allows you to measure the capacitance within 20 pF–2.083 mF, the loss tangent within 0.0001-9999 and apply a bias field. Internal bias up to 2 V, external offset up to 30 V. Measurement accuracy is 0.05%. Test signal frequency 12 Hz -100 kHz.

In this work, the measurements were carried out at a frequency of 1 kHz in the temperature range 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) flow passed through a heat exchanger, the temperature of which is set by the heater. The temperature of the heater is controlled by a thermostat. Feedback from the temperature meter to the thermostat allows you to set the speed of temperature measurement, or to carry out its stabilization. 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 the temperature with an error of 0.1 deg.

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

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

(16)

(17)

№	C(pF)	Re(ε')	T (°K)	tg δ	Qc	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 number 1. Gd x Mn 1-x S, (x=0.1).