Conductivity units. Electrical conductivity. Definition, units of measurement. Experiment: measuring total mineralization and conductivity

In this article we will cover the topic of electrical conductivity, remember what electric current is, how it is related to the resistance of the conductor and, accordingly, to its electrical conductivity. Let us note the basic formulas for calculating these quantities, and touch upon the topic and its connection with the electric field strength. We will also touch on the relationship between electrical resistance and temperature.

First, let's remember what electric current is. If you place a substance in an external electric field, then under the influence of forces from this field, the movement of elementary charge carriers - ions or electrons - will begin in the substance. This will be an electric current. The current strength I is measured in amperes, and one ampere is the current at which a charge equal to one coulomb flows through the cross-section of the conductor per second.

Current can be constant, alternating, or pulsating. Direct current does not change its magnitude and direction at any given moment in time, alternating current changes its magnitude and direction over time (alternating current generators and transformers provide alternating current), pulsating current changes its magnitude, but does not change direction (for example, rectified alternating current the current is pulsating).

Substances have the property of conducting electric current under the influence of an electric field, and this property is called electrical conductivity, which varies from substance to substance. The electrical conductivity of substances depends on the concentration of free charged particles in them, that is, ions and electrons that are not associated with the crystal structure, molecules, or atoms of the substance. Thus, depending on the concentration of free charge carriers in a substance, substances according to the degree of electrical conductivity are divided into: conductors, dielectrics and semiconductors.

They have the highest electrical conductivity, and by physical nature, conductors in nature are represented by two types: metals and electrolytes. In metals, the current is caused by the movement of free electrons, that is, their conductivity is electronic, and in electrolytes (in solutions of acids, salts, alkalis) - by the movement of ions - parts of molecules that have a positive and negative charge, that is, the conductivity of electrolytes is ionic. Ionized vapors and gases are characterized by mixed conductivity, in which the current is caused by the movement of both electrons and ions.

The electronic theory perfectly explains the high electrical conductivity of metals. The connection of valence electrons with their nuclei in metals is weak, therefore these electrons move freely from atom to atom throughout the volume of the conductor.

It turns out that free electrons in metals fill the space between atoms like a gas, an electron gas, and are in chaotic motion. But when a metal conductor is introduced into an electric field, free electrons will begin to move in an orderly manner, they will move towards the positive pole, thereby creating a current. Thus, the ordered movement of free electrons in a metal conductor is called electric current.

It is known that the speed of propagation of the electric field in space is approximately equal to 300,000,000 m/s, that is, the speed of light. This is the same speed at which current flows through the conductor.

What does it mean? This does not mean that each electron in a metal moves at such a huge speed; electrons in a conductor, on the contrary, have speeds from several millimeters per second to several centimeters per second, depending on , but the speed of propagation of electric current through the conductor is exactly equal to the speed of light .

The thing is that each free electron ends up in the general electron flow of that very “electron gas”, and during the passage of current, the electric field affects this entire flow, as a result, the electrons continuously transmit this field effect to each other - from neighbor to neighbor.

But the electrons move in their places very slowly, despite the fact that the speed of distribution of electrical energy along the conductor turns out to be enormous. So, when a switch is turned on at a power plant, current instantly appears throughout the entire network, while the electrons practically stand still.

However, when free electrons move along a conductor, they experience numerous collisions along the way; they collide with atoms, ions, and molecules, transferring part of their energy to them. The energy of moving electrons overcoming such resistance is partially dissipated in the form of heat, and the conductor heats up.

These collisions serve as resistance to the movement of electrons, therefore the property of a conductor to impede the movement of charged particles is called electrical resistance. When the resistance of the conductor is low, the conductor is heated by the current weakly, when it is significant, it is much stronger, and even white-hot; this effect is used in heating devices and in incandescent lamps.

The unit of resistance change is Ohm. Resistance R = 1 Ohm is the resistance of such a conductor, when a direct current of 1 ampere passes through it, the potential difference at the ends of the conductor is equal to 1 volt. The resistance standard of 1 Ohm is a mercury column with a height of 1063 mm, a cross-section of 1 sq. mm at a temperature of 0°C.

Since conductors are characterized by electrical resistance, we can say that to some extent the conductor is capable of conducting electric current. In this regard, a quantity called conductivity or electrical conductivity was introduced. Electrical conductivity is the ability of a conductor to conduct electric current, that is, the reciprocal of electrical resistance.

The unit of electrical conductivity G (conductivity) is Siemens (Cm), and 1 Cm = 1/(1 Ohm). G = 1/R.

Since the atoms of different substances hinder the passage of electric current to varying degrees, the electrical resistance of different substances is different. For this reason, the concept was introduced, the value of which “p” characterizes the conductive properties of a particular substance.

Electrical resistivity is measured in Ohm*m, that is, the resistance of a cube of a substance with an edge of 1 meter. In the same way, the electrical conductivity of a substance is characterized by specific electrical conductivity?, measured in S/m, that is, the conductivity of a cube of a substance with an edge of 1 meter.

Today, conductive materials in electrical engineering are used mainly in the form of tapes, tires, wires, with a certain cross-sectional area and a certain length, but not in the form of meter cubes. And for more convenient calculations of the electrical resistance and electrical conductivity of conductors of specific sizes, more acceptable units of measurement were introduced for both electrical resistivity and electrical conductivity. Ohm*mm2/m - for resistivity, and Sm*m/mm2 - for conductivity.

Now we can say that Electrical resistivity and electrical conductivity characterize the conductive properties of a conductor with a cross-sectional area of ​​1 square mm, a length of 1 meter at a temperature of 20°C, this is more convenient.

Metals such as gold, copper, silver, chromium, and aluminum have the best electrical conductivity. Steel and iron conduct current less well. Pure metals always have better electrical conductivity than their alloys, so pure copper is preferable in electrical engineering. If you need specially high resistance, then use tungsten, nichrome, constantan.

Knowing the value of electrical resistivity or electrical conductivity, one can easily calculate the resistance or electrical conductivity of a particular conductor made of a given material by taking into account the length l and cross-sectional area S of this conductor.

Electrical conductivity and electrical resistance of all materials depend on temperature, since the frequency and amplitude of thermal vibrations of the atoms of the crystal lattice also increases with increasing temperature, the resistance to electric current and electron flow also increases accordingly.

As the temperature decreases, on the contrary, the vibrations of the atoms of the crystal lattice become smaller, the resistance decreases (electrical conductivity increases). For some substances, the dependence of resistance on temperature is less pronounced, for others it is stronger. For example, alloys such as constantan, fechral and manganin slightly change the resistivity in a certain temperature range, so thermally stable resistors are made from them.

Allows you to calculate for a specific material the increase in its resistance at a certain temperature, and numerically characterizes the relative increase in resistance with an increase in temperature by 1 °C.

Knowing the temperature coefficient of resistance and the temperature increment, one can easily calculate the resistivity of a substance at a given temperature.

We hope that our article was useful to you, and now you can easily calculate the resistance and conductivity of any wire at any temperature.

Electrical resistance, expressed in ohms, is different from the concept of resistivity. To understand what resistivity is, we need to relate it to the physical properties of the material.

About conductivity and resistivity

The flow of electrons does not move unimpeded through the material. At a constant temperature, elementary particles swing around a state of rest. In addition, electrons in the conduction band interfere with each other through mutual repulsion due to similar charge. This is how resistance arises.

Conductivity is an intrinsic characteristic of materials and quantifies the ease with which charges can move when a substance is exposed to an electric field. Resistivity is the reciprocal of the material and describes the degree of difficulty electrons encounter as they move through a material, giving an indication of how good or bad a conductor is.

Important! An electrical resistivity with a high value indicates that the material is a poor conductor, while a resistivity with a low value indicates a good conductor.

Specific conductivity is designated by the letter σ and is calculated by the formula:

Resistivity ρ, as an inverse indicator, can be found as follows:

In this expression, E is the intensity of the generated electric field (V/m), and J is the electric current density (A/m²). Then the unit of measurement ρ will be:

V/m x m²/A = ohm m.

For conductivity σ, the unit in which it is measured is S/m or Siemens per meter.

Types of materials

According to the resistivity of materials, they can be classified into several types:

1. Conductors. These include all metals, alloys, solutions dissociated into ions, as well as thermally excited gases, including plasma. Among non-metals, graphite can be cited as an example;
2. Semiconductors, which are actually non-conducting materials, whose crystal lattices are purposefully doped with the inclusion of foreign atoms with a greater or lesser number of bound electrons. As a result, quasi-free excess electrons or holes are formed in the lattice structure, which contribute to the conductivity of the current;
3. Dielectrics or dissociated insulators are all materials that under normal conditions do not have free electrons.

For the transport of electrical energy or in electrical installations for domestic and industrial purposes, a frequently used material is copper in the form of single-core or multi-core cables. An alternative metal is aluminum, although the resistivity of copper is 60% of that of aluminum. But it is much lighter than copper, which predetermined its use in high-voltage power lines. Gold is used as a conductor in special-purpose electrical circuits.

Interesting. The electrical conductivity of pure copper was adopted by the International Electrotechnical Commission in 1913 as the standard for this value. By definition, the conductivity of copper measured at 20° is 0.58108 S/m. This value is called 100% LACS, and the conductivity of the remaining materials is expressed as a certain percentage of LACS.

Most metals have a conductivity value less than 100% LACS. There are exceptions, however, such as silver or special copper with very high conductivity, designated C-103 and C-110, respectively.

Dielectrics do not conduct electricity and are used as insulators. Examples of insulators:

• glass,
• ceramics,
• plastic,
• rubber,
• mica,
• wax,
• paper,
• dry wood,
• porcelain,
• some fats for industrial and electrical use and bakelite.

Between the three groups the transitions are fluid. It is known for sure: there are no absolutely non-conducting media and materials. For example, air is an insulator at room temperature, but when exposed to a strong low-frequency signal, it can become a conductor.

Determination of conductivity

When comparing the electrical resistivity of different substances, standardized measurement conditions are required:

1. In the case of liquids, poor conductors and insulators, cubic samples with an edge length of 10 mm are used;
2. The resistivity values ​​of soils and geological formations are determined on cubes with a length of each edge of 1 m;
3. The conductivity of a solution depends on the concentration of its ions. A concentrated solution is less dissociated and has fewer charge carriers, which reduces conductivity. As the dilution increases, the number of ion pairs increases. The concentration of solutions is set to 10%;
4. To determine the resistivity of metal conductors, wires of a meter length and a cross-section of 1 mm² are used.

If a material, such as a metal, can provide free electrons, then when a potential difference is applied, an electric current will flow through the wire. As the voltage increases, more electrons move through the substance into the time unit. If all additional parameters (temperature, cross-sectional area, length and wire material) are unchanged, then the ratio of current to applied voltage is also constant and is called conductivity:

Accordingly, the electrical resistance will be:

The result is in ohms.

In turn, the conductor can be of different lengths, cross-sectional sizes and made of different materials, which determines the value of R. Mathematically, this relationship looks like this:

The material factor takes into account the coefficient ρ.

From this we can derive the formula for resistivity:

If the values ​​of S and l correspond to the given conditions for the comparative calculation of resistivity, i.e. 1 mm² and 1 m, then ρ = R. When the dimensions of the conductor change, the number of ohms also changes.

Resistivity and Temperature

The resistivity of a conductor is a value that changes with temperature, so it is accurately calculated at 20°. If the temperature is different, the value of ρ must be adjusted based on another coefficient called temperature and denoted α (unit - 1/°C). This is also a characteristic value for each material.

The modified coefficient is calculated based on the values ​​of ρ, α and temperature deviation from 20° – Δt:

ρ1 = ρ x (1 + α x Δt).

If the resistance was known before, then you can directly calculate it:

R1 = R x (1 + α x Δt).

The practical use of various materials in electrical engineering directly depends on their resistivity.

Video

One of the most common metals for making wires is copper. Its electrical resistance is the lowest among affordable metals. It is less only for precious metals (silver and gold) and depends on various factors.

What is electric current

At different poles of a battery or other current source there are opposite electric charge carriers. If they are connected to a conductor, charge carriers begin to move from one pole of the voltage source to the other. These carriers in liquids are ions, and in metals they are free electrons.

Definition. Electric current is the directed movement of charged particles.

Resistivity

Electrical resistivity is a value that determines the electrical resistance of a reference sample of a material. The Greek letter “p” is used to denote this quantity. Formula for calculation:

p=(R*S)/ l.

This value is measured in Ohm*m. You can find it in reference books, in resistivity tables or on the Internet.

Free electrons move through the metal within the crystal lattice. Three factors influence the resistance to this movement and the resistivity of the conductor:

• Material. Different metals have different atomic densities and numbers of free electrons;
• Impurities. In pure metals the crystal lattice is more ordered, therefore the resistance is lower than in alloys;
• Temperature. Atoms are not stationary in their places, but vibrate. The higher the temperature, the greater the amplitude of vibrations, which interferes with the movement of electrons, and the higher the resistance.

In the following figure you can see a table of the resistivity of metals.

Interesting. There are alloys whose electrical resistance drops when heated or does not change.

Conductivity and electrical resistance

Since cable dimensions are measured in meters (length) and mm² (section), the electrical resistivity has the dimension Ohm mm²/m. Knowing the dimensions of the cable, its resistance is calculated using the formula:

R=(p* l)/S.

In addition to electrical resistance, some formulas use the concept of “conductivity”. This is the reciprocal of resistance. It is designated “g” and is calculated using the formula:

Conductivity of liquids

The conductivity of liquids is different from the conductivity of metals. The charge carriers in them are ions. Their number and electrical conductivity increase when heated, so the power of the electrode boiler increases several times when heated from 20 to 100 degrees.

Interesting. Distilled water is an insulator. Dissolved impurities give it conductivity.

Electrical resistance of wires

The most common metals for making wires are copper and aluminum. Aluminum has a higher resistance, but is cheaper than copper. The resistivity of copper is lower, so the wire cross-section can be chosen smaller. In addition, it is stronger, and flexible stranded wires are made from this metal.

The following table shows the electrical resistivity of metals at 20 degrees. In order to determine it at other temperatures, the value from the table must be multiplied by a correction factor, different for each metal. You can find out this coefficient from the relevant reference books or using an online calculator.

Selection of cable cross-section

Because a wire has resistance, when electric current passes through it, heat is generated and a voltage drop occurs. Both of these factors must be taken into account when choosing cable cross-sections.

Selection by permissible heating

When current flows in a wire, energy is released. Its quantity can be calculated using the electric power formula:

In a copper wire with a cross section of 2.5 mm² and a length of 10 meters R = 10 * 0.0074 = 0.074 Ohm. At a current of 30A P=30²*0.074=66W.

This power heats the conductor and the cable itself. The temperature to which it heats up depends on the installation conditions, the number of cores in the cable and other factors, and the permissible temperature depends on the insulation material. Copper has greater conductivity, so the power output and the required cross-section are lower. It is determined using special tables or using an online calculator.

Permissible voltage loss

In addition to heating, when electric current passes through the wires, the voltage near the load decreases. This value can be calculated using Ohm's law:

Reference. According to PUE standards, it should be no more than 5% or in a 220V network - no more than 11V.

Therefore, the longer the cable, the larger its cross-section should be. You can determine it using tables or using an online calculator. In contrast to the choice of cross-section based on permissible heating, voltage losses do not depend on laying conditions and insulation material.

In a 220V network, voltage is supplied through two wires: phase and neutral, so the calculation is made using double the length of the cable. In the cable from the previous example it will be U=I*R=30A*2*0.074Ohm=4.44V. This is not much, but with a length of 25 meters it turns out to be 11.1V - the maximum permissible value, you will have to increase the cross-section.

Electrical resistance of other metals

In addition to copper and aluminum, other metals and alloys are used in electrical engineering:

• Iron. Steel has a higher resistivity, but is stronger than copper and aluminum. Steel strands are woven into cables designed to be laid through the air. The resistance of iron is too high to transmit electricity, so the core cross-sections are not taken into account when calculating the cross-section. In addition, it is more refractory, and leads are made from it for connecting heaters in high-power electric furnaces;
• Nichrome (an alloy of nickel and chromium) and fechral (iron, chromium and aluminum). They have low conductivity and refractoriness. Wirewound resistors and heaters are made from these alloys;
• Tungsten. Its electrical resistance is high, but it is a refractory metal (3422 °C). It is used to make filaments in electric lamps and electrodes for argon-arc welding;
• Constantan and manganin (copper, nickel and manganese). The resistivity of these conductors does not change with changes in temperature. Used in high-precision devices for the manufacture of resistors;
• Precious metals – gold and silver. They have the highest specific conductivity, but due to their high price, their use is limited.

Inductive reactance

Formulas for calculating the conductivity of wires are valid only in a direct current network or in straight conductors at low frequencies. Inductive reactance appears in coils and in high-frequency networks, many times higher than usual. In addition, high frequency current only travels along the surface of the wire. Therefore, it is sometimes coated with a thin layer of silver or Litz wire is used.

Reference. Litz wire is a stranded wire, each core in which is isolated from the rest. This is done to increase surface area and conductivity in high frequency networks.

Copper's resistivity, flexibility, relatively low price and mechanical strength make this metal, along with aluminum, the most common material for making wires.

Video

When an electrical circuit is closed, at the terminals of which there is a potential difference, an electric current occurs. Free electrons, under the influence of electric field forces, move along the conductor. In their movement, free electrons collide with the atoms of the conductor and give them a supply of their kinetic energy.

Thus, electrons passing through a conductor encounter resistance to their movement. When electric current passes through a conductor, the latter heats up.

The electrical resistance of a conductor (denoted by the Latin letter r) is responsible for the phenomenon of converting electrical energy into heat when an electric current passes through the conductor. In the diagrams, electrical resistance is indicated as shown in Fig. 18.

The unit of resistance is taken to be 1 ohm. Om is often represented by the Greek capital letter Ω (omega). Therefore, instead of writing: “The resistance of the conductor is 15 ohms,” you can simply write: r = 15 Ω.

1000 ohms is called 1 kiloohm (1 kohm, or 1 kΩ).

1,000,000 ohms is called 1 megohm (1 mg ohm, or 1 MΩ).

device, having variable electrical resistance and serving to change the current in the circuit is called a rheostat. In the diagrams, rheostats are designated as shown in Fig. 18. As a rule, a rheostat is made of a wire of one or another resistance, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.

A long conductor with a small cross-section creates a large resistance to current. Short conductors with a large cross-section offer little resistance to current.

If you take two conductors from different materials, but the same length and cross-section, then the conductors will conduct current differently. This shows that the resistance of a conductor depends on the material of the conductor itself.

The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel, etc.) almost do not change their resistance with increasing temperature.

So, we see that the electrical resistance of a conductor depends on the length of the conductor, the cross-section of the conductor, the material of the conductor, and the temperature of the conductor.

When comparing the resistance of conductors from different materials, it is necessary to take a certain length and cross-section for each sample. Then we will be able to judge which material conducts electric current better or worse.

The resistance (in ohms) of a conductor 1 m long, with a cross section of 1 mm 2 is called resistivity and is denoted by the Greek letter ρ (rho).

The conductor resistance can be determined by the formula

where r is the conductor resistance, ohm;

ρ - conductor resistivity;

l- conductor length, m;

S - conductor cross-section, mm2.

From this formula we obtain the dimension for resistivity

In table 1 shows the resistivity of some conductors.

The table shows that an iron wire with a length of 1 m and a cross-section of 1 mm2 has a resistance of 0.13 ohms. To get 1 ohm of resistance, you need to take 7.7 m of such wire. Silver has the lowest resistivity - 1 ohm of resistance can be obtained if you take 62.5 m of silver wire with a cross section of 1 mm 2. Silver is the best conductor, but the high cost of silver excludes the possibility of its mass use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm has a resistance of 0.0175 ohms. To get a resistance of 1 ohm, you need to take 57 m of such wire.

Chemically pure copper, obtained by refining, has found widespread use in electrical engineering for the manufacture of wires, cables, windings of electrical machines and devices. Aluminum and iron are also widely used as conductors.

Detailed characteristics of metals and alloys are given in table. 2.

Example 1 Determine the resistance of 200 m of iron wire with a cross section of 5 mm 2:

Example 2. Calculate the resistance of 2 km of aluminum wire with a cross section of 2.5 mm2:

From the resistance formula you can easily determine the length, resistivity and cross-section of the conductor.

Example 3. For a radio receiver, it is necessary to wind a 30 ohm resistor from nickel wire with a cross section of 0.21 mm2. Determine the required wire length:

Example 4. Determine the cross-section of a nichrome wire with a length of 20 F, if its resistance is 25 ohms:

Example 5. A wire with a cross section of 0.5 mm2 and a length of 40 m has a resistance of 16 ohms. Determine the wire material.

The material of the conductor characterizes its resistivity

Based on the resistivity table, we find that lead has this resistance.

It was previously stated that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, an ammeter is included in the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.

For some metals, when heated by 100°, the resistance increases by 40-50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, while the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.

The ability of metals to change their resistance with changes in temperature is used to construct resistance thermometers. This thermometer is a platinum wire wound on a mica frame. By placing a thermometer, for example, in a furnace and measuring the resistance of the platinum wire before and after heating, the temperature in the furnace can be determined.

The change in the resistance of a conductor when it is heated, per 1 ohm of initial resistance and per 1 0 temperature, is called temperature coefficient of resistance and is denoted by the letter α (alpha).

If at temperature t 0 the resistance of the conductor is equal to r 0, and at temperature t is equal to r t, then the temperature coefficient of resistance

We assume that J diff, J conv, J term are equal to zero and J = J migr. The movement of ions in conductors of the second kind and electrons in conductors of the first kind due to the difference in electrical potential determines their ability to pass electric current, i.e. electrical conductivity(electrical conductivity). To quantitatively characterize the ability of conductors of the first and second types to pass electric current, two measures of electrical conductivity are used. One of them - electrical conductivityκ- is the reciprocal of resistivity:

The resistivity is determined from the formula

Where R- total conductor resistance, Ohm; l is the distance between two parallel planes between which the resistance is determined, m; S is the cross-sectional area of ​​the conductor, m2.

Hence

and electrical conductivity is defined as the reciprocal of the resistance of one cubic meter of conductor with a cube edge length equal to one meter. Unit of electrical conductivity: S/m. On the other hand, according to Ohm's law

Where E- potential difference between given parallel planes; I - current.

Substituting this expression into the equation determining the electrical conductivity, we obtain:

At S = 1 and E/l = 1 we have κ = 1. Thus, the electrical conductivity is numerically equal to the current passing through a cross-section of a conductor with a surface of one square meter, with a potential gradient equal to one volt per meter.

Specific electrical conductivity characterizes the number of charge carriers per unit volume. Consequently, the specific electrical conductivity will depend on the concentration of the solution, and for individual substances - on their density.

The second measure of electrical conductivity is equivalentλ e (or molarλ m) electrical conductivity, equal to the product of specific electrical conductivity and the number of cubic meters containing one equivalent or one mole of a substance:

λ e = κφ e; λ m = κφ m

Since φ is expressed in m 3 /eq or m 3 /mol, the unit of λ will be Sm∙m 2 /eq or Sm∙m 2 /mol.

For solutions φ = 1/C, where WITH- concentration expressed in mol/m3. Then

λ e = κ/zC and λ m = κ/C

If WITH expressed in kmol/m 3, then φ e = 1/(zC∙10 3); φ m = 1/(С∙10 3) and

λ e = κ/(zC∙10 3) and λ m = κ/(C∙10 3)

When determining the molar conductivity of an individual substance (solid or liquid), φ m = V M, but V m = M/d (where V m is the molar volume; M is the molecular weight; d- density), following

before v atelno

λ m = κV m = κМ/d

Thus, equivalent (or molar) electrical conductivity is the conductivity of a conductor located between two parallel planes located at a distance of one meter from each other and such an area that one equivalent (or one mole) of a substance (in the form of a solution or individual salt).

This measure of conductivity characterizes the conductivity of the same amount of substance (mole or equivalent), but contained in different volumes and, thus, reflects the influence of interaction forces between ions as a function of interionic distances.

ELECTRONIC CONDUCTIVITY

Metals characterized by a low electron transition energy from the valence band to the conduction band already at normal temperature have a sufficient number of electrons in the conduction band to ensure high electrical conductivity. The conductivity of metals decreases with increasing temperature. This is due to the fact that with increasing temperature in metals, the effect of increasing the vibrational energy of the ions of the crystal lattice, which provides resistance to the directional movement of electrons, prevails over the effect of increasing the number of charge carriers in the conduction band. The resistance of chemically pure metals increases with increasing temperature, increasing by approximately 4∙10 –3 R 0 with an increase in temperature by a degree (R 0 - resistance at 0 ° C). For most chemically pure metals, when heated, there is a linear relationship between resistance and temperature

R = R 0 (1 + αt)

where α is the temperature coefficient of resistance.

The temperature coefficients of alloys can vary over a wide range, for example, for brass α = 1.5∙10 –3, and for constantan α = 4∙10 –6.

The specific conductivity of metals and alloys lies in the range of 10 6 - 7∙10 7 S/m. The electrical conductivity of a metal depends on the number and charge of electrons involved in current transfer and the average travel time between collisions. The same parameters at a given electric field strength determine the speed of the electron. Therefore, the current density in a metal can be expressed by the equation

where is the average speed of ordered movement of charges; P– number of conduction band electrons per unit volume.

Semiconductors in their conductivity occupy an intermediate position between metals and insulators. Pure semiconductor materials such as germanium and silicon have intrinsic conductivity.

Rice. 5.1. Scheme of the formation of a conduction electron (1) – hole (2) pair.

Intrinsic conductivity is due to the fact that when thermal excitation of electrons occurs, they transition from the valence band to the conduction band. These electrons, under the influence of a potential difference, move in a certain direction and provide electronic conductivity semiconductors. When an electron passes to the conduction band, a vacant place remains in the valence band - a “hole”, equivalent to the presence of a single positive charge. A hole can also move under the influence of an electric field as a result of a valence band electron jumping to its place, but in the direction opposite to the movement of conduction band electrons, providing hole conductivity semiconductor. The hole formation process is shown in Fig. 5.1.

Thus, in a semiconductor with intrinsic conductivity there are two types of charge carriers - electrons and holes, which provide electron and hole conductivity of the semiconductor.

In a semiconductor with intrinsic conductivity, the number of electrons in the conduction band is equal to the number of holes in the valence band. At a given temperature in a semiconductor, there is a dynamic equilibrium between electrons and holes, i.e., the rate of their formation is equal to the rate of recombination. Recombination of a conduction band electron with a valence band hole results in the “formation” of an electron in the valence band.

The specific conductivity of a semiconductor depends on the concentration of charge carriers, i.e., on their number per unit volume. Let's denote the electron concentration n i and the hole concentration p i. In a semiconductor with intrinsic conductivity, n i = p i (such semiconductors are briefly called i-type semiconductors). The concentration of charge carriers, for example in pure germanium, is equal to n i = p i ≈10 19 m –3, in silicon it is approximately 10 16 m –3 and is 10 –7 - 10 –10% relative to the number of atoms N.

Under the influence of an electric field, a directed movement of electrons and holes occurs in a semiconductor. The conduction current density consists of the electronic i e and hole i p current densities: i = i e + i p , which, despite the equality of carrier concentrations, are not equal in magnitude, since the speeds of movement (mobility) of electrons and holes are different. The electron current density is equal to:

The average speed of electrons is proportional to the voltage E" electric field:

Proportionality factor w e 0 characterizes the speed of movement of an electron at a unit electric field strength and is called the absolute speed of movement. At room temperature in pure germanium w e 0 = 0.36 m 2 /(V∙s).

From the last two equations we get:

Repeating similar reasoning for hole conductivity, we can write:

Then for the total current density:

Comparing the expression for i with Ohm's law i = κ E", at S = 1 m2 we get:

As stated above, for a semiconductor with intrinsic conductivity n i = p i , therefore

w p 0 is always lower w e 0, for example in Germany w p 0 = 0.18 m 2 /(V∙s), and w e 0 = 0.36 m 2 /(V∙s).

Thus, the specific electrical conductivity of a semiconductor depends on the concentration of carriers and their absolute velocities and is additively composed of two terms:

κ i = κ e + κ p

Ohm's law for semiconductors is satisfied only if the carrier concentration n i does not depend on the field strength. At high field strengths, which are called critical (for germanium E cr ' = 9∙10 4 V/m, for silicon E cr '= 2.5∙10 4 V/m), Ohm's law is violated, which is associated with a change in electron energy in the atom and a decrease in the energy of transfer to the conduction band, as well as the possibility of ionization of lattice atoms. Both effects cause an increase in the concentration of charge carriers.

Electrical conductivity at high field strengths is expressed by Poole's empirical law:

ln κ = ln κ 0 + α (E’ – E cr’)

where κ 0 - conductivity at E’ = E cr ’ .

As the temperature rises in the semiconductor, intensive generation of charge carriers occurs, and their concentration increases faster than the absolute speed of electron motion decreases due to thermal motion. Therefore, in contrast

from metals, the electrical conductivity of semiconductors increases with increasing temperature. To a first approximation, for a small temperature range, the temperature dependence of the conductivity of a semiconductor can be expressed by the equation

Where k- Boltzmann constant; A- activation energy (the energy required to transfer an electron to the conduction band).

Near absolute zero, all semiconductors are good insulators. With an increase in temperature per degree, their conductivity increases by an average of 3 - 7%.

When impurities are introduced into a pure semiconductor, it adds to its own electrical conductivity impurity electrical conductivity. If, for example, elements of group V of the periodic system (P, As, Sb) are introduced into germanium, then the latter form a lattice with germanium with the participation of four electrons, and the fifth electron, due to the low ionization energy of impurity atoms (about 1.6∙10 –21), passes from the impurity atom to the conduction band. In such a semiconductor, electronic conductivity will predominate (the semiconductor is called n-type electronic semiconductor]. If impurity atoms have a greater electron affinity than germanium, for example elements of group III (In, Ga, B, A1), then they take electrons away from the germanium atoms and holes are formed in the valence band. In such semiconductors, hole conductivity predominates (semiconductor p-type]. Impurity atoms that provide electronic conductivity are donors electrons, and hole - acceptors).

Impurity semiconductors have higher electrical conductivity than semiconductors with intrinsic conductivity if the concentration of atoms of the donor N D or acceptor N A impurity exceeds the concentration of intrinsic charge carriers. At large values ​​of N D and N A, the concentration of intrinsic carriers can be neglected. Charge carriers whose concentration predominates in a semiconductor are called main ones. For example, in n-type germanium n n ≈ 10 22 m–3, while n i ≈ 10 19 m~ 3, i.e., the concentration of main carriers is 10 3 times higher than the concentration of intrinsic carriers.

For impurity semiconductors the following relations are valid:

n n p n = n i p i = n i 2 = p i 2

n p p p = n i p i = n i 2 = p i 2

The first of these equations is written for an n-type semiconductor, and the second for a p-type semiconductor. From these relationships it follows that a very small amount of impurity (about 10 –4 0 / o) significantly increases the concentration of charge carriers, as a result of which the electrical conductivity increases.

If we neglect the concentration of intrinsic carriers and assume N D ≈ n n for an n-type semiconductor and N A ≈ р р for a p-type semiconductor, then the electrical conductivity of an impurity semiconductor can be expressed by the equations:

When an electric field is applied in n-type semiconductors, charge transfer is carried out by electrons, and in p-type semiconductors by holes.

Under external influences, such as irradiation, the concentration of charge carriers changes and can be different in different parts of the semiconductor. In this case, as in solutions, diffusion processes occur in the semiconductor. The laws of diffusion processes obey the Fick equations. The diffusion coefficients of charge carriers are much higher than those of ions in solution. For example, in germanium the diffusion coefficient of electrons is 98∙10 –4 m 2 /s, of holes - 47∙10 –4 m 2 /s. Typical semiconductors, in addition to germanium and silicon, at room temperature are a number of oxides, sulfides, selenides, telrides, etc. (for example, CdSe, GaP, ZnO, CdS, SnO 2, In 2 O 3, InSb).

IONIC CONDUCTIVITY

Gases, some solid compounds (ionic crystals and glasses), molten individual salts and solutions of compounds in water, non-aqueous solvents and melts have ionic conductivity. The conductivity values ​​of conductors of the second kind of different classes vary within very wide limits:

Note: Specific conductivity values ​​for solutions are given at 18 °C.

However, in all cases, the given values ​​of κ are several orders of magnitude lower than the κ values ​​of metals (for example, the conductivity of silver, copper and lead is 0.67∙10 8 , 0.645∙10 8 and 0.056∙10 8 S/m, respectively).

In conductors of the second type, all types of particles having an electric charge can take part in the transfer of electricity. If both cations and anions carry current, then electrolytes have bipolar conductivity. If the current carries only one type of ions - cations or anions - then we observe unipolar cationic or anionic conductivity.

In the case of bipolar conduction, ions moving faster carry a larger proportion of the current than ions moving slower. The fraction of current carried by a given type of particle is called carry number of this type of particle (t i). With unipolar conductivity, the transport number of the type of ions that carry the current is equal to one, since all the current is transferred by this type of ions. But with bipolar conductivity, the transport number of each type of ion is less than unity, and

Moreover, the transfer number should be understood as the absolute value of the fraction of the current attributable to a given type of ions, without taking into account the fact that cations and anions transfer electric current in different directions.

The transfer number of any one type of particle (ion) during bipolar conductivity is not a constant value that characterizes only the nature of a given type of ion, but also depends on the nature of the partner particles. For example, the transfer number of chlorine ions in a solution of hydrochloric acid is less than in a solution of KS1 of the same concentration, since hydrogen ions are more mobile than potassium ions. Methods for determining transfer numbers are diverse, and their principles are outlined in the corresponding laboratory workshops on theoretical electrochemistry.

Before moving on to considering the electrical conductivity of specific classes of substances, let us dwell on one general issue. Any body moves in a constant field of forces acting on it with acceleration. Meanwhile, ions in all classes of electrolytes, except gases, move under the influence of an electric field of a given strength at a constant speed. To explain this, let's imagine the forces acting on the ion. If the mass of the ion is m and the speed of its movement w, then Newtonian force mdw/dt will be equal to the difference between the electric field force (M), which moves the ion, and the reactive force (L’), which slows down its movement, because the ion moves in a viscous medium. The greater the ion speed, the greater the reactive force, i.e. L’ = L w(Here L- proportionality coefficient). Thus

After separating the variables we have:

Designating M – L w = v, we get d w= – d v/L and

or

The integration constant is determined from the boundary condition: at t = 0 w = 0, i.e. . We begin counting time from the moment the ion begins to move (the moment the current is turned on). Then:

Substituting its value instead of the constant, we finally get.