conductivity

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This entry is made by Undergraduate Department of Chinese Academy of Sciences, College of Physical Sciences of Chinese Academy of Sciences Participate in editing and review Science Popularization China · Science Encyclopedia authentication.

Conductivity, a physical concept, can also be called conductivity. This amount in the medium is equal to electric field intensity The product of E is equal to conduction current density J. For Isotropic medium , conductivity is scalar; about Anisotropic medium The conductivity is a tensor. In ecology, conductivity is the ability of a solution to conduct electric current expressed in numbers. In Siemens per meter（ S/m ）Represents.^[1]

Conductivity is the reciprocal of resistivity, which represents the ability of materials to conduct current and is the characteristics of materials. Conductivity is usually represented by the Greek letter σ, and sometimes it is also represented by κ in electrical engineering. The dimension of conductivity is M -1 L -3 T three I two In the SI system, the unit of conductivity is Siemens per meter (S · m -1 ）

Chinese name: conductivity

Foreign name: conductivity
application area: physics

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definition

Consider the material of a cuboid, and add electrodes on its two opposite faces. The longer the conductor in the current direction, the smaller the cross section, the greater the resistance

The resistivity is the ratio constant

among

Is the resistance of the material,

Is the length of the material,

Is the cross-sectional area. Resistivity, which describes the blocking effect of materials on current, is a basic characteristic of materials and is independent of the size of materials. Conductivity is the reciprocal of resistivity

If the geometric shape of the material is complex, the resistivity at a certain point is generally defined as the ratio of electric field to current density

Accordingly

Tensor form

When the material is anisotropic, the definition of resistivity is an extension of the above definition. In the case of anisotropy, the relationship between electric field and current density will be extended to tensor form

Explanation of energy band theory

According to the theory of quantum mechanics, electrons in atoms or crystals are distributed on discrete energy levels. When the energy spacing of a large number of energy levels is very small, these close energy levels together are called energy bands. The electrons are filled up from the lowest energy level in turn, and only the electrons close to or above the Fermi level can move freely. The electron easily transitions near the Fermi level.

energy band

In metals, there are many energy levels that are close to Fermi level, and these energy levels are not completely filled, so the resistance of electron movement in them is small. Sometimes, there is a band gap in the energy level: there is no energy level in some energy range. If the Fermi level is in the band gap range and there is no available state near the Fermi level, the resistivity will be very high. Some materials have full filled energy bands below the Fermi level, and empty energy bands above the Fermi level. The Fermi level is in the band gap. This material has very poor conductivity and is an insulator.

In intrinsic semiconductors, the Fermi level is about half the position between the minimum value of the conduction band and the maximum value of the valence band. At absolute zero, intrinsic semiconductors will not have conductive electrons, and the resistance is infinite. In practical materials, the doped atoms increase the carrier concentration by providing electrons in the conduction band or creating holes in the valence band, and the resistance decreases with the increase of the charge carrier density in the conduction band. Highly doped semiconductors have metallic behavior. When the temperature is very high, the carrier contribution exceeds the contribution of the multi doped atoms, and the resistance decreases with the temperature index.

Metal

In most cases, the resistivity of metals will increase with the increase of temperature, and the interaction of electrons and phonons plays a key role in the generation of resistance. At high temperature, the resistivity of metal increases linearly with temperature; With the decrease of temperature, the change of resistivity with temperature gradually becomes a power law. The relationship between metal resistivity and temperature can be approximately described by Bloch Gruneisen formula

among

Is an undetermined constant, which depends on the speed of electrons on the Fermi surface, Debye temperature and electron number density.

Is the Debye temperature.

Is a constant:

Time resistance comes from phonon scattering of electrons

Time resistance is derived from s-d electron scattering

When the resistance comes from the electron electron interaction

When the temperature is close to absolute zero, the resistivity will reach a constant value, which is called residual resistivity

This depends on the type, purity and thermodynamic change process of the metal.

Relation to temperature

The resistivity of most materials varies with temperature. At a certain temperature

The change of resistivity with temperature is usually approximated by the following formula

among

Is the temperature coefficient, which is usually obtained by fitting the measured data.

Relation with thermal conductivity

Wiedemann Franz law points out that the relationship between thermal conductivity and conductivity is

among

Is the thermal conductivity,

Is the Boltzmann constant,

Is the electronic charge.

Material conductivity meter

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The following table shows various materials used in

Resistivity at

, Conductivity

Temperature coefficient of and

Material Science	resistivity	conductivity	temperature coefficient
silver	1.59×10 -8	6.30×10 seven	3.80×10 -3
copper	1.68×10 -8	5.69×10 seven	4.04×10 -3
Annealed copper	1.72×10 -8	5.80×10 seven	3.93×10 -3
gold	2.44×10 -8	4.11×10 seven	3.40×10 -3
aluminum	2.65×10 -8	3.77×10 seven	3.90×10 -3
Brass (5% Zn)	3.00×10 -8	3.34×10 seven	-
calcium	3.36×10 -8	2.98×10 seven	4.10×10 -3
rhodium	4.33×10 -8	2.31×10 seven	-
tungsten	5.60×10 -8	1.79×10 seven	4.50×10 -3
zinc	5.90×10 -8	1.69×10 seven	3.70×10 -3
Brass (30% Zn)	5.99×10 -8	1.67×10 seven	-
cobalt	6.24×10 -8	1.60×10 seven	7.00×10 -3
nickel	6.99×10 -8	1.43×10 seven	6.00×10 -3
ruthenium	7.10×10 -8	1.41×10 seven	-
lithium	9.28×10 -8	1.08×10 seven	6.00×10 -3
iron	9.70×10 -8	1.03×10 seven	5.00×10 -3
platinum	1.06×10 -7	9.43×10 six	3.92×10 -3
tin	1.09×10 -7	9.17×10 six	4.50×10 -3
Phosphor bronze (0.2% P/5% Sn)	1.12×10 -7	8.94×10 six	-
gallium	1.40×10 -7	7.10×10 six	4.00×10 -3
niobium	1.40×10 -7	7.00×10 six	-
carbon steel	1.43×10 -7	6.99×10 six	-
lead	2.20×10 -7	4.55×10 six	3.90×10 -3
Gallium indium tin alloy	2.89×10 -7	3.46×10 six	-
titanium	4.20×10 -7	2.38×10 six	3.80×10 -3
Grain oriented electrical silicon steel sheet	4.60×10 -7	2.17×10 six	-
Manganin	4.86×10 -7	2.07×10 six	2.00×10 -6
Constantan	4.90×10 -7	2.04×10 six	8.00×10 -6
stainless steel	6.90×10 -7	1.45×10 six	9.40×10 -4
mercury	9.80×10 -7	1.02×10 six	9.00×10 -4
bismuth	1.29×10 -6	7.75×10 five	-
manganese	1.44×10 -6	6.94×10 five	-
plutonium	1.46×10 -6	6.85×10 five	-
Nickel chromium iron alloy	1.10×10 -6	6.70×10 five	4.00×10 -4

measuring method

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The resistivity of solid conductor can be measured by Ohm's law And resistance law measurement. electrolyte solution The conductivity is generally measured by the AC signal acting on the two electrode plates of the conductivity cell Conductivity cell constant K and the conductivity G between the two electrode plates to obtain the conductivity σ.

The AC bridge method was first used in conductivity measurement, which directly measured the conductivity value. The most commonly used instruments are constant regulator, temperature coefficient regulator and automatic temperature compensator Temperature sensor Composition, can be measured directly electrolyte solution Conductivity.

measuring principle

The principle of conductivity measurement is to put two parallel plates (or cylindrical electrodes) with a fixed distance L into the solution to be measured, and add a certain amount of potential (In order to avoid solution electrolysis, it is usually a sine wave voltage with a frequency of 1~3 kHz). Then through Conductivity meter Measure the conductivity between plates.

Conductivity measurement requires two aspects of information. One is the conductivity G of the solution, and the other is the conductivity cell constant Q. The conductivity can be measured by current and voltage.

The conductivity value can be obtained according to the relationship K=Q × G. This measuring principle is widely used in direct display measuring instruments.

And Q=L/A

A -- Effective plate area of measuring electrode

L - distance between two plates

This value is called the electrode constant. Between electrodes Uniform electric field The electrode constant can be calculated through the geometric dimension. When the two areas are 1 cm two The constant Q of this electrode is 1 cm when the square electrode plate with an interval of 1 cm is used to form an electrode -1 If the conductivity value G=1000 μ S measured with this pair of electrodes, the conductivity of the measured solution K=1000 μ S/cm.

In general, the electrode often forms partial non-uniform electric field. At this time, the electrode constant must be determined with standard solution. The standard solution generally uses KCl solution because the conductivity of KCl is very stable and accurate under different temperatures and concentrations. The conductivity of 0.1 mol/L KCl solution at 25 ℃ is 12.88 mS/cm.

so-called Non-uniform electric field (Also called stray field, leakage field) has no constant, but is related to the type and concentration of ions. Therefore, a pure stray field electrode is the most complex electrode, which can not meet the needs of a wide measurement range through a single calibration.

type

Conductivity electrode It is generally divided into two types: two electrode type and multi electrode type.

The two electrode conductivity electrode is the most widely used type of conductivity electrode in China. The structure of the experimental two electrode conductivity electrode is to sinter two platinum sheets on two parallel glass sheets or on the inner wall of a circular glass tube. By adjusting the area and distance of the platinum sheets, conductivity electrodes with different constant values can be made. Generally, there are K=1. K=5. K=10 and other types. and Online conductivity meter The two electrode conductivity electrode used on the is usually made of cylindrical symmetrical electrode. When K=1, graphite is often used. When K~0.1 to 0.01, the material can be stainless steel or titanium alloy.

Multi electrode conductivity electrode, generally there are several annular electrodes on the support body, through the different combinations of the serial and parallel connection of the annular electrodes, the conductivity electrodes with different constants can be made. The annular electrode can be made of graphite, stainless steel, titanium alloy and Platinum 。

Conductivity electrode also has four electrode types and electromagnetism Type. The advantage of four electrode conductivity electrode is that it can avoid the measurement error caused by electrode polarization, and it is widely used in foreign experimental and online conductivity meters. Electromagnetic conductivity electrode is suitable for measuring solutions with high conductivity. It is generally used for Industrial conductivity meter Or use its measuring principle to make a single component concentration meter, such as hydrochloric acid concentration meter nitric acid Concentration meter, etc.

Conductivity electrode constant

According to the formula K=S/G, the electrode constant K can be obtained by measuring the conductivity G of the conductivity electrode in a certain concentration of KCl solution. At this time, the conductivity S of KCl solution is known.

Due to the different concentration and temperature of the measuring solution, as well as the different precision and frequency of the measuring instrument, the conductivity electrode constant K Sometimes there will be large errors, and the electrode constant may also change after a period of use. Therefore, the electrode constant of the newly purchased conductivity electrode and the conductivity electrode after a period of use should be re measured and calibrated, and the following points should be paid attention to when measuring the conductivity electrode constant:

1. The matching conductivity meter shall be used for measurement, and other conductivity meters shall not be used.

2. Measure the temperature of KCl solution with electrode constant, which should be close to the temperature of the actual measured solution.

3. Measure the concentration of KCl solution with electrode constant, which should be close to the actual concentration of the measured solution.

temperature compensation

Conductivity measurements are temperature dependent. The influence of temperature on conductivity varies with solution, and can be calculated by the following formula:

G t = G tcal {1 + α(T-T cal )}

Including:

G t =Conductivity at a certain temperature (° C)

G tcal =Conductivity at standard temperature (° C)

T cal =Temperature correction value

α=temperature coefficient of solution at standard temperature (° C).

The following table lists the alpha values of commonly used solutions. To get the α value of other solutions, just measure the conductivity within a certain temperature range and draw a graph with the temperature as the vertical axis

solution （25°C）	Concentration (wt%)	Alpha (α)
hydrochloric acid	ten	one point five six
Potassium chloride solution	ten	one point eight eight
sulphuric acid	fifty	one point nine three
Sodium chloride solution	ten	two point one four
hydrofluoric acid	one point five	seven point two zero
nitric acid	thirty-one	thirty-one

The curve point corresponding to the standard temperature is the α value of the solution.

All conductivity meters sold in the market can be adjusted or automatically compensated with reference to the standard temperature (usually 25 ° C). The α of most fixed temperature compensated conductivity meters is adjusted to 2%/° C (α of sodium chloride solution at approximately 25 ° C). The conductivity meter with adjustable temperature compensation can adjust α to be closer to α of the measured solution.

Conductivity reference

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The conductivity benchmark in China and many countries is a national sub benchmark, which is established by the relative measurement method.

Make a high purity of 99.99% potassium chloride As a conductivity reference material conforming to international recommendations, the reference solution prepared by it shall have the conductivity value recommended internationally. Take the conductivity of the solution at 25 ℃ as the starting point, measure each conductivity constant accordingly, and then calculate the conductivity constant K at other temperatures according to the following formula

K=K zero (1-at)

Where, K zero Is the conductivity cell constant at 0 ℃; A Glass used for making conductivity cell Linear expansion coefficient ; t is the solution temperature, in ℃.

The above formula is an approximate derivation result, which can not exceed plus or minus 1xl0 at most when considering complex situations -5 Differences. Then, the conductivity of each solution at different temperatures is calculated according to the measured resistance value of each solution on the corresponding conductivity cell at different temperatures. Because the temperature coefficient of relative change of conductivity cell constant is -8.49x10 -6 ℃ -1 And the temperature coefficient of conductivity of KCl solution is about

Therefore, if the measured conductivity of 1D, 0.1D and 0.01D solutions at 18 ℃ and 20 ℃ is consistent with the internationally recommended values, it can be considered that this relative measurement method is reliable, which has been verified in the subsequent international sample comparison. The international recommended value of 20 ℃ is 1972 and 1976 IUPAC Recommended value.

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