Resistivity is a property of a material that characterizes its ability to prevent the passage of electric current.

Characteristics of Electrical Materials

The main characteristic in electrical engineering is the specific electrical conductivity, measured in cm / m. It serves as a coefficient of proportionality between the field strength vector and the current density. It is often denoted by the Greek letter gamma γ.The resistivity is recognized as the reciprocal of electrical conductivity. As a result, the formula mentioned above becomes: the current density is directly proportional to the field strength and inversely proportional to the specific resistance of the medium. The unit becomes Om m.

The concept under consideration is relevant not only for solid media. For example, the current is carried out by liquid-electrolytes and ionized gases. Therefore, in each case, it is permissible to introduce the concept of resistivity, because an electric charge passes through the medium. It is difficult to find the values ​​in the reference books, for example, for the welding arc for a simple reason - they are not sufficiently involved in such tasks. This is not claimed. Since the discovery of Davy's glow of the platinum plate by electric current, a century passed before the introduction of glowing bulbs into common use - for a similar reason, the importance and significance of the discovery was not immediately recognized.

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Material property

Depending on the resistivity value, the materials are divided:

  1. For conductors - less than 1/10000 Ohm m.
  2. For dielectrics - more than 100 million Ohm m.
  3. According to the values ​​of specific resistance, there are between dielectrics and conductors.

These values ​​characterize exclusively the ability of the body to resist the passage of electric current and do not affect other aspects( elasticity, heat resistance).For example, magnetic materials are conductors, dielectrics and semiconductors.

How conductivity is formed in a material

In modern physics, resistance and conductivity are usually explained by zone theory. It is applicable to solid crystalline bodies whose lattice atoms are made stationary. According to this concept, the energy of electrons and other types of charge carriers is determined by the established rules. There are three main zones inherent in the material:

  • The valence zone contains electrons associated with atoms. In this region, the electron energy is graded by steps, and the number of levels is limited. The outer of the layers of the atom.
  • Forbidden Zone. In this area, charge carriers are not entitled. It serves as the boundary between the two other zones. Metals are often absent.
  • The free zone is located above the previous two. Here electrons participate freely in the creation of electric current, and any energy. No levels.

Dielectrics are characterized by the highest location of the free zone. With any natural conditions imaginable on Earth, the materials do not conduct electric current. Great width and bandgap. Metals have a mass of free electrons. And the valence band is simultaneously considered the conduction region — there are no forbidden states. As a result, these materials have low resistivity.

Calculation beats.

resistances At the interface of the atomic contacts, intermediate energy levels are formed, unusual effects occur, used by semiconductor physics. Heterogeneities are created intentionally by the introduction of impurities( acceptors and donors).As a result, new energy states are formed, which manifest new properties in the process of electric current flow that the initial material did not possess.

Semiconductors have a forbidden band width. Under the action of external forces, electrons are able to leave the valence region. The cause is electrical voltage, heat, radiation, other types of effects. In dielectrics and semiconductors, as the temperature decreases, electrons pass to lower levels, as a result, the valence band is filled, and the conduction band remains free. Electric current does not flow. According to quantum theory, the class of semiconductors is characterized as materials with a band gap of less than 3 eV.

Fermi Energy

The Fermi energy occupies an important place in the theory of conductivity, explanations of phenomena occurring in semiconductors. Subtleties add vague definitions of the term in the literature. Foreign literature says that the Fermi level is a certain value in eV, and the Fermi energy is the difference between it and the lowest in a crystal. Here are the selected general and understandable sentences:

  1. The Fermi level is the maximum of all that is inherent in an electron in metals at a temperature of 0 K. Therefore, the Fermi energy is the difference between this figure and the minimum level at absolute zero.
  2. The Fermi energy level - the probability of finding electrons is 50% at all temperatures except absolute zero.

The Fermi energy is determined solely for a temperature of 0 K, whereas the level exists under all conditions. In thermodynamics, the concept describes the full chemical potential of all electrons. The Fermi level is defined as the work expended on the addition of an object by a single electron. The parameter determines the conductivity of the material, helps to understand the physics of semiconductors.

The Fermi level does not necessarily exist physically. There are cases when the place of passage was in the middle of the forbidden zone. Physically, the level does not exist, there are no electrons there. However, the parameter is noticeable with a voltmeter: the potential difference between two points of the circuit( readings on the display) is proportional to the difference between the Fermi levels of these points and inversely proportional to the electron charge. Simple addiction. It is permissible to link these parameters with conductivity and resistivity, using Ohm’s law for the chain section.

Materials with low specific resistance

The conductors include most metals, graphite, and electrolytes. Such materials have low resistivity. In metals, positively charged ions form crystal lattice sites surrounded by a cloud of electrons. They are usually called common for entry into the conduction band.

Although it is not fully understood what an electron is, it is customarily described as a particle moving inside a crystal with a thermal velocity of hundreds of km / s. This is much more than is needed to launch a spacecraft into orbit. At the same time, the drift velocity, forming an electric current under the action of a vector of intensity, barely reaches a centimeter per minute. The field is distributed in an environment with the speed of light( 100 thousand km / s).

As a result of these relationships, it becomes possible to express the conductivity in terms of physical quantities( see figure):

The formula for calculating

  • Electron charge, e.
  • Free carrier concentration, n.
  • Electron mass, me.
  • Thermal velocity of carriers,
  • Electron mean free path, l.

The Fermi level for metals lies in the range 3–15 eV, and the concentration of free carriers is almost independent of temperature. Therefore, the specific conductivity, and hence the resistance, is determined by the structure of the molecular lattice and its proximity to the ideal, freedom from defects. The parameters determine the length of the free path of electrons, it is easy to find in reference books, if it is necessary to make calculations( for example, in order to determine the specific resistance).

Metals with a cubic lattice have the best conductivity. Copper is also included here. Transition metals are characterized by much higher resistivity. Conductivity decreases with increasing temperature and at high frequencies of alternating current. In the latter case, a skin effect is observed. Temperature dependence linear above a certain limit, named after the Dutch physicist Peter Debye.

Marked and not so straight line dependencies. For example, temperature treatment of steel increases the number of defects, which naturally reduces the conductivity of the material. An exception to the rule was annealing. The process reduces the density of defects, due to which the resistivity decreases. Deformation has a bright effect. For some alloys, machining results in a marked increase in resistivity.

Spatial representation of the property

Materials with high resistivity

Sometimes it is required to specifically increase the resistivity. A similar situation occurs in cases with heating devices and electronic circuit resistors. Then comes the turn of alloys with high specific resistance( more than 0.3 µOm m).When used as part of measuring instruments, the requirement of a minimum potential at the interface with the copper contact is presented.

The most famous was nichrome. Often, heating devices are constructed of cheap fehrle( brittle, but cheap).Depending on the purpose, copper, manganese and other metals are included in the alloys. It is an expensive pleasure. For example, a manganin resistor costs 30 cents on Aliexpress, where prices are traditionally lower than store prices. There is even an alloy of palladium with iridium. The price of the material should not be spoken out loud.

Printed circuit resistors are often made from pure metals in the form of sputter films. Chromium, tantalum, tungsten, alloys are widely used, among others, nichrome.

Substances that Do Not Conduct An Electric Current

Dielectrics are characterized by impressive resistivity. This is not a key feature. Dielectric materials include materials capable of redistributing the charge under the action of an electric field. As a result, accumulation occurs, which is used in capacitors. The degree of charge redistribution is characterized by dielectric constant. The parameter shows how many times the capacitance of the capacitor increases, where instead of air a specific material is used. Individual dielectrics are able to conduct and emit oscillations under the action of alternating current. Ferroelectricity is known, due to temperature changes.

In the process of changing the field direction losses occur. Just as magnetic tension is partially converted to heat when exposed to mild steel. The dielectric loss depends mainly on the frequency. If necessary, non-polar insulators are used as materials, the molecules of which are symmetric, without a pronounced electric moment. Polarization occurs when the charges are firmly connected to the crystal lattice. Types of polarization:

  1. Electron polarization occurs as a result of the deformation of the outer energy shells of atoms. Reversible. Characteristic of non-polar dielectrics in any phase of a substance. Due to the low electron weight, it occurs almost instantaneously( units of fs).
  2. Ion polarization extends two orders of magnitude slower and is characteristic of substances with an ionic crystal lattice. Accordingly, the materials are applied at frequencies up to 10 GHz and have a large dielectric constant( up to 90 for titanium dioxide).
  3. Dipole-relaxation polarization is much slower. Execution time is hundredths of a second. Dipole-relaxation polarization is characteristic of gases and liquids and depends, respectively, on viscosity( density).The effect of temperature is traced: the effect forms a peak at a certain value.
  4. Spontaneous polarization is observed in ferroelectrics.


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