Thermopower
Encyclopedia
The thermopower, or thermoelectric power
(also called the Seebeck coefficient) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material. The thermopower has units of volt
s per kelvin
(V/K), although it is more often given in microvolts per kelvin (μV/K).
The term thermopower is a misnomer since it measures the voltage or electric potential
(not the electric power
) induced in response to a temperature difference. Note that the unit of thermopower (V/K) is different from the unit of power (watt
s).
The phenomenon quantified by thermopower is called the Seebeck effect. The Seebeck effect and two related phenomena (the Peltier effect and Thomson effect) are together called the "thermoelectric effect
".
, to diffuse from the hot side to the cold side, similar to a gas that expands when heated.
Mobile charged carriers migrating to the cold side leave behind their oppositely charged and immobile nuclei at the hot side thus giving rise to a thermoelectric voltage (thermoelectric refers to the fact that the voltage is created by a temperature difference). Since a separation of charges also creates an electric field, the buildup of charged carriers onto the cold side eventually ceases at some maximum value since there exists an equal amount of charged carriers drifting back to the hot side as a result of the electric field at equilibrium. Only an increase in the temperature difference can resume a buildup of more charge carriers on the cold side and thus lead to an increase in the thermoelectric voltage. Incidentally the thermopower also measures the entropy
per charge carrier in the material.
The thermopower of a material, represented as
, depends on the material's temperature, and crystal structure. Typically metals have small thermopowers because most have half-filled bands. Electrons (negative charges) and holes (positive charges) both contribute to the induced thermoelectric voltage thus canceling each other's contribution to that voltage and making it small. In contrast, semiconductors can be doped with an excess amount of electrons or holes and thus can have large positive or negative values of the thermopower depending on the charge of the excess carriers. The sign of the thermopower can determine which charged carriers dominate the electric transport in both metals and semiconductors.
Superconductors have zero thermopower since the charged carriers carry no entropy
. Equivalently, the thermopower is zero because it is impossible to have a finite voltage across a superconductor. (For example, by Ohm's law
, V=IR=0, since the resistance
, R, is equal to zero in a superconductor.)
where ΔV is the thermoelectric voltage seen at the terminals. (See below for more on the signs of ΔV and ΔT.)
This can also be written in relation to the electric field
and the temperature
gradient
, by the equation:
Strictly speaking, these two expressions are only approximate: The numerator of the first equation should be the difference in (electrochemical potential divided by -e
), not electric potential
, and likewise the second equation should have the gradient of electrochemical potential divided by e rather than the electric field. However, the chemical potential
is often relatively constant as a function of temperature, so using electric potential alone is in these cases a very good approximation.
where "left" and "right" denote two ends of the material, and where the second equation is understood as vector multiplication. Thus, if S is positive, the end with the higher temperature has the lower voltage, and vice-versa, and the electric field will point in the same direction as the temperature gradient.
Note that there is a minus sign in the first equation, but not the second. This is because the electric field points from the higher voltage towards the lower voltages, whereas the temperature gradient points from the lower temperature towards the higher temperature.
Charge carriers tend to respond to a temperature gradient by moving in the opposite direction, i.e. from the hot end to the cold end. They tend to respond to an electric field in different ways depending on their charge: positive charges tend to move in the same direction as the field, while negative charges move in the opposite direction of the field. For equilibrium to be reached, these two tendencies have to cancel out. Thus, for purely p-type
materials which have only positive mobile charges (holes
), the electric field and temperature gradient should point in the same direction in equilibrium, giving S>0. Likewise, for purely n-type
materials which have only negative mobile charges (electron
s), the electric field and temperature gradient should point in opposite directions in equilibrium, giving S<0. In practice, real materials often have both positive and negative charge-carriers, and the sign of S usually depends on which of them predominates.
.
The measured thermopower is then a contribution from both and can be written as:
Superconductors have zero thermopower, as mentioned above. By using superconducting leads, it is possible to get a direct measurement of the absolute thermopower of the material of interest, since it is the thermopower of the entire thermocouple as well.
A measurement of the Thomson coefficient
,
, of a material can also yield the thermopower through the relation: 
, exploiting the temperature difference between a radioactively-heated plate and the cold empty space surrounding the craft. Some researchers hope that, in the future, much wider use could be made of thermoelectric power generation, including using waste heat
from automobiles (see Automotive Thermoelectric Generators
) and power plants. (This is a form of energy recycling
.)
The efficiency with which a thermoelectric material can generate electrical power depends on several material properties, of which perhaps the most important is the thermopower. A larger induced thermoelectric voltage for a given temperature gradient will lead to a higher efficiency. Ideally one would want very large thermopower values since only a small amount of heat is then necessary to create a large voltage. This voltage can then be used to provide power.
There is an active research effort to find materials that could make cheaper and more efficient thermoelectric power generators; to learn more see the article Thermoelectric materials.
Thermoelectric power
Thermoelectric power can refer to two things:# Electrical power generated from a heat source, such as burning fossil fuel-coal,oils, indirectly through devices like steam turbines....
(also called the Seebeck coefficient) of a material is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material. The thermopower has units of volt
Volt
The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...
s per kelvin
Kelvin
The kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
(V/K), although it is more often given in microvolts per kelvin (μV/K).
The term thermopower is a misnomer since it measures the voltage or electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
(not the electric power
Electric power
Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt.-Circuits:Electric power, like mechanical power, is represented by the letter P in electrical equations...
) induced in response to a temperature difference. Note that the unit of thermopower (V/K) is different from the unit of power (watt
Watt
The watt is a derived unit of power in the International System of Units , named after the Scottish engineer James Watt . The unit, defined as one joule per second, measures the rate of energy conversion.-Definition:...
s).
The phenomenon quantified by thermopower is called the Seebeck effect. The Seebeck effect and two related phenomena (the Peltier effect and Thomson effect) are together called the "thermoelectric effect
Thermoelectric effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice-versa. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, it creates a temperature difference...
".
Physics of thermopower
Classically, an applied temperature difference causes charged carriers in the material, whether they are electrons or holesElectron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
, to diffuse from the hot side to the cold side, similar to a gas that expands when heated.
Mobile charged carriers migrating to the cold side leave behind their oppositely charged and immobile nuclei at the hot side thus giving rise to a thermoelectric voltage (thermoelectric refers to the fact that the voltage is created by a temperature difference). Since a separation of charges also creates an electric field, the buildup of charged carriers onto the cold side eventually ceases at some maximum value since there exists an equal amount of charged carriers drifting back to the hot side as a result of the electric field at equilibrium. Only an increase in the temperature difference can resume a buildup of more charge carriers on the cold side and thus lead to an increase in the thermoelectric voltage. Incidentally the thermopower also measures the entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
per charge carrier in the material.
The thermopower of a material, represented as
, depends on the material's temperature, and crystal structure. Typically metals have small thermopowers because most have half-filled bands. Electrons (negative charges) and holes (positive charges) both contribute to the induced thermoelectric voltage thus canceling each other's contribution to that voltage and making it small. In contrast, semiconductors can be doped with an excess amount of electrons or holes and thus can have large positive or negative values of the thermopower depending on the charge of the excess carriers. The sign of the thermopower can determine which charged carriers dominate the electric transport in both metals and semiconductors.Superconductors have zero thermopower since the charged carriers carry no entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
. Equivalently, the thermopower is zero because it is impossible to have a finite voltage across a superconductor. (For example, by Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
, V=IR=0, since the resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, R, is equal to zero in a superconductor.)
Definition
If the temperature difference ΔT between the two ends of a material is small, then the thermopower of a material is conventionally (though only approximately, see below) defined as:where ΔV is the thermoelectric voltage seen at the terminals. (See below for more on the signs of ΔV and ΔT.)
This can also be written in relation to the electric field
Electric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
and the temperatureTemperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....
, by the equation:Strictly speaking, these two expressions are only approximate: The numerator of the first equation should be the difference in (electrochemical potential divided by -e
Elementary charge
The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...
), not electric potential
Electric potential
In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...
, and likewise the second equation should have the gradient of electrochemical potential divided by e rather than the electric field. However, the chemical potential
Chemical potential
Chemical potential, symbolized by μ, is a measure first described by the American engineer, chemist and mathematical physicist Josiah Willard Gibbs. It is the potential that a substance has to produce in order to alter a system...
is often relatively constant as a function of temperature, so using electric potential alone is in these cases a very good approximation.
Sign of the thermopower
Here, again, are the formulas for the Seebeck coefficient, with the sign made explicit:where "left" and "right" denote two ends of the material, and where the second equation is understood as vector multiplication. Thus, if S is positive, the end with the higher temperature has the lower voltage, and vice-versa, and the electric field will point in the same direction as the temperature gradient.
Note that there is a minus sign in the first equation, but not the second. This is because the electric field points from the higher voltage towards the lower voltages, whereas the temperature gradient points from the lower temperature towards the higher temperature.
Charge carriers tend to respond to a temperature gradient by moving in the opposite direction, i.e. from the hot end to the cold end. They tend to respond to an electric field in different ways depending on their charge: positive charges tend to move in the same direction as the field, while negative charges move in the opposite direction of the field. For equilibrium to be reached, these two tendencies have to cancel out. Thus, for purely p-type
P-type semiconductor
A P-type semiconductor is obtained by carrying out a process of doping: that is, adding a certain type of atoms to the semiconductor in order to increase the number of free charge carriers ....
materials which have only positive mobile charges (holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
), the electric field and temperature gradient should point in the same direction in equilibrium, giving S>0. Likewise, for purely n-type
N-type semiconductor
N-type semiconductors are a type of extrinsic semiconductor where the dopant atoms are capable of providing extra conduction electrons to the host material . This creates an excess of negative electron charge carriers....
materials which have only negative mobile charges (electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s), the electric field and temperature gradient should point in opposite directions in equilibrium, giving S<0. In practice, real materials often have both positive and negative charge-carriers, and the sign of S usually depends on which of them predominates.
Measurement
In practice one rarely measures the absolute thermopower of the material of interest. This is because electrodes attached to a voltmeter must be placed onto the material in order to measure the thermoelectric voltage. The temperature gradient then also typically induces a thermoelectric voltage across one leg of the measurement electrodes. Therefore the measured thermopower is a contribution from the thermopower of the material of interest and the material of the measurement electrodes. This arrangement of two materials is usually called a thermocoupleThermocouple
A thermocouple is a device consisting of two different conductors that produce a voltage proportional to a temperature difference between either end of the pair of conductors. Thermocouples are a widely used type of temperature sensor for measurement and control and can also be used to convert a...
.
The measured thermopower is then a contribution from both and can be written as:
Superconductors have zero thermopower, as mentioned above. By using superconducting leads, it is possible to get a direct measurement of the absolute thermopower of the material of interest, since it is the thermopower of the entire thermocouple as well.
A measurement of the Thomson coefficient
Thermoelectric effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice-versa. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, it creates a temperature difference...
,
, of a material can also yield the thermopower through the relation: Thermoelectric power generation
The thermoelectric effect is sometimes used to generate electrical power, starting from a source of a temperature gradient. For example, some spacecraft are powered by a radioisotope thermoelectric generatorRadioisotope thermoelectric generator
A radioisotope thermoelectric generator is an electrical generator that obtains its power from radioactive decay. In such a device, the heat released by the decay of a suitable radioactive material is converted into electricity by the Seebeck effect using an array of thermocouples.RTGs can be...
, exploiting the temperature difference between a radioactively-heated plate and the cold empty space surrounding the craft. Some researchers hope that, in the future, much wider use could be made of thermoelectric power generation, including using waste heat
Waste heat
Waste heat sometimes called Secondary heat or Low-grade heat refers to heat produced by machines, electrical equipment and industrial processes for which no useful application is found. Energy is often produced by a heat engine, running on a source of high-temperature heat...
from automobiles (see Automotive Thermoelectric Generators
Automotive Thermoelectric Generators
An automotive thermoelectric generator is a device that converts waste heat in an internal combustion engine into electricity using the Seebeck Effect. A typical ATEG consists of four main elements: A hot-side heat exchanger, a cold-side heat exchanger, thermoelectric materials, and a compression...
) and power plants. (This is a form of energy recycling
Energy recycling
Energy recycling is the energy recovery process of utilizing energy that would normally be wasted, usually by converting it into electricity or thermal energy. Undertaken at manufacturing facilities, power plants, and large institutions such as hospitals and universities, it significantly...
.)
The efficiency with which a thermoelectric material can generate electrical power depends on several material properties, of which perhaps the most important is the thermopower. A larger induced thermoelectric voltage for a given temperature gradient will lead to a higher efficiency. Ideally one would want very large thermopower values since only a small amount of heat is then necessary to create a large voltage. This voltage can then be used to provide power.
There is an active research effort to find materials that could make cheaper and more efficient thermoelectric power generators; to learn more see the article Thermoelectric materials.
Materials with High Seebeck Coefficient
It is important to note that a material's Seebeck Coefficient is inversely related its carrier density. Therefore, insulators tend to have very high Seebeck coefficients, while metals have lower values due to their high carrier concentrations.- Bismuth tellurideBismuth tellurideBismuth telluride is a gray powder that is a compound of bismuth and tellurium also known as bismuth telluride. It is a semiconductor which, when alloyed with antimony or selenium is an efficient thermoelectric material for refrigeration or portable power generation...
- Uranium dioxideUranium dioxideUranium dioxide or uranium oxide , also known as urania or uranous oxide, is an oxide of uranium, and is a black, radioactive, crystalline powder that naturally occurs in the mineral uraninite. It is used in nuclear fuel rods in nuclear reactors. A mixture of uranium and plutonium dioxides is used...
- Perovskite is a class of compounds many of which have high Seebeck coefficient. This includes SrRuO3 for which the Seebeck coefficient equals 36 μV K−1 (microvolts per kelvin) at room temperature.
- ConstantanConstantanConstantan is a copper-nickel alloy usually consisting of 55% copper and 45% nickel.Also known as Eureka.Its main feature is its resistivity which is constant over a wide range of temperatures...
- Ytterbium Trialuminide