Seebeck and Peltier Effects

Probably the most important of the cross-coupling effects are those that couple heat flow with current flow. Consider the coefficient C31, which connects an electric current to a temperature gradient. Using the matrix Equation 17.38 with Ohm s law. 

The Seebeck coefficient is defined as S(T) = dV/dT and we can identify 31 = S T)o-. The Seebeck effect arises partly from the small temperature dependence of the Fermi level, which causes electrons to migrate from the region of higher Fermi level (higher chemical potential) to the lower. But the dominant effect comes from the interaction of the phonons with the electrons as they move through the solid, dragging the electrons along with them. 

Next consider the case of a homogenous conductor with an applied electric field. From the matrix Equation 17.38 we see that 

From Ohm s law, W = —/e/ / which combined with Equation 17.44 gives 

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It should be noted in the method that the U- or II-shaped specimen is never p-n device but a single p- or n- type material. This was aimed to remove possible errors due to Seebeck and Peltier effects in the resistivity measurement where a large temperature gradient is given to a specimen. An apparent Seebeck coefficients were calculated as the temperature derivatives from the measured electromotive forces. 

The Seebeck and Peltier effects were shown to be related by Thomson (later Lord Kelvin). The relationship is ... 

The choice of thermocouple type is generally related to the temperature and the bare wire environment but accuracy can also be an important consideration it depends on the chosen metals (or alloy) but the geometry of the application is also a factor. Besides the Seebeck and Peltier effects a third effect that might need consideration is the Thomson effect a potential could be created due to a temperature gradient along the length of the thermocouple wires. 

The Seebeck effect is the production of electricity from heat whereas the Peltier effect is the reverse. All these effects are classically presented as independent ones. The Formal Graph theory shows that the Seebeck and Peltier effects correspond to invariable couplings, whereas the Thomson effect is the variable version of these couplings. 

Example Seebeck and Peltier Effect. The Seebeck effect utilizes a temperature difference to generate a potential gradient as illustrated in Fig. 7.4. Two pieces of distinct metals, A and B (i.e. Cu/Al or Fe/Ni), are joined at 1 and 2. The junctions are exposed to different temperatures and this in turn gives rise to a (small) voltage drop, A, at 3. The Seebeck coefficient... 

A third thermoelectric effect, discovered by W. Thomson (1843), later Lord Kelvin, is also related to the Seebeck and Peltier effects. Thomson found that even in a conductor made of one substance, but with a temperature gradient, heat can be removed or added depending on whether the electric current and the temperature gradient coincide or point in opposite directions. 

In 1857, Thomson (Lord Kelvin) placed the whole field on firmer footing by using the newly developing field of thermodynamics (qv) to clarify the relationship between the Seebeck and the Peltier effects. He also discovered what is subsequently known as the Thomson effect, a much weaker thermoelectric phenomenon that causes the generation or absorption of heat, other than Joule heat, along a current-carrying conductor in a temperature gradient. 

Seebeck s outstanding scientific achievement was the discovei"y of one of the three classical thermoelectric effects, which are the Seebeck, the Peltier, and the Thomson effects. Seebeck s discovery was the first, dating from 1822—1823, followed by that of Jean-Charles-Athanase Peltier in 1832 and that of William Thomson in 1854. Seebeck obseiwed that an electric current in a closed circuit comprised different metallic components if he heated the junctions of the components to different temperatures. He noted that the effect increases linearly with the applied temperature difference and that it crucially depends on the choice of materials. Seebeck tested most of the available metallic materials for thermoelectricity. His studies were further systematized by the French physicist... 

The reverse of the Seebeck effect is called the Peltier effect and results from flowing an electric current through the circuits of figure 9.1. If the junctions are initially at the same temperature, a temperature gradient will be developed for instance, in the case of figure 9.1a, one of the junctions will cool and the other will warm. Associated with this electric current there will also be a Joule (resistive) effect, so that the net power (P) produced at each junction is given by... 

The first heat flow calorimeter based on Seebeck, Peltier, and Joule effects was built by Tian at Marseille, France, and reported in 1923 [156-158]. The set-up included two thermopiles, one to detect the temperature difference 7) — 7) and the other to compensate for that difference by using Peltier or Joule effects in the case of exothermic or endothermic phenomena, respectively. This compensation (aiming to keep 7) = T2 during an experiment) was required because, as the thermopiles had a low heat conductivity, a significant fraction of the heat transfer would otherwise not be made through the thermopile wires and hence would not be detected. 

Seebeck effect — is the potential difference that results when the joins of two different metals are at different temperatures and induces a movement of charge through the conductors. The Seebeck effect is the opposite of the Peltier effect (see - Peltier heat). 

In a nonisothermal system, an electric current (flow) may be coupled with a heat flow this effect is known as the thermoelectric effect. There are two reciprocal phenomena of thermoelectricity arising from the interference of heat and electric conductions the first is called the Peltier effect. This effect is known as the evolution or the absorption of heat at junctions of metals resulting from the flow of an electric current. The other is the thermoelectric force resulting from the maintenance of the junctions made of two different metals at different temperatures. This is called the Seebeck effect. Temperature measurements by thermocouples are based on the Seebeck effect. 

While the Seebeck effect enables TE devices to be used for power generation, the Peltier effect allows them to be used for cooling. In Peltier effect devices, heat flows in the same direction as majority carriers. The appropriate metric for this apphcation is called the TE efficiency, t], which is simply the ratio between the load s power input and the net heat flowrate. Essentially, rj gives the fraction of Camot efficiency attainable... 

Explain the emergence of the Seebeck, Peltier and Thomson effects in nonuniform conductors using the tools of phenomenological hnear thermodynamics. What is the physical sense of parameters that deter mine the magnitude of these effects ... 

An elementary thermocouple circuit is shown in Fig. 16.16. The EMF generated in this circuit is a function of the materials used and the temperatures of the junctions. It is useful to describe briefly the basic thermoelectric phenomena or effects that are related to the Seebeck effect and are present in thermocouple measurements. They include two well-known irreversible phenomena—Joule heating and thermal conduction—and two reversible phenomena—the Peltier effect and the Thompson effect. 

There are three thermoelectric phenomena that result from correlation between propagation of heat through a conductor and displacement of the current carriers in the conductor. The Seebeck effect (Ref 1) consists of formation of an electric current in an electrical circuit formed by two dissimilar conductors if the contacts between the conductors are held at different temperatures. A reverse phenomenon, the Peltier effect (Ref 2), consists of formation of a temperature difference between the contacts in a circuit of this type if an electric current is created in the circuit by an external current source to which the circuit is connected. W. Thomson (Lord Kelvin), who explained both effects (Refs. 3,4), predicted and experimentally confirmed the existence of another thermoelectric phenomenon, named the Thomson effect, which consists of absorption or release of heat in a uniform conductor with a current passing through it when a temperature gradient (positive or negative) is present along the current direction. 

When two different metal surfaces are brought into contact, the surface space charges that were present at their interfaces with a vacuum will be modified. The electrons from the metal of lower work function will flow into the other metal until an interface potential develops that opposes further electron flow. This is called the contact potential and is related to the work-function difference of the two metals. The contact potential depends not only on the materials that make up the solid-solid interface but also on the temperature. This temperature dependence is used in thermocouple applications, where the reference junction is held at one temperature while the other Junction is in contact with the sample. The temperature difference induces a potential (called the Seebeck effect), because of electron flow from the hot to the cold Junction, that can be calibrated to measure the temperature. Conversely, the application of an external potential between the two Junctions can give rise to a temperature difference (Peltier effect) that can be used for heat removal (refrigeration). 

Figure 15.12 Thermoelectric effects (a) the Seebeck effect, (h) the Peltier effect and (c) the Thompson effect...

Peltier effect The change in temperature produced at a junction between two dissimilar metals or semiconductors when an electric current passes through the junction. The direction of the current determines whether the temperature rises or falls. The first metals to be Investigated were bismuth and copper if the current flows from bismuth to copper the temperature rises. If the current Is reversed the temperature falls. The effect was discovered In 1834 by the French physicist Jean Peltier (1785-1845) and has been used recently for small-scale refrigeration. Compare Seebeck effect. 

Figure 6.1 The schematic of (a) Seebeck effect When heat flows across the junction, electrical current is generated, (b) Peltier effect When current is run across a TE junction, it heats or cools, depending on the direction of the current flow, (c) The sketch of a TE module composed of p-type and n-type legs.

Thermoelectric devices can also be used for cooling. By forcing a current through the material, a temperature gradient is created. This is the inverse of the Seebeck effect and is referred to as the Peltier effect. 

Due to their compactness and standard fabrication technology, the temperature in thermal flow sensors is often measured by thermocouples, which rely on the thermoelectric effect. The thermoelectric effect describes the coupling between the electrical and thermal currents, especially the occurrence of an electrical voltage due to a temperature difference between two material contacts, known as the Seebeck effect. In reverse, an electrical current can produce a heat flux or a cooling of a material contact, known as the Peltier effect. A third effect, the Thomson effect, is also connected with thermoelectricity, where an electric current flowing in a temperature gradient can absorb or release heat from or to the ambient [10, 11]. The relation between the first two effects can be described by methods of irreversible thermodynamics and the linear transport theory of Onsager in vector form. 

The electrical current density and the thermal entropy flux q /T are linked to the driving forces, the potential gradient A17 and the temperature gradient AT with linear coefficients Cei as the electrical conductivity, Lq for the heat transfer, Ls for the Seebeck effect, and Lp for the Peltier effect. 

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