Thermoelectricity - SpeedyLook encyclopedia

In certain materials the thermoelectric effect binds the flow of Chaleur which crosses them to the Electric current which traverses them. This effect is at the base of applications of Réfrigération and Génération of electricity : A thermoelectric material will make it possible to directly transform Chaleur into electricity, or to move Calorie S by the application of a Electric current.

Historical aspects

Potential applications

The current and potential applications of thermoelectric materials draw part of the two aspects from the Thomson effect:

On the one hand, the establishment of a heat flow, opposed to the thermal diffusion process, when a material subjected to a heat gradient is traversed by a current, makes it possible to consider applications of thermoelectric Réfrigération . This alternative solution with the traditional refrigeration using of the cycles of compression-relaxation does not require any moving part, from where a more great reliability, the absence of vibration and noise. These properties are fundamental in applications for which the temperature must be controlled in a very precise and reliable way, such as for example for the containers used for the transport of bodies to transplant, or for applications in which the vibrations constitute a considerable embarrassment, such as for example the guidance systems Laser or the Integrated circuits. Moreover, the possibility of creating a heat flux starting from an electric current in a direct way makes useless the use of gases of the type Fréon, which contribute to degrade the Couche of ozone.

In addition, the possibility of converting a heat flow into electric current makes it possible to consider applications of generation of electricity by thermoelectric effect, in particular starting from sources of heat lost like the mufflers of the Automobile S, the chimneys of incinerators, the circuits coolant of the nuclear plants… the thermoelectric systems would then constitute auxiliary energy sources “clean”, since, using unutilised existing sources of heat. The use of thermoelectricity in the car could for example make it possible to compensate partially for the Alternateur, reducing about 10% fuel consumption. Moreover, the very great reliability and durability of the systems (thanks to the absence of moving parts) led to their use for the electricity supply of the space probes. It is in particular the case of the probe Voyager, launched in 1977, in which the heat flow established between of fissile PuO2 (PuO2 is Radioactif and disintegrates, it is thus a source of heat) and the external medium crosses a thermoelectric conversion system containing SiGe (alloy of Silicium and Germanium), allowing the power supply of the probe in electricity (indeed, the space probes moving away beyond Mars cannot be supplied with Solar panels, solar flow being too weak). See the thermoelectric article Generating with radioisotope.

As we will see it thereafter, the conversion systems using the thermoelectric effect have weak outputs, whether it is in generation of electricity or refrigeration. They for the moment are thus limited to commercial niches in which reliability and durability are more important than the costs and the output.

Basic principles, in details

The energy transformation per thermoelectric effect ( heat → electricity or electricity → heat ) is based at the same time on the effects Seebeck, Peltier and Thomson.

Short recall of the coefficients Seebeck, Peltier and Thomson

Coefficient Seebeck

A difference in temperature dT enters to the junctions of two materials has and B implies a Potential difference electric FD according to:

$S_ {ab} = \ frac {FD} {dT} \,$

The Seebeck coefficient, also called " To be able Thermoélectrique" express yourself in V.K^-1 (or more generally in µV.K^-1 within sight of the values of this coefficient in usual materials).

The Seebeck coefficients of two materials are connected to the Seebeck coefficient of the couple according to:

$S_ {ab} =S_a-S_b \,$

Coefficient Peltier

In the case of the Peltier effect, a Electric current I is imposed on a circuit made up of two materials, which involves a release of Chaleur Q with a junction and an absorption of Chaleur to the other junction, according to:

$\ Pi_ {ab} = \ frac {Q} {I} \,$

Coefficient Thomson

Contrary to the coefficients Seebeck and Peltier, the Thomson coefficient can be defined directly for only one material. When are present simultaneously a Gradient of temperature and a Electric current, there are generation or absorption of Chaleur in each material segment taken individually. The Gradient of heat flux within material is then given by:

$\ frac {dQ} {dx} =I \ frac {dT} {dx} \ tau \,$

where X is the space coordinate and τ is the Thomson coefficient of material.

Relations between the coefficients Seebeck, Peltier and Thomson

Kelvin showed that the three coefficients Seebeck, Peltier and Thomson are not independent from/to each other. They are bound by the two relations:

$\ Pi_ {ab} =S_ {ab} T \,$

$\ tau_a- \ tau_b=T \ frac {dS_ {ab}} {dT} \,$

Principles of the energy transformation per thermoelectric effect

For the refrigeration or the generation of electricity per thermoelectric effect, a " module" consists of " couples" connected electrically. Each couple makes up of a material Semi-conducteur of the type p (S>0) and of a semiconductor material of type N (S<0). These two materials are joined by a conducting material whose thermoelectric capacity is supposed to be null. Two branches (p and N) of the couple and all the other couples composing the module are connected in series electrically and parallel thermically (see diagram on the right). This provision makes it possible to optimize the heat flux which crosses the module and its Electrical resistance. By preoccupation with a simplicity, we will reason in the continuation on only one couple, formed of two materials of constant sections.

The figure on the right presents the general diagram of a couple p-n used for the thermoelectric refrigeration. The electric current is imposed in such a way that the charge carrier (electrons and holes) move cold source with the hot source (with the direction Thermodynamique) in the two branches of the couple. By doing this, they contribute to a transfer of Entropie of the cold source to the hot source, and thus to a heat flux which will be opposed to that of thermal conduction. If the selected materials have good thermoelectric properties (we will see thereafter which are the important parameters), this heat flux created by the movement of the charge carriers will be more important than that of thermal conductivity. The system will thus make it possible to evacuate heat since the cold source towards the hot source, and will act then like a refrigerator.

In the case of the generation of electricity, it is the heat flow which involves a displacement of the charge carriers and thus the appearance of an electric current.

Output of conversion and parameters important

Calculation of the output of conversion of a thermoelectric system

The calculation of the output of conversion of a thermoelectric system is carried out by determining the relation between the heat flow and the electric current in material. It requires the use of the relations of Seebeck, Peltier and Thomson (see higher), but also laws of propagation of heat and Electric current.

The following example presents the calculation of the output of conversion in the case of the refrigeration (that of the generation of electricity can be carried out by similar reasoning).

Thus let us take again the preceding diagram. In each of the two branches of the couple, the heat flow generated by the Peltier effect is opposed to thermal conductivity. Total flows are thus in the branch p and branch N:

$Q_p=S_pIT- \ lambda_pA_p \ frac {dT} {dx} \,$ and $Q_n=-S_nIT- \ lambda_nA_n \ frac {dT} {dx} \,$

with X coordinates space (see diagram), λ_p and λ_n thermal conductivities of materials, and A_p and A_n their sections.

Heat is thus extracted from the cold source with a Q_f flow:

$Q_f= (Q_n+Q_p) _$

Important parameters to obtain a good output

By maximizing these two outputs of conversion, one can show that they depend only on the temperatures T_f and T_c and an adimensional number (without unit) Z_pnT_M called " factor of mérite" (T_M is the average temperature of the system, T_M= (T_f+T_c) /2) whose expression is:

Z_ {pn} = \ frac {(S_p-S_n) ^2} {RK} \,

It is noticed that Z_pn for a couple is not an intrinsic quantity with material but depends on relative dimensions of the branches of the module through R and K (Electrical resistance and thermal conductance). The output of conversion of the system (in generation of electricity as in cooling) is maximum when Z_pn is maximum, therefore when product RK is minimum, which is checked when:

$\ frac {L_nA_p} {L_pA_n} = \ left (\ frac {\ rho_p \ lambda_n} {\ rho_n \ lambda_p} \ right) ^2 \,$

The figure of Z_pn merit then becomes function only of intrinsic parameters to materials:

$Z_ {pn} = \ frac {(S_p-S_n) ^2} {(\ sqrt {\ lambda_p \ rho_p} + \ sqrt {\ lambda_n \ rho_n}) ^2} \,$

To obtain a maximum output of conversion, it is thus advisable to choose materials constituting the couple so as to maximize Z_pn. In general, that simply does not amount individually optimizing two materials to optimize their respective figures of merit Z=S²/(ρλ). With the majority of the temperatures used in practice, and in particular those used for the generation of electricity, the thermoelectric properties of best materials of the type p and type N are similar. In this case, the figure of merit of the couple is close to the average of the individual figures of merit, and it is reasonable to optimize two materials independently one of the other.

The material optimization for a use in the energy transformation per thermoelectric effect thus passes necessarily by the optimization of their electric and thermal properties of transport so as to maximize the figure of merit:

$ZT= \ frac {S^2} {\ rho \ lambda} \,$

A good thermoelectric material will thus have simultaneously a coefficient high Seebeck, good a electric Conductivité (c.a.d. a low electrical resistance), and weak a thermal Conductivité.

The figure opposite watch evolution of the output of conversion of a thermoelectric system under ideal conditions according to the figure of merit ZT. For example, if ZT=1 and that the difference in temperature is of 300°C, the output of conversion will be of 8%, which means according to the case (generation of electricity or refrigeration) that 8% of the Chaleur crossing material will be converted into electricity, or although the Chaleur extracted by cooling will correspond to 8% of the power electric employee.

Thermoelectric modules

Geometrical optimization

We saw that the properties of conversion of a thermoelectric material couple constituting a module are not only intrinsic: they also depend on the geometry of the system (length and section of the branches of the module) whose the Electrical resistance R and the thermal conductance depend K on the branches. It is necessary indeed that K is sufficiently low so that a thermal Gradient can be maintained, while being sufficiently high so that Chaleur crosses the module: if K is null no heat does not cross the module and there is thus no conversion. In the same way, R must be selected so as to have the best possible compromise between the electric output and the Potential difference electric. Once the selected materials constituting the module (thanks to the figure of merit ZT), it is thus necessary to optimize the geometry of the system to be able to obtain the output of conversion, the electric output or the maximum Chaleur extracted according to the application module.

Segmented modules

The materials used in the modules of thermoelectric conversion are generally effective only in one range of restricted temperature. Thus, the SiGe alloy used for the power supply of the probe Voyager is effective only with higher temperatures with 1000K approximately. It can thus be interesting, for applications or the Gradient of temperature is very large, to use several thermoelectric materials in each branch, each one in the range of temperature for which it is most effective. One then speaks about thermoelectric module segmented .

The figure opposite illustrates the concept of segmented module thermoelectric. We have here a very important Gradient of temperature (700K of difference between the hot zone and the cold zone), and no known material is not effective in all the range of temperature. Each of the two branches of the couple is thus formed of several materials (here two for branch N and three for the branch p). The length of each one of these materials is selected so that it is used in the range of temperature where it is most effective. Such a module will thus make it possible to obtain an output of conversion, a electric output, or a Chaleur extracted, definitely higher than if each branch were made up only of one material. Thus, the best outputs obtained in laboratory with this type of modules are at present close to 15% (what means that 15% of the Chaleur crossing material are converted into electric output). The segmented modules are however price much higher than the modules " simples" , which restricts them with applications for which the cost is not the factor of decisive choice.

Thermoelectric materials

Materials used in the current devices

Low temperatures

The thermoelectric material most usually used at the low temperatures (150K-200K), is formed on the basis of Bi_1-xSb_x (alloy of Bismuth and Antimoine) and unfortunately presents good thermoelectric properties only in type N (conduction the electrons), which restricts the output of conversion of the system since no materials is effective in type p in this range of temperature (let us recall that a thermoelectric conversion system is made up at the same time branches p and N). Curiously, whereas its properties are relatively average (ZT~0,6), the application of a Magnetic field makes it possible to double the figure of merit which exceeds the unit then. This material is thus generally used in partnership with a permanent Aimant.

Vicinity of the room temperature

The material more studied at the present time is Bi₂Te₃ (alloy of Bismuth and Tellure). It is used in all the devices functioning in the vicinity of the room temperature, which includes the majority of the devices of thermoelectric refrigeration. The best performances are obtained when it is combined with Sb₂Te₃ (alloy of Antimoine and Tellure) which has same the crystalline Structure. Samples of the type p as of type N can be obtained by small variations of composition in the vicinity of the Stoechiométrie. In both cases, values of the figure of merit ZT close to 1 are obtained in the vicinity of the room temperature. These good values of ZT are obtained partly thanks to very low thermal conductivity λ, near to 1 W.m^-1.K^-1 in best materials.

Intermediate temperatures

For a use with average temperature (550K-750K approximately), the material more used is the Tellure of Plomb PbTe and its alloys (PbSn) Te (Sn = tin). Both made up PbTe and SnTe can form a complete Solution solid what makes it possible to optimize the gap (forbidden band of the Semi-conducteur) with the desired value. The best materials obtained have figures of merit close to the unit around 700K. However, these values are obtained only in materials of the type N. PbTe cannot thus at the present time constitute with him only the two branches of a thermoelement. The branch p thus generally consists of a material of the type TAGS (for Tellure - Antimoine - Germanium - Argent), which as for him makes it possible to obtain figures of merit higher than the unit 700K only in type p. It thus appears crucial to develop a new material which can be used at the same time in type p and type N in this range of temperature. It is indeed easier industrially to use the same type of material for the two branches (and that would make it possible of more than eliminate the strongly toxic Tellure).

High temperatures

The Alloy S containing Silicon and Germanium have good thermoelectric characteristics at the high temperatures (above 1000K) and are in particular used for the generation of electricity in the space field. It is in particular of the alloys of this type which are used for the electricity supply Voyager probe.

Optimization of thermoelectric materials

The expression of the figure of merit ZT= (S²T)/(ρλ) summarizes with it only the difficulty of optimizing the properties of transport of a thermoelectric material. Intuitively, it appears difficult for a material simultaneously to have a good electric conductivity and a bad thermal conductivity, characteristic of insulators. Ideally, a good thermoelectric material should thus have all at the same time the electric conductivity of a Métal and the thermal conductivity of a Verre!

The numerator of the figure of merit ZT, S²σ (σ is the electric Conductivité, opposite of the electrical resistance: σ=1/ρ) is named power-factor. In generation of electricity per thermoelectric effect, the useful output will be all the more large as the power-factor will be large. Unfortunately, the Seebeck coefficient and electric conductivity are not independent one of the other, and vary in an opposite way with the concentration out of charge carriers (concentration of electrons or holes, to see Semi-conducteur): the best thermoelectric capacities will be obtained in materials of weak concentration out of carriers while best electric conductivities will be it in materials with strong concentration of carriers. By compromise, the best thermoelectric materials will thus belong to the class of the Semi-conducteur S.

The second big factor in the expression of the figure of merit ZT (in addition to the power-factor) is the thermal Conductivité: a material will have optimal thermoelectric properties for a low thermal conductivity. Indeed, in an intuitive way, a good thermal conductivity would tend to be opposed to the establishment of the thermal Gradient: heat would cross material without meeting resistance. The optimization of materials will thus require to seek to decrease thermal conductivity, without degrading electric conductivity. Only the contribution of the vibrations of the network (see thermal Conductivity) will have to thus be decreased, and not the contribution due to the charge carriers (electrons or holes)

Ways of research

We saw in the preceding paragraph that the best materials used at present in the devices of thermoelectric conversion have figures of merit ZT close to 1. This value does not make it possible to obtain outputs of conversion which economically make these systems profitable for " applications; large public". For example, one would need materials for which ZT=3 to be able to develop a competing domestic refrigerator. For the systems of generation of electricity (which could be used for example on the Muffler of cars or trucks, or on Microprocesseur S), two means would make it possible to increase the profitability of the systems: a significant growth of their outputs (with for example ZT>2), or a reduction in the costs. The goal of this paragraph is to present in a nonexhaustive way some currently followed ways of research, as well in industrial laboratories as public.

Structures of low dimensionnalities

One names structure of low dimensionnality a working of a material for which one or more dimensions are very small compared to the others. It is for example the case of the thin layers in Microélectronique S (structure 2D), of nanofils (structure 1D) or nanopoudres (structure 0D), in opposition to massive material which has 3 dimensions. These structures generally have properties rather different from massive material of the same composition. In the field of thermoelectricity, the goal of research is double: to seek to improve the output of conversion by using basic structures dimensionnalities, while profiting from the systems of mass production used in Microelectronic. The study of the structures of low dimensionnalities became very important since notable improvements of the figure of merit ZT were predicted there theoretically then observed in experiments. The two principal effects observed are strong a diffusion Phonon S by the grain boundary (borders between the various grains constituting material) inducing a reduction in the thermal Conductivité of network, and effects of containment (quantum phenomenon of type) of the charge carrier which strongly modify the properties of electric transport (electric Conductivité and coefficient Seebeck). Very high values of the figure of merit ZT, about 2.5 with the room temperature, were thus observed in laboratory in structures in thin layers. At present, these structures are mainly considered for applications to low or average temperatures (<150-200°C). One of the main difficulties is indeed to obtain thermoelectric thin layers whose properties are not degraded with the temperature.

Identification and optimization of new materials

Principles

We saw previously that to obtain a good output of conversion, the materials must have a thermal Conductivité weakest possible and a electric Conductivité strongest possible. It must thus ideally lead the Electric current like a Métal, and the Chaleur like a Verre.

Various properties can allow the thermal Conductivité of a Cristal (metals have a crystallized structure) to approach that of a Verre (glasses are Amorphe S). It is mainly:

a crystalline structure complex . Indeed most of the Chaleur is transported by the acoustic modes of phonons. However a material having NR atoms by Maille will have 3 acoustic modes, and 3 (N-1) optical modes, from where the interest of complex structures for which NR is large and the majority of the phonon methods are optical modes which transport heat little.
Of the Atom S slightly related to the remainder of the crystal lattice (for example of the small atoms in a large cage), or whose positions are not perfectly defined (sub-headings around the same site, amplitudes of important vibrations). These atoms induce an important disorder which contributes to the diffusion of the phonons and thus to the reduction in the thermal Conductivité. On the other hand, as they take part little in the electric Conductivité, the disorder does not cause too important degradation of this conductivity.

Particularly studied promising materials

Currently, three material classes are particularly studied according to these recommendations (complex structure and atoms slightly dependant). It is:

compounds of the type Semi-Heusler , of general formula XYZ with X and Y of the Metals of transition and Z a Metalloid or a metal, for example ZrNiSn (Zirconium, Nickel, tin). These compounds present very high power-factors S²σ, at the same time in type p and type N. One the their most interesting characteristics is the possibility of doping on each of the three sites, which tends moreover to modify the vibrations of the network. However their thermal conductivities are too high, and the best ZT obtained at the present time are about 0,7 with 700K-800K.
the second family of compounds, which presents a very great number of structural varieties, is that of the Clathrate S . These compounds have a relatively open structure made up, for the compounds most studied at the present time, of a network of If (Silicium), GaGe (Gallium Germanium) or GaSn (Gallium tin) formant of large cages in which can be inserted heavy atoms (in particular of the Rare earths or alkaline-earth). Their thermal conductivity is similar to that of glass (the atom inserted in the cage strongly diffuses the phonons) whereas the electronic properties, which are mainly function of the network, are good. The best figures of merit obtained approach the unit around 800K.
the third very studied family is that of the Skutterudite S . These compounds have a cubic structure formed of a network of the MX₃ type (with M a Métal of transition and X = Arsenic, Phosphore or Antimoine), with in the center of this network a large cage in which can be inserted heavy atoms (in particular of the Rare earths). These compounds have very high Seebeck coefficients as well as good a electric Conductivité, but their thermal conductivities remain too high. The best figures of merit obtained are close to 1.4 around 800K.