Thermoelectric effect

The thermoelectric aftereffect is the absolute about-face of temperature differences to electric voltage and vice-versa. A thermoelectric accessory creates a voltage if there is a altered temperature on anniversary side. Conversely, if a voltage is activated to it, it creates a temperature difference. At the diminutive scale, an activated temperature acclivity causes answerable carriers in the actual to broadcast from the hot ancillary to the algid side, agnate to a classical gas that expands if heated; appropriately inducing a thermal current.

This aftereffect can be acclimated to accomplish electricity, admeasurement temperature or change the temperature of objects. Because the administration of heating and cooling is bent by the polarity of the activated voltage, thermoelectric accessories are able temperature controllers.

The appellation "thermoelectric effect" encompasses three alone articular effects: the Seebeck effect, Peltier aftereffect and Thomson effect. Textbooks may accredit to it as the Peltier–Seebeck effect. This break derives from the absolute discoveries of French physicist Jean Charles Athanase Peltier and Estonian-German physicist Thomas Johann Seebeck. Joule heating, the calefaction that is generated whenever a voltage is activated beyond a arresting material, is accompanying admitting it is not about termed a thermoelectric effect. The Peltier–Seebeck and Thomson furnishings are thermodynamically reversible,1 admitting Joule heating is not.

Seebeck effect

The Seebeck aftereffect is the about-face of temperature differences anon into electricity and is alleged for German physicist Thomas Johann Seebeck, who, in 1821 apparent that a ambit aggravate would be deflected by a bankrupt bend formed by two metals abutting in two places, with a temperature aberration amid the junctions. This was because the metals responded abnormally to the temperature difference, creating a accepted bend and a alluring field. Seebeck did not admit there was an electric accepted involved, so he alleged the abnormality the thermomagnetic effect. Danish physicist Hans Christian Ørsted rectified the aberration and coined the appellation "thermoelectricity". The voltage created by this aftereffect is on the adjustment of several microvolts per kelvin difference. One such combination, copper-constantan, has a Seebeck accessory of 41 microvolts per kelvin at allowance temperature.2

The voltage V developed can be acquired from:

V = \int_{T_1}^{T_2} \left( S_\mathrm{B}(T) - S_\mathrm{A}(T) \right) \, dT,

where SA and SB are the thermopowers (Seebeck coefficient) of metals A and B as a action of temperature and T1 and T2 are the temperatures of the two junctions. The Seebeck coefficients are non-linear as a action of temperature, and depend on the conductors' complete temperature, material, and atomic structure. If the Seebeck coefficients are finer affiliated for the abstinent temperature range, the aloft blueprint can be approximated as:

V = (S_\mathrm{B} - S_\mathrm{A}) \cdot (T_2 - T_1).

The Seebeck aftereffect is acclimated in the thermocouple to admeasurement a temperature difference; complete temperature may be begin by ambience one end to a accepted temperature. A metal of alien agreement can be classified by its thermoelectric aftereffect if a brownish delving of accepted composition, kept at a affiliated temperature, is captivated in acquaintance with it. Industrial superior ascendancy instruments use this as thermoelectric admixture allocation to analyze metal alloys. Thermocouples in alternation anatomy a thermopile, sometimes complete in adjustment to access the achievement voltage, back the voltage induced over anniversary alone brace is small. Thermoelectric generators are acclimated for creating ability from calefaction differentials and accomplishment this effect.

edit Thermopower

Main article: Thermopower

The thermopower or Seebeck coefficient, represented by S, of a actual measures the consequence of an induced thermoelectric voltage in acknowledgment to a temperature aberration beyond that material, and the anarchy per allegation carrier in the material.3 S has units of V/K, admitting μV/K is added common. Values in the hundreds of μV/K, behindhand of sign, are archetypal of acceptable thermoelectric materials. The appellation "thermopower" is a misnomer back it does not admeasurement power, but measures the voltage induced in acknowledgment to a temperature difference. An activated temperature aberration causes answerable carriers in the actual to broadcast from the hot ancillary to the algid side. Mobile answerable carriers brief to the algid ancillary leave abaft their abnormally answerable nuclei at the hot ancillary appropriately giving acceleration to a thermoelectric voltage. Back a break of accuse creates an electric potential, the accretion of answerable carriers assimilate the algid ancillary eventually ceases at some best amount back the electric acreage is at equilibrium. An access in the temperature aberration resumes a accretion of allegation carriers on the algid side, arch to an access in the thermoelectric voltage, and carnality versa. The material's temperature and clear anatomy access S; about metals accept baby thermopowers because of half-filled bands acquired by according abrogating and complete accuse cancelling anniversary added accidental to the induced thermoelectric voltage. In contrast, semiconductors can be benumbed with balance electrons or electron holes, causing the consequence of S to be large. The assurance of the thermopower determines which answerable carriers boss the electric transport.citation needed

If the temperature aberration ΔT amid the two ends of a actual is small, again the thermopower of a actual is authentic approximately4 as:

S = - {\Delta V \over \Delta T}

and a thermoelectric voltage of ΔV is apparent at the terminals.

This can be accounting in affiliation to the electric acreage E and the temperature acclivity \nabla T by the approximate4 equation:

S = {E \over \nabla T}.

The complete thermopower of the actual of absorption is rarely about abstinent because electrodes absorbed to a voltmeter accept to be placed assimilate the actual in adjustment to admeasurement the thermoelectric voltage, inducing a thermoelectric voltage beyond one leg of the altitude electrodes. The abstinent thermopower again includes the thermopower of the actual of absorption and the actual of the altitude electrodes and is accounting as:

S_{AB} = S_B-S_A = {\Delta V_B \over \Delta T} - {\Delta V_A \over \Delta T}.

Superconductors accept S = 0 back the answerable carriers aftermath no entropy. This allows a complete altitude of the complete thermopower of the actual of interest, back it is the thermopower of the absolute thermocouple. In addition, a altitude of the Thomson accessory μ, of a actual yields the thermopower through the affiliation S = \int {\mu \over T} dT.

S is an important actual affiliated that determines the ability of a thermoelectric material; a beyond induced thermoelectric voltage and a college S beggarly a college efficiency.

edit Charge-carrier diffusion

The Seebeck ambit configured as a thermoelectric cooler.

The aforementioned ambit configured as a generator.

The Seebeck aftereffect is acquired by two things: charge-carrier circulation and phonon drag. Allegation carriers in the abstracts will broadcast if one end of a aqueduct is at a altered temperature than the other. Hot carriers broadcast from the hot end to the algid end, back there is a lower body of hot carriers at the algid end of the conductor, and carnality versa. If the aqueduct were larboard to ability thermodynamic equilibrium, this action would aftereffect in calefaction getting broadcast analogously throughout the aqueduct (see calefaction transfer). The movement of calefaction (in the anatomy of hot allegation carriers) from one end to the added is a calefaction accepted and an electric accepted as allegation carriers are moving.

In a arrangement area both ends are kept at a affiliated temperature difference, there is a affiliated circulation of carriers. If the amount of circulation of hot and algid carriers in adverse admonition is equal, there is no net change in charge. The diffusing accuse are broadcast by impurities, imperfections, and filigree accordance or phonons. If the drop is activity dependent, the hot and algid carriers will broadcast at altered rates, creating a college body of carriers at one end of the actual and an electrostatic voltage.

This electric acreage opposes the asperous drop of carriers, and an calm is accomplished area the net amount of carriers diffusing in one administration is canceled by the net amount of carriers affective in the adverse direction. This agency the thermopower of a actual depends abundantly on impurities, imperfections, and structural changes that alter with temperature and electric field; the thermopower of a actual is a accumulating of abounding altered effects.citation needed

Early thermocouples were metallic, but abounding added afresh developed thermoelectric accessories are fabricated from alternating p-type and n-type semiconductor elements affiliated by brownish connectors. Semiconductor junctions are accepted in ability bearing devices, while brownish junctions are added accepted in temperature measurement. Allegation flows through the n-type element, crosses a brownish interconnect, and passes into the p-type element. If a ability antecedent is provided, the thermoelectric accessory may act as a acknowledgment by the Peltier aftereffect declared below. Electrons in the n-type aspect move adverse the administration of accepted and holes in the p-type aspect will move in the administration of current, both removing calefaction from one ancillary of the device. If a calefaction antecedent is provided, the thermoelectric accessory functions as a ability generator. The calefaction antecedent drives electrons in the n-type aspect adjoin the acknowledgment region, creating a accepted through the circuit. Holes in the p-type aspect again breeze in the administration of the current. Therefore, thermal activity is adapted into electrical energy.citation needed

edit Phonon drag

Main article: Phonon drag

Phonons are not consistently in bounded thermal equilibrium; they move adjoin the thermal gradient. They lose drive by interacting with electrons (or added carriers) and imperfections in the crystal. If the phonon-electron alternation is predominant, the phonons will tend to advance the electrons to one end of the material, appropriately accident drive and accidental to the thermoelectric field. This addition is a lot of important in the temperature arena area phonon-electron drop is predominant. This happens for

T \approx {1 \over 5} \theta_\mathrm{D}

where θD is the Debye temperature. At lower temperatures there are beneath phonons accessible for drag, and at college temperatures they tend to lose drive in phonon-phonon drop instead of phonon-electron scattering. This arena of the thermopower-versus-temperature action is awful capricious beneath a alluring field.citation needed

Peltier effect

The Peltier aftereffect is the attendance of calefaction at an electrified alliance of two altered metals and is called for French physicist Jean-Charles Peltier, who apparent it in 1834. When a accepted is fabricated to breeze through a alliance composed of abstracts A and B, calefaction is generated at the high alliance at T2, and captivated at the lower alliance at T1. The Peltier calefaction \dot{Q} captivated by the lower alliance per assemblage time is according to

\dot{Q} = \Pi_\mathrm{AB} I = \left( \Pi_\mathrm{B} - \Pi_\mathrm{A} \right) I,

where ΠAB is the Peltier accessory for the thermocouple composed of abstracts A and B and ΠA (ΠB) is the Peltier accessory of actual A (B). Π varies with the material's temperature and its specific composition: p-type silicon about has a absolute Peltier accessory beneath ~550 K, but n-type silicon is about negative.

The Peltier coefficients represent how abundant calefaction accepted is agitated per assemblage allegation through a accustomed material. Since allegation accepted have to be affiliated beyond a junction, the associated calefaction breeze will advance a aperture if ΠA and ΠB are different. Depending on the consequence of the current, calefaction have to accrue or bankrupt at the alliance due to a non-zero alteration there acquired by the carriers attempting to acknowledgment to the calm that existed afore the accepted was activated by appointment activity from one adapter to another. Individual couples can be affiliated in alternation to enhance the effect. Thermoelectric calefaction pumps accomplishment this phenomenon, as do thermoelectric cooling accessories begin in refrigerators.citation needed

Thomson effect

The Thomson aftereffect was predicted and after empiric by Lord Kelvin in 1851. It describes the heating or cooling of a current-carrying aqueduct with a temperature gradient.

Any current-carrying aqueduct (except for a superconductor) with a temperature aberration amid two credibility either absorbs or emits heat, depending on the material. If a accepted body J is anesthetized through a constant conductor, the calefaction assembly q per assemblage aggregate is:

q = \rho J^2 - \mu J \frac{dT}{dx}\,\!

where ρ is the resistivity of the material, dT/dx is the temperature acclivity forth the wire and μ is the Thomson coefficient. The aboriginal appellation is the Joule heating, which does not change in sign; the additional appellation is the Thomson heating, which follows J alteration sign.

In metals such as zinc and copper, whose temperature is anon proportional to their potential, if accepted moves from the hotter end to the colder end, there is a bearing of calefaction and the complete Thomson aftereffect occurs.citation needed Conversely, in metals such as cobalt, nickel, and iron, whose temperature is inversely proportional to their potential, if accepted moves from the hotter end to the colder end, there is an assimilation of calefaction and the abrogating Thomson aftereffect occurs.

If the Thomson accessory of a actual is abstinent over a advanced temperature range, it can be chip application the Thomson relations to actuate the complete ethics for the Peltier and Seebeck coefficients. This needs to be done alone for one material, aback the added ethics can be bent by barometer pairwise Seebeck coefficients in thermocouples complete the advertence actual and again abacus aback the complete thermopower of the advertence material.

Lead is frequently declared to accept a Thomson accessory of zero; in fact, it is non-zero, admitting getting actual small.5 In contrast, the thermoelectric coefficients of all accepted superconductors are zero.citation needed

edit Thomson relations

The Thomson accessory is different a part of the three capital thermoelectric coefficients because it is the alone one anon assessable for alone materials. The Peltier and Seebeck coefficients can alone be bent for pairs of materials; hence, no complete methods abide for free complete Seebeck or Peltier coefficients for an alone material. In 1854, Lord Kelvin begin relationships amid the three coefficients, implying that alone one could be advised unique.citation needed

The aboriginal Thomson affiliation is

\mu = T {dS \over dT},

where T is the complete temperature, μ is the Thomson accessory and S is the Seebeck coefficient. The additional Thomson affiliation is

\Pi = S \cdot T

where Π is the Peltier coefficient. It predicted the Thomson aftereffect afore it was formalized.

Figure of merit

The ability of a thermoelectric accessory for electricity bearing is accustomed by η, authentic as

\eta = {\text{energy provided to the load} \over \text{heat activity captivated at hot junction}}.

The best ability ηmax is authentic as

\eta_{max} = {T_H - T_C \over T_H} {\sqrt{1+Z\bar{T}}-1 \over \sqrt{1+Z\bar{T}} + {T_C \over T_H}},

where TH is the temperature at the hot alliance and TC is the temperature at the apparent getting cooled. Z\bar{T} is the adapted dimensionless amount of merit, which takes into application the thermoelectric accommodation of both thermoelectric abstracts getting acclimated in the accessory and is authentic as

Z\bar{T} = {(S_p - S_n)^2 \bar{T} \over (\rho_n \kappa_n)^{1/2} + (\rho_p \kappa_p)^{1/2}^2}

where ρ is the electrical resistivity, \bar{T} is the boilerplate temperature amid the hot and algid surfaces and the subscripts n and p denote backdrop accompanying to the n- and p-type semiconducting thermoelectric materials, respectively. Since thermoelectric accessories are calefaction engines, their ability is bound by the Carnot efficiency, appropriately the TH and TC agreement in ηmax. Regardless, the accessory of achievement of accepted bartering thermoelectric refrigerators ranges from 0.3 to 0.6, one-sixth the amount of acceptable vapor-compression refrigerators.9

Device efficiency

The ability of a thermoelectric accessory for electricity bearing is accustomed by η, authentic as

\eta = {\text{energy provided to the load} \over \text{heat activity captivated at hot junction}}.

The best ability ηmax is authentic as

\eta_{max} = {T_H - T_C \over T_H} {\sqrt{1+Z\bar{T}}-1 \over \sqrt{1+Z\bar{T}} + {T_C \over T_H}},

where TH is the temperature at the hot alliance and TC is the temperature at the apparent getting cooled. Z\bar{T} is the adapted dimensionless amount of merit, which takes into application the thermoelectric accommodation of both thermoelectric abstracts getting acclimated in the accessory and is authentic as

Z\bar{T} = {(S_p - S_n)^2 \bar{T} \over (\rho_n \kappa_n)^{1/2} + (\rho_p \kappa_p)^{1/2}^2}

where ρ is the electrical resistivity, \bar{T} is the boilerplate temperature amid the hot and algid surfaces and the subscripts n and p denote backdrop accompanying to the n- and p-type semiconducting thermoelectric materials, respectively. Since thermoelectric accessories are calefaction engines, their ability is bound by the Carnot efficiency, appropriately the TH and TC agreement in ηmax. Regardless, the accessory of achievement of accepted bartering thermoelectric refrigerators ranges from 0.3 to 0.6, one-sixth the amount of acceptable vapor-compression refrigerators.9

Applications

Seebeck effect

Main article: Thermoelectric generator

The Seebeck aftereffect is acclimated in the thermoelectric generator, which functions like a calefaction engine, but is beneath bulky, has no affective parts, and is about added big-ticket and beneath efficient. These accept a use in ability plants for converting decay calefaction into added ability (a anatomy of activity recycling), and in automobiles as automotive thermoelectric generators (ATGs) for accretion ammunition efficiency. Space probes generally use radioisotope thermoelectric generators with the aforementioned apparatus but application radioisotopes to accomplish the appropriate calefaction difference.

edit Peltier effect

Main article: Thermoelectric cooling

The Peltier aftereffect can be acclimated to actualize a refrigerator which is bunched and has no circulating aqueous or affective parts; such refrigerators are advantageous in applications area their advantages out counterbalance the disadvantage of their actual low efficiency

edit Temperature measurement

Thermocouples and thermopiles are accessories that use the Seebeck aftereffect to admeasurement the temperature aberration amid two objects, one affiliated to a voltmeter and the added to the probe. The temperature of the voltmeter, and appropriately that of the actual getting abstinent by the probe, can be abstinent alone application algid alliance advantage techniques.citation needed