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So far we have only considered
one conducting material; the unavoidable
contacts between conductors,
implicitly always required, were seemingly devoid of special properties. |
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We know that this is not
true for many other contacts; e.g. combinations of
- semiconductor - semiconductor.
- semiconductor - conductor.
- ionic conductor - conductor.
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What about metal - metal
contacts? |
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We routinely solder wires of different conductors
together or join them in any way, and do not worry about the contacts. Besides,
maybe, a certain (usually small) contact
resistance which is a property of the interface and must be added to
the resistance of the two materials, there seems to be no other specific
property of the contact. |
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But that is only true as
long as the temperature is constant in the
whole system of at least two conductors. |
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The reason for this is that we always get a
contact voltage, as in the case of
semiconductors, but the extension of the charged layers at the interface (the
Debye lengths) is so short that no
specific phenomena result from this. |
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Consider the band diagrams before and after
joining two metals |
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We have a dipole layer of charges at
the interface which, owing to the large carrier density, is
extremely thin and does not hinder
current flow (it is easy for electrons to tunnel through the potential
barrier). |
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We also have a contact
potential, which is called the Volta potential. Since in any closed circuit
(containing, e.g., the wires to the voltmeter), the sum of the Volta potentials must be zero in
thermal equilibrium, it therefore can
not be measured directly. |
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If, however, one of the at least two contacts needed for a closed
circuit is at a temperature T2 that is different from
the temperature T1 of the first contact, we
have non-equilibrium and now a voltage may
be measured. We observe the Seebeck effect, one of several
thermoelectric effects. |
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We will not go into details here (consult the link for this) but will only
mention some applications and related effects. |
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Seebeck Effect |
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The Seebeck effect is the base for
thermoelements or thermocouples, the standard device for measuring
temperatures (the good old mercury thermometer is virtually nonexistent in
technical applications, especially at high temperatures). |
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Lets look at a typical situation: We have a
thermocouple mader with a material 1 and a material 2. It's
"contacted" by whatever (material 3, black lines). The
junction of material1 and material 2 is hot, the rest is cold
(and has the same temperature). |
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The voltmeter will show a thermovoltage that depends on DT and the two materials forming the
thermocouple. |
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Generally, the thermovoltage should
be larger for couples of conductors with very different Fermi energies or
carrier densities, since then the Volta potential is larger. |
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Being more specific, the Volta potential should
follow Nernsts law. But here we
are only interested in the practical aspects of thermocouples. |
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For technically important materials, it is
convenient to construct a voltage scale for thermocouples given in
mV/100K. |
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The voltage measured for a temperature difference
of 100 K is then the difference of the two values given on that scale
for the two materials joined in a thermocouple. The zero point was arbitrarily
chosen for Pt. |
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| Bi |
Ni |
Pd |
Pt |
Hg |
PtRh |
Cu |
Mo |
Fe |
NiCr |
Sb |
| -7,7 |
-1,5 |
-0,3 |
0 |
0 |
0,7 |
0,77 |
1,2 |
1,92 |
2,6 |
4,8 |
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Useful couples are, e.g. Ni/NiCr, with a
thermovoltage of ca. 4 mV/100K and a usable temperature range up to
1000 K. |
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The Seebeck effect, for many years extensively
used for measuring temperatures, can also be used to convert heat energy
directly into electrical energy. Thermoelectric generators are
becoming an exciting field of materials science, because optimized materials,
based on a thorough understanding of the requirements for power generation and
the concomitant requirements for the materials, are becoming available. |
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Other Thermoelectric Effects |
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There are several thermoelectrical
effects which are deeply routed in non-equilibrium
thermodynamics. Essentially, there is a "reciprocating" coupling of gradients in driving forces and currents of any kind (not just electrical currents
but also, e.g. particle currents, heat currents, or even entropy currents).
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Reciprocating means, that if a gradient - e.g. in the temperature - induces an electric current across a junction (the Seebeck effect), than
an electric current induced by some other
means must produce a temperature gradient. And this does not address the heating simply due to ohmic
heating! |
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The "reversed" Seebeck
effect does indeed exist, it is called the Peltier effect. In our schematic diagram it looks like
this: |
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An electrical current, in other words, that is
driven through the system by a battery, would lead to a "heat"
current, transporting thermal energy from one junction to the other one. One
junction then goes down in temperature, the other one goes up. |
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This effect would also occur in hypothetical materials with
zero resistivities (we do not mean superconductors here). If there is some
resistance R , the current will always lead to some heating of
the wires everywhere which is superimposed on the Peltier effect. |
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The temperature difference DT between the two junctions due to the
external current density j induced by the battery and the Peltier
effect then is approximately given by |
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The removal of heat or thermal energy thus is
linear with the current density |
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But there is always heating due to by ohmic
losses, too. This is proportional to j2, so it may
easily overwhelm the Peltier effect and no net cooling is observed in this
case. |
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The Peltier effect is not useful for heating - that is much easier done with resistance
heating - but for cooling! |
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With optimized materials, you can lower the
temperature considerably at one junction by simply passing current through the
device! The Peltier effect actually has been used for refrigerators, but now is
mainly applied for controlling the temperature of specimens (e.g. chips) while
measurements are being made. |
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One can do a third thing with thermoelements:
Generate power. You have a voltage coupled to a temperaturr difference, and
that can drive a current through a load in the form of a resistor. |
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Invariably the question of the efficiency
h of power generation comes up. How much of
the thermal energy in the system is converted to electrical energy? |
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This is not eays to calculate. It is, however, easy to guess
to what h will be proportional:
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There is one more effect worthwhile to mention: If
you have an external current and an
external temperature gradient at the same time, you have the Thomson
effect. But we mention that only for
completeness; so far the Thomson effect does not seem to be of technical
importance. Again, more information is contained in the link. |
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© H. Föll (Electronic Materials - Script)
