1. Thermoelectricity
Prasenjit Roy

2. Thermoelectricity
• Seebeck effect
In 1821, Thomas Seebeck found that
an electric current would flow
continuously in a closed circuit made
up of two dissimilar metals, if the
junctions of the metals
were maintained at two different
temperatures.

3. Thermoelectricity
• Peltier effect
When some current is flowing
The carrier comes as the flow
From one to other side, transferring
the energy . So temperature
difference arises.

4. Seebeck coefficient
Seebeck
coefficient
Thermodynamic figure
Of merit

5. Competition between electrical conductivity
and the Seebeck coefficient
Picture taken from :
Rep. Prog. Phys.
51 (1988) 459-539.
Ref 3.
The power factor depends on these two factors.

6. Increase zT

1. High electrical conductivity
Low Joule heating
2. Large Seebeck coefficient
Large potential difference
3. Low thermal conductivity.
large temperature difference

7. PRESENTLY ACHIEVABLE VALUE OF ZT
Let ZT = 1, e.g. Optimized Bi2Te3 (300 K)
 Resistivity ~ 1.25 mΩ-cm
 Thermopower ~ 220 μV/K
 Thermal Conductivity ~ 1.25 Wm-1K-1

8. Needed value of zT
~
3
So if we have a hypothetical thermal conductivity =0,
we need >220 μV/K of Thermopower.

9. Recently used materials
In the recently
used materials,
AgPbmSbTe2m we mostly
focus on
Skutterudites(fil
led).
We will not
incorporate Pb
or any such
toxic materials
in the alloys.

10. Way to increase zT
• 1. Exploring new materials with complex
crystalline structure.
• 2. Reducing the dimensions of the material.
Reason: IN those materials , the rattling motion of loosely bounded atoms
within a large case generates strong scattering against lattice phonon propagation.
But has less of an impact on transport of electrons.

11. Need of computation
• By the use of computational modeling we can predict the
possible structural properties in bulk as well as special
structures like nanotube nano layer etc.
• We used modeling of samples by Wien 2K. Where we
specified the crystal structure and found out characteristics
like density of states, bandstructure, electronic density by
which we can at least predict what kind of material is
suitable for getting better thermo-electric properties,
namely electrical conductivity, and extending the studies
further with the help of Boltzmann transport properties we
can find out thermoelectric power factor which is directly
proportional to the figure of merit. Although the studies
with phonon is not clear, the group is working on it.

12. Wien 2K
• Wien2K uses LAPW method to solve the many body
problem and finding the energy of the system. The program
utilizes many utility programs to find different
characteristics properties of the system. Like Eos fit ,
supercell, optimization job, structure editor, x-crysden and
lot more. The code is written mostly in Fortran 90 and
some in c+ . All the programs are interlinked via c-shell
scripts.

13. Flow of programs
1. Specify your system. i.e. write the structure file(case.struct) in the system. For that you
must know the crystal structure, that is position of the atom in the unit cell and the
space group, the constituting atoms and the atomic numbers of them. These are the
basic inputs that will be needed in the whole calculation .
2. Then initialize your calculation. i.e. finding the RMT values , number of symmetry
operation and also it compares the calculated number with the available value also
specified in case.struct, and the k point symmetry, the potential using to calculating the
properties etc.
3. Then run a usual self consistent force cycle. Which will help in calculating all other
properties of the crystal . This can also be done with three different preferences,
force(automatic geometry optimization), spin-orbit coupling, spin-polarization(for the
magnetic cases).
4. Then we use to find the usual available properties that we can obtain from the history
file, case.scf.
5. We can calculate DOS, bandstructure with band character plotting, x-ray spectra,
electron density, volume optimization etc.
6. Analyze the obtained results.

14. Diversity in calculation

15. Calculation

22. Thermoelectric material

23. Why only focusing near the Fermi
surface?

24. Possible thermoelectric materials, Mg2Si

27. This is a typical
example of electron
density plot obtained
by Wien2K using
GNUPLOT and
xCrysden respectively.
The green spheres are
Mg and the blue ones
are Si. The coloured
planes as specified by
the picture shows
gradual variation of
electron density with
the real space
variation.
The main difference
with density of states
and electron density is
that DOS is plotted in
momentum space and
electron density in real
space.

28. Approximations:
• In the technique Wien2K provides the freedom to choose different
potentials in order to calculate the properties of the materials. We
can either choose GGA, LDA, LDA-PBE, mBJ potentials in cases.
• I can show the difference arising due to these potential variation.

29. • These two pictures shows the changes arising in the Mg2Si
structures because of the LDA and the mBJ approximation, although
the material and its structures are same.
• Structural details of Mg2si needed for calculations: Space
group=225 Fm-3m. a=b=c=6.35 Angstrom. α=β=γ=90°.
• In our case mBJ turns out to be more realistic since the band gap is
closer to the experimentally obtained value, as shown in the
following pictures.
Mg2Si LDA DOS Mg2Si mBJ DOS

30. Volume optimization

31. Volume optimization
Volume optimization in Mg2si Volume optimization in Mg2Sn

32. Volume optimization
Mg2Si Mg2sn
Using Birch-Murnaghan switch: Using Birch-Murnaghan switch:
1. V0=433.3047373 Bohr^3 1. V0=530.5161274 Bohr^3
2. E0=-690.7210080 2. E0= - 483.6014708
3. B0=53.31241497 Gpa 3. B0= 0.000101233 Gpa
4. B0’’= 0.176933 X 10^-3 4. B0’’= 0.7491 X 10^-4
5. A0=12.0121 Bohr. 5. A0=12.850485 Bohr.

33. Effect of stress: strain.
• We can apply stress, i.e. changing the lattice parameter, and tracing out
what possible changes occurs in its properties. We can interestingly
point out in this experiment that whether the bandstructure is only the
function of the lattice parameter or not. We will plot the bandstructure
of both Mg2Si and Mg2Sn at a range varying from both of the
material’s equilibrium volumes. If the properties as well as the bands
varies the same way in both cases then our approximation is correct.

34. Effect of stress: strain.
• The similarity is clear in case of both material at a particular value of
lattice parameter, a= 12.85 Bohr. So it can be safely concluded that the
bandstructures are mostly dependent on the lattice parameter of the
material.
The bandstructure of both Mg2si and Mg2Sn at a= 12.85 Bohr

35. Effect of stress: strain.
• The band-gap also plays an important role in the
calculation. To prove our assumption I have plotted the
band gap variation with lattice parameter in both the
material. The calculations were done using mBJ
approximation.
The graph shows
Similar variation of
Band gap vs lattice
Parameter in both
Mg2si and Mg2sn.

38. Although there is very small difference
In these two pictures the DOS gives the
Information that the slope is more steeper
In the pic 2 proving it to be a better
thermoelectric. The band gap is
almost similar in both cases,
Approximately 0.5 eV. Most
Interestingly the bands are much
More steeper in these two cases
Than both Mg2Si and Mg2Sn.

39. Thermal conductivity and
nano-structuring
• The thermal conductivity of the material depends on the thermal
diffusivity value, density and the mass of the sample.
• The aggregated thermal conductivity is the sum of two terms. The lattice
thermal conductivity and the electronic thermal conductivity.
• Now the electronic part of K depends on the electrical part of conductivity
multiplied by the Lorentz number. So increasing the electrical conductivity
in turn increases this part.
• The lattice thermal conductivity is independent of the electronic vibration
but depends entirely on the phononic vibration. So we can control this
term to obtain a minimized value of K in order to obtain a larger zT.
• Theoretically and experimentally there are few ways to do that.
1. as in the simple chain vibration of the mass-point, we can insert an atom
greater than twice the mass of the atoms containing chain. Similarly we can
here insert a dissimilar masspoint to damp the phnonic vibration.
2. We can ground the sample up to nanometer level. So the vibration will not
propagate beyond the grain size. Hence reducing the thermal conductivity.
• So in this way we can further improve the zT value.

40. Reference and conclusion
• Reference:
1. The Wien2K software and its ‘Userguide’.
2. Density Functional Theory and the Family of (L)APW-methods: a step-by-
step introduction by S. Cottenier.
3. Materials for thermoelectric energy conversion , C. Wood, Rep. Prog. Phys.
51 (1988) 459-539.
• Conclusion:
The work described here is very fundamental in material characterization.
Electronic properties calculation has done with great details and complication.
Seebeck coefficient and electrical conductivity can easily be found out with
these data. Thermal conductivity can be found out as well with some more
Calculation.
Doping using CPA method could be useful to make both p-type and n-type
Semiconductor with optimized carrier concentration.