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.
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
heating2. Large Seebeck coefficient Large potential difference3.
Low thermal conductivity. large temperature difference
7. PRESENTLY ACHIEVABLE VALUE OF ZTLet ZT = 1, e.g. Optimized
Bi2Te3 (300 K) Resistivity ~ 1.25 m-cm Thermopower ~ 220 V/K
Thermal Conductivity ~ 1.25 Wm-1K-1
8. Needed value of zT ~ 3So if we have a hypothetical thermal
conductivity =0,we need >220 V/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 atomswithin 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 programs1. 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
16. Thermoelectric material
17. Why only focusing near the Fermi surface?
18. Possible thermoelectric materials, Mg2Si
19. This is a typicalexample of electrondensity plot obtainedby
Wien2K usingGNUPLOT andxCrysden respectively.The green spheres
areMg and the blue onesare Si. The colouredplanes as specified
bythe picture showsgradual variation ofelectron density withthe
real spacevariation.The main differencewith density of statesand
electron density isthat DOS is plotted inmomentum space andelectron
density in realspace.
20. 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.
21. 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. ===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
22. Volume optimization
23. Volume optimizationVolume optimization in Mg2si Volume
optimization in Mg2Sn
25. 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 materials
equilibrium volumes. If the properties as well as the bands varies
the same way in both cases then our approximation is correct.
26. 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
27. 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.
28. Although there is very small differenceIn these two
pictures the DOS gives theInformation that the slope is more
steeperIn 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.
29. 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.
30. 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.
