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This document discusses thermoelectric materials and calculations using the Wien2K software. It describes the Seebeck effect and Peltier effect. It discusses using Wien2K to model materials like Mg2Si, calculate properties like density of states, band structure, and optimize volume. Modifying approximations, strain effects, and nanostructuring are discussed to increase thermoelectric figure of merit ZT by increasing power factor and decreasing thermal conductivity.
Roy-document-3
- 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.
- 15. Calculation
- 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
- 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.