Thermoelectric figure of merit of a material with caged structure and rattler atoms

Abstract

A model is proposed to calculate the thermoelectric figure of merit of a framework crystal containing rattler atoms in cages. Such systems are expected to behave like a Phonon Glass and Electron Crystal (PGEC). The model resembles an effective Anderson model for a correlated system. The dispersion of the electronic energies and of the phonon frequencies in the system is calculated exactly. These results are used to evaluate the electronic and the thermal transport coefficients, which in turn give the temperature dependence of the thermoelectric figure of merit. Explicit calculation of the thermoelectric figure of merit for a one-dimensional case shows that the lattice thermal conductivity plays an important role in providing a peak structure to its temperature dependence. The results are presented for three different electronic dispersions and it is found that the room temperature figure of merit attains the highest value for the tight binding case. The calculation provides guidelines for designing a better thermoelectric material for use as a refrigerator.

Keywords:

• Thermal properties of crystalline solids
• Anharmonic lattice modes
• Vibrational states in low-dimensional structures
• Nonelectronic thermal conduction

Acknowledgments

One of us (SNB) acknowledges being introduced to semiconductor clathrates by Professors Alain Perez and Patrice Mellignon of Université Claude-Bernard at Lyon, France. His travel to Lyon was supported by the Indo-French Center through the Project No: IFCPAR 1508-4. He would also like to acknowledge the hospitality at Gerhard-Mercator-University Duisburg and Drexel University, Philadelphia during short visits. SMB would also like to acknowledge Gerhard-Mercator-University Duisburg for its hospitality during a visit when the article was written. We thank the Graduiertenkolleg 277 and the SFB 445 for financial support.

Notes

^‡E-mail: [email protected]

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**E-mail: [email protected]

Additional information

Notes on contributors

J.T. Schick **

‡E-mail: [email protected] †E-mail: [email protected] **E-mail: [email protected]