Theoretical Study of Thermal Conductivities of n- and p-type Doped Mg2Si1-xSnx Thermoelectric Solid Solutions

Year 2017, Volume: 21 Issue: 6, 1221 - 1228, 01.12.2017

Övgü Ceyda Yelgel

https://doi.org/10.16984/saufenbilder.292752

Abstract

Mg₂Si_1-xSn_x
solid solutions are a promising class of thermoelectric materials due to
their high thermoelectric efficiencies at
intermediate temperature range from 500 K to 800 K. Present study presents a theoretical
work of the   thermal conductivities of both n- and
p-type doped Mg₂Si_1-xSn_x solid solutions. The
thermal conductivity contributions arising from carriers (electrons or holes),
electron-hole pairs, and phonons are taken into account separately by employing
the Wiedemann-Franz law, Price's theory, and Debye's isotropic continuum model,
respectively. All phonon scattering mechanisms originate from crystal
boundaries, mass-defects, deformation potentials, and anharmonicity are
investigated rigorously for all solid solutions. The lowest total thermal
conductivity values are obtained as 2.431 WK^-1m^-1 at 700
K for n-type doped Mg₂(Si_0.4Sn_0.6)_0.98Bi_0.02
solid solution and 1.843 WK^-1m^-1 at 600 K for
p-type doped Mg₂(Si_0.3Sn_0.7)_0.95Ga_0.05
solid solution which clearly suggest that p-type doped Mg₂Si_1-xSn_x
based solid solutions are better candidates for the thermoelectric
devices than their n-type doped solid solutions.

Keywords

thermoelectric materials, thermal conductivity, phonon thermal conductivity

N- ve P-tip Katkılı Mg2Si1-xSnx Katı alaşımlarının termal iletkenliklerinin teorik calışması

Abstract

Mg₂Si_1-xSn_x katı
alaşımları yüksek termoelektrik verimlilikleri sebebiyle 500 K’den 800 K’e
kadar olan orta sıcaklılık aralığı için umut vaadeden termoelektrik
materyallerdir. Bu çalışmada hem n- hem p-tip katkılı Mg₂Si_1-xSn_x
katı alaşımlarının termal iletkenlikleri teorik olarak detaylıca incelenmesi
sunulmuştur. Taşıyıcılardan (elektronlar yada holler), elektron-hole
çiftlerinden ve fononlardan kaynaklanan termal iletkenlik katkıları ayrı ayrı
göz önüne alınarak ve sırasıyla Wiedeman-Franz kanunu, Price’in teorisi, ve
Debye’nin izotropik sürekli modeli uygulanarak hesaplanmıştır. Bütün fonon
çarpışma mekanizmaları, kaynağı kristal sınırlarından, kütle bozukluklarından,
bozunum potansiyellerinden ve anharmoniklikten olan katı alaşımların hepsi için
eksiksiz bir şekilde incelenmiştir. En düşük toplam termal iletkenlik değerleri
n-tip katkılı Mg₂(Si_0.4Sn_0.6)_0.98Bi_0.02
katı alaşım için 700 K’de 2.431 WK^-1m^-1 olarak, p-tip
katkılı Mg₂(Si_0.3Sn_0.7)_0.95Ga_0.05
katı alaşım için 600 K’de 1.843 WK^-1m^-1 olarak
bulunmuştur buda açıkca öneriyor ki p-tip katkılı Mg₂Si_1-xSn_x
tabanlı katı alaşımlar n-tip katkılı katı alaşımlarından termoelektrik cihazlar
için daha iyi adaylardır.

Keywords

termoelektrik materyaller, termal iletkenlik, fonon termal iletkenlik

References

• V. K. Zaitsev, M. I. Fedorov, I. S. Eremin, E. A. Gurieva, and D. M. Rowe, ‘Thermoelectrics handbook: macro to nano’, CRC Press. Taylor Fr. Boca Rat., 2006.
• C. Li, Y. Wu, H. Li, and X. Liu, ‘Microstructural formation in hypereutectic Al-Mg2Si with extra Si’, J. Alloys Compd., vol. 477, no. 1, pp. 212–216, 2009.
• P. M. Lee, ‘Electronic structure of magnesium silicide and magnesium germanide’, Phys. Rev., vol. 135, no. 4A, p. A1110, 1964.
• S. K. Bux, M. T. Yeung, E. S. Toberer, G. J. Snyder, R. B. Kaner, and J.-P. Fleurial, ‘Mechanochemical synthesis and thermoelectric properties of high quality magnesium silicide’, J. Mater. Chem., vol. 21, no. 33, pp. 12259– 12266, 2011.
• V. K. Zaitsev et al., ‘Highly effective Mg2Si1- xSnx thermoelectrics’, Phys. Rev. B, vol. 74, no. 4, p. 45207, 2006.
• X. Liu et al., ‘Low electron scattering potentials in high performance Mg2Si0. 45Sn0. 55 based thermoelectric solid solutions with band convergence’, Adv. Energy Mater., vol. 3, no. 9, pp. 1238–1244, 2013.
• W. Liu et al., ‘High figure of merit and thermoelectric properties of Bi-doped Mg2Si0.4Sn0.6 solid solutions’, J. Solid State Chem., vol. 203, pp. 333–339, 2013.
• T. Dasgupta, C. Stiewe, R. Hassdorf, A. J. Zhou, L. Boettcher, and E. Mueller, ‘Effect of vacancies on the thermoelectric properties of Mg2Si1- xSbx (0 ≤ x ≤ 0.1)’, Phys. Rev. B, vol. 83, no. 23, p. 235207, 2011.
• J.-Y. Jung, K.-H. Park, and I.-H. Kim, ‘Thermoelectric Properties of Sb-doped Mg2Si Prepared by Solid-State Synthesis’, IOP Conf. Ser. Mater. Sci. Eng., vol. 18, no. 14, p. 142006, 2011.
• J. Tani and H. Kido, ‘Thermoelectric properties of Sb-doped Mg2Si semiconductors’, Intermetallics, vol. 15, no. 9, pp. 1202–1207, 2007.
• M. I. Fedorov, V. K. Zaitsev, and G. N. Isachenko, ‘High effective thermoelectrics based on the Mg2Si-Mg2Sn solid solution’, Solid State Phenomena, 2011, vol. 170, pp. 286–292.
• A. U. Khan, N. Vlachos, and T. Kyratsi, ‘High thermoelectric figure of merit of Mg2Si0.55Sn0.4Ge0.05 materials doped with Bi and Sb’, Scr. Mater., vol. 69, no. 8, pp. 606–609, 2013.
• P. J. Price, ‘CXXXV. Ambipolar thermodiffusion of electrons and holes in semiconductors’, London, Edinburgh, Dublin Philos. Mag. J. Sci., vol. 46, no. 382, pp. 1252–1260, 1955.
• G. P. Srivastava, ‘The physics of phonons’, CRC press, 1990.
• D. M. Rowe, ‘Thermoelectrics handbook: macro to nano’, Thermoelectr. Handb. Macro to Nano, vol. 80, no. 10, p. 1014, 2005.
• R. R. Heikes and R. W. Ure, ‘Thermoelectricity: science and engineering’, Interscience Publishers, 1961.
• J. Tani and H. Kido, ‘Thermoelectric properties of Bi-doped Mg2Si semiconductors’, Phys. B Condens. Matter, vol. 364, no. 1, pp. 218–224, 2005.
• T. Yi et al., ‘Synthesis and characterization of Mg2Si/Si nanocomposites prepared from MgH2 and silicon, and their thermoelectric properties’, J. Mater. Chem., vol. 22, no. 47, pp. 24805–24813, 2012.
• Ö. C. Yelgel and G. P. Srivastava, ‘Thermoelectric properties of n-type Bi2(Te0.85Se0.15)3 single crystals doped with CuBr and SbI3’, Phys. Rev. B, vol. 85, no. 12, p. 125207, 2012.
• A. H. Wilson, ‘The Theory of Metals Cambridge’, Gt. Britain, p. 26, 1953.
• J. P. McKelvey, ‘Solid state and semiconductor physics’, 1966.
• Ö. Ceyda Yelgel and G. P. Srivastava, ‘Thermoelectric properties of p-type (Bi2Te3) x (Sb2Te3)1- x single crystals doped with 3 wt.% Te’, J. Appl. Phys., vol. 113, no. 7, p. 73709, 2013.
• G. S. Nolas, H. J. Goldsmid, and T. M. Tritt, ‘Thermal Conductivity: Theory, Properties, and Applications’, 2004.
• M. G. Holland, ‘Phonon scattering in semiconductors from thermal conductivity studies’, Phys. Rev., vol. 134, no. 2A, p. A471, 1964.
• M. Grundmann, ‘The Physics of Phonons: An Introduction Including Devices and Nanophysics’. Springer, Berlin, 2006.
• O. Madelung, U. Rössler, and M. Schulz, ‘Non-tetrahedrally bonded elements and binary compounds I’, Landolt-Börnstein Ser., vol. 3, 1998.
• H. Wang, H. Jin, W. Chu, and Y. Guo, ‘Thermodynamic properties of Mg2Si and Mg2Ge investigated by first principles method’, J. Alloys Compd., vol. 499, no. 1, pp. 68–74, 2010.