Einstein-Debye Yaklaşımı Kullanılarak Kalaylı Selenidin (SnSe) Bir Fonksiyon Sıcaklığı Olarak Isı Kapasitelerinin Teorik Olarak İncelenmesi

Abstract

Einstein-Debye yaklaşımına dayalı olarak kalaylı selenidin (SnSe) ısı kapasitelerini değerlendirmek için yeni bir alternatif yaklaşım önerilmiştir. Katıların ısıl davranışının, Einstein, Debye ve yakın zamanda geliştirilen Einstein-Debye yaklaşımları ile iyice araştırılan çok önemli bir teorik problem olduğu iyi bilinmektedir. Malzemelerin birçok ek termofiziksel özelliği, bu çalışmada kullanılan Einstein-Debye yaklaşımı kullanılarak analiz edilebilir. Bir uygulama olarak, ısı kapasiteleri 40 ila 900 K arasındaki sıcaklıklarda SnSe için Einstein-Debye yöntemi kullanılarak hesaplanmıştır. Isı kapasitelerinin sıcaklığa bağlılığı hesaplanmış ve geniş bir sıcaklık aralığında literatürle iyi bir uyum içinde olduğu bulunmuştur.

Keywords

• Einstein-Debye yöntemi
• Isı kapasitesi
• Selenid
• Debye fonsiyonu

Theoretical Investigation of Heat Capacities as a Function Temperature of Stannous Selenide (SnSe) Using Einstein-Debye Approximation

Abstract

A new alternative approach has been suggested for evaluating the heat capacities of stannous selenide (SnSe), based on the Einstein-Debye approximation. It is well known the thermal behavior of solids is a very important theoretical problem that has been explored thoroughly with the development of Einstein, Debye and recently developed Einstein-Debye approximations. Many additional thermophysical characteristics of materials may be analyzed using the Einstein-Debye approach employed in this study. As an application, the heat capacities have been computed by using the Einstein-Debye method for SnSe in the temperatures range between 40 and 900 K. The temperature dependence of heat capacities have been computed and found to be in good accord with the literature throughout a wide temperature range.

Keywords

• Einstein-Debye method
• Heat capacity
• Selenide
• Debye function

References

1. [1] N. K. Reddy, M. Devika, E. S. R. Gopal, “Review on tin (II) sulfide (SnS) material: synthesis, properties, and applications,” Crit. Rev. Solid State Mater. Sci., vol. 40, pp. 359-398, 2015.
2. [2] Y. Xu, N. Alsalim, J. M. Hodgkiss, R. D. Tilley, “Synthesis and size dependent reflectance study of water soluble SnS nanoparticles,” Cryst. Growth Des., vol. 11, pp. 2721-2723, 2011.
3. [3] S. Weiran, G. Minxuan, W. Jinping, G. Jianfeng, F. Chenwei, A. Eric, Li Handong, W. Zhiming, “Tin selenide (SnSe): growth, properties, and applications,” Adv. Sci., vol. 5, pp. 1700602, 2018.
4. [4] L. D. Hicks, M. S. Dresselhaus, “Effect of quantum-well structures on the thermoelectric figure of merit.,” Phys.Rev.B, vol. 47, pp. 12727-12731, 1993.
5. [5] R. Guo, X. Wang, Y. Kuang, B.Huang, “First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS,” Phys. Rev. B, vol. 92, pp. 115202, 2015.
6. [6] G. Duvjir, T. Min, T. Thi Ly, T. Kim, A-T. Duong, S. Cho, S.H. Rhim, J. Lee, J. Kim, “Origin of p-type characteristics in a SnSe single crystal,” Appl. Phys. Lett.,vol. 110, pp. 262106, 2017.
7. [7] L.E. Bell, “Cooling, heating, generating power, and recovering waste heat with thermoelectric systems,” Science, vol. 321, pp. 1457, 2008.
8. [8] Y. Zhang, S. Hao, L-D. Zhao, C. Wolverton, Z. Zeng, “Pressure induced thermoelectric enhancement in SnSe crystals,” J. Mater. Chem. A, vol. 4, pp. 12073, 2016.

9. [9] H. Yu, S. Dai, Y. Chen, “Enhanced power factor via the control of structural phase transition in SnSe,” Sci. Rep., vol. 6, pp. 26193, 2016.
10. [10] G. Li, U. Aydemir, M. Wood, W.A. Goddard III, P. Zhai, Q. Zhang, G. J. Synder, “Ideal strength and deformation mechanism in high-efficiency thermoelectric SnSe,” Chem. Mater., vol. 29, pp. 2382-2389, 2017.
11. [11] Y. Suzuki, H. Nakamura, “A supercell approach to the doping effect on the thermoelectric properties of SnSe,” Phys. Chem. Chem. Phys., vol. 17, pp. 29647-29654, 2015.
12. [12] T-R. Wei, G. Tan, C-F. Wu, C. Chang, L-D. Zhao, J-F. Li, G. J. Synder, M.G. Kanatzidis, “Thermoelectric transport properties of polycrystalline SnSe alloyed with PbSe,” Appl. Phys. Lett., vol. 110, pp. 053901, 2017.
13. [13] H. Wiedemeier, G. Pultz, U. Gaur, B Wunderlich, “Heat capacity measurements of SnSe and SnSe2,” Thermochim. Acta, vol. 43, pp. 297-303, 1981.
14. [14] A. S. Pashinkin, A. S. Malkova, V. A. Fedorov, M. S. Mikhailova, “Heat capacity of tin monoselenide,” Inorganic Material, vol. 42, pp. 593-595, 2006.
15. [15] C. Cifuentes, M. Botero, E. Romero, C. Calderon, G. Gordillo, “ Optical and structural studies on SnS films grown by co-evaporation,” Braz. J. Phys., vol. 36, pp. 1046-1049, 2006.
16. [16] H. Wiedemeier, P. Siemers, U. Gaur, B. Wunderlich, “Heat capacity measurements of GcS, GcSc and GcTc,” Thermochim. Acta, vol. 27, pp. 223-231, 1978.
17. [17] M. Cankurtaran, B. M. Askerov, “Equation of state, isobaric specific heat, and thermal expansion of solids with polyatomic basis in the Einstein-Debye approximation,” Phys. Stat. Sol. B, vol. 194, pp. 499-507, 1996.
18. [18] B. M. Askerov, M. Cankurtaran, “Isobaric Specific Heat and Thermal Expansion of Solids in the Debye Approximation,” Phys. Stat. Sol. B, vol. 185, pp. 341-348, 1994.
19. [19] L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd ed., vol. 5, N.S.W., Australia: Vieweg & Sohn GmbH, 1969, pp. 254-270. [20] I. I. Guseinov and B. A. Mamedov, “Calculation of Integer and Noninteger n Dimensional Debye Functions Using Binomial Coefficients and Incomplete Gamma Functions,” Int. J. Thermophys., vol. 28, pp. 1420-1426, 2007.
20. [21] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, 2rd ed., vol. 19, New York, USA: Academic Press, 1980, pp. 68-78.
21. [22] I. I. Guseinov, B. A. Mamedov, “Evaluation of Incomplete Gamma Functions Using Downward Recursion and Analytical Relations,” J. Math. Chem., vol. 36, pp. 341-346, 2004.