Funct. Mater. 2018; 25 (4): 720-728.
Temperature and concentration dependences of specific heat of Bi1-xSbx solid solutions
National Technical University Kharkiv Polytechnic Institute, 2 Kyrpychova St., 61002 Kharkiv, Ukraine
For Bi1-xSbx solid solutions, the concentration (x = 0 - 0.12) and temperature (170-525 K) dependences of specific heat Cp were obtained. At all temperatures studied, three peaks of Cp were observed near x = 0.015, x = 0.037, and x = 0.07. The observed effects were attributed to critical phenomena accompanying the second-order phase transitions: percolation transition from dilute to concentrated solid solutions, the transition to a gapless state, and the semimetal-semiconductor transition, respectively. It was shown that the values of critical indexes (α = 0.11±0.01) are the same not only for different peaks but also for different temperatures and correspond to the values theoretically calculated within the framework of scale-invariant theory for three-dimensional (3D) models.
1. D.M.Rowe (ed.), Thermoelectrics Handbook: Macro to Nano, CRC Press, Taylor & Francis Group, Boca Raton (2005), p.1008.
2. C.Uher (ed.), Materials Aspect of Thermoelectricity, CRC Press, Boca Raton (2016), p.624.
3. M.Z.Hasan, C.L.Kane, Rev. Mod. Phys., 82, 3045 (2010). https://doi.org/10.1103/RevModPhys.82.3045
4. D.Culcer, Physica E, 44, 860 (2012). https://doi.org/10.1016/j.physe.2011.11.003
5. L.Muchler, F.Casper, B.Yan et al., Phys. Stat. Sol. RRL, 7, 91 (2013). https://doi.org/10.1002/pssr.201206411
6. Ya.A.Ugay, Ye.G.Goncharov, G.V.Semenova, V.B.Lazarev, Phase Equilibria between Phosphorus, Arsenic and Bismuth, Nauka, Moscow (1989) [in Russian].
7. N.B.Brandt, S.M.Chudinov, V.G.Karavaev, Zh. Eksp. Teor. Fiz., 70, 2296 (1976).
8. B.Lenoir, M.Cassart, J.-P.Michenaud, J. Phys. Chem. Solids., 57, 89 (1996). https://doi.org/10.1016/0022-3697(95)00148-4
9. E.I.Rogacheva, A.A.Yakovleva, V.I.Pinegin, M.S.Dresselhaus, J. Phys. Chem. Sol., 69, 580 (2008). https://doi.org/10.1016/j.jpcs.2007.07.042
10. E.I.Rogacheva, A.A.Drozdova, O.N.Nashchekina et al., Appl. Phys. Lett., 94, 202111 (2009). https://doi.org/10.1063/1.3139076
11. E.I.Rogacheva, A.A.Drozdova, O.N.Nashchekina, Phys. Stat. Sol. A, 207, 344 (2010). https://doi.org/10.1002/pssa.200925144
12. E.I.Rogacheva, A.N.Doroshenko, O.N.Nashchekina, Yu.V.Men'shov, J. Electron. Mater., 42, 2098 (2013). https://doi.org/10.1007/s11664-013-2534-y
13. E.I.Rogacheva, A.N.Doroshenko, V.I.Pinegin, M.S.Dresselhaus, J. Thermoelectricity, 6, 13 (2013).
14. E.I.Rogacheva, A.N.Doroshenko, O.N.Nashchekina, M.S.Dresselhaus, Appl. Phys. Lett., 109, 131906 (2016). https://doi.org/10.1063/1.4963880
15. C.T.Anderson, J. Am. Chem. Soc., 52, 2720 (1930). https://doi.org/10.1021/ja01370a019
16. H.L.Bronson, L.E.MacHattie, The Canadian J. Res., 16A, 177 (1938).
17. K.K.Kelley, U.S.Bureau of Mines Bulletin, 584 (1960).
18. P.Franzocini, K.Clusius, Zeitschr. Naturforsch. A, 18, 1243 (1963).
19. F.Gronvold, Acta Chem. Scandin., A29, 945 (1975).
20. W.A.Badawi, H.A.Brown-Acquaye, A.E.Eid, Bull. Chem. Soc. Jpn., 60, 3765 (1987). https://doi.org/10.1246/bcsj.60.3765
21. A.A.Vecher, A.G.Gusakov, A.A.Kozyro, P.A.Poleshchuk, J. Phys. Chem., 59, 2149 (1985).
22. A.A.Vecher, A.G.Gusakov, A.A.Kozyro, P.A.Poleshchuk, J. Phys. Chem., 55, 1609 (1981).
23. A.A.Vecher, P.A.Poleshchuk, A.A.Kozyro, A.G.Gusakov, Bull. Belarus State Univer., Ser., 2, 14, 3 (1982).
24. A.A.Vecher, P.A.Poleshchuk, A.A.Kozyro, A.G.Gusakov, J. Phys. Chem., 57, 871 (1983).
25. V.V.Prudnikov, A.N.Vakilov, P.V.Prudnikov, Phase Transitions and Methods Computer Modeling, Fizmatlit, Moscow (2009) [in Russian].
26. A.Z.Patashinskiy, V.L.Pokrovskiy, The Fluctuation Theory of Phase Transitions, Nauka, Moscow (1982) [in Russian].
27. S.K.Ma, Modern Theory of Critical Phenomena, Frontiers in Physics, v.46, Benjamin, London (1976).
28. H.E.Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York (1971).
29. H.E.Stanley, Rev. Mod. Phys., 71, S358 (1999).
30. M.E.Fisher, Scaling Universality and Renormalization Group Theory, in Critical Phenomena, Lecture Notes in Physics, v.186, Springer-Verlag (1983).
31. L.P.Kadanoff et al., Rev. Mod. Phys., 39, 395 (1967). https://doi.org/10.1103/RevModPhys.39.395
32. D.Stauffer, A.Aharony, Introduction to Percolation Theory, Taylor & Francis, Washington, DC (1992).
33. B.I.Shklovskii, A.L.Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, Heidelberg (1984), p.393.
34. A.G.Gamzatov et al., Low Temp. Phys., 35, 214 (2009). https://doi.org/10.1063/1.3081152
35. I.K.Kamilov, A.K.Murtazaev, Kh.K.Aliev, Physics-Uspekhi, 42, 689 (1999). https://doi.org/10.1070/PU1999v042n07ABEH000498
36. M.A.Anisimov, Critical Phenomena in Liquids and Liquid Crystals, Gordon and Breach Science Publishers, Philadelphia (1991).
37. E.I.Rogacheva, Jpn. J. Appl. Phys., 32, 775 (1993). https://doi.org/10.7567/JJAPS.32S3.775
38. E.I.Rogacheva, J. Thermoelectr., 2, 61 (2007).
39. E.I.Rogacheva, Izv. AN USSR. Neorgan. Mater., 25, 643 (1989).
40. E.I.Rogacheva, A.S.Sologubenko, I.M.Krivulkin, Inorgan. Mater., 34, 545 (1998).
41. E.I.Rogacheva, I.M.Krivulkin, V.P.Popov, T.A.Lobkovskaya, Phys. Stat. Sol. (a), 148, K65 (1995).
42. E.I.Rogacheva, E.V.Martynova, A.S.Bondarenko, J. Thermoelectricity, 5, 5 (2016)
.