Journal of Materials Science

, Volume 54, Issue 8, pp 6347–6360 | Cite as

Influence of internal displacement on band structure, phase transition, and thermoelectric properties of bismuth

  • C. Y. Wu
  • L. Sun
  • H. R. GongEmail author
  • S. F. ZhouEmail author
Electronic materials


First principles calculation and Boltzmann transport theory have been combined to investigate the fundamental influence of internal displacement (u) on lattice stability, band structure, phase transition, and thermoelectric properties of Bi. Calculation reveals that Bi could keep its ground-state rhombohedral structure and mechanical stability within the entire studied range of u (0.2150 ≤ u ≤ 0.2500). It is also shown that the phase transitions of semimetal–semiconductor, semiconductor–semimetal, and semimetal–metal of Bi can happen at the critical u points of 0.2184, 0.2325, and 0.2400, respectively, which are mainly ascribed to the changes of the symmetry points of T, Γ, and L with the increase of u. In addition, the highest Seebeck coefficient of Bi could be achieved when u equals 0.2250 due to the lowest carrier density and is much bigger than the corresponding value of equilibrium Bi (u = 0.2357). The obtained results are in good agreement with experimental observations in the literature and could deepen the understanding of the fundamental relationship between internal displacement, band structure, phase transition, and Seebeck coefficient of Bi.



This work was supported by State Key Laboratory of Powder Metallurgy, Central South University, Changsha, China.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Golin S (1968) Band structure of bismuth: pseudopotential approach. Phys Rev 166(3):643–651. CrossRefGoogle Scholar
  2. 2.
    Liu Y, Allen RE (1995) Electronic structure of the semimetals Bi and Sb. Phys Rev B 52(3):1566–1577. CrossRefGoogle Scholar
  3. 3.
    Xu JH, Wang EG, Ting CS, Su WP (1993) Tight-binding theory of the electronic structures for rhombohedral semimetals. Phys Rev B 48(23):17271–17279. CrossRefGoogle Scholar
  4. 4.
    Fuseya Y, Ogata M, Fukuyama H (2015) Transport properties and diamagnetism of dirac electrons in bismuth. J Phys Soc Jpn 84(1):012001. CrossRefGoogle Scholar
  5. 5.
    Seebeck TJ (1826) Ueber die magnetische polarisation der Metalle und Erze durch Temperaturdifferenz. Ann Phys 82(3):253–286. CrossRefGoogle Scholar
  6. 6.
    Gallo CF, Chandrasekhar BS, Sutter PH (1963) Transport properties of bismuth single crystals. J Appl Phys 34(1):144–152. CrossRefGoogle Scholar
  7. 7.
    Chandrasekhar BS (1959) The seebeck coefficient of bismuth single crystals. J Phys Chem Solids 11:268–273CrossRefGoogle Scholar
  8. 8.
    Issi JP, Michenaud JP, Heremans J (1976) Electron scattering in compensated bismuth. Phys Rev B 14(12):5156–5160. CrossRefGoogle Scholar
  9. 9.
    Issi JP (2006) Thermoelectric properties of the group V semimetals. In: Thermoelectrics handbook: macro to nano-structured materials, vol 7. Taylor and Francis, Boca Raton, p 30Google Scholar
  10. 10.
    Xia F, Xiong S, He Y, Shao Z, Zhang X, Jie J (2017) Tuning the electronic and optical properties of monolayers As, Sb, and Bi via surface charge transfer doping. J Phys Chem C 121(35):19530–19537. CrossRefGoogle Scholar
  11. 11.
    Ersan F, Aktürk E, Ciraci S (2016) Stable single-layer structure of group-V elements. Phys Rev B 94(24):245417. CrossRefGoogle Scholar
  12. 12.
    Yang LM, Yang H, Chen QY, Li ZY, Cao C, He Y (2017) Strain and electric field tunable electronic structure of buckled bismuthene. RSC Adv 7(63):39546–39555. CrossRefGoogle Scholar
  13. 13.
    Zhang DC, Zhang AX, Guo SD, Duan YF (2017) Thermoelectric properties of β-As, Sb and Bi monolayers. RSC Adv 7(39):24537–24546. CrossRefGoogle Scholar
  14. 14.
    Cucka B, Barrett CS (1962) The crystal structure of Bi and of solid solutions of Pb, Sn, Sb and Te in Bi. Acta Cryst 15:865–872CrossRefGoogle Scholar
  15. 15.
    Zouhar M, Šob M (2016) Ab initio study of deformed As, Sb, and Bi with an application to thin films. Phys Rev B 94:184110. CrossRefGoogle Scholar
  16. 16.
    Gonze X, Michenaud JP, Vigneron JP (1990) First-principles study of As, Sb, and Bi electronic properties. Phys Rev B 41(17):11827–11836. CrossRefGoogle Scholar
  17. 17.
    Falicov LM, Golin S (1965) Electronic band structure of arsenic. I. Pseudopotential approach. Phys Rev 137(3A):A871–A882. CrossRefGoogle Scholar
  18. 18.
    Chang KJ, Cohen ML (1986) Rhombohedral phase stability of the group-VA elements. Phys Rev B 33(10):7371–7374. CrossRefGoogle Scholar
  19. 19.
    Shick AB, Ketterson JB, Novikov DL, Freeman AJ (1999) Electronic structure, phase stability, and semimetal-semiconductor transitions in Bi. Phys Rev B 60(23):15484–15487CrossRefGoogle Scholar
  20. 20.
    Wu CY, Han JC, Sun L, Gong HR, Liang CP (2018) Effects of trigonal deformation on electronic structure and thermoelectric properties of bismuth. J Phys Condens Matter Inst Phys J 30(28):285504. CrossRefGoogle Scholar
  21. 21.
    Giardini AA, Samara GA (1965) the compressibility of bismuth and itsupper transition pressure. J Phys Chem Solids 26:1523–1528CrossRefGoogle Scholar
  22. 22.
    Haussermann U, Soderberg K, Norrestam R (2002) Comparative study of the high pressure behavior of As, Sb, and Bi. J Am Chem Soc 124:15359–15367CrossRefGoogle Scholar
  23. 23.
    Brugger RM, Bennion RB, Worlton TG (1967) The crystal structure of bismuth—II at 26 kBar. Phys Lett 24:714–717CrossRefGoogle Scholar
  24. 24.
    Bundy FP (1958) Phase diagram of bismuth to 130000 kg/cm2, 500 °C. Phys Rev 110:314–318CrossRefGoogle Scholar
  25. 25.
    Klement W, Jayaraman A, Kennedy GC (1963) Phase diagrams of arsenic, antimony, and bismuth at pressures up to 70 kbars. Phys Rev 131(2):632–637. CrossRefGoogle Scholar
  26. 26.
    Aguilera I, Friedrich C, Blügel S (2015) Electronic phase transitions of bismuth under strain from relativistic self-consistent GW calculations. Phys Rev B 91(12):125129. CrossRefGoogle Scholar
  27. 27.
    Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54(16):11169–11186CrossRefGoogle Scholar
  28. 28.
    Kresse G, Furthmüller J (1996) Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 6(1):15–50. CrossRefGoogle Scholar
  29. 29.
    Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59(3):1758–1775CrossRefGoogle Scholar
  30. 30.
    Beister HJ, Strossner K, Syassen K (1990) Rhombohedral to simple-cubic phase transition in arsenic under pressure. Phys Rev B 41(9):5535–5540. CrossRefGoogle Scholar
  31. 31.
    Morosin B, Schirber JE (1969) Change in atomic positions for Sb and Bi with hydrostatic pressure. Phys Lett 30:512–513CrossRefGoogle Scholar
  32. 32.
    Madsen GKH, Singh DJ (2006) BoltzTraP. A code for calculating band-structure dependent quantities. Comput Phys Commun 175(1):67–71. CrossRefGoogle Scholar
  33. 33.
    Parker D, Singh DJ (2011) Potential thermoelectric performance from optimization of hole-doped Bi2Se3. Phys Rev X 1(2):021005. Google Scholar
  34. 34.
    Xi L, Zhang YB, Shi XY, Yang J, Shi X, Chen LD, Zhang W, Yang J, Singh DJ (2012) Chemical bonding, conductive network, and thermoelectric performance of the ternary semiconductors Cu2SnX3 (X = Se, S) from first principles. Phys Rev B 86(15):155201. CrossRefGoogle Scholar
  35. 35.
    Ong KP, Singh DJ, Wu P (2011) Analysis of the thermoelectric properties of n-type ZnO. Phys Rev B 83(11):115110. CrossRefGoogle Scholar
  36. 36.
    Liang CP, Gong HR (2010) Phase stability, mechanical property, and electronic structure of Mg–Li system. J Alloy Compd 489(1):130–135. CrossRefGoogle Scholar
  37. 37.
    Liang CP, Gong HR (2010) Structural stability, mechanical property and phase transition of the Ti–H system. Int J Hydrog Energy 35(20):11378–11386. CrossRefGoogle Scholar
  38. 38.
    Yu R, Zhu J, Ye HQ (2010) Calculations of single-crystal elastic constants made simple. Comput Phys Commun 181:671–675CrossRefGoogle Scholar
  39. 39.
    Ma SY, Liu LM, Wang SQ (2014) The microstructure, stability, and elastic properties of 14H long-period stacking-ordered phase in MgZnY alloys: a first-principles study. J Mater Sci 49:737–748. CrossRefGoogle Scholar
  40. 40.
    Colmenero F, Bonales LJ, Cobos J, Timon V (2017) Structural, mechanical and vibrational study of uranyl silicate mineral soddyite by DFT calculations. J Solid State Chem 253:249–257CrossRefGoogle Scholar
  41. 41.
    Norin B (1977) Temperature and pressure dependence of the band structure in bismuth. Phys Scr 15:341–348CrossRefGoogle Scholar
  42. 42.
    Issi JP (1979) Low temperature transport properties of the group V semimetals. Aust J Phys 32(6):585–628. CrossRefGoogle Scholar
  43. 43.
    Armitage NP, Tediosi R, Lévy F, Giannini E, Forro L, Marel DVd (2010) An avoided Lifhitz-type semimetal–semiconductor transition: infrared conductivity of elemental bismuth under pressure. Phys Rev Lett 104:237401CrossRefGoogle Scholar
  44. 44.
    Vaišnys JR, Kirk RS (1967) Effect of pressure on the electrical properties of bismuth. J Appl Phys 38(11):4335–4337. CrossRefGoogle Scholar
  45. 45.
    Snyder GJ, Toberer ES (2008) Complex thermoelectric materials. Nat Mater 5:105–114CrossRefGoogle Scholar
  46. 46.
    Gibbs ZM, Ricci F, Li G, Zhu H, Persson K, Ceder G, Hautier G, Jain A, Snyder GJ (2017) Effective mass and Fermi surface complexity factor from ab initio band structure calculations. NPJ Comput Mater 3(1):41524. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Powder MetallurgyCentral South UniversityChangshaChina
  2. 2.Department of Educational ScienceHunan First Normal UniversityChangshaChina
  3. 3.Laser Technology InstituteTianjin Polytechnic UniversityTianjinChina

Personalised recommendations