Rare Metals

, Volume 37, Issue 4, pp 316–325 | Cite as

Theoretical investigations of electrical transport properties in CoSb3 skutterudites under hydrostatic loadings

  • Chongze Hu
  • Peter Ni
  • Li Zhan
  • Huijuan Zhao
  • Jian He
  • Terry M. Tritt
  • Jingsong Huang
  • Bobby G. Sumpter


CoSb3-based skutterudites have been a benchmark mid-temperature thermoelectric material under intensive experimental and theoretical studies for decades. Doping and filling, to the first order, alter the crystal lattice constant of CoSb3 in the context of “chemical pressure.” In this work, we employed ab initio density functional theory in conjunction with semiclassical Boltzmann transport theory to investigate the mechanical properties and especially how hydrostatic loadings, i.e., “physical pressure,” impact the electronic band structure, Seebeck coefficient, and power factor of pristine CoSb3. It is found that hydrostatic pressure enlarges the band gap, suppresses the density of states (DOS) near the valence band edge, and fosters the band convergence between the valley bands and the conduction band minimum (CBM). By contrast, hydrostatic tensile reduces the band gap, increases the DOS near the valence band edge, and diminishes the valley bands near the CBM. Therefore, applying hydrostatic pressure provides an alternative avenue for achieving band convergence to improve thermoelectric properties of N-type CoSb3, which is further supported by our carrier concentration studies. These results provide valuable insight into the further improvement of thermoelectric performance of CoSb3-based skutterudites via a synergy of physical and chemical pressures.


CoSb3 skutterudite Hydrostatic loadings Mechanical properties Electronic structure Seebeck coefficient Thermoelectrics 



This research was conducted at the Center for Nanophase Materials Sciences, which is a US Department of Energy Office of Science User Facility, and used resources of the National Energy Research Scientific Computing Center, which are supported by the Office of Science of the US Department of Energy (Nos. DE-AC05-00OR22750 and DE-AC02-05-CH11231). Chongze Hu and Jian He would like to acknowledge the support of National Science Foundation (No. DMR-1307740).

Supplementary material

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Supplementary material 1 (DOCX 1483 kb)


  1. [1]
    Snyder GJ, Toberer ES. Complex thermoelectric materials. Nat Mater. 2008;7(2):105.CrossRefGoogle Scholar
  2. [2]
    Nolas GS, Morelli DT, Tritt TM. Skutterudites: a phonon-glass-electron crystal approach to advanced thermoelectric energy conversion applications. Ann Rev Mat Sci. 1999;29(1):89.CrossRefGoogle Scholar
  3. [3]
    Slack GA. CRC Handbook of Thermoelectric: New Materials and Performance Limits for Thermoelectric Cooling. Florida: CRC Press; 1995. 407.Google Scholar
  4. [4]
    Uher C. Skutterudites: prospective novel thermoelectrics. Semicond Semimet. 2001;69:139.CrossRefGoogle Scholar
  5. [5]
    Hu CZ, Zeng XY, Liu YF, Zhou MH, Zhao HJ, Tritt TM, He J, Jakowski J, Kent PRC, Huang JS, Sumpter BG. Effects of partial La filling and Sb vacancy defects on CoSb3 skutterudites. Phys Rev B. 2017;95(16):165204.CrossRefGoogle Scholar
  6. [6]
    Mei ZG, Yang J, Pei YZ, Zhan W, Chen LD. Alkali-metal-filled CoSb3 skutterudites as thermoelectric materials: theoretical study. Phys Rev B. 2008;77(4):045202.CrossRefGoogle Scholar
  7. [7]
    Graff WJ, Zeng XY, Dehkordi AM, He J, Tritt TM. Exceeding the filling fraction limit in CoSb3 skutterudite: multi-role chemistry of praseodymium leading to promising thermoelectric performance. J Mater Chem A. 2014;2(23):8933.CrossRefGoogle Scholar
  8. [8]
    Katsuyama S, Shichijo Y, Ito M, Majima K, Nagai H. Thermoelectric properties of the skutterudite Co1-xFexSb3 system. J Appl Phys. 1998;84(12):6708.CrossRefGoogle Scholar
  9. [9]
    Sharp JW, Jones EC, Williams RK, Martin PM, Sales BC. Thermoelectric properties of CoSb3 and related alloys. J Appl Phys. 1995;78(2):1013.CrossRefGoogle Scholar
  10. [10]
    Sales BC, Mandrus D, Williams RK. Filler skutterudite antimonides: a new class of thermoelectric materials. Science. 1996;272(5266):1325.CrossRefGoogle Scholar
  11. [11]
    Morelli DT, Meisner GP, Chen BX, Hu SQ, Uher C. Cerium filling and doping of cobalt triantimonide. Phys Rev B. 1997;56(12):7376.CrossRefGoogle Scholar
  12. [12]
    Lamberton GA Jr, Tedstrom RH, Tritt TM, Nolas GS. Thermoelectric properties of Yb-filled Ge-compensated CoSb3 skutterudite materials. J Appl Phys. 2005;97(11):113715.CrossRefGoogle Scholar
  13. [13]
    Singh DJ, Du MH. Properties of alkaline-earth-filled skutterudite antimonides: A(Fe, Ni)4Sb12 (A = Ca, Sr, and Ba). Phys Rev B. 2010;82(7):075115.CrossRefGoogle Scholar
  14. [14]
    Ovsyannikov SV, Shchennikov VV. High-pressure routes in the thermoelectricity or how one can improve a performance of thermoelectrics. Chem Mater. 2010;22(3):635.CrossRefGoogle Scholar
  15. [15]
    Munir ZA, Anselmi-Tamburini U, Ohyanagi M. The effect of electric field and pressure on the synthesis and consolidation of materials: a review of the spark plasma sintering method. J Mater Sci. 2006;41(3):763.CrossRefGoogle Scholar
  16. [16]
    Li GD, An Q, Li WJ, Goddard WA III, Zhai P, Zhang QJ, Snyder GJ. Brittle failure mechanism in thermoelectric skutterudite CoSb3. Chem Mater. 2015;27(18):6329.CrossRefGoogle Scholar
  17. [17]
    Rogl G, Rogl P. Mechanical properties of skutterudites. Sci Adv Mater. 2011;3(4):517.CrossRefGoogle Scholar
  18. [18]
    Ruan ZW, Liu LS, Zhai PC, Wen PF, Zhang QJ. Low-cycle fatigue properties of CoSb3-based skutterudite compounds. J Electron Mater. 2010;39(9):2029.CrossRefGoogle Scholar
  19. [19]
    Schmidt RD, Case ED, Ni JE, Sakamoto JS, Trejo RM, Lara-curzio E. The temperature dependence of thermal expansion for p-type Ce0.9Fe3.5Co0.5Sb12 and n-type Co0.95Pd0.05Te0.05Sb3 skutterudite thermoelectric materials. Philos Mag. 2012;92(10):1261.CrossRefGoogle Scholar
  20. [20]
    Yang XQ, Zhai PC, Liu LS, Zhang QJ. Thermodynamic and mechanical properties of crystalline CoSb3: a molecular dynamics simulation study. J Appl Phys. 2011;109(12):123517.CrossRefGoogle Scholar
  21. [21]
    Takizawa H, Miura K, Ito M, Suzuki T, Endo T. Atom insertion into the CoSb3 skutterudite host lattice under high pressure. J Alloys Compd. 1999;282(1):79.CrossRefGoogle Scholar
  22. [22]
    Kraemer AC, Perottoni CA, Da Jornada JAH. Isothermal equation of state for the skutterudites CoSb3 and LaFe3CoSb12. Solid State Commun. 2005;133(3):173.CrossRefGoogle Scholar
  23. [23]
    Jacobsen MK, Liu W, Li B. Enhancement of thermoelectric performance with pressure in Ce0.8Fe3CoSb12.1. J Phys Chem Solids. 2014;75(9):1017.CrossRefGoogle Scholar
  24. [24]
    Kresse G, Hafner J. Ab initio molecular dynamics for liquid metals. Phys Rev B. 1993;47(1):558.CrossRefGoogle Scholar
  25. [25]
    Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B. 1996;54(16):11169.CrossRefGoogle Scholar
  26. [26]
    Blöchl PE. Projector augmented-wave method. Phys Rev B. 1994;50(24):17953.CrossRefGoogle Scholar
  27. [27]
    Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B. 1999;59(3):1758.CrossRefGoogle Scholar
  28. [28]
    Klimeš J, Bowler DR, Michaelides A. Chemical accuracy for the van der Waals density functional. J Phys Condens Matt. 2010;22(2):0953.Google Scholar
  29. [29]
    Tian YH, Huang JS, Sheng XL, Sumpter BG, Yoon M, Kertesz M. Nitrogen doping enables covalent-like π–π bonding between graphenes. Nano Lett. 2015;15(8):5482.CrossRefGoogle Scholar
  30. [30]
    Lebegue S, Harl J, Gould T, Angyan JG, Kresse G, Dobson JF. Cohesive properties and asymptotics of the dispersion interaction in graphite by the random phase approximation. Phys Rev Lett. 2010;105(19):196401.CrossRefGoogle Scholar
  31. [31]
    Zhou J, Huang JS, Sumpter BG, Kent PRC, Terrones H, Smith SC. Structures, energetics, and electronic properties of layered materials and nanotubes of cadmium chalcogenides. J Phys Chem C. 2013;117(48):25817.CrossRefGoogle Scholar
  32. [32]
    Bučko T, Lebegue S, Hafner J, Ángyán JG. Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids. Phy Rev B. 2013;87(6):064110.CrossRefGoogle Scholar
  33. [33]
    Page YL, Saxe P. Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress. Phy Rev B. 2002;65(10):104104.CrossRefGoogle Scholar
  34. [34]
    Perdew JP, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett. 1996;77(18):3865.CrossRefGoogle Scholar
  35. [35]
    Heyd J, Scuseria GE, Ernzerhof M. Hybrid functionals based on a screened coulomb potential. J Chem Phys. 2003;118(18):8207.CrossRefGoogle Scholar
  36. [36]
    Mostofi AA, Yates JR, Lee YS, Souza I, Vanderbilt D, Marzari N. Wannier90: a tool for obtaining maximally-localised Wannier functions. Comput Phys Commun. 2008;178(9):685.CrossRefGoogle Scholar
  37. [37]
    Singh DJ, Pickett WE. Skutterudite antimonides: quasilinear bands and unusual transport. Phys Rev B. 1994;50(15):11235.CrossRefGoogle Scholar
  38. [38]
    Ram S, Kanchana V, Valsakumar MC. Skutterudites under pressure: an ab initio study. J Appl Phys. 2014;115(9):093903.CrossRefGoogle Scholar
  39. [39]
    Pizzi G, Volja D, Kozinsky B, Fornari M, Marzari N. BoltzWann: a code for the evaluation of thermoelectric and electronic transport properties with a maximally-localized Wannier functions basis. Comput Phys Commun. 2014;185(1):422.CrossRefGoogle Scholar
  40. [40]
    Hill R. The elastic behaviour of a crystalline aggregate. Proc Phys Soc A. 1952;65(5):349.CrossRefGoogle Scholar
  41. [41]
    Hu CZ, Huang JS, Sumpter BG, Meletis E, Dumitrica T. Ab initio prediction of hexagonal Zr(B,C,N) polymorphs for coherent interface design. J Phys Chem C. 2017;121(46):26007.CrossRefGoogle Scholar
  42. [42]
    Reuss A. Calculation of the flow limits of mixed crystals on the basis of plasticity of the monocrystals. Angew Math Mech. 1929;9(1):49.CrossRefGoogle Scholar
  43. [43]
    Rotter M, Rogl P, Grytsiv A, Wolf W, Krisch M, Mirone A. Lattice dynamics of skutterudites: inelastic X-ray scattering on CoSb3. Phys Rev B. 2008;77(14):144301.CrossRefGoogle Scholar
  44. [44]
    Guo RQ, Wang XJ, Huang BL. Thermal conductivity of skutterudite CoSb3 from first principles: substitution and nanoengineering effects. Sci Rep. 2015;5:7806.CrossRefGoogle Scholar
  45. [45]
    Rasander M, Moram MA. On the accuracy of commonly used density functional approximations in determining the elastic constants of insulators and semiconductors. J Chem Phys. 2015;143(14):144104.CrossRefGoogle Scholar
  46. [46]
    Keppens V, Mandrus D, Sales BC, Chakoumakos BC, Dai P, Coldea R, Maple MB, Gajewski DA, Freeman EJ, Bennington S. Localized vibrational modes in metallic solids. Nature. 1998;395(6705):876.CrossRefGoogle Scholar
  47. [47]
    Möchel A, Sergueev I, Nguyen N, Long GJ, Grandjean F, Johnson DC, Hermann RP. Lattice dynamics in the FeSb3 skutterudite. Phys Rev B. 2011;84(6):064302.CrossRefGoogle Scholar
  48. [48]
    Ravi V, Firdosy S, Caillat T, Lerch B, Calamino A, Pawlik R, Nathal M, Sechrist A, Buchhalter J, Nutt S. Mechanical properties of thermoelectric skutterudites. AIP Conf Proc. 2008;969:656.CrossRefGoogle Scholar
  49. [49]
    Tang Y, Gibbs ZM, Agapito LA, Li GD, Kim HS, Nardelli MB, Curtarolo S, Snyder GJ. Convergence of multi-valley bands as the electronic origin of high thermoelectric performance in CoSb3 skutterudites. Nat Mater. 2015;14(12):1223.CrossRefGoogle Scholar
  50. [50]
    Pei YZ, Shi XY, LaLonde A, Wang H, Chen LD, Snyder GJ. Convergence of electronic bands for high performance bulk thermoelectrics. Nature. 2011;473(7345):66.CrossRefGoogle Scholar
  51. [51]
    Matsubara K, Iyanaga T, Tsubouchi T, Kishimoto K, Koyanagi K. Thermoelectric properties of (Pd, Co)Sb3 compounds with skutterudite structure. AIP Conf Proc. 1994;316(1):226.CrossRefGoogle Scholar
  52. [52]
    Mandrus D, Migliori A, Darling TW, Hundley MF, Peterson EJ, Thompson JD. Electronic transport in lightly doped CoSb3. Phys Rev B. 1995;52(7):4926.CrossRefGoogle Scholar
  53. [53]
    Goldsmid HJ, Sharp JW. Estimation of the thermal band gap of a semiconductor from seebeck measurements. J Electron Mater. 1999;28(7):869.CrossRefGoogle Scholar

Copyright information

© The Nonferrous Metals Society of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA
  2. 2.Department of Mechanical EngineeringUniversity of Minnesota-Twin CitiesMinneapolisUSA
  3. 3.Montgomery High SchoolSkillmanUSA
  4. 4.Department of Physics and AstronomyClemson UniversityClemsonUSA
  5. 5.Center for Nanophase Materials Sciences and Computational Sciences and Engineering DivisionOak Ridge National LaboratoryOak RidgeUSA

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