Abstract
First principles calculations using the generalized gradient approximation to density functional theory have been carried out to evaluate formation energies of defects and the resultant changes in electronic structure of NaCoO2 and Na0.5CoO2. The calculated formation energies confirm that Na vacancies form readily in this material, particularly through volatilization at elevated temperatures, consistent with experimentally observed behavior. Numerical analysis of the change in charge distribution upon Na vacancy formation shows that the vacancy plays a crucial role in modifying the electronic properties of the material. In these p-type thermoelectric materials, Na vacancies act as a reservoir for the minority carrier (electrons), removing them from the CoO2 layer while simultaneously increasing the concentration of majority carriers (holes) available for conduction in the CoO2 layer.
Similar content being viewed by others
References
I. Terasaki, Y. Sasago, and K. Uchinokura, Phys. Rev. B 56, R12685 (1997).
K. Fujita, T. Mochida, and K. Nakamura, Jpn. J. Appl. Phys. 40, 4644 (2001).
M. Lee, L. Viciu, L. Li, Y. Wang, M.L. Foo, S. Watauchi, R.A. Pascal, R.J. Cava, and N.P. Ong, Nat. Mater. 5, 537 (2006).
D.J. Singh, Phys. Rev. B 61, 13397 (2000).
K.-W. Lee, J. Kuneš, and W.E. Pickett, Phys. Rev. B 70, 045014 (2004).
K.-W. Lee, J. Kuneš, P. Novak, and W.E. Pickett, Phys. Rev. Lett. 94, 026403 (2005).
P. Zhang, W. Luo, V.H. Crespi, M.L. Cohen, and S.G. Louie, Phys. Rev. B 70, 085108 (2004).
H. Okabe, M. Matoba, T. Kyomen, and M. Itoh, J. Appl. Phys. 95, 6831 (2004).
K.-W. Lee and W.E. Pickett, Phys. Rev. Lett. 96, 096403 (2006).
P. Zhang, R.B. Capaz, M.K. Cohen, and S.G. Louie, Phys. Rev. B 71, 153102 (2005).
Z. Li, J. Yang, J.G. Hou, and Q. Zhu, Phys. Rev. B 71, 024502 (2005).
Y.S. Meng, A. Van der Ven, M.K.Y. Chan, and G. Ceder, Phys. Rev. B 72, 172103 (2005).
Y.S. Meng, Y. Hinuma, and G. Ceder, J. Chem. Phys. 128, 104708 (2008).
Y. Hinuma, Y.S. Meng, and G. Ceder, Phys. Rev. B 77, 224111 (2008).
T. Motohashi, R. Ueda, T. Tojo, I. Terasaki, T. Atake, M. Karppinen, and H. Yamauhci, Phys. Rev. B 67, 064406 (2003).
S.P. Bayrakci, I. Mirebeau, P. Bourges, Y. Sidis, M. Enderle, J. Mesot, D.P. Chen, C.T. Lin, and B. Keimer, Phys. Rev. Lett. 94, 157205 (2005).
T.F. Schulze, P.S. Häflinger, Ch. Niedermayer, K. Mattenberger, S. Bubenhofer, and B. Batlogg, Phys. Rev. Lett. 100, 026407 (2008).
M. Weller, A. Sacchetti, H.R. Ott, K. Mattenberger, and B. Batlogg, Phys. Rev. Lett. 102, 056401 (2009).
D. Igarashi, Y. Miyazaki, and T. Kajitani, Phys. Rev. B 78, 184112 (2008).
M. Yokoi, T. Moyoshi, Y. Kobayashi, M. Soda, Y. Yasui, M. Sato, and K. Kakurai, J. Phys. Soc. Jpn. 74, 3046 (2005).
F.C. Chou, J.H. Hou, and Y.S. Lee, Phys. Rev. B 70, 144526 (2004).
J.L. Gavilano, D. Rau, B. Pedrini, K. Magishi, M. Weller, J. Hinderer, H.R. Ott, S.M. Kazakov, and J. Karpinski, Physica B 359–361, 1237 (2005).
Q. Huang, M.L. Hoo, J.W. Lynn, H.W. Zandbergen, G. Lawes, Y. Wang, B.H. Toby, A.P. Ramirez, N.P. Ong, and R.J. Cava, J. Phys.: Condens. Matter 16, 5803 (2004).
Y. Takahashi, Y. Gotoh, and J. Akimoto, J. Solid State Chem. 172, 22 (2003).
M. Tada, M. Yoshiya, T. Nagira, and H. Yasuda (in preparation)
V.I. Anisimov, J. Zaanen, and O.K. Andersen, Phys. Rev. B 44, 943 (1991).
I.V. Solovyev, P.H. Dederichs, and V.I. Anisimov, Phys. Rev. B 50, 16861 (1994).
A.I. Liechtenstein, V.I. Anisimov, and J. Zaanen, Phys. Rev. B 52, R5467 (1995).
S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, and A.P. Sutton, Phys. Rev. B 57, 1505 (1998).
S.B. Zhang and J.E. Northrup, Phys. Rev. Lett. 67, 2339 (1991).
C.G. Van de Walle and R.M. Martin, Phys. Rev. B 35, 8154 (1987).
S. Pöykkö, M.J. Puska, and R.M. Nieminen, Phys. Rev. B 53, 3813 (1996).
T. Mattila and A. Zunger, Phys. Rev. B 58, 1367 (1998).
P.E. Blöchl, Phys. Rev. B 50, 17953 (1994).
G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994).
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
J.P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997).
H.J. Monkhorst and J.D. Pack, Phys. Rev. B 13, 5188 (1976).
C. Fouassier, G. Matejka, J.-M. Reau, and P. Hagenmuller, J. Solid State Chem. 6, 532 (1973).
V.M. Jansen and R. Hoppe, Z. Anorg. Allg. Chem. 408, 104 (1974).
Y. Wang and J. Ni, Phys. Rev. B 76, 094101 (2007).
Q. Huang, M.L. Foo, R.A. Pascal Jr., J.W. Lynn, B.H. Toby, T. He, H.W. Zandbergen, and R.J. Cava, Phys. Rev. B 70, 184110 (2004).
A.J. Williams, J.P. Attfield, M.L. Foo, L. Viciu, and R.J. Cava, Phys. Rev. B 73, 134401 (2006).
M. Onoda and T. Ikeda, J. Phys.: Condens. Matter 19, 18623 (2007).
N.L. Wang, D. Wu, G. Li, X.H. Chen, C.H. Wang, and X.G. Lou, Phys. Rev. Lett. 93, 147403 (2004).
M.L. Foo, Y. Wang, S. Watauchi, H.W. Zandbergen, T. He, R.J. Cava, and N.P. Ong, Phys. Rev. Lett. 92, 247001 (2004).
K. Takada, H. Sakurai, E. Takayama-Muromachi, F. Izumi, R.A. Dilanian, and T. Sasaki, Nature 422, 53 (2003).
D.R. Stull and H. Prophet, 44 Thermochemical Tables, 2nd ed. (Washington, DC: U.S. National Bureau of Standards, 1971).
C. Delmas, J.-J. Braconnier, C. Fouassier, and P. Hagenmuller, Solid State Ionics 3–4, 165 (1981).
F.C. Chou, E.T. Abel, J.H. Cho, and Y.S. Lee, J. Phys. Chem. Solids 66, 155 (2005).
J. Molenda, C. Delmas, P. Dordor, and A. Stokłosa, Solid State Ionics 12, 473 (1989).
M. Roger, D.J.P. Morris, D.A. Tennant, M.J. Gutmann, J.P. Goff, J.-U. Hoffmann, R. Feyerherm, E. Dudzik, D. Prabhakaran, A.T. Boothoroyd, N. Shannon, B. Lake, and P.P. Deen, Nature 445, 631 (2007).
C.B. Alcock, V.P. Itkin, and M.K. Horrigan, Can. Metall. Q. 23, 309 (1984).
G.J. Shu and F.C. Chou, Phys. Rev. B 78, 052101 (2008).
Acknowledgements
This work was in part supported by a Grant- in-Aid for Scientific Research by the Ministry of Education, Science, Sports and Culture. The authors thank Dr T. Nagira for helpful discussions.
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s11664-011-1628-7
Rights and permissions
About this article
Cite this article
Yoshiya, M., Okabayashi, T., Tada, M. et al. A First-Principles Study of the Role of Na Vacancies in the Thermoelectricity of Na x CoO2 . J. Electron. Mater. 39, 1681–1686 (2010). https://doi.org/10.1007/s11664-010-1237-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11664-010-1237-x