The thermodynamic and kinetic properties of mono- and di-vacancy defects in cubic (para-electric) barium titanate are studied by means of density-functional theory calculations. It is determined which vacancy types prevail for given thermodynamic boundary conditions. The calculations confirm the established picture that vacancies occur in their nominal charge states almost over the entire band gap. For the dominating range of the band gap the di-vacancy binding energies are constant and negative. The system, therefore, strives to achieve a state in which, under metal-rich (oxygen-rich) conditions, all metal (oxygen) vacancies are bound in di-vacancy clusters. The migration barriers are calculated for mono-vacancies in different charge states. As oxygen vacancies are found to readily migrate at typical growth temperatures, di-vacancies can be formed at ease. The key results of the present study with respect to the thermodynamic behavior of mono- and di-vacancies influence the initial defect distribution in the ferroelectric phases and therefore the conditions for aging.
REFERENCES
1.
R. E.
Cohen
, Nature (London)
358
, 136
(1992
).2.
W.
Zhong
, D.
Vanderbilt
, R. D.
King-Smith
, and K.
Rabe
, Ferroelectrics
164
, 291
(1995
).3.
P.
Ghosez
, X.
Gonze
, and J. P.
Michenaud
, Ferroelectrics
194
, 39
(1997
).4.
S.
Tinte
, M.
Stachiotti
, M.
Sepliarsky
, R.
Migoni
, and C.
Rodriguez
, Ferroelectrics
237
, 41
(2000
).5.
D. M.
Smyth
, The Defect Chemistry of Metal Oxides
(Oxford University Press
, New York
, 2000
), Chap. 14.6.
M.
Fukunaga
, G.
Li
, Y.
Uesu
, and K.
Kohn
, Ferroelectrics
286
, 79
(2003
).7.
A.
Tombak
, J. P.
Maria
, F.
Ayguavives
, Z.
Jin
, G. T.
Stauf
, A. I.
Kingon
, and A.
Mortazawi
, IEEE Microw. Wirel. Compon. Lett.
12
, 3
(2002
).8.
9.
N. G.
Eror
and D. M.
Smyth
, J. Solid State Chem.
24
, 235
(1978
).10.
N. H.
Chan
, R. K.
Sharma
, and D. M.
Smyth
, J. Am. Ceram. Soc.
64
, 556
(1981
).11.
N. H.
Chan
, R. K.
Sharma
, and D. M.
Smyth
, J. Am. Ceram. Soc.
65
, 167
(1982
).12.
13.
C. -R.
Song
and H. -I.
Yoo
, Solid State Ionics
120
, 141
(1999
).14.
C. -R.
Song
and H. -I.
Yoo
, Phys. Rev. B
61
, 3975
(2000
).15.
16.
17.
W. L.
Warren
, D.
Dimos
, B. A.
Tuttle
, G. E.
Pike
, R. W.
Schwartz
, and D. C.
McIntyre
, J. Appl. Phys.
77
, 6695
(1995
).18.
L.
He
and D.
Vanderbilt
, Phys. Rev. B
68
, 134103
(2003
).19.
W.
Li
, J.
Ma
, K.
Chen
, D.
Su
, and J. S.
Zhu
, Europhys. Lett.
72
, 131
(2005
).20.
W. L.
Warren
, K.
Vanheusden
, D.
Dimos
, G. E.
Pike
, and B. A.
Tuttle
, J. Am. Ceram. Soc.
79
, 536
(1996
).21.
D. J.
Keeble
, B.
Nielsen
, A.
Krishnan
, K. G.
Lynn
, S.
Madhukar
, R.
Ramesh
, and C. F.
Young
, Appl. Phys. Lett.
73
, 318
(1998
).22.
S.
Zafar
, R. E.
Jones
, B.
Jiang
, B.
White
, P.
Chu
, D.
Taylor
, and S.
Gillespie
, Appl. Phys. Lett.
73
, 175
(1998
).23.
C. H.
Park
and D. J.
Chadi
, Phys. Rev. B
57
, R13961
(1998
).24.
S.
Pöykkö
and D. J.
Chadi
, Phys. Rev. Lett.
83
, 1231
(1999
).25.
S.
Pöykkö
and D. J.
Chadi
, Appl. Phys. Lett.
75
, 2830
(1999
).26.
S.
Pöykkö
and D. J.
Chadi
, J. Phys. Chem. Solids
61
, 291
(2000
).27.
S.
Pöykkö
and D. J.
Chadi
, Appl. Phys. Lett.
76
, 499
(2000
).28.
29.
C.
Duque
and A.
Stashans
, Physica B
336
, 227
(2003
).30.
E.
Cockayne
and B. P.
Burton
, Phys. Rev. B
69
, 144116
(2004
).31.
A.
Shigemi
and T.
Wada
, Jpn. J. Appl. Phys., Part 1
43
, 6793
(2004
).32.
A.
Shigemi
and T.
Wada
, Jpn. J. Appl. Phys., Part 1
44
, 8048
(2005
).33.
A. R.
Allnatt
and A. B.
Lidiard
, Atomic Transport in Solids
(Cambridge University Press
, Cambridge
, 2003
).34.
M.
Uludogan
, T.
Çagin
, and W. A.
Goddard
III, in Perovskite Materials
, edited by A.
Navrotsky
, K. R.
Poeppelmeier
, and R. M.
Wentzcovitch
(Materials Research Society
, Pittsburgh
, 2002
), Vol. 718
, p. D10
–1
.35.
36.
S.
Saha
, T. P.
Sinha
, and A.
Mookerjee
, Phys. Rev. B
62
, 8828
(2000
).37.
J. H.
Rose
, J. R.
Smith
, F.
Guinea
, and J.
Ferrante
, Phys. Rev. B
29
, 2963
(1984
).38.
S. H.
Wemple
, Phys. Rev. B
2
, 2679
(1970
).39.
G.
Kresse
and J.
Hafner
, Phys. Rev. B
47
, 558
(1993
).40.
G.
Kresse
and J.
Hafner
, Phys. Rev. B
49
, 14251
(1994
).41.
G.
Kresse
and J.
Furthmüller
, Phys. Rev. B
54
, 11169
(1996
).42.
G.
Kresse
and J.
Furthmüller
, Comput. Mater. Sci.
6
, 15
(1996
).43.
P. E.
Blöchl
, Phys. Rev. B
50
, 17953
(1994
).44.
G.
Kresse
and D.
Joubert
, Phys. Rev. B
59
, 1758
(1999
).45.
D. M.
Ceperley
and B. J.
Alder
, Phys. Rev. Lett.
45
, 566
(1980
).46.
J. P.
Perdew
and A.
Zunger
, Phys. Rev. B
23
, 5048
(1981
).47.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
78
, 1396
(E) (1997
).48.
P.
Ghosez
, X.
Gonze
, and J. P.
Michenaud
, Ferroelectrics
220
, 1
(1999
).49.
Z.
Wu
, R. E.
Cohen
, and D. J.
Singh
, Phys. Rev. B
70
, 104112
(2004
).50.
G. -X.
Qian
, R. M.
Martin
, and D. J.
Chadi
, Phys. Rev. B
38
, 7649
(1988
).51.
S. B.
Zhang
, S. -H.
Wei
, and A.
Zunger
, J. Appl. Phys.
83
, 3192
(1998
a).52.
S. B.
Zhang
, S. -H.
Wei
, A.
Zunger
, and H.
Katayama-Yoshida
, Phys. Rev. B
57
, 9642
(1998
b).53.
Y. -J.
Zhao
, C.
Persson
, S.
Lany
, and A.
Zunger
, Appl. Phys. Lett.
85
, 5860
(2004
).54.
G. V.
Lewis
and C. R. A.
Catlow
, J. Phys. Chem. Solids
47
, 89
(1986
).55.
P.
Erhart
, K.
Albe
, and A.
Klein
, Phys. Rev. B
73
, 205203
(2006
).56.
C.
Persson
, Y. -J.
Zhao
, S.
Lany
, and A.
Zunger
, Phys. Rev. B
72
, 035211
(2005
).57.
G.
Makov
and M. C.
Payne
, Phys. Rev. B
51
, 4014
(1995
).58.
J.
Lento
, J. -L.
Mozos
, and R. M.
Nieminen
, J. Phys.: Condens. Matter
14
, 2637
(2002
).59.
E.
Cockayne
, J. Eur. Ceram. Soc.
23
, 2375
(2003
).60.
G.
Henkelman
, G.
Jóhannesson
, and H.
Jónsson
, Methods for Finding Saddlepoints and Minimum Energy Paths in Progress on Theoretical Chemistry and Physics
(Kluwer Academic
, Dordrecht, The Netherlands
, 2000
), p. 269
.61.
G.
Henkelman
, B. P.
Uberuaga
, and H.
Jónsson
, J. Chem. Phys.
113
, 9901
(2000
).62.
P.
Erhart
and K.
Albe
, Phys. Rev. B
73
, 115207
(2006
).63.
P.
Erhart
and K.
Albe
, Phys. Rev. B
(in press).64.
65.
Handbook of Chemistry and Physics
, 85th ed., edited by D. R.
Lide
(CRC Press
, Boca Raton
, 2004
).66.
A.
Every
and A.
McCurdy
, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology, New Series
(Springer
, Heidelberg
, 1992
), Vol. III
/29A
.67.
S. B.
Zhang
, S. -H.
Wei
, and A.
Zunger
, Phys. Rev. Lett.
84
, 1232
(2000
).68.
P.
Ehrhart
, P.
Jung
, H.
Schultz
, and H.
Ullmaier
, Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology, New Series
(Springer
, Heidelberg
, 1991
), Vol. III
/25
.69.
P.
Erhart
, R. -A.
Eichel
, P.
Träskelin
, and K.
Albe
(unpublished).70.
H.
Meštrić
, R. -A.
Eichel
, T.
Kloss
, K. -P.
Dinse
, S.
Laubach
, S.
Laubach
, P. C.
Schmidt
, K. A.
Schönau
, M.
Knapp
, and H.
Ehrenberg
, Phys. Rev. B
71
, 134109
(2005
).© 2007 American Institute of Physics.
2007
American Institute of Physics
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