e-Journal of Surface Science and Nanotechnology 27 December 2011-IWAMN2009-On Oxygen Deficiency in Nanocrystallites La1−xSrxCoO3∗ Tran Thi Hong† and Pham The Tan Hanoi University of Scie
Trang 1e-Journal of Surface Science and Nanotechnology 27 December 2011
-IWAMN2009-On Oxygen Deficiency in Nanocrystallites La1−xSrxCoO3∗
Tran Thi Hong† and Pham The Tan
Hanoi University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
Hoang Nam Nhat
College of Technology, Vietnam National University, Hanoi, 144 Xuan Thuy, Cau Giay, Hanoi, Vietnam
(Received 10 December 2009; Accepted 3 May 2010; Published 27 December 2011)
The crystal lattice and the bond valence structure of perovskite system La1−xSrxCoO3are reported The atomic valences for the given perovskites were determined on the basis of bond-valence theory For the studied compounds the failure of distortion theorem was observed, and the non-stoichiometry of oxygen was estimated The model for oxygen distribution is then suggested The relationship between the grain diameter and oxygen content is discussed [DOI: 10.1380/ejssnt.2011.469]
Keywords: X-ray scattering, diffraction, and reflection; La
I INTRODUCTION
The term valence is understood strictly according L.
Pauling’s valence principle [1] which states that the
atomic valence (AV) of atom X is the sum over all
va-lences of bonds to the given atom X: v =∑
v i Evidently, this atomic valence is equivalent to the absolute value of
oxidation state and the bond valence (BV) is equivalent
to the number of bonding electrons distributed within the
bond The dependence of bond valence on bond length
(BL) was the subject of extensive studies for decades and
much functional dependences were published in [2] Most
of these functions are the exponential functions of the
form:
v i= exp
(
R0− R B
)
where R0 and B are the empirical constants According
to Eq (1) when BL increases BV must decrease and vice
versa This characteristic dependence was postulated in
a so-called distortion principle which says: “The product
of BV and average BL is always constant in all chemical
bonds” (i.e v i × < R i >= const) Although the validity
of this principle in general is still questionable, it proves
correct in many cases, especially for ionic compounds and
for the hydrogen bondings In fact this principle is an
ex-ample of the elastic bonding model When the BL change,
the BV must change also to preserve the electric neutrality
of molecule and the stoichiometry of total atomic valence
The distortion theorem is important for analysis of the
valence structure of perovskites, especially for cases where
the substitution of various elements of different oxidation
states to the same lattice position usually deforms the
lattice We have investigated the valence structures of
perovskite system La1−xSrxCoO3 and have come to the
conclusion that the distortion theorem does not hold For
∗This paper was presented at the International Workshop on
Ad-vanced Materials and Nanotechnology 2009 (IWAMN2009), Hanoi
University of Science, VNU, Hanoi, Vietnam, 24-25 November, 2009.
†Corresponding author: tthong@vnu.edu.vn
the perovskites with atom X (e.g Sr2+), with lower oxi-dation state replacing atom A (e.g La+3) and with higher
oxidation state with x%, the common opinion is that some
portion of atom B (e.g Co3+) must also change its oxida-tion state to higher (e.g Co4+) This consequently leads
to the increase in valences of bonds around atom B and
to the shortening of lattice constants connecting atoms
B However, the experimental results did not confirm the contract of lattice For studied perovskites, the lattice pa-rameters changed only a little that means no significant variation in bond valences, i.e the number of electrons distributed within the unit cell remains unchanged Thus the unit cell is under-charged This situation points to the variation in stoichiometry of some atoms, namely of oxygen or to the occurrence of B-atom holes in the lattice
II BOND VALENCE THEORY OF
PEROVSKITES
The oblique perovskite lattice is the cubic f-b-c with
lattice constant a ∼ 3.85 ˚A where atom A occupies ori-gin A(0,0,0); B occupies b-c position B(1/2,1/2,1/2); and
O occupies 3 f-c positions O1(1/2,1/2,0), O2(1/2,0,1/2), O3(0,1/2,1/2) These 3 f-c positions are equivalent only
in the cubic lattice, not in lower symmetry The coor-dination number of A is 12 A-O, of B is 6 B-O, of O
is 2+4 (2 B-O and 4 A-O) The cubic structure is usu-ally deformed to lower symmetry, e.g to monoclinic P21
(a = c ̸= b, α = γ = 90 ◦ , β ̸= 90 ◦), or to
rhombohe-dral R-3m (a = b = c, α = β = γ ∼ 90 ◦, note that the
hexagonal lattice [a = b ̸= c, α = β = 90 ◦ , γ = 120 ◦] is
equivalent to the rhombohedral one) or even to triclinic
P-1 (a ̸= b ̸= c, α ̸= β ̸= γ) Despite the change to lower
symmetry we may still assume that the deformed lattice constants remain near the cubic values If this condition
holds, we call the deformed lattices the pseudo-cubic ones.
It is important to obtain the perovskite lattices in the pseudo-cubic form since in this form the atomic distances may be deduced directly from lattice constants
In general triclinic symmetry the coordination of atom
A consists from 6 pairs A-O, of B from 3 pairs B-O and
of O from 1 pair B-O plus 2 pairs A-O Let ⃗a, ⃗b, ⃗ c be the
lattice vectors
ISSN 1348-0391 ⃝ 2011 The Surface Science Society of Japanc (http://www.sssj.org/ejssnt) 469
Trang 2Volume 9 (2011) Hong, et al.
TABLE I: Lattice structures of perovskite system La1−xSrxCoO3
La0.75Sr0.25CoO3 (P212121) 3.831(6) 3.844(8) 3.840(1) 90 56.5(3)
La0.65Sr0.35CoO3 (R-3m) 3.832(3) 90.3(2) 56.3(1)
La0.55Sr0.45CoO3 (R-3m) 3.830(4) 90.3(2) 56.2(2)
TABLE II: Bond valences
Compound < v A > < v B > < v O > ΣBE δ(O)
By using Pauling’s bond-valence sum rule v =∑
v i =
∑
exp[(R0− R)/B] we obtain the following relations for
triclinic symmetry
1 Valence of A: v A = v A1 + v A2 + v A3;
2 Valence of B: v B = v B1 + v B2 + v B3;
3 Valence of O: There are three independent positions
O1, O2 and O3 so the valence is calculated for each
case separately: (3.1) v O1 = v B −O1 + v A −O1; (3.2)
v O2 = v B −O2 + v A −O2 ; (3.3)v O3 = v B −O3 + v A −O3;
The average valence for atom O is: (3.4) < v O >=
(< v O1 > + < v O2 > + < v O3 >)/3.
4 The electric neutrality of molecule: v A + v B −v O1 −
v O2 − v O3= 0
This relation only means v A + v B = v O1 + v O2 + v O3 It
does not say v A +v B= 3×|−2| = 6 In fact this sum may
differ from 6 and this diversity signifies the under-charging
or over-charging of the unit cell We have determined the
oxygen content on the basis of this diversity
III RESULTS AND DISCUSSION
Based on the experimental data taken at the Center for
Materials Science, Hanoi University of Science, by using
X-Ray diffractometer 5005 (Bruker, Germany), we have
determined the lattice structures for perovskite system
La1−xSrxCoO3 In Table I the crystal lattice structures
of the perovskite system La1−xSrxCoO3 are given They
were determined by using three methods: Ito [3], Visser [4] and Taupin [5] The final lattice was chosen so that its vol-ume is smallest and the ratio of measured and calculated reflections is closest to unity The standard deviations
δθ are revealed to be small ( ≤ 0.02) so the pseudo-cubic
lattices may be true For La1−xSrxCoO3 system the unit cell volume is practically constant
In Table II the atomic bond valences for the given perovskites are shown The calculation was performed according to Section 2 The total bonding electrons is
ΣBE =< v A > + < v B > and the oxygen stoichiometry
is δ(O) = ΣBE/2 For La1 −xSrxCoO3the oxygen atomic valences show the deficiency of oxygen in the lattice
3.795 3.800 3.805 3.810 3.815 3.820 3.825 3.830 3.835 3.840 3.845
1.00 0.90 0.80 0.75 0.70 0.65 0.60 0.55 0.50
x [% Sr]
M easured
Predi cted
FIG 1: The predicted lattice constants versus the measured ones for La1−xSrxCoO3
470 http://www.sssj.org/ejssnt (J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/)
Trang 3e-Journal of Surface Science and Nanotechnology Volume 9 (2011)
Figure 1 shows the comparison of the predicted and the
measured pseudo-cubic lattice constants for compounds
La1−xSrxCoO3 As the distortion theorem predicts, the
lattice constants must collapse with increasing
concen-tration of substituted Sr2+ However, the measured
lat-tice constants show no such contraction There must
be a change in oxygen content if the distortion
theo-rem does not hold for these perovskites The mean
oxy-gen stoichiometry < δ(O) >= 2.93 determines one
cient O for every 14.3 molecules, consequently one
defi-cient molecule La1−xSrxCoO3 for every 14.3 × 3 = 42.9
crystallized molecules La1−xSrxCoO3 Let η denotes this
number of grain-forming crystallized molecules, we have:
η = 3 × | < δ(O) > −3| −1.
Since the crystal lattice is solid, the free molecule should
reside out-from the grain at the grain boundary Thus the
smallest grain diameter D is equal to η × < a >, where
< a > is the average lattice constant For La1−xSrxCoO3
the smallest grain diameter estimation is D = 42.9 × 3.87
˚
A= 166 ˚A Note that in this model the valences of the
free molecules provide charge compensation to the grains
IV CONCLUSIONS
We have determined the lattice structures for
per-ovskite system La1−xSrxCoO3, and then evaluated the
bond valence distribution for these perovskites Our
the-oretical model for calculation of valence structure of per-ovskite ABO3 can be used for the general triclinic sym-metry It takes also into account the replacement of atom
A by another atom X and the shift in oxidation state of atom B from 3+ to 4+ According to this model some in-teresting result was obtained For all studied compounds the failure of distortion theorem was observed which con-sequently led to the conclusion that the unit cells of these perovskites are not full-charged Thus the oxygen must exist as non-stoichiometric within the crystallized grains and the charge compensation to the grains must take place somewhere at the grain boundaries We have investi-gated the oxygen contents and suggested the model for oxygen distribution The relationship between the grain diameter and the amount of non-stoichiometric oxygen is also given However, no clear relationship between oxy-gen content and the concentration of substitution atom could be found
Acknowledgments
This work was partly supported by the Asian Research Center’s Grant “Nanoscale Cu-O spin chain systems” (2009-2011) and by the Vietnam National University Re-search Grant QGTD-09.02 “Optomagnetic nanoparticles
in coating technology” (2009-2011)
[1] L Pauling, J Am Chem Soc 51, 1010 (1929).
[2] I D Brown and D Altermatt, Acta Cryst B41, 244
(1985)
[3] T Ito, X-Ray Studies on Polymorphism (Maruzen, Tokyo,
1950), p 187
[4] J V Visser, J Appl Cryst 2, 89 (1969).
[5] D Taupin, J Appl Cryst 21, 485 (1988).
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