e-Journal of Surface Science and Nanotechnology 27 December 2011 Conference -IWAMN2009- e-J Surf Sci Nanotech Vol (2011) 469-471 On Oxygen Deficiency in Nanocrystallites La1−x Srx CoO3 ∗ 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 May 2010; Published 27 December 2011) The crystal lattice and the bond valence structure of perovskite system La1−x Srx CoO3 are 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 valences of bonds to the given atom X: v = vi 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: ( vi = exp R0 − R B the perovskites with atom X (e.g Sr2+ ), with lower oxidation 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 oxidation 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 parameters 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 ) , (1) 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 vi × < Ri >= 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 example 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−x Srx CoO3 and have come to the conclusion that the distortion theorem does not hold For ∗ This paper was presented at the International Workshop on Advanced Materials and Nanotechnology 2009 (IWAMN2009), Hanoi University of Science, VNU, Hanoi, Vietnam, 24-25 November, 2009 † Corresponding author: tthong@vnu.edu.vn 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 origin A(0,0,0); B occupies b-c position B(1/2,1/2,1/2); and O occupies f-c positions O1 (1/2,1/2,0), O2 (1/2,0,1/2), O3 (0,1/2,1/2) These f-c positions are equivalent only in the cubic lattice, not in lower symmetry The coordination number of A is 12 A-O, of B is B-O, of O is 2+4 (2 B-O and A-O) The cubic structure is usually deformed to lower symmetry, e.g to monoclinic P21 (a = c ̸= b, α = γ = 90◦ , β ̸= 90◦ ), or to rhombohedral 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 pairs A-O, of B from pairs B-O and of O from pair B-O plus pairs A-O Let ⃗a, ⃗b, ⃗c be the lattice vectors c 2011 The Surface Science Society of Japan (http://www.sssj.org/ejssnt) ISSN 1348-0391 ⃝ 469 Hong, et al Volume (2011) TABLE I: Lattice structures of perovskite system La1−x Srx CoO3 Compound a [˚ A] LaCoO3 (R-3m) La0.9 Sr0.1 CoO3 (R-3m) La0.8 Sr0.2 CoO3 (R-3m) La0.75 Sr0.25 CoO3 (P21 21 21 ) La0.7 Sr0.3 CoO3 (R-3m) La0.65 Sr0.35 CoO3 (R-3m) La0.6 Sr0.4 CoO3 (R-3m) La0.55 Sr0.45 CoO3 (R-3m) 3.826(2) 3.832(3) 3.836(2) 3.831(6) 3.834(1) 3.832(3) 3.831(1) 3.830(4) b [˚ A] c [˚ A] 3.844(8) 3.840(1) α [◦ ] V [˚ A3 ] 90.7(1) 90.5(3) 90.4(1) 90 90.3(1) 90.3(2) 90.2(2) 90.3(2) 56.0(3) 56.3(2) 56.5(1) 56.5(3) 56.3(1) 56.3(1) 56.2(2) 56.2(2) TABLE II: Bond valences Compound < vA > < vB > < vO > ΣBE δ(O) LaCoO3 La0.90 Sr0.10 CoO3 La0.80 Sr0.20 CoO3 La0.75 Sr0.25 CoO3 La0.70 Sr0.30 CoO3 La0.65 Sr0.35 CoO3 La0.60 Sr0.40 CoO3 La0.55 Sr0.45 CoO3 La0.50 Sr0.50 CoO3 3.01 2.95 2.91 2.89 2.91 2.91 2.90 2.90 2.87 3.00 2.97 2.94 2.92 2.93 2.93 2.93 2.93 2.90 2.00 1.97 1.95 1.94 1.95 1.95 1.94 1.94 1.92 6.00 5.92 5.84 5.82 5.84 5.84 5.84 5.82 5.78 3.00 2.96 2.92 2.91 2.92 2.92 2.92 2.91 2.89 Valence of A: vA = vA1 + vA2 + vA3 ; Valence of B: vB = vB1 + vB2 + vB3 ; Valence of O: There are three independent positions O1 , O2 and O3 so the valence is calculated for each case separately: (3.1) vO1 = vB−O1 + vA−O1 ; (3.2) vO2 = vB−O2 + vA−O2 ; (3.3)vO3 = vB−O3 + vA−O3 ; The average valence for atom O is: (3.4) < vO >= (< vO1 > + < vO2 > + < vO3 >)/3 The electric neutrality of molecule: vA + vB − vO1 − vO2 − vO3 = This relation only means vA + vB = vO1 + vO2 + vO3 It does not say vA +vB = 3×|−2| = In fact this sum may differ from 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−x Srx CoO3 In Table I the crystal lattice structures of the perovskite system La1−x Srx CoO3 are given They 470 were determined by using three methods: Ito [3], Visser [4] and Taupin [5] The final lattice was chosen so that its volume 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−x Srx CoO3 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 The total bonding electrons is ΣBE =< vA > + < vB > and the oxygen stoichiometry is δ(O) = ΣBE/2 For La1−x Srx CoO3 the oxygen atomic valences show the deficiency of oxygen in the lattice a [Å] ∑ vi = ∑By using Pauling’s bond-valence sum rule v = exp[(R0 − R)/B] we obtain the following relations for triclinic symmetry 3.845 3.840 3.835 3.830 3.825 3.820 3.815 3.810 3.805 3.800 3.795 Measured Predicted 1.00 0.90 0.80 0.75 0.70 0.65 0.60 0.55 0.50 x [% Sr] FIG 1: The predicted lattice constants versus the measured ones for La1−x Srx CoO3 http://www.sssj.org/ejssnt (J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology Figure shows the comparison of the predicted and the measured pseudo-cubic lattice constants for compounds La1−x Srx CoO3 As the distortion theorem predicts, the lattice constants must collapse with increasing concentration of substituted Sr2+ However, the measured lattice constants show no such contraction There must be a change in oxygen content if the distortion theorem does not hold for these perovskites The mean oxygen stoichiometry < δ(O) >= 2.93 determines one deficient O for every 14.3 molecules, consequently one deficient molecule La1−x Srx CoO3 for every 14.3 × = 42.9 crystallized molecules La1−x Srx CoO3 Let η denotes this number of grain-forming crystallized molecules, we have: η = × | < 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−x Srx CoO3 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 Volume (2011) oretical model for calculation of valence structure of perovskite ABO3 can be used for the general triclinic symmetry 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 interesting result was obtained For all studied compounds the failure of distortion theorem was observed which consequently 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 investigated 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 oxygen content and the concentration of substitution atom could be found Acknowledgments IV CONCLUSIONS We have determined the lattice structures for perovskite system La1−x Srx CoO3 , and then evaluated the bond valence distribution for these perovskites Our the- [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, 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 Research Grant QGTD-09.02 “Optomagnetic nanoparticles in coating technology” (2009-2011) 1950), p 187 [4] J V Visser, J Appl Cryst 2, 89 (1969) [5] D Taupin, J Appl Cryst 21, 485 (1988) http://www.sssj.org/ejssnt (J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) 471 ... ) La0 .7 Sr0 .3 CoO3 (R-3m) La0 .65 Sr0 .35 CoO3 (R-3m) La0 .6 Sr0.4 CoO3 (R-3m) La0 .55 Sr0.45 CoO3 (R-3m) 3. 826(2) 3. 832 (3) 3. 836 (2) 3. 831 (6) 3. 834 (1) 3. 832 (3) 3. 831 (1) 3. 830 (4) b [˚ A] c [˚ A] 3. 844(8)... the lattice a [Å] ∑ vi = ∑By using Pauling’s bond-valence sum rule v = exp[(R0 − R)/B] we obtain the following relations for triclinic symmetry 3. 845 3. 840 3. 835 3. 830 3. 825 3. 820 3. 815 3. 810 3. 805... < vO > ΣBE δ(O) LaCoO3 La0 .90 Sr0.10 CoO3 La0 .80 Sr0.20 CoO3 La0 .75 Sr0.25 CoO3 La0 .70 Sr0 .30 CoO3 La0 .65 Sr0 .35 CoO3 La0 .60 Sr0.40 CoO3 La0 .55 Sr0.45 CoO3 La0 .50 Sr0.50 CoO3 3. 01 2.95 2.91 2.89