A Atkinson

A Nakamura

AS Nowick

AS Verma

Christodoulos Chatzichristodoulou

D Marrocchelli

DJ Kim

DJD Bevan

G Brauer

G Mogensen

HL Tuller

HW Chiang

JA Kilner

LQ Jiang

M Kajitani

M Mogensen

Mogens B. Mogensen

P Datta

Peter V. Hendriksen

Poul Norby

R Ubic

RD Shannon

RL Moreira

SJ Hong

Springer - Publisher Connector

Size of oxide vacancies in fluorite and perovskite structured oxides

Mogensen, Mogens Bjerg

Norby, Poul

Chatzichristodoulou, Christodoulos

Hendriksen, Peter Vang

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 15, 2017Volume of Oxide Vacancies in Fluorite and Perovskite Structured OxidesMogensen, Mogens Bjerg; Norby, Poul; Chatzichristodoulou, Christodoulos; Hendriksen, Peter VangPublication date:2013Link back to DTU OrbitCitation (APA):Mogensen, M. B., Norby, P., Chatzichristodoulou, C., & Hendriksen, P. V. (2013). Volume of Oxide Vacancies inFluorite and Perovskite Structured Oxides [Sound/Visual production (digital)]. Arthur S. Nowick MemorialSymposium, Kyoto, Japan, 07/06/2013Volume of Oxide Vacancies in Fluorite and Perovskite Structured Oxides Mogens B. Mogensen, Poul Norby, Christodoulos Chatzichristodoulou, Peter V. Hendriksen Department of Energy Conversion and Storage   Arthur S. Nowick Memorial Symposium Kyoto, Japan, June 7, 2013 DTU Energy Conversion, Technical University of Denmark           Introduction Even though I never got to know Prof. Nowick, I know that some of his deep interests were properties of fast ion conductors and defect chemistry in general  I also know that he was Harry Tuller’s PhD supervisor. Apart from all Prof. Nowick’s own seminal scientific contributions, the contribution of educating Harry was - as time has proven – another great contribution to the science of ionic and mixed ceramic conductors  We will in the following minutes discuss about such materials and the volume of defects, i.e. the volume of oxide vacancies, inside them in memory of Prof. Arthur S. Nowick 2 6 January 2014 DTU Energy Conversion, Technical University of Denmark           Why is volume of vacancies interesting?    Some reasons are the observations that:   • the crystal lattice shrinks if a fluorite like CeO2 is doped with a 2 or 3-valent cation of approximately the same size as Ce4+  •  the induced ionic conductivity reaches its maximum as a function of dopant radius for the radius that does not change the lattice parameter of the host crystalline compound  • or expressed differently: The highest conductivity occur if Vegard’s slope is zero  • or the conductivity - for a given dopant concentration - is highest in the stress free lattice 3 6 January 2014 DTU Energy Conversion, Technical University of Denmark           ( )( )4312 2 22 2cat ancat h san O Va r rr x r x rx xr r r= += − ⋅ + ⋅   −   = ⋅ + ⋅      Vacancies (Hong and Virkar 1995, Tuller et al 2012): Empirical (Kim 1989): 0 ( )cat cata a A r B z x= + ⋅∆ + ⋅∆ ⋅Lattice constant empirical relations of doped fluorites DTU Energy Conversion, Technical University of Denmark           rv (Å) Compound Ref. Kim Hong+Virkar Tuller HfO2 0.999-0.484∙Δr 0.909 (Y) (0.830 (La)) ZrO2 0.982-0.328∙Δr 0.924 (Y) (0.870 (La)) 0.993  0.988  CeO2 1.120-0.189∙Δr 1.112 (Y) 1.080 (La)  1.164 1.169  UO2 1.155-0.432∙Δr 1.148 (Y) 1.077 (La)     ThO2  1.189-0.328∙Δr  1.204 (Y) 1.150 (La)     Estimation of the oxide ion vacancy radius 3 (4 3 )v O catr r B A r= − ⋅ − − ⋅ ⋅ ∆DTU Energy Conversion, Technical University of Denmark           Dependence of oxide ion vacancy radius on host size The weaker metal-oxygen bond the larger is the vacancy volume DTU Energy Conversion, Technical University of Denmark           rc (Å) system Ref. Kim Hong+Virkar Tuller HfO2 0.938 ZrO2 0.948 0.937 0.938 CeO2 1.038  1.024 1.024 UO2 1.063     ThO2 1.112     Estimation of (3+)cation matching radius c hBr rA= +DTU Energy Conversion, Technical University of Denmark           Expansion on reduction of ceria 8 6 January 2014 Main data: Chiang et al. Solid State Ionics, 66 (1993) 85–95   Squares:G. Mogensen, M.  Mogensen, Thermochim. Acta, 214 (1993) 47–50;   Line: best fit: M. Mogensen et al., Solid State Ionics, 129 (2000) 63 DTU Energy Conversion, Technical University of Denmark           Stoichiometry expansion coefficients  Stoichiometry expansion coefficient, αS, defined by:   ε = ∆L/L = αS⋅δ  where ε is the measured expansion, L is sample length, and ∆L is the change due to a change in oxygen stoichiometry of δ e.g. in reduced CeO2-δ or in doped La1-xSrxGa1-yMgyO3-δ.  P.V. Hendriksen et al., “Electrical conductivity and dimensional stability of co-doped lanthanum chromites”, In: Ionic and mixed conducting ceramics V; eds. T.A. Ramanarayanan et al. Electrochemical Society Proc. Vol. PV 2004-25, 2008. p. 349-367.  αS is about  in the range of 2.3 – 3 %/vacant O for reduction of various doped LaCrO3 and typically about 11 %/vacant O for reduction of ceria   9 6 January 2014 DTU Energy Conversion, Technical University of Denmark           Perovskite After V. P. Dravid Perovskite structure (Grey atoms: A, Black: B, Blue: O)  The O + A ions form together a cubic closest packed structure if the size of the A-ion is close to the size of the oxide ion.      Very strong B-metal-oxygen bonds DTU Energy Conversion, Technical University of Denmark           Perovskite – a very flexible stucture  SrTiO3 From Cava Lab (J.R. Cava) Most perovskites are not exactly cubic – and thus it is even more controversial to calculate vacancy volume in perovskites DTU Energy Conversion, Technical University of Denmark           ”Ideal” perovskite data  • rO2- = 1.40 Å • rA,ideal = 1.40 Å • rB,ideal = 0.58 Å  • a = 3.96 Å  • V = 62.1 Å3    12 6 January 2014 DTU Energy Conversion, Technical University of Denmark           La1-xSrxGa1-yMgyO3-delta  13 6 January 2014 5959,259,459,659,8600 0,05 0,1 0,15 0,2 0,25Series1Mg+Sr LSGM Volume, Å3 Delta Mg Mg+Sr Mg αv = 4.73, αl = 1.68 Å/O-vac αv = 7.75, αl = 1.98 Å/O-vac Volume per formula unit versus oxygen sub-stoichiometry  Data from: M. Kajitani et al. Chem. Mater. 2003, 15, 3468 and 2005, 17, 4235 (neutron diffraction)  Stoichiometric αs = DTU Energy Conversion, Technical University of Denmark           BaZrO3  14 6 January 2014 From: Donglin Han, Yoshitaro Nose, Kozo Shinoda, Tetsuya Uda Solid State Ionics, 213 (2012) 2–7  rBa = 1.61 Å  Introduction of OH- (r = 1.37 Å) increases the unit cell volume with ≈ ½ - 1 %, i.e. rv < 1.37 Å < rO2- =1.40 Å DTU Energy Conversion, Technical University of Denmark           Conclusion  • Introduction of oxide vacancy without  introducing cations bigger than the corresponding host shrinks the unit cell volume in fluorite and perovskite structured metal oxides  • In fluorites rv increase with decreasing metal – oxygen bond strength  • In perovskites the situation is more complicated, but due to the strong B-ion-oxygen bond the volume changes tend to be less than half of what is typically seen in fluorites   15 6 January 2014 DTU Energy Conversion, Technical University of Denmark           Lattice shrinking contribution of vacancies 0.1 Å 0.16 Å • EXAFS results (and computational simulations) support this relaxation pattern  • This means though that the local volume at a vacant oxide ion site is actually increasing! Yamazaki et al 2000 Tuller et al 2012 DTU Energy Conversion, Technical University of Denmark           Model assumptions and limitations  • The cations have a coordination number less than 8 when the fluorite structure is acceptor doped and has vacancies, which affects their effective ionic radii. This difficulty is somewhat overcome by treating the vacancy as a species in the lattice possessing a certain radius.  • The oxygen vacancy radius is taken to be independent of concentration and dopant type.  • These calculations assume random distribution of the oxygen vacancies (and the dopant) and adopt a linear relationship between lattice parameter and dopant concentration (Vegard’s law). Neither of these assumptions is true at higher dopant concentrations.  • The value of rv does not represent the local structural modifications in the neighborhood of an oxide ion vacancy, but stems from the average lattice constant and acts as a parameter that includes all the structural complexity that is not accounted for by the model. DTU Energy Conversion, Technical University of Denmark           More precise model by Nakamura 2010 

Volume of Oxide Vacancies in Fluorite and Perovskite Structured Oxides

An analysis of the effective radii of vacancies and the stoichiometric expansion coefficient is performed on metal oxides with fluorite and perovskite structures. Using the hard sphere model with Shannon ion radii we find that the effective radius of the oxide vacancy in fluorites increases with increasing ion radius of the host cation and that it is significantly smaller than the radius of the oxide ion in all cases, from 37% smaller for HfO2 to 13 % smaller for ThO2. The perovskite structured LaGaO3 doped with Sr or Mg or both is analyzed in some detail. The results show that the effective radius of an oxide vacancy in doped LaGaO3 is only about 6 % smaller than the oxide ion. In spite of this the stoichiometric expansion coefficient (a kind of chemical expansion coefficient) of the similar perovskite, LaCrO3, is significantly smaller than the stoichiometric expansion coefficient of the fluorite structured CeO2. Our analysis results indicate that the smaller stoichiometric expansion coefficient of the perovskites is associated with the restraining action of the A-O sub-lattice to dimensional changes in the B-O sub-lattice and vice versa

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Journal of Electroceramics

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Volume of Oxide Vacancies in Fluorite and Perovskite Structured Oxides

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