Diffusion in Oxides here: Oxygen Ion Conductors

Transcription

1 Diffusion in Oxides here: Oxygen Ion Conductors M. Martin Institute of Physical Chemistry RWTH Aachen University Germany R.A. De Souza, D. Samuelis, O. Schulz I.V. Belova, G.E. Murch Diffusion in Solids Group The University of Newcastle Australia Diffusion Fundamentals II August 26-29,

2 Walther Nernst filament Filament (Nernstmasse) Chalk, magnesia, zirconia, rare earths Nernst Glower Deutsches Patent Nr vom Carl Wagner Über den Mechanismus der elektrischen Stromleitung im Nernststift, Naturwissenschaften 31 (1943) 265. Zr 4+ Zr 4+ Zr 4+ Zr 4+ Zr 4+ O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- Zr 4+ Zr 4+ Zr 4+ Zr 4+ Zr 4+ O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- Y 3+ Y 3+ O 2- + = O 2- O 2- Zr 4+ Zr 4+ Zr 4+ Zr 4+ Zr 4+ Y 3+ O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- O 2- Zr 4+ Zr 4+ Zr 4+ Zr 4+ Zr 4+ Y 3+ O 2- O 2- O 2- O 2- O 2- O 2- Y Zr O V Y ] = 2[V ] [ Zr O O 2- O 2- O 2- O 2- O 2- O 2- defects Majority 2

3 Vacancies, in Rome already known 27 BC 3

4 Solid Oxide Fuel Cell (SOFC) H 2 (g) U=1,0V e - O 2 (g) O 2- H 2 O 2 O H2(g) 2 + H O + 2e O2(g) + 2e O Oxygen ion conductor C 4

5 Ionic conductivities of oxide electrolytes: σ D V c V GDC Steele, Kilner, 2001 B.C.H. Steele (2001) YSZ Nernst, 1897 Wagner, 1930 LSGM Ishihara, 1994 Goodenough,

6 Ionic conductivities of doped ZrO 2 : σ D V c V Maximum due to: defect clusters defect ordering number of mobile oxygen vacancies decreases mol% of B 2 O 3 or BO H. Tannenberger (1965) H. Schmalzried, Z. Phys. Chem. NF, 105, 47 (1977) A.D. Murray, G.E. Murch,C.R.A. Catlow, Solid State Ionics, 19, 196 (1986) F. Shimojo, T. Okabe, F. Tachibana, M. Kobayashi, H. Okazaki, J. Phys. Soc. Japan, 61, 2842 (1992) M. Meyer, N. Nicoloso, Ber. Bunsenges. Phys. Chem., 101, 1393 (1997) M.S. Khan, M.S. Islam, D.R. Bates, J. Mater. Chem., 8, 2229 (1998) M.O. Zacate, L. Minervini, D.J. Bradfield, R.W. Grimes, K.E. Sickafus, Solid State Ionics, 128, 243 (2000) R. Krishnamurthy, Y.-G. Yoon, D.J. Srolovitz, R. Carr, J. Am. Cer. Soc., 87, 1821 (2004) T. Ishii, T. Ishikawa, Solid State Ionics (2006) 6

7 Ionic conductivities of doped ZrO 2 : σ D V c V Maximum due to: defect clusters defect ordering number of mobile oxygen vacancies decreases O B A V undersized cations: nn oversized cations: nnn Cluster at % dopant level? mol% of B 2 O 3 or BO H. Tannenberger (1965) 7

8 YSZ (fluorite structure) Shimojo et al. (1992): MD Krishnamurthy et al. (2004): DFT Edge E AB / ev Zr Zr 0.58 Zr - Y 1.29 Y - Y 1.86 Y Y edges are blocking maximum in σ oxygen 8

9 YSZ (fluorite structure) Shimojo et al. (1992): MD Krishnamurthy et al. (2004): DFT Edge E AB / ev Zr Zr 0.58 Zr - Y 1.29 Y - Y 1.86 Y Y edges are blocking maximum in σ oxygen But: no Y-V O interactions random vacancy distribution 9

10 Concentrated solution of (A A,B A ) and (O O,V O ) Only nearest neighbor interactions B A -V O Simple model for the oxygen ion conductivity: 1. Random cation distribution, immobile cations 2. Oxygen vacancy distribution (random, non-random) 3. Vacancy jump types 4. Ionic conductivity 10

11 1. Random cation distribution tetrahedron fraction [ijkl] n=0 n=1 [AAAA] [AAAB] [AABB] [ABBB] [BBBB] n=2 f (x n 4 n n B xb(1 xb ) n=3 4 ) = 2 fraction of n tetrahedra with n B-cations n= dopant fraction x B 11

12 2. Vacancy distribution: x x (Zr1 y Yy )O2 x/2 or (Zr1 yyy )(O2 y/2vy/2) V + O O + AAAA AAAB AAAA V AAAB attractive + + K 1 [OAAAA ] [VAAAB ] = ΔE = 1 K1 exp [VAAAA ] [OAAAB ] kt V + O O + V AAAA AAAA AABB ABBB AAAA V + O O + V AAAA BBBB AAAA V + O O + V AAAA AABB ABBB BBBB K 2 [OAAAA ] [VAABB ] = ΔE = 2 K 2 exp [VAAAA ] [OAAABB ] kt Charge neutrality ( ] + [V ] + [V ] + [V ] [V ]) xb = 2 [VAAAA AAAB AABB ABBB + BBBB 12

13 no B-V interaction random vacancy distribution attractive B-V interaction non-random vacancy distribution vacancy fraction [V ijkl ] V AAAA V AAAB V AABB V ABBB V BBBB (x0.5) ΔE 1 =0 vacancy fraction [V ijkl ] V AAAA V AAAB V AABB V ABBB V BBBB (x 0.5) ΔE 1 = -0.1 ev T = 1273 K dopant fraction x B dopant fraction x B more vacancies in B-containing tetrahedra ΔE n = n ΔE 1 13

14 3. Jump types Site energies ω 0,0 ω 1,0 ω 2,0 ΔE n = n ΔE 1 n = 0,1,2,3,4 ω 1,1 ω 2,1 ω 3,1 E AA ω 2,2 ω 3,2 ω 4,2 ΔE 1 4. Oxygen ion conductivity σ ( [V + [V + [V + [V + [V AAAA AAAB AABB ABBB BBBB ] 6 ω ] ([OAAAA ] + [OAAAB] + [OAABB]) ( [OAAAA ] + [OAAAB] + [OAABB]) + 3 ω1,1 ( [OAAAB] + [OAABB] + [OABBB]) ([OAAAA ] + [OAAAB] + [OAABB]) + ω2,2 ( [OAABB] + [OABBB] + [OBBBB]) ( [OAAAB] + [OAABB] + [OABBB]) ( [O ] + [O ] + [O ]) + 3 ω ( [O ] + [O ] + [O ]) { 3 ω } + ω ] + 4ω ] { 3 ω } ] 6 ω 0,0 2,0 4,2 1,0 2,1 3,2 AABB ([O ] + [O ] + [O ])) AABB ABBB ABBB BBBB BBBB 3,1 AAAB AABB Correlated motion ABBB 14

15 Ionic conductivity Conductivity σ (arbitrary units) ΔE 1 = 0.0 ev ΔE 1 = -0.1 ev ΔE 1 = -0.2 ev ident. A-B, B-B barriers blocking T = 1273 K Dopant fraction x B MM, J. Electroceram. 17 (2006)

16 Ionic conductivity Conductivity σ (arbitrary units) Y Sc ΔE 1 = 0.0 ev ΔE 1 = -0.1 ev ΔE 1 = -0.2 ev ident. A-B, B-B barriers blocking T = 1273 K qualitative agreement with exper. mainly pathways across Zr-Zr edges vacancy trapping in Y-tetrahedra Zacate Dopant fraction x B ScSZ: R(Sc) < R(Y) ΔE 1 (Sc) < ΔE 1 (Y) Badwal σ(sc) > σ(y) MM, J. Electroceram. 17 (2006)

17 Ionic conductivities of oxide electrolytes GDC Steele, Kilner, 2001 B.C.H. Steele (2001) YSZ Nernst, 1897 Wagner, 1930 LSGM Ishihara, 1994 Goodenough,

18 Cation diffusion in oxygen ion conductors Why study cation diffusion in an oxygen ion conductor? Cations are the slowest species: t cation << t e,t h << t O They determine the rates of: - defect equilibration - sintering, creep Minority defects - interdiffusion (with electrodes) - kinetic demixing (of electrolyte) Long term degradation effects Complicated diffusion mechanism 18

19 Cation self-diffusion in LSGM La 0.9 Sr 0.1 Ga 0.9 Mg 0.1 O 2.9 curvature frozen in defects at low temperatures SIMSIPC defect formation + migration 4.5 ev migration 2 ev O. Schulz, M. Martin et al., PCCP (2003) 19

20 Cation self-diffusion in LSGM Experiment similar migration energies for all cations 2 ev similar diffusion coeff. for all cations ABO 3 Ionic radii A-site B-site La 3+ : 106 pm Ga 3+ : 62 pm Sr 2+ : 118 pm Mg 2+ : 74 pm Theory E E mig La mig Y = = ev ev E mig Ga mig Cr ev ev Simple cation vacancy mechanisms E = = Khan De et Souza, al. (1998) Maier (2002) More complicated diffusion mechanism? O. Schulz, M. Martin et al., PCCP (2003) 20

21 Cluster formation in LSGM ( V,V,V ) V A + VB + V O A O B cluster Minority defects ΔE C -7.5 ev (point charges) A B O O. Schulz, M. Martin et al., PCCP (2003) Correlatedfourjumpcycle ω >> ω > ω O A B 21

22 Molecular Dynamics Vacancy pair: (V A,V B ) Separated vacancies V A and V B long range B-jumps via V A only forward-backwards jumps M. Kilo, M.A. Taylor, C. Argirusis, G. Borchardt, R.A. Jackson, O. Schulz, M. Martin, M. Weller, Solid State Ionics 175 (2004)

23 Cluster migration in ABO 3 Sum rule expressions for the transport coefficients L ij, e.g. w A w A L AA + 2 LAO + 2 LAB = L w w O B (0) AA w B w O 10 w A w O /w A =1.0 w O /w B =0.1 /D B * D A * 1 w O /w A =0.1 w O /w A =10.0 w O /w A =100.0 w O /w B =1.0 w O /w B =10.0 w O /w B =100.0 SIMSIPC w B /(2w A ) 1.0 2w A /w B 0 I.V. Belova, G.E. Murch, D. Samuelis, M. Martin, Defect and Diffusion Forum 263 (2007)

24 Conclusions Oxygen diffusion in YSZ (and LSGM): - jumps through edges and interactions - simple, analytical model for concentrated defects and conductivity maximum Cation diffusion in LSGM (minority defects) - identical activation energies for all cations - identical diffusion coefficients for all cations - defect clustering - four-jump cycle - qualitative confirmation by GULP, MD and sum rules General mechanism for cation diffusion in perovskites? D B [V B ] [V A ] Thanks: DFG (SPP 1060), CHF, Land NRW 24

25 Vacancies, in Rome already known 27 BC 25