Chapter 4 Defect Chemistry of Barium Cerate by Extended-X-ray Absorption Fine
4.5 Results and Discussion
4 6 8 10 -10
-5 0 5 10
K3χ
K (A-1)
0 2 4 6 8 10
0 2 4 6 8 10
Amp
R+δR (A)
Fig 4-4 Gd LШ edge EXAFS for BaCe0.85Gd0.15O3-δ measured at 10 K: experimental data (solid line), best fit data (open circles)
Fig 4-4 (a) the normalized EXAFS spectrum (k3 weighted)
Fig 4-4 (b) the Fourier transform without the phase shift.
4 6 8 10
-6 -4 -2 0 2 4 6 8
k3 χ
k/(A-1)
0 2 4 6 8 10
0 1 2 3 4 5 6 7 8
Amp
R+δR (A)
Fig 4-5 Gd LШ edge EXAFS for BaCe0.85Gd0.15O3-δ measured at 300 K: experimental data (solid line), best fit data (open circles)
Fig 4-5 (a) the normalized EXAFS spectrum (k3 weighted)
Fig 4-5 (b) the Fourier transform without the phase shift.
4 6 8 10 -8
-6 -4 -2 0 2 4 6 8 10
k3 χ
k (A-1) 0 2 4 6 8 10
0 2 4 6 8
Amp
R+δR (A)
Fig 4-6 Yb LШ edge EXAFS for BaCe0.85Yb0.15O3-δ measured at 10 K: experimental data (solid line), best fit data (open circles)
Fig 4-6 (a) the normalized EXAFS spectrum (k3 weighted)
Fig 4-6 (b) the Fourier transform without the phase shift
4 6 8 10
-8 -6 -4 -2 0 2 4 6 8
k3 χ
K (A-1)
0 2 4 6 8 10
0 1 2 3 4 5 6 7
Amp
R+δR (A)
Fig 4-7 Yb LШ edge EXAFS for BaCe0.85Yb0.15O3-δ measured at 300 K: experimental data (solid line), best fit data (open circles)
Fig 4-7 (a) the normalized EXAFS spectrum (k3 weighted)
Fig 4-7 (b) the Fourier transform without the phase shift.
The structural parameters and refinement statistics obtained from the fitting procedure are summarized in Tables 4-4 and 4-5 for Gd and Yb, respectively. The refinement proceeded smoothly, yielding final residuals in the range 0.022 – 0.041, and χ2 values in the range 1.7 - 25.
Table 4-4 Model refinement statistics and best-fit structural parameters for the Gd LШ edge EXAFS in BaCe0.85Gd0.15O3-δ
Temp. (10 K) Temp. (300 K) Shell
(Gd on B4+-site)
Atom type Multi-
plicity R(Ǻ) σ2(Ǻ2) R(Ǻ) σ2(Ǻ2)
1 O 2 2.298(7) 0.003(1) 2.298(8) 0.004(1) 2 O 2 2.298(7) 0.003(1) 2.298(8) 0.004(1) 3 O 2 2.298(7) 0.003(1) 2.298(8) 0.004(1)
Ave. Gd-O dist. 2.298 2.298
4 Ba 2 3.834(10) 0.006(1) 3.860(11) 0.006(1) 5 Ba 2 3.834(10) 0.006(1) 3.860(11) 0.006(1) 6 Ba 2 3.992(3) 0.006(1) 4.004(7) 0.006(1) 7 Ba 2 3.992(3) 0.006(1) 4.004(7) 0.006(1)
Ave. Gd-Ba dist. 3.913 3.932
Shell
(Gd on A2+-site)
Atom type Multi- plicity
R(Ǻ) σ2(Ǻ2) R(Ǻ) σ2(Ǻ2)
8 O 1 2.463(11) 0.001(1) 2.465(11) 0.001(1) 9 O 2 2.463(11) 0.001(1) 2.465(11) 0.001(1) 10 O 2 2.467(2) 0.001(1) 2.467(10) 0.001(1) 11 O 1 2.467(2) 0.001(1) 2.467(10) 0.001(1) 12 O 2 2.467(2) 0.001(1) 2.467(10) 0.001(1) 13 O 1 2.467(2) 0.001(1) 2.467(10) 0.001(1) 14 O 2 2.470(3) 0.001(1) 2.470(4) 0.001(1) 15 O 1 2.470(3) 0.001(1) 2.470(4) 0.001(1)
Ave. Gd-O dist. 2.467 2.467
16 Ce 2 3.752(12) 0.001(1) 3.757(14) 0.002(1) 17 Ce 2 3.752(12) 0.001(1) 3.757(14) 0.002(1) 18 Ce 2 3.752(12) 0.001(1) 3.757(14) 0.002(1) 19 Ce 2 3.752(12) 0.001(1) 3.757(14) 0.002(1)
Ave. Gd-Ce dist. 3.752 3.757
Frac 0.869(10) 0.866(9)
k range (3,11) (3,11)
Chi2 1.71 2.89
R factor 0.0223 0.022
Table 4-5 Model refinement statistics and best-fit structural parameters for the Gd LШ edge EXAFS in BaCe0.85Gd0.15O3-δ
Temp. (10K) Temp. (300K) Shell
(Yb on B4+-site)
Atom type Multi-
plicity R(Ǻ) σ2(Ǻ2) R(Ǻ) σ2(Ǻ2)
1 O 2 2.239(4) 0.005(1) 2.242(5) 0.007(1) 2 O 2 2.239(4) 0.005(1) 2.242(5) 0.007(1) 3 O 2 2.239(4) 0.005(1) 2.242(5) 0.007(1) Ave. Yb-O dist. 2.239 2.242
4 Ba 2 3.708(5) 0.006(1) 3.734(4) 0.008(2) 5 Ba 2 3.708(5) 0.006(1) 3.734(4) 0.008(2) 6 Ba 2 3.853(6) 0.006(1) 3.890(5) 0.008(2) 7 Ba 2 3.853(6) 0.006(1) 3.890(5) 0.008(2) Ave.Yb-Ba dist. 3.781 3.812
Shell
(Yb on A2+-site)
Atom type Multi- plicity
R(Ǻ) σ2(Ǻ2) R(Ǻ) σ2(Ǻ2)
8 O 1 2.414(8) 0.002(1) 2.416(8) 0.003(1) 9 O 2 2.414(8) 0.002(1) 2.416(8) 0.003(1) 10 O 2 2.414(8) 0.002(1) 2.416(8) 0.003(1) 11 O 1 2.414(8) 0.002(1) 2.416(8) 0.003(1) 12 O 2 2.417(8) 0.002(1) 2.420(7) 0.003(1) 13 O 1 2.417(8) 0.002(1) 2.420(7) 0.003(1) 14 O 2 2.417(8) 0.002(1) 2.420(7) 0.003(1) 15 O 1 2.417(8) 0.002(1) 2.420(7) 0.003(1) Ave. Yb-O dist. 2.416 2.418
16 Ce 2 3.678(8) 0.002(1) 3.679(8) 0.008(2) 17 Ce 2 3.678(8) 0.002(1) 3.679(8) 0.008(2) 18 Ce 2 3.678(8) 0.002(1) 3.679(8) 0.008(2) 19 Ce 2 3.678(8) 0.002(1) 3.679(8) 0.008(2) Ave.Yb-Ce dist. 3.678 3.679
Frac 0.964(8) 0.953(12)
k range (3,11) (3,11)
Chi2 25.48 20.26
R factor 0.0311 0.0413
The defect chemical parameters and overall stoichiometries implied by the fitted models are summarized in Table 4-6, where they are also compared with the results of the X-ray powder diffraction analysis and electron microprobe chemical analysis from Chapter 3. It should be noted that because increased BaO loss and dopant incorporation onto the barium site are expected with high temperature processing73,36, the microprobe results, obtained from sintered pellets, are not directly comparable to the EXAFS and diffraction results, obtained from calcined powders. Rather, a similarity in general trends with dopant species is expected.
Table 4-6 Defect chemical parameters and stoichiometry of nominally BaCe0.85M0.15O3-δ materials (M = Gd, Yb) as derived from EXAFS and compared with the results of X-ray diffraction analysis and microprobe analysis.
Gd Yb Dopant
10 K 300 K 10 K 300 K
[M] on A-site 0.020(2) 0.021(1) 0.005(1) 0.007(2) [M] on B-site 0.133(2) 0.133(1) 0.145(1) 0.144(2)
δ 0.056(2) 0.056(1) 0.070(1) 0.068(2)
Ba:(M+Ce) 0.961(3) 0.960(2) 0.989(2) 0.986(4) Composition by
EXAFS at 300K
(Ba0.980Gd0.020)(Ce0.867Gd0.133)O2.944 (Ba0.993Yb0.007)(Ce0.856Yb0.144)O2.932
Ba:(M+Ce) by XRDa 0.978(0) 0.986(0)
Composition by
XRDa (Ba0.989Gd0.011)(Ce0.859Gd0.141)O2.935 (Ba0.993Yb0.007)(Ce0.856Yb0.144)O2.932
Ba:(M+Ce) by
microprobe analysisa 0.976(12) 0.996(12)
Composition by
Microprobe analysisa (Ba0.988Gd0.012)(Ce0.860Gd0.140)O2.936 (Ba0.998Yb0.002)(Ce0.852Yb0.148)O2.927 a: cited from Chapter 3.
The results of Tables 4-4 to 4-6 reveal several important points. Most significant is that measurable dopant site partitioning indeed occurs, with the frac parameter differing from a value of 1 by several standard deviations for both composition.
Furthermore, as anticipated and consistent with previous studies, the extent of Yb incorporation onto the A site (~ 4%) is less than Gd incorporation onto that site (~ 13%).
From the analysis of the cell volumes in Chapter 3, the extent of Yb, Gd and Nd incorporation onto the Ba site was inferred to be 4.6, 7.2, and 14%, respectively, the first two values being in reasonable agreement with the present EXAFS results. Similarly qualitative, though not quantitative, agreement is found with the results of the electron microprobe chemical analysis. The chemical analysis measurements showed Ba:(Ce+M) molar ratios of 0.996, 0.976 and 0.913 for Yb, Gd, and Nd, respectively, whereas the ratios implied by the EXAFS results for the first two dopant species are 0.989 and 0.961, respectively (at 10 K). Although the EXAFS Nd experiments could not be performed, one can extrapolate from these results and conclude that Nd incorporation onto the Ba site would be greater than the 13% measured here for Gd, and the Ba:(Ce+M) ratio lower than 0.961. As a consequence of the dopant partitioning, the concentration of oxygen vacancies is reduced, as inferred from the EXAFS analysis, from the desired value of 7.5 mol% of the oxygen sites [ = ½ the dopant concentration] to ~ 7% for Yb and ~ 5.5% for Gd.
A second important observation is that, upon doping, the structure of barium cerate undergoes local distortions. That is, the distances from the central dopant atom to the nearest neighbors differ from the comparable distances in undoped barium cerate.
This distortion results directly from the size “mismatch” between Ba, Ce and the dopants.
Furthermore, because the difference in ionic radii is relatively small between Ce and the dopants, the distortion about the B site is substantially less than that about the A site. The mean Ce-O distance in undoped barium cerate is 2.241(4) Å, whereas Gd-O and Yb-O distances for the dopants on the cerium site are 2.298(4) and 2.239(5) Å, respectively. In contrast, the comparable mean A-O distances are 3.13(30), 2.467(2) and 2.418(3) Å for Ba, Gd and Yb, respectively. It is noteworthy that introduction of Yb onto the Ce site, in fact, produces almost no local changes in average bond distances. This, combined with the fact that the extent of Yb incorporation on the Ba site is small, indicates that the observed decrease in cell volume upon Yb doping, Fig. 3-4, is primarily attributable to oxygen vacancies which presumably have a smaller effective ionic radius than occupied oxygen sites 72. These kinds of detailed observations demonstrate the strength of the EXAFS method over conventional X-ray powder diffraction for the study of defect chemistry. The powder diffraction pattern reveals the average structure, which changes only slightly upon dopant introduction. In contrast, the EXAFS spectrum is highly sensitive to the local structure through distinct changes in the sharp features of the radial distribution function.
A final result to note from the data of Figs. 4-4 to 4-7 and Tables 4-4 and 4-5 is the significantly lower thermal disorder in the samples examined at 10 K than at room temperature. In particular, the spectra in Figs. 4-4 and 4-6 are sharper than those of Figs 4-5 and 4-7. The derived Debye-Waller factors, σ2, being slightly smaller for the 10 K refinements, reflect this difference in disorder. The other parameters, however, are comparable for the two temperatures, suggesting no unusual effects on cooling (Tables 4- 4, 4-5).