drawn with the refined crystallographic parameters [11]. This is the high-
temperature form of La
0.64
(Ti
0.92
Nb
0.08
)O
2.99
, which has an A-site-deficient
perovskite-type structure with double perovskite ABO
3–d
units along the
c axis (number of chemical formula in a unit cell: Z = 2), where A=La
0.64
and B = (Ti
0.92
Nb
0.08
). The occupancy factors for La at the La1 and La2 sites
are g(La1) = 1.00 and g (La2) = 0.271 [11]. The dissimilarity of these values
reflects the chemical ordering of La-occupied La1-O1 and La-defective La2-O2
layers [Fig. 6.7(a)]. All the refined atomic displacement parameters increase
with temperature (Table 6.2). The equivalent isotropic atomic displacement
parameters of the oxygen atoms are larger than those of the cations, suggesting
a larger diffusion coefficient for the oxide ions (Table 6.2). The oxygen atoms
also display large anisotropy in terms of atomic displacement parameters,
suggesting directionality in the movement of oxide ions around the stable
positions. Similar large and anisotropic thermal motions of oxide ions were
observed for the cubic perovskite-type oxide ion conductor (La
0.8
Sr
0.2
)-
(Ga
0.8
Mg
0.15
Co
0.05
)O
2.8
(Fig. 6.5) [10].
MEM analysis was conducted using diffraction data in the range 2y ¼4.08–1408,
corresponding to d > 1.0 A
˚
(d, spacing of lattice planes), with the structure
factors obtained by Rietveld analysis. A total of 59 structure factors were
obtained for all data measured at three different temperatures. The 001 reflec-
tion appearing at the lowest 2y position (138) was included, as this peak
provides information on the disordered arrangement of the oxide ions. MEM
calculations were performed with the unit cell divided into 64 64 128 pixels.
Use of the REMEDY cycle resulted in significant improvement in the R factors
based on the Bragg intensities (R
I
) and structure factors (R
F
) (Table 6.2). Figure
6.7(b, c, d) shows the isosurface of nuclear density and the nuclear density
distributions on the (100) and (001) planes obtained afte r the REMEDY cycle.
Figure 6.8 shows the temperature dependence of the nuclear density contour
map at z = 0.2 on the ab plane. Figures 6.7(b, c, d) and 6.8 provide much
information on the positional disorder and diffusion paths of mobile oxide
ions compared to the simple atomistic model (Fig. 6.7(a)).
At 769 K, the O3 atoms are localized near the stable 4i site (1/2, 0, 0.234). The
O3 atoms display small bulges in the <101> direction (B in Fig. 6.7(d)), which
become larger at 1281 and 1631 K (Fig. 6.7(c,b)). The probability density of
each O3 atom is connected with that of its nearest neighbor O3 atoms, indicat-
ing diffusion paths (A in Fig. 6.7(a, b)). The diffusion path is along the [100] or
[010] direction near the stable O3 positions, and along the [110] or ½1
10
direction around the center of the paths. The O3 atoms migrate to the nearest
neighbor 4i site through a triangle formed by adjacent La1, La2, and (Ti,Nb)
atoms. The spatial distribution of the O3 atoms becomes larger with increasing
temperature (Figs. 6.7 and 6.8). Such an increase in the density of oxide ions
with increasing temperature is consistent with the higher conductivity observed
at higher temperatures [21]. The O3 atom migr ates following a curved route to
maintain a relatively constant distance from the (Ti,Nb) atoms (solid curves
A in Figs. 6.7(a, b) and 6.8(a)), rather than a direct linear path along the <110>
6 Perovskite-Type Oxides and Related Materials 129