ARTICLE IN PRESS
D.A. Zyuzin et al. / Journal of Solid State Chemistry 179 (2006) 2965–2971
2969
This suggests that in a similar way ordered defects—
polysynthetic twins observed by TEM in zirconia samples
calcined at 600–650 1C are able to suppress the Raman
spectra.
In agreement with this hypothesis, disappearance of
polysynthetic twins in samples calcined at 750 and 1000 1C
recovers the Raman spectra, while the IR bands position
and splitting remain practically unchanged (Figs. 2 and 4).
units. Coordinates x , y n z were derived by corresponding
i
i
i
calculation from the atom coordinates in the monoclinic
zirconia unit cell. In each modeling series, two types of
layers were used, including one described above (layer 1)
and another related by the mirror reflection in the (001)
plane (layer 2). The layer thickness was constant, and, as
variables, the relative number of layers and their stacking
order were used.
Fig. 6 shows model diffraction patterns with different
alternation probabilities of layers 1 and 2 at the each layer
thickness equal to the c parameter of the monoclinic phase
unit cell (C ¼ c) and an equal number of both types of
layers (W ¼ W ¼ 0.5). In the case of the strict alternation
3
. Modeling of XRD patterns
For dispersed materials, appearance of new peaks is
known to be often generated by their disordering [29]. The
1
2
˚
˚
order (after layer 1 only layer 2 appears, and vice versa,
monoclinic structure of ZrO (a ¼ 5.315 A, b ¼ 5.208 A,
2
˚
P
11 ¼ 0), the diffraction pattern contains a peak at position
corresponding to the (111) peak of the cubic phase (Fig.
.1). In this model diffraction pattern, the peaks corre-
c ¼ 5.148 A; b ¼ 99.2o, S.G. P2 /c) [30] can be considered
1
%
as comprised of alternating layers of oxygen and zirconium
ions situated along the (001) plane. For samples calcined at
6
¯
sponding to (111) and (111) reflections of the monoclinic
phase are absent. As P11 increases, the diffraction peak
broadens (Fig. 6.2 and 6.3), and when only identical layers
alternate (the twinned particle contains only one twinning
plane), the diffraction pattern corresponds to the mono-
clinic phase (Fig. 6.5). Hence, at a given layer thickness, it
is impossible to obtain the diffraction pattern containing
reflections of both cubic and monoclinic phases.
6
00–650 1C, HRTEM data revealed [13] polysynthetic
twins, so that crystallites are comprised of the alternating
slabs with a mirror symmetric structure. Here, the
thickness of slabs, their stacking and alteration can vary.
By using the program for simulation of the diffraction
patterns of layered structures [15], diffraction patterns
from polysynthetically twinned particles of the monoclinic
˚
ZrO with sizes up to 300 A have been computed.
2
For the triplicate layer thickness (C ¼ 3c), keeping
number of different layers equal (W ¼ W ¼ 0.5), diffrac-
The starting data for calculation include distribution of
atoms in two-dimensionally ordered layers; number of
types of different layers (W ); their stacking order
determined by the probability of appearance of a K-type
layer after a M-type layer (PKM).
1
2
tion peaks corresponding by position to both monoclinic
and cubic phases are observed (Fig. 7.1). With the increase
of P , the peak corresponding to the cubic phase is
N
11
smeared, though its integral intensity is preserved until its
complete disappearance (Fig. 7.2–4). Only when the
relative number of different layers in the particle is changed
In the two-dimensional ordered layer, the distribution of
atoms was determined by parameters of the two-dimen-
sional unit cell (A, B, angle b), the layer thickness C,
coordinates x , y , z in the relative units with respect to A,
(
W ¼ 0.3; W ¼ 0.7) while the layer thickness is preserved,
1
2
i
i
i
the ratio of the integral intensities of ‘‘cubic’’ and
‘monoclinic’’ diffraction peaks decreases (Fig. 8). The
B, C parameters.
‘
In our case, for the direction of the uniaxial disordering,
the [001] direction was chosen as a direction of the oxygen
layers stacking (Fig. 5). The unit cell parameters of the
two-dimensional layer—A, B, and b were equal to
parameters a, b, and b of the monoclinic ZrO structure.
2
In different series of modeled diffraction patterns, the layer
thickness C was equal to 1, 2 or 3 monoclinic structure
Fig. 6. Simulated diffraction patterns for model particles of zirconium
dioxide: A ¼ a, W ¼ 0.5: 1—P11 ¼ 0, 2—P11 ¼ 0.5, 3—P11 ¼ 0.6, 4—
¼ 0.8, 5—P ¼ 1.0.
1
Fig. 5. The layered structure of the oxygen sublattice of monoclinic ZrO
2
.
P
11
11