H. Abe1,
2, K. Harada3, R. J. Matsuo3, H. Uwe3
and K. Ohshima3
1Department of Materials Science and Engineering, National Defense Academy,
1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
2Department of Physics, University of Houston, Houston, 77204-5506 Texas,
USA
3Institute of Materials Science, University
of Tsukuba, 1-1-1 Tennoudai, Tsukuba 305-8573, Japan
J. Phys.: Condens. Matter 13, 3257 (2001).
X-ray diffuse scattering for single crystals of
KTa1-xNbxO3 (x=0, 0.007 and 0.011) has
been measured. For the sample of x= 0.011, peculiar X-ray diffuse
scattering is observed above the phonon-frozen-in temperature (30K). By an
analysis of the diffuse scattering intensities, the average radius of the
ferroelectric microregions is found to grow up to around 4 nm with decreasing
temperature from 100K down to 30 K. Anisotropic distributions of the diffuse
scattering indicate off-centered shift of Nb and Ta ions to the<111>-direction.
Moreover, lattice constants for x=0.011 below 30 K exhibit negative expansion
which is found neither in pure KTaO3 nor in KTa1-xNbxO3 (x=0.007) at low-temperatures. These results are successfully explained
by introducing the effective classical potential (ECP) method for the anharmonic
oscillators. The quantum contribution to mean square displacement of Nb
and Ta ions from an average position is also calculated by the ECP method.
 |
Figure 1. Lattice constants of KTa1-xNbxO3
as
a function of Nb composition at room temperature. |
  |
Figure 2. (a) Lattice constants of KTa1-xNbxO3
as a function of temperature. Open circles, open squares and solid circles
are corresponding to x=0.000, x=0.007 and x=0.011, respectively. Each solid
line is calculated by using the effective classical potential (ECP) method
(see text), where only a solid curve in pure KTaO3 is calculated
using parameters in a previous paper [1]. (b) The temperature dependence
of the isotropic temperature factor, B(T). Open circles, open squares and
solid circles are corresponding to x=0.000, x=0.007 and x=0.011, respectively.
B(T) is determined by both of temperature dependence of integrated intensities
and lattice constants. Solid curves are calculated by using ECP method. |
 |
Figure 3. Temperature dependence of full width at half maximum (FWHM)
of 002 Bragg reflection along the radial direction in KTa1-xNbxO3
(x=0.011) (open circles). FWHM also increases below 30 K. To emphasize
the anomaly below 30 K, lattice constants (closed circles) are also seen. |
 |
Figure 4. Temperature dependence of diffuse scattering at =0.629
along the G002 + q [Ā 0 0] direction in KTa1-xNbxO3
(x=0.011), where the unit of q is reciprocal lattice one. A solid line
shows the summation of the calculated thermal diffuse scattering and Huang
diffuse scattering. While, a broken line shows the calculated thermal diffuse
scattering. |
 |
Figure 5. Temperature dependence of the calculated radius of FMR cluster,
Rcl. Rcl values along various direction are analyzed
by the self-consistent Monte Carlo method using the observed diffuse scattering. |
 |
Figure 6. Temperature dependence of (a) the observed diffuse scattering,
(b) the calculated one, (c) the calculated Huang diffuse scattering (HDS)
and (d) the calculated thermal diffuse scattering (TDS) along the G002
+ q [Ā 0 0] in KTa1-xNbxO3 (x=0.011). |
 |
Figure 7. Temperature dependence of the observed diffuse scattering
at 60 K along transverse- and longitudinal-directions around 002, 202 and
103 Bragg reflections. |
 |
Figure 8. The calculated distributions of Huang diffuse scattering
around 202 Bragg reflection using the shift of off-centered Nb, whose direction
is (a) [100]-direction, (b) [110]-direction and (c) [111]-direction. (d)
For comparison, the calculated distribution of thermal diffuse scattering
around 202 Bragg reflection is also shown. |
 |
Figure 9. q dependence of Huang diffuse scattering along the G002 +
q [0 0 ] at 60 K. An crossover point, qc, between q-2
and q-4, can provide the average size of FMR. It is estimated
to be around 10 nm. |
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