Evolution of composition and fractal structure of hydrous zirconia xerogels during thermal annealing

Article abstract of DOI:10.1134/S0036023610020038

The mesostructure of amorphous hydrous zirconia xerogels and the products of their heat treatment was studied for the first time using powder X-ray diffraction and small-angle neutron scattering (SANS). The samples prepared at low and high pH values have

Full text of DOI:10.1134/S0036023610020038

ISSN 0036ꢀ0236, Russian Journal of Inorganic Chemistry, 2010, Vol. 55, No. 2, pp. 155–161. © Pleiades Publishing, Ltd., 2010.
Original Russian Text © V.K. Ivanov, G.P. Kopitsa, A.E. Baranchikov, S.V. Grigor’ev, V.M. Haramus, 2010, published in Zhurnal Neorganicheskoi Khimii, 2010, Vol. 55, No. 2,
pp. 160–166.
SYNTHESIS AND PROPERTIES
OF INORGANIC COMPOUNDS
Evolution of Composition and Fractal Structure
of Hydrous Zirconia Xerogels during Thermal Annealing
a
b
a
b
c
V. K. Ivanov , G. P. Kopitsa , A. E. Baranchikov , S. V. Grigor’ev , and V. M. Haramus
a
Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119991 Russia
Institute of Nuclear Physics, Russian Academy of Sciences, Gatchina, Leningrad oblast, 188300 Russia
b
c
GKSS Research Centre, Geesthacht, Germany
Received June 23, 2009
Abstract—The mesostructure of amorphous hydrous zirconia xerogels and the products of their heat treatꢀ
ment was studied for the first time using powder Xꢀray diffraction and smallꢀangle neutron scattering
SANS). The samples prepared at low and high pH values have fundamentally different phase compositions
(
and structures. The highꢀtemperature annealing of hydrous zirconia xerogels is useful for manufacturing
materials with controlled surface fractal dimensions.
DOI: 10.1134/S0036023610020038
Fractal geometry has recently came into use in varꢀ the chemical and phase composition and surface fracꢀ
ious fields of inorganic chemistry and materials sciꢀ tal dimension during the annealing of hydrous zircoꢀ
ence for the description of complex systems that have nia xerogels.
scaling symmetry, that is, a selfꢀsimilarity of compoꢀ
nents within a certain range of linear sizes. Fractal
dimension D, a quantitative characteristic of such sysꢀ
EXPERIMENTAL
Hydrous ZrO2 xerogels were prepared as follows: to
an aqueous solution of zirconyl nitrate ZrO(NO3)2
tems, is directly related to their structureꢀsensitive
properties, such as adsorption capacity, catalytic activꢀ
ity, and reactivity [1]. Importantly, in some cases fracꢀ
tal geometry principles offer the only means for quanꢀ
tifying the functional properties of compounds and
materials.
(
0.25 mol/L), aqueous ammonia (2.7 mol/L) was
added with stirring until the solution acquired a set pH
value (3, 6, or 9). The precipitates were centrifuged
from the mother solution, washed with distilled water,
and dried in air at 60°С for 6 h. Then, the xerogels were
annealed for 5 h at 270–600°С. In this way, for each
precipitation pH value five samples were prepared
An experimental quantification of the influence of
fractal dimension on the structureꢀsensitive properties
of physicochemical systems requires the existence of
processes for preparing materials with controlled surꢀ
face fractal dimensions where selfꢀsimilarity exists
over a wide range of sizes. The inspection of the related
literature shows that, although seeming diversified,
most of the existing processes for preparing fractal
structures are based on few models and experimental
procedures that have appeared as early as at the initial
stages of investigation of fractal manifestations in
physicochemical systems [2]. Methods employing
various particle aggregation modes in liquid and gas
phases have been mostly developed. However, these
methods are frequently unsuitable for preparing solidꢀ
phase materials or do not produce materials with
desired fractal dimensions.
using differing annealing temperatures ( a
80, 500, and 600°С).
Thermogravimetric analysis (TGA) and differenꢀ
T = 60, 270,
3
tial thermal analysis (DTA) were performed on a Pyris
Diamond (PerkinꢀElmer) thermal analyzer in the
range 20–1000°C in air. The heating rate was
1
0 K/min.
Powder Xꢀray diffraction analysis was carried out
on a Rigaku D/MAX 2500 diffractometer (Cu
K radiꢀ
α
ation). Diffraction peaks were identified with referꢀ
ence to the JCPDS database. The diffraction patterns
were recorded in the 5°–60° (2 ) range in 0.02° steps.
θ
Coherent scattering lengths for tetragonal and monoꢀ
clinic ZrO2 were determined from the Debye–Scherꢀ
rer relationship
Earlier [3, 4], we demonstrated that highꢀtemperaꢀ
ture annealing may be regarded as an efficient means
for altering the fractal properties of the material. In where
DCSL = 0.9λ / βcosθ
,
(1)
λ
is the Xꢀray wavelength and
β
is the widthꢀatꢀ
this work, we highlight the trends of the alteration of halfꢀheight of the diffraction peak.
155

156
IVANOV et al.
Smallꢀangle neutron scattering (SANS) was meaꢀ
(а)
sured on a SANSꢀ1 setup (FRG1 reactor, GKSS
Research Centre, Geesthacht, Germany) [6] operatꢀ
ing in a geometry close to point geometry. The neutron
wavelength
λ
= 8.19 Å; Δλ
/λ = 10%. The measureꢀ
ments were carried out at four sample–detector disꢀ
tances (SD = 0.7, 1.8, 4.5, and 9 m), which allowed
neutron scattering intensities to be measured in the
4
3
2
1
–3
momentum transfer range of 4.5
×
10
<
q
< 2.5
×
–
1
–1
3
1
0
Å . Scattered neutrons were detected by a He
positionꢀsensitive area detector.
ZrO2 H O samples were placed to 1ꢀmm quartz
glass cells. Asꢀrecorded spectra for each
⋅
x
2
q
range were
corrected for the scattering from the setup hardware,
cell, and ambience using a standard procedure [7].
The thusꢀobtained twoꢀdimensional isotropic spectra
were azimuthally averaged and reduced to absolute
magnitudes via scaling to the incoherent scattering
(
b)
cross section of 1 mm of water H O with account for
2
the detector efficiency [7] and bulk density
ρ
for each
b
sample. All measurements were carried out at room
temperature.
4
The SANS intensity Is(q) was determined in this
work as
3
2
1
I (q) = I(q) −TI (q),
(5)
s
0
Here,
I
(
q
)
and I0
(
q
)
are
q
distributions for scattered
neutrons behind the sample and for the beam without
(
– L)
Σ
test sample, respectively; and
transmission coefficient for neutrons behind the samꢀ
ple, where is the integrated cross section,
including nuclear scattering
T
=
I
/I0 = e
is the
20
30
, deg
40
Σ
=
σ
s
+
σ
a
2
θ
σ
s
and absorption a; and
σ
L
is the sample thickness.
Fig. 1. Fragments of Xꢀray diffraction patterns for samples
prepared by annealing ZrO2 H O xerogels at (a) 500 and
b) 600°С: (1–4) annealing products of the xerogel preꢀ
The setup resolution function was fitted to a Gausꢀ
sian and calculated separately for each SD distance
using a routine procedure [8].
⋅
x
2
(
pared at pH of 3, 6, 7.5, and 9, respectively.
RESULTS AND DISCUSSION
The contents of monoclinic (mꢀZrO2) and tetragoꢀ
nal (tꢀZrO2) phases in samples (xm and xt, respectively)
were derived from Xꢀray diffraction data using the xerogels decompose by a complex scenario. At temꢀ
Thermal analysis shows that all tested ZrO2
⋅
xH O
2
relationships found in [5]:
peratures below 220–240°C, the weight loss is excluꢀ
sively due to the elimination of sorbed and chemically
(2) bound water. A subsequent rise in temperature leads to
a noticeable increase in weight loss rate, which may
arise from the concurrent dehydration of the xerogels
I (111 + I (111)
m
m
x =
,
I (111) + I (111) + I (111)
m
m
t
1
.311x
ν =
m
,
(3)
and elimination of residual nitrato groups.
1
+ 0.311x
Powder Xꢀray diffraction shows that all asꢀsyntheꢀ
sized xerogels, as well as the samples annealed at
ν = 1 − ν ,
t
(4)
m
2
~
70°C for 5 h, are Xꢀray amorphous; broad maxima at
30 and ~50 –60°2 appear in the relevant diffracꢀ
tion patterns. Where the annealing temperature rises
tively; It(111) is the integrated intensity of the (111) to 380°С, the thermolysis product of the xerogels in all
peak of tꢀZrO2; and and
are the volume fracꢀ cases is tetragonal zirconia (tꢀZrO2). Lastly, the comꢀ
tions of monoclinic and tetragonal zirconia in the position of the annealing products at 500 and 600°С
Here, Im (111) and Im(111) are the integrated intensiꢀ
ties of the (111) and (111) mꢀZrO peaks, respecꢀ
°
°
θ
2
ν
ν
m
t
test sample.
considerably depends on xerogel preparation parameꢀ
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010

EVOLUTION OF COMPOSITION AND FRACTAL STRUCTURE
157
1000
1000
60
°
C
60°C
270
380
500
600
°
C
C
C
C
270
380
500
600
°
C
C
C
C
°
°
°
°
°
°
1
00
100
10
1
0
1
1
0.1
0.1
0.01
0.01
0.01
0.1
0.01
0.1
Momentum transfer
,
q,
Å–1
Momentum transfer, q,
Å–1
Fig. 2. Differential SANS cross section
d
Σ
(
q)/
d
Ω
for the
xerogel prepared at pH 3 and its annealing products. Here
and in Figs. 3 and 4, solid lines are bestꢀfit curves obtained
using Eqs. (6) and (7).
Fig. 3. Differential SANS cross section
d
Σ
(
q
)/
d
Ω
for the
xerogel prepared at pH 6 and its annealing products.
ters. In particular, as pH at which ZrO2
were precipitated increases, the percentage of monoꢀ annealing products is the existence of two
clinic ZrO2 mꢀZrO2) in the annealing products the scattering curves where the behavior of the smallꢀ
⋅
x
H O gels
A common feature of all xerogel samples and their
2
q
ranges on
(
increases systematically, whereas the tꢀZrO2 percentꢀ angle cross section
d
Σ
(
q
)/
d is dramatically different.
Ω
age decreases (Fig. 1). This effect is probably caused by In the range where
q
<
qc qc is the transition point from
(
the stabilization of tetragonal ZrO2 by residual nitrato one scattering mode to another), for all samples
–
n
groups [9]. Noteworthy, an increase in precipitation
pH also entails a decrease in particle sizes of the
tꢀZrO2 and mꢀZrO2 phases that are formed during the
thermal degradation of xerogels.
dΣ
(
q
)/
d
Ω
obeys the exponential law
q .
The exponent
n
values found from the slopes of linꢀ
ear segments of the experimental log–log
curves for the xerogels prepared at pH of 6 and 9 and
scattering curves their annealing products fall in the range from 3.38 to
for amorphous xerogel samples based on hydrous ZrO2 3.99, these values increasing in response to increasing
precipitated at pH of 3, 6, and 9, respectively) after gel precipitation pH and annealing temperature.
annealing at various temperatures Ta. For all xerogels When 3 < , this means that for all test samples
studied, regardless of precipitation pH, the scattering there is scattering from fractal surfaces with dimenꢀ
cross section )/ increases with rising Ta virtuꢀ sions of Ds = 6 – < 3. This result completely
ally over the entire range of the momentum transfers matches the previous observation [10] of scattering
studied ( ). Noteworthy, this increase is evidently nonꢀ from a porous structure with a fractal interface in
uniform and depends on Тa amorphous hydrous zirconia xerogels precipitated
d
Σ
(
q
)/
dΩ
Figures 2–4 display the
d
Σ
(
q
)/dΩ
(
n
≤
4
dΣ(q
dΩ
2
≤
n
q
.
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010

158
IVANOV et al.
xerogels and the products of their heat treatment at
70°С consist of aggregates with a well developed surꢀ
1000
2
face built of small monodisperse monomeric particles.
A further elevation of the annealing temperature to
60°C
270
380
500
600
°
C
C
C
C
380°С or higher brings about the appearance of a crysꢀ
°
°
°
talline phase whose particle sizes increase with Тa
.
100
These results match the aboveꢀdescribed powder Xꢀray
powder diffraction data. Comparing SANS data for
the asꢀprecipitated xerogels also shows that the incoꢀ
–1
herent scattering background for q > 0.03 Å increases
with precipitation pH indicating the increased conꢀ
tents of sorbed and chemically bound water of the
xerogels.
10
Scattering from amorphous samples that has been
annealed at or below
≤270°С was analyzed as [10, 11]
2
2
dΣ(q) = A(D )
q r
g
1
S
1
+ A exp(−
) + I ,
(6)
n
2
inc
dΩ
where A1 DS
being a function of the fractal dimension of the system
12] and the latter directly proportional to the product
q
3
(
) and A2 are free parameters, the former
[
of the number of monodisperse inhomogeneities in
the scattering volume and the density of neutron scatꢀ
0.1
tering amplitude
ρ
on these inhomogeneities [13]. The
ꢀindependent constant caused by
parameter Iinc is a
q
incoherent scattering on hydrogen atoms contained in
the sample in the form of chemically bound water.
0.01
In analyzing
d
Σ
(
q
)/
d
Ω
scattering curves for the
0.01
0.1
Å–1
samples annealed at temperatures equal to or higher
than 380°С with account for the appearance of a maxꢀ
Momentum transfer
,
q,
imum at
q
>
qc, we used the relationship
Fig. 4. Differential SANS cross section
d
Σ
(
q
)/
d
Ω
for the
dΣ(q) = A(D )
A3
1
S
+
+ I ,
(7)
xerogel prepared at pH 9 and its annealing products.
n
2
2 2
inc
dΩ
where A3
q
((q − qmax) + κ )
=
A0/rc is a free parameter, which is proporꢀ
from aqueous zirconyl nitrate solutions with pH above 6. tional to both the scattering length on nuclear density
Therefore, in further analysis of scattering for qc
fluctuations and the density of these fluctuations;
we used the twoꢀphase (solid–pore) model of a porous 1/rс is the reciprocal correlation radius of nuclear denꢀ
q
<
,
κ
=
structure with a fractal interface [10].
In the range where qc, the behavior of smallꢀ
angle scattering cross section )/ is an explicit
function of annealing temperature. At Тa 270°С, for
example, the scattering curves feature a soꢀcalled
shoulder indicating the existence of small monodisꢀ
sity fluctuations (inhomogeneities) on which scatterꢀ
ing occurs; and qmax corresponds to the maximum
position on the scattering curves. The second term in
relationship (7) is squared Lorenzian and satisfactorily
fits scattering on porous structures having a shortꢀ
range order. In the case at hand, the shortꢀrange order
in the solid phase and pores may be generated by interꢀ
q
>
dΣ(q
dΩ
≤
perse inhomogeneities with an effective gyration actions between particles of the crystal phase at early
radius of rg = (3/5)1 r0 (where 0
monodisperse inhomogeneities). A rise in annealing
temperature to 380°С or higher transforms this
/2
r
is the maximal size of stages of their formation [14].
To arrive at ultimate results, relationship (6) and
7) were convoluted with the setup resolution funcꢀ
≥
(
shoulder to a broad maximum, in our opinion, as a
result of the appearance of a shortꢀrange order in the
system.
tion. The experimentally determined differential scatꢀ
tering cross section data )/ were processed
dΣ(q
dΩ
using leastꢀsquares fits. The fitting results are shown in
Figs. 2–4 and Table 1.
Thus, the observed scattering pattern signifies the
existence of two types of scattering inhomogeneities in
These results show that DS, the surface fractal
the test samples, these inhomogeneities strongly difꢀ dimension, for the xerogels precipitated at pH 6 and 9
fering in characteristic scales. The asꢀprecipitated virtually does not change as the heatꢀtreatment temꢀ
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010

EVOLUTION OF COMPOSITION AND FRACTAL STRUCTURE
159
Table 1. Surface fractal dimensions DS for xerogels prepared at pH of 6, 7.5 [15], and 9 and for the products of their
thermal annealing
Annealing temperature,
380
°C
pH
60
270
500
600
6
2.18 ± 0.04
2.47 ± 0.04
2.62 ± 0.05
2.19 ± 0.03
2.48 ± 0.04
2.59 ± 0.04
2.12 ± 0.04
2.4 ± 0.05
2.55 ± 0.04
2.1 ± 0.04
2.29 ± 0.04
2.48 ± 0.04
2.01 ± 0.03
2.1 ± 0.05
2.4 ± 0.04
7.5
9
perature Тa increases from 60 to 270°С (Fig. 5). Simiꢀ a particle [11]. Assuming that the particles have flat
lar results were obtained for the samples prepared by surfaces, nuclear density will depend only on disꢀ
annealing ZrO2 H O xerogels that had been precipiꢀ tance from the surface to a point inside a particle.
tated at pH of 7.5 [15]. Thus, ZrO2 for our samples may be represented as
ρ
⋅
x
x
2
⋅
x
H O dehydration Thus, (x)
ρ
2
does not induce significant alterations in the xerogel
mesostructure. This is rather a nontrivial result,
because metal hydroxide hydrogels usually change
their structure during air drying as a result of capillary
forces. In particular, Stachs and Gerber [16] menꢀ
tioned that drying leads to the complete disappearance
of fractal properties in gels prepared by Zr(C H O)
4
ρ(x) = 0
x < 0
β
ρ(x) = ρ (x / α)
0 ≤ x ≤ α
(8)
0
ρ(x) = ρ0
x ≥ α
,
where
density
values increase monotonically with increasing
annealing temperature (Fig. 6).
α
is the layer thickness within which nuclear
3
7
ρ
increases from zero to 0, respectively. and
ρ
n
hydrolysis.
β
A further elevation of the annealing temperature of
the xerogels prepared at pH of 6, 7.5 [15], and 9 leads
to a smooth decrease in fractal dimensions. The
decrease in DS with fractal properties being mainꢀ
tained, in general, may be on account of surface
smoothing with the maintenance of the exponential
size distribution of structural elements. We observed
similar trends in fractal dimension during thermal
annealing for other oxide materials [17, 18]. Thus, the
highꢀtemperature annealing may be regarded as an
efficient means for preparing materials with controlled
surface fractal dimensions (to the value corresponding
to the smooth interface, i.e., DS = 2).
2
2
2
.9
.8
.7
pH 6
pH 7.5
pH 9
2.6
2.5
2.4
2.3
2.2
The mesostructure of a hydrous zirconia xerogel
prepared at pH 3 and the products of its heat treatment
differs considerably from the mesostructure of the
samples prepared at higher pH values. As mentioned
in [10], ZrO2 xH O gels precipitated from highly acid
⋅
2
solutions are nonfractal (DS = 2) and have very low
2
specific surface areas (Ssp < 1 m /g). Evidently, the
2.1
dehydration of such gels during heating will be accomꢀ
panied by structural alteration because of the appearꢀ
ance of a system of microcracks, which serve as chanꢀ
nels for removal of gaseous thermolysis products.
2
.0
.9
1
Indeed, SANS shows that the heating of a ZrO2
sample precipitated at pH 3 produced porous samples
with a soꢀcalled diffuse surface for which = 4 + 2
, where ≤ β ≤ is the exponent characterizing the
variation law of nuclear density in the surface layer of
⋅
x
H O
100 200 300 400 500 600 700
T , °C
2
a
n
β
>
4
0
1
Fig. 5. Fractal dimension DS vs. annealing temperature for
hydrous ZrO2 samples prepared at various pH values.
ρ
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010

1
60
IVANOV et al.
0
0
0
0
0
0
.30
.25
.20
.15
.10
.05
0
50
pH 3
pH 6
pH 9
40
30
20
10
0
–
0.05
100
200
300
400
Ta
, °C
500
600
100
200
300
Ta
400
, °C
500
600
Fig. 6. Exponent
with diffuse surfaces formed during the heat treatment of
the xerogel prepared at pH 3.
β
vs. annealing temperature for samples
Fig. 7. Maximal size of individual particles r0 vs. annealing
temperature for hydrous ZrO2 samples prepared at various
pH values.
In turn, r0, the maximal size of individual particles increase in Ta brings about a monotonic rise in r0 assoꢀ
corresponding to the lower selfꢀsimilarity bound of the ciated with the coarsening of crystalline zirconia parꢀ
surface fractal, experiences more complex evolution ticles, which is verified by Xꢀray diffraction.
during heat treatment (Fig. 7, Table 2). For example,
In summary, we have studied for the first time the
the decrease in particle size observed in response to the
mesostructure of amorphous hydrous zirconia xeroꢀ
change in annealing temperature from 60 to 270°С, is
likely due to the elimination of chemically bound and
sorbate water, as well as ammonium ions and nitrate
gels and the products of their heat treatment. We
have discovered that the heating behavior of a samꢀ
ple is fundamentally different depending on
ions sorbed on particle surfaces. In association, scatꢀ whether it was prepared at low or high pH. We have
–1
tering in the range of q > 0.03 Å decreases considerꢀ shown that the highꢀtemperature annealing of
ably compared to the asꢀprecipitated xerogel samples, hydrous zirconia xerogels prepared at various pHs is
evidently, because of the elimination of sorbate and useful for manufacturing materials with controlled
chemically bound water during annealing. A further surface fractal dimensions.
Table 2. Maximal sizes of individual particles r0 as determined by SANS
Annealing temperature,
380
°C
pH
6
0
270
500
600
3
6
9
16.5 ± 0.7
17 ± 0.7
10.7 ± 0.7ꢁ
12.3 ± 0.6
17.4 ± 0.5ꢁ
14.8 ± 0.6ꢁ
17.3 ± 0.5ꢁ
22.3 ± 0.6ꢁ
25.0 ± 0.6
27.1 ± 0.5ꢁ
33.4 ± 0.5ꢁ
38 ± 0.5ꢁ
38.7 ± 05ꢁ
43.5 ± 0.4ꢁ
21.8 ± 0.5
1
/2
ꢁ
Values obtained with r = π/q . The other values were derived using gyration radii as r = (5/3) r .
0 max 0 g
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010

EVOLUTION OF COMPOSITION AND FRACTAL STRUCTURE
161
ACKNOWLEDGMENTS
8. W. Schmatz, T. Springer, J. Schelten, and K. Ibel,
J. Appl. Crystallogr. , 96 (1974).
. S. Shukla and S. Seal, Int. Mater. Rev. 50, 45 (2005).
7
This work was supported by the Russian Foundaꢀ
tion for Basic Research (project nos. 09ꢀ03ꢀ
2191_ofiꢀm and 07ꢀ02ꢀ00290ꢀa).
9
1
0. G. P. Kopitsa, V. K. Ivanov, S. V. Grigoriev, et al., JETP
1
Lett. 85, 122 (2007).
1
1. P. W. Schmidt, Modern Aspects of SmallꢀAngle Scatterꢀ
ing, Ed. by H. Brumberger (Kluwer, Dordrecht, 1995),
p. 30.
REFERENCES
1
. A. Harrison, Fractals in Chemistry (Oxford Univ. Press, 12. H. D. Bale and P. W. Schmidt, Phys. Rev. Lett. 38, 596
Oxford, 1995).
(1984).
2
3
4
5
6
7
. W. G. Rotschild, Fractals in Chemistry (Wiley, New 13. A. Guinier and G. Fournet, SmallꢀAngle Scattering of
York, 1998).
XꢀRays (Wiley, New York, 1955), p. 17.
1
1
1
1
1
4. E. Z. Valiev, S. G. Bogdanov, A. N. Pirogov, et al., Zh.
. V. K. Ivanov, N. N. Oleinikov, and Yu. D. Tret’yakov,
Dokl. Akad. Nauk 386 (6), 775 (2002).
Eks. Teor. Fiz. 103, 204 (1993).
5. V. K. Ivanov, G. P. Kopitsa, S. V. Grigor’ev, et al., Fiz.
Tverd. Tela. (in press).
. V. K. Ivanov, O. S. Polezhaeva, G. P. Kopitsa, et al.,
Neorg. Mater. 44, 324 (2008).
6. O. Stachs and T. Gerber, J. SolꢀGel Sci. Technol. 15, 23
. H. Toraya, M. Yoshimura, and S. Somiya, J. Am.
Ceram. Soc. 67, Cꢀ119 (1984).
(1999).
7. V. K. Ivanov, N. N. Oleinikov, and Yu. D. Tret’yakov,
. H. B. Stuhrmann, N. Burkhardt, G. Dietrich, et al.,
Nucl. Instrum. Meth. A 356, 133 (1995).
Dokl. Akad. Nauk 386, 775 (2002).
8. V. K. Ivanov, A. N. Baranov, N. N. Oleinikov, and
Yu. D. Tret’yakov, Zh. Neorg. Khim. 47 (12), 1925
(2002) [Russ. J. Inorg. Chem. 47 (12), 1769 (2002)].
. D. Wignall and F. S. Bates, J. Appl. Crystallogr. 20, 28
(1986).
RUSSIAN JOURNAL OF INORGANIC CHEMISTRY Vol. 55 No. 2 2010