On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes
The dependency of ionic oxygen conductivity of 10Sc1CeSZ electrolyte made of different nanosized zirconia powders those differ by their impurities and manufacturing technologies, and sintered in air at different temperatures after uniaxial pressing are analyzed in terms of their Arrhenius equations...
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Інститут проблем матеріалознавства ім. І.М. Францевича НАН України
2013
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irk-123456789-635652014-06-04T03:01:27Z On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes Kyrpa, O.L. The dependency of ionic oxygen conductivity of 10Sc1CeSZ electrolyte made of different nanosized zirconia powders those differ by their impurities and manufacturing technologies, and sintered in air at different temperatures after uniaxial pressing are analyzed in terms of their Arrhenius equations in 250—850 °C temperature range. Deviation from a typical linear dependence of conductivity on temperature that is the most clearly visible in the electrolyte made of the purest powder is observed. The inflection point is determined by powder properties and is practically independent on sintering temperature. Йонна провідність електроліту 10Sc1CeSZ залежить від багатьох факторів, зокрема від способу виробництва порошку, анізотропного пресування нанорозмірних порошків в зразок і температури спікання зразків. Так, після спікання у повітрі при різних температурах порошку 10Sc1CeSZ різних виробників залежність його йонної провідності від температури 250—900 °С виражається через рівняння Арреніуса. Опис та аналіз відхилення від прямолінійного ходу залежності електропровідності є важливим аспектом розуміння і покращення властивостей електроліту. Так, точка перегину визначається властивостями порошку і практично не залежить від його температури спікання, тобто є важливою характеристикою матеріалу. Ионная проводимость электролита 10Sc1CeSZ зависит от многих факторов, в частности от способа производства порошка, анизотропного прессования наноразмерных порошков в образец и температуры спекания образцов. Так, после спекания на воздухе при различных температурах порошка 10Sc1CeSZ разных производителей зависимость его ионной проводимости от температуры 250— 900 °С выражается через уравнение Аррениуса. Описание и анализ отклонения от прямолинейного хода зависимости электропроводности является важным аспектом понимания и улучшения свойств электролита. Так, точка перегиба определяется свойствами порошка и практически не зависит от температуры спекания, то есть, является важной характеристикой материала. 2013 Article On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes / O.L. Kyrpa // Электронная микроскопия и прочность материалов: Сб. научн . тр. — К.: ІПМ НАН України, 2013. — Вип. 19. — С. 159-168. — Бібліогр.: 13 назв. — рос. XXXX-0048 http://dspace.nbuv.gov.ua/handle/123456789/63565 620.187:620.1 en Электронная микроскопия и прочность материалов Інститут проблем матеріалознавства ім. І.М. Францевича НАН України |
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The dependency of ionic oxygen conductivity of 10Sc1CeSZ electrolyte made of different nanosized zirconia powders those differ by their impurities and manufacturing technologies, and sintered in air at different temperatures after uniaxial pressing are analyzed in terms of their Arrhenius equations in 250—850 °C temperature range. Deviation from a typical linear dependence of conductivity on temperature that is the most clearly visible in the electrolyte made of the purest powder is observed. The inflection point is determined by powder properties and is practically independent on sintering temperature. |
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| author |
Kyrpa, O.L. |
| spellingShingle |
Kyrpa, O.L. On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes Электронная микроскопия и прочность материалов |
| author_facet |
Kyrpa, O.L. |
| author_sort |
Kyrpa, O.L. |
| title |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes |
| title_short |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes |
| title_full |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes |
| title_fullStr |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes |
| title_full_unstemmed |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes |
| title_sort |
on the temperature dependence of oxygen ionic conductivity of 10sc1cesz electrolytes |
| publisher |
Інститут проблем матеріалознавства ім. І.М. Францевича НАН України |
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2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/63565 |
| citation_txt |
On the temperature dependence of oxygen ionic conductivity of 10Sc1CeSZ electrolytes / O.L. Kyrpa // Электронная микроскопия и прочность материалов: Сб. научн . тр. — К.: ІПМ НАН України, 2013. — Вип. 19. — С. 159-168. — Бібліогр.: 13 назв. — рос. |
| series |
Электронная микроскопия и прочность материалов |
| work_keys_str_mv |
AT kyrpaol onthetemperaturedependenceofoxygenionicconductivityof10sc1ceszelectrolytes |
| first_indexed |
2025-07-05T14:20:36Z |
| last_indexed |
2025-07-05T14:20:36Z |
| _version_ |
1836817042090491904 |
| fulltext |
160
УДК 620.187:620.1
On the temperature dependence of oxygen ionic
conductivity of 10Sc1CeSZ electrolytes
O. L. Kyrpa
Frantcevych Institute for Problems of Materials Science, NAN Ukraine, Kyiv,
e-mail: 3.14pi@ukr.net
The dependency of ionic oxygen conductivity of 10Sc1CeSZ electrolyte made of different
nanosized zirconia powders those differ by their impurities and manufacturing
technologies, and sintered in air at different temperatures after uniaxial pressing are
analyzed in terms of their Arrhenius equations in 250—850 oC temperature range.
Deviation from a typical linear dependence of conductivity on temperature that is
the most clearly visible in the electrolyte made of the purest powder is observed. The
inflection point is determined by powder properties and is practically independent on
sintering temperature.
Keywords: oxygen ionic conductivity, DKKK, IPMS, Praxair powders, 10Sc1CeSZ
electrolyte, influence of sintering temperatur, grain size, activation energy.
Introduction
Cubic zirconia is a typical solid electrolyte for ceramic fuel cells during
more than one hundred years since its invention by Walter Nernst [1]. In this
solid electrolyte, the charge transport is realized by oxygen ions [2].
Historically, the oxygen conduction was first observed in fluorite structures
as John Goodenough has mentioned in his comprehensive review referencing to
Michael Faraday who had observed the fast ion conduction in the electronic
insulator PbF2 [3]. This observation is remarkable because all the tetrahedral
sites of the face-centered-cubic array of Pb2+ ions are fully occupied. The fast
F-ion conduction in PbF2 is due to saddle-point energy between the fully
occupied tetrahedral sites that is nearly the same as that of the tetrahedral sites.
The large charge on the O2- ion increases the coulomb repulsion between
anions and inhibits the coexistence of O2- ions in both saddle-point and
tetrahedral-site position in the MO2 fluorites, but the energy difference between
saddle-point and tetrahedral sites remains small, so the motional enthalpy ∆Hm
for an oxide ion to transfer to a neighboring oxygen vacancy is relatively low.
Bi2O3 has one-quarter of the tetrahedral sites vacant, i. e., c0 = 0,75 and these
vacancies are disordered in the high-temperature δ-Bi2O3 phase. Like Pb2+, the
Bi3+ ion contains a polarizable 6s2 core that reduces the motional enthalpy ∆Hm
for an oxide-ion transfer.
However, coulomb repulsions between the O2- ions stabilize long-range
ordering of the oxygen vacancies below a first-order order-disorder transition at
a temperature Tt. The long-range order creates distinguishable occupied and
empty sites separated by an energy ∆Hg. In this situation, thermal excitation of
anions into the vacancies introduces a disorder that lowers ∆Hg, which
introduces a temperature-dependent feedback:
∆Hg(T) = ∆Hg (O) = cδ. (1)
© O. L. Kyrpa, 2013
161
The data available show that oxygen ionic conductivity, as some thermo-
activated process, may be traditionally described by the typical Arrhenius
equation as
−⋅=σ
kT
E
AT aexp (2)
where σ is the ionic conductivity; T — temperature; A — pre-exponential
constant, and Ea is the activation energy. In general, some dependencies of the
pre-exponential constant and the activation energy on temperature might be
expected also.
The activation energy normally includes energies required for formation and
migration of oxygen vacancies in a perfect crystal. In the extrinsic regime,
the activation energy is dominated by the migration energy. In this case, the
activation energy might be represented by the migration energy for doped oxide
ionic conductors. If the oxygen vacancies are of a defect association within the
oxide, the dissociation energy that is required in order to break this complex at
high temperature has to be considered in the activation energy also.
Indeed, following the existing theory, which considers the ionic conduction
as ion hopping along defects of the crystal lattice, and according to Van Bueren
[4], the hopping frequency may be formally defined as
−⋅=
kT
Q
vv exp0
(3)
where Q is a free activation energy that may depend on temperature too.
By applying an electrical field E, the probability of hopping will become
anisotropic. In the simplest case, when positively charged ion has to move
between ions in isotropic lattice of distance a, it's hopping in direction of the
applying field E is favorable. It means that such the hoppings will occur with
higher frequency v'.
.exp 2
1
0
'
−−⋅ν=ν
kT
eaEU (4)
Against the field direction, the hopping frequencies �'' will be lower as
.exp 2
1
0
''
+−⋅ν=ν
kT
eaEU (5)
As result, at low electrical field when eaF << kT, the current density to be
determined as a total number of ions running in the field direction through an
area unit is
,expexp)
'''
( 2
1
2
1
0
+
−−
−
−⋅ν=ν−ν⋅=
kT
eaEU
kT
eaEU
neaneaj (6)
where n is a number of ions running through a volume unit.
The last equation may be rewriting as
.2exp 2
1
0
⋅
−⋅ν=
kT
eaE
sh
kT
U
neaj (7) f
The sh (x) may be expanded and limited to the first member:
....
!5!3)!12(
)(
53
0
)12(
+++=∑
+
=
∞
=
+ xx
x
n
x
xsh
n
n
(8)
162
After that procedure, the current density will be determined as follows:
.exp0
⋅
−⋅ν=
kT
eaE
kT
U
neaj (9)
Proceeding from the first principles, Walter Nernst [5, 6] had determined
the ionic conduction, σ, as
,µ=σ en (10)
where e and n are the charge and the concentration of its carriers, respectively,
and µ is the ionic mobility.
The ionic mobility may be defined as
./2 kTea ν=µ (11)
It is obvious,
./22 kTena ν=σ (12)
In this case, finally, the ionic conduction may be determined as
.exp 1
0
−⋅σ=σ
kT
U
(13)
Typical experimental data on conductivity of solid electrolytes of different
classes are shown in fig. 1. Most dependencies are linear. Among zirconia
electrolytes, scandia stabilized zirconia (ScSZ) has the highest conductivity.
The latest studies give contradictive data on oxygen ionic conductivity of
zirconia electrolytes stabilized with scandia, 10Sc1CeSZ especially, where
dependencies, which could be described either one or two lines, are observed
(fig. 2) [7, 8].
The purpose of the study was to examine the temperature dependence of
electrical conductivity of 10Sc1CeSZ electrolytes to be related to structural
features and mechanical behavior of different structure ensuring by different
powders and their sintering at different temperatures.
Experimental
10% (mol.) Sc2O3 and 1% (mol.) CeO2 (10Sc1CeSZ) solid electrolyte was
made of three different powders produced by IPMS, Ukraine, DKKK, Japan,
and Praxair, USA, and compared.
The comprehensive analysis of the powders and their ceramics is given in
[9—12]. Here, we remind briefly that the size of initial particles in IPMS’s
powder was 11 ± 2 nm; DKKK’s is 83 ± 20 nm, and Praxair's one is 141 ± 60 nm.
The concentration of impurities in the bulk of DKKK is only 0,001% (wt.),
which is one order of magnitude lower than the corresponding values for IPMS
and Praxair (0,01% (wt.)). IPMS powder contains mainly silica (0,05%) and
alumina (<0,025%) while in Praxair’s one silica (0,05%) and titania (<0,14%)
are present. From the point of surface-bulk distribution revealed with secondary
ion mass-spectrometry, in DKKK powder, the surface of particles is enriched
with Sc and Al; in Praxair one, Sc and Si are mostly present on the surface. In
IPMS powder, the surface is depleted with Sc; Si is localized inside particles.
SEM appearance of 10Sc1CeSZ powders is shown in [9—12]. It is seen
that agglomerates of IPMS powders consist of really nano-sized particles. Their
commercial analogs consist of much larger particles. DKKK powder is non-
agglomerated, but Praxair’s agglomerates are as chips of well-sintered
polycrystalline ceramics.
163
Fig. 1. Typical dependencies of electrical
conductivity vs. temperature for ionic
solid conductors [2].
Density of sintered samples was
measured with the Archimed’s
method. Grains size was measured
with ImageJ and Image Lab
programs of SEM images of sample
cross-sections.
Samples of ceramic electrolytes
were tested for their mechanical
behavior studying their fracture
micromechanisms with SEM and strength at biaxial three points
bend at room temperature.
The electrical properties of ceramic pellets (15 mm diameter) was
performed using AC impedance Solartron 1260 frequency response analyzer
in air in the temperature range 250—850 oC in the range of 6MHz—0,1Hz.
Platinum ink (Engelhard) was used for the electrodes coating on each side of
pellets, followed by annealing at 900 оC for 1 hour.
To determine the inflection point (point of intersection) of two lines, we
have developed an algorithm based on the method of least squares. Thus an
array of input points, a[N] crashed into two halves containing a different
number of elements b[M1], c[M2], but the total number of elements coincides
with the total number of elements in the input array M1 + M2 = N. On the
next step, was conducted in each area approximating straight to the method
of least squares. Next, calculated amount root mean square (rms) deviations
of two lines. Dynamically changing the number of elements in the arrays b,
from 2—N-2, and repeat iteration of the standard deviation obtained
Fig. 2. Typical dependencies of electrical conductivity
vs. temperature for 10Sc1CeSZ and 8YSZ electrolytes
usually used in SOFC [3, 4].
164
K[N-2] averages. Next, using the bubble sort method were the least value of total
deviation K[i]. That factor is clearly displays all essential factors of both lines.
Thus, analytically find the point of intersection of two lines and that will
determine the point of inflection.
,
;
;
11
21
222
111
kk
bb
t
bxky
bxky
k −
−=
+=
+=
(14)
where tk is the x-coordinate of the point of intersection.
Results and discussion
The powders had different ability to sintering [12]. Being sintered, e. g., at
1500 oC for 1,5 hour, DKKK samples had practically zero porosity, ~0,95 for
Praxair one and ~0,80 only for IPMS one. Fig. 3 demonstrates data on porosity,
grain size and biaxial strength of electrolyte samples sintered at different tempe-
ratures as well as their structures revealed with fracture at room temperature.
Uniaxially pressed 10Sc1CeScSZ—IPMS samples demonstrated less
sensitivity to the grain growth at high temperatures than 10Sc1CeScSZ—
Praxair and DKKK ones where the grain growth from 0,3 to 4 µm was detected
instead of 0,8—2,2 µm observed in IPMS electrolyte.
The highest biaxial strength (375 MPa) was obtained for 10Sc1CeSZ—
DKKK ceramics sintered at 1350 оC. The second highest value was obtained for
co-deposited 10Sc1CeScSZ—IPMS samples (250 MPa) sintered at 1500 оC.
The lowest biaxial strength was detected for 10Sc1CeScSZ—Praxair (220 MPa)
sintered at 1450 оC.
Sintered at 1500 оC and higher the 10Sc1CeScSZ—IPMS and Praxair
samples demonstrated the similar biaxial strength around 250 MPa while the
value of biaxial strength for 10Sc1CeScSZ—DKKK was only 150 MPa.
The cleavage fracture mechanism was detected for porous 10Sc1CeScSZ—
IPMS samples with no any changes with sintering temperature while DKKK
samples fail with mixed mode (cleavage and intergranular) and Praxair ones fail
with intergranular mechanism mainly.
So, ceramic electrolyte samples made of 10Sc1CeScSZ—IPMS powder are
less inclined to high temperature recrystallization than Praxair's and DKKK's
ones. Moreover, it was reported also [4, 7] that ceramics made of IPMS and
Praxair’s powders are practically insensitive to cold isostatic pressure (CIP)
applied to powder at formation of green ceramic bodies in comparison with
DKKK’s powder where increasing CIP pressure from 20 to 80 MPa results in
grain growth from 3—7 to 20—30 µ, and pores (up to 20 µ) and final dramatic
decrease of biaxial strength less 50 MPa.
As to the general conductivity, 10Sc1CeSZ electrolyte itself as well as its
temperature dependence demonstrate their strong dependencies on both type of
powders and sintering temperature resulting from presence and redistribution
of stabilizing additives and dopants, density/porosity, grain size and other
structural features (fig. 4). It is seen that samples sintered at 1300—1400 oC are
more sensitive to testing temperature than samples sintered at higher
temperatures, 1450—1550 oC.
165
a b
c
d
e
f
Fig. 3. Biaxial strength, grain size, porosity (a, c, e) and structure of fracture surfaces
(b, d, f) respectively of the uniaxially pressed samples of 10Sc1CeSZ electrolytes made
of IPMS (a, b), DKKK (c, d) and Praxair (e, f) powders sintered at different
temperatures in air.
а
b
c
Fig. 4. The ionic conductivity of 10Sc1CeSZ electrolytes made of IPMS (a) powder
sintered at 1250—1550 oC for 1,5 hour in air vs. temperature, the ionic conductivity
of 10Sc1CeSZ electrolytes made of DKKK (b) and Praxair (c) powder sintered at
1250—1550 oC for 1,5 hour in air vs. temperature.
Fig. 5 summarizes the temperature dependency of the ionic conductivity of
10Sc1CeSZ electrolyte made of different powders. It is seen that testing
temperature has different influence on low and high temperature parts of
the dependencies, and different activation energies Ea, respectively. Each
166
Fig. 5. The temperature dependencies of oxygen ionic
conductivity of 10Sc1CeSZ electrolytes made of IPMS,
DKKK and Praxair powders sintered at 1450 oC for
1,5 h in air: ■ — DKKK; ● — IPMS; ∆ — Praxair.
dependency has own an inflection point, position of which on the temperature
axis depends mainly on impurities: the purer 10Sc1CeSZ electrolyte the lower
temperature of inflection and clearer the inflection.
It is obvious that the temperature dependencies of electrical conductivity of
the 10Sc1CeSZ electrolyte cannot be described by the one linear dependency in
terms of the Arrhenius equation. Any corrections by taking into account, e. g.,
temperature dependence of the A coefficient, porosity and/or grain size were not
able "to straighten" the dependencies.
The temperature dependencies could be easily described by two Arrhenius
equations differing by their activation energies for low and high temperature
ranges separately. The inflection points, Tk, has been determined as the point of
intersection of its approximating straight lines, which might be defined by
minimizing the mean square deviation of experimental points from their
approximating lines in each low and high temperature intervals separately, i. e.,
before and after the inflection point.
In the two term description, the inflection point Tk might be determined
from two the Arrhenius equations:
−⋅σ=σ
kT
U1
1,01 exp (15)
and
Finally, the inflection point Tk is defined as the function
.exp 2
2,02
−⋅σ=σ
kT
U
(16)
.
ln
2,0
1,0
12
σ
σ⋅
−=
k
UU
Tk
(17)f
167
Fig. 6. The dependencies of the inflection points Tk
on temperature dependencies of the ionic
conductivity of 10Sc1CeSZ electrolytes made of
IPMS, DKKK and Praxair powders sintered at 1450
oC for 1,5 h in air on sintering temperature: ■ —
DKKK; ∆ — Praxair; ● — IPMS.
The surprizing independence, or very week dependence, of temperature of
the inflection Tk on sintering temperature is obvious (fig. 6). The positon of Tk
is determined mainly by the type of zirconia powder, and the amounts of its
alloying and doping elements.
As the most likely cause of such the behavior of the oxygen ionic conductivity
of 10Sc1CeSZ electrolyte is the phase transition between its cubic and
rhombohedral states that takes place in the temperature interval studied. The
inflection point, Tk, is, probably, the upper temperature limit of the cubic-
rhombohedral transition [6, 13], after which the structure becomes cubic totally.
Conclusions
The temperature dependencies of oxygen conductivity of 10Sc1CeSZ
electrolyte might be described by two Arrhenius equations with different
Fig. 7. Phase content of the electrolyte sample made of
DKKK 10Sc1CeSZ powder and sintered at 1200 oC
determined with XRD (Rietveld multiphase analysis) [6].
168
activation energies. It has no any visible correlation with their structural
parameters like grain size or porosity and mechanical behaviors. The inflection
point on the entire temperature dependency is mainly determined by type of
zirconia powder and is practically independent on sintering temperature. The
probable cause of such the behavior of electrolyte conductivity is its cubic-
rhombohedral phase transition.
Acknowledgements
The author gratefully thanks all members of the IPMS SOFC team for
fruitful discussions and financial supports from the National Academy of
Science of Ukraine, NATO "Science for Peace" Program, project N980878
"Solid oxide fuel cells for energy security" and EU FP6 project N020089
"Demonstration of SOFC stack technology for operation at 600 oC".
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Температурна залежність йонної електропровідності
цирконієвих електролітів 10Sc1CeSZ
О. Л. Кирпа
Йонна провідність електроліту 10Sc1CeSZ залежить від багатьох факторів,
зокрема від способу виробництва порошку, анізотропного пресування
нанорозмірних порошків в зразок і температури спікання зразків. Так, після
спікання у повітрі при різних температурах порошку 10Sc1CeSZ різних
виробників залежність його йонної провідності від температури 250—900 оС
виражається через рівняння Арреніуса. Опис та аналіз відхилення від
прямолінійного ходу залежності електропровідності є важливим аспектом
розуміння і покращення властивостей електроліту. Так, точка перегину
визначається властивостями порошку і практично не залежить від його
температури спікання, тобто є важливою характеристикою матеріалу.
Ключові слова: киснева йонна провідність, порошки DKKK, IPMS, Praxair,
електроліти 10Sc1CeSZ, вплив температури спікання, розмір зерна, енергія
активації,.
Температурная зависимость ионной проводимости
циркониевых электролитов 10Sc1CeSZ
O. Kирпa
Ионная проводимость электролита 10Sc1CeSZ зависит от многих факторов, в
частности от способа производства порошка, анизотропного прессования
наноразмерных порошков в образец и температуры спекания образцов. Так, после
спекания на воздухе при различных температурах порошка 10Sc1CeSZ разных
производителей зависимость его ионной проводимости от температуры 250—
900 оС выражается через уравнение Аррениуса. Описание и анализ отклонения
от прямолинейного хода зависимости электропроводности является важным
аспектом понимания и улучшения свойств электролита. Так, точка перегиба
определяется свойствами порошка и практически не зависит от температуры
спекания, то есть, является важной характеристикой материала.
Ключевые слова: ионная проводимость кислорода, порошки DKKK, IPMS, Praxair,
электролиты 10Sc1CeSZ, влияние температуры спекания, размер зерна, энергия
активации.
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