Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air
The consequent of mathematical models with elements of theory probability and experimental results, calculations permitted to determinate the energy formation of: anion vacancies (uв∼0.9 eV), border and screw dislocations (u⊥∼ 1.67 eV; us ∼ 2.08 eV), and the energy of movement point defects (ud∼ 1.8...
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Науковий фізико-технологічний центр МОН та НАН України
2011
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irk-123456789-769982015-02-15T03:01:57Z Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air Solovyova, A.E. The consequent of mathematical models with elements of theory probability and experimental results, calculations permitted to determinate the energy formation of: anion vacancies (uв∼0.9 eV), border and screw dislocations (u⊥∼ 1.67 eV; us ∼ 2.08 eV), and the energy of movement point defects (ud∼ 1.8 eV) and of movement the borders grain (uз ∼ 0.65 eV), strain which were connected with cooperation action point defects with admixture (0.25 eV – energy of formation center painting) in CeO2 – x at high temperatures in air. The evaporation and disintegration harden solution on the base CeO2 – x were determinate on the base obtained facts the next structure cubic phases F – F1 – C. The process oxidation at 1500 °C accompanied of disappear the border, spiral dislocations and point defects. Последовательность математических моделей с елементами теории вероятностей и экспериментальные результаты расчеты позволили найти энергии образования: анионных вакансий (uв ~ 0.9 еВ), краевых и винтовых дислокаций (u⊥ ∼ 1.67 еВ; us 2.08 eВ) и энергию движения анионных вакансій (ud ∼ 1.8 eВ), энергию напряжения, которая связана с объединением точечных дефектов с примесями, энергию образования центров окраски в структуре CeO2–х при высоких температурах на воздухе. Восстановление и распад твердого раствора приводит к фазовому превращению и появлению фаз типа F – F1 – C. Процесс окисления при 1500 °C сопровождается исчезновением краевых, винтовых дислокаций, точечных дефектов. Послідовність математичних моделей з елементами теорії ймовірностей та експериментальні результати, розрахунки дозволили знайти енергію утворення: аніонних вакансій – точкових дефектів (uв ∼ 0.9 еВ), крайових та гвинтових дислокацій (u⊥ ∼ 1.67 еВ; us ~ 2.08 eВ) та енергію руху аніонних вакансій (ud ∼ 1.8 eВ), енергію напруження яка пов’язана з єднання точкових дефектів з домішками, енергію утворення центрів окраски (0.25 eВ) у CeO2–х при високих температурах у середі повітря. Випарювання та розпад твердого розчина на базі CeO2–x утримали фазові перетворення у структурі та появи фаз F – F1 – C . Процес окислення при 1500 °C супроводжу зникати крайових та гвинтових дислокацій, точкових дефектів. 2011 Article Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air / A.E. Solovyova // Физическая инженерия поверхности. — 2011. — Т. 9, № 4. — С. 369–375. — Бібліогр.: 14 назв. — англ. 1999-8074 PACS: 546.655.4: 536.42.11 http://dspace.nbuv.gov.ua/handle/123456789/76998 en Физическая инженерия поверхности Науковий фізико-технологічний центр МОН та НАН України |
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| description |
The consequent of mathematical models with elements of theory probability and experimental results, calculations permitted to determinate the energy formation of: anion vacancies (uв∼0.9 eV), border and screw dislocations (u⊥∼ 1.67 eV; us ∼ 2.08 eV), and the energy of movement point defects (ud∼ 1.8 eV) and of movement the borders grain (uз ∼ 0.65 eV), strain which were connected with cooperation action point defects with admixture (0.25 eV – energy of formation center painting) in CeO2 – x at high temperatures in air. The evaporation and disintegration harden solution on the base CeO2 – x were determinate on the base obtained facts the next structure cubic phases F – F1 – C. The process oxidation at 1500 °C accompanied of disappear the border, spiral dislocations and point defects. |
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Article |
| author |
Solovyova, A.E. |
| spellingShingle |
Solovyova, A.E. Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air Физическая инженерия поверхности |
| author_facet |
Solovyova, A.E. |
| author_sort |
Solovyova, A.E. |
| title |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air |
| title_short |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air |
| title_full |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air |
| title_fullStr |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air |
| title_full_unstemmed |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air |
| title_sort |
modeling the mechanism of interaction of defects is in ceo2-x at high temperatures in air |
| publisher |
Науковий фізико-технологічний центр МОН та НАН України |
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2011 |
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http://dspace.nbuv.gov.ua/handle/123456789/76998 |
| citation_txt |
Modeling the mechanism of interaction of defects is in CeO2-x at high temperatures in air / A.E. Solovyova // Физическая инженерия поверхности. — 2011. — Т. 9, № 4. — С. 369–375. — Бібліогр.: 14 назв. — англ. |
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Физическая инженерия поверхности |
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2025-07-06T01:23:17Z |
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2025-07-06T01:23:17Z |
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1836858734086717440 |
| fulltext |
369
INTRODUCTION
The grain boundaries in polycrystalline com-
pounds are imperfections in the crystal structure,
which promotes the release of a new phase in
polymorphic transformations during decompo-
sition of solid solutions [1].
The study of the processes of interaction of
grain boundaries with vacancies, with impurity
atoms and dislocations is an important task for
creating materials with specific properties [2].
The lack of direct observations, which could
explain the mechanism of interaction of defects
with grain boundaries in polycrystalline mate-
rials, indicate the difficulty of the experiments
are therefore used data obtained from indirect
experiments of interaction boundariіes with im-
purity atoms and defects in oxide compounds [3
– 5].
Difficulties in determining the strength of in-
teraction of defects (vacancies, impurity atoms
and dislocations) and grain boundaries consist
of a complex process. In addition to the elastic
interaction, it also depends on the thermody-
namic potentials, that arise is due to the appea-
PACS: 546.655.4: 536.42.11
MODELING THE MECHANISM OF INTERACTION OF DEFECTS IS IN CeO2-x
AT HIGH TEMPERATURES IN AIR
A.E. Solovyova
Sumy State University, Ukraine
Received 30.10.2011
The consequent of mathematical models with elements of theory probability and experimental results,
calculations permitted to determinate the energy formation of: anion vacancies (uв∼ 0.9 eV), border
and screw dislocations (u⊥ ∼ 1.67 eV; us ∼ 2.08 eV), and the energy of movement point defects
(ud∼ 1.8 eV) and of movement the borders grain (uз ∼ 0.65 eV), strain which were connected with co-
operation action point defects with admixture (0.25 eV – energy of formation center painting) in
CeO2 – x at high temperatures in air.
The evaporation and disintegration harden solution on the base CeO2 – x were determinate on the base
obtained facts the next structure cubic phases F – F1 – C. The process oxidation at 1500 °C accompanied
of disappear the border, spiral dislocations and point defects.
Keywords: mathematical models, theory probability, process oxidation, point defects, spiral
dislocations, disintegration harden solution.
Последовательность математических моделей с елементами теории вероятностей и экспери-
ментальные результаты расчеты позволили найти энергии образования: анионных вакансий
(uв ~ 0.9 еВ), краевых и винтовых дислокаций (u⊥ ∼ 1.67 еВ; us 2.08 eВ) и энергию движения
анионных вакансій (ud ∼ 1.8 eВ), энергию напряжения, которая связана с объединением точечных
дефектов с примесями, энергию образования центров окраски в структуре CeO2–х при высоких
температурах на воздухе. Восстановление и распад твердого раствора приводит к фазовому
превращению и появлению фаз типа F – F1 – C. Процесс окисления при 1500 °C сопровождает-
ся исчезновением краевых, винтовых дислокаций, точечных дефектов.
Ключевые слова: математические модели, теория вероятности, процесс окисления, точечные
дефекты, винтовые дислокации, распад твердого раствора.
Послідовність математичних моделей з елементами теорії ймовірностей та експериментальні
результати, розрахунки дозволили знайти енергію утворення: аніонних вакансій – точкових
дефектів (uв ∼ 0.9 еВ), крайових та гвинтових дислокацій (u⊥ ∼ 1.67 еВ; us ~ 2.08 eВ) та енергію
руху аніонних вакансій (ud ∼ 1.8 eВ), енергію напруження яка пов’язана з єднання точкових
дефектів з домішками, енергію утворення центрів окраски (0.25 eВ) у CeO2–х при високих
температурах у середі повітря. Випарювання та розпад твердого розчина на базі CeO2–x утри-
мали фазові перетворення у структурі та появи фаз F – F1 – C . Процес окислення при 1500 °C
супроводжу зникати крайових та гвинтових дислокацій, точкових дефектів.
Ключові слова: математичні моделі, теорія ймовірності, процес окислення, точкові дефекти,
гвинтові дислокації, розпад твердого розчина.
A.E. Solovyova, 2011
ФІП ФИП PSE, 2011, т. 9, № 4, vol. 9, No. 4370
rance of the boundary of the concentration gra-
dients, as well as, electronic and chemical inte-
ractions, that occur noticeably at a considerable
distance from the grain boundary [6].
One of the most important properties of the
grains is their ability to move (migration) due to
the influence of the effort, the interaction of im-
purity atoms, temperature, environment, etc. The
sequence of movements of individual boundaries
is a source of information about the structure of
crystals [7].
In [8] provides information about what certa-
in deviation from regular order in structure con-
trol of phase transformations of cerium dioxide
at high temperature annealing in air and vacuum.
In the present work use mathematical models
with elements of theory probability for the defi-
nitions energy: the formation structural defects
in of cerium dioxide at high temperatures in air;
the interaction of grain boundaries with defects
and movement the borders grain; strain, which
were connected with co-operation action of the
different defects.
EXPERIMENTAL REZULTS
THE MATHEMATICAL MODELS WITH
ELEMENTS OF THEORY PROBABILITY
USE FOR THE FORMATION STRUC-
TURAL DEFECTS IN CERIUM DIOXIDE
AND INTERACTION BETWEEN THEM
The samples of cerium dioxide used for the stu-
dies were obtained by the technology [8, 9] at
1800 °C (3 hours), 1900 °C (3 hours), 2000 °C
(1 h), hardened in water.
They had: mostly single-phase cubic structure
of type F1 with larger unit cell parameters, and
small quantity of Сe2O3 in the samples tempered
from 2000 °C. All samples contained various de-
fects, and grain size (∼ 100 – 138 microns), res-
pectively.
The microstructure of these samples is shown
in fig. 1a; b; c; d: a) – samples obtained at 1800
°C had: wide grain boundaries, the color samples
was of dark brown, which indicates the formation
of anion vacancies, which trap the free electrons
and form the centers of paints; b) – the samples
obtained at 1900 °C contained: wide more angle
boundaries of the grains, edge dislocations with
the density equal ∼ 6⋅1013⋅1/m2, which form low
angle boundaries with different orientations to
the more angular borders, the color samples was
black; c) – microstructure of the grains samples
obtained at 2000 °C, included: the wide boun-
daries of grain, the screw dislocations with dif-
ferent orientations and, cracked, chipped grain,
color patterns was black.
Black paint samples obtained at 1900; 2000 °C
indicate on the formation of new centers of pa-
ints, and the presence of edge and screw disloca-
tions show growing stress in the samples.
The mechanism of formation defects in ce-
rium dioxide can be described of the next formula
СеО2 → Се1-х
4+ Сех
3 + О2–х/2 €х /2 ,
where, € – anion vacancy, x – a deviation from
regular order in structure .
Change the color of the samples at 1900 °С;
2000 °С due to the fact, that there is some proba-
bility of the process
Се3+ + € → Се4+ + centers of paints.
The more of these complexes are in structure
of cerium dioxide it is the stronger change the
color of the samples, the parameter of lattice in-
crease considerable form consist of Се3+. The in-
crease in the unit cell parameter of cerium dio-
xide in F1-phase indicates the formation of a solid
Fig. 1. The microstructure of samples of cerium dioxide, received of tempering from temperature: а) – 1800 °С,
X 340; b) – 1900 °С, X340; c) – 1900 °С, X17000; d) – 2000 °С, X340; e) – 2000 °С (3 hour), X340 – evaporation
of cerium dioxide.
a) b) c)
d) e)
MODELING THE MECHANISM OF INTERACTION OF DEFECTS IS IN CeO2-x AT HIGH TEMPERATURES IN AIR
371
solution with increasing stress in the lattice,
which lead to the formation of edge and screw
dislocations.
The experimental results showed, that at:
1800 °С (х = 0.202); 1900 °С (х = 0.308);
2000 °С – х = 0.500), where x – a deviation from
regular order in structure.
The microstructure of these samples showed,
that in cerium dioxide there is a certain complex
defects at each temperature. Probably, these pro-
cesses have the property of the ordinary and can
be consistently investigate.
CALCULATE OF THE ENERGY OF
MIGRATION BOUNDARY OF THE GRAIN
Perhaps, the energy of formation of the anion
vacancy, the centers of paints, the dislocations,
the migration boundary grain and the mobility
of defects in the structure determined by the
Boltzmann equation for various states of the
system: p[A(T)] = A0⋅exp (–u/kT), where А0 is
about – the total frequency of the oscillations of
atoms starting positions of the lattice, and A is a
function of the physical parameters of the system
depending on the temperature. For two states of
a solid at temperatures Т1;Т2 , use the relative pro-
bability of finding the energy states of a rigid
body can be determined:
p[A(T1)]/p[A(T2)] = exp(–u/kT1)/exp(–u/kT2), (1)
where: u – the energy state of a solid; k – Bolt-
zmann constant; that K – temperature solid state.
v1 = v0exp(–u/kT1); v2 = v0exp(–u/kT2 ), (2)
where v0 – the common velocity of movement
of defects, performed with the initial position;
A(T) = v1; v2 – the rate of the migration boundary
grain at different temperatures; u – the energy of
the migration boundary grain.
Relation:
v1/v2 = exp [– k
u
(1/T1 – 1/T2)], (3)
or
1 2 1
2 1 2
ln v u T T
v k T T
−=
; then
1 2 1
2 1 2
lnT T vu k
T T v
=
− . (4)
The energy of migration of grain can to de-
termine at the change of values of the grain of
samples at different temperatures or the velocity
of the migration boundaries of grain over a wide
temperature range of annealing.
The energy of migration boundaries of grain
in of cerium dioxide, determined by this method
is: ug ∼ 0.65 eV at 1800 – 1900 °С. The activa-
tion energy of the process recovery in cerium dio-
xide is uv ∼ 0.9 eV. Since these processes are in-
terrelated, it is obvious, can assume that the dif-
ference in uv – ug∼ 0.25 eV, and to obtain the
energy formation of centers of paints (anion vac-
ancy + electron) in the structure of cerium dio-
xide equal 0.25 eV. These relations, energy (mig-
ration of the grains; these centers of paints) are
connected with elastic stresses in the lattice of
cerium dioxide.
The energy of migration boundaries of grain
in of cerium dioxide at temperatures 1900 –
2000 °С it equal ug ∼ 0.85 eV. This value is com-
parable with the activation energy of the forma-
tion of anion vacancies, which indicates a signi-
ficant change in the chemical composition of the
cationic and anionic sub lattices of cerium dio-
xide, and the presence of edge and screw dislo-
cations in these samples indicate significant
plastic deformation.
Increased energy of migration of grains and
the presence of screw dislocations at 2000 °С is
the evidence about of evaporation cerium dioxi-
de, which proceeds with the transition in Се2О3-х
and its evaporation by screw dislocations.
According to [10], cerium oxide melts at abo-
ut ∼ 2150 °С. These data indicate that before mel-
ting cerium oxide evaporates in the form of non
regular order in structure of oxides.
CALCULATE OF THE ENERGY OF
FORMATION EDGE AND SCREW
DISLOCATIONS
On the deviation from regular order in structure
at temperatures of 1800° – 1900° – 2000 °С de-
fine the magnitude of the formation energy edge
and screw dislocations, the density of defects
determined from the experiment (fig. 1).
By formula (1) in the cerium dioxide can de-
termine the energy of formation of line defects,
where the quantity A(T) – x – deviation from the
regular order in structure of cerium dioxide at a
suitable temperature, u – formation energy of the
dislocation.
A.E. SOLOVYOVA
ФІП ФИП PSE, 2011, т. 9, № 4, vol. 9, No. 4
ФІП ФИП PSE, 2011, т. 9, № 4, vol. 9, No. 4372
The energy of formation of an edge dislo-
cation in cerium dioxide in 1800 – 1900 °С,
u⊥ ∼ 1.67 eV and the energy of a screw dislocation
in the interval 1900 – 2000 °С: uв ∼ 2.08 eV.
The magnitude of the formation energy of the
dislocation in the grains of cerium dioxide can
be estimated directly from the experience. Since
the experimentally observed shift of the unit cell
parameter for short distances, for small shear
strain, Hooke’s law is valid. Poisson’s coefficient
v = 0.515, the module shear for cerium dioxide,
according to [11] can be determined at different
temperatures by extrapolating the straight-line
relationship to the desired temperature set point.
Using these data can be to estimate the energy
of formation of edge dislocations on the formula,
as follows:
ud = ∫f⋅βdS, (5)
where f – average power (per unit area of S),
which is attached to a point on the surface of the
crystal during the process of displacement; β –
Burger vector of the dislocation [12 – 14].
As a result of these shifts occur in the crystal
lattice strain, which under certain values lead to
plastic deformation. The stresses in the crystals,
which are a function of bias, that leaded to the
formation of certain concentrations of disloca-
tions and may be determined by X-ray method
using the following equation:
00
0 0
2 1 0.515 a aa aE v
a a
−−σ = = µ +
∑ ,
(6)
where σ – stress in the crystal, E – Young’s mo-
dulus; ν – Poisson’s ratio; µ – shear modulus,
a – setting the unit cell strained cubic crystal,
a0 – the lattice parameter of the unstressed crystal.
Force f can be determined depending on:
f = ∑(σ2 – σ1)/ρ, (7)
where σ1; σ2; σ3 – stress in the crystal at different
temperatures; ρ – density of dislocations.
The energy of formation of dislocations is
determined consistently by the formula:
ud ∼ f ⋅(a2. – а1) – for an edge dislocation, (8)
ud ∼ f ⋅(a3 – a2) – for a screw dislocation,
where а1;2;3 – the lattice strain of a cubic crystal.
In this way the energy of formation have been
defined edge and screw dislocations, which occur
at 1900; 2000 °C, respectively.
The presence of screw dislocations in the
structure of cerium dioxide indicates the destru-
ction of the cationic in sub lattice and the be-
ginning of evaporation. The evaporation takes
place on the following reaction: solid solution
based on F1 with a certain amount of Се3+ enters
Се2О3-х, which evaporates on the screw disloca-
tions. In this form the dislocation pipes of various
diameters in height of the dislocation (fig. 1e)
and the length of the tube on both sides can see
the process of evaporation of cerium oxide, as
well as glide of the dislocations.
OXIDATION OF SAMPLES OF CERIUM
DIOXIDE AT LOWER TEMPERATURES
IN AIR
1) Samples of cerium dioxide, obtained at 1800
– 1900 – 2000 °С temperatures, were subjected
to oxidative annealing at lower temperatures in
air (1600 – 1400 °C – 20 hours).
It was found that the samples obtained at
1800 °C are oxidized. This process is accompa-
nied by a decrease in the lattice parameter and
the transition phase of type F1 → F.
By changing the unit cell parameter were de-
termined residual deviation from regular order
in structure at 1600 – 1400 °C and with help of
formula (1) is defined by the migration energy
of anion vacancies equal ud ∼ 1.8 eV at phase
transformation F1 → F.
The free energy migration of defect determi-
ned by the relationship:
F ∼ (ud – TSd), (9)
where ud – energy migration of defects, T – tem-
perature K; Sd – entropy.
The frequency of transition determined by:
vd ∼ Bv0exp(–ud/kT), (10)
where (10) is B – factor ∼ exp(Sd/k) > 1.
A defect in the crystal is moving in the direc-
tion of the force, the rate of this drift is described
by the Einstein relation
vd = Dd F/kT, (11)
where Dd ∼ D0exp(–Q/kT) – (the law of Flick),
(12)
Table 1
Т, К α*, nm σ, Н/m2 ρ, m–2 U, eV
2073 0,5417 15⋅107 – –
2173 0,5425 17⋅107 6⋅1013 1,67 ⊥ – edge
dislocation
2273 0,5435 27⋅107 3⋅1013 2,08 s - screw
dislocation
*α0 = 0,5409 nm. – phase type F 1 unstressed crystal.
MODELING THE MECHANISM OF INTERACTION OF DEFECTS IS IN CeO2-x AT HIGH TEMPERATURES IN AIR
373
where is D0 – called the frequency factor;
Q = (uv + ud) – the energy of activation.
The heterogeneity in the solid phase at tem-
peratures leads to the formation of gradients con-
centration of defects, it cause of force. Thus, the
Einstein relation leads to the flow of defects:
vd ∼ Dd⋅gradn, (13)
where Dd – is the coefficient diffusion of defects;
n – concentration of anion vacancies and for ce-
rium dioxide is: n ∼ x/4, coefficient D0 ∼ 9.5⋅10–5.
We find the parameters of the unit cell and
values x at the temperatures: x – at 1600 °C and
1400 °C and determine the velocity of flow:
at 1600 °C: vd ∼ 2⋅10–13 m2/s and velocity of
movement boundaries of grain ∼ 2.2⋅10–10 m/s;
at 1400 °С: vd ∼ 2.5⋅10–15 m2/s, velocity of mo-
vement boundaries of grain ∼ 1.4⋅10–10 m/s.
2) The samples, cerium dioxide, obtained at
1900 °С and with consisting of the borders dislo-
cations investigated by high-temperature X-ray
at 1500 °С in air with different exposures
(tabl. 2).
The exposures of simple at 1500 °С (30 –
240 minutes) observation a jump of parameter
of the phase cubic type F1 and appear on X-ray
lines characteristic for Се2О3 (fig. 2). The
intensity of these lines increases with increasing
exposure time to 360 minute, indicating a
significant concentration of this phase.
The microstructure of these samples is shown
in (fig. 3a, b, c, d).
After holding of the samples in during 120
minute was drift on the grain boundaries, and
the shift in one direction. Further holding of the
samples at this temperature leads to a square plate
on these borders and these crystals can be seen
as the lists an open book. Then there is a marked
increase in individual of the phase cubic type C
of cerium dioxide and the velocity increase equal
∼ 1.1⋅10–9 m/s. This value is an order of magnitude
greater than the rate of migration of grain
boundaries of cerium dioxide at temperatures of
1400 – 1600 °С, that indicates a large rate of
formation of free complexes containing Се3+, the
decay of solid solutions based on F1, which the
grating was very tense, and the microstructure
contains mixed the phases: F1 and C-type of ce-
rium oxide.
3) The samples, cerium dioxide, obtained at
2000 °С and with consisting of the screw dis-
Table 2
The values of parameters of phase F1-type
fluorite of cerium dioxide at 1500 °С in air
Tame exposures, min а, nm at direction [311]
30 0,5528
60 0,5528
120 0,5526
180 0,5525
240 0,5521
300 0,5521
360 0,5521
A.E. SOLOVYOVA
Fig. 2. X-ray diffractions of phase transformation F1-type
fluorite of cerium dioxide at 1500 °С in air, received
at: 1 – 60; 2 – 120; 3 – 240; 4 – 600; 5 – 1200 minutes,
• – the phase of F1-type, � – the phase C-type.
a) b)
c) d)
Fig. 3. The microstructure samples of phase F1 type fluorite
of cerium dioxide at 1500 °С in air: a) – 120; b) – 240;
c) – 600; d) – 1200, (tame exposures, minutes), X340.
ФІП ФИП PSE, 2011, т. 9, № 4, vol. 9, No. 4
ФІП ФИП PSE, 2011, т. 9, № 4, vol. 9, No. 4374
locations which was obtained at 2000 °С and
then annealed at 1500 °С in air with different
exposures (fig. 4). The oxidation process is
accom-panied by the gradual disappearance of
the rotation and screw dislocations, increasing
the width of the cracks and chips. Isolation of
C-type cubic phase of cerium oxide in these sam-
ples is considerably less, indicating that evapo-
ration of the cubic phase of C-type on the screw
dislocations at 2000 °С.
CONCLUSION
Modeling the mechanism of interaction of
defects is in CeO2–x at high temperatures in air,
was founded on the mathematical models with
elements of theory probability, which use for the
formation of the structural defects in cerium
dioxide and interaction between them.
The evaporation of cerium dioxide in interval
of temperatures 1800 – 2000 °С in air be
a)
b)
Fig. 4. The microstructure of samples of cerium dioxide,
which obtained at 2000 °С, and then annealed at 1500 °С
in the air: а) – 600, b) – 1200, ( tame exposures, minutes),
X340.
accompanied appearance definite complex of
defects (the boundary of grain – anions vacancy,
center of paint; the boundary of grain - border
and spiral dislocations).
The mathematical calculations and experi-
mental results, realization on the by high-tempe-
rature X-ray diffraction – the change of parame-
ters in the unit cell, composition of phases and
the microstructure of samples of cerium dioxide
as at evaporation, so and at oxidation per missed
to define the correctly methods at of interaction
of defects in structure of cerium dioxide.
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