Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure
Ceramic materials based on complex oxides with both the perovskite structure (Ln₂/₃Nb₂O₆) and the structure of tetragonal tungsten bronze (Ba₆−xLn₈+₂x/₃Ti₁₈O₅₄) have been investigated over a wide frequency and temperature ranges. The results obtained for certain structures denote the presence of...
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irk-123456789-1207132017-06-13T03:03:12Z Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure Belous, A.G. Ovchar, O.V. Mischuk, D.O. Ceramic materials based on complex oxides with both the perovskite structure (Ln₂/₃Nb₂O₆) and the structure of tetragonal tungsten bronze (Ba₆−xLn₈+₂x/₃Ti₁₈O₅₄) have been investigated over a wide frequency and temperature ranges. The results obtained for certain structures denote the presence of the temperature anomalies of dielectric parameters (є, tan δ). These anomalies occur over the wide frequency range including submilimeter (SMM) wavelength range, and are related neither with the processing peculiarities nor with the presence of the phase transitions. Temperature behavior of the permittivity has been considered in terms of the polarization mechanism based on the elastic-strain lattice oscillations. It has been assumed that the observed anomalies could be ascribed to a superposition of harmonic and anharmonic contribution to lattice oscillations that determines τe sign and magnitude. Керамічні матеріали на основі оксидiв зі структурою перовскиту (Ln₂/₃Nb₂O₆) та тетрагональної вольфрамової бронзи (Ba₆−xLn₈+₂x/₃Ti₁₈O₅₄) дослiджувались в широкому частотному та діапазонах. Встановлено присутність температурних аномалій діелектричних параметрів (є, tan δ). Виявлені аномалії не пов’язані з технологічними особливостями та присутністю фазових переходів. Поведінка діелектричної проникності розглянута з позиції механізму поляризації, зв’язаного з пружно-деформаційними коливаннями кристалічної ґратки, i пояснюються взаємокомпенсуючим впливом гармонічних i ангармонiчних вкладiв у коливання кристалічної ґратки. 2003 Article Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure / A.G. Belous, O.V. Ovchar, D.O. Mischuk // Condensed Matter Physics. — 2003. — Т. 6, № 2(34). — С. 251-259. — Бібліогр.: 12 назв. — англ. 1607-324X PACS: 77.22.-d, 77.22.Ch DOI:10.5488/CMP.6.2.251 http://dspace.nbuv.gov.ua/handle/123456789/120713 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| description |
Ceramic materials based on complex oxides with both the perovskite structure
(Ln₂/₃Nb₂O₆) and the structure of tetragonal tungsten bronze
(Ba₆−xLn₈+₂x/₃Ti₁₈O₅₄) have been investigated over a wide frequency and
temperature ranges. The results obtained for certain structures denote
the presence of the temperature anomalies of dielectric parameters (є,
tan δ). These anomalies occur over the wide frequency range including
submilimeter (SMM) wavelength range, and are related neither with the
processing peculiarities nor with the presence of the phase transitions.
Temperature behavior of the permittivity has been considered in terms of
the polarization mechanism based on the elastic-strain lattice oscillations.
It has been assumed that the observed anomalies could be ascribed to a
superposition of harmonic and anharmonic contribution to lattice oscillations
that determines τe sign and magnitude. |
| format |
Article |
| author |
Belous, A.G. Ovchar, O.V. Mischuk, D.O. |
| spellingShingle |
Belous, A.G. Ovchar, O.V. Mischuk, D.O. Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure Condensed Matter Physics |
| author_facet |
Belous, A.G. Ovchar, O.V. Mischuk, D.O. |
| author_sort |
Belous, A.G. |
| title |
Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| title_short |
Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| title_full |
Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| title_fullStr |
Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| title_full_unstemmed |
Temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| title_sort |
temperature trends of the permittivity in complex oxides of rare-earth elements with perovskite-type structure |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120713 |
| citation_txt |
Temperature trends of the permittivity
in complex oxides of rare-earth
elements with perovskite-type structure / A.G. Belous, O.V. Ovchar, D.O. Mischuk // Condensed Matter Physics. — 2003. — Т. 6, № 2(34). — С. 251-259. — Бібліогр.: 12 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT belousag temperaturetrendsofthepermittivityincomplexoxidesofrareearthelementswithperovskitetypestructure AT ovcharov temperaturetrendsofthepermittivityincomplexoxidesofrareearthelementswithperovskitetypestructure AT mischukdo temperaturetrendsofthepermittivityincomplexoxidesofrareearthelementswithperovskitetypestructure |
| first_indexed |
2025-07-08T18:27:10Z |
| last_indexed |
2025-07-08T18:27:10Z |
| _version_ |
1837104346261618688 |
| fulltext |
Condensed Matter Physics, 2003, Vol. 6, No. 2(34), pp. 251–259
Temperature trends of the permittivity
in complex oxides of rare-earth
elements with perovskite-type structure
A.G.Belous, O.V.Ovchar, D.O.Mischuk
V.I.Vernadskii Institute of General and Inorganic Chemistry
32/34 Palladina Ave., 03680 Kyiv 142, Ukraine
Received September 4, 2002
Ceramic materials based on complex oxides with both the perovskite struc-
ture (Ln2/3Nb2O6) and the structure of tetragonal tungsten bronze
(Ba6−xLn8+2x/3Ti18O54) have been investigated over a wide frequency and
temperature ranges. The results obtained for certain structures denote
the presence of the temperature anomalies of dielectric parameters (ε,
tan δ). These anomalies occur over the wide frequency range including
submilimeter (SMM) wavelength range, and are related neither with the
processing peculiarities nor with the presence of the phase transitions.
Temperature behavior of the permittivity has been considered in terms of
the polarization mechanism based on the elastic-strain lattice oscillations.
It has been assumed that the observed anomalies could be ascribed to a
superposition of harmonic and anharmonic contribution to lattice oscilla-
tions that determines τε sign and magnitude.
Key words: dielectric permittivity, dielectric loss, microwave dielectrics
PACS: 77.22.-d, 77.22.Ch
1. Introduction
The growing demand for the microwave (MW) products induces the a need
of new ceramic materials that combine a high relative permittivity (ε � 1), low
dielectric loss (tan δ < 10−3) and a low temperature coefficient of permittivity
(τε = ±1−100 ppm/K). These materials are urgently required to reduce the size
and the weight of radio equipment. Recently, very promising temperature stable
ceramic materials with high permittivity (of about 100) have been developed on
the basis of the defect perovskite Ln2/3TiO3 (Ln is rare-earth element) [1,2]. This
structure contains 1/3 vacant positions in the lanthanum sublattice that permits
aliovalent substitution of the lanthanum ions by lower valence ions, for example,
alkali and/or alkaline-earth ions. When vacant sites are filled with alkali ions M+
c© A.G.Belous, O.V.Ovchar, D.O.Mischuk 251
A.G.Belous, O.V.Ovchar, D.O.Mischuk
– for instance, by sodium ions – according to the formula Ln2/3−xM3xTiO3, high-
permittivity dielectrics with the perovskite structure are formed [2].
When titanium ions in Ln2/3TiO3 are replaced by smaller niobium ions, a de-
fect perovskite structure Ln2/3Nb2O6 may be obtained [3,4]. This structure is sim-
ilar to Ln2/3TiO3, and exhibits high permittivity in the medium frequency range
(ε = 200 when Ln = La). However, there are few experimental data related to
MW dielectric properties of Ln2/3Nb2O6 which only assume that complex niobates
Ln2/3Nb2O6 may have negative τε in the vicinity of room temperature. Therefore,
one could expect that partial structure stabilization by sodium ions in the system
(1− 3x/2)Ln2/3Nb2O6 – 3xNaNbO3 may result in the temperature compensation of
the permittivity due to the positive sign of τε of antiferroelectric NaNbO3 close to
room temperature. It is known that the perovskite structure of niobates Ln2/3Nb2O6
could be also stabilized by either alkali or alkaline-earth ions [5,6]. However, complex
barium niobates formed in the latter exhibit ferroelectricity and high dielectric loss
at room temperature in the MW range [6] which forbids their utilization as MW
dielectrics.
In the case when a defect perovskite Ln2/3TiO3 is stabilized by alkaline-earth
ions, for instance barium ions, solid solutions Ba6−xLn8+2x/3Ti18O54 (known as bar-
ium lanthanide titanates – BLTs) with the structure of tetragonal tungsten bronze
are formed [7,8]. Both sign and magnitude of temperature coefficient τε of the above
materials strongly depend on chemical composition, particularly on the ionic radii
of rare-earth elements [7–9]. Moreover, in the materials Ba6−xSm8+2x/3Ti18O54, tem-
perature anomalies of the dependencies of the dielectric parameters (ε, tan δ) have
been revealed, and have shown a direct effect on the temperature coefficient τε [9].
However, physical backgrounds of the observed phenomena are still under discussion.
Therefore, the target of this work was to investigate dielectric properties (ε and
tan δ) of the promising high-ε materials based on complex oxides Ln2/3Nb2O6 (Ln
= La, Nd) and Ba6−xLn8+2x/3Ti18O54 (Ln = La, Nd, Sm) over the wide frequency
and temperature ranges, and to discuss the nature of temperature stabilization of
the permittivity.
2. Experiment
Polycrystalline samples, prepared by conventional ceramic technique, have been
examined. Extra pure and reagent grade oxides and carbonates were used as start-
ing reagents. The starting reagents were initially mixed and ball-milled in agate
bowls in acetone during 4 hours. The mixed blend was then dried and the powders
were calcined at 1000–1200 ◦C in the air, pressed, and sintered at 1300–1400 ◦C
during 2 hours in the air. The phase composition and the lattice parameters of
the materials were analyzed with x-ray powder diffraction (XRD) using a DRON 3
diffractometer and Cu Kα radiation. Temperature and frequency behavior of the
permittivity (ε), and dielectric loss tangent (tan δ) were measured by means of Q-
meters at the frequencies of 104–107 Hz, by means of coaxial line at the frequencies
of about 109 Hz, and by a modified-dielectric-resonator method at the frequency of
252
Temperature trends of the permittivity in complex oxides
1010 Hz. Submilimeter-wave (SMM) frequency measurements were carried out using
a backward-wave tube, by measuring the optical-path length and the absorption (α)
in a parallel-plate sample coated with a quarter-wavelength anti-reflecting coating.
3. Results
3.1. System (1 − 3x/2)Ln2/3Nb2O6 – 3xNaNbO3 (Ln = La, Nd)
The materials La2/3Nb2O6 and Nd2/3Nb2O6 are characterized by high permittiv-
ity of 130 and 160, respectively, and by relatively low dielectric loss in the MW range
(in both cases tan δ is of the order of (2−5) · 10−3). The results of measurements
of electrophysical properties of complex niobates Ln2/3Nb2O6 (Ln = La, Nd) over
wide frequency (106–1010 Hz) and temperature (−100 ◦C – +100 ◦C) ranges de-
note the change in the trends of temperature dependencies of the permittivity ε(T)
with increasing measurement frequency (figure 1). When the measurement frequen-
cy increases, τε value close to the room temperature (τε(20−100◦C)), which is about of
+100 ppm/K at 106 Hz, changes to –1000 ppm/K at 1010 Hz. Moreover, the diffuse
anomalous regions have been revealed for the first time on the temperature depen-
dencies of the permittivity of Ln2/3Nb2O6 collected at 1010 Hz (figure 1a). It should
be noted that the regions of the anomalies revealed are observed at low temperatures,
and shift for about 30 ◦C towards higher temperatures when changing rare-earth el-
ement from La to Nd. Again, the anomalies of the permittivity are accompanied by
the anomalies in the temperature dependencies of tan δ(T) (figure 1b). Most likely,
the nature of the anomalies observed is not related to the presence of spontaneously
polarized state because the variation of ε(T) in the vicinity of the anomalies does
not follow Curie-Weiss law.
According to the results of XRD analysis when introducing sodium ions into the
sublattice of rare-earth element in the systems (1− 3x/2)Ln2/3Nb2O6 – 3xNaNbO3
solid solutions with the perovskite structure are formed. When introducing sodium
ions into sublattice of rare-earth element, the permittivity continuously increases at
0 6 x 6 1/2, and reaches the values of 600 and 1000 at room temperature for the
lanthanum and neodymium containing solid solutions, respectively at x = 1/2 (fig-
ure 2). In the case of x > 1/2, the permittivity decreases towards the values of about
200 (NaNbO3). The dispersion of the permittivity has not been detected for all ma-
terials investigated within the frequency range of 106–1010 Hz. It should be noted
that for all materials studied the magnitude of tan δ continuously increases with
the increasing measurement frequency, and reaches 10−1 at the frequency 1010 Hz
which makes it impossible to use them at extra high frequencies (EHF). Measure-
ment results denote the change in the sign of temperature coefficient τε within the
compositional range corresponding to (1/3 6 x 6 1/2) in the case of La-containing
materials, and (1/2 6 x 6 7/12) in the case of Nd-containing analogues.
Both lanthanum and neodymium containing materials with the composition
(1 − 3x/2)Ln2/3Nb2O6 – 3xNaNbO3 at x > 1/2 have phase transitions above room
temperature which shift towards higher temperatures with the increase of sodium
253
A.G.Belous, O.V.Ovchar, D.O.Mischuk
Figure 1. Temperature dependencies
of the permittivity (1, 2) and dielec-
tric loss tangent (1′, 2′) of the materi-
als Ln2/3Nb2O6 (1, 1′ – Ln = La; 2, 2′
– Ln = Nd) measured at 1010 Hz.
Figure 2. Temperature dependencies
of the permittivity (1−5) and dielectric
loss tangent (1′ − 5′) of the materials
(1 − 3x/2)Ln2/3Nb2O6 – 3xNaNbO3;
x = 0 (1); 1/6 (2); 1/3 (3); 1/2 (4);
2/3 (5) – measured at 106 Hz.
Figure 3. Temperature dependencies of the permittivity of the materials (1 −
3x/2)Ln2/3Nb2O6 − 3xNaNbO3 (1, 1′ – Ln = La, x = 1/2; 2, 2′ – Ln = Nd,
x = 7/12) measured at 106 Hz (1, 2) and 109 Hz (1’, 2’) – dot line.
254
Temperature trends of the permittivity in complex oxides
content. It is interesting to note that unlike pure sodium niobate NaNbO3, tem-
perature dependence of the permittivity of these materials is characterized by both
noticeable hysteresis and by high residual polarization which occur after heating
a ceramic sample above the phase transition temperature (figure 3). The data in
the figure 3 have been obtained under conditions of slow heating and cooling rates
(2 ◦C/min). After heating above the temperature of the phase transition, followed
by slow cooling to room temperature, the permittivity magnitude increased by 200
to 500, and regressed for 50–60 hours. It should be noted that this behavior of the
permittivity remains unchanged up to the frequency of 109 Hz which denotes that
the observed behavior of the permittivity is not related to any effects of processing.
3.2. System Ba6−xLn8+2x/3Ti18O54 (Ln = La, Nd, Sm)
The materials of the system Ba6−xLn8+2x/3Ti18O54 (Ln = La, Nd, Sm) have
got a high permittivity from 70 up to 100 which slightly decreases with the di-
minishing ionic size of the rare-earth element. Within the solid solubility range of
Ba6−xLn8+2x/3Ti18O54, the diffuse maxima of ε(T) and the corresponding maxima
of tan δ(T) have been revealed for different rare-earth elements containing the ana-
logues corresponding to various x values (figure 4). At fixed ratio of composing
oxides (fixed x), the anomalies revealed a shift towards high temperatures when
the ionic radii of the rare-earth element decrease (figure 4). On the other hand,
for a certain rare-earth element (La, Nd, or Sm) the anomaly regions shift towards
high temperatures when the content of rare-earth ions decrease (i.e. increase in x)
(figure 5). It should be noted that similar behavior is observed in solid solutions with
Figure 4. Temperature dependen-
cies of the permittivity and dielec-
tric loss tangent of the materials
Ba6−xLn8+2x/3Ti18O54 (Ln = La, Nd,
Sm, Gd) measured at 1010 Hz.
Figure 5. Temperature dependencies
of the permittivity (1, 2) and dielec-
tric loss tangent (1′, 2′) of the materials
Ba6−xLa8+2x/3Ti18O54 (1, 1′ – x = 1.5;
2, 2′ – x = 2.0) measured at 1010 Hz.
255
A.G.Belous, O.V.Ovchar, D.O.Mischuk
Figure 6. Temperature dependencies
of dielectric permittivity in the mate-
rials (Ba1−yCay)5Sm8.3(3)Ti18O54 (x =
1.0) measured at 1010 Hz; y = 0 (1);
0.13 (2); 0.18 (3); 0.25 (4); 0.30 (5).
Figure 7. Temperature dependencies
of the imaginary component of permit-
tivity (ε′) at 96.7 GHz (1), 134 GHz (2)
in the materials Ba4.5La9Ti18O54 (x =
1.5) and Ba0.8Sr0.2La2Ti4O12 (3).
ferroelectric and antiferroelectric properties. However, in the case of BLTs, the hys-
teresis loop is not detected, and Curie-Weiss behavior is not observed in the vicinity
of the anomalies. Again, partial isovalent substitution of the A-site ions results in
the shift of the anomalies of ε(T) and tan δ(T) towards low temperatures with the
increasing content of substituting ion (Ca2+) (figure 6) which is accompanied by a
change in the sign of τε around room temperature.
The measurements in the submilimeter (SMM) wavelength range revealed diffuse
maxima in the temperature dependencies of both the absorption coefficient (α) and
the imaginary component of the dielectric constant (ε′) at exactly those tempera-
tures where the maxima of ε(T) were observed at microwaves (figure 7). The results
indicate the non-relaxation nature of the anomalies of the dielectric parameters, and
confirm that they are not related to the effects of processing.
4. Discussion
Both of the materials investigated are characterized by common structural frag-
ments: oxygen octahedra [(Ti,Nb)O6], which form an oxygen network. However, the
structure Ba6−xLn8+2x/3Ti18O54 contains different structural A-sites: trigonal sites
(empty), tetragonal sites (shared with barium and rare-earth ions), and pentago-
nal sites (filled with barium ions), whereas the A-sublattice of the defect perovskite
Ln2/3Nb2O6 contains only tetragonal sites. Again, both of the materials studied are
differed by the degree of octahedral tilting which is much higher in the tetragonal
tungsten bronze Ba6−xLn8+2x/3Ti18O54 [10]. Recently, the authors of reference 10
assumed the effect of anharmonicity of the lattice oscillations on temperature be-
havior of the permittivity in Ba6−xLn8+2x/3Ti18O54 solid solutions. Moreover, they
256
Temperature trends of the permittivity in complex oxides
further concluded the direct dependence of lattice anharmonism on the octahedral
tilting: the smaller is the degree of tilt the higher is the lattice anharmonism [10].
Whereas the permittivity of low-loss dielectrics in the MW range is mainly deter-
mined by the contribution of elastic-strain “infrared” polarization temperature, the
behavior of “infrared” permittivity could be discussed in terms of simple harmonic
oscillator model which also considers the anharmonic contribution into the harmonic
restoring force (fRi = −cixi) acting on an ion shifted for a distance xi under the
applied field (E). The magnitude of the harmonic restoring force fRi is equal to the
distorting force fDi = qiE, and, therefore, the elastic coefficient ci can be given as
ci = qE/xi. With the increasing temperature, the ionic interaction is reduced (xi in-
creases due to the increase in the unit-cell volume), which results in the lowering
of ci. The anharmonic contribution of the lattice oscillations to the restoring force
fR in the first approximation could be linearly dependent on the temperature com-
ponent βT , which gives us the following equation: fR = −(csum + βT )x [11], where
csum is the elastic coefficient characterizing the total contribution of the harmonic
components. Taking into account the equality of the distorting and the restoring
forces affecting the ion in the crystal lattice, qiE = (csum + βT )xi, the polarizability
of a single ion (αi = Pi/Ei = qixi/Ei = q2
i /(csum + βT )) is inversely proportion-
al to the restoring force. According to the above consideration, an increase in the
temperature would result in different effects: the first one is related to the lowering
of ci, which consequently leads to an increase in both polarizability αi and permit-
tivity (i.e., the effect of harmonic contribution), whereas the second one is related
to the temperature changes in anharmonic contribution βT (i.e., the effect of an-
harmonic contribution). The latter one causes an increase in the restoring force fR,
and, as a consequence, both the polarizability and the permittivity decrease with
the temperature in such a way that higher β values correspond to higher negative
values of the temperature coefficient of permittivity τε, where τε = (1/ε)(∂ε/∂T ).
Therefore, the ε(T) behavior can be interpreted as a superposition of two different,
competing contributions: an increase in permittivity with temperature (harmonic
contribution), and a decrease in permittivity with temperature (anharmonic con-
tribution). The resulting effect of these two contributions in a certain temperature
interval may be the reason for the anomalies observed on the dependencies of ε(T)
in the materials studied. It should be also noted that the above simple considera-
tion does not allow for either the cooperative interaction of different ions or for the
influence of electronic polarization on the “infrared” permittivity. However, a more
accurate explanation of the observed temperature behavior of permittivity may be
a target of further research.
An analysis of the measured data indicates that the temperature effect of the
anharmonic contribution βT is also related to the flexibility of the oxygen network.
In some tilted structures (BLTs with high average ionic size of A-site ions), the
increasing temperature facilitates the oxygen-network flexibility due to the increase
in the unit-cell volume [10]. This decreases the β value, and consequently, decreases
the slope of the curve ε(T). On the other hand, in highly straightened structures
(Ln2/3Nb2O6) the β value seems to be not temperature dependent, and the anhar-
257
A.G.Belous, O.V.Ovchar, D.O.Mischuk
monic component βT merely increases with the temperature. As a result, highly
straightened structures are characterized by ten times higher τε values in compari-
son with the tilted structures. This agrees well with the authors of reference 12 who
ascribed a weak effect of the dipolar mechanism, observed in the case of a tilted
structure, to the decreasing tilting amplitude. Partial isovalent substitution in the
A-sublattice, which diminishes the average size of A-site ions, increases the flexibil-
ity of the oxygen network. This may result in a slight shift of the ε(T) anomalies
towards low temperatures accompanied by degradation of ε(T) maxima (figure 6)
which enhances the temperature coefficient τε.
Thus, it may be concluded that temperature coefficient τε may be controlled by
varying the correlation between harmonic and anharmonic contributions into the
lattice oscillations which is possible by acting on the crystal lattice of the material.
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258
Temperature trends of the permittivity in complex oxides
Температурна поведінка діелектричної проникності
в складних оксидах рідкісноземельних елементів зі
структурою типу перовскиту
А.Г.Білоус, О.В.Овчар, Д.О.Міщук
Інститут загальної та неорганічної хімії ім. В.І.Вернадського
03680 Київ-142, просп. Палладіна, 32/34
Отримано 4 вересня 2002 р.
Керамічні матеріали на основі оксидiв зі структурою перовскиту
(Ln2/3Nb2O6) та тетрагональної вольфрамової бронзи
(Ba6−xLn8+2x/3Ti18O54) дослiджувались в широкому частотному та ді-
апазонах. Встановлено присутність температурних аномалій діелек-
тричних параметрів (ε, tan δ). Виявлені аномалії не пов’язані з техно-
логічними особливостями та присутністю фазових переходів. Пове-
дінка діелектричної проникності розглянута з позиції механізму по-
ляризації, зв’язаного з пружно-деформаційними коливаннями крис-
талічної ґратки, i пояснюються взаємокомпенсуючим впливом гар-
монічних i ангармонiчних вкладiв у коливання кристалічної ґратки.
Ключові слова: діелектрична проникність, діелектричні втрати,
НВЧ діелектрики
PACS: 77.22.-d, 77.22.Ch
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