Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals
The exciton reflection spectra of Cs₃Bi₂I₉ layered crystals is investigated in the temperature region 4.2–300 K with light polarization E ⊥ c. It is estimated that the energy gap Eg equals 2.857 eV (T = 4.2 K) and the exciton binding energy Ry is 279 meV. A nontraditional temperature shift of...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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Machulin, V.F. Motsnyi, F.V. Peresh, E.Yu. Smolanka, O.M. Svechnikov, G.S. 2017-06-12T06:29:41Z 2017-06-12T06:29:41Z 2004 Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals / V.F. Machulin, F.V. Motsnyi, E.Yu. Peresh, O.M. Smolanka, G.S. Svechnikov // Физика низких температур. — 2004. — Т. 30, № 12. — С. 1283–1286. — Бібліогр.: 30 назв. — англ. 0132-6414 PACS: 64.70.Kb, 71.35.Cc, 78.40.Fy https://nasplib.isofts.kiev.ua/handle/123456789/120368 The exciton reflection spectra of Cs₃Bi₂I₉ layered crystals is investigated in the temperature region 4.2–300 K with light polarization E ⊥ c. It is estimated that the energy gap Eg equals 2.857 eV (T = 4.2 K) and the exciton binding energy Ry is 279 meV. A nontraditional temperature shift of Eg(T) for the layered substances is found for the first time. It is learned that this shift is described very well by the Varshni formula. A transition region in the temperature broadening of the half-width H(T) of the exciton band with the increase of temperature is registered in the interval between 150 and 220 K. It is shown that this region may be identified as the heterophase structure region where ferroelastic and paraelastic phases coexist. A surge of H(T) at the point of the ferroelastic phase transition (Tc = 220 K) is also observed. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Квантовые эффекты в полупpоводниках и диэлектриках Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals |
| spellingShingle |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals Machulin, V.F. Motsnyi, F.V. Peresh, E.Yu. Smolanka, O.M. Svechnikov, G.S. Квантовые эффекты в полупpоводниках и диэлектриках |
| title_short |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals |
| title_full |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals |
| title_fullStr |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals |
| title_full_unstemmed |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals |
| title_sort |
effect of temperature variation on shift and broadening of exciton band in cs₃bi₂i₉ layered crystals |
| author |
Machulin, V.F. Motsnyi, F.V. Peresh, E.Yu. Smolanka, O.M. Svechnikov, G.S. |
| author_facet |
Machulin, V.F. Motsnyi, F.V. Peresh, E.Yu. Smolanka, O.M. Svechnikov, G.S. |
| topic |
Квантовые эффекты в полупpоводниках и диэлектриках |
| topic_facet |
Квантовые эффекты в полупpоводниках и диэлектриках |
| publishDate |
2004 |
| language |
English |
| container_title |
Физика низких температур |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
The exciton reflection spectra of Cs₃Bi₂I₉ layered crystals is investigated in the temperature region
4.2–300 K with light polarization E ⊥ c. It is estimated that the energy gap Eg equals
2.857 eV (T = 4.2 K) and the exciton binding energy Ry is 279 meV. A nontraditional temperature
shift of Eg(T) for the layered substances is found for the first time. It is learned that this shift is
described very well by the Varshni formula. A transition region in the temperature broadening of
the half-width H(T) of the exciton band with the increase of temperature is registered in the interval
between 150 and 220 K. It is shown that this region may be identified as the heterophase structure
region where ferroelastic and paraelastic phases coexist. A surge of H(T) at the point of the
ferroelastic phase transition (Tc = 220 K) is also observed.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/120368 |
| citation_txt |
Effect of temperature variation on shift and broadening of exciton band in Cs₃Bi₂I₉ layered crystals / V.F. Machulin, F.V. Motsnyi, E.Yu. Peresh, O.M. Smolanka, G.S. Svechnikov // Физика низких температур. — 2004. — Т. 30, № 12. — С. 1283–1286. — Бібліогр.: 30 назв. — англ. |
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| first_indexed |
2025-11-27T02:19:38Z |
| last_indexed |
2025-11-27T02:19:38Z |
| _version_ |
1850793780793311232 |
| fulltext |
Fizika Nizkikh Temperatur, 2004, v. 30, No. 12, p. 1283–1286
Effect of temperature variation on shift and broadening of
exciton band in Cs3Bi2I9 layered crystals
V.F. Machulin1, F.V. Motsnyi1, E.Yu. Peresh2,
O.M. Smolanka1, and G.S. Svechnikov1
1 V. Lashkaryov Institute of Semiconductor Physics of the National Academy of Sciences of Ukraine
41 Nauky Ave., Kyiv 03028, Ukraine
E-mail: motsnyi@sun.semicond.kiev.ua
2 Uzhgorod National University, Chemical Faculty, 46 Pidgirna Str., Uzhgorod 88000, Ukraine
Received February 26, 2004, revised April 29, 2004
The exciton reflection spectra of Cs3Bi2I9 layered crystals is investigated in the temperature re-
gion 4.2–300 K with light polarization E � c. It is estimated that the energy gap Eg equals
2.857 eV (T = 4.2 K) and the exciton binding energy Ry is 279 meV. A nontraditional temperature
shift of Eg(T) for the layered substances is found for the first time. It is learned that this shift is
described very well by the Varshni formula. A transition region in the temperature broadening of
the half-width H(T) of the exciton band with the increase of temperature is registered in the inter-
val between 150 and 220 K. It is shown that this region may be identified as the heterophase struc-
ture region where ferroelastic and paraelastic phases coexist. A surge of H(T) at the point of the
ferroelastic phase transition (Tc = 220 K) is also observed.
PACS: 64.70.Kb, 71.35.Cc, 78.40.Fy
1. Introduction
Cs3Bi2I9 crystals belong to an extensive family of
little-studied three-component A3B2X9 layered com-
pounds (A are alkaline atoms, B = As, Sb, Bi, Fe, Cr,
Mo, or W, and X = Br, Cl or I) [1,2], which are kin-
dred to the well-known perovskites. Interest in these
crystals is caused by the manifestation of a ferroelastic
second-order phase transition at the temperature Tc =
= 220 K [2–4] accompanied by a reversible change of
crystal symmetry class from hexagonal 6/mmm to
centrosymmetric monoclinic 2/m, the prediction of
an incommensurate phase at T < 220 K [1,5], and the
possibilities of practical use in recorder systems, pres-
sure and �-emission sensors, and acousto- and opto-
electronics.
The optical data on Cs3Bi2I9 crystals concern to the
birefrigence [2], exciton states [6,7], phonon spectra
[8], and low-temperature optical characteristics [9].
On the other hand, one of the important physical
properties of layered crystals is the anomalous tempe-
rature dependence of energy gap Eg(T), which in-
creases at T < Òm and decreases at T > Òm. For differ-
ent layered crystals Tm varies within a temperature
range of 30–45 K [10–14]. The phenomenon originates
from high anisotropy of the chemical bonding due to
the strong ionic—covalent bonding in separate sand-
wich layers and the weak van der Waals binding
between neighboring sandwiches. This is confirmed by
the presence of low-frequency optical vibrations in the
Raman spectra of layered crystals [8,13,15–18] which
determine the exciton—phonon interaction [14,19,20],
spin—lattice relaxation [21], temperature dependence
of electron paramagnetic resonance (EPR) spectra
[21,22], and also a large difference in linear broaden-
ing coefficients in directions perpendicular to the lay-
ers and in the planes of the layers [23]. Anomalous
temperature behavior of Eg(T) can be explained on
the basis of the essential influence of anharmonic opti-
cal vibrations of the layered lattice starting at low
temperature and of low-frequency optical phonons
starting at higher temperatures [14,24]. However, this
temperature dependence has not been studied for
A3B2X9 compounds in general and for Cs3Bi2I9 crys-
tals in particular.
The aim of this paper is to study the temperature
behavior of the exciton band of Cs3Bi2I9 layered crys-
tals.
© V.F. Machulin, F.V. Motsnyi, E.Yu. Peresh, O.M. Smolanka, and G.S. Svechnikov, 2004
2. Experimental
Cs3Bi2I9 layered crystals were grown by the
Bridgman method. The peculiarities of this technology
are given in [25,26]. Samples with dimensions approxi-
mately 7�5�0.02 mm were cut off from a bulk crystal
in air with a blade. Special care was taken to avoid de-
formations. The samples had the mirror-smooth sur-
face with optical c axis perpendicular to cleavage sur-
face. The reflection spectra were measured in the
heating regime. They were recorded with an auto-
mated experimental setup based on a MDR-23 mono-
chromator in the energy interval of 2.0–3.5 eV in the
temperature range of 4.2–300 K and with light polar-
ization E � c. The energy resolution was better than
0.5 meV. The relative error of measurement of the re-
flection spectra did not exceed 3%. The temperature
was stabilized with accuracy better than 0.1 K.
The resonance energies of the exciton absorption
bands were determined from the inflection point of the
exciton oscillation with quantum number n = 1 by set-
ting the second derivative of the reflection coefficient
with respect to energy equal to zero (d2R/dE2 = 0).
The inflection point found in such a way coincides up
to T � 200 K with the one determined in the ordinary
way as the half energy interval or the half distance on
the reflectance scale between the extrema of the
exciton oscillation. The half-width H(T) of the exci-
ton absorption band was found as the energy diffe-
rence between the maximum and the minimum of the
fundamental exciton oscillation. The insertion errors
in the measured values of the temperature variations
of the energy position of the exciton band Eex(T) and
its half-width are insignificant [11] and do not influ-
ence their qualitative course.
3. Results and discussion
A typical reflection spectrum at 4.2 K and E � c
and the dependence of [�2(�)��]2 as a function of en-
ergy �� for Cs3Bi2I9 crystals are shown in Fig. 1. The
intense oscillation with inflection point at energy
2.578 eV and the two shorter-wave length maxima at
energies of 2.961 and 3.073 eV (Fig. 1,a) are caused
by excitons in the ground state (n = 1) and interband
electron transitions, respectively [6,7]. On the basis
of this spectrum, the extrapolation by the Yahoda
method*, and the Kramers—Kronig relations, we
have previously [9] found the real �1(�) and imagi-
nary �2(�) parts of the complex dielectric function
�(�). Knowing �2(�), we estimated the direct band
gap Eg of Cs3Bi2I9 crystals at 4.2 K and E � c. The
dependence of [�2(�)��]2 as a function of energy ��
was constructed in accordance with [27] (Fig. 1,b).
One can see three intense bands with maxima at ener-
gies of 2.548, 2.986, and 3.079 eV. The calculated
spectrum satisfactorily correlates with the experimen-
tal reflection spectrum. The value of Eg in such a case
is estimated as the energy of the cut off. It equals
2.857 eV. The binding energy Ry of the exciton is
found as the difference between Eg and the maximum
of the exciton band, that is Ry = 279 meV. It should
be noted that Ry in the Cs3Bi2I9 crystals is high, and
higher than in basic BiI3 (Ry = 144 meV) [19]. This
may be explained by that fact that Cs3Bi2I9 crystals
are alkali halide compounds. In such substances the
polar type of chemical bonding takes place, and there-
fore Ry may be high.
1284 Fizika Nizkikh Temperatur, 2004, v. 30, No. 12
V.F. Machulin, F.V. Motsnyi, E.Yu. Peresh, O.M. Smolanka, and G.S. Svechnikov
* The optical functions of a system of two noninteracting classical oscillators were simulated taking into account the
traditional extrapolations by the Philipp—Taft and Yahoda methods. It was found that the functions are in good
agreement with the model functions only in the second case.
0
2.2 2.4 2.6 2.8 3.0 3.2
Ry
b
5
10
15
20
25
30
35
40
R
,%
a
E, eV
200
400
600
800
E = 2.857 eVg
[
(
)
,
e
V
�
�
�
�
2
�
2
2
Fig. 1. Reflection spectrum (T = 4.2 K, E � c (a) and
[�2(�)��]2 (b)) of Cs3Bi2I9 layered crystals.
The temperature shift of the energy gap Eg(T) and
the temperature dependence of the half-width H(T) of
the exciton absorption band of Cs3Bi2I9 crystals are
shown in Fig. 2. In Fig. 2,a the points are experimen-
tal data for Eg(T) and the continuous curve represents
Eg(T) as obtained from the computation by the
Varshni formula [28]
E T E
T
Tg g( ) ( )�
0
2
�
, (1)
where Eg(0) = 2.857 eV,
= –7·10–4 eV/K and � =
= 258.654 K. We would like to stress a few points:
1) the experimental results are described very well by
this formula; 2) the energy position of the energy gap
does not change at T < 45 K and shifts to the long-
wavelength side with increase of temperature up to
300 K without any anomalies at Tc = 220 K. Such
behavior of Eg(T) is not peculiar to layered semi-
conductors but is typical for the majority of the
well-studied ones, for example Ge, Si, SiC, A2B6, and
A3B5. It can therefore be explained in the following
manner. First, at low temperatures the mechanisms
caused by the interaction of electrons and holes with
acoustic and optical phonons are included and then at
higher temperature the other mechanisms connected
with the thermal expansion of the crystal lattice take
place. It is very important that all mechanisms
contribute with the minus sign.
The absence of an anomaly in the temperature shift
of Eg(T) allow us to suppose that the anisotropy of
the optical properties in the monoclinic structure is
not high. This conclusion correlates very well with the
low intensities of the low-frequency doublets (33.4,
38.3), (44.3, 48.2) cm–1 in the Raman spectra at
4.2 K. Therefore Cs3Bi2I9 crystals are not typical lay-
ered compounds. These crystals can be considered as
layered semiconductors in the hexagonal phase and
normal ones in the monoclinic phase.
Thus Cs3Bi2I9 crystals demonstrate nontraditional
temperature behavior of Eg(T) for layered substances.
The experimental temperature dependence of the
half-width H(T) (points) of the exciton band of
Cs3Bi2I9 crystals is depicted in Fig. 2,b. With increas-
ing temperature from 4.2 to 150 K the half-width in-
creases nonlinearly from 48.9 to 99.7 meV. Then H(T)
begins to rise less sharply, forming a plateau (the
transition region) up to T < 220 K with a surge at
T = 220 K. After that H(T) returns almost to the
starting point at T = 225 K and increases linearly
(H(T) = k(T – 225 K) + H0, where k = 0.758 meV/K
and H0 = 116.3 meV) in the temperature range
225 K � T � 300 K.
We made an effort to model the temperature de-
pendence of the half-width of the exciton band. It was
found that the half-width can be described at
T � 150 K by the following equation:
H T H
kT
( ) ( )�
�
�
�
�
�0
2
coth
ph��
, (2)
obtained by Toyozawa [29] for weak exciton—phonon
interaction. Here H(0) is the half-width at absolute
zero temperature and ��ph is the energy of the inter-
acting phonon. The results of the modeling are given
in Fig. 2,b for H(0) = 48.92 meV and two real optical
phonons which were registered in Raman spectra [8]
at 4.2 K. The calculated curves are localized above
(�ph = 99.8 cm–1) and under (�ph = 114.8 cm–1) the
experimental dependence. The best correlation be-
tween experiment and theory exists for an effective
phonon with frequency 105.8 cm–1 (thick curve). Es-
tablished dependence is essentially differed from
H(T) dependence of exciton band of BiI3 classical
layered semiconductor in which the phase transitions
are absent and high exciton—phonon interaction
takes place [14,24].
The deviation of experimental dependence H(T)
from the theoretical (2) and appearance of the transi-
tion region indicates the reconstruction of the
monoclinic crystal lattice between 150 and 220 K. As
Effect of temperature variation on shift and broadening of exciton band in Cs3Bi2I9 layered crystals
Fizika Nizkikh Temperatur, 2004, v. 30, No. 12 1285
40
60
80
100
120
140
160
5 50 100 150 200 250 300
H
,
m
eV
b
2.80
2.81
2.82
2.83
2.84
2.85
2.86
a
T , K
T = 220 Kc
E
,
e
V
g
Fig. 2. Temperature shift of the energy gap Eg(T) (a) and
broadening of half-width H(T) (b) of the exciton band of
Cs3Bi2I9 layered crystals.
was shown in Ref. 30, the region 183–221 K corres-
ponds to a heterophase structure where ferroelastic
and paraelastic phases coexist. Therefore the whole
transition region may be identified with the hetero-
phase structure.
The appearance of a surge at T = 220 K is probably
due to the ferroelastic phase transition (as T = Tc
[2–4]).
Thus the half-width of the exciton band may be
used as a highly sensitive nondestructive probe for re-
vealing a phase transition.
4. Conclusions
We have presented analyses of the effect of tempe-
rature variation on the exciton reflection spectra of
Cs3Bi2I9 layered crystals. It was found that these crys-
tals are not typical layered ones. These crystals are
layered semiconductors in the hexagonal phase and be-
have like conventional semiconductors in the mono-
clinic phase. We have registered the transition region
in the temperature broadening of the half-width of the
exciton band in temperature interval of 150–220 K
and the surge at T = 220 K. Our analyses suggest that
both phenomena are caused by the formation of the he-
terophase structure region and the ferroelastic phase
transition, respectively.
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1286 Fizika Nizkikh Temperatur, 2004, v. 30, No. 12
V.F. Machulin, F.V. Motsnyi, E.Yu. Peresh, O.M. Smolanka, and G.S. Svechnikov
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