The electric field gradient asymmetry parameter in InSe
The complex NQR spectra of ¹¹⁵In caused by presence of structural defects called polytypes are observed in a monocrystalline InSe sample. Multiple ratio of average frequencies of NQR spectra that correspond to four resonance transitions of quadrupole nuclii with spins I = 9/2 testifies to existen...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Цитувати: | The electric field gradient asymmetry parameter in InSe / Z.D. Kovalyuk, A.G. Khandozhko, G.I. Lastivka, A.P. Samila // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 164-166. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1177062017-05-27T03:05:47Z The electric field gradient asymmetry parameter in InSe Kovalyuk, Z.D. Khandozhko, A.G. Lastivka, G.I. Samila, A.P. The complex NQR spectra of ¹¹⁵In caused by presence of structural defects called polytypes are observed in a monocrystalline InSe sample. Multiple ratio of average frequencies of NQR spectra that correspond to four resonance transitions of quadrupole nuclii with spins I = 9/2 testifies to existence of axial symmetry of the electric field gradient in In nucleus positions inside the InSe crystal structure. The latter is confirmed by the dependence of the NQR spectrum amplitude on the angle between the main crystal axis c and vector of high-frequency field H₁. However, presence of a residual intensity in the spectra at c || Н₁ can indicate the existence of crystal blocks in bulk of the sample with weak angular misorientation. 2011 Article The electric field gradient asymmetry parameter in InSe / Z.D. Kovalyuk, A.G. Khandozhko, G.I. Lastivka, A.P. Samila // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 164-166. — Бібліогр.: 8 назв. — англ. 1560-8034 PACS 76.60.Gv http://dspace.nbuv.gov.ua/handle/123456789/117706 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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The complex NQR spectra of ¹¹⁵In caused by presence of structural defects
called polytypes are observed in a monocrystalline InSe sample. Multiple ratio of
average frequencies of NQR spectra that correspond to four resonance transitions of
quadrupole nuclii with spins I = 9/2 testifies to existence of axial symmetry of the
electric field gradient in In nucleus positions inside the InSe crystal structure. The latter
is confirmed by the dependence of the NQR spectrum amplitude on the angle between
the main crystal axis c and vector of high-frequency field H₁. However, presence of a
residual intensity in the spectra at c || Н₁ can indicate the existence of crystal blocks in
bulk of the sample with weak angular misorientation. |
| format |
Article |
| author |
Kovalyuk, Z.D. Khandozhko, A.G. Lastivka, G.I. Samila, A.P. |
| spellingShingle |
Kovalyuk, Z.D. Khandozhko, A.G. Lastivka, G.I. Samila, A.P. The electric field gradient asymmetry parameter in InSe Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kovalyuk, Z.D. Khandozhko, A.G. Lastivka, G.I. Samila, A.P. |
| author_sort |
Kovalyuk, Z.D. |
| title |
The electric field gradient asymmetry parameter in InSe |
| title_short |
The electric field gradient asymmetry parameter in InSe |
| title_full |
The electric field gradient asymmetry parameter in InSe |
| title_fullStr |
The electric field gradient asymmetry parameter in InSe |
| title_full_unstemmed |
The electric field gradient asymmetry parameter in InSe |
| title_sort |
electric field gradient asymmetry parameter in inse |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117706 |
| citation_txt |
The electric field gradient asymmetry parameter in InSe / Z.D. Kovalyuk, A.G. Khandozhko, G.I. Lastivka, A.P. Samila // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 164-166. — Бібліогр.: 8 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT kovalyukzd theelectricfieldgradientasymmetryparameterininse AT khandozhkoag theelectricfieldgradientasymmetryparameterininse AT lastivkagi theelectricfieldgradientasymmetryparameterininse AT samilaap theelectricfieldgradientasymmetryparameterininse AT kovalyukzd electricfieldgradientasymmetryparameterininse AT khandozhkoag electricfieldgradientasymmetryparameterininse AT lastivkagi electricfieldgradientasymmetryparameterininse AT samilaap electricfieldgradientasymmetryparameterininse |
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2025-07-08T12:39:56Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 164-166.
PACS 76.60.Gv
The electric field gradient asymmetry parameter in InSe
Z.D. Kovalyuk1, A.G. Khandozhko2, G.I. Lastivka2, A.P. Samila2
1Chernivtsi Department of the Institute of Materials Science Problems, NAS of Ukraine,
5, Iryna Vilde str., 58001 Chernivtsi, Ukraine
2Yu. Fed’kovych Chernivtsi National University,
2, Kotsyubyns’ky str., 58012 Chernivtsi, Ukraine
Abstract. The complex NQR spectra of 115In caused by presence of structural defects
called polytypes are observed in a monocrystalline InSe sample. Multiple ratio of
average frequencies of NQR spectra that correspond to four resonance transitions of
quadrupole nuclii with spins I = 9/2 testifies to existence of axial symmetry of the
electric field gradient in In nucleus positions inside the InSe crystal structure. The latter
is confirmed by the dependence of the NQR spectrum amplitude on the angle between
the main crystal axis c and vector of high-frequency field H1. However, presence of a
residual intensity in the spectra at c || Н1 can indicate the existence of crystal blocks in
bulk of the sample with weak angular misorientation.
Keywords: NQR, multiplet spectra, structural defects, polytypes.
Manuscript received 14.10.10; accepted for publication 16.03.11; published online 30.06.11.
1. Introduction
Indium selenide belongs to layered semiconductor
materials of GaS group and attracts special interest of
researchers. It is caused not only by a large number of
physical effects related with strong anisotropy of the
crystal structure but also by the possibility of their wide
practical use. The crystal structure of InSe is formed in
such a way that bonds inside the main layer have
covalent character, while between the layers – Van-der-
Waals one. That is why, monoatomic layers Se-In-In-Se
are formed in InSe [1].
The crystalline structure of layered semiconductor
compound InSe admits presence of the axial-symmetrical
gradient of electric field in the direction of the “In-In”
bond (axis c, Fig. 1). It follows from the results of
radiographical researches [2] as well as from spectra of
electron paramagnetic resonance (EPR) [3] inherent to the
crystal structure of GaS group compounds. Though, a
direct proof of the existence of axial-symmetric electric
field inside InSe layered crystals may be obtained using
nuclear quadrupole resonance (NQR). First of all, the
research of NQR spectra is a rather effective method to
research crystal structure perfectness and local symmetry
in the position of a resonance nucleus [4]. Secondly, the
existence of the electric field gradient in the heavily
anisotropic crystal structure of GaS, GaSe and InSe single
crystals caused by quadrupole moments of 69Ga, 71Ga and
115In [5] enables the possibility to research electronic and
crystal structures by means of NQR.
The purpose of this paper is to determine the
structural defects and perfectness of a crystalline lattice
in single crystals of indium selenide by studying the
intendities of NQR spectral lines for 115In depending on
orientation of the main crystal axis c relatively to the
vector of the high-frequency field H1.
2. Experimental
The research of NQR spectra was carried out using a
spectrometer at continuous-wave operation in the radio-
frequency bandwidth 10 to 45 MHz at room temperature
T = 293 K. As a detector of NQR resonance signals, we
used marginal oscillator [6]. Single crystals grown
accordingly to the Bridgman method were used for these
researches. Samples for measurements were cut of the
cylinder part of grown ingot with the diameter 16 to
18 mm. The length of the samples was 20 to 30 mm. The
fact that monoatomic layers are mostly located along the
direction of growth facilitates detection of NQR signals.
In this case, the cylindrical shape of the sample let to fill
the volume of oscillatory circuit coil of spin generator
(Fig. 2a); and the magnetic component of radio-
frequency field H1 was directed normally to the crystal
axis c, that is in the direction of axial symmetry of the
electric field gradient (Fig. 2b).
The maximum intensity of NQR signals was
obtained due to the fact that monoatomic layers of the
crystal structure are directed along the axis of radio-
frequency coil (Fig. 2a).
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
164
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 164-166.
Fig. 1. Structure element of crystal lattice of InSe.
As 115In has the spin I = 9/2, it means that there are
four resonance transitions accordingly to selection rules:
±1/2 ↔ ±3/2; ±3/2 ↔ ±5/2; ±5/2 ↔ ±7/2; ±7/2 ↔ ±9/2.
NQR frequencies (ν1 to ν4) that correspond to these
transitions can be obtained from the following
expressions [4]:
)691.450333.91(
24
1 42
1 η−η+=ν zzeQq ;
)724.113381.11(
24
2 42
2 η−η+=ν zzeQq ;
)1233.01857.01(
24
3 42
3 η−η+=ν zzeQq ;
)0043.00809.01(
24
4 42
4 η−η+=ν zzeQq , (1)
where e is the charge of an electron, Q – quadrupole
moment of the nucleus, q – electric field gradient in the
direction c, and
zz
yyxx
q
qq −
=η the electric field
gradient asymmetry parameter [4]. Generally, a direction
of the main axes x, y, z of the tensor for the electric field
gradient is chosen in such a manner that qxx < qyy < qzz,
and then 0 < η <1. When the electric field has axially-
symmetric distribution, η = 0. That is why it can be
eliminated from the expressions (1). Four zones of
resonance frequencies with average values of 10.25, 20.5,
30.8, and 41 MHz that approximately satisfy the ratio
ν1:ν2:ν3:ν4 = 1:2:3:4 were found in InSe for 115In isotope.
The latter shows insignificant asymmetry of the electric
field gradient on 115In and its distribution can be
considered as axial-symmetric. We have researched the
range of frequencies that correspond to the transition
±3/2 ↔ ±5/2. 115In NQR spectrum at room temperatures is
located within the range of 20.4…20.7 MHz in this case.
NQR spectra of 115In in InSe shown in Fig. 3 were
recorded using the method of frequency modulation [4],
therefore derivatives of the second order for spectral
lines of the Gaussian shape were observed. The
spectrum consists of three multiplet groups with the
maximum intensity of lines at the frequencies 20.485,
20.540, and 20.595 MHz, accordingly.
Fig. 2. Location of crystal InSe layers relatively to the vector
of radio-frequency magnetic field H1: a – location of the
sample (part of the ingot) in the coil of LC oscillatory circuit –
circuit of the NQR spin-detector; b – orientation of H1 vector
relatively to crystal atomic layer.
The orientation dependence of the intensity
inherent to 115In NQR at the angles (α) between the
crystal axis c and direction of actuating radio-frequency
field H1 was also researched within the frequency range
20.4 to 20.7 MHz. A special device with rotary crystal
enclosure was designed for performing these
measurements. Crystal oriented samples with
dimensions 10×10×10 mm were used for researches in
this case. They were rotated in the coil spin-detector
during these measurements by using the angle steps of
5°. Digital averaging was used for enhancement of
signal-to-noise ratio.
Fig. 3. 115In NQR spectrum in InSe that corresponds to the
resonance transition ±3/2 ↔ ±5/2, T = 293 K.
Fig. 4. Diagram of the orientation dependence of the intensity
of NQR lines in InSe sample: 1 – range 20.450-20.520 MHz;
2 – range 20.510-20.600 MHz; 3 – range 20.600-20.700 MHz.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
165
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 164-166.
Fig. 4 shows the diagram of dependence for the
relative integrated intensity of resonance lines for these
three multiplet groups in the NQR spectrum. There is a
dependence of the intensity on the direction of H1 vector
regarding crystallographic axis c for all lines of the
spectrum. The maximum of the resonance intensity really
corresponds to the case when Н1 ⊥ c. If Н1 || c (that
corresponds to α = 90°, Fig. 3), the resonance intensity
falls to zero for all multiplet groups “1”, “2” and “3”.
3. Discussion of the results
Observation of 115In NQR spectra in InSe in four
frequency ranges with average values that satisfy the
ratio ν1:ν2:ν3:ν4 = 1:2:3:4 indicates insignificant
asymmetry of the electric field gradient on 115In nuclii,
and its distribution in the InSe crystal structure can be
considered as axial-symmetric. The character of
orientation dependences of 115In NQR intensity on the
angle between vectors c and H1 is forcible argument for
this statement. Accordingly to [7], the intensity of NQR
signal tends to zero in the case of axial-symmetric
gradient of electric field on the nuclear when rotating the
monocrystalline sample to the congruence of c and H1
directions. Presence of a residual intensity of spectra at
c || Н1 in our case is indicative of the existence of weak
angular misorientation inherent to crystal blocks.
To check the asymmetry parameter η, the
resonance frequencies of two lines in the group “1” for
the transitions ±3/2 ↔ ±5/2 and ±7/2 ↔ ±9/2 have been
measured. At room temperature (T = 293 K) the relations
of resonance frequencies ν4/ν2 for the specified
transitions were: 2.00316 and 2.00307 (for lines of the
group “1”, Fig. 3). It confirms presence of an axial
gradient of electric field near indium nuclii within errors
of frequency measurements (±10-5).
It is possible to explain the obtained results by
peculiarities of InSe layered compound. In the paper [2],
technology of growing the layered single crystals GaS,
GaSe and InSe was described in details, and also
influence of different growth methods on the crystal
structure was shown. It was established that the
considerable role in formation of polytypes is played by
dislocations. The special attention was given in this work
to researching the defects of packing by using electron
microscopy and X-ray diffraction. Using the latter, it was
shown that the crystal InSe possesses a very low energy of
packing defects. Therefore, in this relation it is necessary
to expect occurrence of polytypes when crystal is grown
in non-equilibrium conditions, that is by melting methods.
A multiplet character of lines for all resonance
transitions indicated the existence of a set of polytype
elements in this compound. Accordingly to [2, 8],
usually there is a phase In6Se7 in InSe. It is the existence
of non-equivalent (in crystal sense) positions of In atoms
that causes formation of separate groups of lines –
multiplets (groups “2” and “3”), in our opinion. But
creation of the latter group of lines is associated with
existence of quasi-disproportionate periodical distortion
of the crystal grating [8].
Complicated but simply ordered character of 115In
NQR spectra in InSe is conditioned by the existence of
peculiarities of structural defects that cannot be
identified by other methods.
The performed research of NQR in InSe confirms
complexity of the problem of polymorphism in layered
crystals, which requires further investigations by using
different experimental methods.
4. Conclusions
The following conclusions can be drawn on the basis of
these researches.
1. The existence of multiplet 115In NQR spectra in
InSe indicates the complex polytype structure of
layered crystals of this compound.
2. The ratio of NQR resonance frequencies inherent to
quadrupole transitions of 115In nuclii with the spin
I = 9/2 and orientation dependence of the line
intensity on the direction of the high-frequency field
vector relatively to the main crystal axis confirm
axial symmetry of the electric field gradient in InSe.
3. Presence of the residual intensity of spectra for c || Н1
is indicative of the existence of crystal blocks with
weak angular misorientation in bulk of the sample. In
this case, NQR can be used for the control of
monocrystallinity of the samples grown up.
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© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
166
2. Experimental
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