On the optimum geometric shapes of ZnSe-based scintillation elements
We have carried out Monte-Carlo calculations of the light collection coefficient τ for different shapes of ZnSebased scintillators Applying a theoretical model, it has been shown, that the light collection optimization can be
 reached in scintillators with a geometry where the chaotic light...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2004 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2004
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| Цитувати: | On the optimum geometric shapes of ZnSe-based scintillation elements / K. Katrunov, S. Naydenov, V. Ryzhikov, N. Starzhinskiy, L. Gal’chinetskii, V. Gavril’uk, V. Yanovsky // Вопросы атомной науки и техники. — 2004. — № 2. — С. 174-176. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860096570251280384 |
|---|---|
| author | Katrunov, K. Naydenov, S. Ryzhikov, V. Starzhinskiy, N. Gal’chinetskii, L. Gavril’uk, V. Yanovsky, V. |
| author_facet | Katrunov, K. Naydenov, S. Ryzhikov, V. Starzhinskiy, N. Gal’chinetskii, L. Gavril’uk, V. Yanovsky, V. |
| citation_txt | On the optimum geometric shapes of ZnSe-based scintillation elements / K. Katrunov, S. Naydenov, V. Ryzhikov, N. Starzhinskiy, L. Gal’chinetskii, V. Gavril’uk, V. Yanovsky // Вопросы атомной науки и техники. — 2004. — № 2. — С. 174-176. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | We have carried out Monte-Carlo calculations of the light collection coefficient τ for different shapes of ZnSebased scintillators Applying a theoretical model, it has been shown, that the light collection optimization can be
reached in scintillators with a geometry where the chaotic light collection is realized. Experimentally it was
supported that for detectors of rectangular and cylindrical types with rounded vertexes or edges, the light output
increase of up to 20% has been observed, provided the regular light beam dynamics was changed to chaotic.
З використанням методу Монте-Карло проведені розрахунки коефіцієнта світлозбирання для різних
форм сцинтиляторів на основі ZnSe. Теоретично показано, що оптимізація світлозбирання досягається у
сцинтиляторах з геометрією, у якій реалізується хаотичне збирання світлових променів. Це припущення
експериментально підтверджено на прикладі детекторів прямокутного і циліндричного типу з округленими
вершинами та ребрами, для яких виявлено підвищення світлового виходу до 20 % при заміні регулярної
динаміки світлових променів на хаотичну.
С использованием метода Монте-Карло проведены расчеты коэффициента светособирания для
различных форм сцинтилляторов на основе ZnSe. Теоретически показано, что оптимизация светосбора
достигается в сцинтилляторах с геометрией, для которой реализуется хаотическое собирание световых
лучей. Это предположение экспериментально подтверждено на примере детекторов прямоугольного и
цилиндрического типа со скругленными вершинами или ребрами, для которых обнаружено повышение
светового выхода до 20% при изменении регулярной динамики световых лучей на хаотическую.
|
| first_indexed | 2025-12-07T17:26:16Z |
| format | Article |
| fulltext |
ON THE OPTIMUM GEOMETRIC SHAPES OF ZnSe-BASED
SCINTILLATION ELEMENTS
K. Katrunov, S. Naydenov, V. Ryzhikov, N. Starzhinskiy, L. Gal’chinetskii, V. Gavril’uk,
V. Yanovsky
STC “Institute for Single Crystals”, 60 Lenin Ave., 61001 Kharkov, Ukraine
E-mail: stcri@isc.kharkov.com
We have carried out Monte-Carlo calculations of the light collection coefficient τ for different shapes of ZnSe-
based scintillators Applying a theoretical model, it has been shown, that the light collection optimization can be
reached in scintillators with a geometry where the chaotic light collection is realized. Experimentally it was
supported that for detectors of rectangular and cylindrical types with rounded vertexes or edges, the light output
increase of up to 20% has been observed, provided the regular light beam dynamics was changed to chaotic. This
work has been carried out with support under CRDF Project UE2-2484-KK-02.
PACS: 29.40.Mc
One of the main parameters characterizing quality of
detectors of “scintillator-silicon photodiode” type (SD) is
their sensitivity to β- and γ-radiation [1,2]. Parameters of
the existing SD can be improved by increasing the
scintillator (S) volume and the photodiode (PD) sensitive
surface. However, because of various technological and
physical factors, it is not always possible [3].
A promising way to improve the SD sensitivity is
finding optimum shapes of S, which would ensure
maximum values of light collection coefficient τ and,
consequently, of the light output.
We have carried out calculations of τ for different S
shapes, taking ZnSe(Te) crystals as an example. The
values of τ (fraction of light coming from the output
window of S) were determined by the Monte-Carlo
method (MC). The calculation algorithm accounted for
the sample geometry, absorption in the S material (α
=0,1...0,2 cm-1), refraction index (n=2,58), light scattering
indicatrix at the “crystal-reflecting covering” interface, as
well as several other parameters. Different shapes of
ZnSe(Te) scintillators were considered, including
polyhedrons (parallelepiped, parallelepiped with rounded
upper edge, tetrahedral truncated pyramid, tri- and
hexahedral prism, as well as hemisphere. The obtained
values of τ for scintillators with output windows
corresponding to the PD sensitive area (S=1cm2) are
presented in Table 1.
Table 1
Scintillator shape Light collection
coefficient, τ
Scintillations
uniformly
distributed over
the volume
Scintillations
located in the
surface-
adjacent layer
Pyramid, sides at 60° 0.60 0.668
Pyramid, sides at 450 0,49 0,51
Hemisphere 0.457 0.652
Trihedral prism (variant 1) 0.357 0.378
Hexahedral prism (variant 1) 0.202 0.221
Trihedral prism (variant 2) 0.147 0.146
Hexahedral prism (variant 2) 0.145 0.147
Cube with edge rounding 0.339 0.371
Cube 0.144 0.145
It can be seen from Table 1 that variation of the
scintillator shape can lead to substantial (up to 3
times) changes in τ. The lowest τ values are observed
for scintillators of regular shapes (parallelepiped,
cylinder, prism). From the other side, the shapes of
tetrahedral pyramid with the sides inclined at 600 and
of hemisphere favor the light coming out of the
crystal. For the shape of pyramid, low τ is observed
when the sides are inclined at 450, which corresponds
to the vertex angle of 90°, i.e., the scintillator is an
angular reflector. Light collection processes for this
case are analyzed in the Appendix. This analysis
shows that in this case large fraction of light is
captured by total internal reflection, thus lowering the
values of τ. This seems to be a common picture for
all scintillators of regular shapes (parallelepipeds,
cylinders, prisms).
To find out the optimum shape of a scintillator,
i.e., to obtain the maximum τ, we have proposed to
use a theoretical approach where an adequate model
of physical detectors is mathematical billiard [4,5]. In
this approach, the beam picture is considered in a
special phase space of the dynamic system that
corresponds to the detector (billiard). Then on the
phase portrait of light collection one can see changes
and peculiar features of the beam picture that cannot
be observed in the conventional geometrical space.
This, in particular, allows us to establish more
profound physical reasons of light capture in the
crystal volume and to propose new ways of excluding
it. The light capture is directly related to the presence
of a regular component (RC) of the beam propagation
in detectors of regular shape (spherical, cylindrical,
rectangular). Each specified RC beam occupies its
once and forever fixed region in the phase space.
Location of the regularity zone can be such that RC
beams belonging to it will never reach the output
window of the detector or will not get into the output
aperture (under condition of full internal reflection)
and became captured inside the crystal volume. As
distinct from this, all beams of the chaotic component
(CC) will, in due course of time, fill one and the same
region of the phase space, i.e., chaotic trajectories are
undistinguishable from one another. In addition, CC
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PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.174-176.174
always has intersections with the light output zone (in the
phase space). Independently on the output window
location and the presence of internal total reflection,
chaotic beams always come out of the detector. Therefore,
all CC beams make their contributions to the light output.
As chaotic trajectories are undistinguishable, this
contribution is approximately the same for each of such
beams. Therefore, the larger is CC, the higher is the light
output of a detector. Relationship between RC and CC
contributions, or, in other words, dynamic structure of
mixed phase space of a detector strongly depends upon its
shape. Thus, to improve the detector light output, one can
efficiently use chaotization of light beams in the detector
(billiard). Transition to stochasticity is obtained by
appropriate changes in the detector shape.
We have carried out an experiment to prove viability
of the stochastic approach in choosing the optimum
shapes, taking ZnSe(Te) and CsI(Tl) scintillators as
examples.
We compared light output values for cubic samples
with two characteristic types of rounding: a) rounding of
edges, b) cylindrical segment, c) rounding of angles
(Fig.1) with light output values of a regularly shaped
cubic sample (reference). The degree of rounding (centers
and values of radii) were chosen in accordance with
considerations of the statistical approach.
Fig.1. Shapes of scintillation samples: a) cube with
rounded edges; b) truncated cylinder; c) cube with
rounded vertices
All the samples studied, as well as the reference
sample of 1×1×1cm3 size, were made of one and the same
crystalline ingot. The output window area for all
scintillators was 1х1см2. All sides of the samples were
polished.
The X-ray luminescence light output L of the
scintillators was recorded by an instrument for
measurement of optical radiation power (KVARC – 01).
An X-ray source REIS (effective energy 70 keV) was
used for excitation. The signal obtained from the
reference under the same conditions was taken as 100%.
For the same shapes, Monte Carlo calculations of τ were
carried out.
In Table 2, calculated values of τ, τ/τcube are given, as
well as experimental data on light output with respect to
the reference, L/Lcube.
Experimental data on L, obtained for scintillators of
cubic shape with different types of roundings from the
input window side, have shown that L is increased by 16-
20% as compared with cubic scintillator of the regular
shape. This result is qualitatively confirmed by Monte-
Carlo calculations of τ.
CONCLUSIONS
Our theoretical and experimental studies have
shown that the use of “chaotic billiard” forms if
crystalline detectors lead to increased light output
values. As the problem of light collection is largely a
geometrical one, this conclusion can be also applied
to scintillators of other types.
Table 2
Scintillator
shape from
Fig.1
Material Volume
V, см3
τ τ/τcube L/Lcube
а ZnSe(Te) 0,92 0,1929 1,524 1,17
CsI(Tl) 0,92 0,243 1,504 1,18
с ZnSe(Te) 0,96 0,1787 1,41 1,11
CsI(Tl) 0,96 0,2157 1,336 1,12
в ZnSe(Te) 0,392 0,3292 2,6 1,22
CsI(Tl) 0,392 0,3751 2,32 1,20
reference ZnSe(Te) 1 0,1265 1 1
CsI(Tl) 1 0,1615 1 1
APPENDIX
Light collection processes in the pyramid with
vertex angle 900 (angular reflector)
In the pyramid with its sides at 45° to the base,
i.e., when the vertex angle is 90°, the light collection
coefficient is anomalously decreased. This can be
explained in the following way.
Let us use the mirror reflections method [6]. We
construct a two-dimensional image of the pyramid Ω
and its reflection in the side faces (Fig.2). The
trajectory of beam АВСD, subject to several
reflections from the pyramid sides, is imaged as
straight line А`В`CD. The largest beam trajectories
that do not intersect with the pyramid base, are of
length 2a , where a is the pyramid base side. It is
assumed that height h=const.
Conditions for the beam not coming out from the
side face and going through the output window
require that the incidence angle θ onto the base
should be:
s
ITR
s
ITR
b
ITR θθπθθπθθ >−>+<
4
;
4
; , (1)
where s
ITR
b
ITR θθ , are angles of internal total reflection
on the base and the side surface.
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PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.174-176.175
а в с
Fig.2. Beam trajectories in the angular reflector
(vertex angle 900)
A’
B’
B
A
C
D
Ω
a
A beam subsequently reflected from 2 or 3 faces
comes back to the base at the same incidence angle.
Neglecting non-zero reflection coefficients at normal
incidence, we obtain the maximum beam path in such
pyramid:
smal
s
ITR
43.0
4
cos
max =
−
=
θπ (2)
Fig.3 shows the distribution of beams coming to the
photoreceiver over path lengths in the crystal. Different
curves correspond to pyramids with different inclination
of side faces.
The value of lmax obtained from (2) is in agreement
with that obtained by Monte-Carlo calculations. Thus,
beams with l > lmax go to the photoreceiver, intersecting
with the base not less than twice. Let us denote the
number of such beams as N1, and the total number of
beams - as N. In the angular reflector, in each subsequent
incidence onto the base the angle remains the same. If the
inclination angle differs from 45°, the incidence angle
will change, and the beam can come to the output cone. In
Table 3, calculated data are presented on the light
collection fraction that is due to such beams. The
situation of angular reflector causes light capturing,
leading to worsening of the light collection
coefficient.
Table 3.
Relationship between beams of different spatial
orientation in the tetrahedral pyramid
Size of
pyramid
base, cm
Light
collection,
τ
Fraction of
“long” paths,
N
N1
Additional light
collection,
N
N1τ
0.3 0.568 0.335 0.190
0.4 0.479 0.100 0.048
0.5 0.592 0.199 0.118
REFERENCES
1 L. Atroshchenko, S. Burachas, L. Gal’chinetskii,
B. Grinyov, V. Ryzhikov, N. Starzhinskiy.
Crystals of scintillators and detectors on their
base. Kiev: Naukova Dumka, 1998, р.312.
2 M. Globus, B. Grinyov. Inorganic scintillators.
Kharkov: Acta Publishers, 2000.
3 B.K. Damitov. On the dependence of output
pulse amplitude of a scintillation counter on the
areas ratio of the crystal output window and
PMT photocathode // Atomnaya Energiya. 1971,
v.31, No.6, p.637-639.
4 S. Naydenov, V. Yanovsky // Functional
Materials, 2000, v.7, № 4(2), р.743-752;
Functional Materials, 2001, v.8, №2, р.226-233.
5 V. Gavrilyik, E. Vinograd, B. Grinyov,
V. Goriletsky // Functional Materials. 1997, v.4,
р.578.
6 Yu.A. Tsirlin. Light collection in scintillation
counters. Moscow: Atomizdat, 1975, p.264.
ОБ ОПТИМАЛЬНЫХ ГЕОМЕТРИЧЕСКИХ ФОРМАХ СЦИНТИЛЛЯЦИОННЫХ ЭЛЕМЕНТОВ
НА ОСНОВЕ ZnSe
К.Катрунов, С.Найденов, В.Рыжиков, Н.Старжинский, Л.Гальчинецкий, В.Гаврилюк, В.Яновский
С использованием метода Монте-Карло проведены расчеты коэффициента светособирания для
различных форм сцинтилляторов на основе ZnSe. Теоретически показано, что оптимизация светосбора
достигается в сцинтилляторах с геометрией, для которой реализуется хаотическое собирание световых
лучей. Это предположение экспериментально подтверждено на примере детекторов прямоугольного и
цилиндрического типа со скругленными вершинами или ребрами, для которых обнаружено повышение
светового выхода до 20% при изменении регулярной динамики световых лучей на хаотическую.
ПРО ОПТИМАЛЬНІ ГЕОМЕТРИЧНІ ФОРМИ СЦИНТІЛЯЦІЙНИХ ЕЛЕМЕНТІВ
НА ОСНОВІ ZnSe
К.Катрунов, С.Найдьонов, В.Рижиков, М.Старжинський, Л.Гальчинецький, В.Гаврилюк, В.Яновський
З використанням методу Монте-Карло проведені розрахунки коефіцієнта світлозбирання для різних
форм сцинтиляторів на основі ZnSe. Теоретично показано, що оптимізація світлозбирання досягається у
сцинтиляторах з геометрією, у якій реалізується хаотичне збирання світлових променів. Це припущення
експериментально підтверджено на прикладі детекторів прямокутного і циліндричного типу з округленими
вершинами та ребрами, для яких виявлено підвищення світлового виходу до 20 % при заміні регулярної
динаміки світлових променів на хаотичну.
176
Fig.3. Distribution of beams over path lengths in a
tetrahedral pyramid with side faces at ~ 45° to the
base
Table 1
CONCLUSIONS
APPENDIX
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-79383 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T17:26:16Z |
| publishDate | 2004 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Katrunov, K. Naydenov, S. Ryzhikov, V. Starzhinskiy, N. Gal’chinetskii, L. Gavril’uk, V. Yanovsky, V. 2015-03-31T16:02:03Z 2015-03-31T16:02:03Z 2004 On the optimum geometric shapes of ZnSe-based scintillation elements / K. Katrunov, S. Naydenov, V. Ryzhikov, N. Starzhinskiy, L. Gal’chinetskii, V. Gavril’uk, V. Yanovsky // Вопросы атомной науки и техники. — 2004. — № 2. — С. 174-176. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 29.40.Mc https://nasplib.isofts.kiev.ua/handle/123456789/79383 We have carried out Monte-Carlo calculations of the light collection coefficient τ for different shapes of ZnSebased scintillators Applying a theoretical model, it has been shown, that the light collection optimization can be
 reached in scintillators with a geometry where the chaotic light collection is realized. Experimentally it was
 supported that for detectors of rectangular and cylindrical types with rounded vertexes or edges, the light output
 increase of up to 20% has been observed, provided the regular light beam dynamics was changed to chaotic. З використанням методу Монте-Карло проведені розрахунки коефіцієнта світлозбирання для різних
 форм сцинтиляторів на основі ZnSe. Теоретично показано, що оптимізація світлозбирання досягається у
 сцинтиляторах з геометрією, у якій реалізується хаотичне збирання світлових променів. Це припущення
 експериментально підтверджено на прикладі детекторів прямокутного і циліндричного типу з округленими
 вершинами та ребрами, для яких виявлено підвищення світлового виходу до 20 % при заміні регулярної
 динаміки світлових променів на хаотичну. С использованием метода Монте-Карло проведены расчеты коэффициента светособирания для
 различных форм сцинтилляторов на основе ZnSe. Теоретически показано, что оптимизация светосбора
 достигается в сцинтилляторах с геометрией, для которой реализуется хаотическое собирание световых
 лучей. Это предположение экспериментально подтверждено на примере детекторов прямоугольного и
 цилиндрического типа со скругленными вершинами или ребрами, для которых обнаружено повышение
 светового выхода до 20% при изменении регулярной динамики световых лучей на хаотическую. This work has been carried out with support under CRDF Project UE2-2484-KK-02. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Детекторы и детектирование ядерных излучений On the optimum geometric shapes of ZnSe-based scintillation elements Про оптимальні геометричні форми сцинтіляційних елементів на основі ZnSe Об оптимальных геометрических формах сцинтилляционных элементов на основе ZnSe Article published earlier |
| spellingShingle | On the optimum geometric shapes of ZnSe-based scintillation elements Katrunov, K. Naydenov, S. Ryzhikov, V. Starzhinskiy, N. Gal’chinetskii, L. Gavril’uk, V. Yanovsky, V. Детекторы и детектирование ядерных излучений |
| title | On the optimum geometric shapes of ZnSe-based scintillation elements |
| title_alt | Про оптимальні геометричні форми сцинтіляційних елементів на основі ZnSe Об оптимальных геометрических формах сцинтилляционных элементов на основе ZnSe |
| title_full | On the optimum geometric shapes of ZnSe-based scintillation elements |
| title_fullStr | On the optimum geometric shapes of ZnSe-based scintillation elements |
| title_full_unstemmed | On the optimum geometric shapes of ZnSe-based scintillation elements |
| title_short | On the optimum geometric shapes of ZnSe-based scintillation elements |
| title_sort | on the optimum geometric shapes of znse-based scintillation elements |
| topic | Детекторы и детектирование ядерных излучений |
| topic_facet | Детекторы и детектирование ядерных излучений |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79383 |
| work_keys_str_mv | AT katrunovk ontheoptimumgeometricshapesofznsebasedscintillationelements AT naydenovs ontheoptimumgeometricshapesofznsebasedscintillationelements AT ryzhikovv ontheoptimumgeometricshapesofznsebasedscintillationelements AT starzhinskiyn ontheoptimumgeometricshapesofznsebasedscintillationelements AT galchinetskiil ontheoptimumgeometricshapesofznsebasedscintillationelements AT gavrilukv ontheoptimumgeometricshapesofznsebasedscintillationelements AT yanovskyv ontheoptimumgeometricshapesofznsebasedscintillationelements AT katrunovk prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT naydenovs prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT ryzhikovv prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT starzhinskiyn prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT galchinetskiil prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT gavrilukv prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT yanovskyv prooptimalʹnígeometričníformiscintílâcíinihelementívnaosnovíznse AT katrunovk oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT naydenovs oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT ryzhikovv oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT starzhinskiyn oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT galchinetskiil oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT gavrilukv oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse AT yanovskyv oboptimalʹnyhgeometričeskihformahscintillâcionnyhélementovnaosnoveznse |