Symmetry of induced polar states in noncentral crystals under inhomogeneous heating
В роботі запропоновано використання зовнішньої векторної дії у вигляді просторово неоднорідного нагріву кристала як оригінального і перспективного методу створення нових фізичних властивостей у традиційних кристалах, якими вони не володіють в термодинамічно рівноважному стані. Цей метод розглядаєт...
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Інститут фізики конденсованих систем НАН України
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| Цитувати: | Symmetry of induced polar states in noncentral crystals under inhomogeneous heating / V.F. Kosorotov, L.V. Shchedrina // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 827-833. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1209832017-06-14T03:05:28Z Symmetry of induced polar states in noncentral crystals under inhomogeneous heating Kosorotov, V.F. Shchedrina, L.V. В роботі запропоновано використання зовнішньої векторної дії у вигляді просторово неоднорідного нагріву кристала як оригінального і перспективного методу створення нових фізичних властивостей у традиційних кристалах, якими вони не володіють в термодинамічно рівноважному стані. Цей метод розглядається як альтернатива до загально прийнятого підходу – синтезу нових функціональних матеріалів. Зміна природи зовнішньої дії або її напрямку дає можливість керувати і варіювати поляризаційними властивостями кристалів у досить широких межах. Досліджується третинний піроелектричний ефект, який можна вважати найбільш перспективним для неперервного контролю інтенсивного ІЧ випромінювання. The use of an external vector action in the form of the crystal spatially inhomogeneous heating is advanced as an original and promising method of generating new properties in traditional crystals, which do not possess these properties in the thermodynamically equilibrium state, as an alternative to the universally adopted line – the synthesis of new infrared functional materials. The change of the nature of an external influence or its direction makes it possible to control and vary the crystal polarization properties over a wide range. Tertiary pyroelectric effect is investigated which exhibits the most promising monitoring for an intense IR radiation. 2000 Article Symmetry of induced polar states in noncentral crystals under inhomogeneous heating / V.F. Kosorotov, L.V. Shchedrina // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 827-833. — Бібліогр.: 13 назв. — англ. 1607-324X DOI:10.5488/CMP.3.4.827 PACS: 77.60, 77.70 http://dspace.nbuv.gov.ua/handle/123456789/120983 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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DSpace DC |
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English |
| description |
В роботі запропоновано використання зовнішньої векторної дії у вигляді просторово неоднорідного нагріву кристала як оригінального
і перспективного методу створення нових фізичних властивостей у
традиційних кристалах, якими вони не володіють в термодинамічно рівноважному стані. Цей метод розглядається як альтернатива
до загально прийнятого підходу – синтезу нових функціональних матеріалів. Зміна природи зовнішньої дії або її напрямку дає можливість
керувати і варіювати поляризаційними властивостями кристалів у
досить широких межах. Досліджується третинний піроелектричний
ефект, який можна вважати найбільш перспективним для неперервного контролю інтенсивного ІЧ випромінювання. |
| format |
Article |
| author |
Kosorotov, V.F. Shchedrina, L.V. |
| spellingShingle |
Kosorotov, V.F. Shchedrina, L.V. Symmetry of induced polar states in noncentral crystals under inhomogeneous heating Condensed Matter Physics |
| author_facet |
Kosorotov, V.F. Shchedrina, L.V. |
| author_sort |
Kosorotov, V.F. |
| title |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| title_short |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| title_full |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| title_fullStr |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| title_full_unstemmed |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| title_sort |
symmetry of induced polar states in noncentral crystals under inhomogeneous heating |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2000 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120983 |
| citation_txt |
Symmetry of induced polar states in noncentral crystals under inhomogeneous heating / V.F. Kosorotov, L.V. Shchedrina // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 827-833. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT kosorotovvf symmetryofinducedpolarstatesinnoncentralcrystalsunderinhomogeneousheating AT shchedrinalv symmetryofinducedpolarstatesinnoncentralcrystalsunderinhomogeneousheating |
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2025-07-08T18:58:10Z |
| last_indexed |
2025-07-08T18:58:10Z |
| _version_ |
1837106298002341888 |
| fulltext |
Condensed Matter Physics, 2000, Vol. 3, No. 4(24), pp. 827–833
Symmetry of induced polar states in
noncentral crystals under
inhomogeneous heating
V.F.Kosorotov, L.V.Shchedrina
Institute of Physics, the National Academy of Sciences of the Ukraine,
46 Nauki Ave., UA-252650 Kiev-22, Ukraine
Received April 17, 2000
The use of an external vector action in the form of the crystal spatially in-
homogeneous heating is advanced as an original and promising method
of generating new properties in traditional crystals, which do not possess
these properties in the thermodynamically equilibrium state, as an alterna-
tive to the universally adopted line – the synthesis of new infrared functional
materials. The change of the nature of an external influence or its direction
makes it possible to control and vary the crystal polarization properties over
a wide range. Tertiary pyroelectric effect is investigated which exhibits the
most promising monitoring for an intense IR radiation.
Key words: polar state, tertiary pyroelectric effect, symmetry
PACS: 77.60, 77.70
1. Introduction
There are two reasons for our interest in unconventional polar materials for in-
frared optoelectronics – nonpolar piezoelectrics, which do not belong to pyroelectric
classes. First, elaboration of a general approach to the formation of efficient py-
roactive media with controlled polarization properties and possessing unique phys-
ical characteristics as compared with the true pyroelectrics, is made possible with
a rapid research regarding polarization phenomena under nonequilibrium thermal
conditions in recent years [1–10]. The second point of our interest consists in de-
veloping new technologies in pyroelectric materials and establishing new physical
principles for the construction of infrared sensors in a wide spectral range. This can
be attributed to the necessity of solving a number of the applied problems involved
in registering the superpower and short laser pulses by IR sensors.
A novel approach to the creation of induced pyroelectric media with optimal
physical characteristics (as an alternative to the synthesis of new infrared mate-
rials) based on the existing nonpolar structures makes it possible to control their
polarization properties. New artificial pyroactive structures operate over the crystal
c© V.F.Kosorotov, L.V.Shchedrina 827
V.F.Kosorotov, L.V.Shchedrina
transparency band and therefore the measurements and monitoring of the output
laser radiation are realized without interrupting the technological process. Nonpolar
piezoelectrics reveal pyroactive properties under nonequilibrium thermal conditions
only. Occurrence of pyroactivity in nonpolar crystals is caused by the presence of
the thermoelastic stresses generated as a result of the crystal inhomogeneous heat-
ing. Mechanical stresses, in their turn, induce polarization in the crystal through
the piezoelectric effect. This mechanism of polarization occurrence is known as a
tertiary pyroelectric effect (TPE) [11]. In spite of the active research regarding this
effect, a set of phenomena concerned with a crystal polarization under nonequilib-
rium thermal conditions has not been given a commonly accepted classification up
till now.
2. Symmetry approach under axisymmetric heating
Spatially inhomogeneous heating of a crystal by incident radiation is advanced
as an original and promising method of producing new properties in the traditional
crystals which do not exhibit these properties in the thermodynamically equilibrium
state. Such a heating refers to external vector effects on the crystal and is described
by some point symmetry group Gext. The method idea is reasonably known and
consists in the crystal symmetry change in the field of an external applied action.
According to the Curie principle, such an effect alters the crystal symmetry group
G locally, inducing spatially inhomogeneous polar state in it, since the polar prop-
erties of the crystal depend to a large extent on its symmetry. The change character
of this symmetry depends not only on a type of the group Gext but also on a relative
spatial orientation of the symmetry elements of groups Gext and Gcry (Gcry is the
symmetry group of the unperturbed crystal). The crystal symmetry group in the
field of an external perturbation may be put down as follows
G ⊇ Gcry ⌢ Gext . (1)
Therefore, it is apparent that the crystal properties are subject to wide variations
under the change of an external action nature or its direction. It should be pointed
out that a homogeneous heating likewise is liable to change the crystal symmetry
but only under spatially inhomogeneous elastic boundary conditions. A set of these
elastic conditions and a homogeneous heating in this situation should be considered
as a spatially inhomogeneous effect on the crystal. The potentialities of producing
new properties in crystals employing the method mentioned above within the limits
of spatially homogeneous external actions have been presently exhausted. To accom-
plish these ends we pioneered the use of a vector external action in the form of the
crystal inhomogeneous heating [12].
The polarization spatial distribution in the plate being rather intricate in struc-
ture enables the induced polar states to be used in practice. Derivation of this
information involves severe mathematical difficulties. The problem turns out to be
solvable due to the analysis of the symmetry properties of the polar states. Ad-
vanced symmetry approach proved to be not only an effective method of studying
828
Symmetry of induced polar states. . .
the polar state nature but also fruitful in elaborating the physical principles for
constructing various pyroelectric devices acting on these induced effects. Symme-
try properties of the tertiary pyroelectric effect will be studied for one of the cases
frequently realizable in practice i.e. one-dimensional inhomogeneous temperature
field, when the temperature in a round plate changes only along its radius. This
temperature distribution is realized in the plates subjected to axisymmetric heating
by a sine-modulated radiation flux with a wave length in the transparency band
of the crystal. It should be noted that TPE symmetry analysis in the plates with
temperature varying along the thickness has been previously discussed [13]. This
distribution takes place under uniform irradiation of the plate front face by incident
sine-modulated radiation flux with a wave length inside the lattice absorption band
of the crystal.
Axisymmetric heating creating a temperature radial gradient provides irradiation
of the round plate central region by the laser beam with a uniform energy distribu-
tion over its section. The temperature field with respect to the variable component
involves two zones having a rather uniform temperature distribution within these re-
gions. Transitional layer between zones is very thin (of the order of the temperature
wavelength) and may be ignored. On the one hand, this approximation brings about
the appearance of the first type discontinuities for the thermoelastic stress tensor at
the boundary of regions and hence discontinuity of the polarization vector. On the
other hand, the approximation enables the thermal anisotropy to be neglected and
the symmetry limiting groups to be introduced.
Under the heating in question, the group of external effect Gext is variable in
location – in the heated region, which is determined by the laser beam radius r o,
and beyond it
Gext =
{
∞/mmm, r 6 ro
n/m , r > ro
}
. (2)
It should be pointed out that the polar state symmetry in the heated region (2) is no
different from the one investigated under temperature thickness gradient conditions
in [13]. Clearly it derives from the fact that the external effect groups are coincident
in both cases.
The symmetry axis n is contained in the group Gext only if it is present in the
crystal symmetry group Gcry and if it is perpendicular to the cut plane m. Other-
wise, Gext = m. As is seen, the symmetry group of an external effect under thermo-
dynamically nonequilibrium state conditions is spatially inhomogeneous. Generally
speaking, the symmetry group n/m is conditional for a nonheated region which is
under conditions of a strong spatially inhomogeneous action (i.e., there are loaded
internal and mechanically free external surfaces). Notice that if the symmetry axis n
and plane m coincident with the normal to the plate and the cut plane, respectively,
are absent in the group Gcry, the tertiary pyroelectric effect will manifest itself under
the dissymmetry conditions. Therefore, in this case the complete numerical calcu-
lation of the polar state in a cold region of the plate is requisite for TPE practical
applications.
829
V.F.Kosorotov, L.V.Shchedrina
3. Symmetry properties of induced polar states
Let us present for a nonheated region of the crystal the symmetry analysis re-
sults of the same crystallographic cuts (studied in [13] under temperature thickness
gradient), which are active in relation to the tertiary pyroelectric effect taking into
consideration expression (2) and the Curie principle (1). No consideration will be
given to the cuts perpendicular to the sole polar direction since the longitudinal
TPE must necessarily exist here under heating in question. It makes sense to study
these cuts only for a concurrent occurrence of transverse and longitudinal effects.
Monoclinic syngony.
Class C2. G = I (I is the unit element) in the cuts containing the two-fold axis.
TPE manifests itself in these cuts under dissymmetry conditions.
Class Cs. G = I in the cuts perpendicular to the directions n(n1,0, n3) and TPE
will occur under dissymmetry conditions.
Rhombic syngony.
Class D2. TPE exists in the cuts involving only one of the two-fold symmetry
axes under dissymmetry conditions.
Class C2v. G = m in the cuts normal to the directions n(n1, n2, 0) if only one of
the components ni is equal to zero. In these cuts the transverse effect is found. If
none of these components become zero, TPE exists under dissymmetry conditions.
Tetragonal syngony.
Classes C4, S4. TPE existing under dissymmetry conditions takes place in both
classes in the cuts perpendicular to the directions n(n1, n2, 0).
Class D4. TPE can manifest itself under dissymmetry conditions in those cuts,
a normal to which lies in the plane going through the axis 4 and one of the two-fold
axes.
Classes C4v, D2d. Transverse effect takes place in the cuts coincident with one
of the symmetry planes. Longitudinal effect exists in the D2d class in the cuts per-
pendicular to the two-fold axes.
Trigonal syngony.
Class D3. G = 2 in the cuts perpendicular to any one of the two-fold axes and
the longitudinal TPE is found. TPE manifests itself in the cuts parallel to these
axes under dissymmetry conditions.
Class C3v. G = m in the cut plane coincident with the symmetry plane and the
transverse effect can occur here. TPE is found in the planes perpendicular to the
symmetry planes under dissymmetry conditions.
Hexagonal syngony.
Class C6. TPE takes place under dissymmetry conditions in all cuts excepting
the cut perpendicular to the axis 6. The latter cut is characterized by availability of
a longitudinal effect.
Class C6v. G = m in all cuts containing the axis 6. Transverse TPE exists in
these cuts. To obtain this result the Hermann theorem should be taken into account.
Class D6. This class manifests the same results as the class D4.
830
Symmetry of induced polar states. . .
Cubic syngony.
Classes T, Td.G = 3 (class T ) andG = 3m (class Td ) in the cuts perpendicular to
the three-fold axes. In these classes, respectively, longitudinal and transverse effects
take place. Longitudinal TPE exists in the cuts perpendicular to the two-fold axes.
TPE will occur in the cuts parallel to one of the two-fold axes under dissymmetry
conditions.
4. Some specific features in the behavior of polar states
Consideration must be given to the conditional character of the results obtained
with the use of the Curie principle for the crystals being in thermodynamically
nonequilibrium state. A number of new results not filling in the context of the
existing knowledge is a consequence of such an approach. This is concerned with the
crystallographic cuts the planes of which are perpendicular to the three-fold axes.
To take an example, the crystal symmetry groups in the field of an external action
G = 3 and G = m for the crystallographic cuts [111] in a cubic syngony have been
obtained. It would seem, the polarization vector is to be directed along the sole polar
axis which is contained in these groups. However, the transverse effect is available
along with a longitudinal one, and the polarization vector is not coincident with the
three-fold axis direction. Furthermore, in analogous cuts of the crystallographic class
D3, where a longitudinal piezoelectric effect is rigidly forbidden, the polarization
vector is perpendicular to the sole polar direction. TPE is completely lacking in
the indicated cuts of the crystals possessing the symmetry group D6, where G = 6,
in spite of the fact that the sole polar direction is available. This is due to the
availability of rotations in the group C6 which are not concerned with the three-fold
symmetry axis.
Let us deal with the Z-cuts of crystals with the symmetry groups C3h and D3h,
for which the longitudinal effect is also forbidden. In the case under study G = 6 and
the sole polar direction is simply not in the group. Nevertheless, the transverse TPE
exists in both cases. It is significant that the availability of the sole polar direction
is not needed in the cut plane in all instances of the transverse TPE manifestation
associated with the symmetry axis 3. On the contrary, there is angle dependence of
the effect proportional to cos(ϕ+ ϕo). In such a manner the invariance condition of
the polarization spatial distribution under transformations of the group G is fulfilled
in all cases discussed and for all possible polarization distributions.
Cases considered do not exhaust all the collection of the crystallographic cuts
useful for a practical application. Really, in connection with a formulation of the
problem (cuts in question are common to both heating types: radial and thickness
gradient of temperature) the cuts being active with respect to TPE manifestation in
the plate heated region have been investigated. However, the information reading in
transmission-type power pyroelectric sensors (wavelength of a measurable radiation
lies in the transparency band of the sensor element) is carried out through the
use of the metal electrode system deposited on nonirradiated sections of the plate
surface. Electric potential on these sections in accordance with their spatial location
831
V.F.Kosorotov, L.V.Shchedrina
and also polar state character is generated by both heated and cold plate regions.
Consequently, the use of the cuts, which are active relative to TPE appearance only
in the nonheated region, is quite allowable.
5. Conclusion
In this paper we suggested a symmetry analysis of induced polar states in thin
crystal plates subjected to axisymmetric heating by a radiation sine-modulated flux
with a wavelength in the transparency band of the crystal. Crystallographic cuts
being active relative to the tertiary pyroelectric effect are established in all piezo-
electric classes. The presented symmetry approach proves to be an effective method
for revealing principal peculiarities of the electric potential spatial distribution de-
termining design features of IR sensors. Among physical effects which involve the
polarization response to inhomogeneous heating, TPE is the most promising for
practical applications.
References
1. Kosorotov V.F., Kremenchugskij L.S., Levash L.V., Shchedrina L.V. Tertiary pyro-
electric effect in lithium niobate and lithium tantalate crystals. // Ferroelectrics, 1986,
vol. 70, No. 1/2, p. 27–37.
2. Kosorotov V.F., Kremenchugskij L.S., Levash L.V., Shchedrina L.V. Some specific
features in the behavior of dynamic pyroelectric effect under temperature gradient
conditions. // Ferroelectrics, 1991, vol. 118, No. 1/4, p. 233–240.
3. Wang X.S., Zhang J.Q. A discussion on type II pyroelectric detectors. // Infrared
Phys., 1992, vol. 33, No. 6, p. 475–480.
4. Pereverzeva L.P., PoplavkoYu. M., Prokopenko Y.V., Chepilko A.G. Pyroelectricity
in noncentral crystals. // Acta Physica Polonica A, 1993, vol. 84, No. 2, p. 287–291.
5. Wang X.S. Tertiary pyroelectric effect on thick ferroelectric crystal plates with par-
tially uniform heating.// Ferroelectrics Lett. Sec., 1993, vol. 15, No. 5–6, p. 159–165.
6. Kosorotov V.F., Levash L.V., Shchedrina L.V. et al. Power sensors, based on the
tertiary pyroelectric effect, combined with exit windows of CO and CO2 lasers. //
Quantum Electronics, 1994, vol. 24, No. 6, p. 543–545.
7. Kosorotov V.F., Kremenchugskij L.S., Levash L.V., Shchedrina L.V. Dynamic tertiary
pyroelectric effect and its inertial properties. // Ferroelectrics, 1994, vol. 160, No. 3/4,
p. 125–136.
8. Munshi T.K., Kundu K.K., Mahalanabis R.K. Mechanical response in an N-electrode
piezo-quartz bar under electrical and thermal excitations. // Acta Physica Polonica
A, 1995, vol. 87, No. 6, p. 995–1002.
9. Blonsky I.V., Kosorotov V.F., Levash L.V., Shchedrina L.V. New pyroactive structure
for infrared optoelectronics. // SPIE, 1999, vol. 3890.
10. Kosorotov V.F., Kremenchugskij L.S., Samoilov V.B., Shchedrina L.V. Pyroelectric
Effect and Its Practical Applications, Kiev, Naukova Dumka, 1987 (in Russian).
11. Nye J.F. Physical Properties of Crystals. Their Representation by Tensors and Ma-
trices. Oxford University Press, London, 1957.
832
Symmetry of induced polar states. . .
12. Kosorotov V.F., Kremenchugskij L.S., Shchedrina L.V. Tertiary pyroelectric effect
and its application for registration of the pulse radiation. – In: Proc. of Conf. on
Production and Employment of Ferro- and Piezomaterials. Moscow, 1984, p. 71–75
(in Russian).
13. Kosorotov V.F. Symmetry properties of tertiary pyroelectric effect in inhomogeneous
one-dimensional temperature fields. // Inorganic Materials, 1995, vol. 31, No. 6,
p. 827–830 (in Russian).
Симетрія полярних станів, індукованих
неоднорідним нагрівом нецентросиметричних
кристалів
В.П.Косоротов, Л.В.Щедріна
Інститут фізики НАН України, 252650 Київ, просп. Науки, 46
Отримано 17 квітня 2000 р.
В роботі запропоновано використання зовнішньої векторної дії у ви-
гляді просторово неоднорідного нагріву кристала як оригінального
і перспективного методу створення нових фізичних властивостей у
традиційних кристалах, якими вони не володіють в термодинаміч-
но рівноважному стані. Цей метод розглядається як альтернатива
до загально прийнятого підходу – синтезу нових функціональних ма-
теріалів. Зміна природи зовнішньої дії або її напрямку дає можливість
керувати і варіювати поляризаційними властивостями кристалів у
досить широких межах. Досліджується третинний піроелектричний
ефект, який можна вважати найбільш перспективним для неперерв-
ного контролю інтенсивного ІЧ випромінювання.
Ключові слова: полярний стан, третинний піроелектричний ефект,
симетрія
PACS: 77.60, 77.70
833
834
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