The refractometry of the uniaxially stressed ferroelectrics
The effect of uniaxial mechanical stresses upon the spectral and temperature dependences of birefringences in some ferroelectric crystals with the incommensurate phase are studied. Considerable baric displacements of para-incommensurate-commensurate phases transition points were observed.The calcu...
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| Cite this: | The refractometry of the uniaxially stressed ferroelectrics / M.O. Romanyuk, V.Yo. Stadnyk // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 711-720. — Бібліогр.: 12 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1210122025-02-23T19:04:24Z The refractometry of the uniaxially stressed ferroelectrics Рефрактометрія механічно затиснутих сегнетоелектриків Romanyuk, M.O. Stadnyk, V.Yo. The effect of uniaxial mechanical stresses upon the spectral and temperature dependences of birefringences in some ferroelectric crystals with the incommensurate phase are studied. Considerable baric displacements of para-incommensurate-commensurate phases transition points were observed.The calculated temperature and spectral dependences of combined π⁰im and absolute πim piezooptic constants show a considerable dispersion and anomalies at phase transitions.The increase of the principal refractive indices under stress effect was observed. Досліджено вплив одновісного механічного тиску на температурні і спектральні зміни двозаломлення, баричні зміни точок фазових переходів, температурно-спектральні залежності п’єзооптичних констант, а також проаналізовано температурні, спектральні та баричні зміщення точок інверсії знаку двозаломлення деяких сегнето-електричних кристалів, що володіють несумірною фазою. Виявлено значні баричні зміщення точок фазових переходів параелектрична- несумірна-сумірна фази. Виявлено значну дисперсію та аномалії при фазових переходах у поведінці комбінованих π⁰im та абсолютних πim п’єзооптичних констант. Встановлено, що головні показники заломлення зростають при дії одновісного тиску, що зумовлено збільшенням рефракцій зв’язку та електронної поляризованості. Побудовано температурно-спектрально-баричні діаграми ізотропного стану. 1999 Article The refractometry of the uniaxially stressed ferroelectrics / M.O. Romanyuk, V.Yo. Stadnyk // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 711-720. — Бібліогр.: 12 назв. — англ. 1607-324X DOI:10.5488/CMP.2.4.711 PACS: 77.80.Bh, 77.84.Fa, 78.20.Ci https://nasplib.isofts.kiev.ua/handle/123456789/121012 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
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The effect of uniaxial mechanical stresses upon the spectral and temperature dependences of birefringences in some ferroelectric crystals with
the incommensurate phase are studied. Considerable baric displacements
of para-incommensurate-commensurate phases transition points were observed.The calculated temperature and spectral dependences of combined
π⁰im and absolute πim piezooptic constants show a considerable dispersion and anomalies at phase transitions.The increase of the principal refractive indices under stress effect was observed. |
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Romanyuk, M.O. Stadnyk, V.Yo. |
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Romanyuk, M.O. Stadnyk, V.Yo. The refractometry of the uniaxially stressed ferroelectrics Condensed Matter Physics |
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Romanyuk, M.O. Stadnyk, V.Yo. |
| author_sort |
Romanyuk, M.O. |
| title |
The refractometry of the uniaxially stressed ferroelectrics |
| title_short |
The refractometry of the uniaxially stressed ferroelectrics |
| title_full |
The refractometry of the uniaxially stressed ferroelectrics |
| title_fullStr |
The refractometry of the uniaxially stressed ferroelectrics |
| title_full_unstemmed |
The refractometry of the uniaxially stressed ferroelectrics |
| title_sort |
refractometry of the uniaxially stressed ferroelectrics |
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Інститут фізики конденсованих систем НАН України |
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1999 |
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https://nasplib.isofts.kiev.ua/handle/123456789/121012 |
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The refractometry of the uniaxially stressed ferroelectrics / M.O. Romanyuk, V.Yo. Stadnyk // Condensed Matter Physics. — 1999. — Т. 2, № 4(20). — С. 711-720. — Бібліогр.: 12 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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| first_indexed |
2025-11-24T14:55:53Z |
| last_indexed |
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1849684030957551616 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 4(20), pp. 711–720
The refractometry of the uniaxially
stressed ferroelectrics
M.O.Romanyuk, V.Yo.Stadnyk
The Ivan Franko State University of Lviv,
8 Kyryla and Mefodiya Str., 79005 Lviv, Ukraine
Received March 1, 1999, in final form October 14, 1999
The effect of uniaxial mechanical stresses upon the spectral and temper-
ature dependences of birefringences in some ferroelectric crystals with
the incommensurate phase are studied. Considerable baric displacements
of para-incommensurate-commensurate phases transition points were ob-
served.The calculated temperature and spectral dependences of combined
π0
im
and absolute πim piezooptic constants show a considerable disper-
sion and anomalies at phase transitions.The increase of the principal re-
fractive indices under stress effect was observed.
Key words: ferroelectrics, phase transition, optical properties, refractive
indices, birefringence, piezooptic constants
PACS: 77.80.Bh, 77.84.Fa, 78.20.Ci
1. Introduction
Many works are devoted to the investigation of baric changes of optical properties
of crystals [1]. Piezooptic constants of few crystals were determined, and the birefrin-
gence sign inversion of some mechanically stressed cubic crystals was observed. It was
shown that some piezooptic constants nonlinearly vary in the region of ferroelectric
phase transition [2–5]. High sensibility of incommensurate phase to uniaxial stress
was observed [6,7]. In the present paper the results of piesooptic investigations of sev-
eral ferroelectrics (LiKSO4 (LPS), (NH4)2BeF4 (AFB), RbNH4SO4 (RAS),
KNaC4H4O6 · 4H2O(RS), KH2PO4 (KDP) and KD2PO4 (DKDP)) are presented.
These crystals possess the phase transitions (PT) and birefringence sign inversion
(BSI) [8–12] in a wide temperature region (4.2÷ 1000) K.
The purpose of this paper is to study the effect of uniaxial mechanical stresses
along the principal crystallophysic directions and bisectors between them upon the
spectral and temperature dependences of birefringence, baric displacements of PT
points, as well as to determine the temperature and spectral changes of piezooptic
constants in the above enumerated crystals.
c© M.O.Romanyuk, V.Yo.Stadnyk 711
M.O.Romanyuk, V.Yo.Stadnyk
2. Experiment
The effect of uniaxial mechanical stresses upon the birefringent properties of
crystals are studied by the changes of interference picture. The birefringence is cal-
culated using the formula:
∆ni(λ, T )
∣
∣
∣
∣
σ
=
k(T )λ
di(T, σ)
, ∆ni(λ, σ)
∣
∣
∣
∣
T
=
k(σ)λ
di(T, σ)
, (1)
where the markers used are known.
The measurements are carried out up to the pressure of σm ∼ 200 bar and tem-
perature decreasing. The samples were stressed at room temperature. The KDP
crystals were stressed along the normal to symmetry plane of paraphase. These di-
rections were preliminaryly determined by the interference figures pattern of biaxial
crystals. These figures were obtained when the electric field Ez was applied to the
crystal at room temperature. The combined difference of piezooptic constants is
determined using the formula:
π0
im =
2δ∆ni
σm
+ 2∆nisim , (2)
where δ∆ni is the induced change of birefringence for the i-direction of light prop-
agation; σm is the mechanical pressure along the m-direction; i and m are the crys-
tallophysic axes; sim are the elastic complince coefficients.
3. Results and discussion
It was determined, that the birefringence of crystals is sensitive enough to uniax-
ial stress along the principal crystallophysic directions and is less sensitive to stress
along the bisectors between them (figure 1).
3.1. Uniaxial stress effects the birefringence of crystals
The following regularity is observed: uniaxial stresses along the mutually perpen-
dicular crystallophysic directions lead to the opposite signs of birefringence changes
(see table 1).
As a rule, the birefringence of all crystals studied becomes more sensitive to
stress effect at the decrease of wavelength. The baric sensibility of ∆ni increases at
approaching the BSI point.
3.2. Baric displacement of PT points
The following regularity of baric displacement of PT points are studied (see
table 2). The uniaxial stresses σx and σy lead to expanding the incommensurate phase
(IP) of AFB crystal and to the displacement of temperature range of its occurence
to the low temperature region. The uniaxial stress σz leads to the narrowing of the
IP. It was determined by Ti,c(σ) extrapolation that the IP disappears and the PT
712
The refractometry of the uniaxially stressed ferroelectrics
400 600
0
2
4
4
3
2
1
∆n
y
x
10
-4
λ,nm
Figure 1. Birefringence dispersion for LiKSO4 crystal: 1 – T=294K, σ=150 bar;
2 – T=294K, σ=0bar; 3 – T=226K, σ=100 bar; 4 – T=226K, σ=0bar.
Table 1. Baric changes of birefringence of crystals at room temperature
pressure ∆nx ∆ny ∆nz crystal
X – increase increase
Y decrease – decrease (NH4)2BeF4
Z increase decrease –
X – decrease decrease
Y decrease – increase Rochelle salt
Z increase increase –
X – increase decrease
Y increase – decrease RbNH4SO4
Z decrease decrease –
X – decrease –
Y – – – LiKSO4
Z – increase –
X – increase –
Y – – – KH2PO4
Z – decrease –
X – increase –
Y – – – KD2PO4
Z – decrease –
713
M.O.Romanyuk, V.Yo.Stadnyk
of paraphase-commensurate phase (“triple point”) takes place at σz ∼ 2.3 kbar and
T ∼ 190K. The “triple point” of LPS crystal takes place at σz ∼ 4.3 kbar and
T ∼ 286K.
The PT points are very sensitive to uniaxial stress action along the principal
crystallophysic directions. The summary effect of the whole component σm leads to
the displasement of PT points to the low temperature region (figure 2).
Table 2. The temperature-baric coefficients of PT point displacement
pres. dTi/dσm,K/bar dTc/dσm,K/bar
∑
dT/dσm,K/bar crystal
X − −0, 017 −
Y − −0, 013 −0, 015 RbNH4SO4
Z − 0, 015 −
X −0, 32 −0, 021 −
Y −0, 045 −0, 107 −0, 007(Ti) LiKSO4
Z 0, 070 0, 120 −0, 008(Tc)
X − −0, 003 −
Y − 0, 008 −0, 007 KH2PO4
Z − −0, 007 −
X − −0, 007 −
Y − 0, 011 −0, 008 KD2PO4
Z − −0, 012 −
X −0, 011 −0, 016 −
Y −0, 009 −0, 012 −0, 017(Ti) (NH4)2BeF4
Z 0, 003 0, 005 −0, 023(Tc)
The baric dependences of PT points are caused by the uniaxial stress effect upon
crystal structure, mainly, due to the change of position and orientation of BeF2−
4 ,
SO2−
4 , and PO2
4
− basic tetrahedral groups.
3.3. The piezooptic properties of crystals
Using the experimental dependences ∆ni(λ, T, σ) the temperature and spectral
dependences of piezooptic constants π0
im were calculated using the formula (2).
The significant dispersion of π0
im (|dπ0
im|/dλ < 0) was observed (figure 3). The
anomalies of π0
im(T ) in the region of PT agree with the anomalous changes of ni(T )
and ∆ni(T ). The crossing of the curves π0
im(λ) in the region of BSI was determined
(index i denotes the direction of isotropic point appearing), which testifies to the
rising of symmetry of the fourth order piezooptic constants tensor.
Using the experimental results and the known formula for piezobirefringence of
orthorhombic crystals (Pokkel’s method [1]) we have calculated temperature and
spectral dependences of absolute piezooptic constants of AFB, RAS and RS crystals
714
The refractometry of the uniaxially stressed ferroelectrics
0 100 200
174
177
182
184
3
2
1
Tc
T
i
3
2
1
T
,K
G, bar
Figure 2. Baric dependence of phase transition points for (NH4)2BeF4 crystal: 1
– σz; 2 – σy; 3 – σx
0 50 100 150 200
208
210
212
3
1
2
T
c,
K
σ , bar
Figure 3. Baric dependence of the phase transition point for KDP crystal: 1 –
σy; 2 – σx; 3 – σz
715
M.O.Romanyuk, V.Yo.Stadnyk
(figure 4) by solving the following system of equations:
d∆nim = 1/2(n3
mπmm − n3
kπkm), (3)
where i, k,m=1,2,3; d∆nim are the induced changes of birefringence for i-th direction
of light polarization and m-th direction of pressure action; nm, nk are the known
refractive indices of the mechanically unstressed crystal.
It was established that the rising of |dπ0
im| modulus is caused by the nearness of
edge fundamental absorption (it’s in the ultraviolet region for all crystals studied)
as well as by its displacement under the uniaxial stress effect.
3.4. The refractive indices of mechanically stressed crystals
The analysis of baric changes of the principal refractive indices was carried out
using the calculated piezooptic constants by the formula:
ni(λ, T ) = ni0(λ, T )− 1/2
(
πim(λ, T )σmn
3
i0(λ, T )
)
, (4)
where ni0 is the refractive index of the mechanically unstressed crystal.
On the whole, the ni values of crystals studied increase at the uniaxial stress
effect. The uniaxial stress does not vary the character of the behaviour of ni(λ) and
ni(T ) dependences (figure 5).
The electron polarizability α and molar refraction R i of the crystals studied for
light propagation along X,Y,Z-directions were calculated using the spectral depen-
dences ni(λ, σ) by the formula:
(n2
i − 1)/(n2
i + 2) = 4/3πN0αi = ρRi/µ. (5)
It was determined that bonds refraction and the electron polarizability increase
under the uniaxial stress effect. Obviously, the uniaxial stress varies the degree of
ordering of the crystal structure, which is manifested in increasing the electron polar-
izability. In our case, the changes of bonds refraction and electron polarizability lead
to the changes of the electron subsystem of the crystal, determining the character
of interaction of the environment and the electromagnetic light wave.
Using the dependences ni(λ, σ), the ultraviolet (λ0i, Bi) and the infrared (B ′
i)
oscillator parameters were calculated by Zelmeer’s formula:
n2
i − 1 =
Biλ
2
0iλ
2
λ2 − λ2
0i
− B′
iλ
2 (6)
It was established for AFB, RS and RAS crystals that the uniaxial stress displaces
the position of an effective center of UV absorption band mainly to the long wave
region: dλ0/dσm ∼ (4...8) · 10−3 nm/bar. The increase of absolute refractive indices
ni is caused by the decrement of the effective strength of UV oscillators and by the
displacement of the effective center of UV absorption band to the long wave region.
Higher sensibility of the dependence ni(T ) to stress effect was observed in the region
of IP for AFB crystal. It is caused, to our mind, by the peculiarities of interaction
between the modulated structure and the uniaxial deformation.
716
The refractometry of the uniaxially stressed ferroelectrics
280 320 360 400
10
15
20
25
7
6
5
4
3
2
1
π im
0 x1
0
-1
2 , m
2 / N
λ, nm
Figure 4. Dispersion of the combined piezooptic constants for LiKSO4 crystal:
1 – 294K, 2 – 260K, 3 – 230K, 4 – 190K (π0
13); 5 – 294K, 6 – 260K, 7 – 190K
(π0
12).
200 400 600 800
3
6
9
9
8
7
6
5
4
3
2
1
π im
,B
r
λ,nm
Figure 5. Dispersions of the absolute piezooptic constants for Rochelle salts crys-
tal at room temperature: 1 – π21, 2 – π31, 3 – π12, 4 – π11, 5 – π32, 6 – π13, 7 –
π22, 8 – π23, 9 – π33.
717
M.O.Romanyuk, V.Yo.Stadnyk
3.5. The temperature-spectral-baric diagram of the isotropic state
It was determined that the uniaxial stress along the mutually perpendicular crys-
tallophysic directions, normally to the direction of BSI, displaces the point of BSI to
the opposite spectral regions at a constant temperature and to the opposite temper-
ature regions at a constant wavelength.The temperature-spectral-baric diagram of
isotropic state for AFB, LPS, RS and RAS crystals was constructed. It enables us to
determine singlevaluedly the BSI point for definite temperature and spectral interval
at the stress effect up to σm ∼ 200 bar as well as to propose the possible usage of
these crystals as crystallooptic sensors of temperature and pressure, simultaneously.
4. Conclusion
1. The birefringence ∆ni is relatively sensitive to the uniaxial mechanical stress
along the principal crystallophysic directions k and m and is less sensitive
along the bisectors of these directions. The common regularity was observed,
that the stresses along the mutually perpendicular crystallophysic directions
k and m lead to the opposite by sign values of changes of ∆ni.
2. A considerable baric displacement of para-incommensurate-commensurate
phases PT points and Curie points was observed. The “triple point” of disap-
pearing of IP under the action of σx and σy was observed for LPS and AFB
crystals.
3. The calculated temperature and spectral dependences of combined π0
im and ab-
solute πim piezooptic constants show a considerable dispersion (mainly
|dπ0
im
|
dλ
<
0) and anomalies at PTs, that agree with the changes of ni and ∆ni at PTs.
In the region of BSI the crossing of πim(λ, T ) curves was observed for all the
crystals studied. This fact testifies to the rising of symmetry of the piezooptic
tensor or to the lowering of its anisotropy.
4. The increase of principal refractive indices under stress effect was observed,
which is caused by the increase of bonds refraction and electron polarizability.
A uniaxial stress mainly decreases an effective strength of UV oscillators and
displaces an effective center of UV absorption band to the long wave region.
The refractive indices become more sensitive to the pressure action in the
region of the IP.
5. The temperature-spectral-baric diagrams of the isotropic state of the crystals
studied have been constructed.
718
The refractometry of the uniaxially stressed ferroelectrics
References
1. Narasimhamurty T.S. Photoelastic and electro-optic properties of crystals. New–York
and London, Plenum Press, 1981.
2. Romanyuk N.A., Mytsyk B.G., Varikash V.M. The piezooptic properties of triglicine
sulphate crystals. // Izv. AN BSSR, ser. fiz.-mat. nauk, 1980, No. 6, p. 105–110 (in
Russian).
3. Romanyuk N.A., Mytsyk B.G., Kulyk L.M. The piezochanges of optical properties
of triglicine sulphate crystals. // Ukr. Fiz. Zh., 1986, vol. 31, No. 3, p. 354–359 (in
Russian).
4. Mytsyk B.G., Romanyuk N.A. The temperature dependences of piezooptic coefficients
of diglicine nitrate crystals. // Ukr. Fiz. Zh., 1983, vol. 28, No. 4, p. 538–542 (in
Russian).
5. Romanyuk N.A., Mytsyk B.G., Varikash V.M. The piezooptic properties of triglicine
crystals. // Fiz. Tverd. Tela, 1983, vol. 25, No. 6, p. 1670–1674 (in Russian).
6. Vlokh O.G., Polovynko I.I., Mokryj V.M. Birefringence and piezooptic properties
[N(CH3)4]2FeCl4 crystals. // Ukr. Fiz. Zh., 1990, vol. 45, No. 3, p. 349–353 (in Rus-
sian).
7. Vlokh O.G., Kapustyanyk V.B., Mokryj V.M. Piezooptic effect and phase diagram of
incommensurate [N(CH3)4]2MnCl4 crystals. // Izv. vuzov, 1990, No. 7, p. 92–94 (in
Russian).
8. Aleksandrov K.S., Beznosikov V.B. Structural phase transitions in crystals (β−K2SO4
group). Nauka Publ., Novosibirsk, 1984 (in Russian).
9. Stadnyk V.Y., Gaba V.M., Romanyuk N.A. About of isotropic point in LiKSO4 crys-
tals. // Optika i Spektr., 1990, vol. 68, No. 3, p. 701–703 (in Russian).
10. Romanyuk M.O., Stadnyk V.Y., Brezvin R.S. The influence of pressure on optical
properties of LiKSO4 crystals. // Ukr. Fiz. Zh., 1995, vol. 40, No. 10, p. 1068–1070
(in Ukrainian).
11. Romanyuk N.A., Gaba V.M., Ursul Z.M. The character of optical properties
anisotropy of ammonium fluoroberyllate crystals in isotropic point. – In: “Optics
of anisotropic media” (interdepartment collection), Physics-and-Technical Institute
Publ., Moscow, 1987, p. 105–107 (in Russian).
12. Gaba V.M., Ursul Z.M., Romanyuk N.A. The pecularities of optical indicatrix sym-
metry of ammonium fluoroberyllate crystals in region 4.2–420 K. // Kristallografiya,
1989, vol. 34, No. 4, p. 1038–1040 (in Russian).
719
M.O.Romanyuk, V.Yo.Stadnyk
Рефрактометрія механічно затиснутих
сегнетоелектриків
М.О.Романюк, В.Й.Стадник
Львівський державний університет ім. І.Франка,
79005 Львів, вул. Кирила і Мефодія, 8
Отримано 1 березня 1999 р., в остаточному вигляді –
14 жовтня 1999 р.
Досліджено вплив одновісного механічного тиску на температурні і
спектральні зміни двозаломлення, баричні зміни точок фазових пе-
реходів, температурно-спектральні залежності п’єзооптичних кон-
стант, а також проаналізовано температурні, спектральні та барич-
ні зміщення точок інверсії знаку двозаломлення деяких сегнетое-
лектричних кристалів, що володіють несумірною фазою. Виявлено
значні баричні зміщення точок фазових переходів параелектрична-
несумірна-сумірна фази. Виявлено значну дисперсію та аномалії при
фазових переходах у поведінці комбінованих π0
im
та абсолютних πim
п’єзооптичних констант. Встановлено, що головні показники зало-
млення зростають при дії одновісного тиску, що зумовлено збіль-
шенням рефракцій зв’язку та електронної поляризованості. Побудо-
вано температурно-спектрально-баричні діаграми ізотропного ста-
ну.
Ключові слова: сегнетоелектрики, фазові переходи, оптичні
властивості, показники заломлення, двозаломлення, п’єзооптичні
константи
PACS: 77.80 Bh, 77.84 Fa, 78.20 Ci
720
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