Article
Reference
Optical properties of ferroelectric boracite
KOBAYASHI, Jinzo, et al.
Abstract
The characteristic features of the electrooptical properties of Fe I boracites were elucidated from x-ray diffraction measurements of the lattice strains and from optical ns. The electro-optic consts. of the Fe I boracite are considerably larger compared with the usual ferroelecs., and the electrooptic consts. of Fe I boracite depend strongly on the applied fields.
KOBAYASHI, Jinzo, et al. Optical properties of ferroelectric boracite. Journal of the Physical Society of Japan, 1970, vol. 28, p. 67-70
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Optical Properties of Ferroelectric Boracite
J. KOBAYASHI, I. MiZUTANI, H . HARA, N . YAMADA
Department of Applied Physics, Waseda University, Tokyo, Japan
O. NAKADA, A. KUMADA
Hitachi Central Research Laboratories, Tokyo, Japan
H . SCHMID and
Battelle Memorial Institute, Geneva, Switzerland
% 1. Introduction
The boracite crystals, MesBvOnX, where Me designates divalent metals and X halogen atoms, undergo a phase transition'^ from a high temper- ature form Td^ to a low temperature form Ci^^.
Some of the present authors^' have recently proved the low temperature form of Fe-I-boracite to be ferroelectric through optical observation of do- main reversal under applied electric fields. How- ever, any information of the electro-optical properties of boracites has not yet been obtained.
The inevitable obstacles to be met in the course of elucidating these properties were (i) difficulties in preparing large single crystals, and (ii) diffi- culties in measuring extremely small lattice strains.'^
We have recently succeeded in measuring the lattice strains of Fe-I-boracite very accurately using special X-ray diflFraction methods.^' The purpose of this paper is to manifest the character- istic features of the electro-mechanical and electro- optical properties of Fe-I-boracite elucidated from these X-ray data and optical refractive indices.
§ 2. Spontaneous Lattice Strains
The orthorhombic Civ phase of Fe-I-boracite crystal is based upon a slightly strained lattice of the cubic Td phase as a result of electro-mechanical coupling due to the spontaneous polarization. So it is convenient to describe the lattice of Fe-I- boracite in terms of the orthorhombic {A, B, C) axes which are related to the cubic (a, 6, c) axes by a transformation matrix ^ 0/|, ^, 0/0, 0, 1) as schematically depicted in Fig. 1.
The present measurements of the lattice para- meters and the lattice strains have been performed by applying two different X-ray methods comple- mentarily, viz., a two-dimensional reciprocal lattice method^* and an X-ray strainmeter method both having been developed by Koba- yashi et al..
(i) (ii)
Fig. 1. The crystal lattices of high temperature (cubic) and low temperature (orthorhombic) forms of Fe-I- boracite (distortion exaggerated) projected on (001).
The arrows between them indicate the reversal of the crystal orientation due to the applied electric fields.
The paraelectric phase of Fe-I-boracite has a torsional piezoelectric coefficient ^36°, when re- ferred to the cubic lattice directions. Therefore, under the existence of an electric polarization Pi a pure shear xn^^^^h^^Pi occurs. In the ferro- electric C2„ phase, the strains along the A-, B- and C-axes can be expressed as,
ATI =i636°i'.+G3i°P.^=A:,2<'+Q31
X2^-^b26°Ps + Q2x'Ps'^-Xn° + Q3lPs\ 1 )
X3 = Q33°P.^
where Q3i° and Q33° designate electro-strictive coef- ficients in the Td phase. The lattice parameters of Fe-I-boracite are indicated in Fig. 2 with respect to temperature. From the observed strains xi, xz, and X3, piezo-electric and electro-strictive terms in the strains can be derived separately. The temper- ature dependence of these terms are depicted in Fig. 3. The pure shear is developed suddenly at the Curie point, which is as small as V38", de- creases with decreasing temperature and finally diminishes to zero at the lower transition point.
It must be noted that electro-strictions, Qn'^Ps^
and Qn^Ps^, which are nearly equal in magni-
67
68 J. KOBAYASHI, et al.
1U50
' I ' ' • ' 1 ' ' ' ' I
. a.wo
8.630 8.620
3.600
&590,
-918
, . I
,1, • . • I t I 1 I r I I I I I t I •
-100 -50 0 50 Tc 100 TEMPBUTURE, t °C )
912
910
Fig. 2. The lattice parameters and the lattice volume of Fe-I-boracite with respect to temperature.
TEMPERATURE ( "C )
Fig. 3. Temperature dependence of the linear piezo- electric strain ^636^^, or pure shear xi{>, and the quadratic strains, Qi\°Ps^ and Qzi^Ps^, in the ferro- electric state of Fe-I-boracite.
tude, are twice as large as the linear strain. These conspicuous electro-strictions give important -effects to every physical properties of Fe-I-boracite.
From our measurement of Ps, the electro-strictive constants Qn^ and ^33° are found to be almost temperature-independent and deduced as follows:
(2=e3i°=e33° = 1.1 ±0.5 X lO-'o esu
(Q3i = 3.8xlO-'^esu,
Q33 = 2.9xlO-'2esu''),
where the corresponding values of related com- pound KH2PO4 are shown in parentheses for the sake of comparison. 636° begins to decrease monotonously from the Curie point and vanishes at the lower transition point in the same way as
jci2°. The value at room temperature is:
636" = 1.8±0.5x10-7 esu (at 21 °C)
(Z)36 = 5.0X10-^ esu^O.
§ 3. Electro-Optical Character of Fe-I-Boracite Absolute measurements of refractive indices of Fe-I-boracite have been made by a prism method over both paraelectric and ferroelectric temper- ature range. As has already stated,-' the switching of the spontaneous polarization brings about the interchange of the A- and jB-axes in a crystal, the crystal plane, (010), facing normal to the incident beam contains (A,C) axes and {B,C) axes depend- ing on the sense of the spontaneous polarization.
Thus we were able to measure the principal refractive indices at a single crystal mounting.
The temperature dependence of the principal re- fractive indices and the derived birefringences are shown in Fig. 4(a) and (b).
1.890
1.870
-80 - 60 -40 -20 0.010
0 20 «0 60 80 100 120 TEMPERATURE, C O
( a )
0.008 hi u z
UJ (
z S
^ 0.004 0.902 -
1 1 1 r - r • — r •- - - J - -| •
• ""^——.-^ ^ •
•
1 1 1 1 1 1 1—1—1 1
-80 -60 -40 -20 0 20 40 60 80 100 120 TEMPERATURE, ("C)
(b)
Fig. 4. The temperature dependence of the refractive indices and the birefringences of Fe-I-boracite.
(a) The refractive indices.
(b) The birefringences.
The electro-optic (e.o.) constant rtj is expressed as follows:
where r' represents the electronic response of the constituent atoms in the crystal, and a: is a strain- optic constant. Duly allowing for the large electro-strictive parts in the spontaneous strains
of Fe-I-boracite, the e.o. constants of Fe-I-bora- cite are expressed as:
»-23 = -ir63°'-i636%44 + ^P., ( 2 ) rn=r33' + QP„
where ^=(:rn + 2;ri2)0, and reiP' stands for an e.o. constant of a clamped crystal in the para- electric state, TTij strain-optic constants referring to the cubic axes.
Meanwhile, the spontaneous Kerr eflfects in the principal refractive indices in the ferroelectric state can be evaluated by using the e.o. constants,
8nr = nr—no = — i«o'
X { - K' ' 6 3 ' " + 636«Jr44)i'. + QPs'},
X{i{r63°' + b36''7r,4)Ps + QPs^}, (3)
dna = na-no= -^noHrj^'Ps+QPs^}.
From these quantities, not only linear and quad- ratic but also electronic parts of the e.o. constants can be obtained separately. The linear term ^63°' +
^36^^44 can first be evaluated by comparing tem- perature variations of both birefringence along the C-axis, dn^—dnr, and the spontaneous polari- zation. X-ray study disclosed that bu° vanishes at —70°C. Therefore the value at this temper- ature indicates r63'" itself. Besides strain optic constant :r44 can be calculated since the temper- ature dependence of 636° has already been known.
The results are:
r63<" = 2.4xl0-^esu (-70°C),
;r44=-7.3X10-^ esu (20°C).
Insimilar ways we can obtain i3 = 1.5x 10~'°esu.
Finally rij' is derived,
^33' = 2.2X10-''esu (20°C).
Thus we could evaluate every electro-optic con- stant as the sum of electronic, linear piezo-optic and quadratic piezo-optic terms. They are sum-
-Table I. Electro-optic coefficients of Fe-I-boracite at 20°C.
{ru in 10-'' esu units)
Electronic part piezo-optic piezo-optic Total Linear Quadratic part part
'•13 1.2 0.1 3.3 4.6 2.5
'•23 - 1. 2 - 0 . 1 3.3 2.0 1.1
^•33 2.2 0 3.3 5.5 3.0
marized in Table I, where rij'' stands for the e.o.
constants corresponding to the polarization fields, and r,;^ to the electric field.
The electro-optic constants of Fe-I-boracite are considerably large compared with the usual ferro- electrics. Attention must be paid to the origins of the electro-optic constants. One of the most interesting phenomena in this crystal is that the electronic terms are two orders of magnitude larger than those of linear terms. Moreover, they are about ten times as large as total electro-optic constants of KDP. The other feature is the great contribution of electro-strictive constants to the total electro-optic constants. In another words, the electro-optic constants of Fe-I-boracite are strongly dependent upon the applied fields.
References
1) H. Schmid: J. Phys. Chem. Solids 26 (1965) 973.
2) J. Kobayashi, H. Schmid and E. Ascher: Phys.
Status solidi 26 (1968) 277.
3) T. Ito, N. Morimoto and R. Sadanaga: Acta cryst. 4 (1951) 310.
4) J. Kobayashi, I. Mizutani, H. Schmid and H.
Schachner: to be published in Phys. Rev.
5) J. Kobayashi, N. Yamada and T. Nakamura:
Phys. Rev. Letters 11 (1963) 410.
6) J. Kobayashi, N. Yamada and T. Azumi: Rev.
sci. Instrum. 39 (1968) 1647.
7) F. Jona and G. Shirane: Ferroelectric Crystals.
(Pergamon).
DISCUSSION
G. BURNS: IS this crystal like Gd2(Mo04)3 in the sence that there is no anomaly in eciamped?
If so it is an example of a ferroelectric with an soft acoustic mode as apparently Gd2(Mo04)3.
J. KOBAYASHI: We have not yet measured Cdamped of Fe-I-boracite so far. But according to the data available at present, this crystal is likely to be the same kind of ferroelectric with
Gd2(Mo04)3. Especially, I think it noticeable that in the course of our refractive index measurements, where inclusion of small internal stresses in the specimen was inevitable, excur- sions of «o occur just above the Curie point.
R. C. MILLER: What is the optical region of transparency of Fe-I-boracite?
J. KOBAYASHI: Exact knowledges of the optical region of transparency of Fe-I-boracite are not clear at present.
70 J. KOBAYASHI, et al.
L. E . CROSS: Do you have a direct measurement of the piezoelectric constant to compare with the value deduced from the spontaneous strains?
J. KOBAYASHI: No, we have not made a direct measurement of the piezoelectric constant.
But it would be impossible to do since the size of the crystals available at present are not suf- ficiently large. This is one of .the impetuses by which we developed our X-ray methods capable of deducing very small lattice strains.
