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Submitted on 1 Jan 1972
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STUDY OF FERROELECTRIC DOMAINS IN GADOLINIUM MOLYBDATE
C. Malgrange, M. Glogarova
To cite this version:
C. Malgrange, M. Glogarova. STUDY OF FERROELECTRIC DOMAINS IN GADOLIN- IUM MOLYBDATE. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-159-C2-161.
�10.1051/jphyscol:1972255�. �jpa-00214991�
JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 4, Tome 33, Avrii 1972, page C2-159
STUDY OF FERROELECTRIC DOMAINS IN GADOLINIUM MOLYBDATE
C. MALGRANGE (I) and M. GLOGAROVA ( 2 )
(I) Laboratoire de Minbralogie Cristallographie, Associb au CNRS, UniversitC Paris VI, 9 q. St-Bernard, Paris Ve
(2) Institute of Physics, Czech. Acad. Sci., Na slovance 2 Praha 8
Rhumb. - On a observe les domaines ferroklectriques dans des cristaux de molybdate de gadolinium par une mkthode topographique aux rayons X par transmission. Lorsque les plans rkflecteurs sont perpendiculaires aux parois des domaines (leur gkometrie est analogue B celle des domaines pour les cristaux de KDP), on observe entre les domaines des lignes alternativement noires et blanches. La mesure de leur largeur permet de calculer I'angle de cisaillement de la maille.
Le contraste des topographies permet d'envisager un modkle pour la structure en domaines tenant compte des contraintes mkaniques aux limites entre zones.
Abstract. - Ferroelectric domains are observed in gadolinium molybdate crystals by X-Ray transmission topographic method. When the reflecting planes are normal to the domain walls, the domains are separated by alternatively black and white images from the width of which one can measure the shear angle of the cell (the geometry of domains is similar to that in KDP crystals).
From the contrast of domains, one proposes a model for the domain structure taking the mecha- nical matching conditions into account.
Gadolinium molybdate, Gd,(MoO,),, is a ferro- electric and ferroelastic material up to 159 OC. Its symmetry in the paraelectric phase is tetragonala2 m and below the transition it is orthorhombic mm2.
We investigated gadolinium molybdate crystals by X-ray transmission topographic method (Lang tech- nique [I] [2]) to observe domains and if possible domain walls (*).
We shall call c the symmetry axis of the ferroelectric phase to which the polarization is parallel, a, and a, the two other axes of the tetragonal phase. Domain walls are parallel to c and a, or a, (similar to the geo- metry of domains in KDP crystals).
The crystal we investigated were 001 plates. The walls are thus perpendicular to the crystal faces and go through the whole thickness of the crystal. Between crossed polarizers domains can be optically seen and optical micrographs have been taken (Fig. la). Two kinds of domains can be distinguished : those going from one side of the plate to the other and which form parallel sided lamellae and those which do not go through the whole crystal and look like needles or very thin lenses.
Boundaries between domains are very well seen on X-Ray topographs when the trace of the reflecting planes is perpendicular to the boundaries, which is the case for 200 reflections. The boundaries give images alternatively black and white and their contrast is
(*) Single crystals were grown at Monokrystaly, Turnov, Czechoslovakia.
reversed on 200 reflections (Fig. lb, c, 6). These images are well explained with geometrical considerations on diffraction. Let us consider the domains separated by alternatively black and white images. The (100) reflect- ing planes of one set of domains ((+) polarization, for instance) and the (100) reflecting planes of the other set (-) make a small angle equal to twice the shear angle that is to 21 mn after Cummins [3]. If the crystal is well adjusted that is when the normals to the (100) reflecting planes of (+) and (-) domains form a plane perpendicular to the mean incident plane (Fig. 2), the X ray beam will satisfy Bragg's condition for both (+) and (-) domains simulta- nously (see Authier [4]) and diffraction patterns from both types can be obtained at the same time. But since the normals to the two sets of reflecting planes and therefore the corresponding planes of incidence make an angle a of 21 mn, the reflecting X-Ray beams will make with each other an angle rp equal to 2 a sin 8, if 8, is Bragg angle. In that case, black lines are due to the superposition of X-Ray reflected beams from two adjacent domains and white lines correspond to an absence of reflected intensity (Fig. 3). This effect was confirmed by putting the photographic plate at diffe- rent distances from the crystal. The width of the lines were thus proportional to the crystal to plate distance.
From the measurement of the width of the lines and the distance of the plate from the crystal, the shear angle has been calculated. We obtained ( l o p , 0.3')
in good agreement with Cummins' value. We thus now have a way to easily measure the ahear angle in different cases, for example at different temperatures.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972255
FIG. 1. - A gadolinium molybdate crystal (2.5 X
a) Optical micrograph ; 6, c, d) X-Ray transmission (MoKa-radiation) : b : 020 ; c : 200 ; d : 21
8.5 mmz) : topographs 00.
STUDY OF FERROELECTRIC DOMAINS IN GADOLINIUM MOLYBDATE
FIG. 2. -Reflected beams from two domains of opposite polarization when h is parallel to domain walls. P, P' planes (001) for domain (+) and (-1 respectively. OR, OR' reflected beam
from domain (+) and (-) respectively.
It should be noticed that in some cases, we observed domains parallel to the reflecting plane with a black contrast whatever the direction of h (Fig. l c and d) but this was not always observed and we have not yet a good interpretation for it.
Let us consider a region of the crystal where domains parallel to a, and a, are both present. Figure 4 a represents the configuration of domains when mecha-
[1] LANG ( A . R.), Acta Met., 1957, 5 , 358.
[2] LANG (A. R.), Acta Cryst., 1959, 12, 249.
C r y s t a l
P l a t e
FIG. 3. - Projection of X-Ray beams on the reflecting plane when h is parallel to domain walls.
Fig. 4. - Two different models for the structure of domains.
nical matching conditions are not taken into account.
The interpretation of the contrasts observed on X Ray topographs from such regions would be more in favour of the structure shown in figure 4 b and suggested by A. Authier to take these matching conditions into account but the presence of distortions in the crystals we have studied prevents very accurate measurements.
References
[3] CUMMINS ( S . E.), Ferroelectrics, 1970, 1 , 1 1 . [4] AUTHIER (A.), J. Physique, 1966, 27, 57.
