Article
Reference
X-Ray diffuse scattering study of boracites
FELIX, P., et al.
Abstract
X-ray diffuse scattering from boracite in the cubic phase shows the existence of fluctuation domains, having the form of cigarillos oriented with their main axis parallel to 〈100〉
directions. The relative magnitude of the at. displacements of the metal and halogen atoms in the soft fluctuation corresponds to the conservation of the center of mass, which seems to indicate that the simplest soft optic mode condensation picture of the displacive phase-transition theory may apply to boracites.
FELIX, P., et al . X-Ray diffuse scattering study of boracites. Ferroelectrics , 1974, vol. 7, no. 1, p. 131-133
DOI : 10.1080/00150197408237972
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1974, Vol. 7, pp. 131-133 Printed in Great Britain
X-RAY DIFFUSE SCATTERING STUDY OF BORACITES
P. FELIX,
Jnstitut Max Von Laue-Paul Langevin, Grenoble, France
M. LAMBERT, R. COMES
Laboratoire de Physique des Solides, 91405-0rsay, France
r
andH. SCHMID
Batelle Institute, Geneva Research Center, Geneve, Suisse (Received September 10, 1973)
X·Ray diffuse scattering from boracite in the cubic phase shows the existence of fluctuation domains. having the form of cigarillos oriented with their main axis parallel to< I 00 >directions. The relative magnitude of the atomic displacements of the metal and halogen atoms in the soft nuctuauon is shown to correspond to the conservation of the center of mass, which seems to indicate that the simplest soft optic mode condensation picture of the displacive phase transition theory may apply to boracites.
lNTRODUCfiON
Boracites are rather complex crystals formed by Me3 B, 013 X molecules where Me is a metal (Mg, Zn, Fe, Co, Ni, Cu, Mn) and X a halogen (Cl, Br, 1). The interest in these crystals rests mainly with the possibility of the existence, for those which contain r 'aramagnetic ion, of a low temperature phase which
·~simultaneously ferroelectric and ferromagnetic with
a strong-coupling between magnetization and electric polarization.1•2
Most of the boracites exist in three phases: a high temperature cubic paraelectric phase which is face centered and contains 8Me3B7013X formula units (space group F43C), and two low temperature ferro- electric phases arising essentially from small shifts out of the cubic positions of the metals (along cubic OOO>) and the halogens (along cubic (11 ))) leading
successively to an intermediate orthorhombic symmetry (space group PCa21) and to the low tern·
perature rhombohedral phase (space group R3C) (3-+ 7).
To describe, in a limited space, experimental results obtained by X-Ray diffuse scattering with such complex structures, one is restricted to a very simplified schematic picture. If we keep in mind that the halogen ions, are in the cubic phase, in a tetra-
131
hedral symmetry, we can in a first approximation ignore all the oxygen and boron atoms, and consider that the structure is built from a cubic (or pseudo- cubic in the low temperature phases) unit cell con·
taining one Me3X unit. The atomic displacements of the metal and halogen ions, from the cubic positions leading to the rhombohedral phase, in such a schematic description of the structure, are shown on Figure 1 (for the cubic positions just ignore the arrows). The tetrahedral symmetry around the
I
?
II
/Jf - ---<r
0
ClOMg FIGURE 1 Simplified structural unit of boracite if all the oxygen and borlne atoms are ignored. The arrows indicate the shift of the metal and halogen atoms out of the cubic positions, in the rhombohedral phase.
132 P. FELIX et ol.
(a)
(b)
FIGURE 2 X-Ray scattering patterns obtained with MoKo:
radiation, in the cubic phase of boracites oriented with a [I 00] axis parallel to the incident beam.
a) CuCI boracite.
b) Nil boracite.
halogen ions which is responsible for the only 4 equivalent possible (II)) directions of the polariza- tion in the rhombohedral phase (instead of 8 in the perovskite rhombohedral phase), is the origin of the
"improper·· character of the ferroelectricity in the boracites, and also of particular features of the correlations of the atomic displacements which can be observed by X-Ray diffuse scattering.
X-RAY DIFFUSE SCATIERING
In their essential features, the scattering patterns of figure 2 which correspond to 2 extreme examples of scatte1ing observed with different boracites, show streaks which correspond to intensity restricted to {100} reciprocal planes and have a great similarity
with the scattering patterns from perovskites.8 This is the evidence of correlations of atomic displacements along the (1 00} cubic axis but there are important differences compared with the perovskites:
i) The diffuse streaks are much broader showing that the correlation length is much shorter, about 5 unit ceUs compared to 10 or 20 in the perovskites.
ii) The diffuse streaks are not uniform, and one can see, on the streaks, diffuse spots, or even short segments, broader than the streak itself, and which correspond to a maximum of the scattered intensity along (I 00} reciprocal axis contained in the {I 00}
reciprocal planes (they are particularly visible in the CuCI scattering pattern (Figure 2a).
Such a feature gives the evidence that the one dimensional character of the correlations of the atomic displacements along the 000} directions is less pronounced in the boracites than in the perovskites.
It means that the correlations in the cubic phase are not restricted to single rows of atoms but form· groups of parallel chains giving rise to fluctuation domains having the form of cigarillos with their main axis along a (100} direction (approximate size at I70°C for CuCI is length= 30 A and width= 12 A).
The lower symmetry of the cubic boracites, com- pared to the cubic perovskites seems to be sufficient to explain this difference. While in the cubic perovskites, the cen teo-symmetric structure allows independant displacements of the atoms, and thus independant correlations, along the three (100}
directions, the tetrahedral symmetry of the boracites couples the displacements, and thus the correlations, along these three directions.
A more precise analysis of the distribution of the scattered intensity shows that the local distorsion in the fluctuation domains (or modes in a dynamic phonon language), corresponds to the atomic displace- ments observed in either of the two (orthorhombic or rhombohedral) low temperature ferroelectric phases (Figure I). Considering the drastic approxima- tion which we made by reducing the structure to the metal and halogen atoms it is impossible to distinguish between those two possibilities.
(iii) In the scattering pattern of the Nil boracite (Figure 2b) it is easy to distinguish that the intensity is not only restricted to the {I 00} reciprocal planes, but more precisely to the "odd" {100} reciprocal planes (the reciprocal planes can be numbered from the origin of the reciprocal space, the {1 00} reciprocal plane passing through the origin which is on the pattern the plane passing through the incident beam impact, is then the zeroth plane). This simple fact
X-RAY DIFFUSE SCATIERING STUDY OF BORACITES 133 shows that the displacements of the metal and
halogen atoms in the soft fluctuations correspond very precisely to the conservation of the center of mass. This is again different from the observations made with the perovskites and seems to indicate that the simplest soft optic mode condensation picture of the displacive phase transition theory (9) may apply to boracites.
CONCLUSION
We have insisted above on the common features of the diffuse scattering from the different boracites, but there are also remarkable differences among the boracites themselves. From the comparison of the CuCl and CrCJ scattering patterns which are very similar it can be concluded that the nature of the metal seems to have little influence on the correla- tions of the soft fluctuations. From the comparison of the Nil, FeBr, CuCl and CrCl results it can be further concluded that the correlation lengths increase when the mass of the halogen decreases;
this is visible on the scattering patterns of Figure 2 where the diffuse streaks from the CuCI boracite are thinner than the streaks from the Nil boracite. What is true for the main correlation along the (1 00) directions, is also true for the coupling between parallel chains: the whole size of the cigarillo shaped fluctuation domain increases with decreasing mass and size of the halogen.
The phase transitions in the boracites are of first order, but only weakly, like in most ferroelectrics.
The increase of the correlations lengths in the cubic phase, which means a decreasing difference of entropy between the cubic and orthorhombic phases, shows that this first order character of the phase transition decreases with decreasing mass and size of the halogen
and that the cubic-orthorhombic phase transition in the CuCl boracite is the closest to second order.
This is confirmed by the variation of the scattered intensity as a function of temperature. While this intensity is almost independent for the Nil boracite, it starts to show a weak critical behaviour at the cubic to orthorhombic phase transition with the CuCl boracite, and the intensity in the cubic phase at the reciprocal point H
=
1, K = 6, L=
0 varies as T/T- Tc with Tc=
315°K (transition temperature=
365°K). (The indices refer to the true cubic unit cell a:::. 12 A and not to the simplified picture of Figure 1).The experimental part of this work has been accomplished with the technical help of L. Deschamps to whom we are grateful. A more extensive description can be found in reference (I 0) and is available upon request.
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