Atomistic mechanism of the ferroelectric behavior of colemanite

Solid State Communications Vol. 3, pp. 315-318, 1965. Pergamon P r e s s Ltd. Printed in Great Britain.

ATOMISTIC MECHANISM OF THE FERROELECTRIC BEHAVIOR OF COLEMANITE* F.N. Hainsworth and H . E . Perch Departments of Physics and Metallurgy, McMaster University, H~mLlton, Ontario, Canada. (Received 14 May 1965 and as revised 2 July 1965 by B.N. Brockhouse)

A neutron diffraction investigation of colemanlte, CaBsO,(OH)s. H~O, has revealed that certain hydrogen atoms change from a state of dy~m l C positional disorder to an ordered r e v e r s i b l e configuration and that the other atoms undergo small displacements during the f e r r o e l e c t r i c transition. A model for the atomistlc mechanism of the f e r r o e l e c t r l c behavior is advanced.

COLEMANITE, CaBsO,(OH)s. ~ O , is a hydrated borate mineral which undergoes a transition at about -3°C to a f e r r o e l e c t r t c phase. ~ The space group ~,s changes from P2z/ a in the non-polar phase to P2x in the f e r r o e l e c t r i c phase so that the polar direction is along the b axis. The net spontaneous polarization and the coercive field4 a r e about 0. 45 ~ C / c m ~ and 2 k V / c m , r e s p e c t ively at -20°C.

statistical basis, the hydrogen atom involved in this bond must be contributed equally by the two water molecules to p r e s e r v e the c e n t r e - o f - s y m m e t r y relationship existing between them in the non-polar phase. It has been suggested that this disorder is ~ m i c s and that it disappears at the transition t em perat ure producing an ordere d polar structure. Nuclear magnetic resonance studies% s have confirmed that some r e o r i s n t a tton of the protons is discontinued during the transition to the f e r r o - e l e c t r i c state and have also indicated that a r e a r r a n g e m e n t of the heavier atoms is involved in the transition. It r e mained, however, for a neutron diffraction study to reveal the exact details of the changes that take place during the transition and to clarify the mechanism of the f e r r o e l e c t r t c behavior.

With the exception of the hydrogen atoms, the s tr u ctu r e s,e of colemanite at room t e m p e r a ture has been solved and refined by x - r a y diffraction techniques. The main structural element is a compact polyanion in which two boronoxygen tetr ah ed r a and one boron-c0cygen triangle share common oxygen atoms to form a s i x - m e m bered ring of alternating boron and oxygen atoms. The polyanions a r e linked by sharing oxygen atoms, one from a t e t r ahedr a l unit and the other from the triang~,l,," unit in each polyanion, to form infinite chains running parallel to the a-axis. The remaining three oxygen atoms in t'he tetr ah ed r al units a r e involved in hydroxyl groups. The polyanion chains ar e cross-linked by the Ca ~* cations to form sheets which ar e in turn hydrogen-bonded to one another in the direction of the b axis.

Cylindrical specimens, with the approximate dimensions 2 x 12 mm, were cut from an exceptionally fine crystal of colemanite from Death Valley, Inyo County, California, U.S.A. Neutron intensity data were collected with the dfffractometer described by T o r r i e et al 9 at crystal t e m p e r a t u r e s of +23°C and --'~'C. For the high t e m p e r a t u r e phase, 186 hkO and 121 hO~ reflections were measured, while for the f e r r o e l e c t r i c phase 139 hkO and 172 hO~ r e f l e c tions were measured: These data,----corrected for the Lorentz factor, absorption and secondary extinction, lo were analysed using Fourier diff e r e n c e synthesis techniques and refined using a least squares program. 11

The water molecules occur in pairs, with the c~vgen atoms of each pair separated by only •2.73 A indicating a strong hydrogen bond. On a * This work was supported by the National Research Council of Canada.

The heavy atom configuration at room 315

316

ATOMISTIC MECHANISM OF THE F E R R O E L E C T R I C

temperature, as determined by neutron diffraction, agrees with that deduced by the X-ray study. A Fourier difference synthesis of the hydrogen scattering projected on the (001) plane is shown in Fig. 1. Hydrogen a t o m s a r e labelled with two s u b s c r i p t s ; the f i r s t n u m b e r denotes the donor c~ygen a t o m and the second number denotes the a c c e p t o r axygen or, in the c a s e of weak bonds, the n e a r e s t oxygen. The two hydroxyl hydrogens, He~ and I-~, and one hydrogen of the w a t e r m o l e cule, Hm, a r e involved in strong, a l m o s t linear, bonds and a s s u m e fixed positions within the s t r u c t u r e . The r e m a i n i n g w a t e r hydrogen, Hm, and the t h i r d hydroxyl hydrogen, Hs~, a r e , however,

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FIG. 1 A projection on the (001) plane of the hydrogen scattering in colemanRe obtained from a Fourier difference synthesis of the room temperature data. Contours of positive and negative scattering density are shown as solid a n d dashed lines, respectively, and the zero contour has been omitted. The crosses indicate the two available positions for H99, denoted by A and B, and for H54, denoted by C and D, obtained from a least squares analysis of the experimental data. The atomic numbering system is that used by Clark et ale; the boron, oxygen, water oxygen and calcium atoms are represented by solid, open,double and shaded circles, respectively.

Vol. 3,

No. 10.

in a state of positional disorder at room temperature. They appear in Fig. 1 as elongated peaks of low density, but the projection on the (010) plane shows the scattering for each of H m and H ~ as two resolved pe~_ks, each of half weight. The parameters, as refined by the least squares method, indicate that the two available positions for Hm, denoted~by A and B in Fig. 1, are separated by 1.53 A and the two available positions for H~, denoted by C and D, are separated by 0. 72 A. On the evidence of the n. m.r. studies, this disordered distribution is dynamic, so that H ~ and Hs4 spend half the t i m e in each of their two available sites. The neutron diffractiondata taken at -20°C indicate that the disorder has disappeared, leavIng the H m and Hr~ hydrogen atoms in an ordered reversible co~Iguration. The difference synthesis of the hydrogen scattering projected on the (001) plane, Fig. 2, shows that if H m has settled into sRe B, leaving A vacant, then the equivalent hydrogen, H~, belonging to the neighboring water molecule occupies A' leaving B' vacant, while H ~ and H's4 occupy only the D and C' positions, respectively. This was confirmed by the (010) projection which is not shown. The configuration of the water molecules and their immediate neighbors in the ordered state is illustrated in Fig. 3. Small, but in some cases significant; shifts were noted in the posRions of the heavy atoms, and that of the Ca ~+ ion is believed to be of particular importance. The nearest calcium ion is somewhat shielded from H m in posRion A and, as shown in Fig. 3, the Ca-O~ distance is reduce,d below Rs room temperature value of 2. 449 A. Conversely, the calcium ion is more exposed to H ~ in posRion B and R has moved away from the water molecule, increasing the Ca- Os distance. On the b a s i s of the d i f f e r e n c e s o b s e r v e d between the polar and non-polar s t r u c t u r e s , a m o d e l for the m e c h a n i s m of the t r a n s i t i o n m a y be proposed. Above the t r a n s i t i o n , the hydrogen a t o m of the w a t e r m o l e c u l e , which has two s i t e s available to it, has sufficient t h e r m a l e n e r g y that it m a y move r e a d i l y f r o m one to the other of the two sites, r e s u l t i n g in a dynamically diso r d e r e d state. As the t e m p e r a t u r e is lowered, one such hydrogen atom m a y settle into one of its two a l t e r n a t i v e positions. The r e l a t i v e s t a b ility of the two s t a t e s for the i n v e r s i o n - r e l a t e d a t o m will then be changed such that it s e t t l e s into the non-equivalent a l t e r n a t i v e position. The effect of the o r d e r i n g of the w a t e r hydrogen on the calcium ions is such that they m o v e either toward or away f r o m the w a t e r c~ygens to keep

Vol. 3, No. 10.

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the calcium-hydrogen distance as large as possible. The position taken by a given calcium ion in turn effects the positions of its oxygen neighbars which are part of the polyanion chains, and also determines which of the two aRernative positions m a y be occupied by Hs~ The strength of the interaction throughout the water=cal.ciumpolyanion network is sufficient to ensure that ordering in one small region will be transmitted so that the same relative configuration will be taken up in a macroscopic volume of the crystal. To obtain a reversal of the spontaneous polarization - the criterion for ferroelectricity the b i s t a b l e hydrogen a t o m s m u s t be m o v e d f r o m the A and C positions to the B and D positions (or vice v e r s a ) and the other a t o m s m u s t be dis= placed by r e l a t i v e l y s m a l l a m o u n t s to t h e i r a l t e r native s i t e s . This can be a c c o m p l i s h e d with a s i m p l e r e a r r a n g e m e n t of c e r t a i n hydrogen bonds without b r e a k i n g any s t r o n g bonds. Consequently, the e n e r g y r e q u i r e d to switch the s t r u c t u r e f r o m one state to the other is quite s m a l l and the r e v e r s a l t a k e s place with the application of an el=

Configuration of the water molecules in the polar phase of colemanite. The two molecules shown are related by the center of symmetry in the nonpolar phase.

e c t r i c field c o n s i d e r a b l y w e a k e r than that which would c a u s e d i e l e c t r i c breakdown. This w o r k s u g g e s t s that the spontaneous p o l a r i z a t i o n exhibited by c o l e m a n i t e in its f e r r o e l e c t r i c s t a t e does not a r i s e s i m p l y f r o m the o r d e r i n g of distinguishable dipoles but r a t h e r f r o m a net s e p a r a t i o n of the c e n t r o i d s of the positive and negative c h a r g e s within the c r y s t a l , which can be t r a c e d to the slight d i s p l a c e m e n t s of all the a t o m s f r o m the s t r i c t glide=plane symmetry of the non=polar phase. Using the a t o m i c positions obtained in this w o r k and r e a s o n a b l e assumptions regarding charge assignments, a value of 0. 5 ~ C / c m ~ was calculated for the spontaneous polarization. The close a g r e e m e n t with the m e a s u r e d value of 0.45 ~ C / c m ~ is p r o b a b l y fortuitous, but the fact that the o b s e r v e d d i s p l a c e m e n t s give the c o r r e c t o r d e r of m a g n i tude is significant. A c o m p l e t e account of this w o r k will be s u b m i t t e d to the Canadian J o u r n a l of P h y s i c s .

Aclmowled~ements = The a u t h o r s a r e indebted io Mr. 1b. E. D e s a u t e l s of the Smithsonian Institution for providing the excellent s p e c i m e n of c o l e m a n i t e used in this study.

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ATOMIBTIC M E C ~

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Eine Untersuchung yon Colemantt, CaBsO4(OH) 3. H~O, mittels Neutronenbeugung ergab, class gewtsse Wasserstc~fatome von etnem Zustand mtt dynamtscher T~everschiebung in eine reversible, geordnete Konftguration uebergehen und class die anderen Atome waehrend der ferroelektrtschen Umwandlung geringe Verschiebungen erfahren. Ein Model1 fuer den atomtstischen Mechanismus des ferroelektrischen Verhaltens wird vorgeschtagen.