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research papers Journal of

Applied Crystallography

Aminoguanidinium hexafluorozirconate: a new ferroelectric

ISSN 0021-8898

Received 2 October 2000 Accepted 26 October 2000

M. R. Bauer,a D. L. Pugmire,a B. L. Paulsen,a R. J. Christie,a D. J. Arbogast,b C. S. Gallagher,b W. V. Raveane,b R. M. Nielson,a² C. R. Ross II,c P. Photinosb and S. C. Abrahamsb* a

Department of Chemistry, Southern Oregon University, Ashland, OR 97520, USA, bDepartment of Physics, Southern Oregon University, Ashland, OR 97520, USA, and cDepartment of Structural Biology, St Jude Children's Research Hospital, 332 North Lauderdale St., Memphis, TN 381052794, USA. Correspondence e-mail: [email protected]

# 2001 International Union of Crystallography Printed in Great Britain ± all rights reserved

Analysis of the atomic arrangement in anhydrous aminoguanidinium hexa¯uorozirconate, CN4H8ZrF6, reported by Bukvetskii, Gerasimenko & Davidovich [Koord. Khim. (1990), 16, 1479±1484], led to the prediction that it is a new ferroelectric [Abrahams, Mirsky & Nielson (1996). Acta Cryst. B52, 806±809]. Initial attempts to verify the prediction were inconclusive because of the variety of closely related materials produced under the original preparation conditions. Clari®cation of these conditions led to the formation of pure CN4H8ZrF6 and the growth of single crystals with dimensions as large as 7 7 2 mm. Highly reproducible calorimetric and dielectric permittivity anomalies reveal the Curie temperature Tc = 383 (1) K. At this temperature, the heat capacity Cp exhibits an entropy change of 0.7 (1) J molÿ1 Kÿ1, while the relative permittivity "r exhibits an in¯ection and the dielectric loss a distinct peak; the dielectric anomaly at Tc is observed only at the lowest (0.1±1 kHz) frequencies used. Dielectric hysteresis is demonstrable at 295 K under the application of 1 MV mÿ1 alternating ®elds and remains observable at all T < Tc but not at T Tc; the prediction of ferroelectricity is hence con®rmed. The value of the spontaneous polarization Ps is 0.45 (9) 10ÿ2 C mÿ2 at 298 K, with piezoelectric coef®cient d33 = 1.9 (5) pC Nÿ1 and pyroelectric coef®cient p3 = 4 (1) mC mÿ2 Kÿ1. Tilts of less than 11 by the two symmetry-independent CN4H2 8 ions, combined with rotations of 20 or less by the NÐNH3 and CÐ (NH2)2 groups about the central CÐN bond in each cation, as all H atoms rotate into or become symmetrically distributed about the planes at z = 0 or 12, allow Ê them to conform to mirror symmetry via polar atomic displacements of 0.4 A Ê or less by N or C, and of 0.7 A or less by H. Corresponding displacements of less Ê within the two symmetry-independent ZrF2ÿ than 0.08 A 6 anions also result in mirror symmetry, satisfying the structural criteria required for the development of ferroelectricity.

1. Introduction Analysis of the atomic coordinates listed under space group Pba2 in the 1988 edition of the Inorganic Crystal Structure Database, ICSD (Bergerhoff & Brown, 1987), led to the prediction (Abrahams, 1989) of ferroelectricity in seven new materials. The validity of these predictions was tested by preparing single crystals of two candidates, Na13Nb35O94 and K3Fe5F15. Each was con®rmed to be a new ferroelectric, with predicted Curie temperatures (Tc) acceptably close to the experimental values (Abrahams et al., 1989; Ravez et al., 1989). In addition to the seven newly predicted ferroelectrics, the ² Deceased 27 November 1998. J. Appl. Cryst. (2001). 34, 47±54

listing contained the atomic coordinates of the previously known ferroelectrics Gd2(MoO4)3 and Tb2(MoO4)3, as well as those of antiferroelectric PbZrO3. Analysis of the three new entries listed under space group Pba2 in the 1995 ICSD release resulted in the further prediction (Abrahams et al., 1996) that aminoguanidinium(2+) hexa¯uorozirconate (CN4H8ZrF6, hereinafter AGHFZ) is another new ferroelectric. The relevant force constant relating Tc to the atomic displacements in this structure is unknown; however, the relatively small displacement magnitudes by the ZrF2ÿ 6 anions and strainless rotations within and tilts of the CN4H2 8 cations required for polarization reversal suggested that Tc is unlikely to be high. M. R. Bauer et al.

Aminoguanidinium hexafluorozirconate

47

research papers 2. Structural basis for ferroelectricity in CN4H8ZrF6 AGHFZ was reported by Bukvetskii et al. (1990) to crystallize in the polar space group Pba2, with a = 10.089 (2), b = Ê and Z = 8 at room temperature. The 18.349 (3), c = 7.560 (1) A structure contains in®nite chains of slightly distorted edgesharing ZrF8 dodecahedral groups along the polar axis, connected to the CN4H2 8 cations by multiple hydrogen bonds. Abrahams et al. (1996) showed that all Zr and F atoms in Ê from the mirror planes of AGHFZ are less than 0.08 A symmetry at z = 0 and 12 that are expected to form if the space group undergoes a transition to centrosymmetric Pbam. The cations, however, are nonplanar and slightly inclined to these planes, as shown in Figs. 1(a) and 1(b). Maximum polar Ê Ê displacements z < 0.43 A by a nitrogen atom, 0.18 A by a Ê carbon atom, and 0.7 A by a hydrogen atom are necessary for the cation to become planar and occupy the postulated mirror planes (Abrahams et al., 1996). Rotation of the amino NH 3 groups about the NÐN bond, such that one H comes to lie in the mirror plane and the two other H atoms become symmetrically related above and below the plane, results in all atoms within the cation conforming to planar symmetry (see x9.2). The z magnitudes in AGHFZ are well within the structural criteria of Abrahams (1988) for the prediction of ferroelectricity and are likely to be readily attainable in view of (a) the expected average thermal and/or static atomic Ê in the crystal at room temperature displacements of 0.2 A [the re®ned thermal parameter magnitudes of Bukvetskii et al. (1990) were not stated] and (b) the ability to achieve all C- and N-atom displacements by a combination of strainless rotations (about the C1ÐN3 and C2ÐN7 bonds within the CN4H2 8 cations in the two-molecule asymmetric unit) and tilts of the whole cation (see Fig. 1) together with rotations by all 16 H atoms about an adjacent NÐC or NÐN bond. It may be noted that H-atom positions and their isotropic thermal parameters were `considered' but not necessarily re®ned without constraint by Bukvetskii et al. (1990). Redetermination of the structure to obtain more accurate values for all atomic parameters is in progress (Ross et al., 2000); unit-cell measurements on several crystals indicate a slight distortion toward monoclinic symmetry at room temperature, with = 90.77 (5) . Such a reduction in symmetry does not affect the present conclusions, but its structural implications will be discussed in the report on the re®ned structure. The polar direction in a ferroelectric crystal is reversible, at least in principle, under the application of an appropriate electric ®eld. Polarization reversal in AGHFZ is structurally possible at room temperature if each atom were to undergo double the z shifts listed in Table 1. Although Tc can be estimated in octahedral ferroelectrics from the AKJ relationship (Abrahams et al., 1968), a quantitative estimate of Tc in AGHFZ from such a relationship is not possible at present.

3. Sample preparation Attempts at preparing AGHFZ by means of the reaction between equimolar proportions of (H3O)2ZrF6 and CN4H7Cl

48

M. R. Bauer et al.


Figure 1

(a) View along the a axis of the two independent aminoguanidinium(2+) ions in AGHFZ occupying the asymmetric part of the unit cell, with mirror planes in the postulated paraelectric phase shown dashed. (b) View along the b axis.

(Bukvetskii et al., 1990) led to a variety of products. The following method (see Bauer et al., 1999, for details), reproducibly yields single crystals of pure CN4H8ZrF6. Starting materials are aminoguanidine bicarbonate, CN4H6.H2CO3 (Aldrich; 98.5% pure), ZrF4.3H2O (Aldrich; 97%) and 48± 51% HF aqueous solution (Aldrich; reagent grade). All reactions are undertaken in polypropylene beakers; reactions in glassware lead to the corresponding hexa¯uorosilicates (Ross et al., 1999). A solution of 1.36 g CN4H6.H2CO3 in 10 ml HF is prepared in one beaker; 2.21 g ZrF4.3H2O is dissolved in J. Appl. Cryst. (2001). 34, 47±54

research papers Table 1

Ê ) required for a transition from polar space group Pba2 to AGHFZ atomic coordinates and axial components of the atomic displacements (A centrosymmetric Pbam at 300 K. Ê . x = (x ÿ x0 )a, y = (y ÿ y0 )b and z = (z ÿ z0 )c, where x0, y0 and z0 are the coordinates in Pbam. a = 10.089 (2), b = 18.349 (3), c = 7.560 (1) A Wyckoff position Atom

Pba2

Pbam

Zr1³§

4(c)

Zr2³§ F1} F2 F3 F4 F5

4(c) 4(c) 4(c) 4(c) 4(c) 4(c)

F10 F6

4(c) 4(c)

F9 F7

4(c) 4(c)

F11 F8

4(c) 4(c)

F12 N1²²

4(c) 4(c)

4(g)

N2§

4(c)

4(g)

N3§

4(c)

4(g)

N4

4(c)

4(g)

N5§

4(c)

4(h)

N6

4(c)

4(h)

N7

4(c)

4(h)

N8

4(c)

4(h)

C1§

4(c)

4(g)

C2

4(c)

4(h)

H1

4(c)

4(g)

H2

4(c)

4(g)

H3

4(c)

4(g)

H4

4(c)

4(g)

H5³³

4(c)

4(g)

H6

4(c)

H7 H8

4(c) 4(c)

4(g)

H9

4(c)

4(h)

H10

4(c)

4(h)

H11

4(c)

4(h)

H12

4(c)

4(h)

H13

4(c)

4(h)

H14

4(c)

4(h)

8(i) 4(h) 4(h) 4(g) 4(g) 8(i) 8(i) 8(i) 8(i)

8(i)

J. Appl. Cryst. (2001). 34, 47±54

x

y

z²

z0

0.2724 (1)

0.3697 (1)

ÿ0.2496

0.2709 (1) 0.2186 (6) 0.3185 (6) 0.3791 (5) 0.1695 (5) 0.1815 (7)

0.3686 (1) 0.3102 (3) 0.4259 (3) 0.3404 (3) 0.3996 (3) 0.2749 (3)

0.2496 (2) 0.5060 (23) 0.4906 (18) 0.0005 (21) 0.0047 (24) 0.1827 (4)

ÿ0.2496 0.008 ÿ0.2496

0.1932 (9) 0.3565 (9)

0.2743 (5) 0.4673 (5)

ÿ0.1938 (14) 0.1871 (11)

ÿ0.1882 0.1860

0.3627 (8) 0.4459 (9)

0.4625 (4) 0.3263 (7)

ÿ0.1848 (11) 0.3123 (13)

ÿ0.1860 0.3128

0.4455 (5) 0.0892 (7)

0.3184 (3) 0.4069 (4)

ÿ0.3132 (9) 0.3119 (11)

ÿ0.3128 0.3129

0.0964 (6) 0.1230 (11) 0.1221 0.0837 (10) 0.0845 0.2931 (9) 0.2969 0.3893 (10) 0.3834 0.3575 (12) 0.3549 0.1454 (10) 0.1391 0.1904 (10) 0.1954 0.0567 (9) 0.0572 0.1655 (9) 0.1679 0.2282 (11) 0.2315 0.351 (4) 0.323 0.462 (4) 0.462 0.496 (4) 0.499 0.401 (4) 0.387 0.166 (4) 0.174 0.124 (4) 0.085 0.046 (4) 0.049 (4) 0.034 0.089 (4) 0.086 0.118 (4) 0.121 0.444 (4) 0.444 0.342 (4) 0.337 0.203 (4) 0.246 0.446 (4) 0.452

0.4157 (4) 0.5616 (6) 0.5574 0.6815 (5) 0.6817 0.6357 (6) 0.6405 0.5860 (6) 0.5843 0.5878 (6) 0.5902 0.5538 (6) 0.5530 0.6730 (5) 0.6736 0.6943 (5) 0.6919 0.6267 (6) 0.6276 0.6062 (7) 0.6065 0.039 (4) 0.022 0.053 (4) 0.049 0.175 (4) 0.173 0.220 (4) 0.226 0.181 (4) 0.185 0.046 (4) 0.048 0.050 (4) 0.122 (4) 0.102 0.130 (4) 0.124 0.049 (4) 0.045 0.071 (4) 0.064 0.004 (4) 0.008 0.206 (4) 0.208 0.242 (4) 0.240

ÿ0.3138 (9) ÿ0.0568 (16)

ÿ0.3129 0

x

1 2 1 2

0 0 0.1882

y

z

0.010

0.000

0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000

0.045 ÿ0.071 0.004 0.035

0.059

0.006

ÿ0.042

0.031

0.044

0.008

0.002

0.072

ÿ0.004

0.036

0.081

ÿ0.008

0.009

0.077

ÿ0.429

0.0166 (26)

0

ÿ0.008

ÿ0.004

0.126

0.0447 (16)

0

ÿ0.038

ÿ0.087

0.338

0.0154 (24)

0

0.060

0.031

0.117

0.5403 (21)

1 2

0.026

ÿ0.044

0.305

0.5398 (20)

1 2

0.063

0.015

0.301

0.5281 (24)

1 2

ÿ0.051

ÿ0.011

0.213

0.4897 (30)

1 2

ÿ0.005

0.045

ÿ0.078

0.0109 (27)

0

ÿ0.024

ÿ0.017

0.083

0.5232 (13)

1 2

ÿ0.034

ÿ0.005

0.176

0.013 (4)

0

0.284

0.319

0.102

ÿ0.093 (4)

0

0.002

0.073

ÿ0.700

0.006 (4)

0

ÿ0.034

0.030

0.049

0.003 (4)

0

0.144

ÿ0.107

0.026

0.094 (4)

0

ÿ0.084

ÿ0.066

0.714

0.072 (4)

0.073

ÿ0.074 (4) ÿ0.005 (4)

ÿ0.073 0

0.393

0.037

ÿ0.008

0.150

0.375

ÿ0.035

0.584 (4)

1 2

0.026

0.107

0.638

0.504 (4)

1 2

ÿ0.030

0.069

0.033

0.583 (4)

1 2

ÿ0.003

0.130

0.631

0.584 (4)

1 2

0.054

ÿ0.074

0.638

0.510 (4)

1 2

ÿ0.433

ÿ0.029

0.079

0.501 (4)

1 2

ÿ0.060

0.035

0.011

M. R. Bauer et al.


49

research papers Table 1 (continued) Wyckoff position Atom

Pba2

H15³³

4(c)

H16

4(c)

Pbam

x

y

8(i)

0.481 (4) 0.517 0.554 (4)

0.154 (4) 0.182 0.211 (4)

z0

z² 0.512 (4)

0.511

ÿ0.511 (4)

ÿ0.511

x

y

z

0.373

0.532

0.004

² The z coordinates of Bukvetskii et al. (1989) have been shifted by 0.00043, placing z(Zr1) and z(Zr2) equidistant from the mirror plane of space group Pbam. ³ The coordinates of Zr1 and Zr2 are rounded to four signi®cant ®gures. § Coordinates are symmetry-related to the published values. } x and y for F1, F2, F3 and F4 are not necessarily zero but, in the absence of chemical constraints, represent the simplest assumption. ²² x and y coordinates in italic are hypothetical values corresponding to CN4H2 8 cations constrained to exhibit mirror symmetry, with ideal bond lengths and angles except for H6, H7 and H15, H16, occupying the plane z = 0 or z = 12. ³³ The x(H) and y(H) coordinates in the amino group related by Wyckoff position 8(i) in Pbam are in italic. The resulting geometry departs from ideal tetrahedral.

25 ml HF in another beaker by heating in a hot water bath for about 5 min. The two solutions are combined and diluted to a total volume of 60 ml. Subsequent evaporation at 355 K over a 24 h period to a volume of 5±20 ml produces transparent colorless well formed crystals with maximum dimensions 7 7 2 mm. Ê) X-ray powder patterns obtained with Cu K ( = 1.5418 A compared well with those generated by Lazy-Pulverix software (Yvon et al., 1977) from the results of Bukvetskii et al. (1990). Unit-cell dimensions and space group determined on single crystals in an Enraf±Nonius MACH3 diffractometer con®rmed the identity of this material as that established in a previous report (Ross, 1996).

4. Calorimetry 4.1. Heat capacity

The heat capacity of AGHFZ was measured between 300 and 440 K on polycrystalline samples, weighing 5±10 mg, in a Perkin-Elmer DSC-7 differential scanning calorimeter using both DSC and heat-capacity modes. The heat capacity Cp was found to exhibit a reproducible anomaly at 383 (1) K in all samples, as shown in Fig. 2 (see also x4.2). The onset of HF loss at 435 K (Bauer et al., 1999) is accompanied by a large exotherm and results in a rapidly rising background; hence

there is an increased uncertainty in the corresponding enthalpy change. An approach similar to that used by Glass (1968), in which the background between 328 and 402 K is ®tted analytically, leads to equation (1) with agreement 2 = 0.057: Cp T A B=T ÿ T1 C expfÿT ÿ T2 =T3 2 g;

1

where A = 279.6 and C = 59.59 J molÿ1 Kÿ1, B = ÿ316.0 J molÿ1, T is the thermal variable, T1 = 313.9, T2 = 418.6 and T3 = 14.90 K. Equation (1) results in the dotted line of Fig. 2, thereby enabling evaluation of the enthalpy H as 250 (30) J molÿ1 and the entropy change S as 0.7 (1) J molÿ1 Kÿ1. The anomaly in Cp is taken as the result of the symmetry change at Tc. The heat capacity anomaly in Fig. 2 is comparable with the entropy change at the second-order phase transition in LiTaO3 from the ferroelectric to the paraelectric phase at 938 K, for which Glass (1968) reports S = 0.96 J molÿ1 Kÿ1. The primary atomic displacement in LiTaO3 under polarization reversal, or at the phase transition, is by Ta along the polar axis; the Li- and O-atom displacements for these independent atoms are smaller (Abrahams et al., 1967, 1973). The six positional variables in LiTaO3 below Tc (including polar-axis sense) are reduced to ®ve by symmetry considerations above Tc, in which Ta occupies an inversion center and Li+ is disordered. The entropy change at this phase transition, if considered as ®rst order, may hence be taken as R ln(6/5) = 1.52 J molÿ1 Kÿ1, 50% larger than reported. The broad phase transition and associated entropy change in AGHFZ are consistent with a transition of higher order. 4.2. Dependence of transition temperature on scan rate

Figure 2

Heat capacity of aminoguanidinium(2+) hexa¯uorozirconate in the thermal range 320 to 400 K with the analytic ®t to the background given by equation (1) shown dotted.

50

M. R. Bauer et al.


The apparent calorimetric transition temperature in AGHFZ varies as much as 15 K over the DSC-7 scan-rate range from 5 to 75 K minÿ1. Fig. 3 shows that the variation in resulting peak exotherm and endotherm temperatures with scan rates is linear; their intersection is close to an extrapolated scan rate of 0 K minÿ1 and gives the transition temperature Tc = 383 (1) K, taken as the intrinsic Curie temperature. The slightly negative scan rate at the intersection is attributed to use of peak temperatures; onset temperatures for AGHFZ could be estimated accurately only by ®tting each experimental result to a function such as equation (1) or by use of much slower scan rates. J. Appl. Cryst. (2001). 34, 47±54

research papers

Figure 3

Figure 4

Variation of peak exotherm (circles, cooling) and endotherm (squares, heating) temperatures in aminoguanidinium(2+) hexa¯uorozirconate with scan rate.

Relative dielectric permittivity ("r) and dielectric loss ("00 ) in aminoguanidinium(2+) hexa¯uorozirconate between 373 and 406 K; A and B give the variation of "00 at 0.1 and 1 kHz, respectively; C and D give the corresponding variation of "r.

A similar linear scan-rate dependence is observed with the DSC-7 on measuring a sample of BaTiO3 (see x5), for which the use of either phase onset or peak temperatures gives an identical intersection of the resulting exotherm and endotherm phase-transition temperatures at 396 (1) K.

hysteresis thermal-dependence measurements on fresher samples (see x8.2) gave Tc in close agreement with the calorimetric result. A systematic investigation of aging effects has not been performed.

5. Dielectric permittivity and loss

6. Piezoelectric d33 coefficient at 298 K

The relative dielectric permittivity of AGHFZ is given by "r = Cx/C0, where C0 is the capacitance of the empty cell and Cx is the capacitance of the cell and sample; the dielectric loss "00 is taken from the dissipation factor D = tan , the ratio of real to imaginary impedance. Each was measured over the range 300± 420 K with a Stanford Research Systems SR720 LCR meter. Both the LCR meter and an Instec HS250 heating stage were under the control of a personal computer (PC). The faces of each polycrystalline sample, pressed under 1 GPa into disks of 12 mm diameter and 1±1.5 mm thickness, were coated with ¯exible silver ink (Engelhard-CLAL, 1995) leaving a bare frame, 1 mm wide. The measurement accuracy was checked by similarly treating microcrystalline samples of BaTiO3 (Aldrich; 99.9% purity, sintered chips), for which "r was reproducibly determined as 6±7.5 103 at Tc = 405 K, in acceptable agreement with literature peak values of 104 at 403 K (see Mitsui & Nomura, 1981). The relative permittivity of each AGHFZ sample increases by about a factor of two between 375 and 405 K at a frequency of 100 Hz and exhibits a small in¯ection at Tc = 397 K; the in¯ection is barely discernible at 1 kHz (see Fig. 4), becoming undetectable at 10 kHz and higher frequencies. The proportional change in dielectric loss at 100 Hz, over the 25 K thermal interval immediately below Tc, is less than that in the relative permittivity; the dielectric loss, however, rises to a small but distinct maximum at Tc = 398 K. The peak remains clearly visible at 1 kHz, but becomes undetectable at 100 kHz and higher frequencies. The difference between the calorimetric Curie temperature and the present dielectric values of Tc may arise from the formation of decomposition products in the aging sample, since both dielectric permittivity and

Measurement of the direct piezoelectric effect requires determination of the electric charge generated by the application of a known compressive or tensile stress along an appropriate direction. The prominent (001) faces of crystalline AGHFZ make d33 the most accessible of the ®ve independent coef®cients allowed in point group mm2. Accordingly, both (001) faces of a crystal with approximate dimensions 6 6 0.5 mm were coated with ¯exible silver ink (see x5); before the ink dried on the lower face, it was placed in contact with a silver ink strip painted on and extending to the edge of a microscope slide. The strip terminated in a minicontactor. One end of a thin copper foil, with width comparable to that of the crystal plate, was connected to the upper (001) face by silver ink; the other end extended to a distant edge of the slide with an attached minicontactor. The barrel and plunger of a plastic syringe with square-cut end allowed the application of tensile stress by preloading the AGHFZ crystal with a calibrated force of 0.1 N, the ¯at end of the plunger resting on the copper strip in contact with the crystal. Rapid removal of the load produced tensile stress. The voltage thereby generated was measured with a Tektronix TDS 220 Oscilloscope; the capacitance was measured with an SR720 LCR meter. Measurement on the as-grown crystal failed to generate a detectable signal. However, remeasurement after the application of a direct electric ®eld of 0.7 MV mÿ1 across the (001) faces, followed by the reapplication of tensile stress, led to a reproducible piezoelectric charge. The charge increased further after 2 MV mÿ1 had been applied. The expectation that an approximately equal number of domains with opposite polarity is formed in as-grown ferroelectric crystals, resulting in cancellation of a piezoelectric response, is thus con®rmed.

J. Appl. Cryst. (2001). 34, 47±54

M. R. Bauer et al.


51

research papers present circuit closes the missing connection between Ccomp and Cy2 in Fig. 1 of Singh et al. (1996), replaces the R1, R2 voltage divider circuit, for measuring the voltage Ex, with a 1000:1 Caddock Electronics Inc. THU10 voltage divider network, uses Texas Instruments TL081CP operational ampli®ers instead of TL084 ampli®ers, couples the negative side of the TL081 differential ampli®er to feedback and the positive side to ground, and replaces the four 45 k resistors and 47 k potentiometer in the differential gain circuit by four 50 k resistors with 1% accuracy, thereby giving a gain ratio of unity. Hysteresis loops are displayed as a function of Ex versus Ey voltage in the xy mode of a Tektronix TDS 220 Digital Oscilloscope, with GPIB interface to a PC for subsequent graphical display and analysis. 8.2. Thermal dependence of dielectric hysteresis

Figure 5

Room-temperature ferroelectric hysteresis loop in aminoguanidinium(2+) hexa¯uorozirconate under an a.c. ®eld of 0.9 MV mÿ1.

Following the higher ®eld application, the measured value of d33 is 1.9 (5) pC Nÿ1; the probability that polarization saturation is not reached at 2 MV mÿ1 (see Fig. 5) is small but contributes to the uncertainty in d33. Values for other threedimensional organic ferroelectrics (see x9.1) are: d33 = 0.26 pC Nÿ1 for GASH at 300 K; d32 = 1.05 pC Nÿ1 at 209 K for diglycerine nitrate; d14 = 345 pC Nÿ1 at 307 K for Rochelle salt.

7. Pyroelectric p3 coefficient at 300±325 K Both (001) faces of a single crystal with approximate dimensions 3.5 3.5 1 mm were coated with ¯exible silver ink electrodes (Engelhard-CLAL, 1995) and mounted on a microscope slide, as in x6. The pyroelectric coef®cient is the quotient of charge developed (Pi) along the polar ith axis under a change in temperature (T); in the present geometry, P3 = p3T. After poling, the crystal was heated rapidly from about 300 to 325 K, determining the temperature difference T by use of a Fluke Model 45 multimeter/80TK module with thermocouple in contact with the disk. The voltage thereby produced in a 4.7 mF capacitor connected across the disk, measured by a Keithley 6517 electrometer, integrates the charge P generated in the course of heating. The resulting value of p3 is 4 (1) mC mÿ2 Kÿ1. Pyroelectric coef®cients for other three-dimensional organometallic ferroelectrics (see x9.1) are: p3 = 15 mC mÿ2 Kÿ1 for GASH; p3 = 34 mC mÿ2 Kÿ1 for Rochelle salt; p2 = 4.2 mC mÿ2 Kÿ1 at 294 K for triglycine selenate.

8. Ferroelectric hysteresis and thermal dependence 8.1. Hysteresis circuit

Hysteresis measurements were made by use of a PCcontrolled modi®ed Sawyer & Tower (1930) circuit, with modi®cations based largely on those of Singh et al. (1996). The

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Polycrystalline samples as used for the permittivity measurements were also used in the dielectric hysteresis circuit of x8.1. The resulting hysteresis loop in Fig. 5 is typical of all loops produced by AGHFZ samples at room temperature under the application of 1 MV mÿ1 ®elds at 60 Hz. The shape of the loop remains rather constant as the temperature rises, the spontaneous polarization Ps becoming smaller by only 10% at 370 K; the loop collapses abruptly to a line at 390 K and regenerates on recooling below Tc. Electrical breakdown prevents the application of a ®eld suf®cient to produce full saturation; however, a ®eld of 0.9 MV mÿ1 allows Ps to be estimated from the linear section of the hysteresis loop at highest ®eld strength as 0.45 10ÿ2 C mÿ2 at 298 K1 (see Fig. 5). The major uncertainty in Ps arises from the possibility of incomplete saturation and is estimated as 20%, i.e. Ps = 0.45 (9) 10ÿ2 C mÿ2.

9. Discussion 9.1. Spontaneous polarization in three-dimensional ferroelectrics

The experimental determination of AGHFZ as a new ferroelectric adds it to the slowly growing class of organometallic ferroelectrics, for which Mitsui & Nakamura (1982, 1990) list ten families, several of which contain more than one member, and another that is antiferroelectric. All are threedimensional ferroelectrics, in the classi®cation of Abrahams & Keve (1971) based on the characteristic presence of one-, twoor three-dimensional atomic displacements undergone in the course of polarity reversal. Values of Ps reported in onedimensional ferroelectrics generally exceed 25 10ÿ2 C mÿ2, whereas values ranging from 5 to 25 10ÿ2 C mÿ2 are characteristic of two-dimensional ferroelectrics. Ps in the three-dimensional class of ferroelectrics presented in Table 2 extends from 4.2 10ÿ2 C mÿ2 for TGS to 0.15 10ÿ2 C mÿ2 for DSP. The value of 0.45 10ÿ2 C mÿ2 as determined in 1

Ps magnitudes are customarily given in units of 10ÿ2 C mÿ2 although SI nomenclature requires units such as mC mÿ2. J. Appl. Cryst. (2001). 34, 47±54

research papers Table 2

Representative three-dimensional organometallic ferroelectrics. See Mitsui & Nakamura (1982, 1990) for all ferroelectrics in the table except AGHFZ.

Aminoguanidinium hexa¯uorozirconate Guanidinium aluminium sulfate hexahydrate (GASH)² Tetramethylammonium trichloromercurate³ Dicalcium strontium propionate (DSP)§ Glycine silver nitrate Triglycine sulfate (TGS)²² Diglycine manganese chloride dihydrate Diglycine nitrate Sodium potassium tartrate tetrahydrate (RS)³³ Lithium ammonium tartrate monohydrate (LAT)§§ Tris-sarcosine calcium chloride (TSCC) Betaine calcium chloride dihydrate (BCCD)

Formula

Ps at 300 K (10ÿ2 C mÿ2)

Space group

CN4H8ZrF6 C(NH2)Al(SO4)2.6H2O N(CH3)4.HgCl2 Ca2Sr(CH3CH2COO)6 NH2CH2COOH.AgNO3 (NH2CH2COOH)3.H2SO4 (NH2CH2COOH)2.MnCl2.2H2O (NH2CH2COOH)2.HNO3 NaKC4H4O6.4H2O LiNH4C4H4O6.H2O (CH3NHCH2COOH)3.CaCl2 (CH3)3NCH2COO.CaCl2.2H2O

0.45 0.35 1.2 0.15 0.63 at 75 K 4.2 at 100 K 1.3 at 325 K 1.2 at 195 K 0.37 0.22 at 78 K 0.2 at 160 K 2 at 42 K

Pba2 P31m P21 P41 } P21 P21 Pa P21 P21 n21a }}

² V, Cr and Ga can isostructurally replace Al in GASH and Se can replace S in each material. ³ Br and I can isostructurally replace Cl, and P can replace N. § Ba and Pb can isostructurally replace Ca in DSP. Space group P43 is an alternative. } Not available. Space group in paraelectric phase given as P21/a. ²² Se can isostructurally replace S, and BeF4 can replace SO4. ³³ Rochelle Salt. NH4 can isostructurally replace K. §§ Tl can isostructurally replace NH4. }} Space group at room temperature reported as Pnma, with structural modulation below 164 K.

x8.2 for AGHFZ hence leads to its categorization as a threedimensional ferroelectric. 9.2. Atomic displacements under polarity reversal in AGHFZ

The room-temperature components of axial displacement required for each atom in AGHFZ to change space group from polar Pba2 to centrosymmetric Pbam are presented in Table 1, together with the original atomic coordinates of Bukvetskii et al. (1990). Examination of the x, y and z atomic displacements at 300 K in either independent ZrF2ÿ 6 anion that are necessary in order to undergo a phase transition shows that most are of comparable magnitude; only atoms F1, F2, F3 and F4 have unconstrained x and y magnitudes, taken as zero for simplicity. Atoms F5±F12, unrelated in the ferroelectric phase, become symmetry-related in pairs at Wyckoff position 8(i) in the paraelectric phase. By contrast with the anion, the only pairs of atoms in the organic CN4H2 8 cations for which the x or y coordinates are required by symmetry to adopt related positions at the phase transition are H6 and H7, and H15 and H16, since all others occupy fourfold Wyckoff positions in both space groups, with z = 0 or 12 in Pbam. The polarization caused by each cation may be reduced to zero by tilting the central CÐN axis (by 11 for C1ÐN3, by 2 for C2ÐN7) together with a displacement and torsion about the C1±N3 and the C2±N7 bonds by 19±20 (N1 and N7, respectively) and 7±9 (N2 and N5, respectively), causing both guanidine N atoms to lie in the plane at z = 0 or 12; an additional rotation (of 20 by N3ÐN4, of 15 by N7ÐN8) about the CÐN axis brings the amino N atom into this plane. The two H atoms of each guanidine group in both cations rotate about the central CÐN axis to occupy the plane at z = 0 or 12 as the three amino H atoms rotate about their NÐN axis so that two become related by Wyckoff position 8(i) in Pbam, while the third H atom occupies the special plane. In consequence, both cations lose all polarization. It is noted that the x, y and z component displacements in Table 1 are those required for a transition to a postulated phase that only exists between 383 K and decomposition at 435 K. For the case of polarization J. Appl. Cryst. (2001). 34, 47±54

reversal at 300 K, each displacement is necessarily double that given. The maximum cation z in Table 1 among the non-H Ê , is larger only by a factor of ®ve than atoms, z(N1) = 0.43 A Ê ; the the largest value of x or y, viz. y(N3) = 0.09 A magnitudes of the displacement components of the H atoms vary by less than a factor of two. The atomic displacement components along each axis in AGHFZ are thus of comparable magnitude under polarity reversal, in conformity with the basic structural requirement for three-dimensional ferroelectrics. The dimensional classi®cation hence provides a practical predictor of the range of spontaneous-polarization magnitudes (see x9.1). Conversely, the experimental value of Ps is a predictor of the preponderent atomic displacement dimensionality undergone during polarity reversal. 9.3. Frequency dependence of AGHFZ ionic displacement

The in¯ection at Tc observed in the dielectric permittivity using a frequency of 100 Hz, and the clear peak observed in the dielectric loss at 0.1 and 1 kHz but not at higher frequencies (see Fig. 4), is indicative of the maximum rate at which the ions can undergo the displacements, tilts and rotations necessary to achieve Pbam symmetry. The roomtemperature observation of dielectric hysteresis in Fig. 5 shows unambiguously that the motions by the CN4H2 8 cations and the displacements by the ZrF2ÿ 6 anions, required for polarization reversal, take place primarily at frequencies of the order of 0.1 kHz or lower. The low frequency of the phase transition in AGHFZ makes it an attractive candidate for time- and ®eld-resolved synchrotron studies. 9.4. Techniques for detecting inversion centers

The detection of reliable differences between centrosymmetric and noncentrosymmetric crystals by diffraction methods increases in dif®culty as the deviation of atomic positions from centrosymmetry decreases in the crystal studied. Seven different physical measurement methods are available that greatly strengthen the use of diffraction M. R. Bauer et al.


53

research papers methods alone. Use of several of these methods, at least, was recently recommended (Abrahams et al., 1998) in cases where the presence or absence of inversion centers is in doubt in the course of a structural determination. The methods seek to detect the presence of pyroelectric, piezoelectric, dielectric hysteresis, second harmonic generation, calorimetric, gyration tensor or photorefractive properties. Several of these methods have speci®c limitations; the pyroelectric and dielectric hysteresis properties have non-zero coef®cients only in crystal classes containing one or more polar axes; the gyration tensor has non-zero coef®cients only in 15 classes, but the others are without limitation in all 21 noncentrosymmetric classes. Methods capable of detecting four of these properties were used in obtaining the present results on AGHFZ. It is noteworthy that a crystal structure in which no atom departs by Ê from a centrosymmetric arrangement, hence more than 1 A offering the highest level of dif®culty in detecting the presence or absence of inversion centers, is potentially ferroelectric. In such cases, application of a test for second harmonic generation, pyroelectricity or piezoelectricity is advisable; if positive, then dielectric hysteresis measurement will reveal whether or not the crystal is also ferroelectric. This work forms part of the requirements for the Southern Oregon University degree of BS for chemistry senior undergraduates MRB, RJC, BLP and DLP and physics senior undergraduates DJA, CSG and WVR. Former seniors J. L. Christen and G. R. Brown are thanked for assistance with parts of this study. Support of this research by the National Science Foundation (DMR-9708246) and, in part, by Cancer Center Support CORE Grant, P30 CA 21765, is gratefully acknowledged. Support by the American Lebanese Syrian Associated Charities (ALSAC) is also appreciated by CRR.

References Abrahams, S. C. (1988). Acta Cryst. B44, 585±595.

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