DOI: 10.1021/cg100247g
Proton Disorder in NH 3 3 3 N Bonded [dabcoH]þI- Relaxor: New Insights into H-Disordering in a One-Dimensional H2O Ice Analogue
2010, Vol. 10 4334–4338
Marek Szafra nski* Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Pozna n, Poland
Andrzej Katrusiak* Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Pozna n, Poland
Garry J. McIntyre Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France Received February 23, 2010; Revised Manuscript Received August 1, 2010
ABSTRACT: Protons in the NHþ 3 3 3 N hydrogen bonds linking the cations into strictly linear aggregates in the crystal of 1,4diazabicyclo[2.2.2]octane hydroiodide ([C6H13N2]þ 3 I-, dabcoHI) remain disordered, and the average crystal symmetry (space group P6m2) remains unchanged, down to 1.5 K, as evidenced by single-crystal neutron-diffraction, but against the expectation based on the third law of thermodynamics. This proton disorder reveals the role of the thermal-activation and proton-tunneling processes for the polarizability of hydrogen bonds and for the formation of polar nanodomains, resulting in the unique property of an anisotropic giant dielectric response in the chemically homogeneous compound. The dielectric constant exceeding several thousand in the direction of the crystal [z] axis between 150 and 300 K can be explained by the fluctuations of nanodomains, whereas the dielectric constant of about 100 at 10 K can be due to the residual contribution of tunneling protons in hydrogen bonds. The proton transfers disproportionate the dabco monocations into dications and neutral molecules and generate high crystal-field fluctuations. The consideration of possible crystal-symmetry changes shows that ferroelectric proton ordering would lead to the lowered symmetry of space group P3m1 within the hexagonal system, and antiferroelectric proton ordering would require a transformation to an orthorhombic phase; however, the proton-site correlations are too weak for these transformations to take place, and the resultant structure remains disordered. The crystal symmetry and the lack of FowlerBernal rules distinguish dabcoHI from the H2O ice-Ih, and are essential for the dielectric properties of this substance. Introduction The isostructural crystals of 1,4-diazabicyclo[2.2.2]octane hydroiodide ([C6H13N2]þ 3 I-, dabcoHI) and 1,4-diazabicyclo[2.2.2]octane hydrobromide ([C6H13N2]þ 3 Br-, dabcoHBr) were reported to exhibit giant (exceeding 1000) and strictly one-dimensional dielectric responses.1,2 Such properties are highly sought after for microelectronic applications, where presently mainly inorganic perovskite-type crystals reign. Organic materials potentially possess several advantages over their perovskite counterparts: their technological processing can be more environmentally friendly, as they can be dissolved and easily deposited, they contain no lead nor other heavy poisonous elements, and they can be easily disposed. The dielectric properties of dabcoHI and dabcoHBr have been associated with the positions of the protons in the NHþ 3 3 3 N hydrogen bonds, linking the dabco cations into strictly linear supramolecular aggregates along the hexagonal [z] axis. It has been established that in both compounds, despite the long N 3 3 3 N distance between the cations of about 2.8 A˚, the protons are disordered in the bistable hydrogen bonds.1-5 The dabcoHI and dabcoHBr compounds are nonpolar and therefore considerably different from ferroelectric dabco complexes with tetrahedral AB4- anions (ClO4-, ReO4-, and BF4-), which at room temperature are monoclinic or ortho*Corresponding authors. E-mails:
[email protected] (A.K.); masza@ amu.edu.pl (M.S). pubs.acs.org/crystal
Published on Web 09/02/2010
rhombic. In the dabcoHAB4 complexes, the protons are ordered in the ferroelectric phases, below a TC of about 375 K for all these compounds.4,5 More recently, an unexpected phase transition that induces proton disordering in the NHþ 3 3 3 N bond below 153 K was found in dabcoHBF4.6 The disordering of protons induced by cooling the ordered phase is an exceptional transformation of hydrogen bonds and is connected with the specific one-dimensional contribution to the dielectric response.7 Unusual dielectric properties associated with the proton behavior in NHþ 3 3 3 N hydrogen bonds linking cations into linear chains were also detected in pyrazineHBF4.8 The dabcoHI and dabcoHBr complexes are unique, as the proton dynamics occurs in hydrogen bonds much longer than the OH 3 3 3 O bonds in KH2PO4 (KDP), where the O 3 3 3 O distance is 2.54 A˚.9 In KDP-type ferroelectrics, the H sites are strongly correlated through the ionic (molecular) displacements and π-electron systems of alternative double and single bonds (e.g., OdP-O-H in KDP and OdC-CdO-H in squaric acid). Therefore, the lowering of temperature leads to H ordering below TC. However, it was found more recently that in disquaric acid, where similar H-bonds are present, no signs of H ordering were detected. Such a behavior is characteristic of structures with much weaker H-site correlations,10 like those in H2O ice-Ih, where mainly molecular tumbling is frozen at about 105 K in a continuous manner characteristic of glasses.11-16 Our preliminary X-ray diffraction study1 showed that the dabcoHI crystal retains its high-temperature symmetry and r 2010 American Chemical Society
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Crystal Growth & Design, Vol. 10, No. 10, 2010
thence proton disorder down to 120 K. Moreover, the dielectric response of the crystal strongly suggests that with lowering temperature the contributions to the crystal polarization are successively switched off, whereas proton dynamics of some kind still persist in the temperature range of liquid helium. Hence, the main purpose of this neutrondiffraction study was to determine the structure of dabcoHI and the behavior of the proton down to 1.5 K. Apart from the practical aspects of the exceptional structure-property relationship, dabcoHI constitutes an intriguing model for studying the mechanism of proton disordering in a one-dimensional (1D) H-bonding motif, considerably simpler than the threedimensional (3D) network in ice-Ih and also not restricted by Fowler-Bernal ice rules17 nor Slater-type correlations.18
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Figure 1. Ionic pair of [dabcoH]þ 3 I- at 1.6 K. The thermal ellipsoids have been shown at the 50% probability level. The 50:50 disordered proton sites have been drawn in orange. Only the symmetry-independent atoms have been labeled.
Experimental Section Crystals of dabcoHI were obtained at 290 K from an aqueous solution by slow evaporation of the solvent. The preliminary X-ray diffraction structural determination was performed on a KUMA 4-circle diffractometer equipped with a low-temperature Oxford Cryostream attachment. This was followed by neutron diffraction on the 4-circle diffractometer D9, equipped with an area detector19 and an Orange helium-flow cryostat, installed on the hot source of the high-flux reactor at the Institut Laue-Langevin in Grenoble. An incident beam with a calibrated wavelength of 0.8372(2) A˚ was obtained by reflection from a Cu 2 2 0 monochromator. During data collection, initially at 298 K and then on cooling the sample, particular care was taken to detect possible lowering of the P6m2 space group symmetry or doubling of the lattice, but no sign of any symmetry-element breaking was detected. In the process of crystalstructure refinement, two models, one in space group P6m2 and the other in P3m1, were refined for each of the data sets. None of these refinements gave any sign of the lowering of the symmetry from P6m2: in the Hamilton reliability-factor test,20 the hypothesis that the structure is P6m2 could not be rejected, and the occupations of the proton sites remained equal within error. The final structural information, unit-cell dimensions, details of neutron-diffraction experiments and refinements, and atomic coordinates are in Tables S1-S13 (Supporting Information). The crystallographic information files (CIF) are listed in the Supporting Information, too, and have been also deposited in Cambridge Crystallographic Database Centre with supplementary-publication numbers CCDC 753797-753800 for the data at 298.0, 16.0, 6.0, and 1.5 K respectively (copies can be obtained free of charge on request from deposit@ ccdc.edu). The calculations were carried out with the SHELXL-97 program.21 Measurements of complex electric permittivity ε = ε0 - iε00 (ε0 is the real part of the electric permittivity, and ε00 denotes the dielectric losses) were carried out with a Hewlett-Packard 4192A impedance analyzer in the frequency range 0.5 kHz-3 MHz. The (001) faces of the oriented single-crystal sample were covered with gold electrodes. The amplitude of the ac measuring electric field was 3 V/cm. The temperature of the samples was changed at the rate of 0.5 K/min with the use of a closed-cycle refrigerator (Oxford Instruments CCC1204). Lattice-energy minimizations were carried out with the programs Cerius222 and Materials Studio,23 using the Dreiding/X6 force field.24 Atomic charges were derived from the ESP approach based on MP2/ 6-31G** calculations. Ewald summation was used for Coulomb interactions as well as for van der Waals interactions. Different ordered structural models were set up, including a ferroelectric arrangement with parallel chains in space group P3m1 and an antipolar model with layers of antiparallel chains (space group Pnm21). In the lattice-energy minimizations, the molecules were treated as flexible but constrained by space-group symmetry. The lattice parameters were kept fixed at the values determined experimentally at 1.5 K.
Discussion The symmetry of the dabcoHI crystals remains unchanged down to 1.5 K, which implies that the protons remain
disordered to this low temperature. Also no other features of the dabcoHI structure change significantly; the main differences are in the unit-cell dimensions and in the amplitudes of thermal vibrations. It can be seen in Figures 1 and 2 that the thermal ellipsoids of the carbon, nitrogen, and iodide atoms are elongated along [z], which is consistent with the disorder of the protons in NHþ 3 3 3 N bonds along this direction. The hydrogen atoms have much larger ellipsoids, which is consistent with the stronger vibrations of light atoms and the libration of the CH2 groups. This is also visible in the thermal ellipsoid of the disordered proton. The aggregation of cations into chains running along [z] is unchanged over the entire temperature range, and the shortest CH 3 3 3 I- contacts between the cations and anions support the hexagonal arrangement of the chains. The strictly 1D system of hydrogen bonds in dabcoHI constrains the number of possible polarization states. The local polarization, induced by proton transfers in the bistable NHþ 3 3 3 N hydrogen bonds, can only be directed along [001] or [001]. Therefore, the contribution to the dielectric response of the crystal, arising from the short-range protonic correlations, is huge along the hydrogen bonds and absent in the perpendicular directions. The refined methods of crystallization yielded good quality and large single-crystal samples of dabcoHI, and the repeated measurements for these samples revealed a magnitude of the dielectric constant over 4500 (Figure 3a), several times larger than those recorded before.1 The temperature and frequency ( f ) depends of ε0 indicate a complex nature of the relaxation in this crystal. In particular, the low-temperature dielectric measurements have shown that even at the lowest temperatures accessible in our experiment, ca. 13 K, the electric permittivity is highly dispersive, and its magnitude still remains quite high. To illustrate this behavior, we plotted in Figure 3b the frequency dependencies of the real part of the complex electric permittivity measured at several temperatures. The ε0 ( f ) spectra are broad and tend to logarithmic dependence on f with lowering temperature. Such a dependence mirrors dipolar fluctuations with a broad distribution of rates and a lack of characteristic relaxation time. The linear parts of the spectra converge at f0 ≈ 3 106 Hz. A similar logarithmic behavior of the low-temperature dielectric response has been reported recently for crystalline solutions of ferroelectric RbH2PO4 and antiferroelectric NH4H2PO4, and was explained by proton tunneling in the OH 3 3 3 O- hydrogen bonds.25 By combining dielectric and neutron Comptonscattering data, the frequency of 1011 Hz corresponding to the convergence point f0 has been identified as the transition rate for the tunneling process. By analogy, it can be assumed
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Figure 3. Real part of electric permittivity ε0 of dabcoHI measured along [001] (a) as a function of temperature at several fixed frequencies, f, and (b) at several fixed temperatures as a function of log f. Table 1. Hydrogen Bond NHþ 3 3 3 N0 Dimensions (The Primed Atom Is Transformed According to Symmetry Code: x, y, 2-z) in the dabcoHI, as Determined in This Neutron-Diffraction Study
Figure 2. Autostereographic projections of the dabcoHI structure at 1.5 K, viewed along the direction perpendicular (a) and parallel (b) to the hydrogen bonds.
that the low-temperature dielectric relaxation in dabcoHI is dominated by a quantum-mechanical process involving proton tunneling. The frequency f0 determined from the convergence point in Figure 3b is much smaller than that observed for the proton glass Rb1-x(NH4)xH2PO4, x ≈ 0.5, mixed crystal (abbreviated RADP), but this difference can result from the different characteristics of the OH 3 3 3 O- and NHþ 3 3 3 N hydrogen bonds. The dabcoHþ cations, NHþ 3 3 3 N bonded along [z], and the I anions lie at the special sites of 6m2 symmetry; the midpoint of the hydrogen bond has the same site symmetry. Thus, the proton disorder is consistent with the average crystal symmetry. However, the N 3 3 3 3 N distance of ca. 2.8 A˚ in the hydrogen bond of dabcoHI (Table 1) belongs to the category of
temperature (K)
N1-H1 (A˚)
1.5 6.0 16.0 300.0
1.146(4) 1.146(6) 1.153(3) 1.161(6)
H1 3 3 3 N10 (A˚) 1.644(4) 1.648(6) 1.639(3) 1.663(6)
N1 3 3 3 N10 (A˚) 2.7901(16) 2.7940(22) 2.7914(20) 2.823(3)
medium-length H-bonds, associated with a high-energy barrier. Thus, only very high potential-energy fluctuations could be compatible with the H-atom dynamics at high temperature, while the residual proton dynamics near absolute zero can originate from proton tunneling. The temperature evolution of the dielectric response (Figure 3) and the gradual decay of the field-induced polarization of dabcoHI with increasing temperature (see Figure 4 in ref 1) indicate a complex nature of the polarization mechanisms in this material. This complex nature can be connected with the different dynamics of the protons in fluctuating polar and antipolar domains, in the domain walls, and around structural defects, where the
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dynamics of some of the protons freeze upon lowering the temperature, while others can still persist even at just a few Kelvins. Thus, despite the very similar structural effect of the protons remaining disordered down to the lowest temperature, in this respect the origin of the H-disordering in dabcoHI is quite different from that in hexagonal H2O ice-Ih. The proton disordering in ice-Ih is connected with the tumbling motion of the polar molecules that freeze at about 105 K, and the dielectric effect is typical of dipolar glasses.26 That no giant dielectric response is observed in ice-Ih, where the OH 3 3 3 O distances (of ca. 2.7 A˚) are shorter than the NHþ 3 3 3 N distance in dabcoHI, is due to the absence of polar domains characteristic of the relaxor state. Although a configurational proton disorder exists in both ice-Ih and dabcoHI over the full temperature range from room temperature to liquid-helium temperature, the underlying physics is different. The freezing process of proton dynamics requires that the average crystal symmetry is broken locally. It has been observed in this low-temperature neutron-diffraction study that the average crystal symmetry remains the same even at 1.5 K. Thus, the freezing of protons at off-center sites between the N 3 3 3 N sites does not lead to a long-range order, like in most substances, but to a conglomerate of short-range ordered regions (both polar and antipolar). As the proton dynamics freezes in dabcoHI, there are no detectable changes in the sites of the heavy atoms. Then, these are only the sequences of the protonic sites in small regions, which determine the local crystal symmetry and local polarization. The local displacements of protons do not induce significant changes in structure and orientation of the ions and do not distort the lattice dimensions. In general, many arrangements of the neighboring protons are possible; however, the simplest one (i.e., one with the same unit cell and high trigonal symmetry of the cation preserved) would be polar ordering, with all the protons assuming in the hydrogen bonds the sites consistent with one sense of the [z] axis (see Figure 4a). This ordering would lead to the space group P3m1. Such a polar structure can result from an energetic preference leading to a long-range correlation between the proton sites. However, the observed H disorder at 1.5 K testifies that no correlation like this exists in dabcoHI. The lattice-energy minimizations show that the antipolar arrangement of chains is energetically more favorable than the polar arrangement. However, the energy difference is small. An antipolar arrangement in space group Pnm21, with layers of antiparallel chains is more favored by a mere 0.96 kJ/mol than a polar arrangement of parallel chains in space group P3m1. Furthermore, there is an infinite number of other arrangements with similar lattice energies. It is thus plausible that more electrostatically favored antipolar ordering of the protons results in several patterns of alternating ordering of the protons parallel and antiparallel to the [z] axis. The simplest arrangement consists of alternating rows of the dabcoHþ cations with the protons pointing parallel and antiparallel to the [z] axis, as illustrated in Figure 4b. Its space-group symmetry would be Pnm21; therefore, a transition to this arrangement would require a phase transition involving a change from the hexagonal to an orthorhombic crystallographic system with three domains corresponding to three orientational states with the hexagonal [z] axis of the prototypical state coinciding with the orthorhombic [x] axis, common to all three orientational states. Antiparallel polarization of the H-bonded chains in the hexagonal setting cannot be simultaneously realized along the three equivalent [100], [010],
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Figure 4. Hypothetical dabcoHI structures viewed down [z] in space group (a) P3m1 with the polar arrangement of protons; and (b) Pnm21 with the chains antipolar. The protons directed upward (toward the viewer) are shown as red dots and those directed downward as empty circles, and the symmetry elements within the cell are shown in green.
and [1 10] directions27 but requires a change of the crystallographic system. Our careful check between 300 and 1.5 K revealed no splitting or broadening of high-angle reflections which could be caused by such a transformation. Without any evidence of a low-temperature orthorhombic phase, the hexagonal symmetry appears to be the key factor in the structural and dielectric behavior of the dabcoHI crystal. In terms of the crystal-lattice strain (i.e., the distortion of the hexagonal unit cell), it appears that energetically less demanding one would be the transformation from the prototypical space group P6m2 to the polar arrangement (space group P3m1) rather than to the antipolar arrangement (space group Pnm21). The fact that no long-range ferroelectric ordering is observed confirms that the electrostatic interactions prevent this direction of transition.
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The difference in electrostatic interactions favoring the antiparallel polarization of the neighboring H-bonds, over the parallel one, are too weak, and correlations between the protonic sites too short-ranged, for the antipolar ordering of protons and orthorhombic strain to be induced, when the proton dynamics is frozen. Thus, the system remains in a frustrated state with the symmetry only broken locally within small domains. The low correlation between the orientation of neighboring chains results in an almost random arrangement of up and down chains, which explains the observed dielectric behavior, without deviation from the hexagonal average symmetry. In dabcoHI, the disordered protons constitute a very small mass fraction of the compound, 0.42%, considerably less than in ice Ih where 11.1% of the mass of the structure is disordered and remains so down to liquid-helium temperature. Even this substantial mass of the structure cannot induce the transformation of the ice-Ih crystal to the long-range ordered structure, except in KOH-doped H2O ice, which at 72 K partly transforms to an orthorhombic ferroelectric phase, space group Cmc21 (i.e., only in a part of the ice-Ih crystal volume do the H2O molecules order).28-30 It is likely that this ordering is facilitated close to the structural defects, where enhanced electrostatic interactions of the doping ions favor certain molecular orientations and induce orthorhombic strain in the crystal. The comparison of the disordered-mass fractions in dabcoHI and H2O suggests that the transformation of dabcoHI to the orthorhombic structure is very unlikely. Conclusions The disorder of protons persisting to 1.5 K in dabcoHI is analogous to that in H2O ice, although the proton sites in the NHþ 3 3 3 N hydrogen bonds are not restricted by the ice-type rules. Temperature-dependent single-crystal neutron diffraction combined with the dielectric-constant studies on the dabcoHI crystals has shown that the proton sites in the NHþ 3 3 3 N bonds are trapped in the hexagonal symmetry counteracting the long-range antipolar ordering of protons in orthorhombic orientational states. This results in the formation of short-range ordered regions. Moreover, the local polarization occurs exactly along one axis, coinciding with the direction of the linear hydrogen bonds. Hence, the nonpolar structure of dabcoHI exhibits a strictly 1D giant dielectric response. At room temperature, it is comparable in magnitude to those in most efficient electronic perovskite-type materials, 2 orders of magnitude larger than in KDP-type dipolar glasses, and incomparably higher than the dielectric response of ice-Ih below 273 K. The origin of the anomalous proton disordering down to 1.5 K is associated with specific features of the crystal structure, resulting in its incapability to accommodate the antiparallel ordering of weakly correlated protons within the hexagonal symmetry. The proton disordering in the average dabcoHI structure in low temperature is analogous to the H disordering in the average ice- Ih structure, but there are essential differences at the local level. The stronger correlations between the H sites and the molecular structure of water prevent the formation of ordered fluctuating nanoregions, playing an essential role in the dielectric properties of dabcoHI. Like H2O ice, dabcoHI exhibits a rich phase diagram of 10 polymorphic forms determined so far; however, in all of the dabcoHI polymorphs the NHþ 3 3 3 N bonded chains are present.31
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Acknowledgment. We are grateful to Professor Martin Schmidt of the Chemistry Faculty, University of Frankfurt, Germany, for performing the theoretical calculations of electrostatic interactions in the dabcoHI structural models of Pnm21 and P3m1 space-group symmetries and for helpful discussions. This study was supported by Polish Ministry of Science and Higher Education, Grant N202 14631/2707. Supporting Information Available: Tables with crystal structures of dabcoHI determined at 298.0, 16.0, 6.0, and 1.5 K, unit-cell dimensions, details of neutron-diffraction experiments and refinements, atomic coordinates and molecular dimensions (Tables S1-S13), and the crystallographic information files (CIF) including the lists of reflections intensities. This material is available free of charge via the Internet at http://pubs.acs.org.
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