Bias-Field and Pressure Effects on the One-Dimensional Dielectric

J. Phys. Chem. B 2009, 113, 9479–9488

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Bias-Field and Pressure Effects on the One-Dimensional Dielectric Response in N-H+ · · · N Hydrogen-Bonded 1,4-Diazabicyclo[2.2.2]octane Hydrobromide Crystal Marek Szafran´ski* Faculty of Physics, Adam Mickiewicz UniVersity, Umultowska 85, 61-614 Poznan´, Poland ReceiVed: January 20, 2009; ReVised Manuscript ReceiVed: May 15, 2009

Unusual dielectric properties of 1,4-diazabicyclo[2.2.2]octane hydrobromide [C6H13N2]+ · Br- (dabcoHBr) have been investigated at ambient and hydrostatic pressures and at biasing dc electric field. The crystal exhibits a huge dielectric constant along the hydrogen-bonded chains, exceeding 1500, while in the perpendicular direction it behaves as a typical nonpolar dielectric. Though the dynamics of protons in the N-H+ · · · N hydrogen bonds is essential for these properties, of key importance are weak protonic correlations leading to the formation of short-range ordered regions. The complex dielectric response of dabcoHBr is due to several contributions involving dipolar fluctuation within the polar nanoregions, fluctuations of boundaries, and excitation of solitonic kinks propagating along the chains as a result of coherent proton transfers. A relatively low dc biasing electric field distinctly modifies the dielectric response, making it reminiscent of ferroelectric relaxors. Profound changes are also induced by hydrostatic pressure, which counteracts the proton correlations and the short-range polar order formation. At elevated pressures, the hexagonal structure of dabcoHBr undergoes a phase transition, associated with a loss of the unusual dielectric properties. This is due to the breaking of the N-H+ · · · N hydrogen bonds, which destroys the one-dimensional topology of the polycationic chains and results in formation of the phase built of hydrogen-bonded ionic pairs. The phase diagram, illustrating the phase boundary between the high- and low-dielectric constant phases of dabcoHBr, is presented. Introduction Hydrogen bonding plays a key role in shaping of physical and chemical properties of various molecular systems. This specific interaction, and in particular its directional features, have been employed for the control of crystal structures and tuning the material’s functionality.1-3 In the field of solid state physics, a great deal of attention has been devoted to the role of hydrogen bonds and proton dynamics in dielectric properties of materials. The majority of these studies has been focused on the systems linked by strong homonuclear O-H · · · O bonds. A text-bookish example is KH2PO4 (KDP) and its analogues, in which the ordering of protons in the bistable hydrogen bonds is associated with a long-range ferroelectric or antiferroelectric order.4 The characteristic feature of these compounds is a strong correlation between the proton sites in hydrogen bonds. In KDP, for example, each PO4 group can accept two protons according to Slater’s rule,5 which is essential for the formation of a longrange ferroelectric order. A similar constraint, known as the Bernal-Fowler ice rule,6 is valid for H2O ices. The other important property, observed in the O-H · · · O bonded structures, is a three-dimensional character of the H-bonded networks. There are only several materials which approximately meet the one-dimensional requirements. For example, the quasi-onedimensional H-bonded chains are formed in bisquaric acid7 and in betaine complexes.8,9 The one-dimensional supramolecular H-bonded aggregates are also formed in recently reported ferroelectric cocrystals of 2,5-dihydroxy-p-benzoquinones and pyridine derivatives.10 However, it is characteristic that in all these compounds the hydrogen bonds form zigzag motifs, which disturbs the one-dimensional character of molecular aggregates. The interest in low-dimensional H-bonded systems arises both * Corresponding author. E-mail: [email protected].

from the theoretical predictions of proton transport along the molecular aggregates in the form of solitonic excitations and from the basic research on the role of dimensionality in the critical phenomena of solids.11-17 Besides, the linear H-bonded molecular aggregates can serve as models for more complex biological systems, giving an opportunity for direct studies of the contribution of hydrogen bond transformations to the properties of the substance. From this point of view, of particular interest are the complexes of 1,4-diazabicyclo[2.2.2]octane (C6H12N2, dabco), in which the cations form linear chains linked by N-H+ · · · N hydrogen bonds.18-22 Analogous H-bonded polycationic chains are also formed in perchlorate and tetrafluoroborate pyrazine complexes.23,24 It is characteristic that all these crystals, comprising one-dimensional networks of hydrogen bonds, exhibit interesting dielectric properties. The dabco monosalts with tetrahedral anions, i.e., dabco tetrafluoroborate (dabcoHBF4), dabco perchlorate (dabcoHClO4),and dabco perrhenate (dabcoHReO4), are the room-temperature ferroelectrics.20,21 Their Curie-points are situated between 370 and 380 K, and their transitions to the paraelectric phases are associated with disordering of protons in hydrogen bonds, similarly to in the prototypical H-bonded KDP-type ferroelectrics.4 Moreover, new exciting dielectric properties, associated with the unique onedimensional topology of the dabco salts structures, have been observed recently.25,26 An unusual dielectric anomaly was revealed along the polycationic chains in dabcoHBF4. This additional dielectric activity was relatively small but inexplicable in the frame of the classical ferroelectricity and symmetryproperty relationships of the crystal. Short-range polar order arising from proton transfers in N-H+ · · · N hydrogen bonds has been postulated to explain these properties.25 However, the most surprising is the dielectric response of dabco hydroiodide (dabcoHI), which exhibits extremely huge and strongly aniso-

10.1021/jp900602p CCC: $40.75  2009 American Chemical Society Published on Web 06/19/2009

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tropic electric permittivity, with some features characteristic of ferroelectric relaxors.26 Due to the spherical shape of the anions, the long-range ferroelectric order does not occur, and the structure acquires a nonpolar hexagonal symmetry. In dabcoHI, the N-H+ · · · N bonded polycations are strictly linear, which is bounded by the symmetry requirements. Therefore, the crystal is an ideal object for studying the proton behavior in hydrogen bonds and the properties related with the transformations of hydrogen bonds. The size and the nature of the unprecedented dielectric response in dabcoHI are still intriguing, and the phenomenon requires further systematic examination. The present work is a continuation of our studies on the shortrange polar order formation in the one-dimensional H-bonded systems. The results presented for 1,4-diazabicyclo[2.2.2]octane hydrobromide [C6H13N2]+ · Br- (dabcoHBr) demonstrate that also this crystal exhibits huge and strongly anisotropic dielectric response. To get a better insight into this new phenomenon, related with the transformation of hydrogen bonds and proton correlations, the dielectric properties of dabcoHBr have been studied at ambient and high pressures and at dc biasing electric field.

Szafran´ski TABLE 1: Crystal Data and Structure Refinement Details for dabcoHBr at 120 K empirical formula formula weight wavelength [Å] crystal system space group unit cell [Å]: a, c volume [Å3] Z, calculated density [g/cm3] absorption coefficient [mm-1] F(000) crystal size [mm] θ range for data collection [°] limiting indices reflections collected/unique completeness to θ absorption correction refinement method data/restraints/parameters goodness-of-fit on F2 final indices R1/R2 [I > 2σI] R1/R2 (all data) absolute structure parameter largest diff. peak and hole [e.Å-3]

[C6H13N2]+ · Br240.08 0.71073 hexagonal P6jm2 6.623(2) 5.315(4) 201.90(17) 1, 1.588 5.01 98 0.30 × 0.06 × 0.05 3.55 to 30.01 -8 e h e 8, 0 e k e 8, 0 e l e 7 683/270 [Rint ) 0.0244] 100.0% to 30.01° empirical full-matrix least-squares on F2 270/0/18 1.109 0.0136/0.0337 0.0136/0.0337 0.000(19) 0.312 and -0.221

Experimental Section DabcoHBr was synthesized by dissolving stoichiometric amounts of dabco base and hydrobromic acid in water. The compound was purified by repeated crystallizations from an aqueous solution at room temperature. The final crystallization at 275 K yielded small colorless and transparent crystals, shaped in the form of hexagonal pillars with the largest dimension of 2-7 mm and cross sections between 0.2 and 1.0 mm2. The samples for dielectric measurements were prepared in the form of plates oriented perpendicular to [100] or [001]. The sample cut perpendicular to [100] had a thickness of 0.32 mm and an area of 6.5 mm2. Because of the small size of the crystals, the [001]-oriented samples were prepared as mosaics made of several oriented plates of the total area of 4.5-5 mm2. The samples thickness was of 0.3-0.5 mm. Some experiments were also performed on the small single crystals of a thickness of 0.5-0.6 mm and an area of ca. 1 mm2. The (100)/(001) faces of the samples were covered with sputtered gold electrodes. Measurements of complex electric permittivity were carried out with a Hewlett-Packard 4192A impedance analyzer. The amplitude of the ac measuring electric field did not exceed 3 V/cm. The temperature of the samples was changed at the rate of 0.5 K/min. In the temperature range 90-350 K, the data were obtained in the 0.5 kHz-13 MHz range, while for lowtemperature measurements, with the use of a closed-cycle cooler CCC1204 (Oxford Instruments), the upper frequency limit was reduced to 5 MHz. The experiments with biasing electric field were performed for different dc electric field strengths in the range 0.1-1.3 kV/cm. The following procedure was used. The sample was heated up to 320 K and annealed at this temperature for 30 min. Then the field was applied, and the measurements were performed in the field-heating after field-cooling or zerofield-heating after field-cooling cycles. For high-pressure measurements of the complex electric permittivity, the samples were mounted in a beryllium-copper cell. The pressure was generated by a GCA-10 gas compressor (Unipress) using gaseous helium or nitrogen as a transmitting medium. The pressure was calibrated by means of a manganin gauge with an accuracy of ( 5 MPa. The temperature of the sample was controlled inside the cell by a copper-constantan thermocouple. Calorimetric measurements were carried out using a differential scanning calorimeter Q 2000 (TA Instruments). The

experiments were performed on heating and on cooling the single-crystal samples at the rate of 2-20 K/min. Indium standard was used for temperature and enthalpy calibration. The temperature dependence of polarization of the crystals was determined from pyroelectric charge measurements using a Keithley 6514 electrometer. The X-ray diffraction data were collected on a KUMA KM-4 diffractometer equipped with graphite monochromated Mo KR radiation. The unit-cell dimensions were measured as a function of temperature by the least-squares fits to 33 reflections centered at fixed temperatures. The temperature of the crystal was controlled within 0.1 K with a stream of gaseous nitrogen from an Oxford Cryosystem device. The θ-2θ scan mode at a variable rate, depending on the reflection intensity, was applied to measure the intensities. The data were corrected for Lorentz and polarization effects. The correction for the absorption was made on the basis of the Ψ scans of selected reflections. The crystal structure was solved by the Patterson method with SHELXS97 program27 and refined by full-matrix least-squares method on all F2 data using the SHELXL97 program.28 The experimental and refinement details and the crystal parameters are listed in Table 1. The crystal data have been deposited in the Cambridge Crystallographic Database Centre as supplementary publication No. CCDC 712833. Experimental Results and Discussion Crystal Structure and Phase Situation. At room temperature, dabcoHBr crystallizes in hexagonal space group P6jm2.19 The DSC method was used to determine the temperature stability of this phase. The results of calorimetric studies are shown in Figure 1. As seen in the high-temperature range above 400 K, the crystal undergoes a sequence of two first-order phase transitions. Thus, at ambient pressure dabcoHBr can exist in the three crystalline forms. The high-temperature phase has been denoted as I, the intermediate phase as II, and the lowtemperature phase as III. The transition from the hexagonal phase III to the intermediate phase II, occurring on heating at T32 ) 458 K, is associated with the enthalpy change ∆H32 ) 5.1 kJ · mol-1. The subsequent heating of the intermediate phase II leads to the next transformation of the crystal structure at T21 ) 471 K. This transition is associated with ∆H21 ) 3.33 kJ · mol-1. The corresponding entropy changes are ∆S32 ) 11.1

Bias-Field and Pressure Effects on dabcoHBr Crystal

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Figure 1. DSC runs measured on heating and on cooling the singlecrystal dabcoHBr sample at the rate of temperature changes of 10 K/min. The roman numbers denote the crystal phases.

Figure 3. Structure of the hexagonal phase at 120 K viewed in the direction perpendicular to the H-bonded polycationic chains.

Figure 2. Temperature dependence of the lattice parameters and unitcell volume of dabcoHBr in the hexagonal phase.

J · mol-1 · K-1 (≈R ln 4, where R denotes the gas constant) and ∆S32 ) 7.07 J · mol-1 · K-1 (≈R ln 2.3), respectively. Both transition entropies are large enough to classify these phase transitions as the order-disorder ones. However, from the point of view of this study, the most important is the lack of phase transitions in the T-range below 400 K. A careful DSC examination, made at different rates of temperature changes from 2 to 20 K/min, did not reveal any thermal anomaly, which could indicate a phase transition between 95 and 400 K. A similar conclusion can be deduced from the temperature dependencies of the unit-cell dimensions, shown in Figure 2. The parameters of the dabcoHBr hexagonal unit cell decrease gradually with decreasing temperature without any anomalous behavior. The only distinct feature is a large anisotropy in the crystal thermal expansion. At 300 K, the linear thermal expansion coefficients are Ra ) 4.46 × 10-5 K-1 and Rc ) 1.78 × 10-5 K-1, respectively, in the directions perpendicular and parallel to the hydrogen-bonded polycationic chains. Such an anisotropy is characteristic of the crystals linked by low-dimensional networks of hydrogen bonds.29 The crystal structure determination at 120 K confirmed that at low temperatures dabcoHBr retains the symmetry of hexagonal space group P6jm2. The structural model derived from

the data collected is shown in Figure 3. The formation of hydrogen bonded polycationic chains in the dabco monosalts was evidenced earlier by the structural study and infrared spectra.18 In dabcoHBr, the polycationic aggregates are tied by N-H+ · · · N hydrogen bonds, in which the N · · · N and N-H distances are 2.775(8) and 1.05(6) Å, respectively. For comparison, the structure determination at 293 K gave the intermolecular N · · · N distance of 2.787(8) Å and the N-H distance of 0.707(16) Å. The H atoms in the hydrogen bonds have been located in the difference Fourier maps in split sites separated by 0.68(7) Å along the N · · · N line. The symmetry requirements imply equal occupancy factors of both proton positions as well as the exact linearity of the hydrogen bonds and the chains, and hence the system is perfectly one-dimensional. The twosite proton disorder suggests a double-well symmetric shape of the potential energy. Giant Dielectric Anisotropy. The complex electric permittivity ε ) ε′ - iε′′ was measured along the hydrogen-bonded polycationic aggregates and in the perpendicular direction. The results obtained for selected frequencies are shown in Figure 4. Similarly as in the isostructural dabcoHI,26 the dielectric response of the crystal is strongly anisotropic. For the orientation E || c, i.e., along the hydrogen-bonded chains, the electric permittivity is huge and highly frequency dependent. The dielectric constant exceeding 1500 is rather unexpected for the pure substance whose structure is nonpolar. Besides, it strongly contrasts with the properties observed along the direction perpendicular to the hexagonal axis (E ⊥ c). Along this direction, the crystal behaves as typical nonpolar dielectric with electric permittivity less than 10. For clarity of the picture, in Figure 4(a) only the 10 kHz data are plotted for the E ⊥ c orientation. A small anomaly in the temperature dependence of ε′ results from a possible slight misorientation of the crystal, but it is clear that in this case the unusual response does not take place. Thus, the effect occurring along the hexagonal axis has to originate from the behavior of the protons involved in the N-H+ · · · N hydrogen bonds. The temperature dependence of

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Figure 5. Schematic drawing of the potential energies of protons in the temporarily polarized segment of the polycationic chain (a) and after a single proton transfer (b) and three successive proton transfers (c). The ethylene hydrogen atoms have been omitted for clarity, and the open and crossed circles represent the neutral and charged dabco units, respectively.

Figure 4. Temperature dependencies of the real ε′ (a) and imaginary ε′′ (b) components of the complex electric permittivity measured along the N-H+ · · · N bonded chains in the frequency range 10 kHz-13 MHz. In the chart (a), the ε′(T) dependence measured at a frequency of 10 kHz in the direction perpendicular to the hydrogen bonds is plotted for comparison.

electric permittivity indicates a dynamic character of the proton disorder and suggests a low energy barrier separating the two proton sites in the N-H+ · · · N hydrogen bonds. It is obvious that proton dynamics in the linear polycationic chains can contribute to the dielectric activity of the crystal along this direction, by inducing fluctuations of electric dipole moments directed exclusively along [001] or [001j]. However, it is doubtful that this dynamics itself could explain the temperature dependencies of ε′ and ε′′. In particular, in the high-temperature range above ca. 320 K, ε′ decreases with increasing temperature, while the reverse tendency should be expected when the proton hopping intensifies in higher temperatures. Therefore, the dipolar correlations have to be taken into account to reconcile the dielectric properties of the crystal. The lack of the macroscopic crystal symmetry breaking excludes the formation of a longrange ferroelectric order, but on the other hand, it does not

exclude the occurrence of a local polar order. The formation of nanosize domains with two possible orientations of polarization, pointed at +c or -c, is crucial to understand the strongly anisotropic and giant dielectric response of the crystal. This phenomenon has been discussed in our previous papers on dabcoHBF425 and dabcoHI,26 where we have shown that of key importance is the ability of the organic component of the structure to form monocations, dications, and neutral molecules. The (HdabcoH)2+ dications and neutral dabco0 molecules occur as a result of proton transfers and can coexist in the crystal structure together with the dabcoH+ monocations. Besides, the proton sites in the adjacent hydrogen bonds within the chains are weakly coupled. This coupling is realized first of all through the changes in a charge distribution of the dabco unit, induced by proton transfer. In the ordered chain of the dabco cations, the proton potential energy can be approximated by a symmetric or nearly symmetric double-well potential function [Figure 5(a)]. The change in the shape of the potential energy associated with a single proton transfer is schematically shown in Figure 5(b). This change can be additionally enhanced by lattice vibrations. The diabatical modification of the potential increases the probability for the proton transfers in the adjacent hydrogen bonds along the chain and thus provokes successive transfers, resulting in a short-range ordered region [Figure 5(c)]. A local field associated with a randomly formed polarized segment of the chain can affect the potential and positions of the protons in the nearest surrounding, extending this way the polarized area in the directions perpendicular to the chain. The behavior of protons is more or less coherent, depending on temperature. At high temperatures, the dynamics of protons in the hydrogen bonds becomes independent, and the short-range order disappears, hence the decrease in permittivity above 320 K (see Figure 4). On the other hand, when thermal energy becomes too low to effectively activate the proton hopping, a slowing down of dipolar fluctuations takes place, which is apparent in the dielectric response of the crystal as a decrease in ε′ below 190 K [see Figure 4(a)]. Taking into account the strictly one-dimensional character of the dabcoHBr structure and the nonadiabatic features of the protonic potential in the N-H+ · · · N hydrogen bonds, one can consider a generation of solitonic kinks, as one of the possible mechanisms contributing to the dielectric response. The protonic solitons in the one-dimensional H-bonded networks have been predicted theoretically,11-13 but their experimental evidence is relatively scarce. In dabcoHBr the excitation of solitons is highly



Figure 7. Temperature evolution of the Cole-Cole plots.

Figure 6. Thermal hysteresis between the ε′(T) dependencies in the cooling and heating runs, shown for the frequencies of 100 kHz and 13 MHz.

probable due to the coherent proton transfers and a possible coupling with a longitudinal-type lattice vibration. The mechanism schematically shown in Figure 5(c), but extended to the larger coherence lengths, leads to the solitonic kinks migrating along the chains in the form of charged (HdabcoH)2+ or neutral dabco0 defects. Such kinks can move the existing domain walls and reverse the local polarization. The polarization effects associated with these excitations are enhanced owing to the electrostatic coupling with the highly polarizable Br- anions. The solitonic mechanism has been proposed recently to explain the peculiarities in the dielectric response of bisquaric acid.16 In the case of dabcoHBr, the solitonic contribution occurs together with the dipolar fluctuations within the polar nanodomains and with the fluctuations of the domain walls separating the adjacent regions. The two last contributions are characteristic of the classical ferroelectric relaxors.30 The involvement of several mechanisms in the crystal polarization is mirrored in the complex character of the temperature dependencies of ε′(T) and ε′′(T). The overlapping of different relaxation processes results in a high dielectric constant plateau between 200 and 300 K, occurring for low frequencies of the measuring field [see Figure 4(a)]. A distinct feature is also a sudden drop of permittivity below 190 K. In this temperature region, as well as in higher temperatures, there is a remarkable temperature hysteresis between the cooling and heating cycles, as illustrated in Figure 6. Besides, on heating the permittivity increase proceeds in two successive steps at temperatures practically independent of frequency. These anomalous changes could be interpreted as indicative of two successive phase transitions, but actually neither calorimetric nor structural studies confirm this supposition. Figure 7 shows the temperature evolution of the Cole-Cole diagrams. In the whole temperature range, the plots form distorted semiarcs with the centers situated much below the ε′axis indicating a strongly polydispersive character of the dielectric response. The overlapping of several polarization processes, both in T- and f-scale, makes the analysis difficult, but some conclusions can be derived from the general features of the dielectric spectrum. First of all, worth noticing is an untypical character of the dielectric absorption. As shown in Figure 4(b), the imaginary part of electric permittivity ε′′ is

generally the lowest for low frequencies of the measuring electric field. In the low-temperature range between ca. 100 and 220 K, the losses apparently rise with increasing frequency, while below 100 K they become weakly temperature dependent but still exhibit frequency dependence. Such frequency and temperature dependencies of dielectric absorption at low temperatures are reminiscent of the characteristic features of ferroelectric relaxors, whose dielectric response originates from polar nanodomains.30-32 Remnant Polarization. The extremely high electric permittivity along the H-bonded chains implies a high polarizability of the crystal along this direction. To get some more information on the mechanisms leading to such an unusual dielectric response, a series of experiments with the applied electric field have been performed. The macroscopic polarization of dabcoHBr is symmetry-forbidden according to the space group P6jm2. However, it is known that for some systems like dipolar glasses33 or ferroelectric relaxors34 the crystal polarization can be induced on application of a bias, and this state can be frozen at low temperatures. Recently, it has been reported that even water ice can exhibit a strong pyroelectric effect, comparable to that in most efficient commercial pyroelectrics, such as lead zirconate titanate (PZT).35 The H2O electric dipoles are partially aligned by a strong external electric field, and when cooled below 140-150 K the dipole arrangement is locked in. The temperature-induced depolarization generates the pyroelectric charge. A similar phenomenon was also observed in the crystals of dabcoHB425 and dabcoHI.26 In this experiment, the electric field of 7.4 kV/cm was applied at 320 K along the crystal direction +c or -c, and the sample was cooled under bias. At 80 K, the field was removed and the electrodes short-circuited, and then the pyroelectric charge was measured on heating at the temperature rate of 2 K/min. The temperature-induced depolarization of the sample is represented by curve A in Figure 8. In the next cycle, the procedure was repeated with the reversed poling field, but the depolarization curve B was measured on heating from 80 to 280 K, recooling to 180 K, and subsequently heating to 330 K. The results obtained indicate that the reversible remnant polarization occurs in dabcoHBr along the direction of N-H+ · · · N hydrogen bonds. The large and sudden changes in the dielectric constant around 180-190 K [see Figure 4(a)] suggest a slowing down of the dipolar dynamics, but this process is apparently not mirrored in the depolarization curves. The crystal polarization decreases progressively with increasing temperature, and the pyroelectric effect becomes stronger at higher temperatures above 300 K. Therefore, one can suppose that lattice defects play an important role in the field-induced polarization. The crystal imperfections,

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Figure 8. Depolarization curves of the dabcoHBr crystal along the N-H+ · · · N hydrogen bonds (curves A, B) and in the direction perpendicular (curve C).

such as vacancies or dislocations, can act as pinning centers, around which the polarized regions are built in an external biasing field. The depolarization process of such regions requires higher thermal energy and hence the pyroelectric activity in the temperature range well above the observed “dielectric edge”. The experiment with poling field of comparable strength, but applied perpendicular to the polycationic chains (curve C in Figure 8) has proved that for this configuration the polarization does not develop. Thus, the phenomenon is strictly onedimensional, testifying that the microscopic mechanism leading to the field-induced polarization relies on the proton behavior in the hydrogen bonds. It is worth noticing that the polarization in dabcoHBr does not exhibit ferroelectric features. As illustrated by curve B in Figure 8, on recooling the sample from the point situated on the polarization decay path, the crystal polarization does not return to the previous low-temperature values, as would be expected for a normal ferroelectric, but remains independent of temperature. This type of polarization behavior is characteristic of ferroelectric relaxors or dipolar glasses.34 Influence of dc Bias Field on the Electric Permittivity. Figure 9 shows the temperature dependencies of ε′ measured at the frequency of 30 kHz under various dc biases. The biasing field was applied at 320 K, and then the complex permittivity was measured in the field-cooling and subsequent field-heating runs. The field effect on the dielectric properties of dabcoHBr is apparent even at relatively low fields, especially in the kilohertz frequency range. The plots B in Figure 9 illustrate that even at the small bias of 150 V/cm the low-frequency dielectric anomaly diminishes, and the temperature hysteresis between the heating and cooling cycles is reduced. In low temperatures, the magnitude of the real part of electric permittivity rises. These changes intensify with increasing field, and finally the high-temperature peak practically disappears, as illustrated by the scans C measured at 1.3 kV/cm. At this value of the biasing field intensity, the temperature hysteresis is observed at the peak top only. The anomaly as a whole is shifted toward lower temperatures, and its low-temperature side does not exhibit a sharp edge, but is smeared. Besides in the low-T range, the real part of the electric permittivity is substantially

Szafran´ski

Figure 9. Influence of dc electric field on the dielectric permittivity of dabcoHBr. The measurements were performed at the frequency of 30 kHz, on cooling and heating, for the biasing fields Ebias ) 0, 0.15, and 1.3 kV/cm, as illustrated by the curves A, B, and C, respectively.

higher than without a bias. The field effect on the processes contributing to the dielectric response of the crystal is diversified, and therefore the frequency dispersion above the temperature Tm of the peak maximum is reduced, but still present, while below Tm an essential enhancement of the dispersion takes place, as shown in Figure 10(a). The broad and frequency-dependent peak emerging under bias resembles the dielectric anomaly of ferroelectric relaxors. A similar conclusion is valid for the frequency-temperature dependencies of the imaginary part of the complex electric permittivity, which are presented in Figure 10(b). The amplitude of the loss peak increases with increasing frequency in a similar manner as in classical relaxors. It is worth noticing that above Tm the losses are relatively low when compared to those for the zero bias field [compare Figures 10(b) and 4(b)]. Thus, the dc electric field, by suppressing the contributions occurring above Tm, reveals the relaxor-like behavior of the crystal. The application of biasing electric field along the hydrogen bonds modifies the potential energy wells, shown schematically in Figure 5, such that one of the two wells slightly deepens and the other slightly shallows. As a result, the solitonic excitations are locked-up by the electric field, but the dipolar fluctuations still persist at the domain boundaries and within the polar regions. The low-temperature maxima in the ε′′(T) dependencies were used to determine the characteristic relaxation time as a function of temperature. Figure 11 shows the results obtained at the zero bias and at 0.74 kV/cm. Both dependencies make Arhenius plots. The solid lines represent the best fits to the equation τ ) τ0 exp(Ea/T) with the following parameters Ea ) 2068 and 2478 K and τ0 ) 1.94 × 10-12 and 4.74 × 10-14 s, respectively, for Ebias ) 0 and 0.74 kV/cm. The Arhenius-type behavior of the relaxation time indicates that the complete freezing does not occur, and the crystal remains in an ergodic state up to the lowest temperatures. This conclusion is supported by still large frequency dispersion and high values of electric permittivity in the low-T range below 50 K, observed both without a biasing field and under bias. The next part of the experiment was performed according to the scheme zero-field-heating after field-cooling. As observed, the crystal permittivity is sensitive to both thermal and electricfield history, especially in the region of the high-temperature



Figure 11. Arrhenius plots of the characteristic relaxation times derived from the ε′′(T) dependencies measured at Ebias ) 0 and 0.74 kV/cm. The solid lines represent the best fits to the experimental points.

Figure 10. Temperature and frequency dependencies of ε′ (a) and ε′′ (b) measured at Ebias ) 1.3 kV/cm on cooling.

anomaly around 300 K, and therefore, for these measurements a small virgin single-crystal sample was used. The results are shown in Figure 12. At first the permittivity was measured without a bias (curve A). Then the crystal was cooled at the bias of 0.83 kV/cm (curve B) up to 80 K. As illustrated by the curve B, the peak around 300 K is almost completely suppressed by the dc biasing field. When the field was removed at 80 K, a small and sudden drop in permittivity was observed, but in low temperatures the ε′ magnitude remained high when compared to the zero-bias values. On heating, a gradual restoration of the ε′ magnitude was observed (curve C), but even at high temperatures the permittivity was about 10% lower than before the field treatment. This indicates that the dc electric field leads to some irreversible changes in the distribution of domains or lattice defects. Pressure Effect on the Dielectric Response. The influence of pressure on the complex electric permittivity was studied in the pressure range between 0.1 and 910 MPa. Four samples were used for these measurements, two mosaic-type and two

Figure 12. ε′(T) dependencies measured at 10 kHz for a virgin small single-crystal sample (curve A), in the field-cooling mode at Ebias ) 0.83 kV/cm (curve B), and in the zero-field-heating after field-cooling mode (curve C).

small single crystals, all oriented with their large faces perpendicular to the hexagonal c-axis. The results obtained for different samples were consistent and well reproducible. The representative temperature dependencies of the real and imaginary parts of the electric permittivity are plotted for several pressures in Figure 13. For clarity of the picture, only the lowfrequency data are presented, where the pressure-induced changes are the most spectacular. The pressure effect on the dielectric response of dabcoHBr is very strong but different in the low- and high-T ranges. Below ca. 250 K the permittivity magnitude decreases at elevated pressures, and the edge of the dielectric anomaly shifts toward lower temperatures with increasing pressure. Quite a different behavior is observed in the range 250-350 K. At relatively low pressures, a large and highly frequency-dependent peak emerges in the ε′(T) depend-

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Figure 13. Influence of pressure on the dielectric response of dabcoHBr. The temperature dependencies of the low-frequency real ε′ (a) and imaginary ε′′ (b) parts of the complex electric permittivity at several pressures.

encies around 300 K. As shown in Figure 13(a), the magnitude of the low-frequency electric permittivity is much higher at 50 MPa than at ambient pressure. This anomalous increase in ε′ is associated with an enormous increase in dielectric losses, as is apparent from the comparison of the 50 MPa data plotted in Figure 13(b) and the low-frequency losses in Figure 4(b). The puzzling behavior of the crystal at low pressures has prompted us to verify the results obtained by using gaseous nitrogen as the alternative pressure medium. Owing to the small atomic radius, helium is especially susceptible for penetration into different crystal lattices. Such an effect has been reported, for example, for the water ice Ih36 single crystals and polycrystalline C60.37 In the case of an ionic crystal like dabcoHBr, it seems to

Szafran´ski be very unlikely, especially in the low-pressure range below 100 MPa. The largest and the shortest dimensions of the N2 molecule are, respectively, about 5 and 2.5 times as large as the helium atom diameter. Therefore, one can expect that the penetration of N2 into the lattice would be reduced or excluded. The experiments performed with nitrogen have shown that the results are qualitatively the same as those measured with helium. Thus, it is plausible that the dielectric anomaly growing at low pressures arises from an intrinsic effect of the dabcoHBr crystal. Figure 13 shows that at higher pressures the peaks occurring around 300 K in the ε′(T) and ε′′(T) dependencies gradually diminish and finally around 600 MPa disappear. The highpressure single-crystal structural study38 has excluded the occurrence of a structural phase transition at low pressures, in the temperature range studied. Thus, it is justified to assume that the application of low pressure induces in dabcoHBr a new relaxation process or strongly enhances the existing one, while under higher pressures this process is totally suppressed. The origin of such an unusual pressure effect is strictly related to the one-dimensional H-bonded molecular aggregates. At elevated pressure, the energy barriers between the proton sites in the hydrogen bonds are reduced, and hence the proton transfers are facilitated. For low pressures, the modification of the potential-energy wells is of course small, but it can be enough for an enhancement of the correlated proton transfers along the H-bonded chains in the form of protonic solitons. The charged kinks propagating along the hexagonal axis of the crystal could explain the low-frequency peak in the ε′(T) dependence and the associated high dielectric losses (see Figure 13). When the pressure increases the proton transfers intensify, and the protons in the N-H+ · · · N hydrogen bonds start to behave more independently. This process reduces the solitons moving along the chains and destroys the protonic coherence within the polar regions. Hence, at higher pressures the dielectric anomaly at 300 K diminishes, and the permittivity substantially decreases in the whole T-range. The lowering of the energy barrier for the proton transfer at elevated pressures is mirrored also in the shift of the whole anomaly toward lower temperatures. Such a pressure effect is characteristic of the KDP-type materials, where the protons are disordered in the O-H · · · O hydrogen bonds, in the high-temperature phases. As seen in Figures 13(a) and 14(a), with increasing pressure the dielectric anomaly becomes narrower in the T-range, and the frequency dispersion in the kilohertz range diminishes, while the dispersion at higher frequencies remains still large. The increasing pressure tends to suppress the local polar order in dabcoHBr, but the complete vanishing of the dielectric anomaly in the hexagonal phase does not take place, as before reaching a high enough pressure the crystal undergoes a phase transition. Figure 14(a) shows the results measured at 910 MPa for the single-crystal sample, which was warmed from 155 to 340 K and then cooled to 180 K. During the heating at 314 K, a drop in ε′ was observed for all frequencies, indicative of a phase transition. The low-permittivity phase has been identified as phase II (see Figure 3). In this phase, the frequency dispersion disappears, and the dielectric constant assumes values below 10, typical of classical dielectrics. Under high pressure, the lowpermittivity phase II seems to be metastable because on subsequent cooling no sign of the reverse phase transition was detected. On the other hand, during the pressure release at room temperature, a partial recovery of the high ε′ values was observed with an onset at 420 MPa. All these observations are consistent with the previous high-pressure structural studies of dabcoHBr.38 According to these structural data, the low-


J. Phys. Chem. B, Vol. 113, No. 28, 2009 9487 K/GPa, implies a negative change of the crystal volume at the transition point. Using the Claussius-Clapeyron equation for first-order phase transitions, dT/dp ) ∆V/∆S, the transition volume change was estimated as ∆V ) -2.9 Å3 per molecule, which corresponds to the relative change of -1.4%. This indicates that the orthorhombic polar phase II of dabcoHBr is substantially more densely packed than the nonpolar hexagonal phase III. The large lattice strain associated with the phase transition explains the behavior of the crystals, which became opaque at the transition point and lost the Bragg reflections in phase II. Conclusions

Figure 14. Evidence of the pressure-induced phase transition between the high- and low-dielectric constant phases of dabcoHBr (a) and the T-p phase diagram (b). In the chart (b), the inset illustrates the linear chain of the N-H+ · · · N bonded cations in phase III and three N-H+ · · · Br- hydrogen bonded ionic pairs in phase II. The atoms are represented by the same symbols as in Figure 3.

permittivity phase is orthorhombic; its space group is polar Cmc2; and its structure is built of N-H+ · · · Br- hydrogenbonded ionic pairs. The transformation between the hexagonal phase III and the orthorhombic phase II is schematically illustrated in the inset in Figure 14(b). Thus, the dramatic change in the dielectric properties of the crystal results from breaking of the N-H+ · · · N hydrogen bonds linking the cations and destroying the one-dimensional topology of the crystal structure. This important result testifies directly to the crucial role of the N-H+ · · · N hydrogen bonds in the giant dielectric response of dabcoHBr, in its hexagonal phase. The measurements made for four different samples at different pressures were used to construct the T-p phase diagram, shown in Figure 14(b). The transition temperature T32 decreases linearly with increasing pressure. The negative pressure coefficient, dT32/dp ) -157.5

This study has shown that the nonpolar hexagonal structure of dabcoHBr exhibits giant, strongly frequency-dependent, and strictly one-dimensional dielectric response. These properties are apparently similar to those previously observed in isosymmetric dabcoHI.26 The unique feature of both structures is a perfectly one-dimensional system of N-H+ · · · N hydrogen bonds, which link the dabcoH+ cations to polycationic chains. The microscopic mechanism leading to the high values of electric permittivity originates from proton transfers in the hydrogen bonds and protonic correlations, resulting in the formation of short-range ordered polar regions. These correlations are too weak to produce a long-range ferroelectric/ antiferroelectric order but give rise to the unprecedented dielectric properties. This is the main difference distinguishing the dabco salts from the O-H · · · O bonded crystals like KDP, where the strong correlations of the proton sites are dominant and have a decisive influence on the crystal properties. The main contributions to the dielectric response of dabcoHBr arise from the dipolar fluctuations within the ordered polar regions, from the moving of domain walls, and from the charged kinks propagating along the chains in the form of solitonic excitations. This picture must be completed by the presence of lattice dislocations and other structural defects, which can act as traps. In consequence, the temperature and frequency characteristics of the complex electric permittivity consist of several coexisting components, hardly distinguishable. The peculiarities induced in the dielectric response of the crystal by pressure and by dc electric field are not comparable to any others of the known ferroelectric or ferroelectric-like systems. These distinctive features can be attributed to the specific properties of the strictly one-dimensional polycationic aggregates and, in particular, to the solitonic-type excitations. The field-induced changes are especially large for the lowfrequency electric permittivity. Due to this effect, the magnitude of the room-temperature dielectric constant can be easily controlled by an external biasing field, which may be of interest for electronic applications. The increasing pressure tends to suppress the local polar order, but the complete vanishing of the dielectric anomaly in the hexagonal phase does not take place, as before reaching a high enough pressure the crystal transforms to the orthorhombic phase built of ionic pairs, divested of unique one-dimensional structural and dielectric properties. Though the relaxation spectrum of dabcoHBr is very broad, the characteristic relaxation time obeys the Arrhenius law. This behavior and the substantial frequency dispersion observed below 50 K indicate that some dynamics persists in the crystal to the lowest temperatures. Acknowledgment. This work was supported by the Polish Ministry of Science and Higher Education, Grant N202 14631/ 2707.

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JP900602P

Bias-Field and Pressure Effects on the One-Dimensional Dielectric

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