Article pubs.acs.org/JPCA
Dynamics of Ferroelectric Bis(imidazolium) Pentachloroantimonate(III) by Means of Nuclear Magnetic Resonance 1H Relaxometry and Dielectric Spectroscopy A. Piecha-Bisiorek,† R. Jakubas,† W. Medycki,‡ M. Florek-Wojciechowska,§ M. Wojciechowski,§,∥ and D. Kruk*,∥ †
Faculty of Chemistry, University of Wrocław, Joliot-Curie 14, 50-383 Wrocław, Poland Institute of Molecular Physics, PAS, M. Smoluchowskiego 17, 60-179 Poznań, Poland § Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland ∥ Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Słoneczna 54, 10-710 Olsztyn, Poland ‡
S Supporting Information *
ABSTRACT: Some of haloantimonates(III) and halobismuthates(III) are ferroelectric. Bis(imidazolium) pentachloroantimonate(III), (C3N2H5)2SbCl5 (abbreviation: ICA) is the first example of such compounds with a one-dimensional anionic chain which exhibits ferroelectric properties. The relation between the ionic dynamics and network structure and the ferroelectric features is not clear. Here Nuclear Magnetic Resonance (NMR) 1H spin−lattice relaxation experiments at 25 MHz are reported for ICA in the temperature range of 80 K-360 K, covering ferroelectric-paraelectric and structural phase transitions of the compound occurring at 180 and 342 K, respectively. The relaxation process is biexponential in the whole temperature range indicating two dynamically nonequivalent types of imidazolium cations. Temperature dependences of both relaxation contributions allow for identifying three motional processes. Two of them are cation-specific − i.e. they are attributed to the two types of imidazolium cations, respectively. The third process involves both types of cations, and it is characterized by much lower activation energy. Moreover, the relaxation data (combined with 1H second moment measurements) show that the ferroelectric-paraelectric phase transition mechanism is governed, to a large extent, by the anionic network arrangement. The NMR studies are complemented by dielectric spectroscopy experiments performed in the vicinity of the Curie temperature, TC = 180 K, to get insight into the mechanism of the ferroelectric-paraelectric phase transition. The dielectric dispersion data show critical slowing down of the macroscopic relaxation time, τ, in ICA when approaching TC from the paraelectric side, indicating an order−disorder type of ferroelectrics. chain − SbCl5 chain of cis-connected octahedra. ICA undergoes a reversible (second order) phase transition (PT) from paraelectric phase (Pbcn) to ferroelectric phase (Pna21), and its ferroelectric activity occurs below the TC = 180 K (Curie temperature) with the spontaneous polarization PS = 8 × 10−3 C/m2 (at 120 K).6 Single crystal X-ray diffraction measurements of ICA suggest a complex mechanism of the ferroelectric PT which consist of an “order−disorder” contribution assigned to dynamical features of imidazolium cations and a “displacive”type contribution originating from distortion of the strong polar polyanionic structures.6 It should be underlined that the influence of the anionic network structure on the ferroelectric properties in ICA is far from being understood. As far as cations
1. INTRODUCTION Haloantimonates(III) and halobismuthates(III) of the general formula RaMbX(3a+b) (R denotes an organic cation, M = Sb(III) or Bi(III), X = Cl, Br or I) are characterized by a rich diversity of the anionic network in the crystal lattices which is connected with their ferroelectric properties.1,2 For instance, all R5M2X11 compounds synthesized so far show ferroelectricity, and all of them contain discrete bioctahedral units M2X11−5 including only one bridging halogen atom in the structure.3 At the same time for R3M2X9 one observes ferroelectric properties only when the anions exhibit a layered structure,4,5 although the anions can form, besides two-dimensional layers, also onedimensional chains, discrete bioctahedra, and discrete tetramer units. Bis(imidazolium) pentachloroantimonate(III), [C3N2H5]2[SbCl5] (ICA), is the first example of R2MX5-type of ferroelectric compounds6 with one-dimensional anionic © XXXX American Chemical Society
Received: February 6, 2014 Revised: April 13, 2014
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frequency region observed in vicinity of TC is a fingerprint of ferroelectric-paraelectric PT. The paper is organized as follows. In Section 2 the experimental details are provided, in Section 3 the dielectric and NMR results are presented and discussed, while Section 4 contains concluding remarks.
are concerned, it is believed that their dynamics play a key role in the mechanism of the ferroelectric PT of RaMbX(3a+b) compounds. ICA exhibits a second PT at 342 K.6 The crystal structure of the high temperature phase (above 342 K) of ICA has not been fully studied yet; however, as optical measurements do not reveal a domain structure below 342 K, one can expect that its orthorhombic symmetry does not change. The present paper is meant to inquire into the dynamics of the imidazolium cations and reveal the relationship between the dynamical features and the phase transitions (PTs). Moreover, it is meant to get inside into how the structure of the cationic and anionic networks is affected by the PTs. For this purpose 1H Nuclear Magnetic Resonance (NMR) relaxation studies have been performed for ICA in a broad temperature range of about 80 K-360 K, covering two PTs: at 180 and 342 K. Nuclear Magnetic Resonance (NMR) relaxometry is a wellestablished method probing dynamics of solids and liquids. The principle is as follows. In an external magnetic field the sample gains magnetization which results from a difference between the populations of the 1H (for 1H relaxometry) Zeeman states (energy levels) corresponding to the proton magnetic quantum numbers +1/2 and −1/2 (the energy levels are populated according to Boltzmann distribution). The time needed to reach the equilibrium populations at a given magnetic field is referred to as spin−lattice relaxation time, T1. This time constant, which reflects the probability of 1H spin transitions between the energy levels, is determined by quantities referred to as spectral density functions.7−10 The spectral densities are Fourier transforms of a time correlation function describing stochastic fluctuations of 1H−1H dipole−dipole interactions. The dipolar interactions are the predominant relaxation mechanism for protons. Their time fluctuations stem from the dynamics of the 1 H containing molecular units (imidazolium cations in this case); in this way one gets access to their dynamical features. NMR relaxation experiments are also highly sensitive to the molecular (crystal) structure. When the relaxation mechanism is provided by dipolar interactions, the relaxation rate R = T−1 1 (reciprocal relaxation time) is proportional to r−6, where r denotes the distance between the interacting nuclei (protons); for several dipolarly coupled nuclei a summation over all spin (nuclei) pairs is performed.7−10 This implies that even a slight rearrangement of the molecular surrounding caused by PT is reflected by the relaxation rate. Nevertheless, when the rearrangement is not rapid (i.e. one cannot specify a narrow temperature range in which the structural changes occur), this effect might be less visible as it is masked by temperature changes of the dynamics of the system. Generally saying, the NMR relaxation time reflects a combined effect of structural and dynamical features of the system both varying with temperature. Dielectric spectroscopy is used in this work as a complementary source of information on the dynamical properties of imidazolium cations and the mechanism of the ferroelectric-paraelectric PT of ICA. The dielectric experiments have been performed in the temperature range of 120 K-350 K; special attention has been put to the close vicinity of the Curie temperature (T C = 180 K). For ferroelectric crystals characterized by continuous PTs (as it is in ICA) dielectric spectroscopy is a highly sensitive method probing subtle changes in dynamics−more precisely: characteristic critical slowing down of the macroscopic relaxation time in the radio
2. EXPERIMENTAL DETAILS The ICA compound was obtained from an aqueous solution of a stoichiometric mixture of imidazole amine and antimony(III) trichloride with an excess of HCl acid. Single crystals of this compound were grown by a slow evaporation method at constant room temperature (25 °C). The complex dielectric permittivity, ε* = ε′ − ε″, was measured with HP 4284A Precision LCR Meter in the frequency range of 100 Hz−1 MHz between 120 and 350 K. The ac amplitude was 1 V. The samples for dielectric measurements were prepared by cutting the single crystal perpendicularly to the c-axis. The specimen with graphite electrodes had the dimension of 4 × 4 × 1 mm3. The uncertainty of the real and imaginary parts of the complex dielectric permittivity was less than 5%. 1 H relaxation experiments were performed at the frequency of 25 MHz using ELLAB TEL −Atomic CWS spectrometer. A saturation recovery method was applied. The temperature of the sample was controlled with stability better than 1 K using a UNIPAN 660 temperature controller operating on a Pt 100 sensor. A powder sample was degassed at room temperature and sealed under vacuum in glass ampule. In the experiment it was heated up from the liquid nitrogen temperature up to 360 K. Biexponential relaxation was observed; the uncertainty of the measured relaxation rates did not exceed 5%. The second moment of the 1H NMR spectral line was measured in the temperature range of 107 K-300 K. The values of the second moment were obtained by integrating numerically the recorded derivative of the absorption NMR spectrum. 3. RESULTS AND DISCUSSION As already explained, ICA is ferroelectric below 180 K. At TC = 180 K it undergoes ferroelectric-paraelectric PT, while at 342 K a structural PT. We refer to the paraelectric phase above 342 K as phase I, between 342 and 180 K as phase II, while the ferroelectric phase below 180 K is referred to as phase III as indicated in Figure 1.6
Figure 1. PT diagram of ICA.
Figure 2 shows the structure of ICA in paraelectric and ferroelectric phases. In the paraelectric (disordered) phase only one type of imidazolium cations (symmetry related cations types B and C) is ordered. The two remaining imidazolium cations (types A and D) are disordered. One of them (type A) reveals two B
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Figure 4. Cole−Cole plots, ε″versus ε′ for selected temperatures showing the relaxation character of the dielectric dispersion in the paraelectric phase (II) of ICA. Solid lines−fits of the Cole−Cole expression (eq 1) for (T − TC) yielding the following: (a) 0.2 K, (b) 0.3 K, (c) 0.4 K, (d) 0.5 K, (e) 0.6 K, (f) 0.8 K, (g) 1 K, (h) 1.1 K, (i) 1.2 K.
Figure 2. Crystal structure of ICA in the (a) paraelectric (disordered) phase and (b) ferroelectric (ordered) phase. One can distinguish two types of cations; A and D, which contribute to the dynamic properties of ICA.
frequency, τ is the macroscopic dielectric relaxation time, while the parameter α represents a measure of distribution of the relaxation times. The parameter α increases from 0.07 up to 0.21 when approaching TC from the paraelectric side. A polydispersive nature of the relaxation process (for α > 0.1) is observed for temperatures close to TC: (T − TC) < 0.4 K. The distribution of relaxation times may be explained by the presence of two dielectric relaxators (two kinds of dynamically disordered dipolar imidazolium cations − A and D − c.f. Figure 2). The macroscopic relaxation time, τ, as a function of temperature in the close vicinity of the ferroelectric −paraelectric PT is displayed in Figure 5. The relaxation process in ICA shows a critical slowing down when approaching TC from the higher temperatures side. The relaxation time τ fulfills the relationship τ ∝(T − TC)−1 (in the temperature range (T − TC) ≤ 3 K) (Figure 6). For ferroelectrics with the “order-disorder” mechanism of PT the dynamics of the dielectric relaxator may be described by the microscopic relaxation time, τ′, defined as11
positioned models of the disorder, while the other is characterized by a multipositioned disorder.6 In the ferroelectric phase all cations are ordered.6 We shall refer to these features when discussing the experimental results. A. Dielectric Relaxation Studies. We begin the discussion with the dielectric results. Figure 3a presents temperature
Figure 3. (a) Temperature dependence of the real part, ε′, of the complex dielectric permittivity, ε* = ε′ + iε″, along the a-axis of the crystal at selected frequencies near TC = 180 K; vertical line indicates the Curie temperature, TC = 180 K. (b) Frequency dependence of the imaginary part, ε″, at selected temperatures, T, given by ΔT = T − TC in phase II (above TC) of ICA.
dependencies of the real part, ε′, of the complex electric permittivity, ε*, at selected frequencies in the vicinity of the Curie temperature, TC = 180 K, whereas in Figure 3b the dielectric losses, ε″, versus frequency at selected temperatures close to the ferroelectric-paraelectric PT are shown. It is clearly seen that in the radio frequency range (135 Hz−1 MHz) the dielectric dispersion in ICA is significant. The results shown in Figures 3a,b, for (T − TC) ≤ 3 K, are replotted in Figure 4 as ε″ versus ε′ (Cole−Cole plot). The values of the complex dielectric constant, ε*, has been fitted with the Cole−Cole relation: ε0 − ε∞ ε* = ε∞ + 1 + (iωτ )(1 − α) (1)
Figure 5. Temperature dependence of the main relaxation time, TC, its inverse, τ−1 and τ′ in the close vicinity of TC in the paraelectric phase (II).
In eq 1 ε0 and ε∞ denote the low and high frequency limits of the dielectric permittivity, respectively, ω denotes the angular C
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the first step the magnetization curves for all temperatures have been fitted with adjustable Ta1, Tb1, and C. As it has turned out that the parameter C only slightly fluctuates around C = 0.5 in the whole temperature range, it has been fixed to C = 0.5 (which means equal contributions of both exponents), and the fits have been repeated with only Ta1 and Tb1 adjustable. When Ta1 ≅ Tb1 at high temperatures, eq 4 converges to a singleexponential relaxation process. The value of C = 0.5 corresponds to the results of X-ray studies, which indicate two types of imidazolium cations being in the ratio 1:1.6 In Figure 7 the obtained relaxation times, Ta1 and Tb1, are presented versus reciprocal temperature. Both relaxation times
Figure 6. Activation energy, EA, for ICA in the vicinity of the ferroelectric - paraelectric PT obtained by means of the modified Arrhenius equation (eq 3).
τ′ = τ
ε∞ ε0 − ε∞
Figure 7. 1H spin−lattice relaxation times at 25 MHz versus reciprocal temperature for ICA. Solid lines−fits by means of eq 3 with the spectral density of eq 4; blue line: τa0 1.0 × 10−13 s, EaA = 19.6 kJ/mol, CaHH = 1 × 109 Hz2, green line: τb0 = 2.0 × 10−11 s, EaA = 10.3 kJ/mol, CbHH = 2 × 108 Hz2. Vertical lines indicate the PT temperatures determined by means of DSC measurements.6
(2)
Then, the activation energy EA may be calculated according to the modified Arrhenius equation for ferroelectrics12 ⎛ h ⎞ ⎛ E ⎞ τ′ = ⎜ ⎟ exp⎜ A ⎟ ⎝ kBT ⎠ ⎝ kBT ⎠
show minima at about 194 K. At lower temperatures their temperature dependence becomes weaker; one can say that eventually the relaxation times become almost temperature independent. The measured spin−lattice relaxation rates, Rx1 = (Tx1) (x = a,b), result from four relaxation pathways
(3)
where h and kB are Plank and Boltzmann constants, respectively. The activation energy obtained by means of eq 3 is shown in Figure 6 versus ΔT = (T −TC). The activation energy significantly changes when approaching TC - from about 16 kJ/mol for ΔT > 3 K, 42 kJ/mol for 3 K > ΔT > 1 K up to above 100 kJ/mol for ΔT < 1 K. Summarizing, the dielectric results point toward an “orderdisorder” mechanism of the phase transition at TC = 180 K as the main relaxation process is observed in a low frequency range (radio frequency), and it shows a critical slowing down when the Curie temperature is approached (Figure 5) − this effect appears only in ferroelectrics characterized by an order− disorder mechanism.12,13 B. 1H NMR Studies. The 1H spin−lattice relaxation process in ICA is biexponential, which is rather an exception. One should stress at this stage that 1H spin−lattice relaxation in Im5Bi2Br11 is single exponential.13 The 1H magnetization curves (magnetization versus time) for ICA, M(t), (normalized to unity) have been fitted according to the formula M(t ) = C exp(−t /T1a) + (1 − C) exp(−t /T1b)
Ta1
Tb1
R1x(ω) = R1(x H → H ) + R1(x H → N ) + R1(x H → Sb) + R1(x H → Cl) (5)
that correspond to 1H−1H, 1H−14N, 1H-121(123)Sb, and 1 H-35(37)Cl dipole−dipole (DD) interactions. The relaxation rate originating from dipolar interactions between the same nuclei (equivalent spins), Rx1(H→H) = (Tx1), is given by the wellknown expression7−10 x R1(x H → H )(ω) = CHH [J x (ω) + 4J x (2ω)]
(6)
x where ω denotes now the H resonance frequency; CHH 1 1 denotes the dipole−dipole ( H− H) relaxation constant, x which is defined as CHH = (3/10)((μ0/(4π))γH2ℏ)2Σi 0.4 K. The dielectric behavior is consistent with the X-ray diffraction results which suggests that only D-type cations contribute to the critical dielectric response. The appearance of a polydispersive relaxation process close to TC may stem from a motional correlation between cations A and D. Moreover, the characteristic minima of ε′ at 180 K observed at higher frequencies confirm the continuous nature of the ferroelectric PT. Comparing the activation energy of EA = 16 kJ/mol, obtained by means of dielectric spectroscopy with the value obtained from 1H NMR studies for the faster relaxation process EaA = 19.6 kJ/mol (the values are close), one might conclude that this process is associated with the dynamics of the disordered imidazolium cations in the paraelectric phase, while the slower 1 H spin−lattice relaxation process is attributed to the ordered cations.
MII2
where and denote the values of M2 before and after the motional averaging, respectively (these quantities are indicated in Figure 9). Assuming the Arrhenius dependence of the correlation time on temperature (i.e. τ = τ0 exp((EA)/(kBT))) one gets τ0 = 8.8 × 10−10 s and EA = 13.3 kJ/mol. Comparing the values with the parameters obtained from the analysis of the relaxation data one can conclude that the agreement is reasonable taking into account that the values obtained from the M2 analysis reflect the effect of all motional contributions identified above. For the activation energies determined from dielectric and NMR experiments one should note that the activation energy of the main dielectric relaxation process is not constant in the temperature range (T − TC) < 5 K − it changes from 16 kJ/ mol to 42 kJ/mol when approaching TC (Figure 6). The 1H NMR relaxation studies, performed in a broad temperature range, 80 K-360 K, have led to EaA = 19.6 kJ/mol and EbA = 10.3 kJ/mol for the two groups of dynamically nonequivalent imidazolium cations. The activation energy, EaA, well agrees with the activation energy obtained from dielectric studies for (T− TC) > 3 K. As the dielectric results confirmed that the reorientational motions of dipolar units (organic cations) contribute to the critical dielectric response in the vicinity of ferroelectric transition, the motional process characterized by the activation energy about 16 kJ/mol may be assigned to the dynamics of the disordered imidazolium cations in the paraelectric phase. The already mentioned X-ray diffraction studies on ICA suggested that the disordered cations form pairs with one cation exhibiting multisite jump dynamics, while the second one shows a two-site dynamics.6 It is worth noting that the second moment shows a “step” decay at about 235 K which corresponds to the temperatures at which the motional processes represented by τ̃a0 ≅ τ̃b0 and Ẽ aA = Ẽ bA become of importance for the 1H spin−lattice relaxation, confirming the presence of an additional mechanism contributing to the averaging. Moreover the second moment does not exhibit other abrupt (“step”) decays, which shows that the phase transitions do not cause changes in the proton structure of the compound. The temperature dependencies of the relaxation rates lead to the same conclusion as they do not show discontinuities due to rapid changes in the dipolar relaxation constants, CaHH and CbHH (which are related to the second moment). As the dipolar constants differ by a factor of five (CaHH = 1 × 109 Hz2, CbHH = 2 × 108 Hz2), they (at least the larger one) cannot entirely stem from the interactions within a single imidazolium cation, i.e. a significant contribution to the relaxation is provided by interactions with neighboring cations. This implies that the 1 H relaxation processes are sensitive to possible structural changes in the cationic network. As there are no abrupt changes in the relaxation rates at the PT temperatures, one can conclude that structural rearrangements associated with the transitions concern the anionic network. The absence of “anomalies” in the G
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(17) Gutowsky, H. S.; Pake, G. E. Structural investigation by means of nuclear magnetism. II. Hinder rotation in solids. J. Chem. Phys. 1950, 18, 162−170. (18) Grigas, J.; Sobiestiankas, R. Microwave spectroscopy of new organic-inorganic ferroelectrics. Ferroelectrics 1994, 156, 279−284. ́ (19) Medycki, W.; Holderna-Natkaniec, K.; Swiergiel, J.; Jakubas, R. Molecular dynamics in ferroelectric 4-aminopyridinium tetrachloroantimonate(III), [4-NH2C5H4NH][SbCl4]. Solid State Nucl. Magn. Reson. 2003, 24, 209−217. (20) Kruk, D.; Medycki, W.; Przesławski, J.; Dacko, S.; Piecha, A.; Jakubas, R. Thermodynamic properties and molecular motions in ferroelectric (C3N2H5)5Sb2Br11. Chem. Phys. 2011, 380, 86−91. (21) Józḱ ów, J.; Medycki, W.; Zaleski, J.; Jakubas, R.; Bator, G.; Ciunik, Z. Structure, phase transition and molecular motions in (C5H5NH)BiCl4. Phys. Chem., Chem. Phys. 2001, 3, 3222−3228.
ASSOCIATED CONTENT
S Supporting Information *
Examples of biexponential behavior of 1H magnetization curves for (C3N2H5)2SbCl5. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +48 89 524 60 11. Fax: +48 89 524 60 89. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This research was supported by the National Science Centre, Poland, under Grant No. DEC-2012/05/B/ST3/03190.
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