High Resolution NMR Evidence for Displacive Behavior in Hydrogen-Bonded Ferroelectrics and Antiferroelectrics

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1 Ferroelectrics, 337:3 12, 2006 Copyright Taylor & Francis Group, LLC ISSN: print / online DOI: / High Resolution NMR Evidence for Displacive Behavior in Hydrogen-Bonded Ferroelectrics and Antiferroelectrics N. S. DALAL, O. GUNAYDIN-SEN, R. FU, R. ACHEY, AND K. L. PIERCE Department of Chemistry and Biochemistry, and National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL The high NMR spectral resolution attained via magic angle spinning (MAS-NMR) on single crystals have enabled us to detect new aspects of mechanism of phase transitions in hydrogen-bonded ferroelectrics and antiferroelectrics. Results are summarized for anomalous changes in the temperature dependence of the isotropic part of the NMR chemical shifts for 13 C and 17 Oinsquaric acid (SQA), and for 31 PfromNH 4 H 2 PO 4, KD 2 PO 4 and RbH 2 PO 4, and more recently on 15 NinNH 4 H 2 AsO 4 and NH 4 H 2 PO 4. These data are interpreted as providing an unambiguous evidence of a displacive component, together with an order-disorder behaviour at the same time scale for both SQA and KDP-type lattices. Keywords KDP-type ferroelectrics; order-disorder phase transition; displacive phase transition; high resolution NMR 1. Introduction KH 2 PO 4 (KDP) and H 2 C 4 O 4 (Squaric acid, henceforth abbreviated as SQA) are two of the most studied hydrogen-bonded ferroelectrics and antiferroelectrics, and are considered as models of simple lattices exhibiting order-disorder phenomenon [1, 2]. SQA (structure shown in Fig. 1) exhibits an antiferroelectric (AFE) transition at T N 373 K [3 9], while KDP undergoes a ferroelectric (FE) transition at T C 123 K [1, 2]. In both compounds, the order-disorder motion of the H s in the O H... O bonds are considered to play an important role in the transition mechanisms, since on H D substitution (i.e.,deuteration), their T N or T C increases by about 80% [1 10]. Blinc was the first to attribute this large H D isotope shift to quantum mechanical tunnelling [1], invoking the critical role of the much larger zero-point energy of the D. Later, Blinc and coworkers proposed a more refined model, the so-called pseudo-spin model of the order-disorder mechanism which has been successful in explaining several dynamical aspects [1, 2, 11]. Recently, however, the socalled geometrical models have been advanced, which are able to explain the deuteration effect without explicitly invoking quantum tunnelling [12 14]. While this development is Paper originally presented at IMF-11, Iguassu Falls, Brazil, September 5 9, 2005; received for publication January 26, Corresponding author. dalal@chem.fsu.edu [1175]/3

2 4/[1176] N. S. Dalal et al. Figure 1. Structure of squaric acid: (a) skeleton (b) a hydrogen-bonded pentamer. a significant step forward, additional questions remain regarding the microscopic details of the transitions. One important question is whether the mechanism involves a displacive component, in addition to the above mentioned order-disorder character, and if so, then at what time-scales. With the view of providing additional insight, we have initiated studies of these lattices by means of modern high resolution NMR in the solid state. Our basic tenet is that one can unambiguously probe this question by measuring the temperature dependence of the isotropic component of the NMR chemical shift, δ ISO. This is based on the fact, as has been noted earlier [8, 15 21], that δ ISO is invariant to rotational and translational changes in the molecule, so it should remain essentially unchanged through the phase transition if the transition is of a purely order-disorder nature. If, on the other hand, the transition involved electronic structural changes as well, then δ ISO should exhibit a clear anomaly in the vicinity of the phase transition. This presentation summarizes our recent measurements of the temperature dependence of δ ISO for SQA, using both 13 C and 17 O isotopes over a wide temperature range around its T N of 373K. We also report on similar studies of δ ISO for 31 PinKDP,KD 2 PO 4 (DKDP) and RbH 2 PO 4 (RDP). Preliminary results are reported also for their antiferroelectric analogues NH 4 H 2 PO 4 and for 15 NinNH 4 H 2 AsO 4 and NH 4 H 2 PO 4. All these compounds exhibit a clear anomaly in δ ISO at the respective phase transitions, which we attribute to the presence of the displacive component in the phase transition mechanisms. Some of the earlier data can be found in more detail in [20 22]. 2. Experimental Details Squaric acid, structure shown in Figure 1 below, was purchased from Sigma and used as received. The 17 O labeling was accomplished by heating the dissolved compound in about 20% 17 O-labeled H 2 O, in a closed vessel. The labelled water was obtained from Isotec. Both the labelled water and squaric acid were refrigerated until used. The isotope labelling was confirmed by mass spectrometry, and was found to be about 15% (exact number not critical to this study), sufficient for the NMR signal detection within a few minutes. The T N of the labelled sample was determined to be 372 K by independent specific heat measurements in our laboratory, using a Quantum Design PPMS Model 6000, with temperature accuracy of about 0.05 K. 15 N labeling of NH 4 H 2 AsO 4 (ADA) and NH 4 H 2 PO 4 (ADP) was obtained by using 15 N enriched 15 NH 4 NO 3.Asuitable amount of 15 NH 4 NO 3 was added to the ADA solution

3 Displacive and Order-Disorder Behavior in KDP [1177]/5 before the crystallization started. The 15 N enrichment in the ADA crystals was estimated at 9 ± 1%, using NMR. 31 P and 13 C magic angle spinning (MAS) [25, 26] measurements were made using a Bruker 300 MHz spectrometer, while the 17 O data were obtained using a Bruker 600 MHz wide bore spectrometer available at the National High Magnetic Field Laboratory. 15 N data was obtained by using a Varian UNITY INOVA 500 MHz wide-bore solid-state NMR spectrometer. The 17 O resonance frequency was close to 81 MHz, with the sample spinning at 12.5 khz. The variable temperatures were achieved by nitrogen gas flow, and controlled to within 0.1 K. The sample temperature was checked using the 13 C NMR procedure, based on the phase transition itself, as described previously [25 27]. Both powders and single crystals were used in the study for SQA; the crystal providing narrower lines by a factor of about four [18, 19, 21]. Only powder was used for the KDP-type materials since only a single peak was expected in the 31 P spectrum. 3. Results and Discussion 3.1. Resolution Enhancement from MAS Using Single Crystals Figure 2 shows 13 C spectrum powder and single crystal of SQA. The four peaks observed can be assigned to the four different carbon atoms in the squaric acid structure ( Figure 1). As discussed in details elsewhere [16 19], the temperature dependence of the peak positions exhibits an anomalous change within 2-3 K of the antiferroelectric transition at 373 K. An expanded view of this change is shown in Fig. 3. Figure 4 depicts typical 17 O NMR spectra from 17 O-labeled samples of SQA powder and a single crystal in the low temperature phase (T < T N ). It is seen that both the powder and the crystal show four distinct peaks, marked 1, 2, 3 and 4 using the numbering in Figure 1. The remaining peak(s) in Figure 4 are the spinning side bands, as was verified Figure 2. Comparison of the 13 C CP-MAS NMR spectra of squaric acid powder (top) and single crystal (bottom). Note that crystal utilization leads to a 400% enhancement of the spectral resolution.

4 6/[1178] N. S. Dalal et al. Figure 3. Temperature dependence of the δ ISO for the 13 C NMR peaks in squaric acid in the close vicinity of the phase transition. Note that the change starts as a smooth curve, followed by a jump due to the first-order character of the phase transition, considered as an evidence of the coexistence of an order-disorder and displacive character in the phase transition mechanism [19]. by the fact that their relative positions change in proportion to the spinning frequency. The doublet around 250 ppm can be assigned to the carbonyl (>C= 17 O) oxygens, while that around 100 ppm can be assigned to the >C- 17 O-H hydroxyl oxygens, in analogy with the earlier reported 13 C peaks [18, 19], and theoretical calculations [8]. Figure 4 shows also that the peaks for the single crystal are narrower by at least a factor of four as compared to those for the powder sample. At first it appeared to be related Figure O MAS NMR spectra of the central (1/2 1/2) transition of a 17 O-labeled SQA in the form of: (a) powder; (b) single crystal. Note: the narrower peaks in (b). The peak numbering corresponds to that in Figure 1. The sharp line at 105 ppm corresponds to a spinning side band [21].

5 Displacive and Order-Disorder Behavior in KDP [1179]/7 to the reduction of the anisotropic bulk magnetic susceptibility (ABMS) broadening, as described in general by Van der Hart et al. [24]. However, the powder spectra did not exhibit a significantly narrowing on dispersion of the sample in silica, as would be the case if ABMS were the cause. The exact mechanism by which this narrowing occurs is still unclear and is a topic of additional studies. Comparison of these spectra with those for 13 C reported earlier [21, 23 26] clearly point to the much higher sensitivity of the 17 O peaks to the effect of the proximity of the H: the splitting within a doublet is about 30 ppm for 17 O, but only about 1 ppm in the case of 13 C. This extra dispersion enabled us to follow the phase transition in a much more precise manner (vide infra) than was possible with 13 C Temperature Dependence of 17 O NMR Spectra As reported earlier [21], the 17 O spectra exhibit a strong temperature dependence. Temperature increase leads to their merging and finally the coalescence. At T>T C, they merge to a narrow doublet with a separation of about 10 ppm. An important observation was that the position of the coalesced peak (doublet) did not coincide with the average of the four low-temperature peaks; this point is discussed in detail in the following section. We tried several crystal orientations in the MAS experiments with the view of eliminating the crystal orientation effect, but could never get the double splitting to lower than about 5 10 ppm. This was also then verified by MAS measurements on powder samples, which showed a similar doublet splitting as well. Hence we conclude that the splitting is not an artifact of crystal orientation in the MAS measurements. Disregarding the actual amount of this doublet separation, it is important to note that the presence of this doublet at T well above T C, rather than a singlet,implies two different electronic environments for the oxygen atoms in the paraelectric phase, i.e., it is direct evidence that the structure of SQA at temperatures up to T C actually is a dynamic average of the low (C i )-symmetry structures made possible by placing the H s in two different O-H... O bonds. It may also be noted the doublet structure persists to at least 20 K above the T N. Finally, there is the interesting observation in Figure 3 that over a few degree range around T N, signals from the paraelectric and antiferroelectric phases are simultaneously present. This is reminiscent of what was found in the earlier 13 C NMR studies [18 20] and is consistent with the fact that the SQA phase transition is complex: it is essentially of the first order, but exhibits some features of a second-order type. The above discussed peak coalescence is reminiscent of a similar observation of peak coalescence in our earlier 13 C chemical shift data [8]. This can be understood by invoking a time averaging statistical contribution from a carbonyl and a hydroxyl group with different hydrogen bond environments of the partially disordered SQA structure. This was similar to the pseudo-rotation mechanism proposed for the proton motion by Semmingsen et al. [5] Applying this hypothesis to the case of 17 O NMR, the environments of O 2 and O 4 after the proton flip of H 2 should correspond closely to those of the ordered O 3 and O 1 sites, respectively. In addition, the initial O 1 and O 3 gradually obtain O 4 and O 2 character, respectively, through such +90 pseudo-rotation. In Figure 5 we present the 17 O chemical shift of SQA obtained applying the refined site occupancies for the hydrogen atoms, obtained at different temperatures [5], (and also the occupation probabilities of the double-well potential given Samuelsen et al [28] as fractional function of the carbonyl and hydroxyl contributions to the 17 O chemical shifts. We observe that the pseudo-rotational model predicts the emergence of two peaks in the middle zone of the 17 O NMR spectra above T C, supporting the postulate that the two chains of the compound retain their difference at T > T N.

6 8/[1180] N. S. Dalal et al. Figure 5. Temperature dependence of the average 17 O δ ISO in the close vicinity of the paraelectric antiferroelectric phase transition of SQA. Figure 6. Comparison of the standard and MAS 31 P NMR spectra for partially deuterated KDP. Figure 7. Temperature dependence of the 31 P NMR isotropic chemical shift for ADP crystal, showing an anomaly around the phase transition temperature, T c.

7 Displacive and Order-Disorder Behavior in KDP [1181]/9 Figure 8. Temperature dependence of the 31 P linewidths for ADP crystal, showing an anomaly around the phase transition temperature, T c Temperature Dependence of the Average Value of 17 OPeaks Figure 5 shows the temperature dependence of δ ISO for all four oxygens in SQA. Even when the broadening of the peaks leads to some dispersion of the data, we can note that the average δ ISO increases steadily as T T N, and exhibits an anomalous increase of about 13 ppm within 2 3 K of the T N.Itisthus seen that the high temperature position of 17 O δ ISO is different from that expected from the motional averaging of the four low temperature peaks. This result implies that the chemical structure in the paraelectric phase is not just a time-average of the various low symmetry forms, but must include a definitive change in molecular geometry. The transition mechanism must thus involve both an order-disorder and a displacive component. 4. Measurements on KDP-type Crystals P NMR of NH 4 H 2 PO 4 Similar high resolution NMR data on the change in the isotropic chemical shift around T c have been obtained for several of the KDP-type crystals. Figure 6 shows a typical 31 P spectrum for deuterated-kdp (DKDP), comparing the standard spectrum (top) with the MAS spectrum (bottom). A resolution enhancement by at a least an order of magnitude is clearly evident. Figures 7 and 8 show the measured temperature dependence of the 31 P isotropic chemical shift and the linewidth for ADP. A clear break anomaly can be noted within the phase transition temperature regime. We note that a fully deuterated DKDP crystal, known to not exhibit any ferroelectric transition, showed an essentially flat chemical shift response over K range [20] N NMR of NH 4 H 2 AsO 4 and NH 4 H 2 PO 4 We also made high resolution 15 N MAS NMR measurements on NH 4 H 2 AsO 4 to observe the behavior of the isotropic chemical shift, δ ISO, within the range of the phase transition temperature (T N = 216 K). Typical spectra of ADA at the paraelectric phase and the antiferroelectric phase could be seen in figure 9a and 9b. The observation of the temperature dependence of 15 N isotropic chemical shift, δ ISO showed clear anomaly at the antiferroelectric

8 10/[1182] N. S. Dalal et al. Figure N NMR spectrum of ADA at a) Paraelectric phase b) Antiferroelectric phase. phase transition that is plotted in figure 10. We have also observed similar results for ADP; the details will be reported elsewhere. 5. Summary and Conclusions Summarizing, this study yielded two major results. First, in cases such as the hydrogenbonded solids studied here, MAS using single crystals can afford several times higher resolution than obtained through the more routine procedure of using powdered samples. The present study constitutes, to our knowledge, the first report of such resolution enhancement for 17 O. Additionally, relative to 13 C, the 17 O nucleus affords by a higher spectral resolution factor of nearly 5. Second, the observation of four clearly resolved 17 O NMR peaks at T < T N constitutes a direct evidence of the presence of two different hydrogen-bonded Ising chains in SQA. The detection of a doublet rather than a singlet at T > T N, together with the fact that the higher temperature peaks are not at the algebraic average of the four lowtemperature signals, implies that the transition mechanism consists of both an order-disorder Figure 10. Temperature dependence of δ ISO of 15 NinADA.Agradual change and then a clear jump marks the phase transition.

9 Displacive and Order-Disorder Behavior in KDP [1183]/11 and a displacive component. The temperature dependence of 15 N isotropic chemical shift, δ ISO,inADA [22] and 31 PinADP showed increases at the antiferroelectric phase transitions. The detection of such a change in δ ISO implies that there is a distortion in the molecular structure at the phase transition at the cationic (NH + 4 This change is evidence of displacive component in the phase transition mechanism of ADA and ADP. We thus believe that this study will stimulate significant new theoretical as well as experimental investigations and helps to explain some features, such as cluster formation above T a in these materials [29, 30]. )aswell as the anionic (PO3 4 ) sites. Acknowledgments This research was supported in part by a grant from the National Science Foundation and Florida State University. References 1. R. Blinc, Ferroelectrics Ferroelectrics 267, 3 22 (2002). 2. R. Blinc and B. Zeks, Soft Modes in Ferroelectrics and Antiferroelectrics, Elsevier, NY (1974). 3. D. Semmingsen, The structure of Squaric acid (3,4-dihydroxy-3-cyclobutene-1,2 dione. Tetrahedron Lett. 14, (1973). 4. E. J. Samuelsen and D. Semmingsen, Squaric acid, a two dimensional hydrogen bonded material with a phase transition. Sol. St. Commun. 17, (1975). 5. D. Semmingsen and J. Feder, A structural phase transition in Squaric acid. Sol. St. Commun. 15, (1974). 6. D. Semmingsen, Z. Tun, R. J. Nelms, R. K. McMullan, and T. F. Koetzele, On the temperature dependence of the hydrogen bond order in squaric acid: Neutron diffraction studies at four different temperatures. Zeit. Kristall. 210, (1995). 7. C. Rovira, J. Novoa, and P. Ballone, Hydrogen bonding and collective proton modes in clusters and periodic layers of squaric acid: a density functional study. J. Chem. Phys. 115, (2001). 8. J. Palomar and N. S. Dalal, Quantum theoretical evidence for two distinct hydrogen- bonding networks and for an ising chain model of the antiferroelectric transition in Squaric acid. J. Phys. Chem. B 106, (2002). 9. K. D. Ehrhardt, U. Buchenau, E. J. Sammuelsen, and H. D. Maier, One-dimensional molecular correlations in squaric acid as observed by neutron scattering. Phys. Rev. B 29, (1984). 10. R. Blinc, On the isotopic effects in the ferroelectric behaviour of crystals with short hydrogen bonds. J. Phys. Chem. Solids 13, (1960). 11. R. Blinc, B. Zeks, J. F. Xampiao, A. S. T. Pires, and F. C. Barreto, Ising model in a transverse tunneling field and proton-lattice interaction in H-bonded ferroelectrics. Phys Rev B 20, (1979). 12. M. Ichikawa, K. Motida, and N. Yamada, Negative evidence for proton tunneling mechanism in the phase transition of KH 2 PO 4 -type crystals. Phys. Rev. B 36, (1987). 13. Z. Tun et al., J. Phys. C 21, 245 (1988); R. J. Nelmes, A high resolution neutron diffraction study of the effects of deuteration on the crystal structure of KH 2 PO 4. J. Phys. C, 21, (1988); McMahon, et al., Nature 348, (1990). 14. S. Koval, J. Kohanoff, R. L. Migoni, and E. Tosatti, Ferroelectricity and isotope effects in hydrogen-bonded KDP crystals. Phys. Rev. Lett. 89, (2002). 15. R. Blinc, M. Burger, V. Rutar, J. Seliger, and I. Zupancic, 31 P chemical shift study of the ferroelectric transition in KD 2 PO 4. Phys. Rev. Lett. 38, (1977).

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