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Study of the molecular dynamics and phase transitions of A2ZnCl4 (A=NH4 , Rb, and Cs) single crystals
Solid State Communications 151 (2011) 1631–1634
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Study of the molecular dynamics and phase transitions of A2 ZnCl4 (A = NH4 , Rb, and Cs) single crystals Ae Ran Lim ∗ Department of Science Education, Jeonju University, Jeonju 560-759, Republic of Korea
article
info
Article history: Received 1 June 2011 Received in revised form 3 July 2011 Accepted 8 July 2011 by E.V. Sampathkumaran Available online 18 July 2011 Keywords: A. Ferroelectrics B. Crystal growth D. Phase transitions E. Nuclear magnetic resonance (NMR)
abstract The spin–lattice relaxation time of the 1 H nuclei in the ammonium groups in (NH4 )2 ZnCl4 crystals has been measured as a function of temperature for a range of temperatures that includes those of the phase transitions. The temperature dependence of this relaxation time is more or less continuous near TC , and is not affected by the phase transitions. A minimum was found in the 1 H spin–lattice relaxation time that is related to NH+ 4 tunneling. Our results for (NH4 )2 ZnCl4 are compared with previously reported results for Rb2 ZnCl4 and Cs2 ZnCl4 crystals. The differences between the atomic weights of NH4 , Rb, and Cs are responsible for the differences between the molecular motions and phase transitions of these single crystals. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction A2 BX4 crystals have received a great deal of attention because of their nonlinear optical properties. This family of crystals has also attracted the attention of investigators for many decades because of the great diversity of their structural phase transitions [1]. (NH4 )2 ZnCl4 belongs to the family characterized by the general formula A2 BX4 . The prototype of the crystal structures of this family is that of β -K2 SO4 , which consists of isolated BX24− tetrahedra and monovalent A+ cations placed in two inequivalent cavities. The crystals of this family exhibit a number of interesting phase transitions and can exhibit phases with ferroelectric or ferroelastic ordering [2,3]. (NH4 )2 ZnCl4 undergoes five phase transitions, including those between phases I and II at 406 K (=TC 1 ) and phases II and III at 364 K (=TC 2 ) [4–7]. In addition, successive phase transitions at 319 K (=TC 3 ), 271 K (= TC4 ), and 266 K (=TC5 ) have been reported [8]; the phases involved in these transitions are denoted by III, IV, V, and VI of the order of decreasing temperature. Above 406 K, the structure of (NH4 )2 ZnCl4 in the normal phase, phase I, is orthorhombic with space group D16 2h (Pnma) with a = 9.274 Å, b = 12.620 Å, and c = 7.211 Å [4]. Upon cooling, there is a phase transition at 406 K to an incommensurate phase that is stable down to 364 K [9]. The structure in phase III between 364 and 319 K is orthorhombic with space group C29v (Pn21 a) [9,10].
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The room temperature phase, phase IV, is antiferroelectric with a pseudo-orthorhombic monoclinic structure and space group Cs2 2− (Pa) [9,11]. This structure consists of NH+ 4 and ZnCl4 tetrahedra that are connected by a network of hydrogen bonds. In the unit cell, there are two types of NH+ 4 ions, which are inequivalent. Phase V between 271 and 266 K is characterized by the coexistence of several commensurate modulated phases with different periods of modulation. On the other hand, Rb2 ZnCl4 undergoes successive phase transitions from a paraelectric phase to an incommensurate phase at TC 1 = 303 K, to a ferroelectric commensurate phase at TC 2 = 192 K, and to a low temperature phase at TC3 = 75 K [12–16]. The paraelectric unit cell contains eight Rb ions, which belong to two crystallographically inequivalent sites, Rb(1) and Rb(2). In addition, Cs2 ZnCl4 does not undergo any structural phase transitions, and there are two types of crystallographically inequivalent sites, Cs(1) and Cs(2), in its unit cell [17,18]. According to the previously reported, 1 H nuclear magnetic resonance (NMR) relaxation studies of (NH4 )2 ZnCl4 have mainly investigated dynamical processes at lower temperatures [19,20]. The proton spin–lattice relaxation time at 10 MHz of polycrystalline (NH4 )2 ZnCl4 has been reported; double minima were observed in the proton spin–lattice relaxation time T1 [21]. Michel et al. [22] reported the quadrupolar perturbed 14 N NMR spectra of the normal, incommensurate and various commensurate phases of (NH4 )2 ZnCl4 crystals. The effects of grain size on polycrystalline samples of (NH4 )2 ZnCl4 were studied with NMR [23]. The deuteron NMR spectra and relaxation of polycrystalline fully and partly deuterated (NH4 )2 ZnCl4 were recently studied between 300 and 5 K [24]. However, although the physical properties of (NH4 )2 ZnCl4
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have been reported, the NMR results for A2 ZnCl4 (A = NH4 , Rb, and Cs) single crystals of A2 BX4 type have not previously been compared. The NMR method makes it possible to study the local properties of lattices, and is particularly useful in those cases for which information on the behavior of individual structural groups is required. In order to explain the mechanisms of the successive phase transitions of (NH4 )2 ZnCl4 , it is necessary to examine the molecular motions of all phases in detail. The aim of this paper is to clarify the structural changes in (NH4 )2 ZnCl4 associated with the successive phase transitions. Further, the temperature dependence of the spin–lattice relaxation time, T1 , of the 1 H nuclei was investigated by using a pulse NMR spectrometer. We also carried out spin–lattice relaxation measurements for ammonium in (NH4 )2 ZnCl4 to obtain further information about the phase transitions and their connection with the NH+ 4 ion dynamics. We compare our results for (NH4 )2 ZnCl4 with previously obtained results for Rb2 ZnCl4 and Cs2 ZnCl4 crystals. We are particularly interested in understanding the role of the alkali-metal ions in the structural phase transitions and the molecular motions in these compounds. Based on these results, the relaxation mechanisms for these crystals are compared. The results of this study should be applicable to other isomorphic systems.
Fig. 1. Energy diagram of the spin I = 3/2, and transition probability between them for the quadrupole relaxations.
2. Experimental method
(NH4 )2 ZnCl4 crystals were obtained by the slow evaporation at room temperature of aqueous solutions with the appropriate molar ratios of NH4 Cl and ZnCl2 . The (NH4 )2 ZnCl4 crystals were transparent and colorless. The NMR signals of the 1 H nuclei in the (NH4 )2 ZnCl4 single crystals were measured by using the Varian 200 FT NMR spectrometer at the Korea Basic Science Institute. The static magnetic field was 4.7 T and the central radio frequency was set at ωo /2π = 200 MHz for the 1 H nucleus. The spin–lattice relaxation times were measured by using a saturation recovery pulse sequence, sat − t −π /2: the nuclear magnetizations of the 1 H nuclei at time t after the sat pulse, a combination of one hundred π /2 pulses applied at regular intervals, were determined following the π /2 excitation pulse. The width of the π /2 pulse was 2.4 µs for 1 H. The temperaturedependent NMR measurements were obtained over the temperature range 180–430 K. The samples were maintained at constant temperatures by controlling the nitrogen gas flow and the heater current. 3. Experimental results and discussion The saturation recovery traces of the 1 H (I = 1/2) nuclei in (NH4 )2 ZnCl4 can each be represented by a single exponential function. The 1 H spin–lattice relaxation time was determined by fitting the recovery patterns to the following equation [25]:
[S (∞) − S (t )]/S (∞) = exp(−Wt )
(1)
where S (t ) is the nuclear magnetization at time t and W is the transition probability corresponding to ∆m = ±1. The relaxation time is given by T1 = 1/W . We now describe the recovery laws for the quadrupole relaxation processes of the 87 Rb (I = 3/2) nuclei in Rb2 ZnCl4 single crystals. For the quadrupole relaxation, the transition probability for ∆m = ±1 as W1 and that for ∆m = ±2 as W2 is shown in Fig. 1 [26,27]. The saturation recovery function for the central resonance line is [28,29]
[S (∞) − S (t )]/S (∞) = 0.5[exp(−2W1 t ) + exp(−2W2 t )]
(2)
where S (t ) is the nuclear magnetization corresponding to the central transition at time t after saturation.
Fig. 2. The intensity of 1 H NMR in (NH4 )2 ZnCl4 crystals as a function of temperature (inset: The 1 H NMR spectrum of the crystallographically inequivalent ammonium ions in (NH4 )2 ZnCl4 crystals).
When only the central line is excited, the magnetization recovery of the 133 Cs(I = 7/2) nuclei in Cs2 ZnCl4 crystals does not follow a single exponential function, but can be represented by a combination of four exponential functions. The signal for W1 = W2 is given by [30,31]:
[S (∞) − S (t )]/S (∞) = 0.048 exp(−0.476 W1 t ) + 0.818 exp(−1.333 W1 t ) + 0.050 exp(−2.381 W1 t ) + 0.084 exp(−3.810 W1 t )
(3)
where S (t ) is the nuclear magnetization at time t. The NMR spectrum of 1 H in the crystallographically inequivalent NH4 (1) and NH4 (2) sites was obtained; the contributions of these sites to the spectrum overlap somewhat ( and ), as shown in the inset in Fig. 2. The intensities of the resonance line with strong intensity () depend strongly on temperature, as shown in Fig. 2. The intensities of the resonance line with low intensity () are not easy to measure. For the signals with strong intensity, the change in the intensity near TC 2 (=364 K) is related to the phase transition. The other phase transitions are not evident in the 1 H intensity results. The magnetization decay of the 1 H nuclei in NH4 ions with strong intensity ( in the inset in Fig. 2) was measured for several delay times. Here, the crystallographic c-axis was oriented parallel to the static magnetic field. Fig. 3 shows the recovery traces of 1 H at 200, 300, and 400 K, respectively. The slopes of the recovery traces are different at each temperature. The recovery data for the temperatures investigated here can all be fitted with Eq. (1), as shown by the solid curves in Fig. 3. This figure exhibits the vast variation in the proton dynamics of hydrogen bond networks. The 1 H spin–lattice relaxation time in (NH4 )2 ZnCl4 was obtained as a function of temperature, as shown in Fig. 4. The proton T1 passes through a small discontinuity near TC 4 (=271 K), and undergoes a change in slope at 271 K, which is probably due to the phase transition from the ferroelectric phase to the antiferroelectric phase. In the high temperature region, T1 increases monotonically
A.R. Lim / Solid State Communications 151 (2011) 1631–1634
Fig. 3. The saturation recovery behaviors of 1 H in (NH4 )2 ZnCl4 as a function of delay time at 200, 300, and 400 K. The solid lines are fits with the function in Eq. (1).
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Fig. 4. Temperature dependence of the 1 H spin–lattice relaxation time in (NH4 )2 ZnCl4 crystals as a function of temperature (inset: The correlation time for 1 H as a function of inverse temperature).
with temperature. T1 is more or less continuous at the other phase transition temperatures, excluding TC 4 . Further, the 1 H spin–lattice relaxation time passes through a minimum value in the vicinity of 220 K; the presence of this minimum is attributed to the effects of rotational tunneling motion. From the 1 H T1 curves, we conclude that the relaxation process is affected by molecular motion, as described by the Bloembergen–Purcell–Pound (BPP) theory [32]. From the 1 H T1 data shown in Fig. 4, we can derive the correlation time τH for the reorientation of NH4 ions in (NH4 )2 ZnCl4 . The proton spin–lattice relaxation is mainly controlled by the H–H interdipolar interaction modulated by NH4 reorientation, yielding the following equation for T1 [33]: 1/T1 = (µ0 /4π )2 (γ 2 h¯ /r 3 )2 [τH /(1 + (ωH τH )2 )
+ 4τH /(1 + (2ωH τH )2 )],
(4)
where γ is the gyromagnetic ratio for the H nucleus, h¯ = h/2π (h: Planck’s constant), r is the proton–proton distance, and ωH is the proton Larmor frequency. The minimum in T1 occurs when ωH τH = 0.616. Since the T1 curve contains a minimum, it is possible to determine the value of the constant in the BPP formula. The correlation time can be calculated as a function of temperature from that constant by using the proton Larmor frequency ωH /2π = 200 MHz and the values of T1 obtained from our experimental results. The correlation time for the proton nuclei is shown as a function of inverse temperature in the inset in Fig. 4. Since, the correlation time τH of 1 H for a thermally activated reorientation follows the usual Arrhenius expression τH = τo exp(−Ea /kB T ), the activation energy Ea and the preexponential factor τo can be determined from the slopes of the straight line portions of the semilog plots of the correlation time vs. 1000/T . The activation energy in the low temperature range was found to be 29.95 ± 0.85 kJ/mol for 1 H; this T1 minimum at lower temperatures is related to NH+ 4 rotational tunneling motion. The relaxation time minimum is attributed to ions undergoing threefold uniaxial reorientation at low temperatures. The activation energy of the molecular motion for the high temperature side of this minimum is 10.99 ± 0.37 kJ/mol. The NMR spectrum of 87 Rb(I = 3/2) in Rb2 ZnCl4 crystals was obtained at a frequency of ωo /2π = 130.93 MHz. When such crystals are rotated about the crystallographic axis, crystallographically equivalent nuclei would be expected to give rise to three lines: one central line and two satellite lines. The NMR spectrum of 87 Rb (I = 3/2) consists of two central lines at room temperature. The magnitudes of the quadrupole parameters of 87 Rb nuclei are of the order of MHz, so usually only central lines are obtained. Thus, the two resonance lines are for 1
Fig. 5. Temperature dependences of the 87 Rb spin–lattice relaxation time in Rb2 ZnCl4 crystals as functions of temperature and frequency.
the central transition of the 87 Rb NMR spectrum. These two Rb signals are the 87 Rb central NMR lines due to the two inequivalent Rb nuclei, Rb(1) and Rb(2), as reported by our group [34]. The nuclear magnetization recovery curves of the 87 Rb nuclei were obtained by measuring the nuclear magnetization after applying saturation pulses at several temperatures. The recovery trace for the central resonance line of 87 Rb, with dominant quadrupole relaxation, can be represented by a combination of the two exponential functions in Eq. (2). The temperature dependences of the 87 Rb spin–lattice transition rates W1 and W2 were obtained from Eq. (2). We measured the variations in the relaxation times of the central lines for Rb(1) and Rb(2) with temperature. The trends in the relaxation times for Rb(1) and Rb(2) are very similar; their values are consistent within the error range. The temperature dependences of T1 for the 87 Rb nuclei are shown in Fig. 5. The 87 Rb relaxation times for a Rb2 ZnCl4 crystal at the two Larmor frequencies 65.47 and 130.94 MHz are nearly frequency independent. The relaxation times for the 87 Rb nuclei undergo significant changes near 75 K (=TC 3 ), 192 K (=TC 2 ), and 303 K (=TC 1 ), which indicates that there are drastic alterations of the spin dynamics at the transition temperatures. Thus the phase transition near TC 3 is second-order type, and the phase transitions near TC 2 and TC 1 are first-order type [34,35]. The NMR spectrum of 133 Cs (I = 7/2) in Cs2 ZnCl4 was obtained along the crystallographic a-axis at room temperature, and two distinct groups of Cs resonance lines were found [36]. The distinct resonance lines of the two groups are associated with the two crystallographically inequivalent positions of cesium atoms in the unit cell, i.e., Cs(1) and Cs(2). The shifts of these two
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between the spin–lattice relaxation times of the A2 ZnCl4 single crystals can be attributed to the different electric quadrupole moments of Rb and Cs. The molecular motions and phase transition behaviors of these crystals can also be explained in terms of the + masses of their respective ions: NH+ 4 ions are lighter than Rb + and Cs ions. Further, as the radii of the metal ions increase, a corresponding increase in the spin–lattice relaxation times of the A nuclei is observed. The differences observed in the spin–lattice relaxation times of the A nuclei upon changing the alkali-metal ion may be related to the ionic radius. This result suggests that the differences in the chemical properties of A are responsible for the variations in the molecular motions and the phase transition properties observed in the crystals studied. Therefore, it seems that the occurrence of phase transitions in these materials essentially depends on the presence of the metal ions. Fig. 6. Temperature dependences of the spin–lattice relaxation time for Cs(1) and Cs(2) in Cs2 ZnCl4 crystals as a function of temperature (inset: The 133 Cs NMR spectrum of Cs2 ZnCl4 crystals at room temperature).
groups are smaller and larger respectively, and are shown in the inset in Fig. 6 [36]. The nuclear magnetization recovery traces for Cs(1) and Cs(2) were measured at several temperatures, and can be represented by a combination of four exponential functions, as in Eq. (3). The 133 Cs relaxation time was obtained in terms of W1 (T1 = 1/1.333W1 ), and its temperature dependence is shown in Fig. 6. The relaxation times of Cs(1) and Cs(2) decrease with increasing temperature [36]. The 133 Cs nucleus in Cs2 ZnCl4 has a very long relaxation time of approximately 600 s at room temperature. Further, this relaxation time does not abruptly vary with temperature, so this material does not undergo a structural phase transition within the investigated temperature range. 4. Conclusion NMR spectroscopy is a sensitive tool for obtaining information about molecular dynamics. Here, we can draw conclusions based on analysis of intensities and relaxation times, and NMR study is particularly suitable for the study of molecular motions. The spin–lattice relaxation time, T1 , of the 1 H nuclei in (NH4 )2 ZnCl4 crystals was determined as a function of temperature. The intensities of the 1 H NMR resonance lines were found to be more sensitive than the relaxation time to the phase transitions in this crystal. The 1 H T1 was observed to vary continuously with temperature without jumps or changes. These smooth transitions demonstrate that the phase changes in (NH4 )2 ZnCl4 crystals are not of first-order type. The high activation energy in (NH4 )2 ZnCl4 at low temperatures suggests that there is considerable degree of rotational freedom for NH+ 4 ions. We compared the A (=NH4 , Rb, and Cs) NMR results for A2 ZnCl4 single crystals. The phase transition temperatures of (NH4 )2 ZnCl4 are 266, 271, 319, 364, and 406 K, and the phase transition temperatures of Rb2 ZnCl4 are 75, 192, and 303 K. Cs2 ZnCl4 does not undergo any phase transitions. Our comparison of the 1 H, 87 Rb, and 133 Cs NMR results showed that the Cs relaxation time is longer than that of Rb or H. The trend in T1 for 1 H in (NH4 )2 ZnCl4 crystals is different from the trends in the T1 values of Rb and Cs in Rb2 ZnCl4 and Cs2 ZnCl4 crystals respectively; rotational tunneling motion occurs in (NH4 )2 ZnCl4 , but does not occur in Rb2 ZnCl4 and Cs2 ZnCl4 . Thus the A2 ZnCl4 single crystals differ in their phase transition temperatures and the molecular motions. The difference
Acknowledgment This study was supported by the Mid-Career Researcher Program through an NRF grant funded by the MEST (No. 20100000356). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36]
A.M. Gillet, Y. Luspin, G. Mauret, Solid State Commun. 64 (1987) 797. N.G. Zamkova, V.I. Zinenko, Sov. Phys. JEPT 80 (1995) 713. Y. Koyama, T. Nagata, K. Koike, Phys. Rev. B 51 (1995) 12157. H. Matsunaga, J. Phys. Soc. Japan 51 (1982) 864. H. Matsunaga, J. Phys. Soc. Japan 51 (873) (1982) 873. J.L. Burris, L. Tereshchenko, P. Kabos, H.D. Hochheimer, Y. Luspin, C.R. Evenson, P.K. Dorhout, J. Phys. Chem. Soc. 61 (719) (2000) 719. Z. Tylczynski, A.D. Karaev, Physica B 307 (2001) 224. M. Amin, A. El-Korashy, S.S. Ibrahim, M. Dabour, S. Arafa, J. Phys. Chem. Solids 63 (2002) 869. T. Sata, T. Osaka, Y. Makita, J. Phys. Soc. Japan 53 (1984) 1907. H. Matsunaga, E. Nakamura, J. Phys. Soc. Japan 50 (1981) 2789. H. van Konigsveld, Acta Cryst. C 39 (1983) 15. K. Gesi, M. Iizumi, J. Phys. Soc. Japan 46 (1979) 697. E. Francke, M.L. Postollec, J.P. Mathieu, H. Poulet, Solid State Commun. 33 (1980) 155. I. Noiret, Y. Guinet, A. Hedoux, Phys. Rev. B 52 (1995) 13206. M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc. Japan 47 (1979) 1185. M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc. Japan 50 (1981) 531. O.P. Lamba, S.K. Sinha, Solid State Commun. 57 (1986) 365. P.T.T. Wong, J. Chem. Phys. 64 (1976) 2186. C.S. Sundaram, J. Ramakrishna, K. Chandrasekhar, V.S.S. Sastry, Ferroelectrics 69 (1986) 299. A.H. Vuorimaki, M. Punkkinen, E.E. Ylinen, Chem. Phys. Letters 161 (1989) 561. L.P. Ingman, M. Punkkinen, A.H. Vuorimaki, E.E. Ylinen, J. Phys. C: Solid State Phys. 18 (1985) 5033. D. Michel, B. Muller, J. Petersson, A. Trampert, R. Walisch, Phys. Rev. B 43 (1991) 7507. Z.S. Liu, M. Punkkinen, A.H. Vuorimaki, E.E. Ylinen, Physica B 202 (1994) 343. G. Stoch, E.E. Ylinen, M. Punkkinen, B. Petelenz, A. Birczynski, Solid State Nucl. Mag. Reson. 35 (2009) 180. A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, 1961. G. Bonera, F. Borsa, A. Rigamonti, Phys. Rev. B 2 (1970) 2784. A.R. Lim, K.S. Hong, J. Appl. Phys. 98 (2005) 43906. J.J. van der Klink, D. Rytz, F. Borsa, U.T. Hochli, Phys. Rev. B 27 (1983) 89. M. Igarashi, H. Kitagawa, S. Takahashi, R. Yoshizak, Y. Abe, Z. Naturforsch, A: Phys. Sci. 47a (1992) 313. M.I. Gordon, M.J.R. Hoch, J. Phys. C 11 (1978) 783. A.R. Lim, Solid State Nucl. Magn. Reson. 36 (2009) 45. N. Bloembergen, E.M. Purcell, R.V. Pound, Phys. Rev. 73 (1948) 679. R. Bohmer, K.R. Jeffrey, M. Vogel, Prog. Nucl. Magn. Reson. Spectrosc. 50 (2007) 87. A.R. Lim, J. Appl. Phys. 107 (2010) 93508. A.R. Lim, J.K. Jung, S.Y. Jeong, Solid State Commun. 118 (2001) 453. A.R. Lim, O.H. Han, S.Y. Jeong, J. Phys. Chem. Solids 64 (2003) 933.
Contents lists available at SciVerse ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Study of the molecular dynamics and phase transitions of A2 ZnCl4 (A = NH4 , Rb, and Cs) single crystals Ae Ran Lim ∗ Department of Science Education, Jeonju University, Jeonju 560-759, Republic of Korea
article
info
Article history: Received 1 June 2011 Received in revised form 3 July 2011 Accepted 8 July 2011 by E.V. Sampathkumaran Available online 18 July 2011 Keywords: A. Ferroelectrics B. Crystal growth D. Phase transitions E. Nuclear magnetic resonance (NMR)
abstract The spin–lattice relaxation time of the 1 H nuclei in the ammonium groups in (NH4 )2 ZnCl4 crystals has been measured as a function of temperature for a range of temperatures that includes those of the phase transitions. The temperature dependence of this relaxation time is more or less continuous near TC , and is not affected by the phase transitions. A minimum was found in the 1 H spin–lattice relaxation time that is related to NH+ 4 tunneling. Our results for (NH4 )2 ZnCl4 are compared with previously reported results for Rb2 ZnCl4 and Cs2 ZnCl4 crystals. The differences between the atomic weights of NH4 , Rb, and Cs are responsible for the differences between the molecular motions and phase transitions of these single crystals. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction A2 BX4 crystals have received a great deal of attention because of their nonlinear optical properties. This family of crystals has also attracted the attention of investigators for many decades because of the great diversity of their structural phase transitions [1]. (NH4 )2 ZnCl4 belongs to the family characterized by the general formula A2 BX4 . The prototype of the crystal structures of this family is that of β -K2 SO4 , which consists of isolated BX24− tetrahedra and monovalent A+ cations placed in two inequivalent cavities. The crystals of this family exhibit a number of interesting phase transitions and can exhibit phases with ferroelectric or ferroelastic ordering [2,3]. (NH4 )2 ZnCl4 undergoes five phase transitions, including those between phases I and II at 406 K (=TC 1 ) and phases II and III at 364 K (=TC 2 ) [4–7]. In addition, successive phase transitions at 319 K (=TC 3 ), 271 K (= TC4 ), and 266 K (=TC5 ) have been reported [8]; the phases involved in these transitions are denoted by III, IV, V, and VI of the order of decreasing temperature. Above 406 K, the structure of (NH4 )2 ZnCl4 in the normal phase, phase I, is orthorhombic with space group D16 2h (Pnma) with a = 9.274 Å, b = 12.620 Å, and c = 7.211 Å [4]. Upon cooling, there is a phase transition at 406 K to an incommensurate phase that is stable down to 364 K [9]. The structure in phase III between 364 and 319 K is orthorhombic with space group C29v (Pn21 a) [9,10].
∗
Tel.: +82 0 63 220 2514; fax: +82 0 63 220 2053. E-mail addresses: [email protected], [email protected].
0038-1098/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2011.07.014
The room temperature phase, phase IV, is antiferroelectric with a pseudo-orthorhombic monoclinic structure and space group Cs2 2− (Pa) [9,11]. This structure consists of NH+ 4 and ZnCl4 tetrahedra that are connected by a network of hydrogen bonds. In the unit cell, there are two types of NH+ 4 ions, which are inequivalent. Phase V between 271 and 266 K is characterized by the coexistence of several commensurate modulated phases with different periods of modulation. On the other hand, Rb2 ZnCl4 undergoes successive phase transitions from a paraelectric phase to an incommensurate phase at TC 1 = 303 K, to a ferroelectric commensurate phase at TC 2 = 192 K, and to a low temperature phase at TC3 = 75 K [12–16]. The paraelectric unit cell contains eight Rb ions, which belong to two crystallographically inequivalent sites, Rb(1) and Rb(2). In addition, Cs2 ZnCl4 does not undergo any structural phase transitions, and there are two types of crystallographically inequivalent sites, Cs(1) and Cs(2), in its unit cell [17,18]. According to the previously reported, 1 H nuclear magnetic resonance (NMR) relaxation studies of (NH4 )2 ZnCl4 have mainly investigated dynamical processes at lower temperatures [19,20]. The proton spin–lattice relaxation time at 10 MHz of polycrystalline (NH4 )2 ZnCl4 has been reported; double minima were observed in the proton spin–lattice relaxation time T1 [21]. Michel et al. [22] reported the quadrupolar perturbed 14 N NMR spectra of the normal, incommensurate and various commensurate phases of (NH4 )2 ZnCl4 crystals. The effects of grain size on polycrystalline samples of (NH4 )2 ZnCl4 were studied with NMR [23]. The deuteron NMR spectra and relaxation of polycrystalline fully and partly deuterated (NH4 )2 ZnCl4 were recently studied between 300 and 5 K [24]. However, although the physical properties of (NH4 )2 ZnCl4
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A.R. Lim / Solid State Communications 151 (2011) 1631–1634
have been reported, the NMR results for A2 ZnCl4 (A = NH4 , Rb, and Cs) single crystals of A2 BX4 type have not previously been compared. The NMR method makes it possible to study the local properties of lattices, and is particularly useful in those cases for which information on the behavior of individual structural groups is required. In order to explain the mechanisms of the successive phase transitions of (NH4 )2 ZnCl4 , it is necessary to examine the molecular motions of all phases in detail. The aim of this paper is to clarify the structural changes in (NH4 )2 ZnCl4 associated with the successive phase transitions. Further, the temperature dependence of the spin–lattice relaxation time, T1 , of the 1 H nuclei was investigated by using a pulse NMR spectrometer. We also carried out spin–lattice relaxation measurements for ammonium in (NH4 )2 ZnCl4 to obtain further information about the phase transitions and their connection with the NH+ 4 ion dynamics. We compare our results for (NH4 )2 ZnCl4 with previously obtained results for Rb2 ZnCl4 and Cs2 ZnCl4 crystals. We are particularly interested in understanding the role of the alkali-metal ions in the structural phase transitions and the molecular motions in these compounds. Based on these results, the relaxation mechanisms for these crystals are compared. The results of this study should be applicable to other isomorphic systems.
Fig. 1. Energy diagram of the spin I = 3/2, and transition probability between them for the quadrupole relaxations.
2. Experimental method
(NH4 )2 ZnCl4 crystals were obtained by the slow evaporation at room temperature of aqueous solutions with the appropriate molar ratios of NH4 Cl and ZnCl2 . The (NH4 )2 ZnCl4 crystals were transparent and colorless. The NMR signals of the 1 H nuclei in the (NH4 )2 ZnCl4 single crystals were measured by using the Varian 200 FT NMR spectrometer at the Korea Basic Science Institute. The static magnetic field was 4.7 T and the central radio frequency was set at ωo /2π = 200 MHz for the 1 H nucleus. The spin–lattice relaxation times were measured by using a saturation recovery pulse sequence, sat − t −π /2: the nuclear magnetizations of the 1 H nuclei at time t after the sat pulse, a combination of one hundred π /2 pulses applied at regular intervals, were determined following the π /2 excitation pulse. The width of the π /2 pulse was 2.4 µs for 1 H. The temperaturedependent NMR measurements were obtained over the temperature range 180–430 K. The samples were maintained at constant temperatures by controlling the nitrogen gas flow and the heater current. 3. Experimental results and discussion The saturation recovery traces of the 1 H (I = 1/2) nuclei in (NH4 )2 ZnCl4 can each be represented by a single exponential function. The 1 H spin–lattice relaxation time was determined by fitting the recovery patterns to the following equation [25]:
[S (∞) − S (t )]/S (∞) = exp(−Wt )
(1)
where S (t ) is the nuclear magnetization at time t and W is the transition probability corresponding to ∆m = ±1. The relaxation time is given by T1 = 1/W . We now describe the recovery laws for the quadrupole relaxation processes of the 87 Rb (I = 3/2) nuclei in Rb2 ZnCl4 single crystals. For the quadrupole relaxation, the transition probability for ∆m = ±1 as W1 and that for ∆m = ±2 as W2 is shown in Fig. 1 [26,27]. The saturation recovery function for the central resonance line is [28,29]
[S (∞) − S (t )]/S (∞) = 0.5[exp(−2W1 t ) + exp(−2W2 t )]
(2)
where S (t ) is the nuclear magnetization corresponding to the central transition at time t after saturation.
Fig. 2. The intensity of 1 H NMR in (NH4 )2 ZnCl4 crystals as a function of temperature (inset: The 1 H NMR spectrum of the crystallographically inequivalent ammonium ions in (NH4 )2 ZnCl4 crystals).
When only the central line is excited, the magnetization recovery of the 133 Cs(I = 7/2) nuclei in Cs2 ZnCl4 crystals does not follow a single exponential function, but can be represented by a combination of four exponential functions. The signal for W1 = W2 is given by [30,31]:
[S (∞) − S (t )]/S (∞) = 0.048 exp(−0.476 W1 t ) + 0.818 exp(−1.333 W1 t ) + 0.050 exp(−2.381 W1 t ) + 0.084 exp(−3.810 W1 t )
(3)
where S (t ) is the nuclear magnetization at time t. The NMR spectrum of 1 H in the crystallographically inequivalent NH4 (1) and NH4 (2) sites was obtained; the contributions of these sites to the spectrum overlap somewhat ( and ), as shown in the inset in Fig. 2. The intensities of the resonance line with strong intensity () depend strongly on temperature, as shown in Fig. 2. The intensities of the resonance line with low intensity () are not easy to measure. For the signals with strong intensity, the change in the intensity near TC 2 (=364 K) is related to the phase transition. The other phase transitions are not evident in the 1 H intensity results. The magnetization decay of the 1 H nuclei in NH4 ions with strong intensity ( in the inset in Fig. 2) was measured for several delay times. Here, the crystallographic c-axis was oriented parallel to the static magnetic field. Fig. 3 shows the recovery traces of 1 H at 200, 300, and 400 K, respectively. The slopes of the recovery traces are different at each temperature. The recovery data for the temperatures investigated here can all be fitted with Eq. (1), as shown by the solid curves in Fig. 3. This figure exhibits the vast variation in the proton dynamics of hydrogen bond networks. The 1 H spin–lattice relaxation time in (NH4 )2 ZnCl4 was obtained as a function of temperature, as shown in Fig. 4. The proton T1 passes through a small discontinuity near TC 4 (=271 K), and undergoes a change in slope at 271 K, which is probably due to the phase transition from the ferroelectric phase to the antiferroelectric phase. In the high temperature region, T1 increases monotonically
A.R. Lim / Solid State Communications 151 (2011) 1631–1634
Fig. 3. The saturation recovery behaviors of 1 H in (NH4 )2 ZnCl4 as a function of delay time at 200, 300, and 400 K. The solid lines are fits with the function in Eq. (1).
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Fig. 4. Temperature dependence of the 1 H spin–lattice relaxation time in (NH4 )2 ZnCl4 crystals as a function of temperature (inset: The correlation time for 1 H as a function of inverse temperature).
with temperature. T1 is more or less continuous at the other phase transition temperatures, excluding TC 4 . Further, the 1 H spin–lattice relaxation time passes through a minimum value in the vicinity of 220 K; the presence of this minimum is attributed to the effects of rotational tunneling motion. From the 1 H T1 curves, we conclude that the relaxation process is affected by molecular motion, as described by the Bloembergen–Purcell–Pound (BPP) theory [32]. From the 1 H T1 data shown in Fig. 4, we can derive the correlation time τH for the reorientation of NH4 ions in (NH4 )2 ZnCl4 . The proton spin–lattice relaxation is mainly controlled by the H–H interdipolar interaction modulated by NH4 reorientation, yielding the following equation for T1 [33]: 1/T1 = (µ0 /4π )2 (γ 2 h¯ /r 3 )2 [τH /(1 + (ωH τH )2 )
+ 4τH /(1 + (2ωH τH )2 )],
(4)
where γ is the gyromagnetic ratio for the H nucleus, h¯ = h/2π (h: Planck’s constant), r is the proton–proton distance, and ωH is the proton Larmor frequency. The minimum in T1 occurs when ωH τH = 0.616. Since the T1 curve contains a minimum, it is possible to determine the value of the constant in the BPP formula. The correlation time can be calculated as a function of temperature from that constant by using the proton Larmor frequency ωH /2π = 200 MHz and the values of T1 obtained from our experimental results. The correlation time for the proton nuclei is shown as a function of inverse temperature in the inset in Fig. 4. Since, the correlation time τH of 1 H for a thermally activated reorientation follows the usual Arrhenius expression τH = τo exp(−Ea /kB T ), the activation energy Ea and the preexponential factor τo can be determined from the slopes of the straight line portions of the semilog plots of the correlation time vs. 1000/T . The activation energy in the low temperature range was found to be 29.95 ± 0.85 kJ/mol for 1 H; this T1 minimum at lower temperatures is related to NH+ 4 rotational tunneling motion. The relaxation time minimum is attributed to ions undergoing threefold uniaxial reorientation at low temperatures. The activation energy of the molecular motion for the high temperature side of this minimum is 10.99 ± 0.37 kJ/mol. The NMR spectrum of 87 Rb(I = 3/2) in Rb2 ZnCl4 crystals was obtained at a frequency of ωo /2π = 130.93 MHz. When such crystals are rotated about the crystallographic axis, crystallographically equivalent nuclei would be expected to give rise to three lines: one central line and two satellite lines. The NMR spectrum of 87 Rb (I = 3/2) consists of two central lines at room temperature. The magnitudes of the quadrupole parameters of 87 Rb nuclei are of the order of MHz, so usually only central lines are obtained. Thus, the two resonance lines are for 1
Fig. 5. Temperature dependences of the 87 Rb spin–lattice relaxation time in Rb2 ZnCl4 crystals as functions of temperature and frequency.
the central transition of the 87 Rb NMR spectrum. These two Rb signals are the 87 Rb central NMR lines due to the two inequivalent Rb nuclei, Rb(1) and Rb(2), as reported by our group [34]. The nuclear magnetization recovery curves of the 87 Rb nuclei were obtained by measuring the nuclear magnetization after applying saturation pulses at several temperatures. The recovery trace for the central resonance line of 87 Rb, with dominant quadrupole relaxation, can be represented by a combination of the two exponential functions in Eq. (2). The temperature dependences of the 87 Rb spin–lattice transition rates W1 and W2 were obtained from Eq. (2). We measured the variations in the relaxation times of the central lines for Rb(1) and Rb(2) with temperature. The trends in the relaxation times for Rb(1) and Rb(2) are very similar; their values are consistent within the error range. The temperature dependences of T1 for the 87 Rb nuclei are shown in Fig. 5. The 87 Rb relaxation times for a Rb2 ZnCl4 crystal at the two Larmor frequencies 65.47 and 130.94 MHz are nearly frequency independent. The relaxation times for the 87 Rb nuclei undergo significant changes near 75 K (=TC 3 ), 192 K (=TC 2 ), and 303 K (=TC 1 ), which indicates that there are drastic alterations of the spin dynamics at the transition temperatures. Thus the phase transition near TC 3 is second-order type, and the phase transitions near TC 2 and TC 1 are first-order type [34,35]. The NMR spectrum of 133 Cs (I = 7/2) in Cs2 ZnCl4 was obtained along the crystallographic a-axis at room temperature, and two distinct groups of Cs resonance lines were found [36]. The distinct resonance lines of the two groups are associated with the two crystallographically inequivalent positions of cesium atoms in the unit cell, i.e., Cs(1) and Cs(2). The shifts of these two
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between the spin–lattice relaxation times of the A2 ZnCl4 single crystals can be attributed to the different electric quadrupole moments of Rb and Cs. The molecular motions and phase transition behaviors of these crystals can also be explained in terms of the + masses of their respective ions: NH+ 4 ions are lighter than Rb + and Cs ions. Further, as the radii of the metal ions increase, a corresponding increase in the spin–lattice relaxation times of the A nuclei is observed. The differences observed in the spin–lattice relaxation times of the A nuclei upon changing the alkali-metal ion may be related to the ionic radius. This result suggests that the differences in the chemical properties of A are responsible for the variations in the molecular motions and the phase transition properties observed in the crystals studied. Therefore, it seems that the occurrence of phase transitions in these materials essentially depends on the presence of the metal ions. Fig. 6. Temperature dependences of the spin–lattice relaxation time for Cs(1) and Cs(2) in Cs2 ZnCl4 crystals as a function of temperature (inset: The 133 Cs NMR spectrum of Cs2 ZnCl4 crystals at room temperature).
groups are smaller and larger respectively, and are shown in the inset in Fig. 6 [36]. The nuclear magnetization recovery traces for Cs(1) and Cs(2) were measured at several temperatures, and can be represented by a combination of four exponential functions, as in Eq. (3). The 133 Cs relaxation time was obtained in terms of W1 (T1 = 1/1.333W1 ), and its temperature dependence is shown in Fig. 6. The relaxation times of Cs(1) and Cs(2) decrease with increasing temperature [36]. The 133 Cs nucleus in Cs2 ZnCl4 has a very long relaxation time of approximately 600 s at room temperature. Further, this relaxation time does not abruptly vary with temperature, so this material does not undergo a structural phase transition within the investigated temperature range. 4. Conclusion NMR spectroscopy is a sensitive tool for obtaining information about molecular dynamics. Here, we can draw conclusions based on analysis of intensities and relaxation times, and NMR study is particularly suitable for the study of molecular motions. The spin–lattice relaxation time, T1 , of the 1 H nuclei in (NH4 )2 ZnCl4 crystals was determined as a function of temperature. The intensities of the 1 H NMR resonance lines were found to be more sensitive than the relaxation time to the phase transitions in this crystal. The 1 H T1 was observed to vary continuously with temperature without jumps or changes. These smooth transitions demonstrate that the phase changes in (NH4 )2 ZnCl4 crystals are not of first-order type. The high activation energy in (NH4 )2 ZnCl4 at low temperatures suggests that there is considerable degree of rotational freedom for NH+ 4 ions. We compared the A (=NH4 , Rb, and Cs) NMR results for A2 ZnCl4 single crystals. The phase transition temperatures of (NH4 )2 ZnCl4 are 266, 271, 319, 364, and 406 K, and the phase transition temperatures of Rb2 ZnCl4 are 75, 192, and 303 K. Cs2 ZnCl4 does not undergo any phase transitions. Our comparison of the 1 H, 87 Rb, and 133 Cs NMR results showed that the Cs relaxation time is longer than that of Rb or H. The trend in T1 for 1 H in (NH4 )2 ZnCl4 crystals is different from the trends in the T1 values of Rb and Cs in Rb2 ZnCl4 and Cs2 ZnCl4 crystals respectively; rotational tunneling motion occurs in (NH4 )2 ZnCl4 , but does not occur in Rb2 ZnCl4 and Cs2 ZnCl4 . Thus the A2 ZnCl4 single crystals differ in their phase transition temperatures and the molecular motions. The difference
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