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Temperature dependence of 23Na NMR quadrupole parameters and spin-lattice relaxation rate in NaNO2 powder
PERGAMON
Solid State Communications 110 (1999) 547–552
Temperature dependence of 23Na NMR quadrupole parameters and spin-lattice relaxation rate in NaNO2 powder J.K. Jung a, O.H. Han a,*, S.H. Choh b a
Magnetic Resonance Research Group, Korea Basic Science Institute, Yeueundong 52, Yoosung-goo, Taejeon 305-333, South Korea b Department of Physics, Korea University, Seoul 136-701, South Korea Received 18 January 1999; accepted 5 March 1999 by H. Akai
Abstract The nuclear quadrupole coupling constant (e 2qQ/h) and the spin-lattice relaxation rate (1/T1) of 23Na NMR in the NaNO2 powder were investigated by employing a magic angle spinning probe and a wideline probe, respectively, at 9.4 T as a function of temperature (T) in the range of 300–458 K. The linearity between e 2qQ/h and the squared spontaneous polarization (Ps2) was obeyed up to near the critical temperature (Tc 437 K), which is consistent with the previous reports. Moreover, the asymmetry parameter (h ) at 23Na site is found to be linear with Ps, firstly noticed in this work. The linearity between ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps and 1/T is found to be satisfied up to near the Tc, where (1/T1)reo is the relaxation rate for the reorientational motion of the NO2⫺. From this linearity, the reorientational motion of NO2⫺ ion in powder samples is found to have an activation energy, DU 0.22 ^ 0.01 eV, which is in good agreement with the value obtained with single crystals. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Ferroelectrics; D. Phase transitions; D. Order–disorder effects; E. Nuclear resonances
The spontaneous polarization (Ps) of the ferroelectric NaNO2 which undergoes an order–disorder transition [1–5] at Tc 437 K, influences directly the quadrupole coupling constant (e 2qQ/h) of 23Na and its spin-lattice relaxation [6–8]. Betsuyaku [6], and Dening and Casabella [7] showed that the quadrupole coupling constant of 23Na in the NaNO2 single crystal should be proportional to the square of the spontaneous polarization, because the Na ⫹ ion resides at a site of inversion symmetry in the paraelectric phase. Meanwhile, Pandey and Hughes [8] reported that the 23 Na NMR relaxation is mainly caused by the reorientational motion of NO2⫺ ions in the range of * Corresponding author. Tel.: ⫹ 82-42-865-3436; fax: ⫹ 82-42865-3419. E-mail address: [email protected] (O.H. Han)
230–437 K, which was explained by introducing the spontaneous polarization. 23Na NMR studies of NaNO2 have been mostly carried out with single crystals [6–11], in relation to the spontaneous polarization. However, the investigations with the powder sample are quite rare because of the low spectral resolution as a result of the quadrupole broadening and distributions of both chemical shift and quadrupole interaction parameters. The magic angle spinning (MAS) at fast spinning rate was applied for increased spectral resolution which has made it easy to obtain the quadrupole interaction parameters with improved accuracy. In this work, the temperature dependence of e 2qQ/h and spin-lattice relaxation rate (1/T1) for 23Na NMR in NaNO2 powder sample has been investigated by employing a MAS and a wideline probe, respectively.
0038-1098/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00128-3
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Fig. 1. Experimental: (a) satellite transition sidebands and (b) central transition centerband of 23Na MAS NMR spectra of NaNO2 powder. Simulated spectra of: (c) satellite transition sidebands and (d) central transition centerband. (centerbands of CT are clipped for the better view of ST sidebands).
The temperature behavior of e 2qQ/h and 1/T1 are related to the spontaneous polarization of the sample. From the temperature dependence of T1, the activation energy for the reorientational motion of NO2⫺ ion is obtained and compared with single crystal data [8]. 23 Na MAS NMR spectra and spin-lattice relaxation times (T1) were measured at 105.805 MHz Larmor frequency (B0 9.4 T) with a Bruker DSX 400 spectrometer in the temperature range of 300–458 K. In addition, the data on the spin-lattice relaxation times measured at 52.9 MHz resonance frequency (B0 4.7 T) are compared to investigate the external magnetic field dependence of T1. In the case of 23Na NMR MAS, short single pulses of 0.6 ms were applied in order to excite a large spectral range of about 1.2 MHz. The pulse width of 0.6 ms, which implies the band width of an order of t 2 MHz, can cover the whole range of the 23Na MAS spectrum. Up to 1024 scans were accumulated for each spectrum. The repetition delay time was 2 s. The chemical shift was referenced to the external 1 M aqueous NaCl solution.
The 90⬚ pulse length of the solution was 4 ms. The spinning speed of 10 kHz with a fluctuation less than ^ 5 Hz was employed. The spin-lattice relaxation time for 23Na NMR line in NaNO2 powder was measured with an inversion recovery (p ⫺ t ⫺ p /2) by employing a wideline probe, where p and p /2 pulse lengths are 6.4 and 3.2 ms, respectively. The signal measured here is dominantly the central transition, and broadened by the second-order quadrupole interaction. For the case of the central transition for 23Na NMR in NaNO2, the magnetization recovery is given by the following equation [12]. S ∞ ⫺ S t S ∞
1 2
exp ⫺2W1 t ⫹ exp ⫺2W2 t; 1
where S(t) is the nuclear magnetization at time t, W1 and W2 are the transition probabilities corresponding to Dm ^ 1 and Dm ^ 2, respectively. Thus, the recovery curve is generally not a single exponential. W1 and W2 are angular dependent with respect to the
J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
549
Fig. 2. Quadrupole coupling constant (e 2qQ/h) of NaNO2 powder (A) and a single crystal (B) as a function of temperature.
applied magnetic field. The relaxation of 23Na NMR in NaNO2 at room temperature is known to be entirely quadrupolar [13]. In the case of powder sample with the quadrupole relaxation, it was reported [14] that W1 and W2 become equal to each other after an orientational average. In fact, the recovery traces of magnetization in the temperature range investigated are well fitted with a single exponential function. This indicates that perhaps W1 W2 ⬅ W. Thus, the spin-
lattice relaxation rate W ⬅ 1/T1 was determined from a fit of the recovery pattern given by the form A exp( ⫺ 2 Wt.). 23 Na MAS NMR spectra of NaNO2 is composed of a big center peak of the central transition and many relatively small sidebands mainly from satellite transitions, as shown in Fig. 1(a) and (b). From a computer simulation of the central transition centerband and satellite transition sidebands experimentally obtained
Fig. 3. e 2qQ/h of 23Na in NaNO2 powder versus Ps2. Tc of NaNO2 is 437 K.
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Fig. 4. h of 23Na in NaNO2 single crystals versus Ps.
in Fig. 1(a) and (b), the quadrupole coupling constant of 23Na in NaNO2 is determined to be e 2qQ/h 1.10 ^ 0.03 MHz at room temperature. This value is in good agreement with those reported previously [15–17]. The simulated spectra are shown in Fig. 1(c) and (d). The asymmetry parameter can be also obtained from the simulation. However, the error range in the determination of the asymmetry parameter is large compared to the parameter with the single crystal
case. Thus, the asymmetry parameter from the powder sample is not considered. The quadrupole coupling constants obtained from our NaNO2 powder samples are plotted as a function of temperature in Fig. 2, together with those obtained by Weiss and Biedenkapp from a single crystal [15]. The abrupt change of the quadrupole coupling constant is observed at Tc in both data sets. However, the difference of the quadrupole coupling constants of
Fig. 5. Spin-lattice relaxation rate (1/T1) of NaNO2 powder as a function of temperature.
J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
551
Fig. 6. ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps is plotted against the reciprocal temperature. The slopes are identical within the experimental uncertainties at two different Larmor frequencies.
powder and single crystal samples become pronounced on approaching Tc in Fig. 2. The e 2qQ/h of NaNO2 powder versus Ps2 is shown in Fig. 3, where Ps values are taken from single crystal data by Yamada et al. [18]. A linear relationship of e 2qQ/h versus Ps2 is obeyed almost up to the critical temperature (Tc 437 K), as expected from previous reports [6,7]. The quadrupole coupling constant is strongly affected by the spontaneous polarization of the material. Thus, the deviation near Tc in Figs. 2 and 3 may be explained with the common reason that the difference of the spontaneous polarizations in powder and single crystal samples is greater near Tc. The asymmetry parameter, h , had been measured as a function of temperature in 23Na NMR of NaNO2 single crystal by many researchers. However, up to now, the relationship of the asymmetry parameter with the spontaneous polarization was not noticed as far as we know. When the asymmetry parameter is plotted as a function of spontaneous polarization with the data measured by others [11,15], the linearity is satisfied up to Tc as shown in Fig. 4. This behavior is similar to the Landau’s theory for the second-order phase transition, as shown in 51V NMR in ferroelastic BiVO3 [19]. The study on the origin of this phenomenon is in progress in terms of order–disorder phase transition of NaNO2. The spin-lattice relaxation rates measured with the
resonance frequencies of 105.8 and 52.9 MHz are displayed in Fig. 5 as a function of temperature. The rate measured at 105.8 MHz shows the maximum 6.2 Hz at Tc (437 K). Both data show little dependence of the resonance frequency. The spin-lattice relaxation values measured with the resonance frequency of 8 and 24 MHz were reported to be the same [13]. The independence of the spin-lattice relaxation rate on the Larmor frequencies implies that the characteristic frequency associated with the reorientational motion of NO2⫺ group, n t 1/t , is much larger than the resonance frequency of 10 7 –10 8 Hz. Actually, the correlation frequency for the reorientation of the NO2⫺ group was found to be t 10 13 Hz [20]. In the ferroelectric phase the random motion of individual NO2⫺ ions converts progressively to a cooperative one accompanying with growing a net polarization as temperature decreases. In the temperature range between 230 and 437 K, Pandey and Hughes [8] deduced the relaxation of 23Na NMR due to the random thermal motion of the NO2⫺ ions as 1=T1 reo ⬃ 1 ⫺ P2s 1 ⫺ Ps exp DU=kT;
2
where reduced spontaneous polarization, Ps, is defined as tanh Tc =T Ps ⫹ P3s D: (1/T1)reo is the relaxation rate caused by the reorientational motion of NO2⫺ ion, D an anomalous volume expansion parameter which
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J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
was found to be 0.39, and DU is the potential barrier or activation energy for the reorientational motion of NO2⫺ ion. The magnetic and quadrupole interactions can contribute to relaxation of 23Na in NaNO2. In order to analyze 1/T1 data (Fig. 5) with Eq. (2), the contributions of the magnetic and quadrupole relaxation are removed. According to a previous report [21], the magnetic relaxation (1/T1)mag is dominant only below 150 K and its effect may be negligible in the temperature range investigated in this work. The contribution of the quadrupole relaxation, (1/T1)ph, caused by phonon of the crystal lattice is proportional to T 2 except at very low temperature, and reported as 4 × 10 ⫺7 T 2 s ⫺1 [7]. Thus, (1/T1)reo can be obtained by subtracting the values of estimated (1/T1)ph from 1/T1 in the range of 300–437 K from the relaxation data experimentally obtained. The linear relationship between ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps and 1/T is observed with DU 0.22 ^ 0.01 eV, as shown in Fig. 6. This DU value from powder samples agrees with a previously reported one [8] of 0.209 ^ 0.005 eV measured with a single crystal. The spontaneous polarization values in this study are taken from those measured in a single crystal. The spontaneous polarization in powder sample is generally known to be different from that of a single crystal because of the depolarization effect at grain boundary of powder samples [22,23]. Thus, a greater deviation near Tc shown in Figs. 2, 3 and 6 may be attributed to the larger spontaneous polarization difference of single crystal and powder samples near Tc. From this, it is tentatively inferred that the effect of depolarization at grain boundary of the powder samples becomes greater near Tc. In summary, the quadrupole coupling constant and spin-lattice relaxation time of 23Na NMR in the NaNO2 powder sample were investigated in the temperature range of 300–458 K. The temperature dependent behavior of the quadrupole coupling constant, asymmetry parameter and spin-lattice relaxation is analyzed in terms of the spontaneous polarization. The results are consistent with those of single crystals except near Tc. The deviation near Tc may be attributed to the greater spontaneous polarization difference of single crystal and powder samples near Tc. The linearity between the asymmetry
parameter and the spontaneous polarization in NaNO2 single crystals is newly reported.
Acknowledgements This work is partially supported by the MOST (the Korean Ministry of Science and Technology) through the KOYOU project in the KBSI (the Korean Basic Science Institute). The financial support from KOSEF (the Korea Science and Engineering Foundation) to Dr J.K. Jung through the Postdoctral Training Support Program in Korea is also fully acknowledged.
References [1] A. Rigamonti, Phys. Rev. Lett. 19 (1967) 436. [2] G. Petersen, P.J. Bray, J. Chem. Phys. 64 (1976) 522. [3] R. Ambrosetti, R. Angelone, A. Colligiani, A. Rigamonti, Phys. Rev. B15 (1977) 4318. [4] S. Towta, D.G. Hughes, J. Phys.: Condens. Matter 2 (1990) 2021. [5] S.H. Choh, J. Korean Phys. Soc. 32 (1998) S624. [6] H. Betsuyaku, J. Phys. Soc. Jpn. 27 (1969) 1485. [7] D.C. Dening, P.A. Casabella, J. Mag. Res. 38 (1980) 277. [8] L. Pandey, D.G. Hughes, J. Phys.: Condens. Matter 4 (1992) 6889. [9] I.P. Aleksandrova, R. Blinc, B. Topic, S. Zumer, A. Rigamonti, Physca Stat. Sol. (a) 61 (1980) 95. [10] S.H. Choh, J. Lee, K.H. Kang, Ferroelectrics 36 (1981) 297. [11] K.T. Han, J.C. Ho, S.H. Choh, New Physics (Korean Phys. Soc.) 32 (1992) 553. [12] M.H. Cohen, F. Reif, Solid St. Phys. 5 (1957) 321. [13] G. Bonera, F. Borsa, A. Rigamonti, Phys. Rev. B2 (1970) 2784. [14] N. Okubo, M. Igarashi, R. Yoshizaki, Z. Naturforsch. 51a (1996) 277. [15] V.A. Weiss, D. Biedenkapp, Z. Naturforsch. 17a (1962) 794. [16] A. Samoson, E. Kundla, E. Lippmaa, J. Magn. Reson. 49 (1982) 350. [17] J. Skibsted, N.C. Nielsen, H. Bildsoe, H.J. Jakobsen, J. Magn. Reson. 95 (1991) 88. [18] Y. Yamada, I. Shibuya, S. Hoshino, J. Phys. Soc. Jpn. 18 (1963) 1594. [19] T.H. Yeom, S.H. Choh, J. Korean Phys. Soc. 33 (1998) L529. [20] K.D. Ehrhardt, K.H. Michel, Z. Phys. 41 (1981) 329. [21] D.G. Hughes, J. Phys.: Condens. Matter 5 (1993) 2025. [22] W.L. Zhong, Y.G. Wang, P.L. Zhang, B.D. Qu, Phys. Rev. B50 (1994) 698. [23] W.Y. Shih, W.H. Shih, I.A. Aksay, Phys. Rev. B50 (1994) 15575.
Solid State Communications 110 (1999) 547–552
Temperature dependence of 23Na NMR quadrupole parameters and spin-lattice relaxation rate in NaNO2 powder J.K. Jung a, O.H. Han a,*, S.H. Choh b a
Magnetic Resonance Research Group, Korea Basic Science Institute, Yeueundong 52, Yoosung-goo, Taejeon 305-333, South Korea b Department of Physics, Korea University, Seoul 136-701, South Korea Received 18 January 1999; accepted 5 March 1999 by H. Akai
Abstract The nuclear quadrupole coupling constant (e 2qQ/h) and the spin-lattice relaxation rate (1/T1) of 23Na NMR in the NaNO2 powder were investigated by employing a magic angle spinning probe and a wideline probe, respectively, at 9.4 T as a function of temperature (T) in the range of 300–458 K. The linearity between e 2qQ/h and the squared spontaneous polarization (Ps2) was obeyed up to near the critical temperature (Tc 437 K), which is consistent with the previous reports. Moreover, the asymmetry parameter (h ) at 23Na site is found to be linear with Ps, firstly noticed in this work. The linearity between ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps and 1/T is found to be satisfied up to near the Tc, where (1/T1)reo is the relaxation rate for the reorientational motion of the NO2⫺. From this linearity, the reorientational motion of NO2⫺ ion in powder samples is found to have an activation energy, DU 0.22 ^ 0.01 eV, which is in good agreement with the value obtained with single crystals. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Ferroelectrics; D. Phase transitions; D. Order–disorder effects; E. Nuclear resonances
The spontaneous polarization (Ps) of the ferroelectric NaNO2 which undergoes an order–disorder transition [1–5] at Tc 437 K, influences directly the quadrupole coupling constant (e 2qQ/h) of 23Na and its spin-lattice relaxation [6–8]. Betsuyaku [6], and Dening and Casabella [7] showed that the quadrupole coupling constant of 23Na in the NaNO2 single crystal should be proportional to the square of the spontaneous polarization, because the Na ⫹ ion resides at a site of inversion symmetry in the paraelectric phase. Meanwhile, Pandey and Hughes [8] reported that the 23 Na NMR relaxation is mainly caused by the reorientational motion of NO2⫺ ions in the range of * Corresponding author. Tel.: ⫹ 82-42-865-3436; fax: ⫹ 82-42865-3419. E-mail address: [email protected] (O.H. Han)
230–437 K, which was explained by introducing the spontaneous polarization. 23Na NMR studies of NaNO2 have been mostly carried out with single crystals [6–11], in relation to the spontaneous polarization. However, the investigations with the powder sample are quite rare because of the low spectral resolution as a result of the quadrupole broadening and distributions of both chemical shift and quadrupole interaction parameters. The magic angle spinning (MAS) at fast spinning rate was applied for increased spectral resolution which has made it easy to obtain the quadrupole interaction parameters with improved accuracy. In this work, the temperature dependence of e 2qQ/h and spin-lattice relaxation rate (1/T1) for 23Na NMR in NaNO2 powder sample has been investigated by employing a MAS and a wideline probe, respectively.
0038-1098/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00128-3
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J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
Fig. 1. Experimental: (a) satellite transition sidebands and (b) central transition centerband of 23Na MAS NMR spectra of NaNO2 powder. Simulated spectra of: (c) satellite transition sidebands and (d) central transition centerband. (centerbands of CT are clipped for the better view of ST sidebands).
The temperature behavior of e 2qQ/h and 1/T1 are related to the spontaneous polarization of the sample. From the temperature dependence of T1, the activation energy for the reorientational motion of NO2⫺ ion is obtained and compared with single crystal data [8]. 23 Na MAS NMR spectra and spin-lattice relaxation times (T1) were measured at 105.805 MHz Larmor frequency (B0 9.4 T) with a Bruker DSX 400 spectrometer in the temperature range of 300–458 K. In addition, the data on the spin-lattice relaxation times measured at 52.9 MHz resonance frequency (B0 4.7 T) are compared to investigate the external magnetic field dependence of T1. In the case of 23Na NMR MAS, short single pulses of 0.6 ms were applied in order to excite a large spectral range of about 1.2 MHz. The pulse width of 0.6 ms, which implies the band width of an order of t 2 MHz, can cover the whole range of the 23Na MAS spectrum. Up to 1024 scans were accumulated for each spectrum. The repetition delay time was 2 s. The chemical shift was referenced to the external 1 M aqueous NaCl solution.
The 90⬚ pulse length of the solution was 4 ms. The spinning speed of 10 kHz with a fluctuation less than ^ 5 Hz was employed. The spin-lattice relaxation time for 23Na NMR line in NaNO2 powder was measured with an inversion recovery (p ⫺ t ⫺ p /2) by employing a wideline probe, where p and p /2 pulse lengths are 6.4 and 3.2 ms, respectively. The signal measured here is dominantly the central transition, and broadened by the second-order quadrupole interaction. For the case of the central transition for 23Na NMR in NaNO2, the magnetization recovery is given by the following equation [12]. S ∞ ⫺ S t S ∞
1 2
exp ⫺2W1 t ⫹ exp ⫺2W2 t; 1
where S(t) is the nuclear magnetization at time t, W1 and W2 are the transition probabilities corresponding to Dm ^ 1 and Dm ^ 2, respectively. Thus, the recovery curve is generally not a single exponential. W1 and W2 are angular dependent with respect to the
J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
549
Fig. 2. Quadrupole coupling constant (e 2qQ/h) of NaNO2 powder (A) and a single crystal (B) as a function of temperature.
applied magnetic field. The relaxation of 23Na NMR in NaNO2 at room temperature is known to be entirely quadrupolar [13]. In the case of powder sample with the quadrupole relaxation, it was reported [14] that W1 and W2 become equal to each other after an orientational average. In fact, the recovery traces of magnetization in the temperature range investigated are well fitted with a single exponential function. This indicates that perhaps W1 W2 ⬅ W. Thus, the spin-
lattice relaxation rate W ⬅ 1/T1 was determined from a fit of the recovery pattern given by the form A exp( ⫺ 2 Wt.). 23 Na MAS NMR spectra of NaNO2 is composed of a big center peak of the central transition and many relatively small sidebands mainly from satellite transitions, as shown in Fig. 1(a) and (b). From a computer simulation of the central transition centerband and satellite transition sidebands experimentally obtained
Fig. 3. e 2qQ/h of 23Na in NaNO2 powder versus Ps2. Tc of NaNO2 is 437 K.
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Fig. 4. h of 23Na in NaNO2 single crystals versus Ps.
in Fig. 1(a) and (b), the quadrupole coupling constant of 23Na in NaNO2 is determined to be e 2qQ/h 1.10 ^ 0.03 MHz at room temperature. This value is in good agreement with those reported previously [15–17]. The simulated spectra are shown in Fig. 1(c) and (d). The asymmetry parameter can be also obtained from the simulation. However, the error range in the determination of the asymmetry parameter is large compared to the parameter with the single crystal
case. Thus, the asymmetry parameter from the powder sample is not considered. The quadrupole coupling constants obtained from our NaNO2 powder samples are plotted as a function of temperature in Fig. 2, together with those obtained by Weiss and Biedenkapp from a single crystal [15]. The abrupt change of the quadrupole coupling constant is observed at Tc in both data sets. However, the difference of the quadrupole coupling constants of
Fig. 5. Spin-lattice relaxation rate (1/T1) of NaNO2 powder as a function of temperature.
J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
551
Fig. 6. ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps is plotted against the reciprocal temperature. The slopes are identical within the experimental uncertainties at two different Larmor frequencies.
powder and single crystal samples become pronounced on approaching Tc in Fig. 2. The e 2qQ/h of NaNO2 powder versus Ps2 is shown in Fig. 3, where Ps values are taken from single crystal data by Yamada et al. [18]. A linear relationship of e 2qQ/h versus Ps2 is obeyed almost up to the critical temperature (Tc 437 K), as expected from previous reports [6,7]. The quadrupole coupling constant is strongly affected by the spontaneous polarization of the material. Thus, the deviation near Tc in Figs. 2 and 3 may be explained with the common reason that the difference of the spontaneous polarizations in powder and single crystal samples is greater near Tc. The asymmetry parameter, h , had been measured as a function of temperature in 23Na NMR of NaNO2 single crystal by many researchers. However, up to now, the relationship of the asymmetry parameter with the spontaneous polarization was not noticed as far as we know. When the asymmetry parameter is plotted as a function of spontaneous polarization with the data measured by others [11,15], the linearity is satisfied up to Tc as shown in Fig. 4. This behavior is similar to the Landau’s theory for the second-order phase transition, as shown in 51V NMR in ferroelastic BiVO3 [19]. The study on the origin of this phenomenon is in progress in terms of order–disorder phase transition of NaNO2. The spin-lattice relaxation rates measured with the
resonance frequencies of 105.8 and 52.9 MHz are displayed in Fig. 5 as a function of temperature. The rate measured at 105.8 MHz shows the maximum 6.2 Hz at Tc (437 K). Both data show little dependence of the resonance frequency. The spin-lattice relaxation values measured with the resonance frequency of 8 and 24 MHz were reported to be the same [13]. The independence of the spin-lattice relaxation rate on the Larmor frequencies implies that the characteristic frequency associated with the reorientational motion of NO2⫺ group, n t 1/t , is much larger than the resonance frequency of 10 7 –10 8 Hz. Actually, the correlation frequency for the reorientation of the NO2⫺ group was found to be t 10 13 Hz [20]. In the ferroelectric phase the random motion of individual NO2⫺ ions converts progressively to a cooperative one accompanying with growing a net polarization as temperature decreases. In the temperature range between 230 and 437 K, Pandey and Hughes [8] deduced the relaxation of 23Na NMR due to the random thermal motion of the NO2⫺ ions as 1=T1 reo ⬃ 1 ⫺ P2s 1 ⫺ Ps exp DU=kT;
2
where reduced spontaneous polarization, Ps, is defined as tanh Tc =T Ps ⫹ P3s D: (1/T1)reo is the relaxation rate caused by the reorientational motion of NO2⫺ ion, D an anomalous volume expansion parameter which
552
J.K. Jung et al. / Solid State Communications 110 (1999) 547–552
was found to be 0.39, and DU is the potential barrier or activation energy for the reorientational motion of NO2⫺ ion. The magnetic and quadrupole interactions can contribute to relaxation of 23Na in NaNO2. In order to analyze 1/T1 data (Fig. 5) with Eq. (2), the contributions of the magnetic and quadrupole relaxation are removed. According to a previous report [21], the magnetic relaxation (1/T1)mag is dominant only below 150 K and its effect may be negligible in the temperature range investigated in this work. The contribution of the quadrupole relaxation, (1/T1)ph, caused by phonon of the crystal lattice is proportional to T 2 except at very low temperature, and reported as 4 × 10 ⫺7 T 2 s ⫺1 [7]. Thus, (1/T1)reo can be obtained by subtracting the values of estimated (1/T1)ph from 1/T1 in the range of 300–437 K from the relaxation data experimentally obtained. The linear relationship between ln 1=T1 reo = 1 ⫺ P2s 1 ⫺ Ps and 1/T is observed with DU 0.22 ^ 0.01 eV, as shown in Fig. 6. This DU value from powder samples agrees with a previously reported one [8] of 0.209 ^ 0.005 eV measured with a single crystal. The spontaneous polarization values in this study are taken from those measured in a single crystal. The spontaneous polarization in powder sample is generally known to be different from that of a single crystal because of the depolarization effect at grain boundary of powder samples [22,23]. Thus, a greater deviation near Tc shown in Figs. 2, 3 and 6 may be attributed to the larger spontaneous polarization difference of single crystal and powder samples near Tc. From this, it is tentatively inferred that the effect of depolarization at grain boundary of the powder samples becomes greater near Tc. In summary, the quadrupole coupling constant and spin-lattice relaxation time of 23Na NMR in the NaNO2 powder sample were investigated in the temperature range of 300–458 K. The temperature dependent behavior of the quadrupole coupling constant, asymmetry parameter and spin-lattice relaxation is analyzed in terms of the spontaneous polarization. The results are consistent with those of single crystals except near Tc. The deviation near Tc may be attributed to the greater spontaneous polarization difference of single crystal and powder samples near Tc. The linearity between the asymmetry
parameter and the spontaneous polarization in NaNO2 single crystals is newly reported.
Acknowledgements This work is partially supported by the MOST (the Korean Ministry of Science and Technology) through the KOYOU project in the KBSI (the Korean Basic Science Institute). The financial support from KOSEF (the Korea Science and Engineering Foundation) to Dr J.K. Jung through the Postdoctral Training Support Program in Korea is also fully acknowledged.
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