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Correlation between NMR and nonlinear optical properties at boron sites in nonlinear optical β-BaB2O4 single crystals
Solid State Communications 159 (2013) 41–44
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Correlation between NMR and nonlinear optical properties at boron sites in nonlinear optical b-BaB2O4 single crystals Ae Ran Lim a,n, In Gyoo Kim b a b
Department of Science Education, Jeonju University, Jeonju 560-759, Republic of Korea Electronics and Telecommunications Research Institute, Daejeon 305-700, Republic of Korea
a r t i c l e i n f o
abstract
Article history: Received 7 October 2012 Received in revised form 10 December 2012 Accepted 21 January 2013 by F. Peeters Available online 29 January 2013
To obtain detailed information about the nonlinear optical (NLO) properties of b-BaB2O4 crystals, the spin–lattice relaxation time T1 of 11B was measured. In addition, the T1 values for 11B in Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals were obtained. We analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, T1, and the NLO properties at the boron sites in these crystals. A correlation seems to exist between the asymmetry parameter of the 3-coordinated boron nucleus, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons, and the NLO coefficient of each crystal, whereas the quadrupole coupling constant and T1 showed no correlation with the NLO coefficient. & 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Single crystal C. Crystal structure D. Nonlinear optical properties E. NMR
1. Introduction Nonlinear optical (NLO) materials have played an important role in laser science and technology, and the search for NLO materials, particularly those suitable for ultraviolet (UV) and farinfrared applications, is still very active. Borate crystals such as Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 have received a great deal of attention with regard to the generation of UV light using wavelength conversion because of their excellent NLO properties in the UV region [1,2]. Among the NLO crystals, beta barium metaborate (b-BaB2O4) is promising because of its large second harmonic generation (SHG) coefficients [1]. Developments in the rapidly evolving field of nanoscience and nanotechnology, where the size and shape of materials are crucial to their optoelectronic properties, are worth noting, especially the preparation of various b-BaB2O4 nanostructures such as nanowires, nanorods, and nanotubes and studies of their SHG performance on the nanoscale [3–6]. Anisotropy in the electrical and dielectric properties of b-BaB2O4 single crystals was recently reported and discussed [7,8]. In addition, progress in the growth techniques of large b-BaB2O4 single crystals has been reported [5,9,10]. The 11B environment has been characterized by magic angle spinning analysis of 11B and nuclear magnetic resonance (NMR) studies of 11B in b-BaB2O4 single crystals [11,12]. The 11B NMR work reported two B-sites with very similar quadrupolar coupling constants and asymmetry parameters: e2qQ/h ¼2.455 MHz and
n
Corresponding author. Tel.: þ82 63 220 2514; fax: þ82 63 220 2053. E-mail addresses: [email protected], [email protected] (A.R. Lim).
0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2013.01.020
Z ¼0.684 for B(1), and e2qQ/h¼2.486 MHz and Z ¼0.644 for B(2). Further, the quadrupolar coupling constants for 135Ba and 137Ba were e2qQ/h ¼1.49 MHz and e2qQ/h¼22.8 MHz, respectively [13]. However, the local 11B environment has never been probed directly by examining the 11B spin–lattice relaxation time. In this study, the mechanisms underlying the NLO properties of b-BaB2O4 are determined from its NMR parameters and relaxation time measurements. Specifically, to obtain detailed information about the dynamics of this crystal, the spin–lattice relaxation time T1 of 11B NMR was measured using a pulse NMR spectrometer as a function of temperature. In addition, the T1 values of 11B in NLO Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals were measured at room temperature to determine the relationship between the relaxation time and the NLO properties. Finally, we analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, the spin–lattice relaxation time, and the NLO properties at boron sites in these crystals.
2. Crystal structure BaB2O4 has two known phases: the quenched high-temperature form (a-BaB2O4) of space group R3c (C63v), and the low-temperature phase (b-BaB2O4) of the same space group. Because a-BaB2O4 is centrosymmetric, it does not exhibit NLO properties. The crystal structure of the low-temperature phase is trigonal with unit cell ˚ dimensions of a¼8.380 and a ¼96.651 (hexagonal cell: a¼12.519 A, ˚ as shown in Fig. 1 [14–16]. A primitive unit cell c¼12.723 A),
42
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
4. Experimental results and analysis We describe the recovery laws for the quadrupole relaxation process in the 11B (I ¼3/2) nuclear spin system, which are given by non-exponential functions. The temperature dependence of the relaxation time indicates fluctuations in the electric field gradient (EFG) tensor driven by thermally activated motion. The saturation recovery traces for the central line of 11B with dominant quadrupole relaxation can be represented by a combination of two exponential functions, as shown in Eq. (1) [19,20]: ½Sð1Þ2SðtÞ=Sð1Þ ¼ 0:5½expð22W 1 tÞ þ expð22W 2 tÞ
Fig. 1. Crystal structure of b-BaB2O4, which consists of nearly planar (B3O6)3 rings perpendicular to the polar axis that are bonded through the barium atoms at room temperature.
contains two Ba3(B3O6)2 molecules. The structure consists of nearly planar anionic (B3O6)3 ring groups with D3h symmetry, and the anion plane is perpendicular to the three-fold axis. Two types of boron atoms, B(1) and B(2), form different boron–oxygen rings and therefore lie at chemically inequivalent sites [17]. These anionic groups are bonded ionically through barium ions. There are four anionic groups in each primitive unit cell; they are distributed over two symmetrically independent positions. The BaB2O4 crystal consists of planar (B3O6)3 rings. The nearest-neighbor B(1)–O bond ˚ 1.415 A, ˚ and 1.396 A, ˚ and the average distance lengths are 1.329 A, ˚ whereas the B(2)–O bond lengths are 1.336 A, ˚ 1.398 A, ˚ is 1.377 A, ˚ and the average distance is 1.371 A. ˚ and 1.378 A,
ð1Þ
where S(N) is the thermal equilibrium magnetization, and S(t) is the nuclear magnetization at time t. Further, W1 and W2 are the transition probabilities for Dm¼ 71 and Dm¼ 72, respectively. Thus, the relaxation time is given by T1 ¼5/[2(W1 þ4W2)]. 11 B is a quadrupolar nucleus with a nuclear spin of 3/2. The 11B NMR spectrum of b-BaB2O4 crystals consists of a central line and two satellite lines. When the magnetic field was applied along the aþ501-axis in the ac plane of the crystal, the resonance lines were observed. Therefore, if the local symmetry around the boron atoms is not cubic, a boron atom yields three resonance lines, and 12 boron atoms in a BaB2O4 unit cell yields a total of 24 satellite lines, as shown in Fig. 2. The 11B spectrum obtained at room temperature (Fig. 2) indicates the presence of two types of chemically inequivalent 11B nuclei, which correspond to B(1) and B(2) as described in Section 1 [12]. The zero point of the horizontal axis corresponds to the resonance frequency of the 11 B nucleus (i.e., 128.34 MHz). The satellite transitions are well resolved from the central line, and the signal intensity of the central line is stronger than those of the other lines. The magnitudes of the quadrupole parameters of 11B nuclei are in the order of MHz, so the central resonance line is typically split and shifted. The separations between the resonance lines do not vary with temperature for both B(1) and B(2). The no variation in temperature independence of the splitting of the 11B resonance lines indicates that the EFG at the B-sites remains unchanged, which in turn means that the atoms neighboring the 11B nuclei are not displaced when the temperature changes. Nuclear magnetization recovery curves for the central lines of 11 B were obtained by measuring the nuclear magnetization after applying saturation pulses. Fig. 3 shows the saturation recovery
3. Experimental method Single crystals of b-BaB2O4 were grown by the modified flux method at crystal manufacturing company (CASIX) in China [18]. The crystal was cut along two crystallographic axes (the a- and c-axes), and on another axis (the b-axis) perpendicular to these axes. The NMR signals of the 11B nuclei in the BaB2O4 single crystals were measured using a Bruker DSX 400 FT NMR spectrometer at the Korea Basic Science Institute. The static magnetic field was 9.4 T, and the central radio frequency was set to o0/ 2p ¼128.34 MHz. The spin–lattice relaxation times were measured by applying a pulse sequence of p/2 t p/2. The nuclear magnetizations S(t) of the 11B nuclei at time t after the p/2 pulse were determined from each saturation recovery sequence following the pulse. The width of the p/2 pulse was 0.25 ms for 11B. Temperature-dependent NMR measurements were made over the temperature range 180–430 K. The samples were maintained at a constant temperature by controlling the nitrogen gas flow and heater current.
Fig. 2. 11B NMR spectra of BaB2O4 single crystal at room temperature. Static magnetic field B is parallel to the a þ501-axis in the ac plane. Inset: central 11B NMR lines indicating the presence of two types of chemically inequivalent 11B nuclei, B(1) and B(2).
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
traces for the central resonance lines of B-sites in b-BaB2O4 crystals at various delay times at room temperature. T1 was determined directly from the slope of a plot of log [S(N) S(t)]/ S(N) versus time t. It is very well known that the relaxation time
Fig. 3. Saturation recovery traces of
43
T1 can be defined only if the delay time dependence of the magnetization can be described by the two exponential functions given in Eq. (1). Of course, one might introduce a useful combination of the transition probabilities W1 and W2 according to Eq. (1) and explain that the introduction of this constant is reasonable because it leads to the correct relaxation time, T1 ¼1/2W1 for W1 ¼W2, where a single exponential relaxation function can be derived from Eq. (1). The slopes of the recovery traces at each temperature differ. The temperature dependences of the spin– lattice relaxation time T1 of 11B NMR are shown in Fig. 4. The relaxation times of the 3-coordinated B(1) atoms and 3-coordinated B(2) atoms can be distinguished. T1 decreases slowly with increasing temperature. The spin–lattice relaxation times for the B(1) and B(2) atoms are very similar. In simple NMR theory, the overall behavior of the spin–lattice relaxation time for random motions is described in terms of the fastmotion region, where it is given by T1 exp(Ea/kBT). Here Ea is the activation energy, which was determined from the slopes of the straight-line portions of the semilog plots of the relaxation time vs. 1000/T, as shown in Fig. 4. The activation energy for B(1) was determined to be 2.9970.22 kJ/mol and 3.0770.24 kJ/mol, respectively, which are the same within the experimental error range. Further, the activation energy for B(2) was 4.1670.08 kJ/mol.
11
B-site as functions of delay time t.
5. Discussion
Fig. 4. Temperature dependence of spin–lattice relaxation time T1 for B(1) and B(2) in a BaB2O4 single crystal.
Many studies have discussed bond parameter methods, anharmonic oscillator models, and the bond charge model. After this work, Chen’s group [1,2] turned its attention to borates. They recognized that borate compounds have numerous structural types because borate atoms may have either 3- or 4-fold coordination. This structural complexity of borate compounds produces a great variation in the possible structural types favorable for NLO effects, and anionic group theory can be used to systematically elucidate which structural unit is most likely to exhibit large nonlinearities. In addition, Chen’s group [21–23] suggested that the p-conjugated orbital system of an acentric planar organic molecule with charge transfer between the donor and acceptor substituent groups was mainly responsible for the presence of a large second-order susceptibility in such molecules. We propose NMR studies as a microscopic tool for evaluating and identifying NLO borate materials. The parameters of the quadrupole Hamiltonian and the NLO properties have an interesting feature. An inspection of our previous results seems to reveal close relationships between the parameters of the quadrupole Hamiltonian and the effective NLO coefficients for SHG [24]. We considered the relationship between the asymmetry parameter Z, the quadrupole coupling
Table 1 Values for the largest nonlinear optical coefficient, dlar, the asymmetry parameter, Z, the quadrupole coupling constants, e2qQ/h, the spin–lattice relaxation time, T1, and the ratio of number of 3-coordination for number of 3-coordination plus number of 4-coordination, N3, for 11B nucleus in Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals at room temperature. dlar (1064 nm) (pm/V)
Z
e2qQ/h (kHz)
T1 (s)
N3
References
Li2B4O7
0.93
0.167 0.53
3-coordinated B(1) 2600 4-coordinated B(2) 526.8
421 (present work)
0.5
[25,26]
LiCsB6O10
0.95
0.275 0.455
3-coordinated B(1) 2580 4-coordinated B(2) 230
6 (present work)
0.5
[24]
LiB3O5
1.05
0.279 0.203 0.120
3-coordinated B(1) 2615 3-coordinated B(1) 2695 4-coordinated B(2) 177.1
1181 (present work)
0.7
[27,28]
BaB2O4
2.2
0.684 0.644
3-coordinated B(1) 2455 3-coordinated B(2) 2486
769 (present work)
1
[12]
44
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
used to explain the structure–property relationships in most known NLO crystals of various structural types and to establish guidelines for identifying and developing new NLO materials.
Acknowledgment This research was supported by the Basic Science Research program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2012001763).
References
Fig. 5. Correlation between the asymmetry parameter Z, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons N3, the quadrupole coupling constant e2qQ/h, and the largest NLO coefficient.
constant e2qQ/h, the spin–lattice relaxation time T1, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons N3, and the largest secondorder NLO coefficient, as listed in Table 1 [12,24–28]. Fig. 5 shows the relationship between the largest NLO coefficient and Z, N3, and e2qQ/h. Note that NLO borate materials with NLO coefficients of 1.2–2.0 pm/V have not yet been reported.
6. Conclusion To obtain detailed information about the NLO properties of bBaB2O4 crystals, the spin–lattice relaxation time T1 of 11B was measured. We analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, T1, and the NLO properties at the boron sites in these crystals. A correlation seems to exist between Z, N3, and the NLO coefficient of each crystal, whereas e2qQ/h and the spin–lattice relaxation time T1 show no correlation with the NLO coefficient. This research can be
[1] C.T. Chen, B.C. Wu, A.D. Jiang, G.M. You, Sci. Sin. B 28 (1985) 235. [2] C.T. Chen, Development of New Nonlinear Optical Crystals in the Borate Series, Harwood Academic Publishers, Switzerland, 1993. [3] J. Hu, T.W. Odom, C.M. Lieber, Acc. Chem. Res. 32 (1999) 435. [4] Y.N. Xia, P.D. Yang, Y.G. Sun, Y.Y. Wu, B. Mayer, B. Gates, Y.D. Yin, F. Kim, H.Q. Yan, Adv. Mater. 15 (2003) 353. [5] Q. Zhao, X. Zhu, X. Bai, H. Fan, Y. Xie, Eur. J. Inorg. Chem. 1829 (2007). [6] J. Zhang, S. Liang, G. He, Chem. Lett. 38 (2009) 500. [7] V. Trnovcova, P.P. Fedorov, A.E. Kokh, I. Furar, J. Phys. Chem. Solid 68 (2007) 1024. [8] V. Trnovcova, M. Kubliha, A. Kokh, P.P. Fedorov, R.M. Zakalyukin, Russ. J. Electrochem. 47 (2011) 531. [9] D. Perlov, S. Livneh, P. Czechowicz, A. Goldgirsh, D. Loiacono, Cryst. Res. Technol. 46 (2011) 651. [10] A.E. Kokh, T.B. Bekker, V.A. Vlezko, K.A. Kokh, J. Cryst. Growth 318 (2011) 602. [11] N.J. Clayden, S. Esposito, A. Aronne, P. Pernice, J. Non-Cryst. Solids 249 (1999) 99. [12] I.G. Kim, S.H. Choh, J. Phys.: Condens. Matter 11 (1999) 8283. [13] A. Sutrisno, C. Lu, R.H. Lipson, Y. Huang, J. Phys. Chem. C 113 (2009) 21196. [14] S.F. Lu, M.Y. He, J.L. Huang, Acta Phys. Sin. 31 (1982) 948. [15] J. Liebertz, S. Stahr, Z. Kristallogr. 165 (1983) 91. [16] R. Frohlich, Z. Kristallogr. 168 (1984) 109. [17] S.F. Lu, Z.X. Huang, J.L. Huang, Acta Crystallogr. C62 (2006) i73. [18] R.S. Feigelson, R.J. Raymakers, R.K. Route, J. Cryst. Growth 97 (1989) 352. [19] J. Dolinsek, D. Arcon, B. Zalar, R. Pirc, R. Blinc, R. Kind, Phys. Rev. B 54 (1996) R6811. [20] A. Abragam, The Principles of Nuclear Magnetism, Oxford University Press, 1961. [21] C. Chen, B. Wu, A. Jiang, G. You, Sci. Sin. B28 (1985) 235. [22] Y. Wu, C. Chen, Acta Phys. Sin. 35 (1986) 1. [23] C. Chen, Y. Wu, A. Jiang, B. Wu, G. You, R. Li, S. Lin, J. Opt. Soc. Am. B6 (1989) 616. [24] A.R. Lim, J.W. Kim, C.S. Yoon, J. Phys. Soc. Jpn. 72 (2003) 1774. [25] I. Yu, V. Ivanov, K.S. Burak, Sov. Alexandrov, Phys. Solid State 32 (1990) 1955. [26] N.K. Sung, S.H. Choh, A.R. Lim, J.N. Kim, Sae Mulli 35 (1995) 670. [27] I.G. Kim, S.H. Choh, J.N. Kim, J. Kor, Phys. Soc. 32 (1998) S669. [28] A.R. Lim, J.W. Kim, C.S. Yoon, J. Appl. Phys. 94 (2003) 5095.
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Correlation between NMR and nonlinear optical properties at boron sites in nonlinear optical b-BaB2O4 single crystals Ae Ran Lim a,n, In Gyoo Kim b a b
Department of Science Education, Jeonju University, Jeonju 560-759, Republic of Korea Electronics and Telecommunications Research Institute, Daejeon 305-700, Republic of Korea
a r t i c l e i n f o
abstract
Article history: Received 7 October 2012 Received in revised form 10 December 2012 Accepted 21 January 2013 by F. Peeters Available online 29 January 2013
To obtain detailed information about the nonlinear optical (NLO) properties of b-BaB2O4 crystals, the spin–lattice relaxation time T1 of 11B was measured. In addition, the T1 values for 11B in Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals were obtained. We analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, T1, and the NLO properties at the boron sites in these crystals. A correlation seems to exist between the asymmetry parameter of the 3-coordinated boron nucleus, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons, and the NLO coefficient of each crystal, whereas the quadrupole coupling constant and T1 showed no correlation with the NLO coefficient. & 2013 Elsevier Ltd. All rights reserved.
Keywords: A. Single crystal C. Crystal structure D. Nonlinear optical properties E. NMR
1. Introduction Nonlinear optical (NLO) materials have played an important role in laser science and technology, and the search for NLO materials, particularly those suitable for ultraviolet (UV) and farinfrared applications, is still very active. Borate crystals such as Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 have received a great deal of attention with regard to the generation of UV light using wavelength conversion because of their excellent NLO properties in the UV region [1,2]. Among the NLO crystals, beta barium metaborate (b-BaB2O4) is promising because of its large second harmonic generation (SHG) coefficients [1]. Developments in the rapidly evolving field of nanoscience and nanotechnology, where the size and shape of materials are crucial to their optoelectronic properties, are worth noting, especially the preparation of various b-BaB2O4 nanostructures such as nanowires, nanorods, and nanotubes and studies of their SHG performance on the nanoscale [3–6]. Anisotropy in the electrical and dielectric properties of b-BaB2O4 single crystals was recently reported and discussed [7,8]. In addition, progress in the growth techniques of large b-BaB2O4 single crystals has been reported [5,9,10]. The 11B environment has been characterized by magic angle spinning analysis of 11B and nuclear magnetic resonance (NMR) studies of 11B in b-BaB2O4 single crystals [11,12]. The 11B NMR work reported two B-sites with very similar quadrupolar coupling constants and asymmetry parameters: e2qQ/h ¼2.455 MHz and
n
Corresponding author. Tel.: þ82 63 220 2514; fax: þ82 63 220 2053. E-mail addresses: [email protected], [email protected] (A.R. Lim).
0038-1098/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ssc.2013.01.020
Z ¼0.684 for B(1), and e2qQ/h¼2.486 MHz and Z ¼0.644 for B(2). Further, the quadrupolar coupling constants for 135Ba and 137Ba were e2qQ/h ¼1.49 MHz and e2qQ/h¼22.8 MHz, respectively [13]. However, the local 11B environment has never been probed directly by examining the 11B spin–lattice relaxation time. In this study, the mechanisms underlying the NLO properties of b-BaB2O4 are determined from its NMR parameters and relaxation time measurements. Specifically, to obtain detailed information about the dynamics of this crystal, the spin–lattice relaxation time T1 of 11B NMR was measured using a pulse NMR spectrometer as a function of temperature. In addition, the T1 values of 11B in NLO Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals were measured at room temperature to determine the relationship between the relaxation time and the NLO properties. Finally, we analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, the spin–lattice relaxation time, and the NLO properties at boron sites in these crystals.
2. Crystal structure BaB2O4 has two known phases: the quenched high-temperature form (a-BaB2O4) of space group R3c (C63v), and the low-temperature phase (b-BaB2O4) of the same space group. Because a-BaB2O4 is centrosymmetric, it does not exhibit NLO properties. The crystal structure of the low-temperature phase is trigonal with unit cell ˚ dimensions of a¼8.380 and a ¼96.651 (hexagonal cell: a¼12.519 A, ˚ as shown in Fig. 1 [14–16]. A primitive unit cell c¼12.723 A),
42
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
4. Experimental results and analysis We describe the recovery laws for the quadrupole relaxation process in the 11B (I ¼3/2) nuclear spin system, which are given by non-exponential functions. The temperature dependence of the relaxation time indicates fluctuations in the electric field gradient (EFG) tensor driven by thermally activated motion. The saturation recovery traces for the central line of 11B with dominant quadrupole relaxation can be represented by a combination of two exponential functions, as shown in Eq. (1) [19,20]: ½Sð1Þ2SðtÞ=Sð1Þ ¼ 0:5½expð22W 1 tÞ þ expð22W 2 tÞ
Fig. 1. Crystal structure of b-BaB2O4, which consists of nearly planar (B3O6)3 rings perpendicular to the polar axis that are bonded through the barium atoms at room temperature.
contains two Ba3(B3O6)2 molecules. The structure consists of nearly planar anionic (B3O6)3 ring groups with D3h symmetry, and the anion plane is perpendicular to the three-fold axis. Two types of boron atoms, B(1) and B(2), form different boron–oxygen rings and therefore lie at chemically inequivalent sites [17]. These anionic groups are bonded ionically through barium ions. There are four anionic groups in each primitive unit cell; they are distributed over two symmetrically independent positions. The BaB2O4 crystal consists of planar (B3O6)3 rings. The nearest-neighbor B(1)–O bond ˚ 1.415 A, ˚ and 1.396 A, ˚ and the average distance lengths are 1.329 A, ˚ whereas the B(2)–O bond lengths are 1.336 A, ˚ 1.398 A, ˚ is 1.377 A, ˚ and the average distance is 1.371 A. ˚ and 1.378 A,
ð1Þ
where S(N) is the thermal equilibrium magnetization, and S(t) is the nuclear magnetization at time t. Further, W1 and W2 are the transition probabilities for Dm¼ 71 and Dm¼ 72, respectively. Thus, the relaxation time is given by T1 ¼5/[2(W1 þ4W2)]. 11 B is a quadrupolar nucleus with a nuclear spin of 3/2. The 11B NMR spectrum of b-BaB2O4 crystals consists of a central line and two satellite lines. When the magnetic field was applied along the aþ501-axis in the ac plane of the crystal, the resonance lines were observed. Therefore, if the local symmetry around the boron atoms is not cubic, a boron atom yields three resonance lines, and 12 boron atoms in a BaB2O4 unit cell yields a total of 24 satellite lines, as shown in Fig. 2. The 11B spectrum obtained at room temperature (Fig. 2) indicates the presence of two types of chemically inequivalent 11B nuclei, which correspond to B(1) and B(2) as described in Section 1 [12]. The zero point of the horizontal axis corresponds to the resonance frequency of the 11 B nucleus (i.e., 128.34 MHz). The satellite transitions are well resolved from the central line, and the signal intensity of the central line is stronger than those of the other lines. The magnitudes of the quadrupole parameters of 11B nuclei are in the order of MHz, so the central resonance line is typically split and shifted. The separations between the resonance lines do not vary with temperature for both B(1) and B(2). The no variation in temperature independence of the splitting of the 11B resonance lines indicates that the EFG at the B-sites remains unchanged, which in turn means that the atoms neighboring the 11B nuclei are not displaced when the temperature changes. Nuclear magnetization recovery curves for the central lines of 11 B were obtained by measuring the nuclear magnetization after applying saturation pulses. Fig. 3 shows the saturation recovery
3. Experimental method Single crystals of b-BaB2O4 were grown by the modified flux method at crystal manufacturing company (CASIX) in China [18]. The crystal was cut along two crystallographic axes (the a- and c-axes), and on another axis (the b-axis) perpendicular to these axes. The NMR signals of the 11B nuclei in the BaB2O4 single crystals were measured using a Bruker DSX 400 FT NMR spectrometer at the Korea Basic Science Institute. The static magnetic field was 9.4 T, and the central radio frequency was set to o0/ 2p ¼128.34 MHz. The spin–lattice relaxation times were measured by applying a pulse sequence of p/2 t p/2. The nuclear magnetizations S(t) of the 11B nuclei at time t after the p/2 pulse were determined from each saturation recovery sequence following the pulse. The width of the p/2 pulse was 0.25 ms for 11B. Temperature-dependent NMR measurements were made over the temperature range 180–430 K. The samples were maintained at a constant temperature by controlling the nitrogen gas flow and heater current.
Fig. 2. 11B NMR spectra of BaB2O4 single crystal at room temperature. Static magnetic field B is parallel to the a þ501-axis in the ac plane. Inset: central 11B NMR lines indicating the presence of two types of chemically inequivalent 11B nuclei, B(1) and B(2).
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
traces for the central resonance lines of B-sites in b-BaB2O4 crystals at various delay times at room temperature. T1 was determined directly from the slope of a plot of log [S(N) S(t)]/ S(N) versus time t. It is very well known that the relaxation time
Fig. 3. Saturation recovery traces of
43
T1 can be defined only if the delay time dependence of the magnetization can be described by the two exponential functions given in Eq. (1). Of course, one might introduce a useful combination of the transition probabilities W1 and W2 according to Eq. (1) and explain that the introduction of this constant is reasonable because it leads to the correct relaxation time, T1 ¼1/2W1 for W1 ¼W2, where a single exponential relaxation function can be derived from Eq. (1). The slopes of the recovery traces at each temperature differ. The temperature dependences of the spin– lattice relaxation time T1 of 11B NMR are shown in Fig. 4. The relaxation times of the 3-coordinated B(1) atoms and 3-coordinated B(2) atoms can be distinguished. T1 decreases slowly with increasing temperature. The spin–lattice relaxation times for the B(1) and B(2) atoms are very similar. In simple NMR theory, the overall behavior of the spin–lattice relaxation time for random motions is described in terms of the fastmotion region, where it is given by T1 exp(Ea/kBT). Here Ea is the activation energy, which was determined from the slopes of the straight-line portions of the semilog plots of the relaxation time vs. 1000/T, as shown in Fig. 4. The activation energy for B(1) was determined to be 2.9970.22 kJ/mol and 3.0770.24 kJ/mol, respectively, which are the same within the experimental error range. Further, the activation energy for B(2) was 4.1670.08 kJ/mol.
11
B-site as functions of delay time t.
5. Discussion
Fig. 4. Temperature dependence of spin–lattice relaxation time T1 for B(1) and B(2) in a BaB2O4 single crystal.
Many studies have discussed bond parameter methods, anharmonic oscillator models, and the bond charge model. After this work, Chen’s group [1,2] turned its attention to borates. They recognized that borate compounds have numerous structural types because borate atoms may have either 3- or 4-fold coordination. This structural complexity of borate compounds produces a great variation in the possible structural types favorable for NLO effects, and anionic group theory can be used to systematically elucidate which structural unit is most likely to exhibit large nonlinearities. In addition, Chen’s group [21–23] suggested that the p-conjugated orbital system of an acentric planar organic molecule with charge transfer between the donor and acceptor substituent groups was mainly responsible for the presence of a large second-order susceptibility in such molecules. We propose NMR studies as a microscopic tool for evaluating and identifying NLO borate materials. The parameters of the quadrupole Hamiltonian and the NLO properties have an interesting feature. An inspection of our previous results seems to reveal close relationships between the parameters of the quadrupole Hamiltonian and the effective NLO coefficients for SHG [24]. We considered the relationship between the asymmetry parameter Z, the quadrupole coupling
Table 1 Values for the largest nonlinear optical coefficient, dlar, the asymmetry parameter, Z, the quadrupole coupling constants, e2qQ/h, the spin–lattice relaxation time, T1, and the ratio of number of 3-coordination for number of 3-coordination plus number of 4-coordination, N3, for 11B nucleus in Li2B4O7, LiCsB6O10, LiB3O5, and BaB2O4 crystals at room temperature. dlar (1064 nm) (pm/V)
Z
e2qQ/h (kHz)
T1 (s)
N3
References
Li2B4O7
0.93
0.167 0.53
3-coordinated B(1) 2600 4-coordinated B(2) 526.8
421 (present work)
0.5
[25,26]
LiCsB6O10
0.95
0.275 0.455
3-coordinated B(1) 2580 4-coordinated B(2) 230
6 (present work)
0.5
[24]
LiB3O5
1.05
0.279 0.203 0.120
3-coordinated B(1) 2615 3-coordinated B(1) 2695 4-coordinated B(2) 177.1
1181 (present work)
0.7
[27,28]
BaB2O4
2.2
0.684 0.644
3-coordinated B(1) 2455 3-coordinated B(2) 2486
769 (present work)
1
[12]
44
A.R. Lim, I.G. Kim / Solid State Communications 159 (2013) 41–44
used to explain the structure–property relationships in most known NLO crystals of various structural types and to establish guidelines for identifying and developing new NLO materials.
Acknowledgment This research was supported by the Basic Science Research program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2012001763).
References
Fig. 5. Correlation between the asymmetry parameter Z, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons N3, the quadrupole coupling constant e2qQ/h, and the largest NLO coefficient.
constant e2qQ/h, the spin–lattice relaxation time T1, the ratio of the number of 3-coordinated borons to the number of both 3-coordinated and 4-coordinated borons N3, and the largest secondorder NLO coefficient, as listed in Table 1 [12,24–28]. Fig. 5 shows the relationship between the largest NLO coefficient and Z, N3, and e2qQ/h. Note that NLO borate materials with NLO coefficients of 1.2–2.0 pm/V have not yet been reported.
6. Conclusion To obtain detailed information about the NLO properties of bBaB2O4 crystals, the spin–lattice relaxation time T1 of 11B was measured. We analyzed the correlation between the parameters of the quadrupole interaction, the number of 3-coordinated borons, T1, and the NLO properties at the boron sites in these crystals. A correlation seems to exist between Z, N3, and the NLO coefficient of each crystal, whereas e2qQ/h and the spin–lattice relaxation time T1 show no correlation with the NLO coefficient. This research can be
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