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Multiple rotary echoes in nitrogen-14 quadrupolar spin-system
Chemical Physics Letters 410 (2005) 365–369 www.elsevier.com/locate/cplett
Multiple rotary echoes in nitrogen-14 quadrupolar spin-system T.N. Rudakov
*
Research Group, QRSciences Limited, 8-10 Hamilton Street, Cannington, Perth, WA 6107, Australia Received 26 April 2005; in final form 24 May 2005 Available online 21 June 2005
Abstract This is a study of the influence of multi-pulse sequences consisting of blocks of short-repetition pulses on the nitrogen-14 NQR spin-system. The experiment demonstrated that the application of such sequences generates multiple rotary echo signals in the effective field of the pulse sequence similar to those generated by conventional spin-locking multi-pulse sequences. The detected RE signals were analysed and the obtained results presented, adding to the understanding of the dynamic properties of the quadrupolar spin-system. The experimental results are obtained for polycrystalline NaNO2. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction The investigation of the effect of multi-pulse irradiation on the nitrogen-14 quadrupolar spin-system can provide direct information about the spin dynamics and contributes to the development of experimental technique of the nuclear quadrupole resonance (NQR) spectroscopy. Besides a general scientific interest understanding the behaviour of the quadrupolar spin-systems has a direct impact on the successful application of NQR for practical purposes, namely the detection of specific dangerous or illicit substances. In previous work by the author [1,2], we studied the results of irradiating a spin-system that has a non-axial symmetry electric field gradient (EFG) with multi-pulse sequences similar to those used in nuclear magnetic resonance (NMR) for detecting Ôthe magic echoÕ [3–6]. In our experiments we used the pulsed version of the Ômagic sandwichÕ where the continuous spin-lock pulse is broken down into pulses separated by the Ôobservation windowsÕ for data acquisition. It was shown that these sequences cause refocussing of the transverse magnetisation and permit detecting other echo signals known in NMR as Ôrotary echoÕ (RE) [3,4] and observed in the *
Fax: +61 08 9351 9322. E-mail address: [email protected].
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.05.093
effective field of the pulse sequence. The RE appears during the spin-lock period and therefore its behaviour helps to investigate the dynamics of the spin-system. It was also found that using a two block sequence one can detect several RE signals in the same way as when using a conventional three pulse sequence [2]. One of these RE signals was called Ôa stimulated REÕ. The present work is a further development of this research. Here, we expected to observe multiple RE signals similar to those generated by conventional spin-locking multipulse sequences. Therefore, the main purpose of this work was to detect multiple RE signals and investigate their behaviour in a quadrupole spin-system. The sample used in these experiments was polycrystalline NaNO2. 2. Pulse technique description A multi-pulse sequence used to detect a single RE signal can be written as h0u s1 ðh10 ss h1180 ss ÞN ; 0
ð1Þ
where h is the flipping angle of the preparatory pulse, h1 is the flipping angle of a pulse in the spin-locking sequence, u is the phase of the preparatory pulse, s1 is a time interval between the preparatory pulse and the
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T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
spin-locking sequence, ss is the pulse repetition time in the spin-locking sequence which is set so as to be shorter than s1 and N is the number of repetitions. The multipulse sequence consists of a preparatory pulse and a comprised spin-locking sequence which is a well known phase alternated pulse sequence (PAPS). The ss should be set to be at least several times shorter than the spin–spin relaxation time T2. Normally in sequence (1) the preparatory pulse would be a so-called Ô90° pulseÕ and its phase u would equal either 90° or 270°. Note that the version of sequence (1), where phase u equals either 0° or 180° can also be applied to detect RE. It was shown [2] that using a two block sequence which is a modification of sequence (1) one can detect several RE signals in the same way as after a conventional three pulse sequence. The sequence can be written as h0u s1 ðh10 ss h1180 ss ÞN 1 ðh1180 ss h10 ss ÞN 2 .
ð2Þ
This sequence contains two blocks with alternating reversed phases. Therefore, for detecting multiple RE signals we modified sequence (2) to be h0u s1 ððh10 ss h1180 ss ÞN
ðh1180
ss
h10
ss ÞN ÞN 0 .
ð3Þ
Using this sequence we expected to observe multiple RE signals usually observed when using a conventional spinlocking multi-pulse sequence [7–9]. We expected to see a train of 2N0 echo signals. In order to avoid the contribution of a free induction component in the detected signal a phase-cycling multipulse method as in [2] was employed. As the phase of the spin-echo components strictly depends on the phase of the preparatory pulse, these components can be distinguished by reversing the phase of the preparatory pulse at each repetition of the multi-pulse sequence. Obviously, the phase of the receiving system should be changed in the same manner. We started this research with PAPS because we supposed that it renders itself easily to theoretical analysis. The PAPS is a cyclic sequence consisting of a number of two pulse cycles and the extensively elaborated average Hamiltonian theory can be used for its description. We also plan to undertake research for both the noncyclic and cyclic sequences and make an appropriate comparison.
3. Experimental The sample used in our experiments consisted of 60 g of polycrystalline sodium nitrite (NaNO2). A transition frequency of m+ = 4.64 MHz was used in all experiments. The spin-lattice relaxation time T1 measured at room
temperature (297 K) was about 90 ms and the spin–spin relaxation time T2 in the sample was about 5.5 ms. The line shape parameter was about 2 ms. The relaxation time measurements are estimated to be accurate to within ±10%. In order to avoid the piezoelectric effect in polycrystalline NaNO2 and eliminate spurious signals, which can be quite strong, the sample was ground into fine powder. The experiments were carried out using the pulsed NQR spectrometer which employs a TECMAG ÔApolloÕ console for pulse generation and data collection in the low-frequency band (0.3–10 MHz). Some details of the spectrometer were reported previously [10]. The sample to be investigated was contained in a glass test-tube with the diameter of 2.8 cm and the length of 8 cm placed in the centre of a one-litre RF solenoid coil. In our experiments the duration of a single Ô90° pulseÕ was about 80 ls, i.e., a pulse duration when the maximum FID amplitude was observed. All experiments were performed at exact on resonance frequency.
4. Results and discussion As was expected, pulse sequence (3) permits detecting a long train of RE signals. This is clearly demonstrated in Fig. 1a, where one can see a train of 2N0 signals. Note that an important condition for observing the RE train was s1 ’ ðss þ sw ÞN ;
ð4Þ
where sw is the RF pulse duration. The duration of each pulse in the sequence was equal to the duration of a Ô90°-pulseÕ (sw = 80 ls), s1 = 1.6 ms, ss = 0.2 ms, N = 6, N0 = 14 and the phase of the preparatory pulse u = 0° (180°). In order to show the structure of the RE signals we present the first ten RE signals of the train (Fig. 1b). The observed effect is similar to that found in a conventional multi-pulse spin-locking experiment however we need to keep in mind that in our case all multiple echoes are detected in the effective field of the multi-pulse sequence. We would like to note that the intensity of the RE signals comes up to only about half of the intensity of the corresponding SE signals obtained with a conventional spin-locking spin-echo (SLSE) multi-pulse sequence with the pulse repetition time s = s1. Obviously it means that the applied version of sequence (3) causes refocussing of only a small part of the transverse magnetisation. We experimentally investigated the decay constant of the RE signals (effective relaxation time T2e) on the parameter s1 and the result is presented in Fig. 2. The measurements were made at exact on resonance frequency and condition (4) was met. Although, the effective relaxation time T2e must be described by the sum of two exponential terms containing the short (T2eS)
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
367
Fig. 2. The long decay constant of a rotary echo signal train (effective time T2eL) from 14N in a powdered sample of sodium nitrite (NaNO2) as a function of pulse spacing s1 at room temperature obtained with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 .
Fig. 1. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact on resonance frequency with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 at s1 = 1.6 ms, ss = 0.2 ms, N = 6, u = 0°(180°), h1 . 90° and (a) N0 = 14, (b) N0 = 5.
and long (T2eL) relaxation times [11,12] in the present work we only measured the long effective relaxation time T2eL, which is the significant parameter in describing the spin-locking effect. Fig. 2 shows a strong dependence of T2eL on pulse spacing s1 for sequences (3); this dependence is similar to that observed in the case of a conventional SLSE multi-pulse sequence. It was also found that when u = 90° (270°), the long train of RE signals was not observed. This is clearly shown in Fig. 3, where one can see two RE signals. It proves yet again that orientation of the effective field of the multi-pulse sequence is a very important factor for reversing nuclear magnetisation and particularly for obtaining multiple RE signals. Further, in order to get a better refocussing effect we tried to modify sequence (3) and the attempt was quite successful. The best result was obtain by using a pulse sequence which can be written as
Fig. 3. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 at s1 = 1.6 ms, ss = 0.2 ms, N = 6, u = 90°(270°), h1 . 90° and N0 = 8.
h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 .
ð5Þ
Similar to (3) this sequence contains two sub-blocks of pulse sequences. Unlike (3) where PAPS is used, these sub-blocks contain trains of equivalent pulses. The phase of the preparatory pulse u = 90° (270°). In contrast to (3) each of the two sub-blocks generates only half of the total RE signal. It was established that the duration of each of the h1 pulses should be shorter than that of a Ô90°-pulseÕ. For notation (5) the condition for time s1 can be written in the same form as (4). A typical train of RE signals obtained with pulse sequences (5) is presented in Fig. 4. In this case the
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T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
Fig. 4. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 at s1 = 1.6 ms, ss = 0.24 ms, N = 6, u = 90°(270°), h1 . 45° and (a) N0 = 5, (b) N0 = 14.
duration of each pulse of the sequence was equal to the duration of a Ô45°-pulseÕ (except for the preparatory pulse the duration of which was equal to the duration of a Ô90°-pulseÕ) (sw . 40 ls), s1 = 1.6 ms, ss = 0.24 ms and N = 6. It would be seen that the intensity of the signals almost doubles as compared with that obtained with sequence (3) and is very close to the intensity of the SE signals obtained with a conventional SLSE multi-pulse sequence. While applying sequence (5) it was found that the optimal duration of h1pulses was equal or close to that of a Ô45°-pulseÕ. This result is quite interesting and may be useful for practical applications which require limited pulse power. It should also be noted here that multiple RE signals were not observed when the duration of the h1 pulses was equal to or longer than to that of the Ô90°-pulseÕ. This is shown in Fig. 5 for the cases of Ô90°-Õ and Ô180°-Õpulses. The obtained re-
Fig. 5. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 at s1 = 1.6 ms, ss = 0.24 ms, N = 6, u = 90°(270°), N0 = 14 and (a) h1 . 90°, (b) h1 . 180°.
sult differs from that where transient signals in the effective field were detected when the duration of the pulses was equal to that of the Ô180°-pulseÕ [13,14]. The results presented here for sequence (5) should be considered as preliminary. Taking into account the novelty of this sequence future research should be required to further investigate all aspects of its application.
5. Conclusion In this Letter, the results of subjecting NQR spinsystem with non-axial symmetry EFG to multi-pulse sequences consisting of several blocks of short-repetition pulses were presented. These sequences, as was expected, cause refocussing of the transverse magnetisation and permit detecting the RE signals in the effective field of the pulse sequence. The experiments
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
showed that using this kind of multi-pulse technique one can observe multiple RE signals similar to those detected when using the conventional spin-locking multi-pulse sequences. In order to get this effect the conventional refocussing pulses should be replaced with blocks of RF pulses. When the dependence of the effective relaxation time on the time interval after the preparatory pulse was investigated the presence of the spin-locking effect was obvious and the dependence was close to that normally obtained in the case of a conventional SLSE sequence. A modified version of the RE multi-pulse sequence which causes much better refocussing of the transverse magnetisation was proposed. This sequence looks very promising and can prove to be a useful tool in spin-locking experiments. All the obtained results contribute to a better understanding of the quadrupole spin-system dynamics.
369
References [1] T.N. Rudakov, P.A. Hayes, V.T. Mikhaltsevich, Phys. Lett. A 330 (2004) 280. [2] T.N. Rudakov, Chem. Phys. Lett 398 (2004) 471. [3] B. Blumich, NMR Imaging in Materials, Clarendon press, Oxford, 2000. [4] W.-K. Rhim, A. Pines, J.S. Waugh, Phys. Rev. B 3 (1971) 684. [5] W.-K. Rhim, H. Kessemeier, Phys. Rev. B 3 (1971) 3655. [6] A. Pines, W.-K. Rhim, J.S. Waugh, J. Magn. Reson. 6 (1972) 457. [7] E.D. Ostroff, J.S. Waugh, Phys. Rev. Lett. 16 (1966) 1097. [8] P. Mansfield, J.S. Waugh, Phys. Lett. 22 (1966) 133. [9] R.A. Marino, S.M. Klainer, J. Chem. Phys. 67 (1977) 3388. [10] T.N. Rudakov, V.T. Mikhaltsevich, Phys. Lett. A 309 (2003) 465. [11] Y. Abe, J. Phys. Soc. Jpn. 23 (1967) 51. [12] G. Petersen, P.J. Bray, J. Chem. Phys. 64 (1976) 522. [13] D.Ya. Osokin, R.H. Kurbanov, V.A. Shagalov, JETP Lett. 62 (1995) 309. [14] D.Ya. Osokin, V.A. Shagalov, Solid State Nucl. Mag. Reson. 10 (1997) 63.
Multiple rotary echoes in nitrogen-14 quadrupolar spin-system T.N. Rudakov
*
Research Group, QRSciences Limited, 8-10 Hamilton Street, Cannington, Perth, WA 6107, Australia Received 26 April 2005; in final form 24 May 2005 Available online 21 June 2005
Abstract This is a study of the influence of multi-pulse sequences consisting of blocks of short-repetition pulses on the nitrogen-14 NQR spin-system. The experiment demonstrated that the application of such sequences generates multiple rotary echo signals in the effective field of the pulse sequence similar to those generated by conventional spin-locking multi-pulse sequences. The detected RE signals were analysed and the obtained results presented, adding to the understanding of the dynamic properties of the quadrupolar spin-system. The experimental results are obtained for polycrystalline NaNO2. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction The investigation of the effect of multi-pulse irradiation on the nitrogen-14 quadrupolar spin-system can provide direct information about the spin dynamics and contributes to the development of experimental technique of the nuclear quadrupole resonance (NQR) spectroscopy. Besides a general scientific interest understanding the behaviour of the quadrupolar spin-systems has a direct impact on the successful application of NQR for practical purposes, namely the detection of specific dangerous or illicit substances. In previous work by the author [1,2], we studied the results of irradiating a spin-system that has a non-axial symmetry electric field gradient (EFG) with multi-pulse sequences similar to those used in nuclear magnetic resonance (NMR) for detecting Ôthe magic echoÕ [3–6]. In our experiments we used the pulsed version of the Ômagic sandwichÕ where the continuous spin-lock pulse is broken down into pulses separated by the Ôobservation windowsÕ for data acquisition. It was shown that these sequences cause refocussing of the transverse magnetisation and permit detecting other echo signals known in NMR as Ôrotary echoÕ (RE) [3,4] and observed in the *
Fax: +61 08 9351 9322. E-mail address: [email protected].
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.05.093
effective field of the pulse sequence. The RE appears during the spin-lock period and therefore its behaviour helps to investigate the dynamics of the spin-system. It was also found that using a two block sequence one can detect several RE signals in the same way as when using a conventional three pulse sequence [2]. One of these RE signals was called Ôa stimulated REÕ. The present work is a further development of this research. Here, we expected to observe multiple RE signals similar to those generated by conventional spin-locking multipulse sequences. Therefore, the main purpose of this work was to detect multiple RE signals and investigate their behaviour in a quadrupole spin-system. The sample used in these experiments was polycrystalline NaNO2. 2. Pulse technique description A multi-pulse sequence used to detect a single RE signal can be written as h0u s1 ðh10 ss h1180 ss ÞN ; 0
ð1Þ
where h is the flipping angle of the preparatory pulse, h1 is the flipping angle of a pulse in the spin-locking sequence, u is the phase of the preparatory pulse, s1 is a time interval between the preparatory pulse and the
366
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
spin-locking sequence, ss is the pulse repetition time in the spin-locking sequence which is set so as to be shorter than s1 and N is the number of repetitions. The multipulse sequence consists of a preparatory pulse and a comprised spin-locking sequence which is a well known phase alternated pulse sequence (PAPS). The ss should be set to be at least several times shorter than the spin–spin relaxation time T2. Normally in sequence (1) the preparatory pulse would be a so-called Ô90° pulseÕ and its phase u would equal either 90° or 270°. Note that the version of sequence (1), where phase u equals either 0° or 180° can also be applied to detect RE. It was shown [2] that using a two block sequence which is a modification of sequence (1) one can detect several RE signals in the same way as after a conventional three pulse sequence. The sequence can be written as h0u s1 ðh10 ss h1180 ss ÞN 1 ðh1180 ss h10 ss ÞN 2 .
ð2Þ
This sequence contains two blocks with alternating reversed phases. Therefore, for detecting multiple RE signals we modified sequence (2) to be h0u s1 ððh10 ss h1180 ss ÞN
ðh1180
ss
h10
ss ÞN ÞN 0 .
ð3Þ
Using this sequence we expected to observe multiple RE signals usually observed when using a conventional spinlocking multi-pulse sequence [7–9]. We expected to see a train of 2N0 echo signals. In order to avoid the contribution of a free induction component in the detected signal a phase-cycling multipulse method as in [2] was employed. As the phase of the spin-echo components strictly depends on the phase of the preparatory pulse, these components can be distinguished by reversing the phase of the preparatory pulse at each repetition of the multi-pulse sequence. Obviously, the phase of the receiving system should be changed in the same manner. We started this research with PAPS because we supposed that it renders itself easily to theoretical analysis. The PAPS is a cyclic sequence consisting of a number of two pulse cycles and the extensively elaborated average Hamiltonian theory can be used for its description. We also plan to undertake research for both the noncyclic and cyclic sequences and make an appropriate comparison.
3. Experimental The sample used in our experiments consisted of 60 g of polycrystalline sodium nitrite (NaNO2). A transition frequency of m+ = 4.64 MHz was used in all experiments. The spin-lattice relaxation time T1 measured at room
temperature (297 K) was about 90 ms and the spin–spin relaxation time T2 in the sample was about 5.5 ms. The line shape parameter was about 2 ms. The relaxation time measurements are estimated to be accurate to within ±10%. In order to avoid the piezoelectric effect in polycrystalline NaNO2 and eliminate spurious signals, which can be quite strong, the sample was ground into fine powder. The experiments were carried out using the pulsed NQR spectrometer which employs a TECMAG ÔApolloÕ console for pulse generation and data collection in the low-frequency band (0.3–10 MHz). Some details of the spectrometer were reported previously [10]. The sample to be investigated was contained in a glass test-tube with the diameter of 2.8 cm and the length of 8 cm placed in the centre of a one-litre RF solenoid coil. In our experiments the duration of a single Ô90° pulseÕ was about 80 ls, i.e., a pulse duration when the maximum FID amplitude was observed. All experiments were performed at exact on resonance frequency.
4. Results and discussion As was expected, pulse sequence (3) permits detecting a long train of RE signals. This is clearly demonstrated in Fig. 1a, where one can see a train of 2N0 signals. Note that an important condition for observing the RE train was s1 ’ ðss þ sw ÞN ;
ð4Þ
where sw is the RF pulse duration. The duration of each pulse in the sequence was equal to the duration of a Ô90°-pulseÕ (sw = 80 ls), s1 = 1.6 ms, ss = 0.2 ms, N = 6, N0 = 14 and the phase of the preparatory pulse u = 0° (180°). In order to show the structure of the RE signals we present the first ten RE signals of the train (Fig. 1b). The observed effect is similar to that found in a conventional multi-pulse spin-locking experiment however we need to keep in mind that in our case all multiple echoes are detected in the effective field of the multi-pulse sequence. We would like to note that the intensity of the RE signals comes up to only about half of the intensity of the corresponding SE signals obtained with a conventional spin-locking spin-echo (SLSE) multi-pulse sequence with the pulse repetition time s = s1. Obviously it means that the applied version of sequence (3) causes refocussing of only a small part of the transverse magnetisation. We experimentally investigated the decay constant of the RE signals (effective relaxation time T2e) on the parameter s1 and the result is presented in Fig. 2. The measurements were made at exact on resonance frequency and condition (4) was met. Although, the effective relaxation time T2e must be described by the sum of two exponential terms containing the short (T2eS)
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
367
Fig. 2. The long decay constant of a rotary echo signal train (effective time T2eL) from 14N in a powdered sample of sodium nitrite (NaNO2) as a function of pulse spacing s1 at room temperature obtained with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 .
Fig. 1. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact on resonance frequency with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 at s1 = 1.6 ms, ss = 0.2 ms, N = 6, u = 0°(180°), h1 . 90° and (a) N0 = 14, (b) N0 = 5.
and long (T2eL) relaxation times [11,12] in the present work we only measured the long effective relaxation time T2eL, which is the significant parameter in describing the spin-locking effect. Fig. 2 shows a strong dependence of T2eL on pulse spacing s1 for sequences (3); this dependence is similar to that observed in the case of a conventional SLSE multi-pulse sequence. It was also found that when u = 90° (270°), the long train of RE signals was not observed. This is clearly shown in Fig. 3, where one can see two RE signals. It proves yet again that orientation of the effective field of the multi-pulse sequence is a very important factor for reversing nuclear magnetisation and particularly for obtaining multiple RE signals. Further, in order to get a better refocussing effect we tried to modify sequence (3) and the attempt was quite successful. The best result was obtain by using a pulse sequence which can be written as
Fig. 3. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss h1180 ss ÞN ðh1180 ss h10 ss ÞN ÞN 0 at s1 = 1.6 ms, ss = 0.2 ms, N = 6, u = 90°(270°), h1 . 90° and N0 = 8.
h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 .
ð5Þ
Similar to (3) this sequence contains two sub-blocks of pulse sequences. Unlike (3) where PAPS is used, these sub-blocks contain trains of equivalent pulses. The phase of the preparatory pulse u = 90° (270°). In contrast to (3) each of the two sub-blocks generates only half of the total RE signal. It was established that the duration of each of the h1 pulses should be shorter than that of a Ô90°-pulseÕ. For notation (5) the condition for time s1 can be written in the same form as (4). A typical train of RE signals obtained with pulse sequences (5) is presented in Fig. 4. In this case the
368
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
Fig. 4. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 at s1 = 1.6 ms, ss = 0.24 ms, N = 6, u = 90°(270°), h1 . 45° and (a) N0 = 5, (b) N0 = 14.
duration of each pulse of the sequence was equal to the duration of a Ô45°-pulseÕ (except for the preparatory pulse the duration of which was equal to the duration of a Ô90°-pulseÕ) (sw . 40 ls), s1 = 1.6 ms, ss = 0.24 ms and N = 6. It would be seen that the intensity of the signals almost doubles as compared with that obtained with sequence (3) and is very close to the intensity of the SE signals obtained with a conventional SLSE multi-pulse sequence. While applying sequence (5) it was found that the optimal duration of h1pulses was equal or close to that of a Ô45°-pulseÕ. This result is quite interesting and may be useful for practical applications which require limited pulse power. It should also be noted here that multiple RE signals were not observed when the duration of the h1 pulses was equal to or longer than to that of the Ô90°-pulseÕ. This is shown in Fig. 5 for the cases of Ô90°-Õ and Ô180°-Õpulses. The obtained re-
Fig. 5. Multiple rotary echoes in sodium nitrite (NaNO2) obtained at exact resonance frequency with pulse sequence h0u s1 ððh10 ss ÞN ðh1180 ss ÞN Þ2N 0 at s1 = 1.6 ms, ss = 0.24 ms, N = 6, u = 90°(270°), N0 = 14 and (a) h1 . 90°, (b) h1 . 180°.
sult differs from that where transient signals in the effective field were detected when the duration of the pulses was equal to that of the Ô180°-pulseÕ [13,14]. The results presented here for sequence (5) should be considered as preliminary. Taking into account the novelty of this sequence future research should be required to further investigate all aspects of its application.
5. Conclusion In this Letter, the results of subjecting NQR spinsystem with non-axial symmetry EFG to multi-pulse sequences consisting of several blocks of short-repetition pulses were presented. These sequences, as was expected, cause refocussing of the transverse magnetisation and permit detecting the RE signals in the effective field of the pulse sequence. The experiments
T.N. Rudakov / Chemical Physics Letters 410 (2005) 365–369
showed that using this kind of multi-pulse technique one can observe multiple RE signals similar to those detected when using the conventional spin-locking multi-pulse sequences. In order to get this effect the conventional refocussing pulses should be replaced with blocks of RF pulses. When the dependence of the effective relaxation time on the time interval after the preparatory pulse was investigated the presence of the spin-locking effect was obvious and the dependence was close to that normally obtained in the case of a conventional SLSE sequence. A modified version of the RE multi-pulse sequence which causes much better refocussing of the transverse magnetisation was proposed. This sequence looks very promising and can prove to be a useful tool in spin-locking experiments. All the obtained results contribute to a better understanding of the quadrupole spin-system dynamics.
369
References [1] T.N. Rudakov, P.A. Hayes, V.T. Mikhaltsevich, Phys. Lett. A 330 (2004) 280. [2] T.N. Rudakov, Chem. Phys. Lett 398 (2004) 471. [3] B. Blumich, NMR Imaging in Materials, Clarendon press, Oxford, 2000. [4] W.-K. Rhim, A. Pines, J.S. Waugh, Phys. Rev. B 3 (1971) 684. [5] W.-K. Rhim, H. Kessemeier, Phys. Rev. B 3 (1971) 3655. [6] A. Pines, W.-K. Rhim, J.S. Waugh, J. Magn. Reson. 6 (1972) 457. [7] E.D. Ostroff, J.S. Waugh, Phys. Rev. Lett. 16 (1966) 1097. [8] P. Mansfield, J.S. Waugh, Phys. Lett. 22 (1966) 133. [9] R.A. Marino, S.M. Klainer, J. Chem. Phys. 67 (1977) 3388. [10] T.N. Rudakov, V.T. Mikhaltsevich, Phys. Lett. A 309 (2003) 465. [11] Y. Abe, J. Phys. Soc. Jpn. 23 (1967) 51. [12] G. Petersen, P.J. Bray, J. Chem. Phys. 64 (1976) 522. [13] D.Ya. Osokin, R.H. Kurbanov, V.A. Shagalov, JETP Lett. 62 (1995) 309. [14] D.Ya. Osokin, V.A. Shagalov, Solid State Nucl. Mag. Reson. 10 (1997) 63.