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Multiple NQR spin echoes in phase cycled pulse experiments
Physics Letters A 309 (2003) 465–469 www.elsevier.com/locate/pla
Multiple NQR spin echoes in phase cycled pulse experiments T.N. Rudakov ∗ , V.T. Mikhaltsevich Research Group, QRSciences Limited, 8-10 Hamilton Street, Cannington, WA 6107, Australia Received 3 October 2002; accepted 29 January 2003 Communicated by J. Flouquet
Abstract The pulsed spin locking effect has been observed in nitrogen-14 NQR spin-system using the phase cycled pulse sequence (PCPS). The dependence of the effective relaxation time on parameters of PCPS has also been investigated. This dependence and spin-echo signal behavior are very similar to those observed in conventional pulsed spin locking experiments. 2003 Elsevier Science B.V. All rights reserved. PACS: 76.60.Gv; 76.60.Lz Keywords: Nuclear quadrupole resonance; Pulsed spin locking; Multi-pulse sequence
1. Introduction The pulsed spin locking (PSL) is one of most interesting effects in nuclear magnetic resonance (NMR) [1–3]. This effect is also known and widely used in pure nuclear quadrupole resonance (NQR) for the detection of weak signals [4–6]. The basic spin-locking multi-pulse (SLMP) sequence which was proposed in NMR by Ostroff and Waugh [1] can be represented as 0 1 , θ90 (1) ◦ – τ –θ0◦ –τ – N where θ 0 is the flipping angle of the preparatory pulse and θ 1 is the flipping angle of the other pulses in the sequence (phase shifted by 90◦ in relation to the preparatory pulse), τ is the time interval between the pulses. This sequence causes a refocussing of the transverse magnetisation for periods much longer than * Corresponding author.
E-mail address: [email protected] (T.N. Rudakov).
the spin–spin relaxation time T2 . The first experimental investigation of this type of sequence in pure NQR was made by Marino and Klainer [4] who observed the unexpected persistence of the spin-echo train for times much greater than T2 . Now the sequence (1) is known in NQR as spin-locking spin-echo (SLSE) multi-pulse sequence because in some respects the observed effect is similar to the spin locking by a constant amplitude RF field. It is interesting to note that the results obtained by Marino and Klainer are very similar to those obtained earlier in the NMR experiments [1]. This fact seems not obvious and was investigated in the light of the difference between the NMR and NQR spinsystems [7–10]. The so-called phase alternated pulse sequence (PAPS) has also been used in pure NQR experiments [10–13]. This is another variant of a SLMP sequence and can be represented as 1 1 . θ00◦ – τ –θ180 ◦ –2τ –θ0◦ –τ – N
0375-9601/03/$ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0375-9601(03)00207-X
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T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
This sequence differs from a non-cyclic SLSE sequence by the inversion of the phase between any two adjacent pulses and is therefore a cyclic sequence consisting of a number of two-pulse cycles. Thus it was possible to use the average Hamiltonian theory to discuss the effects of PAPS on the magnetization in pure NQR, but it is difficult to apply this theory to the SLSE sequence [9]. However experimental research showed that the application of both pulse sequences to the NQR spin-system produces similar results. Recently we have also obtained that both PAPS and SLSE sequence have a practically identical effect on the spinsystem with zero asymmetry parameter [14]. All this suggested that the spin locking effect can be obtained by using other types of pulse sequences.
2. Phase cycled pulse sequence It is well known that steady-state free precession (SSFP) multi-pulse technique is used to increase the sensitivity of NMR and NQR experiments [15–18] and contains different kinds of pulse sequences. In general most of them present a long train of RF pulses (without any preparatory pulses) of the same flipping angle θ applied with a short repetition time (pulse spacing) τ . One of commonly used version is the sequences with phase cycling. This technique is very effective against spurious signals and can help to eliminate or reduce other effects of distortions on the computed spectra [19,20]. In our experiments we used the phase cycling idea to create the SLMP sequence which can be written as 1 1 1 , θϕ0 – τ –θ01◦ –2τ –θ90 (3) ◦ –2τ –θ180◦ –2τ –θ270◦ –τ – N where ϕ is the phase of the preparatory pulse θ 0 . This phase cycled pulse sequence (PCPS) contains a preparatory pulse followed by a train of cyclically ordered RF pulses in the phases of 0◦ , 90◦ , 180◦ and 270◦ . In this Letter, we report the observation of the pulsed spin locking effect in phase cycled pulse experiments. The effect is analogous to that observed in the case of commonly used SLMP sequences. This work also presents some experimental results of the effects of PCPS on nitrogen-14 nuclei in a powdered sample of sodium nitrite (NaNO2 ).
3. Experimental details The experiments were carried out using the pulsed NQR spectrometer based on the TECMAG “Apollo” console and designed to operate in a low-frequency band (0.3–10 MHz). This instrument also contains a power amplifier (Model A150), a preamplifier Miteq (Model AU-2A-0150-BNC) and a home-made probe which is of a standard design. We used a special system for damping the transients signals in the resonance tank circuit after the transmit RF pulses as reported earlier [21]. The sample employed in the experiments 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. The duration of a single so-called “90◦ -pulse” was about 90 µs, when the maximum FID amplitude was observed. In all experiments the delay between the end of an RF pulse and the beginning of detection was 0.2 ms. The sample used in these experiments consisted of 60 g of polycrystalline sodium nitrite (NaNO2 ). We used the transition frequency ν+ = 4.640 MHz. The spin-lattice relaxation time T1 was measured at room temperature (297 K) using the saturation method and T1 ≈ 90 ms. The spin–spin relaxation time T2 in the sample was about 5 ms and it was measured by the well-known two-pulse Hahn sequence method. Most of our experiments were carried out at the exact resonance frequency. It was found that at resonant condition the phase ϕ of the preparatory pulse θ 0 for sequence (3) is not very essential. However in offset experiments it seemed that the phase ϕ can influence the signal behaviour and obviously should be taken into account.
4. Results and discussion Using sequence (3) we could detect a spin-echo train for times much greater than T2 in a sample of NaNO2 which is shown in Fig. 1. In this figure one can see trains of spin-echo signals obtained using PCPS (Fig. 1(a)) and SLSE sequence (Fig. 1(b)) with τ = 2 ms. These experiments were carried out at exact resonance frequency at room temperature. Two hundred averages have been performed. The ϕ phase of the preparatory pulse θ 0 for sequence (3) was 270◦.
T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
(a)
(a)
(b)
(b)
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Fig. 1. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with a 20 pulse sequence at τ = 2.1 ms at exact resonance frequency: (a) spin-locking spin-echo pulse sequence, (b) phase cycled pulse sequence.
We can see that the trains of spin-echo signals in both cases are very similar. It was found that the spin-echo train in NaNO2 is also detected at resonance offset. In Fig. 2 one can see NQR signals obtained at the offset f = 2 kHz for sequence (3). As an illustration we present the real components (Fig. 2(a)), the imaginary ones (Fig. 2(b)) and the magnitude (Fig. 2(c)) of NQR signals. We experimentally investigated the dependence of the effective relaxation time T2e on the duration of pulses in NaNO2 for sequence (3) and the result is presented in Fig. 3. These measurements were made at the exact resonance frequency. It is essential to
(c) Fig. 2. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with a 20 pulse sequence at τ = 2.1 ms at resonance offset f = 2 kHz: (a) real component, (b) imaginary component, (c) magnitude.
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T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
Fig. 3. The long decay constant of the spin-echo signal train (effective time T2eL ) from 14 N in a powdered sample of sodium nitrite (NaNO2 ) as a function of the pulse duration at room temperature (297 K) obtained with the phase cycled pulse sequence. Pulse spacing τ = 2.1 ms.
(a)
(b) Fig. 5. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with the phase cycled pulse sequence (20 pulses) at exact resonance frequency: (a) τ = 1.6 ms, (b) τ = 1.0 ms. Fig. 4. The long decay constant of the spin-echo signal train (effective time T2eL ) from 14 N in a powdered sample of sodium nitrite (NaNO2 ) as a function of the pulse spacing τ at room temperature (297 K) obtained with the phase cycled pulse sequence.
keep in mind that the nitrogen-14 quadrupolar spinsystem in this sample has three energy levels. For this kind of system the spin-echo train decays as the sum of two exponentials. Therefore the effective relaxation time T2e must be described by the sum of two exponential terms containing the short (T2eS ) and long (T2eL ) relaxation times [22,23]. In the present work we only measured the long effective relaxation time T2eL , which is very important for describing the spin locking effect. However the short time T2eS needs to be investigated
as well and we plan to do it in the immediate future. From Fig. 3 we can see that the T2eL time slowly grows with the decrease of pulse duration or flipping angle θ 0 . However, our experiments helped to establish that when the pulse duration is shorter then the “90◦ -pulse”, the amplitudes of the SE signals begin to decrease sharply with the decrease of the preparatory pulse and pulse durations. Besides, at some short and some sufficiently long pulse durations the spin-echo train was not observed at all. This case corresponds to the zero value of T2eL in Fig. 3. As expected, the pulse duration equal or close to “90◦ -pulse” was optimal for the detection. Therewith note that the optimal prepara-
T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
tory pulse duration can be set from 1 to 1.5 times the duration of the “90◦ -pulse”. Fig. 4 shows the strong dependence of T2eL on the time spacing τ between the first two pulses for sequences (3). The pulse durations equal “90◦ -pulse”. From this picture one would expect that for τ → 0 one would obtain T2eL → T2ρ , the spin-lattice relaxation time in the rotating frame, and T2ρ seems to be around 50 ms. It is well known that the pulsed spin-locking occurs when τ becomes less than T2 . Under this condition with a SLMP sequence, the magnetization rapidly evolves to a quasistationary state which does not persist. This state decays slowly to equilibrium. Our experiments demonstrated that both quasistationary and equilibrium states emerge when using PCPS (Fig. 5). The quasistationary and equilibrium magnetization depend strongly on the time spacing τ . This fact becomes obvious when if we compare NQR signals obtained at τ = 1.6 ms (Fig. 5(a)) and τ = 1 ms (Fig. 5(b)). A more detailed study of these dependences can require additional experimental and theoretical research.
5. Conclusion We have performed spin-echo experiments using the phase cycling pulse technique. The spin-echo train for times much greater than T 2 was observed. It means that the pulsed spin-locking effect obviously can be obtained using this kind of multi-pulse technique. Investigation of the dependence of the effective relaxation time T2e on pulse parameters did not reveal any essential peculiarities compared with the commonly used technique. Therefore one can draw a conclusion that PCPS effects the NQR spin-system in a way very similar to the conventional SLMP sequences. Probably some peculiarities of the effect of PCPS on a spin-
469
system might be observed in the case on non-resonant experiments. However at the moment we can only make assumptions. As the phase cycling pulse technique has some very useful properties we expect that it should be very promising for the pulsed spin locking experiments and especially for some NQR applications.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
[21] [22] [23]
E.D. Ostroff, J.S. Waugh, Phys. Rev. Lett. 16 (1966) 1097. P. Mansfield, J.S. Waugh, Phys. Lett. 22 (1966) 133. D. Suwelack, J.S. Waugh, Phys. Rev. B 22 (1980) 5110. R.A. Marino, S.M. Klainer, J. Chem. Phys. 67 (1977) 3388. J.P. Yesinowski, M.L. Bues, A.N. Garroway, M. Ziegeweid, A. Pines, Anal. Chem. 67 (1995) 2256. T.N. Rudakov, V.T. Mikhaltsevich, O.P. Selchikhin, J. Phys. D 30 (1997) 1377. R.S. Cantor, J.S. Waugh, J. Chem. Phys. 73 (1980) 1054. A.K. Hitrin, G.E. Karnaukh, B.N. Provotorov, J. Mol. Struct. 83 (1982) 269. M. Matti Maricq, Phys. Rev. B 33 (1986) 4501. D.Ya. Osokin, J. Mol. Struct. 83 (1982) 243. D.Ya. Osokin, Mol. Phys. 48 (1983) 283. A.K. Dubey, P.T. Narasimhan, J. Mol. Struct. 192 (1989) 321. D.Ya. Osokin, V.L. Ermakov, R.H. Kurbanov, V.A. Shagalov, Z. Naturforsch., Teil A 47 (1992) 439. T.N. Rudakov, V.T. Mikhaltsevich, Chem. Phys. Lett. 363 (2002) 1. H.Y. Carr, Phys. Rev. 112 (1958) 1701. R. Freeman, H.D.W. Hill, J. Magn. Reson. 4 (1971) 366. Y.L. Zhuang, R.A. Marino, Z. Naturforsch., Teil A 45 (1990) 587. M.L. Buess, A.N. Garroway, J.B. Miller, J. Magn. Reson. 92 (1991) 348. I.P. Gerothanassis, Prog. Nucl. Magn. Reson. Spectrosc. 19 (1987) 267. R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford, 1987. T.N. Rudakov, V.V. Fedotov, A.V. Belyakov, V.T. Mikhaltsevich, Instrum. Exp. Tech. 43 (2000) 78. Y. Abe, J. Phys. Soc. Jpn. 23 (1967) 51. G. Petersen, P.J. Bray, J. Chem. Phys. 64 (1976) 522.
Multiple NQR spin echoes in phase cycled pulse experiments T.N. Rudakov ∗ , V.T. Mikhaltsevich Research Group, QRSciences Limited, 8-10 Hamilton Street, Cannington, WA 6107, Australia Received 3 October 2002; accepted 29 January 2003 Communicated by J. Flouquet
Abstract The pulsed spin locking effect has been observed in nitrogen-14 NQR spin-system using the phase cycled pulse sequence (PCPS). The dependence of the effective relaxation time on parameters of PCPS has also been investigated. This dependence and spin-echo signal behavior are very similar to those observed in conventional pulsed spin locking experiments. 2003 Elsevier Science B.V. All rights reserved. PACS: 76.60.Gv; 76.60.Lz Keywords: Nuclear quadrupole resonance; Pulsed spin locking; Multi-pulse sequence
1. Introduction The pulsed spin locking (PSL) is one of most interesting effects in nuclear magnetic resonance (NMR) [1–3]. This effect is also known and widely used in pure nuclear quadrupole resonance (NQR) for the detection of weak signals [4–6]. The basic spin-locking multi-pulse (SLMP) sequence which was proposed in NMR by Ostroff and Waugh [1] can be represented as 0 1 , θ90 (1) ◦ – τ –θ0◦ –τ – N where θ 0 is the flipping angle of the preparatory pulse and θ 1 is the flipping angle of the other pulses in the sequence (phase shifted by 90◦ in relation to the preparatory pulse), τ is the time interval between the pulses. This sequence causes a refocussing of the transverse magnetisation for periods much longer than * Corresponding author.
E-mail address: [email protected] (T.N. Rudakov).
the spin–spin relaxation time T2 . The first experimental investigation of this type of sequence in pure NQR was made by Marino and Klainer [4] who observed the unexpected persistence of the spin-echo train for times much greater than T2 . Now the sequence (1) is known in NQR as spin-locking spin-echo (SLSE) multi-pulse sequence because in some respects the observed effect is similar to the spin locking by a constant amplitude RF field. It is interesting to note that the results obtained by Marino and Klainer are very similar to those obtained earlier in the NMR experiments [1]. This fact seems not obvious and was investigated in the light of the difference between the NMR and NQR spinsystems [7–10]. The so-called phase alternated pulse sequence (PAPS) has also been used in pure NQR experiments [10–13]. This is another variant of a SLMP sequence and can be represented as 1 1 . θ00◦ – τ –θ180 ◦ –2τ –θ0◦ –τ – N
0375-9601/03/$ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0375-9601(03)00207-X
(2)
466
T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
This sequence differs from a non-cyclic SLSE sequence by the inversion of the phase between any two adjacent pulses and is therefore a cyclic sequence consisting of a number of two-pulse cycles. Thus it was possible to use the average Hamiltonian theory to discuss the effects of PAPS on the magnetization in pure NQR, but it is difficult to apply this theory to the SLSE sequence [9]. However experimental research showed that the application of both pulse sequences to the NQR spin-system produces similar results. Recently we have also obtained that both PAPS and SLSE sequence have a practically identical effect on the spinsystem with zero asymmetry parameter [14]. All this suggested that the spin locking effect can be obtained by using other types of pulse sequences.
2. Phase cycled pulse sequence It is well known that steady-state free precession (SSFP) multi-pulse technique is used to increase the sensitivity of NMR and NQR experiments [15–18] and contains different kinds of pulse sequences. In general most of them present a long train of RF pulses (without any preparatory pulses) of the same flipping angle θ applied with a short repetition time (pulse spacing) τ . One of commonly used version is the sequences with phase cycling. This technique is very effective against spurious signals and can help to eliminate or reduce other effects of distortions on the computed spectra [19,20]. In our experiments we used the phase cycling idea to create the SLMP sequence which can be written as 1 1 1 , θϕ0 – τ –θ01◦ –2τ –θ90 (3) ◦ –2τ –θ180◦ –2τ –θ270◦ –τ – N where ϕ is the phase of the preparatory pulse θ 0 . This phase cycled pulse sequence (PCPS) contains a preparatory pulse followed by a train of cyclically ordered RF pulses in the phases of 0◦ , 90◦ , 180◦ and 270◦ . In this Letter, we report the observation of the pulsed spin locking effect in phase cycled pulse experiments. The effect is analogous to that observed in the case of commonly used SLMP sequences. This work also presents some experimental results of the effects of PCPS on nitrogen-14 nuclei in a powdered sample of sodium nitrite (NaNO2 ).
3. Experimental details The experiments were carried out using the pulsed NQR spectrometer based on the TECMAG “Apollo” console and designed to operate in a low-frequency band (0.3–10 MHz). This instrument also contains a power amplifier (Model A150), a preamplifier Miteq (Model AU-2A-0150-BNC) and a home-made probe which is of a standard design. We used a special system for damping the transients signals in the resonance tank circuit after the transmit RF pulses as reported earlier [21]. The sample employed in the experiments 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. The duration of a single so-called “90◦ -pulse” was about 90 µs, when the maximum FID amplitude was observed. In all experiments the delay between the end of an RF pulse and the beginning of detection was 0.2 ms. The sample used in these experiments consisted of 60 g of polycrystalline sodium nitrite (NaNO2 ). We used the transition frequency ν+ = 4.640 MHz. The spin-lattice relaxation time T1 was measured at room temperature (297 K) using the saturation method and T1 ≈ 90 ms. The spin–spin relaxation time T2 in the sample was about 5 ms and it was measured by the well-known two-pulse Hahn sequence method. Most of our experiments were carried out at the exact resonance frequency. It was found that at resonant condition the phase ϕ of the preparatory pulse θ 0 for sequence (3) is not very essential. However in offset experiments it seemed that the phase ϕ can influence the signal behaviour and obviously should be taken into account.
4. Results and discussion Using sequence (3) we could detect a spin-echo train for times much greater than T2 in a sample of NaNO2 which is shown in Fig. 1. In this figure one can see trains of spin-echo signals obtained using PCPS (Fig. 1(a)) and SLSE sequence (Fig. 1(b)) with τ = 2 ms. These experiments were carried out at exact resonance frequency at room temperature. Two hundred averages have been performed. The ϕ phase of the preparatory pulse θ 0 for sequence (3) was 270◦.
T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
(a)
(a)
(b)
(b)
467
Fig. 1. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with a 20 pulse sequence at τ = 2.1 ms at exact resonance frequency: (a) spin-locking spin-echo pulse sequence, (b) phase cycled pulse sequence.
We can see that the trains of spin-echo signals in both cases are very similar. It was found that the spin-echo train in NaNO2 is also detected at resonance offset. In Fig. 2 one can see NQR signals obtained at the offset f = 2 kHz for sequence (3). As an illustration we present the real components (Fig. 2(a)), the imaginary ones (Fig. 2(b)) and the magnitude (Fig. 2(c)) of NQR signals. We experimentally investigated the dependence of the effective relaxation time T2e on the duration of pulses in NaNO2 for sequence (3) and the result is presented in Fig. 3. These measurements were made at the exact resonance frequency. It is essential to
(c) Fig. 2. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with a 20 pulse sequence at τ = 2.1 ms at resonance offset f = 2 kHz: (a) real component, (b) imaginary component, (c) magnitude.
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T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
Fig. 3. The long decay constant of the spin-echo signal train (effective time T2eL ) from 14 N in a powdered sample of sodium nitrite (NaNO2 ) as a function of the pulse duration at room temperature (297 K) obtained with the phase cycled pulse sequence. Pulse spacing τ = 2.1 ms.
(a)
(b) Fig. 5. The spin-echo signal train in sodium nitrite (NaNO2 ) obtained with the phase cycled pulse sequence (20 pulses) at exact resonance frequency: (a) τ = 1.6 ms, (b) τ = 1.0 ms. Fig. 4. The long decay constant of the spin-echo signal train (effective time T2eL ) from 14 N in a powdered sample of sodium nitrite (NaNO2 ) as a function of the pulse spacing τ at room temperature (297 K) obtained with the phase cycled pulse sequence.
keep in mind that the nitrogen-14 quadrupolar spinsystem in this sample has three energy levels. For this kind of system the spin-echo train decays as the sum of two exponentials. Therefore the effective relaxation time T2e must be described by the sum of two exponential terms containing the short (T2eS ) and long (T2eL ) relaxation times [22,23]. In the present work we only measured the long effective relaxation time T2eL , which is very important for describing the spin locking effect. However the short time T2eS needs to be investigated
as well and we plan to do it in the immediate future. From Fig. 3 we can see that the T2eL time slowly grows with the decrease of pulse duration or flipping angle θ 0 . However, our experiments helped to establish that when the pulse duration is shorter then the “90◦ -pulse”, the amplitudes of the SE signals begin to decrease sharply with the decrease of the preparatory pulse and pulse durations. Besides, at some short and some sufficiently long pulse durations the spin-echo train was not observed at all. This case corresponds to the zero value of T2eL in Fig. 3. As expected, the pulse duration equal or close to “90◦ -pulse” was optimal for the detection. Therewith note that the optimal prepara-
T.N. Rudakov, V.T. Mikhaltsevich / Physics Letters A 309 (2003) 465–469
tory pulse duration can be set from 1 to 1.5 times the duration of the “90◦ -pulse”. Fig. 4 shows the strong dependence of T2eL on the time spacing τ between the first two pulses for sequences (3). The pulse durations equal “90◦ -pulse”. From this picture one would expect that for τ → 0 one would obtain T2eL → T2ρ , the spin-lattice relaxation time in the rotating frame, and T2ρ seems to be around 50 ms. It is well known that the pulsed spin-locking occurs when τ becomes less than T2 . Under this condition with a SLMP sequence, the magnetization rapidly evolves to a quasistationary state which does not persist. This state decays slowly to equilibrium. Our experiments demonstrated that both quasistationary and equilibrium states emerge when using PCPS (Fig. 5). The quasistationary and equilibrium magnetization depend strongly on the time spacing τ . This fact becomes obvious when if we compare NQR signals obtained at τ = 1.6 ms (Fig. 5(a)) and τ = 1 ms (Fig. 5(b)). A more detailed study of these dependences can require additional experimental and theoretical research.
5. Conclusion We have performed spin-echo experiments using the phase cycling pulse technique. The spin-echo train for times much greater than T 2 was observed. It means that the pulsed spin-locking effect obviously can be obtained using this kind of multi-pulse technique. Investigation of the dependence of the effective relaxation time T2e on pulse parameters did not reveal any essential peculiarities compared with the commonly used technique. Therefore one can draw a conclusion that PCPS effects the NQR spin-system in a way very similar to the conventional SLMP sequences. Probably some peculiarities of the effect of PCPS on a spin-
469
system might be observed in the case on non-resonant experiments. However at the moment we can only make assumptions. As the phase cycling pulse technique has some very useful properties we expect that it should be very promising for the pulsed spin locking experiments and especially for some NQR applications.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
[21] [22] [23]
E.D. Ostroff, J.S. Waugh, Phys. Rev. Lett. 16 (1966) 1097. P. Mansfield, J.S. Waugh, Phys. Lett. 22 (1966) 133. D. Suwelack, J.S. Waugh, Phys. Rev. B 22 (1980) 5110. R.A. Marino, S.M. Klainer, J. Chem. Phys. 67 (1977) 3388. J.P. Yesinowski, M.L. Bues, A.N. Garroway, M. Ziegeweid, A. Pines, Anal. Chem. 67 (1995) 2256. T.N. Rudakov, V.T. Mikhaltsevich, O.P. Selchikhin, J. Phys. D 30 (1997) 1377. R.S. Cantor, J.S. Waugh, J. Chem. Phys. 73 (1980) 1054. A.K. Hitrin, G.E. Karnaukh, B.N. Provotorov, J. Mol. Struct. 83 (1982) 269. M. Matti Maricq, Phys. Rev. B 33 (1986) 4501. D.Ya. Osokin, J. Mol. Struct. 83 (1982) 243. D.Ya. Osokin, Mol. Phys. 48 (1983) 283. A.K. Dubey, P.T. Narasimhan, J. Mol. Struct. 192 (1989) 321. D.Ya. Osokin, V.L. Ermakov, R.H. Kurbanov, V.A. Shagalov, Z. Naturforsch., Teil A 47 (1992) 439. T.N. Rudakov, V.T. Mikhaltsevich, Chem. Phys. Lett. 363 (2002) 1. H.Y. Carr, Phys. Rev. 112 (1958) 1701. R. Freeman, H.D.W. Hill, J. Magn. Reson. 4 (1971) 366. Y.L. Zhuang, R.A. Marino, Z. Naturforsch., Teil A 45 (1990) 587. M.L. Buess, A.N. Garroway, J.B. Miller, J. Magn. Reson. 92 (1991) 348. I.P. Gerothanassis, Prog. Nucl. Magn. Reson. Spectrosc. 19 (1987) 267. R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford, 1987. T.N. Rudakov, V.V. Fedotov, A.V. Belyakov, V.T. Mikhaltsevich, Instrum. Exp. Tech. 43 (2000) 78. Y. Abe, J. Phys. Soc. Jpn. 23 (1967) 51. G. Petersen, P.J. Bray, J. Chem. Phys. 64 (1976) 522.