Echoes in spin systems with dipolar interactions (original) (raw)
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Theoretical study of a simple rotational-echo double-resonance NMR for homonuclear spin-1/2 pairs
Magnetic Resonance in Chemistry, 2015
We investigate theoretically intriguing aspects of a simple rotational-echo double-resonance (REDOR) NMR technique for homonuclear spin-1/2 pairs undergoing MAS. The simple technique sets Gaussian soft π pulses at every half MAS rotational period in the pulse sequence. The reduction in rotational echo amplitude (the REDOR echo reduction) is observed at the end of the evolution period t e = (n + 1)T r , where T r is a MAS rotational period. The exact average Hamiltonians for the homonuclear REDOR (hm-REDOR) technique are calculated by dividing the evolution period into four periods. We show theoretically and experimentally that the hm-REDOR technique produces the REDOR echo reductions for homonuclear spin-1/2 pairs. In addition, the theoretical results reveal that the REDOR echo reductions are independent of the chemical-shift difference, δ, under a simple condition of κ = δ/ω r ≥ 6 and t e < 10 Á (1/d′), where ω r is the sample spinning frequency and d′ is the dipolar coupling constant expressed in Hz. We call this simple condition the master condition. This means that the REDOR echo reductions for a homonuclear spin-1/2 pair can be calculated under the master condition by considering only d′ and ω r , which is the case for a heteronuclear spin pair. Finally, we demonstrate that four-phase cycling yields the multiple-quantum filtered hm-REDOR experiment, where the appearance of the REDOR echo reductions shows that the echo reductions are definitely attributable to the homonuclear dipolar interaction even if there is a slight unwanted effect from the recovered chemical-shift anisotropy in these reductions.
Importance of the magnetic dipolar coupling on the quadrupolar spin-echo amplitude
1969
Quadrupolar spins are multienergy level systems and the coupling wQ with the electric field gradient (efg) of their surroundings can be much larger than the amplitude wRF of the radiofrequency pulse. These two facts complicate the study of spin dynamics. Considerable attention has been focused on spin Z = 1 ( Z-5). The measurements are based on the spin-echo sequence (6). But only some papers ( 7-l Z ) deal with higher spins excited by two RF pulses for any wQ/w-ratio. Two approaches have been adopted, the first using the multipole operator formalism and the second the fictitious spin-5 operator formalism ( 10, 11). They extend early work which dealt mainly with the special case of a small wQ/ w RF ratio ( 12-21) . However, only the firstorder quadrupolar interaction was taken into account in the calculations. The main limitation of these results ( 9-11) concerning a spin Z = $ system excited by two RF pulses of same phase ( ( x } -TV-( x } -TV-[acquisition(y)] , where y is the receiver phase) is that they do not predict the formation of the central-transition echo at 74 = 72 for 72 > Trio (duration of the FID) . Recently ) we have introduced a new term $Z, between the two pulses and during the acquisition period as in pioneering papers . This time a spin-echo due to the central transition was predicted and verified experimentally with 37C1 in a single crystal of NaCl(22). However, the echo is very small due to the fact that the interpulse duration 72 was taken as double TLID in order to separate the echo and the FID following the second pulse.
Influence of molecular motions on NQR echoes
Applied Magnetic Resonance, 2004
The influence of thermal molecular motions on spin echo decay in pure nuclear quadrupole resonance (NQR) is considered. Our calculations show that the Hahn echo decay is caused by dipole-dipole interaction of the nuclear spins and is strongly affected by molecular mobility that can lead to the shortening of the echo decay with increased temperatare. Slow molecular motion yields ah exponential ~.3 time dependence, while fast motion yields an exponential decay. The outlined theory allows us to explain ah unusual shortening of the "CI NQR echo decay on heating in thiourea-C2Cl ~ inclusion compound.
Attenuation of homo- and heteronuclear multiple spin echoes by diffusion
The Journal of Chemical Physics, 2001
Multiple spin echoes arise after “nonlinear” evolution of coherences in the presence of modulated demagnetizing fields. Such modulations can be prepared, for example, with the aid of a sequence of two 90° radio-frequency pulses in the presence of pulsed or steady field gradients. The echo amplitudes are sensitively attenuated by translational diffusion so that diffusivities can be determined on this basis. Homo- and heteronuclear variants of multiple-echo pulse sequences are considered here. A formalism based on the Bloch/Torrey equations is presented that describes the features displayed by the experimental data. The resulting attenuation formula for the homonuclear case generally accounts for all radio-frequency and field gradient pulse intervals occurring in the frame of this “pulsed gradient nonlinear spin echo” technique. Furthermore, an analogous formalism is reported for the heteronuclear case where the two nuclear species may populate different molecules with different diffu...
Multifrequency resonances in multiple-pulse NMR on a spin-1/2 system
Physical Review A, 2003
We have observed multifrequency resonances in a system with a spin 1/2 located in dc magnetic field and irradiated simultaneously by a multiple-pulse radio frequency sequence and a low-frequency field swept in the range 0-80 kHz. The used excitation scheme allowed us to measure the effective field of the radio frequency sequence. A peculiarity of this scheme is that the intensity of the resonance lines decreases slowly with the mode number. The theoretical description of the effect is presented using both the rotating frame approximation and the Floquet theory. Both approaches give identical results at the calculation of the resonance frequencies, transition probabilities, and shifts of resonance frequency. The calculated magnetization vs the frequency of the low-frequency field agrees well with the obtained experimental data. The multifrequency spectra give a way for studying slow atomic motion in solids.
Shift-driven modulations of spin-echo signals
Proceedings of the National Academy of Sciences, 2012
Since the pioneering works of Carr-Purcell and Meiboom-Gill [Carr HY, Purcell EM (1954) Phys Rev 94:630; Meiboom S, Gill D (1985) Rev Sci Instrum 29:688], trains of π-pulses have featured amongst the main tools of quantum control. Echo trains find widespread use in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI), thanks to their ability to free the evolution of a spin-1/2 from several sources of decoherence. Spin echoes have also been researched in dynamic decoupling scenarios, for prolonging the lifetimes of quantum states or coherences. Inspired by this search we introduce a family of spin-echo sequences, which can still detect site-specific interactions like the chemical shift. This is achieved thanks to the presence of weak environmental fluctuations of common occurrence in high-field NMR-such as homonuclear spinspin couplings or chemical/biochemical exchanges. Both intuitive and rigorous derivations of the resulting "selective dynamical recoupling" sequences are provided. Applications of these novel experiments are given for a variety of NMR scenarios including determinations of shift effects under inhomogeneities overwhelming individual chemical identities, and model-free characterizations of chemically exchanging partners. chemical exchange | dynamic decoupling | magnetic field inhomogeneity | magnetic resonance | quantum control T he unprecedented scope of applications achieved by contemporary magnetic resonance reflects the degree of control that can be imparted on the spins' evolution. Using judicious combinations of multiple-pulse sequences one can tailor Hamiltonians that highlight a variety of interactions. When coupled to the long-lived coherences typical of spin-1/2 nuclei, this enables probing matter over a broad range of conditions and scenarios -from nanomaterials to rocks under the oceans; from proteins to human metabolism and disease (1-4). Besides its wide scope of applications, NMR awakes constant interest as a benchmark for other fields of physics; in particular, the quantum information community has adopted a number of NMR paradigms as tools of its own (5-16). The most prominent example among these is the spin-echo sequence, proposed over half a century ago for removing inhomogeneous broadenings . When extrapolated to trains of π-pulses spaced by a constant delay , the resulting CPMG sequences eventually became associated to a long list of landmark measurements including T 2 determinations, structural-oriented experiments, diffusion measurements, ex situ investigations in inhomogeneous fields, kinetic chemical and biophysical determinations, spin decoupling, and single scan MRI . Overall, the extremely wide range of useful measurements that this single sequence enabled is truly remarkable.
Rotational resonance echoes in the nuclear magnetic resonance of spinning solids
Chemical Physics Letters, 1995
A procedure is described which leads to the reversal of the rotor driven evolution of nuclear spins at rotational resonance, inducing the formation of a new class of spin echoes. The echoes are produced by radio-frequency pulse sequences which suspend the evolution of the nuclear spin states for a finite fraction of a sample rotation period. Experimental demonstrations are given. The echoes may be exploited to extract scalar J-couplings and to investigate the relaxation behavior of coupled spins in a rotating powdered solid.
Journal of Magnetic Resonance, 2005
Experimental evidence of observing a rather unusual spin-locking spin echo (SLSE) effect in the fields of two multi-pulse sequences (u 0) x À (s À u x À 2s À u x À 2s À u Àx À 2s À u Àx À s) n and (u 0) x À (s À u x À 2s À u y À s) n in 14 N nuclear quadrupole resonance is presented. It was demonstrated that the SLSE effect is observed only in the even pulse intervals of both sequences. All experiments were carried out at room temperature on a powder sample of NaNO 2. A theoretical description of the effect is given.