EPR Free Induction Decay Coherence Observed after a Single Pulse in Saturation Recovery Experiments for Samples with Resolved Multiline CW Spectra

An electron paramagnetic resonance (EPR) spin-coherence signal has been observed following a single pulse for rapidly tumbling radicals with well-resolved nuclear hyperfine splitting in fluid solution when B ₁ is large enough to excite multiple hyperfine lines. This signal, which has the shape of a spin echo, arises from constructive interference of overlapping free induction decays (FIDs) from the hyperfine lines. It has been observed for 2,6-di-t-butyl-1,4-benzosemiquinone, 2,5-di-t-butyl-1,4-benzosemiquinone, 2,3,5,6-tetramethoxy-1,4-benzosemiquinone, 2,4,6-tri-t-butylphenoxyl radical, and 3-carbamoyl-2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy. It occurs at a time after the pulse that is equal to the inverse of the nuclear hyperfine splitting, independent of EPR resonance frequency from 250 MHz to 9.1 GHz. As the length of the pulse is increased, separate coherence signals can be observed that correspond to the beginning and end of the pulse. This coherence is distinct from the "single-pulse echo" signals discussed in the literature. For 2,6-di-t-butyl-1,4-benzosemiquinone, which has two resolved couplings (1.24 and 0.052 G), FID oscillations with a period that corresponds to the larger hyperfine coupling are observed on the coherence signal that arises from the smaller hyperfine coupling. If phase cycling is not perfect, the coherence signal can interfere with measurements of T ₁ by saturation recovery. Authors' address: Gareth R. Eaton, Department of Chemistry and Biochemistry, University of Denver, Denver, CO 80208, USA     

Spin echo SPI methods for quantitative analysis of fluids in porous media

Fluid density imaging is highly desirable in a wide variety of porous media measurements. The SPRITE class of MRI methods has proven to be robust and general in their ability to generate density images in porous media, however the short encoding times required, with correspondingly high magnetic field gradient strengths and filter widths, and low flip angle RF pulses, yield sub-optimal S/N images, especially at low static field strength. This paper explores two implementations of pure phase encode spin echo 1D imaging, with application to a proposed new petroleum reservoir core analysis measurement.In the first implementation of the pulse sequence, we modify the spin echo single point imaging (SE-SPI) technique to acquire the k-space origin data point, with a near zero evolution time, from the free induction decay (FID) following a 90° excitation pulse. Subsequent k-space data points are acquired by separately phase encoding individual echoes in a multi-echo acquisition. T₂ attenuation of the echo train yields an image convolution which causes blurring. The T₂ blur effect is moderate for porous media with T₂ lifetime distributions longer than 5 ms. As a robust, high S/N, and fast 1D imaging method, this method will be highly complementary to SPRITE techniques for the quantitative analysis of fluid content in porous media.In the second implementation of the SE-SPI pulse sequence, modification of the basic measurement permits fast determination of spatially resolved T₂ distributions in porous media through separately phase encoding each echo in a multi-echo CPMG pulse train. An individual T₂ weighted image may be acquired from each echo. The echo time (TE) of each T₂ weighted image may be reduced to 500 μs or less. These profiles can be fit to extract a T₂ distribution from each pixel employing a variety of standard inverse Laplace transform methods. Fluid content 1D images are produced as an essential by product of determining the spatially resolved T₂ distribution. These 1D images do not suffer from a T₂ related blurring.The above SE-SPI measurements are combined to generate 1D images of the local saturation and T₂ distribution as a function of saturation, upon centrifugation of petroleum reservoir core samples. The logarithm mean T₂ is observed to shift linearly with water saturation. This new reservoir core analysis measurement may provide a valuable calibration of the Coates equation for irreducible water saturation, which has been widely implemented in NMR well logging measurements.     

Second-Order Echo Signals in Two-Pulse Delayed Nutation

Nonstationary magnetic nutation signals of the second-order echo that occur during the effect of a resonance radiofrequency pulse of length t ₂ on a two-level inhomogeneously broadened spin system preliminarily excited by a pulse of length t ₁ < t ₂ have been studied theoretically. It has been found that in contrast to the delayed nutation echo whose formation is attributed to the restoration of the longitudinal magnetization that arose by the end of the first pulse, these signals result from the reversal in time of three effective signals of free precession generated after the termination of the first pulse. The theoretical results are in good agreement with the experimental data obtained in NMR of protons in glycerin. A conclusion on the validity of the theorem of coherent transient processes occurring in two-level systems in the presence of an exciting field is drawn.     

Multiple structure of two-pulse nuclear spin echo in cobalt films

The conditions for the formation of two-pulse echo signals from ⁵⁹Co nuclei in thin magnetic films at T=4.2 K are investigated. In the framework of the existing mechanisms, numerical simulation of the conditions for the formation of extra 3τ and 4τ echo signals (τ is the time delay between pulses) is carried out. It is shown that the multiple structure of the echo from ⁵⁹Co nuclei at T=4.2 K is due to a mechanism in which an additional hyperfine magnetic field proportional to nuclear magnetization is acting on the nuclear spin system.     

Influence of Reversible and Irreversible Relaxation on the Single-Pulse Echo Signal

An analytical expression for a signal of the single-pulse echo generated in nonresonant pulse excitation of an inhomogeneously broadened two-level quantum system has been obtained, with the reversible and irreversible relaxation taken into account. It is shown that the rate of decay of the single-pulse echo is determined by the rate of reversible and irreversible transverse relaxation. It has been established that the contribution of the reversible and irreversible relaxations to decay of the single-pulse echo depends on the ratio between the detuning of the pulse-carrying frequency from resonance to the Rabi frequency. The difference between the times of transverse irreversible relaxation measured in manganese ferrite MnFe₂O₄ by the methods of single and two-pulse echo of nuclear magnetic resonance has been explained within the framework of the theoretical expressions obtained.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

A Comparative Study of CT and MRI for Evaluating Hepatic Malignant and Focal Nodules Based on ROC Curves

The clinical use of magnetic resonance imaging (MRI) and multiphase enhanced computed tomography (CT) with the contrast media (Gd-EOB-DTPA) for detecting hepatic malignant and focal nodules prior to operation was examined based on the receiver operating characteristic (ROC) curve. This study included 70 patients with malignant and focal liver nodules who underwent MRI and multiphase CT scans before operation. Both scans for each patient were conducted within 1 month. For MRI, the T ₂-weighted image (single shot fast spin echo) and two-dimensional (2-D) and 3-D T ₁-gradient magnetic signals were obtained for all patients before administering the contrast media. The 2-D and 3-D T ₁-gradient magnetic signals were obtained in the same location after delivering the contrast media. For the CT scans, images of artery phase, portal phase, and delayed phase were obtained at a thickness of 5 mm or less after administering contrast similar to MRI. An ROC curve was used (paired-samples T test, P < 0.05) to evaluate the images. When the analysis was based on the ROC curve, MRI showed high values (P < 0.05) for area under curve (AUC), sensitivity, and specificity in terms of detection rates of small lesions (less than 2 cm and more than 2 cm) compared to multidetector computed tomography (MDCT) (for ≤2 cm, MRI: 0.928, 70, 93%, CT: 0.775, 30, 90%; for ≥2 cm, MRI: 0.744, 80%, 84%; CT: 0.692, 40%, 84%). Gd-EOB-DTPA contrast media-enhanced MRI scanner for detecting malignant and focal liver nodules before operation showed the higher detection rate of lesion and classification of lesion as either benign or malignant than multiphase enhanced MDCT when the ROC curve was used for analysis. Based on these results, we believe that analysis based on the ROC curve will provide guidelines for evaluating malignant and focal hepatic lesions prior to operation.     

Reducing ghosting due to k-space discontinuities in fast spin echo (FSE) imaging by a new combination of k-space ordering and parallel imaging

In multi-echo imaging sequences like fast spin echo (FSE), the point spread function (PSF) in the phase encoding direction contains significant secondary peaks (sidebands). This is due to discontinuities in adjacent k-space data obtained at different echo times caused by T₂ decay, and leads to ghosting and hence reduced image quality. Recently, utilising multiple coils for signal reception has become the standard configuration for MR systems due to the additional flexibility that parallel imaging (PI) methods can provide. PI methods generally obtain more data than is required to reconstruct an image. Here, this redundancy in information is exploited to reduce discontinuity-related ghosting in FSE imaging. Adjacent phase encoded k-space lines are acquired at different echo times alternately in the regions of discontinuity (called ‘feathering’). This moves the resulting ghost artefacts to the edges of the field of view. This property of the ghost then makes them amenable to removal using PI methods. With ‘feathered’ array coil data it is possible to reconstruct data over the region of the discontinuity from both echo times. By combining this data, a significant reduction in ghosting can be achieved. We show this approach to be effective through simulated and acquired MRI data.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

Phonon-assisted spin diffusion in solids

The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance r_ij and enhance the transition rate via the change of the 1/r³_ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T², and in the limit T → 0, where the rate varies as T⁷. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Primary acoustic echo during excitation of a paramagnetic crystal by picosecond elastic video pulses

The primary acoustic echo formed during excitation of a paramagnetic crystal with effective spin S=1 by two transverse picosecond elastic video pulses is investigated theoretically. Both exciting video pulses are applied perpendicular to the external magnetic field. It is shown that the primary acoustic echo in the general case consists of six longitudinal and transverse signals at the frequencies of the transitions within a Zeeman triplet. The optimal parameters of the exciting video pulses for the appearance of different echo signals are determined. Fiz. Tverd. Tela (St. Petersburg) 41, 623–628 (April 1999)     

Numerical Determination of the Relaxation Parameters of NMR in Complex Heterogeneous Systems

The methods of mathematical processing of the envelopes of spin-echo signals have been considered within the framework of the multiphase relaxation theory. A mathematical model for separation of multiexponential relaxation curves into individual exponential components of spin-spin relaxation times T _2i and amplitudes I _i is described. The multiphase nature of the relaxation of protons in complex heterogeneous systems has been revealed, and the relaxation characteristics of individual components — spin-spin relaxation times and amplitudes — have been determined.     

Homogeneous FID signals in polypyrroles:T 1-estimate from a two-pulse sequence in homogeneous systems

Several experiments using pulse electron spin resonance (ESR) equipment reveal that homogeneous free induction decay (FID) signals are given by electron spins in polypyrrole (PPy). FID signals obtained from PPy are accurately fitted via single-exponential curves, thus indicating that PPy can be used as a standard sample for several experiments with pulse ESR. We particularly pay attention to the nutation phenomena resulting from two-pulse irradiation (θ-t−2θ-t) in the homogeneous systems. The analysis by the vector model suggests that the nutation curves are affected by spin-lattice relaxation. Such a tendency is actually observed for two types of PPy used as examples ofT ₁ >T ₂ andT ₁ ≈T ₂. Thus the fitting over the nutation curve can be utilized for estimatingT ₁. We particularly point out that such a procedure can be advantageously performed for electron spins with a short spin-lattice relaxation time.     

Secondary Nuclear Spin Echo Signals in Thin Yttrium Iron Ferrite Garnet Films

The results are presented of experimental and theoretical study of the phenomenon of secondary nuclear spin echo in magnetically ordered materials in which the formation of additional echo signals is due to dynamic hyperfine coupling. Numerical simulation of the effect of the amplitude (ω1) and the durations of the first (t1) and the second (t2) exciting pulses on the echo signals is performed. It is found that the maximum amplitude of the secondary echo is formed under the conditions ω1t1 = 0.5π and ω1t2 ≈ 0.6π. It is shown that secondary echo signals can be observed upon inhomogeneous excitation of the spectral line ω1 ≤ Δω, where Δω is the inhomogeneous spectral line width. At a temperature of T = 4.2 K, additional double-pulse spin 3τ-echo signals from iron nuclei are experimentally observed in an epitaxial yttrium ferrite garnet film enriched with 57Fe magnetic isotope to 96%. The experimentally observed phase relationships between the primary and secondary echo signals, as well as the dependence of the echo signal amplitude on the amplitude and duration of the exciting pulses, are in good agreement with the results of numerical simulation of the dynamics of nuclear magnetization with regard to the dynamic hyperfine coupling. It is shown that the secondary echo exhibits the effect of spectral line narrowing, and the amplitude of the secondary echo is proportional to the nuclear magnetic resonance (NMR) enhancement factor in magnets, η. In the case of 57Fe NMR in an yttrium iron garnet (YIG) film, the amplitude of the 3τ-echo is two to three orders of magnitude smaller than the amplitude of the primary 2τ-echo, which corresponds to η ≈ 440. The detection of weak secondary echo signals proves to be possible due to the use of a phase-coherent NMR spectrometer with digital quadrature detection at the carrier frequency and signal accumulation.     

Electron spin echo modulation and relaxation in polythiophene

Electron spin echo measurements on neutral poly (thiophene) show a clear modulation of the spin-echo decay. Analysis of the modulation and its Fourier transformed (ω) power spectrum indicates that the wave function of the spin defect is extended over ～ 25 proton nuclei. The functional behavior of the longitudinal relaxation, T₁, versus temperature is very similar to that observed previously for (CH)_x, although T₁ values for poly (thiophene) are significantly longer.     

Mechanically Detected Nuclear Magnetic Resonance at Room Temperature and Normal Pressure

Mechanically detected magnetic resonance (MMR) is a new technique for detecting electron or nuclear spin signals. All preceding experiments have been carried out in a <10⁻³Torr vacuum at room temperature or at low temperatures down to 6 K. In this article the first MMR experiments at normal pressure and room temperature are presented. The mechanically detected NMR signals resulted from ammonium nitrate and ammonium sulfate. In addition, techniques for determiningT₁andT_1ρwith mechanical experiments were developed. IfT_1ρis not more than two or three times smaller thanT₁, an inversion-recovery technique, first used for the detection of¹⁹F spins at low temperatures, can be used. It could be shown that this technique also works in principle at room temperature.     

CPMG echo amplitudes with arbitrary refocusing angle: explicit expressions, asymptotic behavior, approximations

Exact explicit analytical expression for echoes in the Carr–Purcell–Meiboom–Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T₁, T₂ and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.     

Phonon echo in L-alanine

Phonon echo signals have been observed in a finely-dispersed crystalline powder of the L-alanine amino acid. Measurements of the relaxation time T ₂ have revealed a phase transition in L-alanine crystals at a temperature of about 170 K. Fiz. Tverd. Tela (St. Petersburg) 40, 2119–2120 (November 1998)