Spin Echo Amplitude Research Articles

Enhanced Transverse Relaxation in Porous Media due to Internal Field Gradients

We present a detailed comparison between the theoretically computed spin echo decay of a fluid-saturated periodic porous medium with strong internal field gradients and that obtained from various approximations using the free diffusion formula which is strictly valid only for infinite uniform fluids. The theoretical computation of the spin echo amplitude was carried out by using the diffusion eigenstates in Fourier representation, and the internal field gradients induced by magnetic susceptibility contrast were calculated by using a two-component composite theory. The comparison allows us to have an assessment of the regime of validity of various approximations for a periodic porous medium where a rigorous theoretical computation of the enhanced transverse relaxation due to magnetic susceptibility contrast induced field heterogeneity is possible.

Nuclear magnetic resonance spin-spin relaxation of the crystals of bone, dental enamel, and synthetic hydroxyapatites.

Studies of the apatitic crystals of bone and enamel by a variety of spectroscopic techniques have established clearly that their chemical composition, short-range order, and physical chemical reactivity are distinctly different from those of pure hydroxyapatite. Moreover, these characteristics change with aging and maturation of the bone and enamel crystals. Phosphorus-31 solid state nuclear magnetic resonance (NMR) spin-spin relaxation studies were carried out on bovine bone and dental enamel crystals of different ages and the data were compared with those obtained from pure and carbonated hydroxyapatites. By measuring the 31P Hahn spin echo amplitude as a function of echo time, Van Vleck second moments (expansion coefficients describing the homonuclear dipolar line shape) were obtained and analyzed in terms of the number density of phosphorus nuclei. 31P magnetization prepared by a 90 degree pulse or by proton-phosphorus cross-polarization (CP) yielded different second moments and experienced different degrees of proton spin-spin coupling, suggesting that these two preparation methods sample different regions, possibly the interior and the surface, respectively, of bone mineral crystals. Distinct differences were found between the biological apatites and the synthetic hydroxyapatites and as a function of the age and maturity of the biological apatites. The data provide evidence that a significant fraction of the protonated phosphates (HPO4(-2)) are located on the surfaces of the biological crystals, and the concentration of unprotonated phosphates (PO4(-3)) within the apatitic lattice is elevated with respect to the surface. The total concentration of the surface HPO4(-2) groups is higher in the younger, less mature biological crystals.

Magnetism of mixed bismuth–boron oxides. [formula omitted] NQR of Bi3B5O12 in external magnetic fields

The 209Bi NQR spectra of oriented single crystal Bi3B5O12 were studied in external magnetic fields 0<Hext<500Oe, applied in various directions with respect to the crystal axes. The splitting patterns in the spectrum of the crystal were considerably different from conventional Zeeman-perturbed NQR spectra: as in Bi4Ge3O12, they displayed, upon applying magnetic fields, orientationally dependent superposition of the split patterns and strong increase in the intensity of the resonances. In addition, at certain orientations of the crystal, deep oscillations of the spin-echo amplitudes were, for the first time, observed as Hext increased from 0 to 90Oe. As a whole, the spectrum of Bi3B5O12 showed a behaviour basically similar to that reported for Bi4Ge3O12. Four magnetically nonequivalent Bi positions, two per each crystallographically nonequivalent bismuth sites, could be identified by the Zeeman-perturbed NQR patterns in Bi3B5O12.

NMR diffusion of hyperpolarised 3He in aerogel: a systematic pressure study

Diffusion of hyperpolarised 3He in a silica aerogel sample with 98% porosity was measured by NMR, and systematically studied as a function of pressure P in the range 20 mbar −1 bar. Spin-echo amplitudes, recorded with pulsed gradients in the usual CMPG sequence, follow a monoexponential decay, and the decay rate varies quadratically with the gradient intensity: thus the apparent diffusion coefficient of the gas D can be evaluated. Our results show a power-law (1/D proportional to P 0.55), which could be consistent with a fairly broad mean free path distribution, implying some inhomogeneity in the aerogel structure. We have observed a spatial non-uniformity of D, and some deviation to the quadratic dependence of the decay rate with the gradient intensity, possibly related to sample structure inhomogeneity.

Morphology of porous media studied by nuclear magnetic resonance line shapes and spin–echo decays

The line shape and spin–echo decays of liquids confined in small pores have been studied as a function of saturation. The samples used were of silica with nominal pore diameters of 60, 200, and 500 Å and had been saturated either with cyclohexane or water. The proton nuclear magnetic resonance linewidth and peak shift were measured as a function of saturation. For water samples the peak shift increased and linewidth decreased up to a critical saturation level above which the peak shift decreased and linewidth increased. This critical saturation point occurs when the surface layer is complete, and is related to the morphology of the pores. It provides evidence to suggest that the internal surface of the 200 Å silica sample was more irregular than the 60 Å sample. For the cyclohexane samples the peak shift increased and the linewidth decreased with saturation. The spin–echo amplitude decays were found to be faster than those seen in previous work. This is attributed to diffusion through a range of field gradients caused by susceptibility variations within the system. The nature of such variations depends on the saturation level. The decays were fitted to a stretched exponential function. Values for the average field gradients and the stretching parameter provide a measure of the range of gradients found and have been deduced for each experiment. Most information on the internal pore morphology is found by studying the systems at low levels of water content. The average field gradient and the stretching exponent may be related to the pore morphology.

Spin echoes and diffusion in normal-fluid 3He

Nonlinear spin dynamics in a bulk fluid 3He sample at 0 bar were investigated in pulsed NMR experiments at temperatures of 5–150 mK in field gradients 1–7 mT/cm at a frequency of 26.4 MHz in order to elucidate the influence of a high molecular field parameter μM∼136/T 2 [ mK] on spin diffusion. Multiple Spin Echo amplitudes were monitored and analyzed after the application of a π/2− τ−π/2 pulse sequence. For the time dependence of the first echo amplitude, the typical exp(− t 3) decay was only found for small effective diffusion coefficients. In addition, neither numerical simulations nor analytic approximations to Leggetts equations for the precession of spin currents around the local molecular field could explain the observed time evolution of the MSE-structure.

Molecular diffusion in periodic porous media

The diffusion of fluid through a porous medium was modeled for a periodic array. The time dependent bulk effective diffusion coefficient D(t) was calculated using Bloch type eigenfunctions. The calculations were made for periodic media composed of octahedron-like obstacles which ranged from completely separated to highly overlapping obstacles (porosity of 3%). The calculation of D(t) involves evaluation of the nuclear magnetic resonance pulsed field gradient spin echo amplitude M(k,t), which is a measurable quantity. The method, which is most effective for long times, produces results which also agree with short time asymptotics. This method is applicable for any periodic microgeometry and virtually any porosity.

Dynamic Nuclear Polarization in Pulsed ENDOR Experiments

Properly prepared pulse sequences of microwave and radio frequency have been employed to investigate the effect of polarization transfer from the polarized photo excited triplet state of pentacene inp-terphenyl crystals to the surrounding protons in pulsed ENDOR experiments. The ENDOR signal, measured as the change of electron spin echo (ESE) amplitude, is affected by the mode of RF pulses. WhenB0∥x(the long molecular axis), the ESE amplitude of the high-field transition of the triplet state changes from the maximum positive to zero with a π RF pulse, and to the maximum negative with a 2π pulse, while that of the low-field transition changes from nearly zero to the maximum negative as the RF pulse width increases. The effect is attributed to the strong electron spin polarization produced in the creation of the photoexcited triplet state and the subsequent efficient electron– nuclear polarization transfer process.

Dynamic MRI of cerebrospinal fluid flow in endoscopic percutaneous ventriculostomy

A bstract Endoscopic percutaneous ventriculostomy (EPV) is a new technique to restore the flow of the cerebrospinal fluid (CSF) tothe basal cistern in patientswith non-communicating hydrocephalus(NCH). Cardiac gated MRI techniqueshave been applied to demonstrate normal and abnormal CSF flow in humans. The aim of this study was to evaluate the ability of a new multislice spin echo dynamic MRI technique and amplitude and phase reconstruction to demonstrate the impairment of CSF flow through the aqueduct preoperatively and to assess the patency of the ventriculostomy after surgery. Thirteen patients with NCH were studied with dynamic MRI before and after EPV using multiple sagittal multislice gated SE acquisitions to demonstrate the CSF flow. Nine patients were clinically improved by EPS, two remained unchanged and two deteriorated. The permeability of the ventriculostomy was confirmed in all patients. We think that MRI flow studiesare useful todemonstrate the site of impairment of CSF flow and itsaetiology preoperatively, and to assess the permeability of the ventriculostomy after surgery in a non invasive way.

Pulsed EPR study of the S′ 3 signal in the Ca 2+-depleted photosystem II

The Ca 2+-depleted photosystem II (PS II) was studied by pulsed EPR spectroscopy. A short (5 s) illumination of the PS II in the S′ 2 state resulted in formation of the doublet S′ 3 signal at g ≈ 2.02 with a splitting of about 15 mT concomitant with the decrease of the modified Mn multiline signal by about 40%. Further illumination up to three minutes led to the formation of another S′ 3 signal with a singlet-like feature at g ≈ 1.98 and to the complete disappearance of the modified Mn multiline signal. Computer simulations of the shape of the doublet S′ 3 signal and the dependence of its electron spin echo amplitude on the microwave field strength suggest that dipole and exchange interactions between two organic radicals are responsible for the doublet S′ 3 signal. The pulsed ENDOR-induced EPR measurements indicate that the ENDOR spectrum of the tyrosine radical Y Z + is associated with the doublet S′ 3 signal only.

A model for domain and domain wall NMR signals in magnetic materials

Spin echo NMR signals in magnetic materials (simple metals, alloys or intermetallic compounds) generally result from mixed contributions of distinct magnetic regions of the sample, the magnetic domains and the domain walls. The amplitude of the signal is proportional to the so-called enhancement factor which in most of the cases greatly differs in these two regions, depending upon the wall mobility, the magnetic anisotropy, etc. The experimental access to domain and domain walls is possible, in principle, by a careful control of the RF power applied to the sample. In this paper a simple superposition model is proposed which includes both contributions to the NMR signal. We calculate the amplitude of the spin echo in magnetic powder samples and compare it with experimental situations where it has been possible to separate different contributions to the signal. This has been done in some RCo 2 magnetic rare-earth intermetallic compounds by analyzing the spectral line widths and the curve of the spin echo amplitude versus the applied RF field. Despite its simplicity, the present model allows the understanding of the main features of the NMR spectra and the dependence of the echo amplitude with the RF power in these compounds.

Diffusion eigenstates of a porous medium with interface absorption

The eigenvalues and general shapes of the low lying diffusion eigenstates are studied for the case of diffusion in a fluid-filled porous medium of arbitrary, though macroscopically homogeneous, microstructure with nonzero absorption at the pore walls. Those eigenstates are then used to discuss the tensor D-|${\mathrm{Ax}}_{\mathrm{e}}$ of bulk effective stationary diffusion coefficients and other aspects of the diffusion at long times, such as the pulsed-gradient spin-echo amplitude and the return to the origin probability (RTOP). It is shown that, under quite general conditions the localized states are unimportant, and only the low-lying extended states make a significant contribution to the long time behavior of these quantities. The eigenvalues or decay rates of those states always have the form ${\ensuremath{\lambda}}_{\mathbf{q}}$ for small wave vectors q, and ${\ensuremath{\lambda}}_{\mathbf{q}}$ is bounded from above by ${\ensuremath{\lambda}}_{0}$+q\ensuremath{\cdot}D-|${\mathrm{Ax}}_{\mathrm{e}}$\ensuremath{\cdot}q. A general connection is found between D-|${\mathrm{Ax}}_{\mathrm{e}}$ and an electrical conductivity problem in the same medium. Using the bound on ${\ensuremath{\lambda}}_{\mathbf{q}}$, it is shown that the relative RTOP (i.e., the RTOP in a fluid-filled porous medium divided by the RTOP in the uniform fluid) exhibits a nonmonotonic dependence on time, reaching a maximum at some finite characteristic value. Similar considerations also lead to the possibility of nonmonotonic behavior of the bulk effective time-dependent diffusion coefficient.

Normal and Reverse Vesicles with Nonionic Surfactant: Solvent Diffusion and Permeability

Normal and reverse vesicle systems with nonionic surfactants were investigated. The solvent self-diffusion coefficient was measured using the 1H-NMR Fourier transform pulsed gradient spin-echo technique. In the case of normal vesicles, the water solvent is found to exchange rapidly between the inside and outside of the vesicles on the experimental time scale (≈0.1 s). Here, only an average self-diffusion coefficient can be measured from which the fraction of entrapped water can be determined. In the reverse vesicle case, we observe either a fast or a slow exchange, depending, on the oil and the bilayer composition. In particular we have investigated a semipermeable membrane system, where with a solvent mixture, one of the two types of solvent molecules exchanges fast while the other exchanges slowly on the experimental time scale. Here, the lifetime of a solvent molecule inside the reverse vesicles was found to depend on the composition of the mixed reverse bilayers, leading to an observed transition from fast to slow exchange conditions when varying the bilayer composition. In the slow exchange case, the self-diffusion coefficients of solvent molecules on the outside and inside of the vesicles, where the latter reports on the vesicle self-diffusion coefficient, are in principal resolved. From the bimodal type of decay of the spin-echo amplitude, it is also possible to determine directly the fraction of solvent molecules entrapped inside the vesicles.

High temperature hydrogen diffusion in Zr0.33Ni0.67[sbnd]Hx amorphous alloys

The proton content in Zr0.33Ni0.67Hx amorphous alloy was monitored by changes in electrical resistivity and with the extraplated spin echo amplitude measured by the Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance pulse sequence in the temperature interval 300 to 450 K. Both methods show that the hydrogen desorption processes can be approximately divided into two ranges. The first is a fast process which is at present not interpretable. In the second stage, the process is thermally activated, and the activation energy calcualted from the resistivity changes is equal to 0.32 ± 0.04 eV. The CPMG spin echo measurements also give the spin-spin relaxation time of diffusing protons and the activation energy of this process, 0.34 ± 0.02 eV, is exactly the same as extracted from the resistivity measurements.

Observation of vortex-lattice melting by NMR spin-lattice relaxation in the mixed state

For anisotropic layered superconductors a NMR technique is proposed to study the structure of the moving vortex state in the presence of transport current flowing in the layers. The internal field in an anisotropic superconductor will have a component perpendicular to an applied field which is tilted away from the c axis. The moving ordered vortex lattice produces an alternating magnetic field which causes nutation of nuclear spins and contributes to the decay of the spin-echo amplitude. This decay rate will display an array of peaks as a function of frequency. In the liquid phase this alternating field contributes to the longitudinal relaxation rate ${\mathit{W}}_{1}$ which has a single peak.

Self-diffusion in a periodic porous medium with interface absorption.

A matrix eigenvalue problem for the diffusion eigenstates of a periodic porous medium with interface absorption is set up by expanding those eigenstates in terms of the eigenstates of the zero absorption diffusion problem in the same medium. This approach enables us to obtain accurate numerical solutions for many aspects of self-diffusion. We use our approach to evaluate the time-dependent bulk effective or restricted diffusion coefficient of the fluid filled porous medium and other properties that can be measured using NMR techniques, such as the spectrum of spin relaxation times and the spin echo amplitude in the presence of a pulsed magnetic field gradient.

Scaling of spin-echo amplitudes with frequency, diffusion coefficient, pore size, and susceptibility difference for the NMR of fluids in porous media and biological tissues.

Both Carr-Purcell-Meiboom-Gill (CPMG) measurements and single-spin-echo measurements have been made at frequencies of \ensuremath{\nu}=10, 20, and 50 MHz for two relatively homogeneous porous porcelain materials with different pore sizes, both saturated separately with three liquids of different diffusion coefficients. The CPMG transverse relaxation rate is increased by an amount R by diffusion in the inhomogeneous fields caused by susceptibility differences \ensuremath{\chi}; R shows the dependence on \ensuremath{\tau} (half the echo spacing) given by the model of Brown and Fantazzini [Phys. Rev. B 47, 14 823 (1993)] if relaxation is slow enough that there are several CPMG echoes in a transverse relaxation time. For \ensuremath{\tau} values over a range of a factor of about 40, the increase of R with \ensuremath{\tau} is nearly linear, with a slope that is independent of pore dimension a and diffusion coefficient D. For this nearly linear region and a short initial region quadratic in \ensuremath{\tau}, we find R\ensuremath{\propto}(\ensuremath{\chi}\ensuremath{\nu}${)}^{2}$. In these regions we can scale and compare measurements of R taken for different values of \ensuremath{\chi} \ensuremath{\nu}, a, and D by plotting RD/(1/3\ensuremath{\chi}\ensuremath{\nu}a${)}^{2}$ vs D\ensuremath{\tau}/${\mathit{a}}^{2}$. The asymptotic values of R for large \ensuremath{\tau} for CPMG data can be inferred from the asymptotic slope, -${\mathit{R}}_{\mathit{s}}$, of lnM (magnetization) for single spin echoes as a function of echo time t=2\ensuremath{\tau}.It is shown from the Bloch-Torrey equations for NMR with diffusion that, for any combination of parameters \ensuremath{\chi}, \ensuremath{\nu}, a, or D, the magnetization M is a function of both a dimensionless time (either ${\mathit{t}}_{\mathit{u}}$=Dt/${\mathit{a}}^{2}$ or ${\mathit{t}}_{\mathit{v}}$=1/3\ensuremath{\chi}\ensuremath{\nu}t) and a dimensionless parameter \ensuremath{\xi}=1/3\ensuremath{\chi}\ensuremath{\nu}${\mathit{a}}^{2}$/D. If \ensuremath{\xi}2 (for our particular porous media and definition of the distance a), the asymptotic slope of -lnM is approximately ${\mathit{R}}_{\mathit{s}}$=1/3\ensuremath{\chi}\ensuremath{\nu}, that is, it is proportional to only the first power of \ensuremath{\chi}\ensuremath{\nu} and does not depend on either a or D. These results are compatible with the existence of a long-tailed distribution of phases, such as a truncated Cauchy distribution, at echo time. Diffusion does not lead to a reduction of ${\mathit{R}}_{\mathit{s}}$ because averages of choices from a Cauchy distribution give the same distribution rather than a narrower one as for the Gaussian distribution. For larger \ensuremath{\xi} the decay of lnM decreases and no longer approaches a linear asymptote during measurement times. A semiempirical expression for the large-\ensuremath{\xi} case is given. These scaling laws should help in predicting the effects of changes in frequency and of susceptibility contrast as well as of changes in temperature, fluid, or range of pore sizes or other characteristic dimensions.

NMR Spin echo measurement of vortex motion and the penetration depth of a type II superconductor

An NMR spin echo measurement of driven vortex motion in a type II superconductor is reported. The effect of vortex displacement during the measurement is to reduce the spin echo amplitude. A model for the effect is used to obtain the penetration depth (λ) of multifilament NbTi alloy wire as a function of temperature. A limiting low temperature value λ(0) = 250 ± 25 nm is found.

Basics and features of spin-locked electron spin echo envelope modulation

It is demonstrated that the spin-locked electron spin echo envelope modulation (ESEEM) experiment recently introduced by Zhong and Pilbrow [Chem. Phys. Letters 222 (1994) 592] does not yield the same information as the conventional three-pulse ESEEM experiment because of the hyperfine decoupling inherent in the spin-lock pulse. A short theoretical description of the spin-locked ESEEM approach is given and conditions are discussed under which the hyperfine decoupled NMR spectrum can indirectly be measured via the electron spin echo amplitude. The theoretical predictions are verified experimentally for different spin-lock fields.

Autler-Townes modulation of coherent transients in photoexcited color centers.

It is shown that for inhomogeneously broadened transitions Autler-Townes interactions can be resolved in the time domain by performing a modified echo experiment. Constructive and destructive interferences of the Autler-Townes components in electron spin triplet states are observed in the optically detected spin-echo amplitude decay signals for two different triplet-state color center model systems in calcium oxide and diamond crystals, respectively.