A Pulsed Field Gradient Spin-Echo Method for Diffusion Measurements in the Presence of Internal Gradients

Over the past decade several pulsed field gradient stimulated-echo methods have been presented for diffusion measurements in heterogeneous media. These methods have reduced or eliminated the coupling between the applied magnetic field gradient and a constant internal magnetic field gradient caused by susceptibility changes throughout the sample. For many research purposes thez-storage delay between the second and third π/2 RF pulse has been included in order to increase the decay of the echo attenuation to an appropriate level and to increase the signal-to-noise ratio by avoidingT₂relaxation of the magnetization in parts of the pulse sequence. For these reasons a stimulated-echo method has been applied instead of a spin-echo method. When studying systems where it is necessary to keep the duration of the pulse sequence at a minimum, and one is not dependent on usingz-storage time to increase the echo attenuation or to study diffusion as a function of observation time, a spin-echo method should be chosen. Here we propose a bipolar pulsed field gradient spin-echo method which is well suited to this purpose, and preliminary diffusion measurements are presented as illustration.     

Constant gradient stimulated echo studies of diffusion in porous materials at high spectrometer fields

A high field strength, constant gradient stimulated-echo pulse sequence is applied to a model heterogeneous system consisting of randomly packed beds of glass microspheres. A multiple exponential analysis of the dependence of the stimulated echo amplitude on diffusion time, Δ, yields coefficients that depend explicitly on both the wavevector, q and on the time delay, δ. The wavevector and δ-dependence of the coefficients is analyzed both theoretically and experimentally and shown to be sensitive to the effects of coupled relaxation and diffusion. It is proposed that these effects could be exploited as a new probe of microstructure.     

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.     

Removal of J-coupling peak distortion in PGSE experiments

Peak distortion caused by homonuclear J-coupling is a major problem that limits the utility of the pulsed-field gradient spin–echo (PGSE) method for studying translational diffusion. This unwanted effect can be removed by incorporation of anti-phase magnetization purging pulse elements at the end of the spin–echo sequence. Three methods, namely, trim-pulse, homospoil pulse gradient and chirp based z-filter were evaluated as potential candidates for an improved NMR diffusion method that is less sensitive to J-coupling peak distortion. The chirp based z-filter was found to be excellent in suppressing anti-phase magnetization while leaving the in-phase magnetization basically intact in spin–echo and stimulated-echo based experiments. The incorporation of chirp based z-filter into PGSE could allow diffusion analysis that would otherwise be impossible by conventional means.     

Self-diffusion measurements by a mobile single-sided NMR sensor with improved magnetic field gradient

A simple and fast method of measuring self-diffusion coefficients of protonated systems with a mobile single-sided NMR sensor is discussed. The NMR sensor uses a magnet geometry that generates a highly flat sensitive volume where a strong and highly uniform static magnetic field gradient is defined. Self-diffusion coefficients were measured by Hahn- and stimulated echoes detected in the presence of the uniform magnetic field gradient of the static field. To improve the sensitivity of these experiments, a Carr-Purcell-Meiboom-Gill pulse sequence was applied after the main diffusion-encoding period. By adding the echo train the experimental time was strongly shortened, allowing the measurement of complete diffusion curves in less than 1min. This method has been tested by measuring the self-diffusion coefficients D of various organic solvents and poly(dimethylsiloxane) samples with different molar masses. Diffusion coefficients were also measured for n-hexane absorbed at saturation in natural rubber with different cross-link densities. The results show a dependence on the concentration that is in good agreement with the theoretical prediction. Moreover, the stimulated-echo sequence was successfully used to measure the diffusion coefficient as a function of the evolution time in systems with restricted diffusion. This type of experiment proves the pore geometry and gives access to the surface-to-volume ratio. It was applied to measure the diffusion of water in sandstones and sheep Achilles tendon. Thanks to the strong static gradient G(0), all diffusion coefficients could be measured without having to account for relaxation during the pulse sequence.     

Electrical conductivity and chemical diffusion in Perovskite-type proton conductors in H2-H2O gas mixtures

The electrical conductivities of SrZr_0.9Y_0.1O_3-δ (SZY10) and BaCe_0.95Y_0.05O_3-δ(BCY5) were measured as a function of hydrogen partial pressure P(H₂), oxygen partial pressure P(O₂), steam partial pressure P(H₂O) and temperature. Their relaxation processes were analyzed using the solution of Fick's diffusion equation to determine the chemical diffusion coefficients and surface reaction rate constants. There were the differences in chemical relaxation kinetics and the conductivity dependence on P(H₂O) between the both oxides. The chemical diffusion coefficients depend on temperature but are essentially independent of P(H₂), P(O₂) and P(H₂O). The ambipolar diffusion treatment can explain the temperature dependence of chemical diffusion coefficients quantitatively. The chemical diffusion coefficients of SZY10 is one or two order of magnitude smaller than those of BCY5 at low temperature. The sluggish conductivity relaxation in SZY10 was due to considerably small oxygen vacancy diffusion coefficients at low temperatures. The total conductivity depends on P(H₂O) in the case of SZY10, but not for BCY5. This different dependence on P(H₂O) is caused by the difference in the ratio between proton mobility and oxide-ion mobility.     

Dependence of temporal diffusion spectra on microstructural properties of biological tissues

The apparent diffusion coefficient (ADC) measured using magnetic resonance imaging methods provides information on microstructural properties of biological tissues, and thus has found applications as a useful biomarker for assessing changes such as those that occur in ischemic stroke and cancer. Conventional pulsed gradient spin echo methods are in widespread use and provide information on, for example, variations in cell density. The oscillating gradient spin echo (OGSE) method has the additional ability to probe diffusion behaviors more readily at short diffusion times, and the temporal diffusion spectrum obtained by the OGSE method provides a unique tool for characterizing tissues over different length scales, including structural features of intracellular spaces. It has previously been reported that several tissue properties can affect ADC measurements significantly, and the precise biophysical mechanisms that account for ADC changes in different situations are still unclear. Those factors may vary in importance depending on the time and length scale over which measurements are made. In the present work, a comprehensive numerical simulation is used to investigate the dependence of the temporal diffusion spectra measured by OGSE methods on different microstructural properties of biological tissues, including cell size, cell membrane permeability, intracellular volume fraction, intranucleus and intracytoplasm diffusion coefficients, nuclear size and T₂ relaxation times. Some unique characteristics of the OGSE method at relatively high frequencies are revealed. The results presented in the paper offer a framework for better understanding possible causes of diffusion changes and may be useful to assist the interpretation of diffusion data from OGSE measurements.     

Paramagnetic relaxation in sandstones: distinguishing T1 and T2 dependence on surface relaxation, internal gradients and dependence on echo spacing

This work provides a generalized theory of proton relaxation in inhomogeneous magnetic fields. Three asymptotic regimes of relaxation are identified depending on the shortest characteristic time scale. Numerical simulations illustrate that the relaxation characteristics in the regimes such as the T(1)/T(2) ratio and echo spacing dependence are determined by the time scales. The theoretical interpretation is validated for fluid relaxation in porous media in which field inhomogeneity is induced due to susceptibility contrast of fluids and paramagnetic sites on pore surfaces. From a set of measurements on model porous media, we conclude that when the sites are small enough, no dependence on echo spacing is observed with conventional low-field NMR spectrometers. Echo spacing dependence is observed when the paramagnetic materials become large enough or form a 'shell' around each grain such that the length scale of the region of induced magnetic gradients is large compared to the diffusion length during the time of the echo spacing. The theory can aid in interpretation of diffusion measurements in porous media as well as imaging experiments in presence of contrast agents used in MRI.     

Nutation electron spin echo ofE-centers in quartz

Attenuation of the signals of the nutation echo of E’-centers in crystalline and glass quartz was experimentally investigated at room temperature. The nutation echo in EPR was excited in the single-photon regime and formed by two Zeeman-field pulses with duration t₁ and t₂ (t₁<t₂) and time interval between them τ. The echo signal was recorded during the second pulse at t≈2t₁+τ. It was established that this signal attenuation, measured as t₁ increased, follows an, exponential law, its rate Γ is much less than 1/T₂ (T₂ is the transverse relaxation time), and it linearly increases with an increase in the amplitude of the exciting SHF field B₁. The parameters of the dependence of Γ on B₁ correlate with the parameters of the analogous dependence revealed previously for attenuation of nutation of E’-centers in quartz in the two-photon regime at T=4.2 K. At the same time, the value of Γ measured with different values of τ is independent of B₁ and is equal to 1/T₁, where T₁ is the longitudinal relaxation time. A. N. Sevchenko Scientific Research Institute of Applied Physical Problems, 7, Kurchatov St., Minsk, 220064, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 3, pp. 405–411, May–June, 1998.     

Diffusion measurements using the nonlinear stimulated echo

The nonlinear stimulated echo that is generated by a sequence of three radiofrequency pulses, 90 degrees-tau(1)-90 degrees-tau(2)-45 degrees, in high magnetic fields (or at low temperatures) in the presence of pulsed or steady field gradients can be applied for measurements of the diffusion coefficient. Corresponding test experiments are reported. Steady gradients can be used without knowledge of the relaxation times. Remarkably the attenuation of the nonlinear stimulated echo by diffusion is substantially stronger than in the case of the ordinary stimulated echo.     

Photon echo and stimulated photon echo study of various collisional-relaxation channels

Collisional relaxation in SF₆ gas and its mixtures with He and Xe is studied by photon echo and stimulated photon echo methods from the standpoint of the possibility of identifying the contributions of different types of collisions. The nonexponential nature of the kinetic curve of the photon echo is clearly observed for pure SF₆, it is weaker in the mixture SF₆+Xe, and it is virtually completely absent for high degrees of dilution of SF₆ with helium. These features can be explained on the basis of estimates, made from experimental data, of the critical delay between the exciting pulses (for which the nonexponential behavior should be most strongly manifested). In pure SF₆ it is possible to distinguish the contribution of the inelastic channel (rotational relaxation) and the contribution of weak collisions. To distinguish successfully the relaxation channels in mixtures with buffer gases a heavier buffer gas and a much better time resolution must be used. It is shown that data obtained on the orientation and alignment relaxation rates by the stimulated photon echo method can serve as an upper limit for the rates of inelastic processes which cannot be measured by the photon echo method. The combined use of photon echo and stimulated photon echo methods made it possible to obtain data on the cross sections for elastic and inelastic scattering of the collisional pairs SF₆–SF₆, SF₆–Xe, and SF₆–He. Zh. éksp. Teor. Fiz. 116, 47–56 (July 1999)     

Ultrasonic relaxation in Zinc-Borate glasses

Borate glasses in the system (1 − x) [29Na₂O − 4Al₂O₃ − 67B₂O₃] − x ZnO with (x = 0, 5, 10, 15, 20, 25, 30, and 35 mol%), have been prepared by the melt quenching technique. The longitudinal ultrasonic attenuation of the prepared sample has been measured using the pulse echo technique at ultrasonic frequencies 2, 4, 6 and 8 MHz in the temperature range between 160 and 300 K. The results showed well-defined peak whose position shifts toward higher temperature with increasing frequency. The mean activation energy is strongly composition sensitive. The position and overall shape of the loss peaks in dependence on composition were analyzed in terms of an assumed loss of standard linear solid type with low dispersion, and a broad distribution of Arrhenius-type relaxation with temperature independent relaxation strength. The dependence of ultrasonic attenuation on temperature has been interpreted in terms of a thermally activated relaxation process which arises when ultrasonic waves disturb the equilibrium of an atom moving in a double-well potential in the glass network. The dependence of activation energy on composition suggests that the structure of these glasses changes at 15 mol% ZnO concentration.     

From ultraslow to fast lithium diffusion in the 2D ion conductor Li0.7TiS2 probed directly by stimulated-echo NMR and nuclear magnetic relaxation

7Li stimulated-echo NMR and classical relaxation NMR techniques are jointly used for the first time for a comprehensive investigation of Li diffusion in layer-structured Li0.7TiS2. One single 2D Li diffusion process was probed over a dynamic range of almost 10 orders of magnitude. So far, this is the largest dynamic range being measured by 7Li NMR spectroscopy directly, i.e., without the help of a specific theoretical model. The jump rates obey a strict Arrhenius law, determined by an activation energy of 0.41(1) eV and a preexponential factor of 6.3(1)x10(12) s-1, and range between 1x10(-1) s-1 and 7.8x10(8) s-1 (148-510 K). Ultraslow Li jumps in the kHz to sub-Hz range were measured directly by recording 7Li spin-alignment correlation functions. The temperature and, in particular, the frequency dependence of the relaxation rates fully agree with results expected for 2D diffusion.     

Electron spin-lattice relaxation time and spectral diffusion in γ-irradiated l-alanine

We performed continuous (CW) wave and pulsed ESR experiments to obtain information on the relaxation behavior of the l-alanine radical in an irradiated single crystal. The analysis of the CW saturation behavior gives a relaxation time of 2.8 μs. The echo detected saturation recovery was obtained for a number of different experimental conditions. In any case only a portion of the 120 G wide ESR spectrum can be affected by the microwave (MW) pulses, spectral diffusion is active and a multi-exponential decay is therefore obtained. We measured characteristic spectral diffusion times of 1–10 and 20–50 μs. We found that a long time of about 200 μs can be measured only by using a train of long selective saturating pulses and short detecting pulses. The stimulated echo decay is bi-exponential, and the characteristic times are very short. A variable temperature investigation in the range 200 to 290 K showed that the decay is governed by the spectral diffusion and by the transverse nuclear spin relaxation timeT _2n of the methyl protons.     

Diffusion and relaxation effects in general stray field NMR experiments

We analyze the evolution of magnetization following any series of radiofrequency pulses in strongly inhomogeneous fields, with particular attention to diffusion and relaxation effects. When the inhomogeneity of the static magnetic field approaches or exceeds the strength of the RF field, the magnetization has contributions from different coherence pathways. The diffusion or relaxation induced decay of the signal amplitude is in general nonexponential, even if the sample has single relaxation times T(1), T(2) and a single diffusion coefficient D. In addition, the shape of the echo depends on diffusion and relaxation. It is possible to separate contributions from different coherence pathways by phase cycling of the RF pulses. The general analysis is tested on stray field measurements using two different pulse sequences. We find excellent agreement between measurements and calculations. The inversion recovery sequence is used to study the relaxation effects. We demonstrate two different approaches of data analysis to extract the relaxation time T(1). Finite pulse width effects on the timing of the echo formation are also studied. Diffusion effects are analyzed using the Carr--Purcell--Meiboom--Gill sequence. In a stray field of a constant gradient g, we find that unrestricted diffusion leads to nonexponential signal decay versus echo number N, but within experimental error the diffusion attenuation is still only a function of g(2)Dt(3)(E)N, where t(E) is the echo spacing.     

Molecular Diffusion in NMR Microscopy

The signal-to-noise ratio and the T₂ contrast in ¹H NMR microscopy are strongly affected by self-diffusion effects. Here, we investigate the free diffusion of water within imaging gradients. As a result we obtain an apparent relaxation time T₂ which in NMR microscopy is at least one order of magnitude smaller than the true T₂ value of water in the object. This apparent T₂ relaxation is considerably reduced by improving spatial resolution. We conclude that quantitative true T₂ values cannot be calculated from series of images with increasing echo time. Furthermore, from the knowledge of the apparent T₂, an optimum short echo time can be found in order to maximize signal-to-noise ratio. Our theoretical findings are confirmed by phantom experiments at 11.75 T field strength.     

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.     

Correlation functions in the theory of atomic collision cascades: Ion location and the distribution in depth and size of damage clusters

Abstract

Simple depth distribution functions of ion bombardment damage predict the spatial extension of the cumulative damage caused by a beam of ions. Correlation functions need to be considered when more detailed information is desirable, such as the average size or depth of individual damage clusters, the average location of an ion within its damage cluster, and the fluctuations of these quantities. In this paper we establish an integral equation for the pair correlation function, coupling the individual ion range with the deposited energy. This pair correlation function determines the damage caused by all those ions that come to rest at a specific penetration depth. Solutions of the integral equation are found by standard methods. Explicit results are presented for elastic scattering governed by power cross sections. The depth distribution of damage clusters turns out to be significantly narrower than the gross damage distribution at all mass ratios except for M ₁ ? M ₂, and the size distribution appears insensitive to depth when measured perpendicular to the ion beam, but varying with depth when measured parallel. Predictions on ion location suffer from a surprizingly sensitive dependence on the scattering cross section. A note on the fluctuation of the sputtering yield by individual ions concludes the paper.     

Microstructural analysis of foam by use of NMR R2 dispersion

The spin–spin relaxation rate R₂ (=1/T₂) in hydrogel foams measured by use of a multiple spin echo sequence is found to be dependent on the echo time spacing. This property, referred to as R₂-dispersion, originates to a large extent from molecular self-diffusion of water within internal field gradients that result from magnetic susceptibility differences between the gel and air phase. Another contribution to the R₂ relaxation rate is surface relaxation. Numerical simulations are performed to investigate the relation between the foam microstructure (the mean air bubble radius and standard deviation of the air bubble radius) and foam composition properties (such as magnetic susceptibilities, diffusion coefficient and surface relaxivity) at one hand and the R₂-dispersion at the other hand. The simulated R₂-dispersions of gel foam are in agreement with the measured R₂-dispersions. By correlating the R₂-dispersion parameters and simulated microstructure properties a semi-empirical relationship is obtained that enables the mean air bubble size to be derived from measured R₂-dispersion curves. The R₂-derived mean air bubble size of a hydrogel foam is in agreement with the bubble size measured with X-ray micro-CT. This illustrates the feasibility of using ¹H R₂-dispersion measurements to determine the size of air bubbles in hydrogel foams and of alveoli in lung tissue.     

双光子共振非简并四波混频测量Ba原子里德伯态的碰撞展宽和频移

采用双光子共振非简并四波混频测量了Ar缓冲气压引起的Ba原子里德伯6snd ¹D₂谱线系的碰撞展宽和频移, 计算了n=16---33的碰撞展宽截面和频移截面. 本方法是一种纯光学的测量技术, 当采用窄带激光器时可以获得里德伯态的消多普勒光谱. 与传统实验方法测量到的里德伯态纵向弛豫的碰撞展宽不同, 本方法可以研究碰撞引起的两能态间横向弛豫的展宽.