The internal magnetic field distribution, and single exponential magnetic resonance free induction decay, in rocks

When fluid saturated porous media are subjected to an applied uniform magnetic field, an internal magnetic field, inside the pore space, is induced due to magnetic susceptibility differences between the pore-filling fluid and the solid matrix. The microscopic distribution of the internal magnetic field, and its gradients, was simulated based on the thin-section pore structure of a sedimentary rock. The simulation results were verified experimentally. We show that the 'decay due to diffusion in internal field' magnetic resonance technique may be applied to measure the pore size distribution in partially saturated porous media. For the first time, we have observed that the internal magnetic field and its gradients in porous rocks have a Lorentzian distribution, with an average gradient value of zero. The Lorentzian distribution of internal magnetic field arises from the large susceptibility contrast and an intrinsic disordered pore structure in these porous media. We confirm that the single exponential magnetic resonance free induction decay commonly observed in fluid saturated porous media arises from a Lorentzian internal field distribution. A linear relationship between the magnetic resonance linewidth, and the product of the susceptibility difference in the porous media and the applied magnetic field, is observed through simulation and experiment.     

Restricted diffusion and exchange of water in porous media: average structure determination and size distribution resolved from the effect of local field gradients on the proton NMR spectrum

NMR Pulsed field gradient measurements of the restrained diffusion of confined fluids constitute an efficient method to probe the local geometry in porous media. In most practical cases, the diffusion decay, when limited to its principal part, can be considered as Gaussian leading to an apparent diffusion coefficient. The evolution of the latter as a function of the diffusion interval yields average information on the surface/volume ratio of porosities and on the tortuosity of the network. In this paper, we investigate porous model systems of packed spheres (polystyrene and glass) with known mean diameter and polydispersity, and, in addition, a real porous polystyrene material. Applying an Inverse Laplace Transformation in the second dimension reveals an evolution of the apparent diffusion coefficient as a function of the resonance frequency. This evolution is related to a similar evolution of the transverse relaxation time T2. These results clearly show that each resonance frequency in the water proton spectrum corresponds to a particular magnetic environment produced by a given pore geometry in the porous media. This is due to the presence of local field gradients induced by magnetic susceptibility differences at the liquid/solid interface and to slow exchange rates between different pores as compared to the frequency differences in the spectrum. This interpretation is nicely confirmed by a series of two-dimensional exchange experiments.     

The dependence on magnetic field strength of correlated internal gradient relaxation time distributions in heterogeneous materials

Magnetic susceptibility differences in porous media produce local gradients within the pore space. At high magnetic fields, these inhomogeneities have the potential to greatly affect nuclear magnetic resonance measurements. We undertake a study using a new NMR technique to measure the internal gradients present in highly heterogeneous samples over a wide range of magnetic field strengths. Our results show that even at ultra-high fields there can exist signal at internal gradient strengths sufficiently small that techniques for suppressing unwanted side effects have the possibility to be used. Our findings encourage the use of these high and ultra-high field strengths for a broader range of samples. Our results also give experimental evidence to support the theory of internal gradient scaling as a function of field strength within pores.     

Multi-dimensional inverse Laplace spectroscopy in the NMR of porous media

Multi-dimensional NMR methods based on Inverse Laplace Transformations (ILT) may be used to examine the behavior of liquid state molecules in a porous matrix. The ILT is particularly useful when the signal is characterized by multi-exponential decay, for example in spin relaxation or in the dephasing of the NMR spin echo signal associated with molecular diffusion under the influence of pulsed magnetic or internal field gradients. Both correlation and exchange experiments are possible, the latter providing insight regarding the migration of molecules between regions characterized by different local dynamics.     

Correlation functions for inhomogeneous magnetic field in random media with application to a dense random pack of spheres

In porous media subject to applied magnetic field, the internal field arises out of susceptibility contrast of the constituents. We have examined the spatial inhomogeneity of the internal fields in a random pack of spheres using numerical computation. We find that the pair-correlation function of the internal field (K2) is a close approximation to the structure factor of the material, thus K2 can be used to characterize pore geometry. The magnetic length scale LambdaM exhibited in K2 is shown to be related to the fluid transport in the medium.     

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.     

Study of diffusion in erythrocyte suspension using internal magnetic field inhomogeneity

Transport of water and ions through cell membranes plays an important role in cell metabolism. We demonstrate a novel technique to measure water transport dynamics using erythrocyte suspensions as an example. This technique takes advantage of inhomogeneous internal magnetic field created by the magnetic susceptibility contrast between the erythrocytes and plasma. The decay of longitudinal magnetization due to diffusion in this internal field reveals multi-exponential behavior, with one component corresponding to the diffusive exchange of water across erythrocyte membrane. The membrane permeability is obtained from the exchange time constant and is in good agreement with the literature values. As compared to the other methods, this technique does not require strong gradients of magnetic field or contrast agents and, potentially, can be applied in vivo.     

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T₂ spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T₂-G maps based on the internal magnetic field gradient correction.     

A new probe of pore geometry: diffusive MASS NMR

NMR methods are widely used to probe the structure and fluid dynamics of porous materials, as they are uniquely suited to these studies since NMR records the correlation of changing local magnetic fields over a time scale of ns to seconds. The local magnetic fields are established by local variations in the bulk magnetic susceptibility of the sample (and so are directly tied to the sample's local structure). The fluctuation in field that a spin sees is due to molecular transport (including molecular diffusion) through these local fields, and so reports on the length scales of structures and impediments to transport. We have developed a new set of methods DIFFUSIVE-MASS to provide a means of systematically varying the effective time scale of the measurement and thus the effective length scale. This new handle permits a detailed, microscopic picture of the structure and dynamics. Diffusive MASS NMR methods will permit a systematic set of methods and analysis for characterizing the chemistry, structure and fluid dynamics of the mobile phase in porous materials. The approach will be applicable to any diamagnetic material. In particular, the industry of oil discovery depends on understanding heterogeneous porous media.     

Spatial encoding and the single-scan acquisition of high definition MR images in inhomogeneous fields

We have recently proposed a protocol for retrieving multidimensional magnetic resonance spectra and images within a single scan, based on a spatial encoding of the spin interactions. The spatial selectivity of this encoding process also opens up new possibilities for compensating magnetic field inhomogeneities; not by demanding extreme uniformities from the B(0) fields, but by compensating for their effects at an excitation and/or refocusing level. This potential is hereby discussed and demonstrated in connection with the single-scan acquisition of high-definition multidimensional images. It is shown that in combination with time-dependent gradient and radiofrequency manipulations, the new compensation approach can be used to counteract substantial field inhomogenities at either global or local levels over relatively long periods of time. The new compensation scheme could find uses in areas where heterogeneities in magnetic fields present serious obstacles, including rapid studies in regions near tissue/air interfaces. The principles of the B(0) compensation method are reviewed for one- and higher-dimensional cases, and experimentally demonstrated on a series of 1D and 2D single-scan MRI experiments on simple phantoms.     

Fabrication of CoFe_2O_4 ferrite nanowire arrays in porous silicon template and their local magnetic properties

CoFe_2O_4 ferrite nanowire arrays are fabricated in porous silicon templates. The porous silicon templates are prepared via metal-assisted chemical etching with gold(Au) nanoparticles as the catalyst. Subsequently, CoFe_2O_4 ferrite nanowires are successfully synthesized into porous silicon templates by the sol–gel method. The magnetic hysteresis loop of nanowire array shows an isotropic feature of magnetic properties. The coercivity and squareness ratio(M_r/M_s) of ensemble nanowires are found to be 630 Oe(1 Oe = 79.5775 A·m~(-1) and 0.4 respectively. However, the first-order reversal curve(FORC) is adopted to reveal the probability density function of local magnetostatic properties(i.e., interwire interaction field and coercivity). The FORC diagram shows an obvious distribution feature for interaction field and coercivity. The local coercivity with a value of about 1000 Oe is found to have the highest probability.     

Collective spin excitations in 2D paramagnet with dipole interaction

The collective spin excitations in the unbounded 2D paramagnetic system with dipole interactions are studied. The model Hamiltonian includes Zeeman energy and dipole interaction energy, while the exchange vanishes. The system is placed into a constant uniform magnetic field which is orthogonal to the lattice plane. It provides the equilibrium state with spin ordering along the field direction, and the saturation is reached at zero temperature. We consider the deviations of spin magnetic moments from its equilibrium position along the external field. The Holstein-Primakoff representation is applied to spin operators in low-temperature approximation. When the interaction between the spin waves is negligible and only two-magnon terms are taken into account, the Hamiltonian diagonalisation is possible. We obtain the dispersion relation for spin waves in the square and hexagonal honeycomb lattice. Bose-Einstein statistics determine the average number of spin deviations, and total system magnetization. The lattice structure does not influence on magnetization at the long-wavelength limit. The dependencies of the relative magnetization and longitudinal susceptibility on temperature and external field intensity are found. The internal energy and specific heat of the Bose gas of spin waves are calculated. The collective spin excitations play a significant role in the properties of the paramagnetic system at low temperature and strong external magnetic field.     

Arrayed acquisition of 2D exchange NMR spectra within a single scan experiment

We have recently demonstrated that magnetic field gradients in combination with frequency selective pulses, can be employed to collect a complete multi-dimensional NMR spectrum within a single scan. Following similar guidelines, field gradients could also be exploited to parallelize other types of NMR experiments where the final results arise from the collection and analysis of a series of time-incremented spectra. The present Communication exemplifies this concept by showing how a combination of gradients can be employed to monitor within a single continuous acquisition, a slow dynamic process which is in turn followed by systematic increments in the duration of a magnetization transfer time. Further, since 2D exchange NMR spectra can nowadays be themselves collected within one scan, the acquisition of a complete set of mixing-incremented 2D exchange patterns could be achieved within a single experiment entailing a total time of approximately 1 s.     

Investigation of the correlation between internal gradients and dephasing effect in inhomogeneous field

Internal magnetic gradient plays a significant role in Nuclear Magnetic Resonance (NMR) measurements of fluid saturated porous media. The quantitative characterization and application of this physical phenomenon could effectively improve the accuracy of NMR measurements and interpretations. In this paper, by using the equivalent magnetic dipole method, the three-dimensional distribution of internal induced magnetic field and its gradients in the randomly packed water saturated glass beads are quantitatively characterized. By simulating the diffusive motion of water molecules in porous media with random walk method, the computational dephasing effects equation related to internal gradients is deduced. Thereafter, the echo amplitudes are obtained and the corresponding T ₂-G spectrum is also inverted. For the sake of verifying the simulation results, an experiment is carried out using the Halbach core analyzing system (B ₀=0.18 T, G=2.3 T/m) to detect the induced internal field and gradients. The simulation results indicate the equivalent internal gradient is a distribution of 0.12–0.3 T/m, which matched well with the experimental results.     

Magnetic properties of 2D nano-islands II: Ising spin model with out-of-plane magnetic field

An Ising effective field theory model is presented to calculate the magnetic properties of 2D nano-islands on a nonmagnetic substrate, subject to an externally out-of-plane applied magnetic field. The system Hamiltonian contains nearest neighbor exchange interactions, single-atom magnetic anisotropies, and the Zeeman term. The calculations yield, in particular, the single site spin correlations, the magnetizations, and the isothermal susceptibilities, for the core and periphery domains of the nano-island. The choice of a spin S=1 for the atoms of the system permits the analysis of local spin fluctuations via the single site spin correlations. We investigate in this respect the effects due to the different magnetocrystalline anisotropies and reduced dimensionalities, for the core and periphery domains, and in particular the critical influence of the applied magnetic field. Detailed theoretical results are presented for the square and hexagonal lattice symmetries, with numerical applications for the 2D monolayer Co nano-islands on a Pt substrate. It is shown that the remarkable differences between the magnetic properties of the core and periphery domains in zero field are washed out when an out-of-plane field is applied. The applied field also provokes critical discontinuities for the spin correlations and magnetization reversals, for the core and periphery domains, which are especially evident for the hexagonal lattice nano-island in the range of fields of interest. The discontinuities and magnetization reversals occur over elementary temperature widths, and shift to lower temperatures with increasing field. The field-dependant isothermal susceptibilities show new features very different from those for the susceptibilities in zero field. The present Ising model does not show any blocking temperature transition to superparamagnetism.     

Quasi-2D Monte Carlo simulations of phase transitions and internal aggregate structures in a highly dense suspension composed of magnetic plate-like particles

The phase transitions and the internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis have been investigated by means of the Monte Carlo method. The present study considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and the magnetic field strength on particle aggregations and phase transitions. The internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation functions, orientational pair correlation functions, nematic and polar order parameters. The main results obtained here are summarized as follows. When the influence of the magnetic interaction between particles is of the same order of that of the perpendicular magnetic field strength, the particles form column-like clusters, and the internal structure of the suspension shows solid-like structures. For the case of a strong applied magnetic field, the internal structure is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under the situation of a strong applied magnetic field, and the internal structure exhibits solid-like ones. The brick wall-like structures also appear for a relatively weak magnetic field applied along the in-plane direction despite a slightly smaller volumetric fraction compared with the case of the perpendicular applied magnetic field.     

Partial magnetization reversal using laser annealing in patterned NiFe/FeMn film

We have studied local magnetization reversal by laser annealing in exchange biased NiFe/FeMn bilayer. Local magnetization reversal was performed by using the Nd:YAG laser under external magnetic field. When the laser illuminated the patterned film with the power of above 300 mW during 15 min, a magnetoresistance (MR) curve with symmetric peaks at the opposite field was obtained due to the local reversal of exchange biasing. A similar result was observed in NiFe/FeMn/NiFe trilayer. As the exposed area expanded, the intensity of opposite MR peak increased. The direction of exchange anisotropy in the partially reversed region can be restored by local laser annealing under alternating magnetic field, even if its MR peak was reduced by the damage and interdiffusion. The magnetic new domain structures of the partially reversed region was generated by laser annealing near the exposed area.     

The elimination of magnetic susceptibility artifacts in the micro-image of liquid-solid interfaces: internal gradient modulation by the CPMG RF train

Distortions of magnetic resonance images near solid-liquid interface appear as the result of the restriction to spin self-diffusion in the proximity of impermeable boundary as well as of a susceptibility difference. The spectral analysis of spin echo enables to resolve, in a simple way, how various RF-gradient pulse sequences reduce the effect of the internal magnetic field induced by the susceptibility difference at interfaces. The 1D diffusion-weighted imaging of water in the narrow notch tested efficiency of some sequence. The notch was milled in a piece of Plexiglas. The method can be used to distinguish the susceptibility effect from the effects of applied gradients when investigating the transport of fluid through a porous structure.     

A modified PGSE for measuring diffusion in the presence of static magnetic field gradients

With a proper timing of pi pulses, it is possible to reduce the effect of the static internal magnetic field gradient on the measurement of diffusion with the pulsed gradient spin echo (PGSE). A pulse sequence that in the first order eliminates the effect of weak internal static gradients in a standard PGSE experiment is introduced. The method should be applied in the cases, where strong and short magnetic gradient pulses are used to investigate the motion of liquid in heterogeneous samples with large susceptibility differences such as porous media.     

Detection of susceptibility effects using simultaneous T(2)* and magnetic field mapping

Tracking susceptibility effects is a convenient way to detect small inclusions in a bulk tissue matrix by MRI. We propose a quantitative assessment of these susceptibility effects by simultaneously mapping T(2)* and magnetic field from the time course of magnitude and phase using a multiple GE sequence at 4.7 T. A high-pass scheme is also introduced to highlight the mesoscopic magnetic field variations due to local susceptibility differences specifically in the magnetic field map. Applying this method to muscle tissue, we demonstrate that connective tissue generates detectable susceptibility effects through concomitant local magnetic field variation and T(2)* shortening.