Measurement of thermal diffusivity by magnetic resonance imaging

Nuclear magnetic resonance (NMR) may be used for monitoring temperature changes within samples based on measurements of relaxation times, the diffusion coefficient of liquids, proton resonance frequency or phase shifts. Such methods may be extended to the explicit measurement of the thermal diffusivity of materials by NMR imaging. A method based on measuring nuclear spin phase shifts or changes in the equilibrium nuclear magnetization has been developed for measuring transient thermal diffusion effects and thermal diffusivity with potential applications in NMR thermotherapy and materials science. In this method, a thermal pulse is applied to a medium, and the resultant temporal variations of the nuclear spin phase or of the magnitude of the nuclear magnetization produced by the thermal pulse are monitored at a spatial distance. The results obtained on common fluids agree well with the data from other methods.     

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.     

NMR studies of two unusual f-electron metals

We present the results of nuclear magnetic resonance (NMR) studies down to very low temperatures for two U compounds, UCu_3.5Pd_1.5 and U_0.8Y_0.2Pd₃, where the conduction electrons experience strong interactions and for which the temperature dependences of the thermal and transport properties do not obey the expectations of a simple Fermi-liquid model. Also the temperature and field dependences of the nuclear magnetization recovery of UCu_3.5Pd_1.5 in Cu nuclear quadrupole resonance show unusual features that cannot be reconciled with common expectations for a simple metal, but they are well accounted for by the Kondo disorder model. For U_0.8Y_0.2Pd₃, our Y NMR results indicate a distribution of internal static magnetic fields at the Y sites and a small temperature-dependent enhancement of the spin-lattice relaxation rateT ₁ ^? with respect to YPd₃. The NMR spectra are consistent with the presence of very small frozen U moments, but the temperature dependence of the spin-lattice relaxation rate indicates a more complicated situation.     

Refrigeration into the microkelvin range

We describe a double stage nuclear demagnetization refrigerator (4.2 moles of PrNi₅ in 6 T and 10 moles of Cu in 8 T) which has cooled about 2 kg Cu to a measured electronic temperature of 50 μK. Temperatures are determined by NMR measurements of nuclear magnetization and from spin-lattice relaxation times of Pt and Cu.     

Structural, static and dynamic magnetic properties of dextran coated γ-Fe(2)O(3) nanoparticles studied by (57)Fe NMR, M?ssbauer, TEM and magnetization measurements

The structural and magnetic properties and spin dynamics of dextran coated and uncoated γ-Fe(2)O(3) (maghemite) nanoparticles have been investigated using high resolution transmission electron microscopy (HRTEM), (57)Fe nuclear magnetic resonance (NMR), M?ssbauer spectroscopy and dc magnetization measurements. The HRTEM observations indicated a well-crystallized system of ellipsoid-shaped nanoparticles, with an average size of 10 nm. The combined M?ssbauer and magnetic study suggested the existence of significant interparticle interactions not only in the uncoated but also in the dextran coated nanoparticle assemblies. The zero-field NMR spectra of the nanoparticles at low temperatures are very similar to those of the bulk material, indicating the same hyperfine field values at saturation in accord with the performed M?ssbauer measurements. The T(2) NMR spin-spin relaxation time of the nanoparticles has also been measured as a function of temperature and found to be two orders of magnitude shorter than that of the bulk material. It is shown that the thermal fluctuations in the longitudinal magnetization of the nanoparticles in the low temperature limit may account for the shortening and the temperature dependence of the T(2) relaxation time. Thus, the low temperature NMR results are in accord with the mechanism of collective magnetic excitations, due to the precession of the magnetization around the easy direction of the magnetization at an energy minimum, a mechanism originally proposed to interpret M?ssbauer experiments in magnetic nanoparticles. The effect of the surface spins on the NMR relaxation mechanisms is also discussed.     

A field-cycling NMR investigation of resonant spin-lattice relaxation features arising from tunnelling methyl groups

(1)H nuclear spin-lattice relaxation has been investigated in sodium acetate trihydrate and sorbic acid using field-cycling NMR in the solid state. The relaxation is dominated by the reorientation of the methyl groups. Resonant features arising from coherent tunnelling are observed in both the magnetic field dependence of the spin lattice relaxation rate, T(1)(-1)(B(z)) and in the inverse temperature dependence, T(1)(-1)(1/T). The two systems have different barrier heights and tunnelling frequencies, providing different perspectives on the tunnel resonance phenomena. The magnetic field dependence enables different spectral density components to be separately investigated and in the carboxylic acid, sorbic acid, concerted proton transfer in the hydrogen bonds is also identified at low field and low temperature. The methyl hindering barriers and the correlation times characterising the reorientational dynamics has been accurately determined in both materials.     

Rapid T1 measurement via decay-recovery decomposition: applications in fringe field and distributed relaxation experiments

Spin-lattice relaxation time (T(1)) measurements are often time-consuming due to the need to measure the full equilibrium magnetization with a long wait time. However, any magnetization recovery can be decomposed into pure recovery and pure decay components, the latter of which lends itself to a much simpler and faster extraction of T(1). We demonstrate several pulse sequences that accomplish this decomposition experimentally and illustrate its applications in a steady magnetic field gradient, and in materials possessing a broad distribution of T(1).     

A global inversion method for multi-dimensional NMR logging

We describe a general global inversion methodology of multi-dimensional NMR logging for pore fluid typing and quantification in petroleum exploration. Although higher dimensions are theoretically possible, for practical reasons, we limit our discussion of proton density distributions as a function of two (2D) or three (3D) independent variables. The 2D can be diffusion coefficient and T(2) relaxation time (D-T(2)), and the 3D can be diffusion coefficient, T(2), and T(1) relaxation times (D-T(2)-T(1)) of the saturating fluids in rocks. Using the contrast between the diffusion coefficients of fluids (oil and water), the oil and water phases within the rocks can be clearly identified. This 2D or 3D proton density distribution function can be obtained from either two-window or regular type multiple CPMG echo trains encoded with diffusion, T(1), and T(2) relaxation by varying echo spacing and wait time. From this 2D/3D proton density distribution function, not only the saturations of water and oil can be determined, the viscosity of the oil and the gas-oil ratio can also be estimated based on a previously experimentally determined D-T(2) relationship.     

Measurement of the relaxation rate of the magnetization in Mn12O12-acetate using proton NMR echo

We present a novel method to measure the relaxation rate W of the magnetization of Mn 12O (12)-acetate (Mn12) magnetic molecular cluster in its S = 10 ground state at low T. It is based on the observation of an exponential growth in time of the proton NMR signal during the thermal equilibration of the magnetization of the molecules. We can explain the novel effect with a simple model which relates the intensity of the proton echo signal to the microscopic reversal of the magnetization of each individual Mn12 molecule during the equilibration process. The method should find wide application in the study of magnetic molecular clusters in off-equilibrium conditions.     

Hydration water dynamics in biopolymers from NMR relaxation in the rotating frame

Assuming dipole-dipole interaction as the dominant relaxation mechanism of protons of water molecules adsorbed onto macromolecule (biopolymer) surfaces we have been able to model the dependences of relaxation rates on temperature and frequency. For adsorbed water molecules the correlation times are of the order of 10(-5)s, for which the dispersion region of spin-lattice relaxation rates in the rotating frame R(1)(ρ)=1/T(1)(ρ) appears over a range of easily accessible B(1) values. Measurements of T(1)(ρ) at constant temperature and different B(1) values then give the "dispersion profiles" for biopolymers. Fitting a theoretical relaxation model to these profiles allows for the estimation of correlation times. This way of obtaining the correlation time is easier and faster than approaches involving measurements of the temperature dependence of R(1)=1/T(1). The T(1)(ρ) dispersion approach, as a tool for molecular dynamics study, has been demonstrated for several hydrated biopolymer systems including crystalline cellulose, starch of different origins (potato, corn, oat, wheat), paper (modern, old) and lyophilized proteins (albumin, lysozyme).     

High-frequency dynamic nuclear polarization in the nuclear rotating frame

A proton dynamic nuclear polarization (DNP) NMR signal enhancement (epsilon) close to thermal equilibrium, epsilon = 0.89, has been obtained at high field (B(0) = 5 T, nu(epr) = 139.5 GHz) using 15 mM trityl radical in a 40:60 water/glycerol frozen solution at 11 K. The electron-nuclear polarization transfer is performed in the nuclear rotating frame with microwave irradiation during a nuclear spin-lock pulse. The growth of the signal enhancement is governed by the rotating frame nuclear spin-lattice relaxation time (T(1rho)), which is four orders of magnitude shorter than the nuclear spin-lattice relaxation time (T(1n)). Due to the rapid polarization transfer in the nuclear rotating frame the experiment can be recycled at a rate of 1/T(1rho) and is not limited by the much slower lab frame nuclear spin-lattice relaxation rate (1/T(1n)). The increased repetition rate allowed in the nuclear rotating frame provides an effective enhancement per unit time(1/2) of epsilon(t) = 197. The nuclear rotating frame-DNP experiment does not require high microwave power; significant signal enhancements were obtained with a low-power (20 mW) Gunn diode microwave source and no microwave resonant structure. The symmetric trityl radical used as the polarization source is water-soluble and has a narrow EPR linewidth of 10 G at 139.5 GHz making it an ideal polarization source for high-field DNP/NMR studies of biological systems.     

Complex molecular dynamics of (CH3NH3)5Bi2Br11 (MAPBB) protons from NMR relaxation and second moment of NMR spectrum

Molecular dynamics of a polycrystalline sample of (CH(3)NH(3))(5)Bi(2)Br(11) (MAPBB) is studied on the basis of the proton T(1) (55.2 MHz) relaxation time and the proton second moment of NMR line. The T(1) (55.2 MHz) was measured for temperatures from 20K to 330 K, while the second moment M(2) for those from 40K to 330 K. The proton spin pairs of the methyl and ammonium groups perform a complex stochastic motion being a resultant of four components characterised by the correlation times τ(3)(T), τ(3)(H), τ(2), and τ(iso), referring to the tunnelling and over the barrier jumps in a triple potential, jumps between two equilibrium sites and isotropic rotation. The theoretical expressions for the spectral densities in the cases of the complex motion considered were derived. For τ(3)(H), τ(2), and τ(iso) the Arrhenius temperature dependence was assumed, while for τ(3)(T)-the Schr?dinger one. The correlation times τ(3)(H) for CH(3) and NH(3) groups differ, which indicates the uncorrelated motion of these groups. The stochastic tunnelling jumps are not present above the temperature T(tun) at which the thermal energy is higher than the activation energy of jumps over the barrier attributed to the hindered rotation of the CH(3) and NH(3) groups. The T(tun) temperature is 54.6 K for NH(3) group and 46.5 K for CH(3) group in MAPBB crystal. The tunnelling jumps of the methyl and ammonium protons are responsible for the flattening of T(1) temperature dependence at low temperatures. The isotropic tumbling is detectable only from the M(2) temperature dependence. The isotropic tumbling reduces the second moment to 4 G(2) which is the value of the intermolecular part of the second moment. The motion characterised by the correlation time τ(2) is well detectable from both T(1) and M(2) temperature dependences. This motion causes the appearance of T(1) minimum at 130 K and reduction of the second moment to the 7.7 G(2) value. The small tunnelling splitting ω(T) of the same value for the methyl and ammonium groups was estimated as 226 MHz from the Haupt equation or 80 MHz from the corrected by us Haupt equation. These frequencies correspond to 0.93 μeV and 0.34 μeV tunnel splitting energy.     

Angular dependence of the relaxation times of <Superscript>139</Superscript>La nuclei in La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript>

Relaxation of the magnetization of ¹³⁹La nuclei is considered in lanthanum manganites, which are materials with anisotropic interactions of localized electronic spins, namely, the Dzyaloshinski?-Moriya interactionand the interaction with a crystal field. Expressions are derived for the relaxation times of the longitudinal and transverse components of the nuclear magnetization, and the angular dependences of these relaxation times are found for the La_0.95Sr_0.05MnO₃ compound. In contrast to electronic relaxation, the anisotropy of nuclear relaxation contains a contribution from the shift in the electron Zeeman frequency. The theoretically calculated numerical values of the nuclear relaxation times and their ratios correspond to the range of experimental values in the compounds studied. The results can be of importance for designing devices based on these materials and for further investigation.     

Spin-wave description of nuclear spin-lattice relaxation in Mn12O12 acetate

In response to recent nuclear-magnetic-resonance (NMR) measurements on the molecular cluster Mn12O12 acetate, we study the nuclear spin-lattice relaxation rate 1/T(1), developing a modified spin-wave theory. Our microscopic new approach, which is distinct from previous macroscopic treatments of the cluster as a rigid spin of S=10, not only excellently interprets the observed temperature and applied-field dependences of 1/T(1) for 55Mn nuclei but also strongly supports the 13C NMR evidence for spin delocalization over the entire molecule.     

Molecular dynamics as studied by static-powder and magic-angle spinning 2H NMR

The 2H NMR magic-angle spinning (MAS) technique is compared to the static-powder quadrupole echo (QE) and Jeener-Brockaert (JB) pulse sequences for a quantitative investigation of molecular dynamics in solids. The linewidth of individual spinning sidebands of the one-dimensional MAS spectra are observed to be characteristic of the correlation time from approximately 10(-2) to approximately 10(-8) s so that the dynamic range is increased by approximately three orders of magnitude when compared to the QE experiment. As a consequence, MAS 2H NMR is found to be more sensitive to the presence of an inhomogeneous distribution of correlation times than the QE and JB experiments which rely upon lineshape distortions due to anisotropic T2 and T1Q relaxation, respectively. All these results are demonstrated experimentally and numerically using the two-site flip motion of dimethyl sulfone and of the nitrobenzene guest in the alpha-p-tert-butylcalix[4]arene-nitrobenzene inclusion compound.     

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-lattice relaxation in radicals containing two methyl groups,generated by gamma-irradiation of polycrystalline solids

The effects of methyl rotation on electron spin-lattice relaxation times were examined by pulsed electron paramagnetic resonance for the major radicals in gamma-irradiated polycrystalline alpha-amino isobutyric acid, dimethyl-malonic acid, and L-valine. The dominant radical is the same in irradiated dimethyl-malonic acid and alpha-amino isobutyric acid. Continuous wave saturation recovery was measured between 10 and 295 K at S-band and X-band. Inversion recovery, echo-detected saturation recovery, and pulsed electron-electron double resonance (ELDOR) data were obtained between 77 and 295 K. For the radicals in the three solids, recovery time constants measured by the various techniques were not the same, because spectral diffusion processes contribute differently for each measurement. Hyperfine splitting due to the protons of two methyl groups is resolved in the EPR spectra for each of the samples. Pulsed ELDOR data were obtained to characterize the spectral diffusion processes that transfer magnetization between hyperfine lines. Time constants were obtained for electron spin-lattice relaxation (T(1e)), nuclear spin relaxation (T(1n)), cross-relaxation (T(x1)), and spin diffusion (T(s)). Between 77 and 295 K rapid cross-relaxation (deltaM(s) = +/- 1, deltaM(I) = -/+ 1) was observed for each sample, which is attributed to methyl rotation at a rate that is approximately equal to the electron Larmor frequency. The large temperature range over which cross-relaxation was observed suggests that methyl groups in the radical and in the lattice, with different activation energies for rotation, contribute to the rapid cross-relaxation. Activation energies for methyl and amino group rotation between 160 and 1900 K (1.3-16 kJ/mol) were obtained by analysis of the temperature dependence of 1/T(1e) at S-band and X-band in the temperature intervals where the dynamic process dominates T(1e).     

NMR spin locking of proton magnetization under a frequency-switched Lee-Goldburg pulse sequence

The spin dynamics of NMR spin locking of proton magnetization under a frequency-switched Lee-Goldburg (FSLG) pulse sequence is investigated for a better understanding of the line-narrowing mechanism in PISEMA experiments. For the sample of oriented 15N(1,3,5,7)-labeled gramicidin A in hydrated DMPC bilayers, it is found that the spin-lattice relaxation time T(1rho)(H) in the tilted rotating frame is about five times shorter when the 1H magnetization is spin locked at the magic angle by the FSLG sequence compared to the simple Lee-Goldburg sequence. It is believed that the rapid phase alternation of the effective fields during the FSLG cycles results in averaging of the spin lock field so that the spin lock becomes less efficient. A FSLG supercycle has been suggested here to slow the phase alternation. It has been demonstrated experimentally that a modified PISEMA pulse sequence with such supercycles gives rise to about 30% line narrowing in the dipolar dimension in the PISEMA spectra compared to a standard PISEMA pulse sequence.     

Single-slice mapping of ultrashort T(2)

In this communication we present a method for single-slice mapping of ultrashort transverse relaxation times T(2). The RF pulse sequence consists of a spin echo preparation of the magnetization followed by slice-selective ultrashort echo time (UTE) imaging with radial k-space sampling. In order to keep the minimum echo time as small as possible, avoid out-of-slice contamination and signal contamination due to unwanted echoes, the implemented pulse sequence employs a slice-selective 180° RF refocusing pulse and a 4-step phase cycle. The slice overlap of the two slice-selective RF pulses was investigated. An acceptable Gaussian slice profile could be achieved by adjusting the strength of the two slice-selection gradients. The method was tested on a short T(2) phantom consisting of an arrangement of a roll of adhesive tape, an eraser, a piece of modeling dough made of Plasticine?, and a 10% w/w agar gel. The T(2) measurements on the phantom revealed exponential signal decays for all samples with T(2)(adhesive tape)=(0.5 ± 0.1)ms, T(2)(eraser)=(2.33 ± 0.07)ms, T(2)(Plasticine?)=(2.8 ± 0.06)ms, and T(2)(10%agar)=(9.5 ± 0.83)ms. The T(2) values obtained by the mapping method show good agreement with the T(2) values obtained by a non-selective T(2) measurement. For all samples, except the adhesive tape, the effective transverse relaxation time T(2)(?) was significantly shorter than T(2). Depending on the scanner hardware the presented method allows mapping of T(2) down to a few hundreds of microseconds. Besides investigating material samples, the presented method can be used to study the rapidly decaying MR-signal from biological tissue (e.g.: bone, cartilage, and tendon) and quadrupolar nuclei (e.g.: (23)Na, (35)Cl, and (17)O).     

Quantitative interpretation of magnetization transfer in spoiled gradient echo MRI sequences

A method for analyzing general pulsed magnetization transfer (MT) experiments in which off-resonance saturation pulses are interleaved with on-resonance excitation pulses is presented. We apply this method to develop a steady-state signal equation for MT-weighted spoiled gradient echo sequences and consider approximations that facilitate its rapid computation. Using this equation, we assess various experimental designs for quantitatively imaging the fractional size of the restricted pool, cross-relaxation rate, and T(1) and T(2) relaxation times of the two pools in a binary spin bath system. From experiments on agar gel, this method is shown to reliably and accurately estimate the exchange and relaxation properties of a material in an imaging context, suggesting the feasibility of using this technique in vivo.