Korringa Constant Research Articles

Brown and Korringa constants for heterogeneous thinly layered poroelastic media

AbstractMacromechanical characterization of a layered poroelastic package treated as a homogeneous (upscaled) medium is presented. The characterization is based on the knowledge of the poroelastic properties of the package's constituents. Specifically, we provide closed‐form expressions for the sum of the fourth‐order average elastic compliances tensor of the solid frame and pore space compressibility 1/Kϕ, previously defined in Brown and Korringa's extended formulation of the Gassmann's fluid substitution equations. These constants allow, thus, to perform fluid substitution on an upscaled composite consisting of poroelastic layers. Each layer within the layered package is assumed to have isotropic symmetry, uniform porosity, and single pore‐filling fluid and composed of several homogeneously distributed mineral phases such that each layer is approximately Gassmann consistent; however, the fluid and mineral phases as well as the porosity may vary from one layer to the next along the package. In addition, we obtain insights into the sensitivity of and 1/Kϕ when an approximate fluid substitution operation is used. Moreover, it is shown that the of the upscaled medium can have transverse isotropy symmetry. The degree of anisotropy is controlled by the volume fractions of individual layers and the contrast of elastic properties between the layers. The results for and 1/Kϕ are compared to those obtained by Berryman and Milton (BM) for a two‐phase isotropic composite. At a limiting case of an effectively isotropic medium, this paper's results coincide with those of BM.

Combined In Situ Seiras and NMR Investigations of Ru@Pt Electrocatalysts for Methanol Oxidation Reaction

In this presentation, we will discuss a combined in situ SEIRAS (surface enhanced IR reflection absorption spectroscopy) and NMR (nuclear magnetic resonance) study of Ru core–Pt shell (Ru@Pt) electrocatalysts for methanol oxidation reaction (MOR) [1. 2]. The Ru@Pt electrocatalysts were synthesized with commercial Ru black (~ 3 nm, Johnson-Matthey) as starting material. Ethylene glycol (EG) was used as both reaction medium and reducing agent in the synthesis [3]. First, the Ru black was reduced at 140 °C. Then a given volume of H2PtCl6·6H2O solution was added to the EG suspension of the pre-reduced Ru black and Pt was deposited onto Ru black at 120 °C.We have carried out in situ SEIRAS investigation of the Ru@Pt nanoparticles (NPs) of different Pt packing densities (PDs). We were able to identify the most active sites and surface water species involved in the carbon monoxide oxidation reaction (COR) and MOR on these NPs. We discovered that exposing the as- synthesized Ru@Pt NPs to air could turn them into largely surface-ruthenated NPs whose structure was rather stable under multiple potential cyclings between -0.2 and 0.7 V (vs Ag/ AgCl, 3 M) and reduction at -0.3 V but could be annealed by the COR. The SEIRAS data enabled the identification of the Ru-coordinated-to-Ru, Ru-coordinated-to-Pt, and Pt-islands- on-Ru-core sites on the COR-annealed Ru@Pt NPs among which the most active sites were the Pt-islands-on-Ru-core sites for the COR and MOR, as evidenced by an onset potential as low as -0.1 V for the COR. Among the three different surface water species, namely the water monomer, the weakly hydrogen-bonded water, and the strongly hydrogen-bonded water, the SEIRAS data pointed to the weakly hydrogen-bonded water as the dominant source that provided oxygen for the COR and MOR.Point-by-point 195Pt NMR spectra of the as- received and EC-cleaned samples of Ru@Pt NPs in comparison with that of pure Pt/C NPs [4], all recorded in a supporting electrolyte (0.1 M HClO4) at 80 K. The vertical dashed line indicates the peak position (1.100 G/kHz, G stands for magnetic field). The as-received Ru@Pt NPs were freshly synthesized with a shelf life of only a few hours. With the protection of ethylene glycol, little surface oxidation would be expected in such a short time. Indeed, no significant surface oxidation was observed in the corresponding 195Pt NMR spectrum. The clean-surface peak now appeared at 1.1053 G/kHz, corresponding to a 4795 ppm negative shift with respect to the clean-surface peak position (1.1000 G/kHz) of the pure Pt NPs, revealing a strong electronic effect of Ru on Pt, which is opposite to that of Au. A Gaussian deconvolution of the surface peak gave a surface atoms fraction of ≈74%, indicating a dominant Ru core Pt shell structure. Results of T2 and T1 measurements at different spectral positions of the surface fall onto their respective single relaxation curves, indicating the same highly similar surface structural and electronic properties. 13C NMR spectra of 13CO on the Ru@Pt sample were also obtained. The peaks at ≈300 and ≈219 ppm can be assigned to CO on Pt and on Ru sites, respectively, based on literature values. The results of temperature-dependent T 1 measurements show the pass-through-the-origin straight lines that are the hallmark of the Korringa relaxation behavior [5] which indicates that the adsorbed CO molecules on three different sites all acquired metallic characteristics through surface bonding. For CO on Ru sites, the shift (219 ppm) and Korringa constant T1T = 138 s·K (where T is the absolute temperature at which T1 is measured) are very close to those observed on pure Ru [6] and on Ru deposited on Pt NPs [7], which lends strong support to our peak assignment that is also consistent with the expected exposure of Ru core for a Pt PD of 40%. On the other hand, the Korringa constants measured at the same spectral position (333 ppm) were different for CO on surface Pt atoms of the Au@Pt and on those of the Ru@PtThe above discussed combined in situ SEIRAS and NMR investigation enabled us to gain deeper insights into how Ru core influences the electronic properties of he Pt core by which highly active sites were identified. Acknowledgments The authors thank financial support from DOE (DE-FG02-07ER15895) and NSF (CHE-0923910).

Effect of substitutional Cr on hydrogen diffusion and thermal stability for the BCT monohydride phase of the V–H system studied by 1H NMR

The diffusion of hydrogen in the monohydride phase (β phase) of the V1−xCrx–H (x≤0.1) system was studied by means of 1H nuclear magnetic resonance (NMR). Hydrogen atoms in the hydrides occupied the octahedral (O) sites in a body centered tetragonal (BCT) structure. The BCT lattice was contracted by addition of Cr because Cr has a smaller atomic radius than V. The activation energy for hydrogen diffusion, EH, and the Korringa constant, T1eT, were estimated from the temperature and frequency dependence of 1H spin–lattice relaxation times, T1. The value of EH increased with increase in the Cr content. The contraction of the BCT lattice by addition of Cr suppressed the diffusion of hydrogen which occupied the interstitial sites. Addition of Cr also increased the T1eT, which was accompanied by reducing in the stability of the monohydride phase of the V–H system.

31P Nuclear Spin Dynamics in Metallic Si:P at Very Low Temperature and High Magnetic Fields

Phosphorus-doped silicon (Si:P) is one of the most extensively studied condensed matter systems since a variety of physical phenomena accompanies with doping P in Si, such as impurity-band conduction, metal–insulator transition (M–I). Recently, it has attracted new interest for possible applications to quantum computer where P nuclear spins serve qubits and electron spins are completely polarized for isolated spins bound at the donor. This model of silconbased quantum computer requires NMR control of P nuclear spins under extreme conditions of several tesla magnetic field and millikelvin temperature. Spin dynamics of both nuclei and electrons are of great interest in this regard. However, despite a large amount of works devoted to the magnetic properties of Si:P, P-NMR has never been investigated under such experimental conditions. Here we present the P-NMR of metallic Si:P investigated at temperature between 40mK and 4K and a magnetic field of 7 T. We tried P-NMR in insulator Si:P but could not detect it. Our NMR data show several novel features in longitudinal relaxation time T1 and transverse relaxation time T2 associated with very low temperature and high magnetic field. We prepared a powdered sample from single crystalline silicon wafers with phosphorus dopant concentration of n 1⁄4 5:6 10 cm 3 which is above the critical concentration for M–I, nc ’ 3:7 10 cm . The dopant concentration of Si:P was determined by measuring room temperature resistivity with the Mousty scale. The sample was immersed in He–He mixture which was cooled by a dilution fridge. The NMR spectra at 120MHz were obtained by recording the spin-echo height with varying magnetic fields. The T2 was measured by decay of the echo height with varying time delay of the pulse sequence =2 . The T1 was obtained from the magnetization recovery after -pulse with varying waiting time t of the sequence t =2 . The NMR spectra were typical for metallic sample and did not depend on temperature. The linewidth of about 24mT and the Knight shift agree with those reported in the literature for similar dopant concentrations. The linewidth is believed to be determined by inhomogeneous broadening of hyperfine interactions. The longitudinal relaxation showed a substantial change only below 0.6K from the previous data. Nuclear magnetization was recovered in two steps, following double-exponential curves below 0.6K while the recovery followed single-exponential curves above 0.6K. Typical recovery curves are shown in the inset of Fig. 1. Below 0.6K, we obtained T1 separately for the fast and slow components of the relaxation, T1f and T1s. The T1f and T1s are plotted against temperatures in Fig. 1. T1f above 0.2K follows the Korringa’s relation as, T1T 1⁄4 ( is Korringa constant). It shows, however, a gradual deviation from the Korringa’s relation below 0.2K. The long T1s increases with decreasing temperature as T1s / T n with n ’ 1:3. A double-exponential form of recovery curve was observed only when the nuclear Zeeman bath decays through the electron bath to a third bath in series and the heat capacity of Zeeman bath, CN, becomes comparable to that of the electron bath, Ce. The second stage for the slow recovery process appeared in the magnetization recovery at T 1⁄4 0:6K when CN=Ce ’ 0:01 and [1 MðtÞ=M0] was measured in the range between 2 and 0.01. We understand that both the deviation of T1f from the Korringa’s relation and the appearance of long T1s arise from the large nuclear Zeeman heat capacity at high B=T . Because CN goes with ðB=TÞ while Ce with T , the temperature of electrons actually rises during nuclear spin relaxation when the electron system is decoupled to the third bath (He–He mixture bath) by T1s since T1f T1s. Due to heating up the electron temperature Te the nuclear spins relax at faster rate =Te than that expected from =T where Te > T . The T1s was first observed and was the time constant for the Zeeman and conduction electron baths to decay together to the He–He bath. The T1s is needed to cool down the nuclear spins at low temperatures and may be due to the Kapitza resistance between the sample and He–He mixture. Fig. 1. Longitudinal relaxation times T1f (circle) and T1s (square) with temperature. The inset shows the recovery curves. Dotted line represents the Korringa’s relation derived from the data above 1K. Solid line is a guide to the eye.

Formula omitted] NMR analysis of nuclear relaxation mechanisms in Pd–H and Pd–Ag–H alloys

Crystalline Pd 1− x Ag x –H y ( x = 0 – 0.35 ) alloys were studied as model systems representing a chemically disordered system for hydrogen-storage materials. Extensive H 1 relaxation rate ( R 1 , R 1 ρ and R 2 ) measurements were carried out in a wide temperature range of 2.4–400 K. Palladium–silver alloys of silver concentration as high as 35 at.% were studied by NMR spectroscopy for the first time. The relaxation mechanisms magnetic dipolar relaxation (hydrogen diffusion), Korringa relaxation, relaxation by paramagnetic impurity ions and cross-relaxation to quadrupolar metal nuclei were identified and characterized. The presence of cross-relaxation between H 1 and quadrupolar Pd 105 nuclear spins was assumed and demonstrated for the first time in Pd–H and Pd 1− x Ag x –H systems. More than one jump processes of diffusing hydrogen were found to be present in the studied palladium–silver alloys. Only lower estimated limit values of Korringa constants could be obtained since no frequency independent R 1 versus T region was found. These values are significantly higher than the ones reported by others.

NMR study of the new filled skutterudite superconductor YFe 4P 12

We report the results of 31P NMR measurements on YFe 4P 12, a new member of the family of the filled skutterudite compounds, which displays superconductivity below T c = 7 K . In the normal state, the nuclear spin-lattice relaxation time T 1 obeys the Korringa relation T 1 T = constant below 40 K, but it changes its behavior at higher temperatures. The Korringa constant ( T 1 T ) - 1 for YFe 4P 12 is smaller than that for LaFe 4P 12, suggesting that the density of states at Fermi energy N ( E F ) for YFe 4P 12 is lower than the case of LaFe 4P 12. In the superconducting state, T 1 - 1 ( T ) shows a small coherence peak just below T c , followed by an exponential decrease below 4 K revealing on energy gap 2 Δ ( 0 ) / k B T c = 3.3 . Our results indicate that YFe 4P 12 is a conventional type s-wave superconductor.

Attenuation of Nuclear Orientation of 127In in Gd and the InGd Korringa Spin–Lattice Relaxation Time Constant

The nuclear spin–lattice relaxation of 127In implanted into pure gadolinium metal has been measured using the method of integral attenuation of on-line nuclear orientation. The Korringa constant is determined to be CK (127InGd, Bpol = 0.5 T) = 0.133(18) sK. The result is compared with relaxation of In nuclei inFe.

27Al NMR Study in ZrNiAl

We have studied the microscopic properties of the hexagonal ZrNiAl, a model compound for a wide family of intermetallic compounds crystallizing in this type of structure, by using 27Al NMR spectroscopy. We have investigated the lineshape of static and MAS NMR spectra as a function of magnetic field strength (4.7–9.4 T) and temperature (5–300 K). Our data indicate that the 27Al NMR spectra result from a combined effect of quadrupole and anisotropic shift interactions. The 27Al nuclei are in an environment characterized by the quadrupole coupling constant e2qQ/h of 3.3 MHz, asymmetry parameter ηQ of 0.42, isotropic shift δiso of 393 ppm, shift anisotropy δanis=δzz−(δxx+δyy)/2 of 150 ppm, and asymmetry factor ηS of 0.5. They are found to be temperature independent. The spin–lattice relaxation rate measured at 7.05 T is proportional to the temperature with T1T=135 s K. The mechanisms responsible for observed values of δiso, δanis, T1T, and the enhanced Korringa constant are discussed.

Spin-lattice relaxation time of Sc metal

The spin-lattice relaxation time T 1 of Sc metal was measured at low temperatures to investigate the nuclear spin ordering of Sc metal. The Korringa constant gives information about the nuclear spin–spin interaction in metals. The reported values of the Korringa constant for Sc by several authors are distributed between 0.09 and 1.6 s K. We measured the temperature dependence, field dependence and anisotropy of T 1 of Sc metal.

The impact of nuclear magnetism on superconductivity

The influence of nuclear magnetism on the superconducting critical field B c has been measured in the nuclear magnets Al, AuIn 2, and Sn, at ultralow temperatures, 17 μK⩽ T⩽1 K. The materials have been chosen in respect to their distinctive Korringa constants κ( Al, AuIn 2, Sn)=(1.8, 0.1, 0.05) Ks. Both in the weakly and in the strongly coupled nuclear magnets, Al and Sn, a reduction of B c is observed being proportional to the nuclear magnetization at T⩽4 mK. However, using the high resolution of the experiment performed on Sn, the decrease of B c at cooling down to 70 μK is found to be nonmonotonic. The features of the recently measured B c( T) curve of Sn which are not understood yet as well as the formerly observed results of the interplay of nuclear ferromagnetism and superconductivity in AuIn 2 have motivated ongoing experiments which try to clear up the pair breaking contribution of nuclear magnetism.

Some metallic properties in the framework of Tsallis generalized statistics

Some metallic quantities are calculated on the grounds of Tsallis generalized statistics: the specific heat at constant volume, c V (T); the chemical potential, \(\mu (T)\); the Pauli paramagnetic susceptibility,X(T) and the Korringa constant, CK. First it is found that for a general value of q, the Sommerfeld expansion series will exhibit both, odd and even terms, contrary to what is obtained if we use the Fermi-Dirac (FD) statistics, where only even terms appear. It follows that: (i) the specific heat coefficient,μ, is q-dependent, but the temperature dependence of cV remains linear, as in the FD case; (ii) the Fermi energy, EF, differs from the chemical potential by a linear term in T, and not quadratic, as in FD, the same happening for x(T) (iii) the Korringa constant is q-dependent, but notT-dependent. In the limit \(q \to 1\) the results of FD statistics are recovered. Metallic thin films and multilayers exhibiting fractal surface structures are possible systems where the present results could be tested.

Static Nuclear Magnetisation of Aluminium Measured by Its Influence on the Superconducting Critical Field

We have measured the temperature dependence of the superconducting critical field of Al in the temperature range 17μK ≤ T ≤ 600mK. The external magnetic field necessary to suppress superconductivity in Al decreases significantly with decreasing T below about 1 mK. This effect is due to the paramagnetic contribution of the nuclear magnetic moments of Al to the total magnetic flux. Our method enables us to determine the static nuclear magnetisation of the Al nuclei. The results are in agreement with the theory for a Langevin nuclear paramagnet. In addition, we have measured the spin lattice relaxation time τ 1 . For the Korringa constant we get τ 1 ·T = (2.0±0.2)K sec in good agreement with previous NMR results.

Measurement of the nuclear spin-lattice relaxation of 90Nb on low-field sites in Fe

Radioactive 90Nb ( T 1 2 = 14 h ) was recoil implanted into thin Fe foils. The magnetic hyperfine interaction was measured with nuclear magnetic resonance on oriented nuclei. The resonance signal consists of two dominant contributions: About 90% is concentrated around 125 MHz, which is attributed to Nb nuclei on substitutional (“S”) sites with a more or less undisturbed surrounding. About 10% of the NMR-ON signal appears in a broad resonance centered at ∼ 108 MHz, the details of the lattice (“N”) site being unknown. For both sites, the nuclear spin-lattice relaxation was measured. Whereas ( B HF ( N) B HF ( S) ) 2 = 0.74 , the ratio of the Korringa constants for the spin-lattice relaxation on N and S sites is found to be C K ( N) C K ( S) = 1.03(5) .

Neutron thermometry applied to magnetization and spin-lattice relaxation measurements on silver nuclei

We have studied spin-lattice relaxation in silver metal at temperatures and magnetic fields beyond the validity of the normal Korringa relation τ1 = κ/Tc using transmission of polarized and unpolarized neutrons. For the Korringa constant of 109Ag we obtained κ = (10.0± 0.3) sK. Unpolarized neutrons were also used to measure the critical value of entropy S for nuclear antiferromagnetic ordering and to determine the induced magnetization M in the ordered state. The nuclear susceptibility X = μ0M/B = 0.36 ± 0.01 was found to be constant, independent of S and B (Bc ≈ 100 μT).

Proton spin-lattice relaxation time and proton NMR spectrum of titanium hydrides between 300K and 50mK

TiH x has been studied by pulsed NMR from 300K to 4.2K and SQUID CW NMR from 4.2K to 50mK. The proton spectra of TiH2 obtained by the two methods are identical and do not change in the whole temperature range. The line shape can be well described by the dipole-dipole interaction of protons as shown by a moment analysis. Below 100K, the spin-lattice relaxation time(T1) of TiH x , contains two contributions, one which obeys Korringa law and one constant term which is strongly influenced by magnetic impurities. The Korringa constant for TiH2 is 110±10K·s at high magnetic fields. Above 100K, the spin lattice relaxation time is influenced by the lattice distortion caused by thermal expansion which is in good agreement with former measurements.

Susceptibility and relaxation measurements on rhodium metal at positive and negative spin temperatures in the nanokelvin range

We have measured the susceptibility of polycrystalline rhodium foils, down to nuclear spin temperaturesT = 280 pK and “up” toT = −750 pK. AtT > 0, the static susceptibility follows the antiferromagnetic Curie-Weiss law with θ = −1.8±0.3 nK. AtT < 0, the expected ferromagnetic behavior in the vicinity ofT = −0 changes into antiferromgnetic tendency around −6 nK. If only nearest and next nearest neighbor interactions are assumed, our data yieldJn/h = −17±3 Hz andJnnn/h = 10±3 Hz for the exchange interaction coefficients. We have also investigated the field and polarization dependence of the spin-lattice relaxation time τ1 at positive and negative nanokelvin temperatures; surprisingly τ1 is longer whenT< 0. Infields below 1 mT, the Korringa constant shows a strong decrease, which becomes more pronounced as the conduction electron temperature decreases. Observed behavior is consistent with conduction electrons scattering from magnetic impurities, provided that the impurity-induced contribution to spin-lattice relaxation is proportional to the inverse of the nuclear spin temperature in small fields.

Spin echo and Knight shift in the intermetallic compound AuIn 2

We have investigated two bulk samples of AuIn 2 from the same batch by pulsed NMR on 115In. The first sample (I) was as received from rf-melting. The second sample (II) was annealed. The magnetic field was varied between 0.06 and 0.35 T and the nuclear spin temperature ranged from 0.4 mK to 20 mK. For sample I, a temperature independent T 2=32(5) μs was found in spin echo experiments. Temperature and field dependences of Knight shift and Korringa constant were insignificant, with K=+0.00811(5) and κ=0.110(5)sK, respectively. However, the annealed sample II even did not follow Curie's law over the whole temperature and field ranges. The NMR line could only be seen in fields above 90 mT and showed at higher fields an intensity loss and a line broadening by roughly factors of 3 and 2, respectively, with respect to sample I. No spin echo could be detected. The Knight shift depended on magnetic history. At 270 mT we got K=+0.00789(5). Some speculations on the influence of magnetic impurities and/or superconducting inclusions on the NMR line of this compound will be presented.

Pressure dependence of 1H-NMR relaxation rate in the organic superconductor, β-(BEDT-TTF) 2I 3

Proton spin-lattice relaxation rate, T −1 1, was measured in the organic superconductor, β-(BEDT-TTF) 2I 3, under pressure up to 9.3kbar. A large pressure dependence of the Korringa constant, (T 1T) −1, was observed at low temperatures (T<77K). This result shows that the density of states decreases by 30 percent at 9.3kbar, which is consistent with the previous result of magnetic susceptibility measurement. The anomalous pressure dependence of T c of this compound is discussed in relation to the present result.

Spin-lattice relaxation of Ra in Tl and g factor of the 213Ram, tau =2.1 ms isomer.

The nuclear spin-lattice relaxation of Ra in Tl is found to be mainly due to the magnetic dipole interaction of the nuclear spins with the conduction electrons in the Tl metal. The influence of magnetic spin-lattice relaxation on an initially oriented system of nuclear spins has been calculated as a function of the lattice temperature. Measurements of the time-integrated anisotropy as a function of the temperature permit to extract the Korringa constant for $^{213}\mathrm{Ra}^{\mathit{m}}$Tl and $^{214}\mathrm{Ra}^{\mathit{m}}$Tl. The Korringa relation has been used to derive the Knight shift K(RaTl) and to obtain the g factor for the $^{213}\mathrm{Ra}$ isomer.

Erratum: Heat flow between nuclei and conduction electrons in metals at very low temperature

Magnetic field and thermal gradients not only affect the heat flow between different parts of metallic samples but can also lead to anomalies in the observed energy transport between the electronic and nuclear energy reservoirs. Nuclear spin-lattice relaxation is considered in conditions of applied field and temperature such that the contribution of nuclear spins to the heat capacity dominates by far that of the electrons. The model presented is discussed with respect to recent steady state heat flow experiments on copper at submillikelvin temperatures in which a non-Korringa like, anomalously weak coupling between electrons and nuclei was observed. We show that in heat flow experiments at sufficiently low conduction electron temperatures, Te, when thermal gradients are present in the sample, the apparent Korringa constant takes the form κ = κ0 (1 + γ(kTe2)−1) where γ depends on the heat current and the nuclear heat capacity, κ0 is the actual Korringa constant, and K is the thermal heat conductance of copper which in part depends on the applied field B0 as B0−1assuming that the Wiedemann-Franz law holds. In fact, a B0Te−2 dependence was reported for the anomalous nuclear spin electron coupling which we therefore conclude could be explained by the finite thermal conductivity in an inhomogeneously heated sample. From a quantitative comparison of our model and the reported κ values, K would have to be one order of magnitude smaller than that expected for the used sample of high purity. Difficulties in comparing the over-simplified model with a real experiment are discussed and a comment concerning the effect of impurities in Pt-NMR thermometry at very low temperatures is given.