Muon spin-lattice relaxation and muonium diffusion in ice

Longitudinal muon spin relaxation is measured in ice, using samples with and without enrichment in H₂ ¹⁷O, with a view to studying the mobility of the muonium fraction. A conventional analysis of the data, on the assumption that relaxation of the diamagnetic fraction is negligible, suggests that more than one mechanism of muonium relaxation is at work. A Bayesian analysis warns that separation of the diamagnetic and paramagnetic signals may not be so straightforward.     

Control of Charge Transfer Phase Transition in Iron Mixed-Valence System (n-C n H2n+1)4N[FeIIFeIII(dto)3] (n=3–6; dto = C2O2S2)

The spin flop behaviour of low anisotropy Mn ions within the mixed halide (⁵⁴Mn)Mn(Br _x Cl_1−x )₂·4H₂O is shown to be interpolative with that of the two terminal compounds, in striking contrast with the dynamics of nuclear spin lattice relaxation.     

Quantum diffusion of muonium in insulators

In this paper we review our recent experiments conducted at TRIUMF on muonium diffusion in alkali halides. First, the technique of longitudinal-field muonium spin relaxation (T ₁) due to nuclear hyperfine interaction, an indispensabletour de force for the present work. is described. It is demonstrated in KCl that the technique provides spectacular sensitivity for muonium diffusion as well as determining the average nuclear hyperfine coupling constant. The muonium hop rate shows a minimum (T ^*≃80 K) and steep increase with decreasing temperature. The result is compared with the current theory of quantum diffusion in non-metallic crystals. A few more sets of new data may be presented for other alkali halides. In addition, we show that muonium forms a delocalized state in NaCl as evidenced by a large change of the average nuclear hyperfine parameter. Related topics of local tunneling system may be briefly reviewed.     

Low temperature quantum diffusion of muonium in KCl

T ₁ spin relaxation of muonium in KCl has been studied at low temperatures (20 mK to 2 K), where the motion is believed to be band-like, i.e. the mean free path is longer than the lattice constant. The Celio model, based on the assumption of stochastic hopping of muonium, accurately describes the field dependence ofT ₁ at higher temperatures but fails below 4 K. The measuredT ₁ spin relaxation rates vary weakly with temperature below 2 K even thoughk _BT at the lowest temperature is well below the estimated muonium bandwidth obtained from the data at higher temperatures. This is taken as evidence that muonium is not completely thermalized on the time-scale of the muon lifetime due to the weak interaction with phonons at low temperatures.     

Measurement of17O quadrupole interactions and identification of the diamagnetic fraction in ice by muon level crossing resonance

By means of Level Crossing Resonance in a sample of ice which is enriched in H₂ ¹⁷O, the final diamagnetic state of implanted positive muons is determined to be the muonium-substituted molecule HMuO, accommodated in the regular and fully relaxed Ih structure. The¹⁷O quadrupole coupling constant is measured to be 6.1 MHz at 200 K assuming an asymmetry parameter close to unity, a decrease of about 5% relative to that in normal ice Ih at 77 K. The isotope effect is attributed to a greater polarization in the vicinity of a muonium (as opposed to a normal hydrogen) bond. At 50 K, an additional resonance is observed which could correspond to a precursor state, so far not definitely identified. One possibility is a muon trapped at a Bjerrum L-defect, giving a {H₂O−Mu−OH₂}⁺ species with an,¹⁷O quadrupole coupling constant of 8.2 MHz and asymmetry parameter of 0.55. Above this temperature, the fall in the (Gaussian) line-width parameter is attributed to the increasing rate of proton or muon migration, the correlation time dropping from 4 μs at 80 K to 1 μs near the melting-point. The increase in the diamagnetic fraction with rise in temperature is attributed to the increasing proportion of trapping sites available for muon capture.     

Proton dipolar spin-lattice relaxation in hexagonal ice

The ultraslow motion of defects in high purity hexagonal H₂O ice has been studied by proton dipolarT _1D measurements in the strong collision limit, using the Jeener technique. The obtained NMR correlation times agree rather well with both the Schottky H₂O diffusion timest _s=r ²/6D and the deuteron correlation times in D₂O ice, suggesting that Schottky rather than interstitial diffusion dominates spin-lattice relaxation in both H₂O and D₂O ice.On leave of absence from University of Ljubljana, Institute J. Stefan.     

Elastic properties of D<Subscript>2</Subscript>O ices in solid-state amorphization and transformations between amorphous phases

Nonequilibrium phase transformations in D₂O ices, including the solid-state amorphization of ice 1h (1h-hda) and the heating-induced transition cascade hda-lda-1c-1h from high-density amorphous (hda) ice to low-density amorphous (lda) ice followed by crystallization in cubic ice 1c and phase transition to ordinary hexagonal ice 1h, were studied using an ultrasonic technique. It has been shown that, as in H₂O ice, the softening of a crystal lattice or an amorphous network precedes nonequilibrium transformations. However, noticeable isotopic differences in the behavior of the elastic properties of H₂O and D₂O, in particular, their 1h and hda modifications, call for a more detailed study of the structural features of these H₂O and D₂O phases.     

Diffusion von18O in Eis-Einkristallen

The coefficient of¹⁸O diffusion in single crystals of ice was measured at various temperatures ranging from ?5°C to ?29,5°C. The¹⁸O concentration was determined by the nuclear reaction¹⁸O(p, n)¹⁸F caused by recoil protons due to fast neutron irradiation. It was found that the coefficients of¹⁸O and³H diffusion are of the same order of magnitude and that they have the same activation energy. This shows that¹⁸O and³H diffusion is caused by the migration of whole H₂O-molecules. A mechanism of migration over molecular vacancies is discussed.     

Inhomogeneous muonium diffusion in solid nitrogen

The spin dynamics of the muonium (Mu) atom diffusing quantum mechanically in solid nitrogen (s-¹⁴N₂) has been studied using the technique of Mu spin relaxation. A strong relationship between longitudinal (T ₁ ^–1 ) and transverse (T ₂ ^–1 ) relaxation rates (familiar in NMR) has been experimentally demonstrated for the first time for muonium relaxation. At low temperatures the results are inconsistent with diffusion models using a single correlation time _c; this is taken as evidence for the intrinsic inhomogeneity of the problem. The temperature dependence of theaverage Mu hop rate _c ^–1 gives clear evidence that Mu quantum diffusion ins-N₂ is governed by the two-phonon interaction.     

Muonic study of type II superconductors

A theory of μSR method is developed for uniaxial anisotropic high-T _c superconductors. In two extreme cases ofH _ext‖c andH _ext⊥c analytical formulas are obtained which makes it possible to determine from the position of van Hove singularities in the Fourier-spectrum of muonium polarization, the type and parameters of the vortex lattice, such as λ _ab (λ _c ). In caseH _ext≲H _c2 we obtained the shape of the Fourier-spectrum in analytical form and the simple method of determining the Ginsburg-Landau parameter κ. Convenient expressions for numerical calculations are obtained for the arbitrary orientation of the external field, and an algorithm is provided to compute the mean fieldB, the vortex lattice parameters and the bulk field distribution in anisotropic superconductor. The Fourier spectrum of polarization based on these calculations can be used to independently check the validity of the high-T _c parameters determination for “appropriate” orientations.     

μ+SR study of two-dimensional antiferromagnets,delafossite-type compounds

⁺SR experiments were performed on delafossite-type compounds, CuCrO₂, AgCrO₂, CuFeO₂, which are model compounds of triangular lattice antiferromagnets. The initial asymmetries are much smaller than the expected value, implying muonium formation. The time spectra are composed of slow andfast relaxation components. We attributed the components to signals from ⁺ stopped at the center of O^2– ions andmuonium far from nuclear dipole moments, respectively. The asymmetries decrease belowT _N but no precession spectra were observed. Relaxation rates of slow andfast relaxation components show maxima atT _N.     

Synthesis of CoFe<Subscript>2</Subscript>O<Subscript>4</Subscript> nanoparticles with tunable magnetism by the modified hydrothermal method

Cobalt ferrite (CoFe₂O₄) nanoparticles were synthesized by using the hydrothermal route with the addition of trisodium citrate dihydrate (Na₃CA·2H₂O). The formation of CoFe₂O₄ nanoparticles with size ranging from 13 to 19 nm was confirmed by X-ray diffraction, energy dispersive X-ray analysis, and Fourier transform infrared spectroscopy; the clear-cut sharp of the nanoparticles was observed by transmission electron microscopy. By these characterization methods, the evolution of lattice constant and morphologies of the nanoparticles with the addition of Na₃CA·2H₂O is observed. Furthermore, the magnetic hysteresis loops measured at room temperature indicate that the magnetic properties of the products also show clear relationship with the masses of Na₃CA·2H₂O. For example, coercivity and high-field paramagnetic susceptibility increase with the increasing masses of Na₃CA·2H₂O, whereas the saturation magnetization and the effective magnetic anisotropy constant have the maximum values as the mass of Na₃CA·2H₂O is 1 g. This change of magnetic properties is related with the expanded lattice and the varied size and shape because of the addition of Na₃CA·2H₂O.     

Ultrasonic study of solid-phase amorphization and polyamorphism in an H2O-D2O (1: 1) solid solution

The elastic moduli and volume of H₂O-D₂O (1: 1) isotopically mixed ice (solid solution) have been studied at the solid-phase amorphization of normal 1h ice under compression at a temperature of 77 K and at the transition from high-density amorphous ice to low-density amorphous ice with subsequent successive crystallization to cubic (1c) and hexagonal (1h) ice at isobaric (0.05 GPa) heating. Comparison of the results with the respective data for H₂O and D₂O ices indicates that the observed concentration (in the isotopic composition) dependences of the elastic moduli and their derivatives for different phases of ice at isotopic hydrogen substitution in the H₂O, H₂O-D₂O (1: 1), and D₂O chain can be both monotonic and significantly nonmonotonic.     

Löslichkeit,Diffusion und Ultrarotabsorption von Wassermolekülen in Alkalihalogenidkristallen

Following a former communication, further experiments of solubility, diffusion and infraredabsorption of water molecules in KCl-, KBr- and KJ-crystals are given. Substituted mono- and bivalent ions to the refined crystals strongly increase the solubility of water at lower temperatures but there is practically no increase at higher temperatures. This points to two mechanisms for solubility: An interstitial at lower temperatures and probably by vacancies at higher temperatures. — The penetration of water into crystals containing K₂O orF-centers produces a colorless layer by chemical reaction. From investigation of such layers we get diffusion constants for the diffusion of water molecules. In crystals containingF-centers we find an additionalKH- layer. — The chemical reactions in the solid state produce H^?-, OH^?- and O^??-centers of well known concentration. This allows determination of the oscillator strengths of the characteristical ultraviolett absorptions. — The absorption in the near infrared by crystals containing water shows especially at low temperatures sharp peaks from single H₂O-molecules and broad peaks from precipitated water. An interstitial lattice model is discussed for the single H₂O-molecules.     

A photoelectron spectroscopic investigation of the interaction between H2O and oxygen on Ag(110)

The adsorption and reaction of H₂O with adsorbed oxygen atoms on Ag(110) was examined by UPS. In agreement with previous EELS results, H₂O formed multilayers of ice upon adsorption at 140 K. The ice layers could be easily distinguished from monolayer coverages of chemisorbed H₂O (present above 160 K) by UPS. The ice layers produced (1) strong attenuation of the emission from the Ag d-bands, (2) a nearly 2 eV shift of H₂O valence levels to higher binding energy and (3) strong attenuation of emission from the H₂O 3a₁ orbital. H₂O was observed to react stoichiometrically with O(a) above 250 K to produce a pure layer of adsorbed hydroxyl species. The UPS spectra for these species exhibited features at ?5.8 and ?8.7 eV, as well as strong features above the d-bands. These spectra were compared with those for OH(a) on other surfaces, and the difficulties of identifying OH by UPS due to contamination by excess H₂O are discussed.     

The growth of ice clusters on the Si(100)(2 × 1)-H(D) surface: Electron energy loss spectroscopy and thermal desorption studies

The growth of ice clusters on the Si(100)(2 × 1)-H surface has been investigated mainly by the use of high-resolution electron energy loss spectroscopy and thermal desorption spectroscopy. At 90 K, H₂O molecules are adsorbed on the (2 × 1)-H surface to form ice clusters by the hydrogen-bonding interaction. Four H₂O peaks are observed at 165, 185, 215 and 270 K in the thermal desorption spectra for the ice-covered surface. The peaks at 165 and 185 K correspond to the ice clusters and the peaks at 215 and 270 K to the strongly-bound H₂O species which play a role as the nucleation centers of the ice clusters desorbing as H₂O at 185 and 165 K, respectively.     

H and Mu diffusion in ice

Detailed studies of muonium in ice carried out at TRIUMF in the mid eighties directly inspired EPR investigation of H and D atoms in ice at the Argonne National Laboratory, using a pulsed EPR spectrometer in conjunction with a Van de Graaff electron accelerator. T₂ measurements were made by the spin-echo method, Subsequent work resulted in a measurement of the longitudinal spin relaxation time T₁ at a single temperature. In combination with T₂ this permits an unambiguous determination of the strength of the magnetic interaction giving rise to relaxation, and hence permits conversion of all the existing T₂ data to diffusional correlation times, . We have recently initiated a further study of muonium in ice, this time concentrating on T₁ measurements. Preliminary work shows the feasibility of determining from the field dependence of T₁ at a given temperature. The result is in good agreement with our earlier, less direct determinations.     

Wärmeausdehnung von H2O- und D2O-Einkristallen

The linear thermal expansion coefficients of ice and heavy ice single crystals have been measured in both hexagonal crystallographic axes between the melting point and 18° K. The expansion coefficients of H₂O and D₂O become negative below 63° K.     

Fuel-dilution effect on differential molecular diffusion in laminar hydrogen diffusion flames

Laminar flame calculations have been made for a Tsuji counterflow geometry to investigate salient features caused by the differential diffusion effect in nitrogen-diluted hydrogen diffusion flames. A strong dependence of the differential diffusion parameter z_H on fuel dilution is found, where z_H is the difference of the mixture fractions based on H and O elements. The strain rate, however, appears to have a relatively minor impact on z_H. A simplified transport equation for the z_H parameter has been derived to explain qualitatively the behaviours exhibited in the numerical solutions. Two source terms of z_H are identified in the transport equation; one is due to mixing among species of different diffusion coefficients and the other one is associated with chemical reactions of H₂. More importantly, the second source term is found to be dominant in reacting flows, and it increases with inert gas dilution. This feature causes the differential diffusion parameter to increase with the amount of fuel dilution. The z_H values at the stoichiometric position are shown to correlate well with the ratio, Y_H2O|_max/(Z_H,1?Z_H,2), which may be useful for quantifying the influence of chemical reactions on the differential diffusion effect. For flames at low strain rates, the scalar dissipation rate exhibits a local minimum near the stoichiometric position. This peculiar feature is found to be caused by the differential diffusion effect modulated by chemical reactions. The local minimum in the scalar dissipation rate disappears at high strain rates when the convective transport overwhelms the molecular diffusion.     

Comparative Theoretical Study of Hyperfine Interactions of Muonium in A- and B-Form DNA

Muon Spin Relaxation (μSR) experiments in A- and B-form DNA have shown evidence for an enhanced electron mobility in the more closely-packed A-form. Besides dynamic effects (electronic diffusion) that could cause the observed difference in muon spin relaxation, one should also carefully examine the difference in the strengths of the hyperfine interactions of the muon (μ ⁺) with the moving electron in the two forms of DNA, since this could contribute to the observed difference in the muon spin relaxation rates as well. We have therefore investigated the (static) trapping properties of muon and muonium (μ ⁺ e ⁻) in A-form and B-form DNA from first-principles with the aim to understand how the different structural geometries of A- and B-form DNA can influence the hyperfine interaction of trapped muonium.