Dynamical behavior of muonium on silica surfaces

The behavior of muonium on the surface of finely divided silica (amorphous SiO₂) powder (mean grain diameter 70 Å) has been studied as a function of the surface concentration of hydroxyl groups. The temperature dependence of the Mu relaxation rate in transverse field was measured for samples prepared with 0%, 50% and 70% of the surface hydroxyl groups removed over the temperature range 4 K <T < 300 K. The relaxation rate shows a distinct maximum at about 25 K and a minimum at about 16 K for all three samples, and shows a dramatic decrease below 16 K as the concentration of surface hydroxyls is reduced. A three-state nonequilibrium model describing the diffusion and trapping of muonium on the silica surface is used to interpret the data.On leave from Department of Physics, University of Saskatchewan, Saskatoon, Sask. S7N OWO, Canada.     

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.     

Muonium in ice

Muonium has been studied in single crystals of H₂O and D₂O. Two-frequency precession in low transverse fields and a single zero-field oscillation indicate a small anisotropy of axial symmetry in the muonium hyperfine interaction. The anisotropy is shown to be the cause of the hitherto unexplained temperature independent contribution to muonium spin relaxation in polycrystalline samples. Relaxation rates for 99 K–263 K are reported for muonium in a single crystal of H₂O. Relaxation is attributed to electron-nuclear dipolar coupling of muonium to lattice protons, modulated by translational diffusion of muonium alongc-axis channels of the ice lattice. A simple model for H and Mu diffusion in ice is investigated.This work was supported by the Natural Sciences and Engineering Research Council of Canada through an Intermediate Energy Physics Project Grant.     

Mu+H2 and Mu+D2 reaction kinetics from 480 To 675 K

This paper reports preliminary new measurements of the thermal reaction rate constants of muonium (Mu) with hydrogen and deuterium gases in the range 480–675 K. From Arrhenius plots of the measured reaction rate constants new values of the pre-exponential factors log₁₀ (A) and activation energies E_a have been determined for these reactions, representing a significant improvement over earlier results.     

Diffusion and trapping of muonium on silica surfaces

The spin relaxation rate λ_Mu of muonium atoms on fine silica powder surfaces was measured as a function of temperature and of the surface concentration of hydroxyl groups. Results indicate two-dimensional diffusion, trapping and detrapping of the muonium atoms on the silica surface. At low temperatures λ_Mu decreases dramatically as the concentration of surface hydroxyls is reduced. A three-state model is used to extract the muonium adsorption energy and other physical parameters.     

Interaction of muonium with oxygen on silica powder surfaces

Results of the first μSR studies using Merck FO Optipur silica powder, which contains paramagnetic impurities at the ppb level and has a surface area of 610±20 m²/g. are reported. Above 20 K, the transverse field muonium relaxation rate is roughly constant at 0.5 μs⁻¹. Upon the addition of oxygen at ppm levels, the relaxation rate increases linearly with O₂ concentration in the temperature range from 40–100 K yielding two-dimensional depolarization rate constants on the order of 10⁻⁴ cm² molecule⁻¹ s⁻¹. As the temperature is increased further, both oxygen and muonium desorb from the surface yielding a three-dimensional rate constants at 300 K of 3.1(3)×10–10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, in agreement with the gas phase value. Longitudinal field measurements suggest that MuO₂ is formed and is able to spin exchange with other oxygen molecules.     

Muon behaviour in diamond grown by chemical vapour deposition

Transverse‐field μSR spectroscopy was used to study the behaviour of positive muons implanted in polycrystalline chemical‐vapour‐deposited (CVD) diamond. Measurements were made at sample temperatures of 10 K, 100 K, and 300 K at a magnetic field of 7.5 mT to study the behaviour of the “normal” (isotropic) muonium state (Mu_T) and the diamagnetic states (μ^d), and at 10 K and 300 K at the so‐called “magic field” of 407.25 mT to study the anomalous (bond‐centred) muonium state (Mu_BC) and μ^d. The absolute fractions of the muonium states in the CVD diamond are observed to be close to those in high‐quality natural type‐IIa single crystal diamond. This revised version was published online in August 2006 with corrections to the Cover Date.     

Evidence for muonium emission from an SiO2 layer on n-type Si and the positive muon state in Si

Evidence for the emission of slow muonium atoms from a 3.0-nm-thick SiO₂ layer covered on an n-type Si is reported. Also, upon applying an rf-resonance technique at the muon frequency, a time-differential observation of a delayed state-change from muonium to diamagnetic muon at room temperature was observed. Combining results obtained by use of longitudinal field decoupling and transverse spin rotation methods, the conversion rate was estimated to be 5 to 10 μs⁻¹. Both of the above results, namely the observation of the emission and state-change of muonium, suggest a process in which μ⁺ initially captures an electron from Si, then quickly converts to μ⁺ again during thermal diffusion in the Si towards the SiO₂ layer. Within the oxide layer, muonium is again formed and subsequently is emitted from the SiO₂ surface.     

Muonium and micelles

A pseudo first-order term has been added to the kinetic analysis of micelle-mediated muonium reactions. It is discussed with respect to enhancements of several orders of magnitude for reactions such as that of 2-propanol. It covers the possibility of ‘trapping’ of muonium followed by tunneling.     

Muon spin relaxation for Ar+NO2 systems in transverse and longitudinal magnetic fields

Surface muons produced in UT-MSL were introduced into argon gas of 4.0±0.2 atm with NO₂ (0–30 ppm), and muonium signals were detected in the presence of a transverse (1.7–3.4 G) and a longitudinal magnetic field (0–3.5 kG) at 295±1 K. The cross section for the transverse relaxation was (11.0±1.0)×10⁻¹⁶ cm². The relaxation rates in different longitudinal magnetic fields show that the rate does not follow the conventional equation which assumes that the relaxation occurs mainly by spin-exchange interaction. Similar measurements were performed for the Mu+O₂ system. These findings indicate that chemical reactions contribute to these relaxation rates.     

MuSR/μ+SR studies in KDP and DKDP

The temperature dependence of muon interactions has been studied in ferroelectric KDP ( H₂KPO₄) and DKDP ( D₂KPO₄) using conventional μSR and muon spin resonance spectroscopy. In longitudinal field measurements, a fast relaxing component and a slow relaxing component were observed. The slow relaxing component is attributed to diamagnetic muons. The muon spin resonance measurements indicate that the fast relaxing component results from some muonium like species: either normal or anomalous. In zero field and weak longitudinal field μSR (0–100 G), a remarkable peak in the fast relaxing component is observed around 220 K in both KDP and DKDP. An additional feature is also seen around 300 K. The amplitude of the resonance measurement has a broad minimum around 200 K which corresponds to the maximum in the relaxation rate in longitudinal field (100 G). The temperature dependence of the muonium relaxation rate in KDP is almost identical to that of DKDP. The diamagnetic fraction also shows almost no difference in relaxation rate or asymmetry for DKDP and KDP. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamics of gas-phase reactions of muonium

Applications of variational transition state theory with semiclassical adiabatic transmission coefficients to the reactions of muonium with H₂, D₂, F₂, and Cl₂ are reviewed. In addition new calculations are presented for the Mu+Cl₂ and Br₂ reactions. The comparison of calculated rate constants and kinetic isotope effects (KIE's) with experiment is used as a test of the validity of semiempirical potential energy surfaces. Furthermore the VTST-plus-tunneling calculations allow an analysis of the KIE's that identifies those features of the potential which control the isotope effects.     

Muon spin relaxation in spin gap state of BaVS3

Positive muon spin relaxation measurements were performed on a spin-1/2 system BaVS₃, which shows a metal-insulator transition at T_MI= 70 K. We found a marked muon-spin depolarization below T_X= 30 K without appreciable critical divergence. The possibility of muonium formation in the insulating state rather than electron spin freezing is discussed taking into account the quenching of V spins evidenced by ⁵¹V NMR and NQR measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

Motion of positively charged muonium in ZnO

We report on a study of the motional characteristics of positively charged muonium defect centers in ZnO as an analog for H⁺ behavior. Muon spin depolarization measurements at zero applied magnetic field were completed from 20 K to 400 K, with preliminary results to 750 K. Results at the lower temperatures imply that Mu⁺ occupied two sites, and indicate local motion as thermally assisted tunneling with a characteristic energy of ∼60 meV, as well as a site change transition above 200 K with barrier energy ∼440 meV. Based on theoretical results, we have tentatively assigned these features to tunneling among three equivalent oxygen anti-bonding sites (AB_⊥) and a transition to a lower-energy bond-centered site (BC_‖) oriented along the c-axis. Preliminary fits suggest that global diffusion of muonium occurs above 400 K, with a diffusion barrier energy of ∼0.7 eV.     

Muonium in semiconductors: Recent experimental developments

Recent experiments covering a range of problems including the nuclear hyperfine structure of bond-centered muonium in diamond and GaP, charge-cycling reactions of muonium in Si at high temperatures, muonium state dynamics in Si probed by RF-SR, and endohedral muonium in semiconducting C₆₀ compounds, are discussed. These examples show that as traditionalSR techniques are continually being refined and new methods are being developed,SR is becoming an increasingly powerful tool to investigate the behavior of muonium and the in many respects analogous, and technologically relevant, hydrogen centers in semiconductors.     

Muonium states in silicon carbide

Implanted muons in samples of silicon carbide have been observed to form paramagnetic muonium centers (μ ⁺ e⁻). Muonium precession signals in low applied magnetic fields have been observed at 22 K in a granular sample of cubic β-SiC, however it was not possible to determine the hyperfine frequency. In a single crystal sample of hexagonal 6H-SiC, three apparently isotropic muonium states were observed at 20 K and two at 300 K, all with hyperfine frequencies intermediate between those of the isotropic muonium centers in diamond and silicon. No evidence was seen of an anisotropic muonium state analogous to the Mu^* state in diamond and silicon.     

Muonium desorption to vacuum from hot iridium surface

Slow muonium (Mu) emission from the surface of iridium (Ir) foil has been observed in vacuum above \sim1200\ K with a yield of 5(1)% Mu per incident muon stopped in the foil. The relative Mu signal was found to be thermally activated with E_a=1.86(1)\ eV. Analysis of the time‐differential evolution of Mu in vacuum at T_Ir=1580\ K showed that the trapping rate of positive muons during diffusion in the bulk Ir was nearly zero. In situ measurements of the surface of Ir with X‐ray photoelectron spectroscopy verified that the main source of impurities in the 99.9%‐Ir was molybdenum (Mo). This revised version was published online in August 2006 with corrections to the Cover Date.     

μSR study of intermediate heavy fermion system CeRuSi2

We have studied the magnetic spinel (Zn)[Fe₂]O₄ (T_ N\approx10.5\ K) and the non‐magnetic spinels (Zn)[Al₂]O₄, (Zn)[Ga₂]O₄, (Zn)[ZnTi]O₄ and (Zn)[ZnSn]O₄ , both with surface and decay channel muons. In (Zn)[Fe₂]O₄ the relaxation rate increases monotonically from room temperature down, typical for a paramagnet. Around 30 K, an additional, stronger damped signal appears which is the signature of short‐range ordered (SRO) regions. Their total volume fraction increases drastically towards T_ N (reaching 75%) and astonishingly, continues to be present also below T_ N where the rest of the material has become long‐range ordered. Longitudinal field μSR proves the SRO to be dynamic. In (Zn)[Al₂]O₄ and (Zn)[Ga₂]O₄ muon depolarization is caused solely by ²⁷Al or ^69,71Ga nuclear dipoles. In the inverse spinel (Zn)[ZnTi]O₄, half of the implanted muons depolarize rapidly (\lambda\approx 3μs^-1 at room temperature). This, together with repolarization behavior in longitudinal fields indicates that the muon in (Zn)[ZnTi]O₄ undergoes a chemical reaction after implantation forming muonium. The fact that no such muonium formation occurred in another inverse spinel ( (Zn)[ZnSn]O₄) means that the presence of muonium is not connected to the inverse structure but rather due to the presence of Ti which offers two d‐electrons to participate in the chemical bonding. Additional evidence for d‐electron participation is provided by ⁶⁷Zn‐Mössbauer data which indicate unusual electron densities at the ⁶⁷Zn nuclei only in (Zn)[ZnTi]O₄.     

Muonium quadrupole interaction in ferroelectric substances KDP and KHCO3

The muonium quadrupole interaction is determined in KDP and KHCO₃. Using single crystal the field gradient tensor was obtained from muonium precession under the transverse field at room temperature. The muonium signal relaxes very fast at lower temperature, from this temperature dependence the dynamics of muonium was obtained. This revised version was published online in August 2006 with corrections to the Cover Date.