Muon diffusion in nanocrystalline copper

A systematic μSR study on nano‐Cu has demonstrated that the diffusion of μ⁺ in nanocrystalline metals is influenced by both features of the nanostructure, i.e., by the very small grain size and by the comparatively large fraction of grain boundaries. The former feature yields a size effect of the phonon‐assisted muon tunneling, but only at particle diameters below 20 nm. The latter feature, in samples with crystallite sizes above 20 nm diameter, i.e., with bulk diffusional behaviour, establishes a connection between μ⁺ diffusion coefficient and particle size: if one of these quantities is known, the other could be evaluated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Muon states in metals: Recent progress

We report on our results in two interesting questions related to muon spin rotation studies in condensed matter: (i) energetics of muons in metals, including lattice relaxation and zero point motion in self-trapping phenomena, and (ii) systematics of Knight shifts and hyperfine fields.In the former topic, a comprehensive theory is developed which entails the construction of the muon potential energy field in terms of the effective-medium or quasi-atom theory first introduced by Zaremba, Stott, NØrskov and Lang. The muon wave function is then solved by numerical (3-D) relaxation techniques. From this the forces exerted by the muon on the neighbouring lattice atoms are calculated, and the ensuing relaxations are evaluated by lattice Green's function techniques. These in turn modify the potential energy field, and the calculation is iterated to self-consistency. We search for the stable trapping sites in bcc and fcc metals, calculate self-trapping energies, diffusion barriers and excitation energies. Other hydrogenic imputies are also considered, and isotopic effects in e.g. heats of solution are investigated.In the latter topic, the spin-density functional theory is applied, including in the Knight shift calculation both the contact spin density and the diamagnetic shielding. The lattice potential is described in terms of the spherical solid model. A systematic behaviour as a function of the electron density and the host valency is found in good agreement with the experimental results.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Muon diffusion in copper bolow 2K

Transverse field SR experiments were performed on several different samples of copper in the temperature range below 2K, including isotope separated copper, Fe and Si doped polycrystalline copper and monocrystalline copper. No strong isotope dependent effect was observed. A⁶³Cu and a natural copper sample of identical purity both yield 0.16 s^–1 for the low-temperature plateau, while an increased linewidth inthe⁶⁵Cu case may be related to the strong effects of Fe impurities. Careful transverse field measurements on large single crystals at 0.08K reveal non-Gaussian lineshapes in accordance with the picture of diffusing muons at this temperature. This allows us to reject several of the existing models for muon behaviour in copper below 2K.     

Muon diffusion in Nb−H systems

We have studied the muon diffusion in various Nb−H_X systems with 0.75<x<0.95, with special attention to the concentrations x<0.9. For x>0.9 the muon linewidth as function of temperature has a smooth behaviour and the muon mobility is strongly correlated to the hydrogen diffusion in the beta phase. The activation energy for the μ⁺ diffusion is 160 meV, which is lower than that for protons. At hydrogen concentrations below 0.9, the muon diffusion behaviour is more complicated, and the influence of Nb−H phase transitions is evident. The implications for the local environment of the muon are discussed.     

Muon diffusion in β-V2H

Hydrogen diffusion in the ordered hydride β-V₂H is mainly brought about by a minority fraction of interstitial atoms on antistructural sites. Recently, this mechanism was elucidated in a single crystal QNS study at temperatures close to the critical point (390 K≤T≤440 K) where already an appreciable amount of antistructural sites is occupied. Here we use the positive muon as a radioactive hydrogen tracer in order to show that the same diffusion mechanism is also valid at low temperatures (80 K≤T≤320 K) where the different jump processes are very slow and where the fraction of antistructural atoms is tiny but nevertheless dominates the long range diffusion.     

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.     

Muon method for structural defects investigation in ferromagnetic metals

Equations describing depolarization of positive muons implanted in a pure crystalline ferromagnetic metal with structural defects are derived. In particular cases, solutions of these equations are obtained. In terms of the proposed model some experimental consequences are discussed.     

Muon diffusion and trapping studies in high purity vanadium

We present the first results of a study of the effects of varying impurity concentration on the temperature dependence of the depolarization rate of positive muons implanted into vanadium. Data are reported for the most highly purified polycrystalline sample yet measured, and the same sample subsequently doped with about 500 ppm oxygen by weight. The data for the pure sample shows a low depolarization rate (<.15 sec^–1) at all temperatures measured, showing a broad minimum centered at 35 K, followed by a sharp peak near 90 K and a rapid drop to negligible values at 200 K. The data is contrasted with previously published data [2] on less pure samples, and calls into question previous interpretations of the behavior of the ⁺ at low temperatures in impure vanadium [1] as one-phonon-assisted tunneling.This work was supported by the U. S. Department of Energy     

Positron diffusion in metals

Calculations are presented of the positron diffusion constant, mobility and other diffusion related quantities in simple metals. The mobility is found to be largely limited by the positron-phonon interaction which is treated in the deformation potential model. The effect of positron conduction electron scattering is also evaluated and found to be small. The effect of positron impurity scattering is discussed and detailed estimates given for Li in Al. In dilute alloys at moderate temperatures the positron phonon interaction will dominate also over this effect.     

Muon diffusion and trapping by defects in electron-irradiated Nb and Ta

The transverse spin relaxation of positive muons ( ⁺) has been measured on Nb and Ta after irradiation with 3 MeV electrons. In high-purity Nb the ⁺ diffusivity derived from the trapping at irradiation-induced defects above 100 K is explained in terms of adiabatic hopping. At lower temperatures there is evidence for the dominating processes to be fewphonon incoherent tunnelling and coherent hopping. Annealing results in the formation of new defects capable of trapping the ⁺. In Ta at least two types of irradiation-induced defects capable of trapping ⁺ survive up to annealing temperatures of 400 K.