Positive Muons Research Articles

Muon Spectroscopy for Investigating Diffusion in Energy Storage Materials

We review recent applications of positive muon spin relaxation (μSR) spectroscopy as an active probe of ion diffusion in energy storage materials. μSR spectroscopy allows the study of ionic diffusion in solid-state materials on a time scale between 10−5 and 10−8 s where most long-range and consecutive short-range jumps of ions between interstitial sites occur. μSR also allows one to probe and model ionic diffusion in materials that contain magnetic ions, since both electronic and nuclear contributions to the muon depolarization can be separated, making μSR an excellent technique for the microscopic study of the ionic motions in crystalline materials. We highlight a series of battery materials for which μSR has provided insight into intrinsic ionic conduction and magnetic properties without interference of external factors, such as the presence of magnetic ions, macroscopic particle morphologies, or elaborate measurement setups.

Searching for correlations of geomagnetic activities with high-energy EAS muons

The paper aims to explore the asymmetry of the muon content of non-vertical and very high energy Monte Carlo showers due to the influence of Earth's geomagnetic field. Simulations have shown that the geomagnetic field modifies the trajectories of muons in a shower producing a polar asymmetry in the density/number of positive and negative muons in the shower front plane. The asymmetry is quantified by a transverse separation between the positive and negative muons barycentric positions through opposite quadrants across the shower core. The dependence of this transverse muon barycenter separation (TMBS) on polar position shows a clear maximum at a position that is correlated with the primary composition and geomagnetic activities. It is noticed that the maximum TMBS parameter exhibits sensitivity to any transient weakening of Earth's magnetic shield caused by geomagnetic storm originated from bursting solar processes. Obtained simulation results are quite important to design any possible new experiment based on these features of muons in extensive air showers.

Magnetic phase boundary of BaVS3 clarified with high-pressure μ+SR

The magnetic nature of the quasi-one-dimensional BaVS3 has been studied as a function of temperature down to 0.25 K and pressure up to 1.97 GPa on a powder sample using the positive muon spin rotation and relaxation (mu(+) SR) technique. At ambient pressure, BaVS3 enters an incommensurate antiferromagnetic ordered state below the Neel temperature (T-N)31 K. T-N is almost constant as the pressure (p) increases from ambient pressure to 1.4 GPa, then T-N decreases rapidly for p > 1.4 GPa, and finally disappears at p similar to 1.8 GPa, above which a metallic phase is stabilized. Hence, T-N is found to be equivalent to the pressure-induced metal-insulator transition temperature (T-MI) at p > 1.4 GPa.

Constraints on the χc1 versus χc2 Polarizations in Proton-Proton Collisions at s=8 TeV

The polarizations of promptly produced $\chi_\mathrm{c1}$ and $\chi_\mathrm{c2}$ mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at $\sqrt{s} = $ 8 TeV. The $\chi_\mathrm{c}$ states are reconstructed via their radiative decays $\chi_\mathrm{c}$ $\to$ $\mathrm{J}/\psi\, \gamma$, with the photons being measured through conversions to e$^+$e$^-$, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the $\chi_\mathrm{c2}$ to $\chi_\mathrm{c1}$ yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the $\mathrm{J}/\psi$ $\to$ $\mu^+\mu^-$ decay, in three ranges of $\mathrm{J}/\psi$ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum.

Optical spectroscopy of muon/hydrogen defects in 6H-SiC

Positive muons can be implanted into silicon carbide (SiC), where they model the isolated hydrogen defect in the negative, neutral, or positive charge states and act as either an acceptor or a donor with midgap energy levels [Lichti et al., Phys. Rev. B 70, 165204 (2004); Lichti et al., Phys. Rev. Lett. 101, 136403 (2008)]. The charge states evolve after implantation depending on the temperature and material doping. We have measured optically induced effects on muons implanted in 6H-SiC using a pulsed, tunable laser [Yokoyama et al., Rev. Sci. Instrum. 87, 125111 (2016)]. In n-type 6H-SiC at 85 K and 40 K, with a laser pulse of energy below the bandgap, we observe photoionization of the doubly occupied level (Mu−) to the neutral defect Mu0 and also ionization of Mu0 to Mu+. Varying the timing of the laser pulse relative to muon arrival confirms that the laser interacts directly with the muons in a stable or metastable state. There is no evidence of any interaction when the laser pulse is timed to arrive before the muons, so either few free carriers are generated by absorption at other dopant sites or the excess carriers have a very short lifetime (≪100ns). Wavelength scans show absorption edges corresponding to the possible interstitial sites within the structure. Combining these data and the existing muon results shows that at low temperature, we have co-existence of Mu0 and Mu− charge states, with the muon or hydrogen acting as a deep compensating impurity. The technique can be applied to many other semiconductors where the muon has been observed to be electrically active, modeling hydrogen.

Comment on “Role of the transition state in muon implantation” and “Thermal spike in muon implantation”

Vil\~ao et al. (Phys. Rev. B 96, 195205 (2017) and Phys. Rev. B 99, 195206 (2019)) have reported positive muon spin rotation/relaxation (${\ensuremath{\mu}}^{+}\mathrm{SR}$) experiments on various insulating metal oxides, solar cell materials, and alloyed Ge. They note the presence of a separate early component in the ${\ensuremath{\mu}}^{+}$ polarization time dependence which relaxes more rapidly than the longer lived signal and also exhibits (in ${\mathrm{ZrO}}_{2}$:Mg) a slightly increased frequency at low temperature in transverse field. They interpret this early component as a weakly bound ``transition state'' of the neutral muonium ($\mathrm{Mu}={\ensuremath{\mu}}^{+}{e}^{\ensuremath{-}}$) atom formed epithermally by the incoming 4-MeV muon, in which the hyperfine interaction between the muon and the electron is ``motionally narrowed'' by rapid spin exchange, resulting in a ``diamagneticlike'' Larmor precession signal. This ``diamagneticlike transition state'' supposedly takes microseconds to relax into its final ground state due to the reluctance of the surrounding lattice to deform around the Mu atom. However, numerous earlier experiments (including those in electric fields) on various liquids and solids ranging from wide-gap insulators to narrow-gap semiconductors have convincingly shown that Mu formation proceeds through capture of radiolysis electrons by thermalized muons---a process crucially dependent on the electron mobility rather than epithermal dynamics. Therefore, we question the validity of the interpretation by Vil\~ao et al. and raise some important issues that need clarification.

Non-Born–Oppenheimer study of the muonic molecule ion 4He μ+**Project supported by the National Natural Science Foundation of China (Grant No. 11704399), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030300), and the National Key Research and Development Program of China (Grant No. 2017YFA0304402).

Accurate non-Born–Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ+ have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors. All the energies obtained are accurate in the order of 10−6 Hartree (1 Hartree = 27.2114 eV). Compared with the binding energies obtained from calculations based on the Born–Oppenheimer potential with the mass-weighted adiabatic corrections (Chem. Phys. Lett. 110 487 (1984)), the largest relative deviation is up to 15%. By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system, it is confirmed that the Born–Oppenheimer approximation is reasonable for this system and that 4He μ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.

Irradiation Test of 65-nm Bulk SRAMs With DC Muon Beam at RCNP-MuSIC Facility

Negative and positive muon irradiation tests of static random access memories (SRAMs) were performed at Muon Science Innovation Channel (MuSIC) of Research Center for Nuclear Physics (RCNP), Osaka University. The muon-induced single event upset (SEU) cross sections for 65-nm bulk SRAMs were measured. The SRAM device was irradiated by the muon beams with average momenta ranging from 37.8 to 41.0 MeV/c at the beam exit. The incident muon fluence was measured using a one-by-one muon detection system with a plastic scintillator by taking advantage of the direct current (dc) muon beam and reliable absolute values of SEU cross sections were obtained. In addition to the measurement of the SEU cross sections, we measured muonic X-rays from the irradiated device to investigate the relation between the measured SEU cross section and the emission rate of muonic X-rays associated with the stopping position of the muons as a function of incident muon momentum. The result suggested that negative muons have a significant effect on SEUs by the emission of secondary light ions via negative muon capture reaction when negative muons stop near sensitive volumes (SVs) in SRAMs.

Muon implantation experiments in films: Obtaining depth-resolved information.

Implanted positive muons with low energies (in the range 1-30 keV) are extremely useful local probes in the study of thin films and multi-layer structures. The average muon stopping depth, typically in the order of tens of nanometers, is a function of the muon implantation energy and of the density of the material, but the stopping range extends over a broad region, which is also in the order of tens of nanometers. Therefore, an adequate simulation procedure is required in order to extract the depth dependence of the experimental parameters. Here, we present a method to extract depth-resolved information from the implantation energy dependence of the experimental parameters in a low-energy muon spin spectroscopy experiment. The method and corresponding results are exemplified for a semiconductor film, Cu(In,Ga)Se2, covered with a thin layer of Al2O3, but can be applied to any heterostructure studied with low-energy muons. It is shown that if an effect is present in the experimental data, this method is an important tool to identify its location and depth extent.

Path integral molecular dynamics simulations for muoniated and hydrogenated thioacetone radicals

SynopsisTheoretical understanding of hyperfine coupling constant (HFCC) is important to analyze muon spin rotation/relaxation/resonance (μSR) spectrum. We performed ab initio path integral molecular dynamics simula-tions to predict and analyze the reduced HFCCs of muoniated thioacetone radical (Mu-TACE) and hydrogenated thioacetone radical (H-TACE). Our predicted HFCC value of Mu in Mu-TACE was larger than that of H in H-TACE, because of the larger nuclear quantum effect of positive muon.

CdS versus ZnSnO buffer layers for a CIGS solar cell: a depth-resolved analysis using the muon probe

The influence of a buffer layer in the surface of a Cu(In,Ga)Se2 (CIGS) solar cell material is studied using implanted positive muons as a probe. A depth resolved analysis of the muon data suggests that both CdS and ZnSnO reduce the width of a defect layer present at the CIGS surface to about half its original value. Additionaly, CdS is able to reduce the intensity of the distur¬bance in the defected region, possibly due to a surface reconstrution in CIGS.

Moderation of Positive Muons by Helium Gas

Efficiently creating beams of spin-polarized positive muons with energies between eV and keV (so-called slow muon beams) is important for further development and application of muon spin rotation, relaxation, and resonance techniques. One existing moderation method involves the use of wide-band-gap materials as moderators such as rare gas solids and solid nitrogen thin films (band-gap energy between 11 eV and 22 eV). Based on this moderation method, we have studied the use of helium gas as a moderator, with the goal of producing the slow muon beam more efficiently. Because of helium’s high (24.6 eV) ionization energy and because the cross section for muonium formation is suppressed in helium gas, we expect the production of slow muons using helium gas to be highly efficient.

Moderation of positive muons by helium gas

Efficiently creating beams of spin-polarized positive muons with energies between eV and keV (so-called slow muon beams) is important for further development and application of muon spin rotation, relaxation, and resonance techniques. One existing moderation method involves the use of wide-band-gap materials as moderators such as rare gas solids and solid nitrogen thin films (band-gap energy between 11 eV and 22eV). Based on this moderation method, we have studied the use of helium gas as a moderator, with the goal of producing the slow muon beam more efficiently. Because of helium’s high (24.6 eV) ionization energy and because the cross section for muonium formation is suppressed in helium gas, we expect the production of slow muons using helium gas to be highly efficient.

Muon charge ratio using the corsika simulation code

Using the corsika code, in 21 energy states between 7 and 900 GeV, in each state, $2\ifmmode\times\else\texttimes\fi{}{10}^{4}$ extensive air showers were simulated separately with 88% protons and 12% alpha as primary particles. The zenith and azimuth angles of the primary particles were between 0\ifmmode^\circ\else\textdegree\fi{} to 60\ifmmode^\circ\else\textdegree\fi{} and 0\ifmmode^\circ\else\textdegree\fi{} to 360\ifmmode^\circ\else\textdegree\fi{}, respectively. These simulations are carried out at Tehran's level ($35\ifmmode^\circ\else\textdegree\fi{}4{3}^{\ensuremath{'}}\mathrm{N}$, $51\ifmmode^\circ\else\textdegree\fi{}2{0}^{\ensuremath{'}}\mathrm{E}$; 1200 m $\mathrm{a}.\mathrm{s}.\mathrm{l}=897\text{ }\text{ }{\mathrm{g}\text{ }\mathrm{cm}}^{\ensuremath{-}2}$) and with two models GHEISHA and UrQMD for hadronic interactions at low energy and the QGSJET-II model for high-energy interactions. Using the positive and negative muons produced from these air showers, the muon charge ratios are obtained at various angles and energies. An east-west anisotropy is also achieved for this ratio.

Estimation of dose and light distributions in water during irradiation of muon beams

High-intensity muon beams are now available at the Japan Proton Accelerator Research Complex and their use in radiotherapy may become possible in the future. Dose and range estimation are therefore important and optical imaging of the dose or range may be a promising method for that purpose. We calculated the dose and light distributions in water during irradiation of a positive muon beam using Monte Carlo simulation. First, we simulated the dose deposited in water for pencil beams with 30 and 50 MeV positive muons. We were able to clearly identify the Bragg peak in the depth dose profiles by muons and observed that the dose from positrons are added to the Bragg peak area with a ∼10% muon dose. We also found that the lateral dose widths increased as the depth increased and that it was ∼3–5 times wider at the Bragg peak position. With the light distribution of the muon in water, light produced by the positrons was dominant and distributed around the Bragg peak, and the peak positions were estimated within 2 mm differences of the peak position of the dose distributions. It is therefore possible to monitor the Bragg peak position of muons using an optical method.

Muon spin rotation (µSR) study of a sterically encumbered thioaldehyde

Here we report a preliminary muon spin rotation (µSR) analysis of a sterically encumbered 2,4,6-tri-t-butylthiobenzaldehyde. A powder sample of the thiobenzaldehyde was placed in a beam of positive muons, and the transverse-field muon spin rotation (TF-µSR) spectroscopy was performed. The observed muon-electron hyperfine coupling constant (Aµ) was considerably smaller than that of cyclohexadienyl radicals, indicating that the aromatic ring in the thiobenzaldehyde did not capture muonium (Mu = µ+e–). DFT calculations concluded that Mu added to the C = S sulfur atom, which was comparable to the previous report on thiobenzophenone.

Solid State Battery Cells for in Operandi Diffusion Measurements Using µ+sr Spectroscopy

Solid state lithium ion batteries (SSBs) have been widely tipped to revolutionise energy storage technology. The combination of increased safety, longer lifetime, larger electrochemical potential window and higher energy density offered has led to sustained global research into their development. One important aspect of that development is the dynamics of ion diffusion, particularly through the bulk solid electrolyte but also at the electrode/electrolyte interface. Ion diffusion rates can limit how fast batteries can be charged/discharged, with charge movement across the electrode/electrolyte boundary especially key in SSBs, which can experience poor interfacial contact. An increased understanding of microscopic level ion behaviour at these boundaries will prove valuable, but has so far been elusive with techniques such as NMR and impedance spectroscopy yielding inconsistent results.1,2 Muon spin relaxation (µ+SR) spectroscopy is a relatively new technique used to investigate Li+ migration mechanisms, using spin-polarised positive muons created using a synchrotron. The muons can be controlled to stop at any point within a battery, acting as an atomic scale probe of charge movement in a particular area within the crystal structure. This occurs as an implanted muon’s spin is perturbed by the magnetic field of nearby diffusing ions. After an average lifetime of 2.2 µs the muon will decay into a positron, emitted preferentially along the direction of the muon spin at the instant of decay. Detection of the asymmetry of emitted positrons gives a time evolution of the muon ensemble’s spin polarisation, yielding information on ion diffusion dynamics and activation energies. µ+SR has been proven a successful technique to study in situ batteries, producing accurate measurements that are consistent with first-principle calculations.2,3 This research will focus on the study of the promising solid-state battery electrolyte material Al-doped LLZO (Li7La3Zr2O12), using µ+SR spectroscopy as a reliable and reproducible probe. The anode and cathode materials used will be Li4Ti5O12 and LiCoO2 to complete the cell. This cell will be tested in situ from room temperature to around 80ºC on the EMU beamline at ISIS Pulsed Neutron and Muon Source. Any insights gained will be translated back to design principles to optimise battery performance. Power Source, 2014, 268, 153–162Mater. Chem. A, 2017, 5, 8653Mater. Chem. A, 2016, 4, 1729Phys. Scr., 2013, 88, 068509

Decay of muons generated by laser-induced processes in ultra-dense hydrogen H(0)

This work reports identification of muons by their characteristic life-time of 2.20 μs after laser-induction of their precursor mesons, both kaons K± and KL0 and pions π± in ultra-dense hydrogen H(0). The pair-production signal from scattered muons at a metal converter in front of a photo-multiplier detector is observed with its decay. The observed signal intensity is decreased by a metal beam-flag which intercepts the meson and muon flux to the detector. Using D(0), the observed decay time is (2.23 ± 0.05) μs in agreement with the free muon lifetime of 2.20 μs. This signal is apparently due to the preferential generation of positive muons. Using p(0), the observed decay time is in the range 1–2 μs, thus shorter than the free muon lifetime, as expected when the signal is mainly caused by negative muons which interact with matter by muon capture.

Comparison between density functional theory and density functional tight binding approaches for finding the muon stopping site in organic molecular crystals.

Finding the possible stopping sites for muons inside a crystalline sample is a key problem of muon spectroscopy. In a previous study, we suggested a computational approach to this problem when dealing with muonium, the pseudoatom formed by a positive muon that has captured an electron, using density functional theory software in combination with a random structure searching approach that relies on a Poisson sphere distribution. In this work, we test this methodology further by applying it to muonium in three organic molecular crystal model systems: durene, bithiophene, and tetracyanoquinodimethane. Using the same sets of random structures, we compare the performance of density functional theory software CASTEP and the much faster lower level approximation of Density Functional Tight Binding provided by DFTB+ combined with the use of the 3ob-3-1 parameter set. We show the benefits and limitations of such an approach, and we propose the use of DFTB+ as a viable alternative to more cumbersome simulations for routine site-finding in organic materials. Finally, we introduce the Muon Spectroscopy Computational Project software suite, a library of Python tools meant to make these methods standardized and easy to use.

Characterizing SRAM and FF soft error rates with measurement and simulation

Soft error originating from cosmic ray is a serious concern for reliability demanding applications, such as autonomous driving, supercomputer, and public transportation system. Also, as the number of electronic devices increases, consumer electronics may require higher reliability than ever. On the other hand, device miniaturization and lower voltage operation degrade the immunity of SRAM and flip-flops in VLSI, and then soft error countermeasures will be demanded in more and more products. This paper characterizes and discusses soft error rates of SRAM and flip-flops in the terrestrial environment. Measured soft error rates of bulk and FDSOI SRAMs are presented. Also, the multiplicity and mechanism of multiple cell upsets (MCUs), which can spoil error correction code (ECC), are discussed. Flip-flops are also sensitive to radiation, but its protection is not well established since ECC cannot be applied. This paper reviews redundant FFs that are developed aiming at higher radiation immunity and demonstrates the resilience improvement with irradiation test results. Also, the importance of layout design is pointed out with a comparative study. Simulation, on the other hand, is a key technology to understand the soft error mechanism and guide radiation aware design for higher reliability. This paper outlines a physics-based multi-scale Monte Carlo simulation framework tailored for soft error simulation. The simulation flow and the model construction are explained, and some important implications are derived from the simulation results that assume 65-nm to 25-nm SRAMs. Finally, this article touches on future trends regarding device structure and overlooked secondary cosmic rays. The advantage and unique features of FinFET recently reported in literature are introduced. Also, muon-induced soft error is discussed focusing on the difference between positive and negative muons.