Vacancy formation energies from positron trapping measurements

The threshold temperatureT _t at which thermally generated vacancies produce measurable positron trapping is a linear function of the energy of self-diffusionQ. SinceQ is also linearly related to the vacancy formation energyE _1v ^f , a measurement ofT _t leads directly to a determination of the latter. It is possible to make a precise determination ofE _1v ^f without approaching the melting point—a major advantage in dealing with refractories or with metals having a high vapour pressure in the solid state.     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

TDPAC studies of Hf doped YBCO

Time differential perturbed angular correlation measurements of the 133–482 keVγ-γ cascade of¹⁸¹Ta in Hf-doped YBa₂Cu₃O_7−x are presented. The¹⁸¹Hf precurser nuclei are incorporated into the sample by thermal neutron irradiation. Two quadrupole interaction frequencies are observed in the as-irradiated sample:v _Q1=161±10 MHz with intensityf ₁=75%, asymmetry parameterη ₁=0.32 and damping parameter Λ₁=0.42, andv _Q2=1108±40 MHz withf ₂=25%,η ₂=0.62, and Λ₂=0.60. On annealing the sample in air at various temperaturesT _a and quenching to room temperature,f ₁ remained nearly constant forT _a<600°C andv _Q1 for all annealing temperatures indicating that these are insensitive to oxygen stoichiometry. This frequency is interpreted to be due to¹⁸¹Hf substitutingY sites. BeyondT _a=600°C,f ₁ increased and reached a constant value of 90% forT _a=800°C. The value ofv _Q2 showed a slight variation between 1086 and 1160 MHz, whilef ₂ remained nearly constant at 25% forT _a<600°C. This component is identified to be due to¹⁸¹Hf substituting Cu 1 sites in the Cu-O chains of YBCO. Above 600°Cv _Q2 decreased and reached a value of 808 MHz beyond 750°C.     

The activation energy for γ-Fe precipitates inCuFe

The precipitation of the fcc γ-phase of iron has been studied by a systematic series of isothermal and isochronal (0–48 h) heat treatments (300–800°C) on a supersaturated solution ofCuFe containing 3 at% Fe. The optimal conditions (450–600°C) for precipitation of the maximum fraction (90%) of iron attainable within 48 h in the form of γ-Fe have been delineated from analysis of the room temperature spectra. The time dependence for formation of γ-Fe precipitates is well described by the equation for long term annealing. An activation energyE _a ≈0.6 eV for the formation of γ-Fe in Cu is obtained. It indicates short range rather than long range diffusion in theCuFe sample studied.     

Properties of the πη,$ \eta{^\prime}$,σ, f0(980) and a0(980) mesons and their relevance for the polarizabilities of the nucleon

The signs and values of the two-photon couplings F _Mγγ of mesons (M) and their couplings g_MNN to the nucleon as entering into the t -channel parts of the difference of the electromagnetic polarizabilities (α - β) and the backward angle spin polarizabilities γ_π are determined. The excellent agreement achieved with the experimental polarizabilities of the proton makes it possible to make reliable predictions for the neutron. The results obtained are α_n = 13.4±1.0 , β_n = 1.8±1.0 (10^-4fm^3), and γ⁽ⁿ⁾ _π = 57.6±1.8 (10^-4fm^4). New empirical information on the flavor wave functions of the f ₀(980) - and the a ₀(980) -meson is obtained.     

μ+SR study of vacancies in thermal equilibrium in ferromagnets

Muon spin precession frequencies and transverse relaxation rates have been measured on demagnetized iron, cobalt, and FeCo alloys (3 at%–50 at% Co) between room temperature and the Curie temperatureT _c. The increase of the relaxation rate in iron between 930 K and 1010 K could be quantitatively attributed to the trapping of positive muons by vacancies in thermal equilibrium, resulting in an enthalpy of monovacancy formation ofH _1V ^F =(1.7±0.1) eV. the smallest vacancy concentrations detected are = 10⁻⁸.     

Positron trapping and self-diffusion activation energies in chromium

The activation energy for self-diffusion in chromium is found to be 3.51±0.13 eV from positron trapping measurements. The 4.51 eV activation energy seen in tracer diffusion work is therefore ascribed to divacancies, theQ ₂/Q ₁ ratio being typical of the bcc refractory group. The positron data give 0.55 for the ratioH _1v ^M /H _1v ^F of vacancy migration and formation energies, in agreement with quenching data for tungsten.     

Magnetic properties of Zr doped Y9Co7

Detailed measurements of magnetization and ac susceptibility at low temperatures of 1% Zr-substituted Y₉Co₇ are presented. All results are indicative of itinerant weak ferromagnetism withT _c ∼ 9.5 K. The zero-field magnetizations followT ² orT ^4/3 behaviour as in the Ni-substituted system. The estimated critical exponents areβ=0.38±0.03,γ=1.16±0.05. It is argued that the main effect of the non-magnetic Zr-substitution in Y₉Co₇ is to stabilize the ferromagnetic ordering by suppressing the ‘hopping’ of Co atoms along thec-axis sites of the hexagonal structure.     

Observation of the radiative kaon decay K − → µ−π0γν

Using data collected with the ISTRA+ spectrometer during the 2001 run of the U-70 proton synchrotron in Protvino, the first observation of the radiative kaon decay K ⁻ → μ⁻π⁰γν is reported. The ratio Br(K _μ3γ, 5 < E*_γ < 30 MeV)/Br(K _μ3) is found to be [0.270 ± 0.029(stat.) ± 0.026(syst.)]% and the ratio Br(K _μ3γ, 30 < E*_γ < 60 MeV)/Br(K _μ3) = [0.0448 ± 0.0068(stat.) ± 0.0099(syst.)]%. These ratios are consistent with the theoretical predictions 0.21 and 0.047%, respectively. The measured angular distribution asymmetry for the region 5 < E*_γ < 30 MeV, A(cos ϑ*_μγ) = 0.093 ± 0.141, is two standard deviations away from the theoretical prediction of 0.354. The measured asymmetry in the T-odd variable ξ = p_γ · (p_μ × p_π)/m _K ³ is −0.03 ± 0.13. The text was submitted by the authors in English.     

Observation of the muon inner bremsstrahlung at?LEP1

Muon bremsstrahlung photons converted in front of the DELPHI main tracker (TPC) in dimuon events at LEP1 were studied in two photon kinematic ranges: 0.2<E _γ ≤1 GeV and transverse momentum with respect to the parent muon p _T <40 MeV/c, and 1<E _γ ≤10 GeV and p _T <80 MeV/c. A good agreement of the observed photon rate with predictions from QED for the muon inner bremsstrahlung was found, contrary to the anomalous soft photon excess that has been observed recently in hadronic Z ⁰ decays. The obtained ratios of the observed signal to the predicted level of the muon bremsstrahlung are 1.06±0.12±0.07 in the photon energy range 0.2<E _γ ≤1 GeV and 1.04±0.09±0.12 in the photon energy range 1<E _γ ≤10 GeV. The bremsstrahlung dead cone is observed for the first time in the direct photon production at LEP. Deceased.     

Maximum of a Fractional Brownian Motion: Probabilities of Small Values

Let b _γ (t), b _γ(0)= 0 be a fractional Brownian motion, i.e., a Gaussian process with the structure function , 0 < γ < 2. We study the logarithmic asymptotics of P _T = P{b _γ (t) < 1,□t∈TΔ} as T→∞, where Δ is either the interval (0,1) or a bounded region that contains a vicinity of 0 for the case of multidimensional time. It is shown that ln P _T = - D ln T(1 + o(1)), where D is the dimension of zeroes of b _γ (t) in the former case and the dimension of time in the latter. Received: 28 September 1998 / Accepted: 19 February 1999     

Pressure and volume dependence of thelo-to phonons in InAs

The pressure dependence of thelo-to phonons in InAs has been investigated by Raman scattering using the diamond anvil cell. Indium arsenide transforms, presumably to the rock-salt structure at 70±1 kbar. The mode Grüneisen parameters for thelo-to phonons are γ _lo =0.99±0.03, γ _to =1.2±0.03 respectively. The effective charge,e* _T , for InAs decreases slightly with pressure and this trend is in accordance with the behaviour of other III–V zinc blende structured semiconductors: The structural phase transition is discussed in the light of theoretical calculations for phase stability of III–V compounds, as well as recent high pressure x-ray diffraction studies.     

Optical radiation and ionization of hydrogen atoms in heterogeneous exothermal reactions proceeding in an electric field

Optical radiation related to the Balmer series (H_α, H_β, H_γ) of hydrogen atoms is discovered when studying the isothermal reaction of trimeric acetone peroxide decomposition on the surface of oxidized tungsten in a static electric field with a strength of up to 4 × 10⁶ V/cm at T = 300 K. The distance from the surface over which desorbing excited hydrogen atoms radiate is determined from the Stark splitting of the lines. Electronically excited atoms remaining on the surface ionize according to the surface ionization mechanism.     

Measurement of vibrational energy transfer of OH (A2Σ+,v′=1→0) in low-pressure flames

2 Σ⁺) was measured in a low-pressure H₂/O₂ flame for three rotational levels of OH (v^′=1). Rate coefficients for collisions with H₂O and N₂ were determined. At 1600 K, k_VET (N₂) is (in 10^-11 cm³s^-1) 10.1±2, 6.1±1.8, and 3.8±1.3 for N^′=0, 5, and 13, respectively. The k_VET (H₂O) is <1.1±1.8. The k_Q (N₂) is <2.4±8 for both vibrational levels. The k_Q (H₂O) in v^′=1 is 59.1±6.5, 54.7±6.4, and 54.9±6.6 for N^′=0, 5, and 13, respectively, and, determined indirectly, 74.6±10.4, 70.6±10.3, and 63.4±7.3 for N^′=0, 5, and 13 in v^′=0. A multi-level model of OH population dynamics, which is being developed for the quantitative simulation of experimental LIF spectra, was extended to include VET. It was attempted to simulate state-to-state-specific VET coefficients for N₂ collisions. From these simulations it appears that angular momentum conservation does not determine the N dependence of the vibrational relaxation step. Received: 9 September 1996/Revised version: 6 January 1997     

Phase transformations and vacancy formation energies of transition metals by positron annihilation

The technique of the coincidence count rate at the peak of the angular correlation curve (CCR) in positron annihilation has been applied to the investigation of vacancy formation energies in thermal equilibrium in nickel, cobalt, and iron. The monovacancy formation energyE ^1v/F has been determined to (1.55±0.05) eV and (1.34±0.07) eV for nickel and cobalt, and (1.60±0.10) eV for α-iron, and (1.40±0.15) eV for γ-iron, respectively. The structural phase transformations in cobalt (693 K) and iron (1183 K, 1663 K) are exhibited by discontinuities of the CCR. In the case of cobalt the CCR follows exactly the change of the thermal expansion at the transition temperature. The temperature dependence of the CCR in the prevacancy region is found to be proportional to the thermal expansion for all metals investigated.     

Monovacancy formation energy in copper,silver, and gold by positron annihilation

Monovacancy formation energies in copper, silver, and gold have been deduced from the temperature variation of the peak counting rate in the angular correlation curve of positron annihilation radiation from these metals. The counting rate was temperature dependent over the entire temperature range, including temperatures so low that no trapping of positrons at vacancies is effective. At these temperatures the increase in counting rate results from thermal expansion of the lattice. By separating this thermal expansion effect from the vacancy trapping effect at higher temperatures, we obtained values for the monovacancy formation energyE _1v for copper, silver, and gold to 1.29±0.02 eV, 1.16±0.02 eV, and 0.97±0.01 eV, respectively.     

Spin-orbit coupling,spin-lattice relaxation,and spin-memory studies ofF-center-molecular-ion pairs in alkali halides

Summary The spin-orbit parameter Δ, spin-lattice relaxation timeT ₁, and spin-mixing parameter ɛ ofF _H(OH⁻) andF _H(CN⁻) centers in several alkali halides have been studied with magnetic circular dichroism at ∼2 K. A close comparison of the experimental results before and after optically induced association of theF center with the molecular ion has been made. In crystals of NaCl structure the negative spin-orbit parameter Δ changes little betweenF andF _H centers in the same host. For CsCl and CsBr two values of Δ have been derived forF _H(CN⁻) centers with axis parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation timeT ₁ is already shorter before aggregation compared toF formation. The spin-mixing parameter ɛ decreases slightly forF _H(OH⁻) compared toF centers, while it increases drastically forF _H(CN⁻) defects and reaches its maximum possible value ɛ=0.5 in cesium halides. First attempts to interpret these magneto-optical results will be presented. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Diffusion Coefficient of a Brownian Particle with a Friction Function Given by a Power Law

Nonequilibrium biological systems like moving cells or bacteria have been phenomenologically described by Langevin equations of Brownian motion in which the friction function depends on the particle’s velocity in a nonlinear way. An important subclass of such friction functions is given by power laws, i.e., instead of the Stokes friction constant γ ₀ one includes a function γ(v)∼v ^2α . Here I show using a recent analytical result as well as a dimension analysis that the diffusion coefficient is proportional to a simple power of the noise intensity D like D ^{(1−α)/(1+α)} (independent of spatial dimension). In particular the diffusion coefficient does not depend on the noise intensity at all, if α=1, i.e., for a cubic friction F _fric=−γ(v)v∼v ³. The exact prefactor is given in the one-dimensional case and a fit formula is proposed for the multi-dimensional problem. All results are confirmed by stochastic simulations of the system for α=1, 2, and 3 and spatial dimension d=1, 2, and 3. Conclusions are drawn about the strong noise behavior of certain models of self-propelled motion in biology.     

Shape co-existence and structural evolution of thevi13/2 band in157Yb

The high-spin states of¹⁵⁷Yb have been studied via the reaction of¹⁴⁴Sm(¹⁶O, 3n) at¹⁶O energy of 90 MeV using techniques of in-beam γ-ray spectroscopy. Measurement of γ-γ-t coincidences was performed with 11 BGO(AC)HPGe detectors. Based on the γ-γ coincidence relationships and the measured results of γ-ray anisotropies and DCO ratios, the level scheme for¹⁵⁷Yb was established. The shape co-existence and structural evolution of thevi_13/2 band with increasing angular momentum in¹⁵⁷Yb have been discussed. The systematics of thevi_13/2 bands in theN=87 odd-A isotones have been compared.