New evaluation of the angular correlation of positron annihilation spectra for noble and d-transition metals

A new fit to the long-range angular correlation of annihilation radiation data of the sum of a parabola, so-called Ferrell function, and a Gaussian for noble and d-transition metals is presented. The three functions are considered to describe the positron annihilation with three different electron groups: nearly free, d-like and rare-gas core electrons, respectively.     

d Electron momentum densities for position annihilation in transition metals

The relative contribution of 3d electrons to the momentum densities for positron annihilation in the iron series transition metals are calculated, using the atomic Hartree-Fock-Slater orbitals. A discussion is given of the observed systematics. The per electron contribution to the angular correlations is found to decrease with the filling up of the d shell. The high momentum components are found to be relatively enhanced in case of higher Z metals. The built in spin dependence of the electron HFS wavefunction is reflected in the calculated curves.     

Doppler broadening of positron annihilation photons in metals

The Doppler broadening of positron annihilation photons was measured in 17 metals. A model which considers the positron lifetime spectra in metals to be composed of terms for annihilation with conduction and core electrons and surface centers of low electron momentum is used to correlate calculated core annihilation rates with the Doppler lineshape. Ta metal was doped with defects with high energy implantations of¹⁴N⁺⁴ ions at variable doses. Differences in the Doppler linewidths were ascribed as being principally a reflection of the probabilty of annihilation with core electrons relative to annihilation with conduction electrons.     

Pseudo-potential caculations of positron annihilation rates in bubbles of helium contained in the metals Mg,Ag and Au

Abstract

A pseudo-potential technique has been applied to calculate the annihilation rates for positrons in bubbles of helium gas in gold and silver. The positron pseudo-wavefunction in each case was found to be in a surface state of the metal, the exact form of which displayed a slight dependance on the density of the helium gas. The annihilation rate of the positron was the sum of a nearly constant surface rate and a strongly density dependant annihilation rate with the helium electrons. There is a trend for annihilation with the helium to be greater in metals with low free electron densities, the helium in such metals resting closer to the metal surface thus increasing the overlap of the positron wavefunction with the helium.     

Position annihilation in transition metals

The positron annihilation rate in a ferromagnetic electron system which is described by a generalized Anderson model has been studied. Because of the spin polarization ofs-type electrons, the difference in the annihilation rate between the majority and the minority spins changes its sign at the momentum corresponding to the virtuald-level. The enhancement factor due to the effective Coulomb interaction between the electrons and a positron has been calculated using the dielectric constant for a ferromagnetic electron gas derived by Kim and Schwatz.     

High-momentum analysis in Doppler spectroscopy

Unique information about the chemical vicinity of positron annihilation sites is provided by the contribution of high electron momenta to the Doppler spectrum, since this momentum range is characteristic for the annihilation with core electrons and hence element specific. However, the corresponding energy region in the spectrum is overlaid by a huge background caused by the annihilation radiation itself and the Compton spectrum of other gamma lines having an energy above 511 keV. Usually these backgrounds are reduced by measuring both annihilation quanta in coincidence.By mathematically analyzing the background contributions, we open another possibility to obtain the high-momentum region employing one single germanium detector. A necessary precondition is employing either background-free positron beams or a low-background positron source, e.g. ⁶⁸Ge, instead of the widely used positron emitter ²²Na. The ⁶⁸Ge-source emits positrons with an endpoint energy of about 1.9 MeV, where as the contribution of gamma quanta having higher energies than the annihilation radiation at 511 keV is negligible low.When analyzing spectra from metals and semiconductors according to the described background subtraction, the same information contained in the momentum range up to 35 × 10⁻³m₀c or beyond can be extracted, as if the spectra were measured employing a coincidence setup with two Ge-detectors.     

Oxidation and thermal reduction of the Cu(1 0 0) surface as studied using positron annihilation induced Auger electron spectroscopy (PAES)

Changes in the surface of an oxidized Cu(1 0 0) single crystal resulting from vacuum annealing have been investigated using positron annihilation induced Auger electron spectroscopy (PAES). PAES measurements show a large increase in the intensity of the annihilation induced Cu M_2,3VV Auger peak as the sample is subjected to a series of isochronal anneals in vacuum up to annealing temperature 300 °C. The intensity then decreases monotonically as the annealing temperature is increased to ∼600 °C. Experimental probabilities of annihilation of surface-trapped positrons with Cu 3p and O 1s core-level electrons are estimated from the measured intensities of the positron annihilation induced Cu M_2,3VV and O KLL Auger transitions. Experimental PAES results are analyzed by performing calculations of positron surface states and annihilation probabilities of surface-trapped positrons with relevant core electrons taking into account the charge redistribution at the surface, surface reconstructions, and electron-positron correlations effects. The effects of oxygen adsorption on localization of positron surface state wave function and annihilation characteristics are also analyzed. Possible explanation is proposed for the observed behavior of the intensity of positron annihilation induced Cu M_2,3VV and O KLL Auger peaks and probabilities of annihilation of surface-trapped positrons with Cu 3p and O 1s core-level electrons with changes of the annealing temperature.     

On the broadening of the annihilation line

The broadening of annihilation line was studied with a Ge detector. The annihilation line was deconvoluted taking into account the instrumental resolution of 1.08 keV. The P_f in several metals are found. The contribution of core electrons to annihilation is deduced.     

Self-trapping of positively charged particles in metals

It is shown that the existence of a metastable state in which positrons in metals are “self-trapped” by strong interaction with the lattice gives rise to an anomalous temperature dependence in positron annihilation properties. The “intermediate” temperature variation of the shape of the annihilation photon line discovered by MacKenzieet al. is well accounted for by this mechanism; alternative interpretations in terms of thermal expansion effects may be refuted. This result calls for considerable revision of some of the published monovacancy formation energies obtained from positron annihilation measurements. Approximate criteria for the existence and the metastability of a selftrapped state of positively charged particles in metals are given. It is found that metastable self-trapping may occur for positrons; hydrogen isotopes and positive muons should be self-trapped in configurations that are always stable relative to the Bloch-wave states of these particles.     

Effective concentration of electrons in metals upon measurements via positron annihilation spectroscopy

Calculations are performed together with the summarization of published data on the measurement of positron annihilation rates in a number of simple substances. The information potential of different methods underlying positron annihilation spectroscopy is analyzed as applied to the study of condensed matter. The features of the mechanism of positron annihilation in metals are discussed. The possibility of investigating the electronic and defect structures of metals and alloys using the method of the time distribution of annihilation photons is considered.     

Properties of positron annihilation in metals

Positron annihilation in bulk metals has been studied by examining the angular distribution of the annihilation photons in polycrystalline samples of magnesium, aluminum, copper, zinc, indium, tin, lead, and bismuth. It has been shown that conduction electrons as well as core electrons take part in this process. The conduction electron densities and Fermi energies have been determined. It is found that the electron density in the vicinity of a positron is significantly higher than the density of the free electron gas. We believe that this is due to the formation of Wheeler complexes and we estimate its charge. We have analyzed various means of measuring the conduction electron density and conclude that the positron method gives the most reliable information. Fiz. Tverd. Tela (St. Petersburg) 41, 929–934 (June 1999)     

Evaluation of the formation entropy of a single vacancy by means of positron annihilation

Analyzing positron annihilation data it was found that the formation energy of a single vacancy is proportional to the characteristic temperature T_c in f.c.c. metals. Assuming that the equilibrium fractional concentrations of single vacancies at T_c are constant, one finds that the formation entropy of a single vacancy is (1.6 ± 0.1)k for all f.c.c. metals. For zinc and cadmium, the formation entropies are 2.5k and 3.3k respectively.     

Positron lifetime as a function of grain size

Published data on positron annihilation lifetime in copper as a function of grain size have been analyzed to show that there is a linear relationship between the internal grain boundary surface area, per unit volume,S _v, and the positron lifetime, τ. The analysis indicates that grain boundaries are important in the trapping of positrons. It is suggested that the slope of the resulting straight line,dS _v/dτ, can be used to determine the annihilation rate of the grain boundaries.     

Applications of slow positrons to cancer research: Search for selectivity of positron annihilation to skin cancer

Slow positrons and positron annihilation spectroscopy (PAS) have been applied to medical research in searching for positron annihilation selectivity to cancer cells. We report the results of positron lifetime and Doppler broadening energy spectroscopies in human skin samples with and without cancer as a function of positron incident energy (up to 8 μm depth) and found that the positronium annihilates at a significantly lower rate and forms at a lower probability in the samples having either basal cell carcinoma (BCC) or squamous cell carcinoma (SCC) than in the normal skin. The significant selectivity of positron annihilation to skin cancer may open a new research area of developing positron annihilation spectroscopy as a novel medical tool to detect cancer formation externally and non-invasively at the early stages.     

Analysis of the strain-rate sensitivity of flow stresses in nanocrystalline FCC and BCC metals

The dependence of the strain-rate sensitivity coefficient of flow stresses S = dlnσ/dln\(\dot \varepsilon \) on temperature, strain rate, and grain size in nanocrystalline (NC) metals is analyzed quantitatively in terms of the dislocation-kinetics approach taking into account the properties of grain boundaries as sources, sinks, and barriers for moving dislocations. The interaction of moving dislocations with a dislocation forest in nanograin boundaries is shown to be responsible for the fact that the values of this coefficient in NC fcc metals (Cu, Ni) are an order of magnitude greater than those in coarse-grained metals and for the strong dependence of the coefficient S on the above factors. This dependence is largely caused by the annihilation of lattice dislocations in grain boundaries controlled by the activation energy of grain boundary diffusion. The values of the coefficient S in NC bcc metals (α-Fe) are an order of magnitude lower than those in coarse-grained samples, because dislocations move in a Peierls relief in nanograins     

Thermalization of positrons and positronium atoms in ionic crystals

It is shown that total positron scattering on acoustic and optical lattice vibrations in atomic semiconductors and ionic crystals causes total positron thermalization before annihilation at both high and low (T≤10 K) temperatures.     

Electron energy-loss spectroscopy applied to solids

Several illustrating examples of recent electron energy-loss investigations of the electronic structure of solids are reviewed. In particular, studies on rare-gas bubbles in metals, on conducting polymers, and onL _2,3 edges of 3d transition metals are reported. Moreover, the electron energy-loss spectrometer, which was used for these investigations, is described briefly.     

Electronic structure and positron annihilation in alkali metals: Isolation of ionic core contribution and valence high-momentum components

Momentum densities of annihilation pairs from valence as well as from ionic core electrons in alkali metals are calculated ab initio and compared with the experimental results. It is shown that the valence high-momentum components constitute a great deal (23–34% in Na-Cs and probably even more in Li) of the Gaussian part of the angular correlation curves. The average core enhancement factor γ_c ranges from 1.5 (Li) to 7.1 (Cs) and may be well expressed by a logarithmic function of ionic core polarizability. The presented values of γ_c are much higher than the core enhancement factors in the high-momentum (?15 mrad) region which, according to the recent theory of Bonderup, Andersen and Lowy, should not be very different from unity.     

Anisotropy of positron wave function in 4d transition metals

The positron wave functions have been calculated employing the method of expansion of symmetrized plane waves in some 4d transition metals. Systematics of the positron wave functions along the three symmetry directions [100], [110], [111] in these metals, have been discussed. The anisotropies of the ψ₊ have been found to be strongly dependent upon the crystal symmetries. The results of the band structure calculation of 2γ-angular correlation in Rh and Ag are presented.