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.     

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.     

Positron annihilation in polycrystalline metals

The empirical relation θ _p ⁶ /I _p=aK (where θ _p is the limiting angle of the parabolic component in the angular distributions of annihilation photons in metals, I _p is the integrated contribution of this component, K=1, 2, 3, ... is an integer, and a is a constant independent of the type of metal) observed earlier has been tested on magnesium, aluminum, copper, zinc, lead, and bismuth samples. The validity of this relation has been substantiated. The value of the dimensionless constant a has been determined and was found to coincide within experimental error with the result obtained in previous measurements. It is shown that the value of K for the same metal but for different samples may be different. It is conjectured that this may be due to different defect concentrations in samples. Fiz. Tverd. Tela (St. Petersburg) 40, 600–602 (April 1998)     

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)     

Positron annihilation in metals and alloys

This review article summarizes the present knowledge of positron-annihilation research in metallic substances. Including a short historical survey, the annihilation processes in metals and alloys are discussed and various physical conditions such as ordering processes, magnetic phenomena, liquid state, superconductivity and lattice imperfections are considered. Finally, the present state of theoretical investigation is given and the outlook for the new and very useful technique in metal physics is pointed out.     

Positron annihilation in solid and liquid metals

The angular correlation of the gamma rays resulting from the annihilation of positrons in 15 solid and liquid metals and semiconductors has been studied. Experiments have been done on each material at room temperature and at temperatures above and below the melting point.

The elements investigated fall into three categories according to the way the angular correlation distribution changes as the melting point is reached. To within the experimental angular resolution (0.5 milliradians) no change in the angular correlation distribution is observed for Li, Se, Na, and Tl upon heating from room temperature to beyond the melting point. The elements Sb, Bi, Ga, Hg, Sn and Te exhibit changes in their angular correlation distributions only upon being melted, whereas for the metals Al, Cd, In, Pb and Zn changes occur when the specimen is heated from room temperature to temperatures below the melting point.

Changes in the angular correlation distribution upon heating or melting are generally manifested as (a) a narrowing of the central part of the curve, (b) a rounding-off of the parts of the curve near the Fermi cut-off angle and (c) a change in the area of the broad background curve as compared with the area under the central peak.     

Positron annihilation in some transition metal oxides

The constant value of the total half-width of the angular correlation spectrum and the momentum corresponding to the absolute maximum of the annihilation photon distribution was found for TiO₂, VO₂, NbO₂, MoO₂ and Al₂O₃ in agreement with the “optical” model. Its value follows also from the Gaussian curve fitting experimental results.     

Magnetic field effects on positron annihilation in metals

It is shown that the positron annihilation rate from a state with momentum k parallel to the magnetic field is periodic in $\text{1}\text{B}$, and that the periodicity is determined by the area of the section of the fermi surface whose z component of momentum is k.     

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.     

Positron annihilation in vacancies at grain boundaries in metals

The behavior of vacancies in selected coherent grain boundaries (GBs) in Fe and Ni is studied by means of molecular dynamics simulations. Corresponding positron lifetimes are calculated using the atomic superposition method. There is a difference between the vacancy behavior in Fe and Ni in dependence on temperature. In Ni, vacancies at GBs appear to diminish substantially their free volume (and lifetime) with the increasing temperature, which can be attributed to ‘vacancy delocalization’. Contrary, GB vacancies remain stable up to apparently higher temperatures in Fe.     

Systematics of the rare-gas core contributions to the positron annihilation spectra of some simple and transition metals

Taking into account the core electron enhancement factor the rare-gas core contribution to the angular correlation positron annihilation spectra and to the total annihilation rate in some simple and transition metals are calculated. It is shown that the valence high-momentum part of the Gaussian fraction is not negligible in simple metals. In 3d and 4d metals, the rare-gas core part of the total annihilation rate amounts from 9 to 37%. The results are expected to help in the correct interpretation of the positron annihilation data.     

Deconvolution of Doppler-broadened positron annihilation energy spectra in metals

The development of computer programmes to deconvolute and fit the Dopplerbroadened annihilation radiation from a moving positron-electron pair is discussed. An analysis is presented for the annihilation line observed in a series of metals using a high-resolution Ge(Li) detector.     

Interatomic potentials in transition metals

The different roles played by the valence s and d electrons in determining the bulk properties of pure transition metals is described. In the light of this the expected behaviour of the inert gas-metal and metal-metal interatomic potentials is discussed.     

Electron-phonon interactions in transition metals

The tight-binding method is used to calculate 〈I²〉, the Fermi surface average of the squared electron-phonon coupling constant for 4d b.c.c.—transition metals and alloys. When nonorthogonality effects are properly included, our results for 〈I²〉 agree very well with empirical values. Moreover, the variation of 〈I²〉 can be understood in simple physical terms.     

Positron work functions in transition metals

Calculations of positron and positronium atom work functions in transition metals are described with an analysis of the surface and internal contributions. Negative work functions are obtained for elements towards the centre of the transition series, in qualitative agreement with experimental observations.     

Radionuclide emitters for high-temperature measurements on metals using positron annihilation

The fabrication of⁶⁸Ge and⁴⁴Ti positron sources which can withstand temperatures up to 1000°C is described. The sources are designed for use in the measurement of thermally-generated vacancy concentrations by the positron trapping technique. Measurements of positron lifetimes and Doppler-broadened annihilation photon lineshapes indicate that if suitable corrections are made the contribution of source matrix annihilations to experimental data can be reduced to less than 0.5% of the total annihilation events.     

Contact melting of transition metals

Contact melting of transition metals is discussed on the basis of ideas about the formation of stable electron configurations in condensed systems. It is shown that the contact-melting temperature increases as the statistical weight and energetic stability of the most stable electronic configurations of the crystals in contact increase. The statistical weight of the stable electronic configurations of a crystal is associated with its stability determinant, constructed from the second derivatives of the thermodynamic potential. A proposed dependence of the contact-melting temperature on the statistical weight of stable electronic configurations is confirmed experimentally.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 99–104, October, 1969.