Positron annihilation models

A fascinating insight into the impact that modelling can make in polymer science is provided in an article by Miiller-Plathe and co-workers [136]. They summarise work in two areas of experimental study, the first involves positron annihilation studies as a technique for the measurement of free volume in polymers, and the second is the use of MD as a tool for aiding the interpretation of NMR data. In the first example they show how the previous assumptions about spherical cavities representing free volume must be questioned. Indeed, they show that the assumptions of a spherical cavity lead to a systematic underestimate of the volume for a given lifetime, and that it is unable to account for the distribution of lifetimes observed for a given volume of cavity. The NMR example is a wonderful illustration of the impact of a simple model with the correct physics. 

The variations in the positron intensities in HDPE with different amounts of glass filler were satisfactorily explained by the proposed composite model for positron annihilation. The composite model takes into account the size of the filler particles and the density difference between the filler and matrix. 

I.A. Ivanov, J. Mitroy, Optical model theory for positron annihilation during scattering, J. Phys. B At. Mol. Opt. Phys. 33 (2000) L831. 

Studies on other high-temperature superconductors Positron annihilation measurements across Tc, coupled with the calculations of PDD have been carried out in a variety of hole-doped superconductors that include YBa2Cu40g [48], Bi-Sr-Ca-Cu-0 [49], and Tl-Ba-Ca-Cu-0 [50, 51] systems. We will not labor with the details here, except to state that a variety of temperature dependencies are seen and these can be rationalized when the results are analysed in terms of positron density distribution and the electron-positron overlap function [39]. These calculations show that the positron s sensitivity to the superconducting transition arises primarily from the ability to probe the Cu-O network in the Cu-0 layer. The different temperature dependencies of lifetime, i.e., both the increase and decrease, can be understood in terms of a model of local electron transfer from the planar oxygen atom to the apical oxygen atom, after taking into account the correct positron density distribution within the unit cell of the cuprate superconductor. 

The calculation of PAES intensities largely reduces to the calculation core annihilation probabilities for positrons in the surface state [11]. This follows from the fact that almost all of the core hole excitations of the outer cores relax via Auger emission and that almost all of the positrons incident at low energies become trapped in a surface state before annihilation. First-principles calculations of the positron states and positron annihilation characteristics at metal and semiconductor surfaces are based on a treatment of a positron as a single charged particle trapped in a "correlation well" in the proximity of surface atoms. The calculations were performed within a modified superimposed-atom method using the corrugated-mirror model of Nieminen and Puska [12]. 

Almost a linear dependence between pore size and positrons lifetime can be observed which was not clearly obtained in previous studies. This relationship is expected because when the pores are wider the probability of interaction between the positrons and the surface electron density in the pore walls decreases. This results in a lower rate of positrons annihilation with the surrounding electrons and then a higher lifetime. A simple model for the annihilation process can be constructed assuming that the positron is trapped in a spherical pore of radius R of constant potential. The resolution of the Schroedinger equation shows that the lifetime of positrons is a function of R [5]. 

Despite all simplifications the model of particle in the rectangular potential well, extended to include the population of excited le els. describes quite well the dependence of ortho-positronium lifetime on the pore radius. In this model the o-Ps lifetime is ruled entirely by geometrical factors, however, maybe the chemical composition of the medium should be taken into account. The lifetime vs. average radius dependence is particularly steep below 5 nm. and in this range the positron annihilation method can be useful for determination of average pore radii. The specific surface determines the distribution of o-Ps between small voids in the bulk and pores. 

Typically, therefore, a PALS spectrum consists of a minimum of three components the short-lived p-Ps component with intensity 7i and lifetime ti = 125 ps a free positron annihilation component, with intensity I2 and lifetime T2 and the o-Ps component, with intensity I3 and lifetime T3. Theory predicts the ratio /3//1 = 3, but as discussed in Chapter 11, certain effects may lead to a decrease in this ratio. The theoretical basis for relating the o-Ps lifetime to free volume is based on a model proposed by Tao [1972], in which < -Ps is assumed to be trapped in a potential well of... 

These models have been quite useful as a means of explaining some of the phenomena associated with the rate of positron annihilation. Other experiments, however, seemed to indicate that the "free volume" model includes far too few properties apart from the factor of density as to satisfactorily explain variations in the positron lifetimes which occur as a result of phase transitions. It would appear that in this case an important part in the positron annihilation process is played by the nature of the intermolecular Interaction and by the internal order of the structures of the molecular substance. 

A spectrum is built up from at least a million lifetime measurements from individual positrons. Standard computer codes are available for the decomposition of the spectra including POSITRONFIT in which a least squares fit is used to fit a model spectrum with a given number of decay components to the observed spectrum. Maximum entropy techniques have also been used to determine the most probable underlying distribution of trap lifetimes. As the number of different traps increases, interpretation becomes increasingly difficult. Several research groups have published positron annihilation lifetime data on irradiated RPV steels (see Section 9.11.1). 

PA studies on RPV steels are important because they have the potential to provide information on matrix defects. However, since interpretation of the data from complex commercial steels is difficult, many studies have focused on model alloys. In Section 9.11.1 we include a brief review of a selection of PA data from the literature, focusing first on model alloys and then on steels. It is shown that, in combination with post-irradiation annealing and other microstructural techniques, positron annihilation techniques can help elucidate the nature of the positron traps. 

Phythian et al performed a series of isochronal annealing experiments on model Fe-Cu-Mn-Ti-N alloys. Positron annihilation lifetime measurements indicated the presence of a long lifetime component (-265ps) associated with very stable precipitates possibly also associated with C. Further interpretation of the results indicated a strong association between vacancy-type defects and Cu atoms. 

It should be noted that there are some experimental measurements (such as positron annihilation) which are apparently inconsistent with these valences. The difficulty arises from the fact that, although this valency scheme is useful and is consistent with many experimental facts, it is an over simplified description of the electronic nature of cerium and its alio tropes. This problem is dealt with in the discussions concerning the various models proposed to explain the a y transformation and the electronic nature of a, a and y phases (sections 5.1-5.7). 

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