Positron trap

In solids the free positron lifetime r lies in the approximate range 100-500 ps and is dependent upon the electron density. Following implantation, the positrons are able to diffuse in the solid by an average distance L+ = (D+t)1//2, where D+ is the diffusion coefficient. This quantity is usually expressed in cm2 s-1 and is of order unity for defect-free metallic moderators at 300 K (Schultz and Lynn, 1988). The requirement of very low defect concentration arises because the value of D+ is otherwise dramatically reduced owing to positron trapping at such sites. 

Traditionally, experimental values of Zeff have been derived from measurements of the lifetime spectra of positrons that are diffusing, and eventually annihilating, in a gas. The lifetime of each positron is measured separately, and these individual pieces of data are accumulated to form the lifetime spectrum. (The positron-trap technique, to be described in subsection 6.2.2, uses a different approach.) An alternative but equivalent procedure, which is adopted in electron diffusion studies and also in the theoretical treatment of positron diffusion, is to consider the injection of a swarm of positrons into the gas at a given time and then to investigate the time dependence of the speed distribution, as the positrons thermalize and annihilate, by solving the appropriate diffusion equation. The experimentally measured Zeg, termed Z ), is the average over the speed distribution of the positrons, y(v,t), where y(v,t) dv is the number density of positrons with speeds in the interval v to v + dv at time t after the swarm is injected into the gas. The time-dependent speed-averaged Zef[ is therefore... 

Fig. 6.6. Schematic illustration of the electrode structure of the positron trap of Greaves, Tinkle and Surko (1994). The variation of the electrical potential along the trap, together with the gas pressure in the various regions, is also shown. The letters A, B and C indicate energy-loss collisions of the positrons with the N2 buffer gas. Reprinted from Phys. Plasmas 1, Greaves et at, Creation and uses of positron plasmas, 1439-1446, copyright 1994, by the American Institute of Physics.

In this section we review the results from positron annihilation experiments, predominantly those performed using the lifetime and positron trap techniques described in section 6.2. Comparisons are made with theory where possible. The discussion includes positron thermalization phenomena and equilibrium annihilation rates, and the associated values of (Zeff), over a wide range of gas densities and temperatures. Some studies of positron behaviour in gases under the influence of applied electric fields are also summarized, though the extraction of drift parameters (e.g. mobilities) is treated separately in section 6.4. Positronium formation fractions in dense media were described in section 4.8. 

Thermalization in N2 gas has also been studied using the positron-trap apparatus developed by Surko and coworkers and described in subsection 6.2.2. By storing positrons in the trap at a known pressure for various lengths of time before ejecting them and measuring their mean... 

The positron-trap technique has been used to measure the annihilation rate of positrons interacting with a wide variety of molecules. The species investigated by Iwata et al. (1995) include many hydrocarbons, substituted (e.g. fluorinated and chlorinated) hydrocarbons and aromatics as mentioned in section 6.1, large values of (Zeff) (in excess of 106) were found for some molecules. Several distinct trends are exhibited in the data of Iwata et al. (1995). Though much of the detailed physics involved in the annihilation process on these large molecules is still unclear, the model of Laricchia and Wilkin (1997), described in section 6.1, may offer a qualitative explanation of the observations. 

The temperature, or energy, dependence of the annihilation rate, or (Zeflf), has also been investigated using a positron trap. In this technique positrons are first accumulated at room temperature, and then their... 

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

Greaves, R.G. and Surko, C.M. (1996). Solid neon moderator for positron trapping experiments. Can. J. Phys. 74 445-448. 

Murphy, T.J. and Surko, C.M. (1992). Positron trapping in an electrostatic well by inelastic collisions with nitrogen molecules. Phys. Rev. A 46 5696-5705. 

H is formed form clouds of antiprotons and positrons trapped in Penning... 

Since the positron traps in vacancy like open volume and positronium in pores, it will be possible to selectively detect impurities next to vacancies [71]. For metal indiffusion experiments one can design test structures of silicon, metal, low-/ layer samples. Two detector coincident measurements would be performed as a function of temperature and time to observe the chemical signature of the metal in the low-/ layer. The effectiveness of diffusion barriers can be tested by depositing the barrier prior to the low-/ layer. 

In some of the experiments [30, 31], variation of lifetime uncorrelated with Tc, has been observed. This has prompted explanations for the observed temperature dependence of lifetime in terms of positron trapping behaviour... 

In order to account for this, further calculations [84] have been carried out envisaging various possible defect structures, such as monovacancies at carbon site, Y site, and clusters of carbon vacancies, etc. Based on these calculations, it is inferred [84] that the measured lifetime at room temperature in YM2B2C is best accounted for in terms of positron trapping at clusters of carbon vacancies... 

Khatri, R. Asoka-Kumar, P. Nielsen, B. Roellig, L.O. et al. (1993) Positron trap centers in X-ray and gamma-ray irradiated Si02 , Appl. Phys. Lett. 63, 385. 

The basis for this technique is that positrons are preferentially trapped in a low electron density site, such as a vacancy or a void. The positron trapped at a vacancy will interact with a lower electron density than in the bulk material and its lifetime is therefore increased [1]. 

I2, T2) attributed to positrons trapped at the crystalline-amorphous interface had T2 0.32 ns and h exhibited a precipitous decrease from about 58% to about 50% at the yield point, followed by recovery back to about 58%. This phenomenon interpreted as indicating interfacial loss of defects occurs during the initial deformation process and then some unknown recovery process takes place subsequently. 

PA techniques can therefore be used to assess the amount of damage in a material, if that damage gives rise to vacancies or other positron trap sites. 

The presence of vacancy defects, or other positron traps, disturbs the balance of positron annihilation statistics between annihilations with core and conduction electrons. At positron traps, annihilation is most likely to be with unlocalised conduction electrons which have a smaller momentum distribution than the core electrons. Thus as, for instance, the vacancy defect concentration is increased so also is the probability of the positron annihilating with conduction electrons rather than core electrons. This results in a slight reduction in the width of a histogram of the energies of the annihilation y-rays and also in the angular range between the coincidentally emitted y-rays. 

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. 

---