Lifetime spectra

Five lifetime components, Xi - r5, were used in the fitting procedure for resolving our experimentally obtained lifetime spectra. The obtained results for gel-a are shown in Table 1 and for gel-b in Table 2. 

The applicability of positron lifetime spectroscopy for the characterization of the partly charged nickel hydroxide was investigated [90]. The positron lifetime spectra of 8-Ni(OH)2/j8-NiOOH systems were presented. Three different parts of the annihilation curves were observed and identified. 

The positron lifetime spectra of polyethylene and glass-filled polyethylene were resolved in four exponentials, representing different annihilation processes. The... 

Additional, but rather less direct, evidence for the accuracy of the variational results for models H5 and H14 is provided by the excellent agreement between the theoretical and experimental lifetime spectra for positrons diffusing in helium gas, where calculation of the theoretical spectrum requires a knowledge of the momentum transfer and annihilation cross sections, both of which are derived from the wave functions generated in the calculations of the elastic scattering phase shifts. A detailed discussion of positron lifetime spectra is given in Chapter 6. 

Experiments on these two gases, reported by Griffith and Heyland (1978), showed that a fast component, with a density-dependent decay rate, was present in the lifetime spectra, and this was tentatively linked to the dearth of long-lived ortho-positronium. Furthermore, it was found for mixtures of krypton with helium that the maximum value of F, which was observed at a concentration of around 0.01% of krypton, was in excess of the sum of the individual F-values for the two gases when pure. 

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... 

Lifetime spectra obtained for the noble gases argon and xenon are shown in Figures 6.5(a) and (b) respectively. These spectra serve to... 

Fig. 6.5. Examples of positron lifetime spectra for (a) argon and (b) xenon gases. The argon data are for a density of 6.3 amagat at 297 K. The channel width is 1.92 ns. In (a), (i) shows the raw data, (ii) shows the signal with background removed, (iii) shows the free-positron component and (iv) shows the fitted ortho-positronium component. In (b), the spectrum for xenon is for room temperature and 9.64 amagat and has a channel width of 0.109 ns. The inset shows the fast components as extracted and discussed by Wright et al. (1985).

Tawel and Canter (1986) extended these investigations using a pulsed electric field of varying amplitude, which was applied at a minimum time of 26 ns after the emission of a positron from the 22Na radioactive source. The field was triggered by detecting the 1.274 MeV gamma-ray. Their work established that the two thresholds, ER and E+, were distinct, which led to observable differences between the lifetime spectra when the electric field was pulsed on at different times after positron emission. 

Fig. 6.13. Superimposed zero field and pulsed field (81 V cm-1 peak amplitude) positron lifetime spectra. The pulsed field spectrum has been decomposed into heated components (broken line) and unheated components (crosses) to illustrate how the electric field splits up the positron ensemble. This is also illustrated by the inset, which shows, schematically, the energy distribution p(E,t) of the positron ensemble in the two-threshold model (see text). Reprinted from Physical Review Letters 56, Tawel and Canter, Observation of a positron mobility threshold in gaseous helium, 2322-2325, copyright 1986 by the American Physical Society.

Positron lifetime spectra for the noble gases. J. Phys. B At. Mol. Phys. 8 1734-1743. 

Farazdel, A. and Epstein, I.R. (1978). Monte Carlo studies of positrons in matter. Temperature and electric field effects on lifetime spectra in low-temperature, high-density helium gas. Phys. Rev. A 17 577-586. 

Osmon, P.E. (1965). Positron lifetime spectra in molecular gases. Phys. Rev. 140 A8-A11. 

Ps02 1959 > 2.3 Positron lifetime spectra in liquid oxygen [62] gas-phase quenching data with a Born cycle interpretation [63]. 

PsF 1969 2.9(5) Interpretation of positron lifetime spectra in liquid C6H6 vs C6H5F [64]. 

Figure 3.4 illustrates two lifetime spectra collected by methods similar to those outlined above, (a) exhibits the non-exponential shoulder region associated with the annihilation of non-thermalised positrons. After thermalisation (essentially at time zero for condensed matter) the spectra are sums of exponential components associated with each decay mode, and a background component B, A] = 2 A, exp(-Ajt,) + B. For long lifetime components (> Ins) each X can be extracted by non-linear least squares fitting. For short X values characteristic of condensed matter, however, a... 

Figure 3.4 Positron lifetime spectra for Ar gas (left) and In (right). Note time scales.

Fig. 5.9 Concentration dependencies of the o-Ps component I3 in the lifetime spectra, yields of ej, Gg- = Giep P,-, and radiolytic hydrogen, Gh2 = Giep Ph2/3, in...

Figure 9.1 Positron lifetime spectra of the PECVD grown a-Si H films prepared at power densities of 0.03 W/cm2, 0.13 W/cm2,0.51 W/cm2, and 0.76 W/cm2. (Suzuki et a ., 1991)...

Figure 9.3(a) shows positron lifetime spectra of a porous Si thin film at the sample temperatures of 25°C (initial), 300°C, and 500°C, and Figure 9.3(b) shows positron lifetime spectra measured at 500°C and at 200°C after 500°C annealing. Strong temperature dependence was observed in the long-lived component. 

Figure 9.4 Positron lifetime spectra of amorphous Si02 (500 nm) on Si(100) at the positron incident energy of 2 keV and 15 keV.

Figure 9.8 (a) Positron lifetime spectra and (b) annihilation rate probability function for low-k films grown by a double-frequency PECVD method with different LF powers. (Suzuki et al., 2001)... 

Figure 9.9. (a) Positron lifetime spectra of porous Si02 with and without a Si02 cap layer (511 keV photo peak), (b) Pulse height spectra of the y-ray detector for the long-lived component in the annihilation time range between 14.4 ns and 220 ns from the peak. 

The analysis of the positron annihilation lifetime spectra is a very important aspect of using the PAL techniques to analyze polymers. Without proper data analysis interpretation of data might be misleading and important scientific information will be lost. In PAL studies of polymers the PAL spectrum can be analyzed in two ways (1) a finite lifetime analysis or (2) continuous lifetime analysis. In the finite lifetime analysis the PAL spectra is resolved into a finite number of negative exponentials decays. The experimental data y(t) is expressed as a convoluted expression (by a symbol ) of the instalment resolution function R(t) and a finite number (n) of negative exponentials ... 

A number of authors have found that the lifetime spectra of semicrystalline polymers are best resolved into three components. In a study of PEEK (poly(ether ether ketone)), Nakanishi et al [14] found that a three component fit was best. They observed that the o-Ps lifetime (r3) did not change with an increasing amounts of crystallinity, but the o-Ps yield (I3) decreases linearly with an increasing amount of crystallininty. It was also demonstrated that I3 extrapolates to 0 at 100% crystallinity. No o-Ps lifetime was observed that might be attributed to the annihilation within the crystalline regions of the polymer. Lind et al [43] found a similar result for polypropylene where the x3 component changed very little with the amount of crystallinity, but the I3 value decreased with an increasing amount of... 

Insert of Figure 13.2 shows the positron lifetime spectra for MgO (open circles), Au-implanted MgO (crosses) and Au nanoparticles embedded in MgO (solid circles). These spectra were deconvoluted using Laplace inversion [CONTIN, 7] into the probability density functions (pdf) as a function of vacancy size. Figure 13.2 shows the pdf spectra for the MgO samples accordingly. The positron lifetime components obtained for the MgO layer are 0.22 0.04 ns with 89 3% contribution and 0.59 0.07 ns with 11 3% contribution. For the Au-implanted sample without annealing, the major lifetime component is at 0.32 ns. For the Au nanoparticle-embedded MgO, lifetime components are 0.41 0.08 ns at 90% and 1.8 0.3 ns at 7%. 

Figure 13.2-Probabil-ity density functions (pdf) as a function of defect size, resulting from Laplace inversion (CONTIN) of lifetime spectra (insert) for MgO (open circles), Au-implanted MgO (crosses) and Au nanoparticles embedded in MgO (solid cir-...

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