Positron lifetime, measurement

A broad overview of traditional methods and recent developments in experimental positron spectroscopy is presented. A discussion of the generation and detection of positrons and their annihilation radiation is followed by a survey of techniques used for positron lifetime measurement, Doppler broadening spectroscopy and angular correlation of annihilation radiation, and the opportunities presented by combining these methods (e.g. in age-momentum correlation) and/or extending their capabilities by the use of monoenergetic positron beams. Novel spectroscopic and microscopic techniques using positron beams are also described. 

Further examples of positron study of defects in HTSC are studies carried out to understand the nature of flux-pinning defects that lead to an increase in critical-current density on neutron-irradiated Y 1 2 3. Experiments [59] on positron lifetime and critical-current density measurements on various neutron-irradiated samples of Y 1 2 3 indicate that the critical current density is correlated with the micro-void density, as obtained from the analysis of positron lifetime measurements. Investigation of defects in other HTSC superconductors, such as La-Sr-Ca-Cu-0 [60], Bi-Sr-Ca-Cu-0 [49], and Nd-Ce-Cu-O [52], have also been carried out. 

Figure 8.14(a) shows the results [83] of positron lifetime measurements in a series of rare earth borocarbides. The lifetime is seen to increase linearly with the lattice volume, as obtained from x-ray diffraction measurements. Calculations [83, 84] of positron density distribution in these rare earth borocarbides indicate that the positron samples the unit cell uniformly (unlike many of the cuprate superconductors) and the calculated lifetime is seen to increase slightly with the unit cell volume as shown in the top panel. It is also noted from Figure 8.14(a) that the lifetime in YNi2B2C is significantly larger than this linear trend. 

The measurements were performed in vacuum on dry samples, thus the annihilation technique can be especially useful in the case of soft media (e.g. polymers), prone to swell when filled with a liquid. It is to be noted that positron lifetime measurements can be performed at arbitrary temperature. 

Positron lifetime measurements can be used to investigate the type and the density of lattice defects in crystals [293]. In solid materials positrons have a typical lifetime of 300 to 500 ps until they are annihilated by an electron. When positrons diffuse through a crystal they may be trapped in crystal imperfections. The electron density in these locations is different from the density in a defect-free crystal. Therefore, the positron lifetime depends on the type and the density of the crystal defects. When a positron annihilates with an electron two y quanta of 511 keV are emitted. The y quanta can easily be detected by a scintillator and a PMT. 

The positrons for the lifetime measurement are conveniently obtained from the deeay of Na. In Na a 1.27 MeV y quantum is emitted simultaneously with the positron. This 1.27 MeV quantum is used as the timing reference for the positron lifetime measurement. The general experimental setup is shown in the Fig. 5.139. 

Algers, J., Suzuki, R., Ohdaira, T., and Maurer, F. H. J., Characterization of free volume and density gradients of polystyrene surfaces by low-energy positron lifetime measurements. Polymer, 45, 4533-4539 (2004a). 

Bandzuch, R, Kristiak, J., Sausa, O., and Zrubcova, J., Direct computation of the free volume fraction in amorphous polymers from positron lifetime measurements, Phys. Rev. B, 611, 8784-8792 (2000). 

Figure 3. The experimental setup for the PALS measurements of sorption of liquid vapor in polymers. The positron source together with the sample polymer is contained in one arm of the glassware and the liquid to be sorbed is contained in the other arm. The positron lifetime measurement is performed by detecting the gamma-rays emitted from the source and from positron annihilation in the sample.

Since positronium formation and positronium reactions can he easily identified by positron lifetime measurements this technique has been applied to the steady of micelles, reversed micelles, microemulsions, liquid crystals, and microphase changes occurring in these systems. By adding probe molecules to these solutions it is also possible to study their location in e.g., micelles. 

Positron lifetime measurements were carried out by the usual delayed coincidence method (25), The resolution the system, as measured by the prompt time distribution of Co source and without changing the 1.27- and 0.511-MeV bias, was found to be 0.390 ns fwhm. Corrections for the source component, which had an intensity of less than 4%, were made in the usual way by using conventional computational methods. 

This prompt gamma photon marks the moment of positron formation, making positron lifetime measurements possible. 

Figure 27.2 outlines a general scheme of fast-fast coincidence systems. For positron lifetime measurements, several special requirements should be fulfilled. In positron lifetime spectroscopy, the whole system should be very fast because of the expected very short lifetimes (from lOO ps to 100 ns). Thus, the response of detectors (Leo 1987a) should be as fast as possible (rise time 2 ns). To ensure the sharp response signal, fast plastic scintillators... 

The method of positron lifetime measurement with Na as positron source is shown schematically in Figure 27.3a. The positron source emits, almost simultaneously, a gamma ray of 1278 keV energy along with a positron indicating birth of... 

The decay curve of positron lifetimes measured experimentally can be represented mathematically as ... 

It is evident from the above discussion that the free volume data derived from positron lifetime measurements is incapable of providing information on the composition-dependent miscibility level of the blend. At this point, a new method based on the same free volume data measured from positron lifetime measurements was introduced to determine the miscibility of binary blends. The new method was based on hydrodynamic interactions (the mathematics required have been explained in detail earlier), and calculations of the y parameter derived from the hydrodynamic interaction approach were made for three selected polymer blends, namely poly(styrene-co-acrylonitrile) (SAN)/poly(methyl methacrylate) (PMMA) (completely miscible), poly(vinyl chloride) (PVC)/poly(methyl methacrylate) (PMMA) (partially miscible) and poly(vinylchloride) (PVC)/polystyrene (PS) (immiscible) (see Figure 27.13). As can be seen, this parameter behaves similar to the interchain interaction parameter /3, in the sense that it exhibits a complex behavior making it difficult to determine the composition-dependent miscibility of the blends. 

The measured quantity in positron lifetime measurements is the time when the positron annihilates, t = 0 corresponds to positron emission. This means that the shape of the positron lifetime spectrum S is... 

The specific trapping rates vd for dislocations were obtained by correlating positron lifetime measurements and data from transmission electron microscopy (TEM) or other techniques capable of determining dislocation density (e.g., X-ray diffraction profiles) [118]. In metals, vd lies in the range 10 to 10 " m s ... 

Densities were determined for the fully cured polyimide films in a density gradient tube prepared with aqueous ZnQj solutions according to ASTM D1505-60T. Dielectric constants of the potyimide films were determined using a Hewlett Padcard 8510 Automated Network Analyzer over the frequenty range of 8-12 GHz. All films were desiccated in a heated vacuum oven prior to positron lifetime measurements. 

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