Thermalisation

Another relatively recent technique, in its own way as strange as Mossbauer spectrometry, is positron annihilation spectrometry. Positrons are positive electrons (antimatter), spectacularly predicted by the theoretical physicist Dirac in the 1920s and discovered in cloud chambers some years later. Some currently available radioisotopes emit positrons, so these particles arc now routine tools. High-energy positrons are injected into a crystal and very quickly become thermalised by... 

From a chemist s viewpoint, the most important act of ionizing radiation (usually X-rays, y-rays or high energy electrons) is electron ejection. Initially the ejected electrons have sufficient energy to eject further electrons on interaction with other molecules, but the electrons ultimately become thermalised and then are able to interact "chemically". We consider first various reaction pathways for these electrons, and then consider the fate of the "hole" centres created by electron ejection. [We refer to electron-gain and electron-loss centres rather than to radical-anions and -cations since, of course, the substrate may comprise ions rather than neutral molecules. 

Bonhoeffer and Farkas estimated k3/k2 100 and claimed that at 15 % decomposition the photolysis is completely self inhibited. More recent work by Ogg and Williams9,10 showed that for the photolysis with 2537 A radiation, k3/k2 is independent of HI pressure (50-150 torr), independent of temperature and has a value 3.5+0.3. The effect of cyclohexane as an inert diluent11 was to increase k3/k2 to 7.0+0.4 at 155°, which value remained constant at high cyclohexane hydrogen iodide ratios. This result was attributed to collisional thermalisation of the hot H atoms produced by 2537 A radiation and this limiting high-pressure value of k3/k2 = (k3/k2)aa was considered to be that for thermally equilibrated H atoms. 

The Acid Effect. The possible mechanistic role of hydrogen atoms in the current radiation grafting work becomes even more significant when acid is used as an additive to enhance the copolymerisation. At the concentrations utilised, acid should not affect essentially the physical properties of the system such as precipitation of the polystyrene grafted chains or the swelling of the polyethylene. Instead the acid effect may be attributed to the radiation chemical properties of the system. Thus Baxendale and Mellows (15) showed that the addition of acid to methanol increased G(H2) considerably. The precursors of this additional hydrogen were considered to be H atoms from thermalised electron capture reactions, typified in Equation 5. 

Range parameters, b (nm), for solvated electrons in various hydrocarbon solvents at room temperature, assuming a gaussian initial distribution of distances from the ionisation site to the thermalisation point... 

Flydrides, which are easily thermalised at around 1000 K, liberate the atoms of an element. An electrodeless lamp is preferably used as a light source. 

Secondary electrons, i.e. those that have been ejected from atoms by incident radiation, will cause further ionisations or excitations until their energy is reduced to — kT, when they are said to be thermalised. They may then be captured by positive ions or neutral molecules. Since all ionising radiations then basically give rise to these secondary electrons, it is to be expected that their chemical effects will be essentially similar. 

Although ionic species are undoubtedly produced as a result of the initial act of absorption of ionising radiation, there is considerable variation in the lifetime of such species. An electron ejected from a parent molecule will travel through the medium against the coulombic attraction of the parent ion until it is thermalised. The distance travelled by the electron will depend on its energy and its rate of energy loss. There are considerable theoretical difficulties in the treatment of this rate of energy loss. 

Early theories of the radiolysis of liquid water usefully illustrate two extreme possibilities. Samuel and Magee11 estimated that a 10 eV electron would travel approximately 20 A in 10 13 sec before being thermalised, after which, as it would still be effectively within the electrostatic field of the positive ion, charge neutralisation would take place to give an excited molecule. 

Thus although ionic intermediates may be formed, their lifetime is too short for them to be chemically significant. Lea12 had previously suggested that the electron could escape from the field of the parent ion. Calculations by Platzman13 indicated that the electron might well travel a distance of 50 A before thermalisation. 

Recent experimental work has demonstrated the existence of the hydrated electron as will be discussed subsequently. It has, however, been proposed14 that this could still arise from capture of the thermalised electron by a positive ion according to the reaction scheme... 

At lower altitudes where significant concentrations of ozone exist, O- ions are generated by dissociative attachment [reaction (10b)]. These electron attachment processes and the laboratory techniques used to determine their rate coefficients were reviewed some time ago by Phelps1 S4 In the stratosphere and troposphere, negative ions can also be generated by dissociative attachment reactions of thermalised electrons with pollutants1 s5,1561 such as the freons e.g. 

Mass addition to reactor (hydrogenous material) Damage of SSC Reactivity spike due to neutron thermalisation Chemical attack of TRISO layers and graphite... 

The Raman scattering strength of E,(LO) in the vicinity of the fundamental bandgap has been investigated in resonant Raman scattering as a function of temperature between 77 K and 870 K [35], Studies of photocarrier thermalisation have been performed by time resolved Raman spectroscopy [36],... 

While EQN (1) can be used to verify an NEA for wide bandgap semiconductors, another aspect that signals the presence of an NEA is the appearance of a sharp peak at the low kinetic energy end of the spectrum. This feature is attributed to electrons thermalised to the conduction band minimum. For a positive electron affinity, these electrons would be bound in the sample and not observed in the spectrum. 

The measurement of the mean lifetimes of positrons in matter has been one of the cornerstones of positron science over the past half-century. The lifetime of a positron in matter—gas, liquid or solid—will depend on the electronic environment in which it finds itself, and this in turn tells us much about the submicroscopic nature of the material. In condensed matter a positron will approach thermal energies within about lps, so that measured lifetimes are essentially those of a thermal positron in the material under study. In some gaseous environments—particularly in the noble gases—the time taken for a positron to come to thermal equilibrium with its surroundings is much longer—10°-102 ns—and this thermalisation time has to be taken into account in the analysis of time spectra. 

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... 

Simultaneous measurement of positron lifetime and the momentum of the annihilating pair can give information on thermalisation and transitions between positron states (and hence on chemical reactions of positrons or Ps). The most recent version uses MeV positron beams [35]. A full description of AMOC can be found elsewhere in this volume. 

Positron beams essentially separate the thermalisation of positrons implanted into a material from their eventual annihilation in another. While the field has been enlivened by a number of ingenious and exciting experiments— LEPD, PAES, etc. (reviews are to be found in 4, 35, 41, 42), in this section we shall concentrate on the basic elements of positron beam experimentation. 

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