Irradiated volume

With M = He, experimeuts were carried out between 255 K aud 273 K with a few millibar NO2 at total pressures between 300 mbar aud 200 bar. Temperature jumps on the order of 1 K were effected by pulsed irradiation (< 1 pS) with a CO2 laser at 9.2- 9.6pm aud with SiF or perfluorocyclobutaue as primary IR absorbers (< 1 mbar). Under these conditions, the dissociation of N2O4 occurs within the irradiated volume on a time scale of a few hundred microseconds. NO2 aud N2O4 were monitored simultaneously by recording the time-dependent UV absorption signal at 420 run aud 253 run, respectively. The recombination rate constant can be obtained from the effective first-order relaxation time, A derivation analogous to (equation (B2.5.9). equation (B2.5.10). equation (B2.5.11) and equation (B2.5.12)) yield... 

A commonly used measure of irradiation damage is displacements per atom (dpa). A unit of 1 dpa means that on the average, every atom in the irradiated volume has been displaced once from its equiUbrium lattice site. The approximated dpa in the implanted region is given by equation 16 where 0 (ions/cm ) is the dose, and (NJE)) is the damage function given by equation 14. 

As scattering intensity is computed from p (r) in this book, the symbol p (r) has two different meanings. Only in the field of WAXS it is identical to the plain electron density. However, in the area of SAXS it indicates the electron density difference1, i.e., the deviation of the local electron density from the average electron density (p (r))v in the irradiated volume V. 

V is the irradiated volume. It is defined by the sample thickness multiplied... 

Smearing. Because scattering is emanating from every point of the irradiated volume, the recorded scattering pattern is smeared by the shape of the effective cross-section of the primary beam measured in the detector plane. In terms of mathematics this smearing is accomplished by convolution (Eq. (2.17)) with the primary beam profile. 

If the X-rays reflected from a large sample are detected and the sample is thicker than 3/jU, the assumption of infinite thickness is justified. Then the equation for the intensity It transmitted into the detector enjoys peculiar simplicity, because it is only a function of the effective irradiated volume... 

Guinier [6], p. 181), with the cross-section, F0, of the incident X-ray beam, the angle of incidence on the sample surface, a, and the angle of exit with respect to the sample surface being ae. For symmetrical-reflection geometry (a = Ofe = 6) the irradiated volume becomes Fq/ (2id), and 1 /2fi is the penetration depth into the sample. We thus have... 

Calibration to absolute intensity means that the scattered intensity is normalized with respect to both the photon flux in the primary beam and the irradiated volume V. Thereafter the scattering intensity is either expressed in terms of electron density or in terms of a scattering length density. Both definitions are related to each other by Compton s classical electron radius. 

Electron Density. Continuing the preceding considerations, calibration to absolute intensity means normalization to the scattering of a single electron , Ie that can be expressed in electron units, [e.u.]. Inevitably a calibration to absolute units involves also a normalization with respect to the irradiated volume V. Thus, for the field of materials science a suitable dimension of the absolute intensity is [I/V] = e.u./nm3 - The intensity measured in the detector is originating from a material with an average electron density of 400 electrons per nanometers cubed . The electron density itself is easily computed from mass density and chemical composition of the material (cf. Sect. 2.2.1). 

This is the differential definition of the absolute intensity. The total absolute intensity can be deduced by integration from Eq. (7.19) and Eq. (7.20) for any normal transmission geometry. Geometries are discriminated by the shape and size of the irradiated volume, the image of the primary beam in the registration plane17 of the detector, and the dimensions of the detector elements18. 

Cylindrical Filaments. If cylindrical filaments are studied, the last-mentioned assumption is not be fulfilled. In this case it is more suitable to cross an elongated24 primary beam and the fiber in such a way that the irradiated height of the beam, Bgo, is constant. Then the irradiated volume becomes V = Bbo nrj, with /y being the radius of the fiber. In many practical applications the studied fiber is very thin, and the effective absorption coefficient can be approximated by exp (—fiteff) 1. If this approximation is not feasible, the absorption factor exp (—ji ) must be integrated for the chord length distribution gc ( ) of a circle with radius ry (cf. p 168) in order to yield the effective absorption. 

Intensity at s=0. The requested intensity 7(0) is obtained by integration of the correlation function over the irradiated volume V. As the result of this operation, each particle k contributes with its m to 7(0). Thus, with N particles present in the irradiated volume we Anally have... 

Reason The standard is measured with the same primary beam cross-section as is the studied sample. After division by the intensity of the standard and the thickness of the studied sample, a division by the irradiated volume has been accomplished. 

Basic Equations. Scattering according to Porod s law [18,137] is a consequence of phase separation in materials. In a two-phase system (e.g., a semicrystalline polymer) every point of the irradiated volume belongs to one of two distinct phases (in the example to the crystalline phase or to the amorphous phase). In a multiphase system there are more than two distinct phases. 

Frequently at least one of the phases forms particles (e.g., crystalline lamellae). The shape and position of the ith particle from the irradiated volume is described by a shape function Yi (r). It is obvious that the scattering intensity of an ideal multiphase system can be expressed in terms of autocorrelations Y 2 (r) and cross-correlations of the shape functions and the average electron densities of each phase (cf. Sect. 2.5). 

Thus for an ideal two-phase system the total calibrated intensity that is scattered into the reciprocal space is the product of the square of the contrast between the phases and the product of the volume fractions of the phases, Vi (1 — Vi) = V1V2. V1V2 is the composition parameter66 of a two-phase system which is accessible in SAXS experiments. The total intensity of the photons scattered into space is thus independent from the arrangement and the shapes of the particles in the material (i.e., the topology). Moreover, Eq. (8.54) shows that in the raw data the intensity is as well proportional to the irradiated volume. From this fact a technical procedure to adjust the intensity that falls on the detector is readily established. If, for example, we do not receive a number of counts that is sufficient for good counting statistics, we may open the slits or increase the thickness of a thin sample. 

If we can exclude a change of the irradiated volume by viscous flow of die material. 

The irradiation of a polymer surface with the high intensity, pulsed, fer-UV radiation of the excimer laser causes spontaneous vaporization of the excited volume. This phenomenon was first described by Srinivasan (1) and called ablative photodecomposition. The attention of many researchers was drawn to the exceptional capabilities of photoablation (2). Etching is confined to the irradiated volume, which can be microscopic or even of submicron dimensions, on heat-sensitive substrates like polymers. In most experimental conditions, there is no macroscopic evidence of thermal damage, even when small volumes are excited with pulses of... 

In particular, it is recognized that when optimizing the treatment parameters in order to improve, e.g., the conformity index in conformal therapy or IMRT, other indices can change adversely, for example, the size of the irradiated volume, the integral dose, and the dose homogeneity throughout the PTV. 

Another advantage of protons, relative to the best photon techniques, is a reduction of the integral dose and of the irradiated volumes. This factor could influence the risk of radio-induced cancers, although, so far, epidemiological evidence is still lacking. 

The absorption is small and homogeneous within the irradiated volume. 

When heat is produced in the sample after the photolytic flash, the refractive index of the liquid changes and the probe beam is deflected. The intensity of this probe beam measured by a photomultiplier tube placed behind the pinhole decreases as the temperature of the irradiated volume increases (then its density and its refractive index decrease). The total optical signal change is a measurement of all the heat produced in the sample, i.e. the sum of non-radiative transitions, chemical reactions and solvation energies. Luminescence does not contribute to this signal (nor does scattered light) and for this reason thermal lensing can be used to determine luminescence quantum yields. 

Figures 1-3 show the observed reciprocal excess intensities of scattered light multiplied by sin 0 (to correct for the irradiated volume observed at each angle) plotted against sin2 (0/2) at constant polymer concentration for several temperatures above the phase-separation temperature. To give a clearer presentation the intensities are expressed in relation to intensities at the scattering angle 0 = 90°, as was also done by Eskin and Nesterow (11). In accord with the Debye theory, the plots give straight lines and can be represented by...

If the energy of an electron passing through an irradiated volume changes from E to , the average relative yield of VCR for this volume is given by the formula... 

In gases the track structures usually contain a small number of active particles and are separated from each other by considerable distance. Owing to efficient diffusion, the initial inhomogeneity in the distribution of active particles rapidly smoothes out, and by the time the chemical reactions begin, the intermediate chemically active particles are distributed practically homogeneously in the irradiated volume. For this reason the influence of tracks on radiation-chemical processes in gaseous media... 

As a rule the radiation effect produced by any type of emission is a superposition of direct effects of the primary radiation and of the secondary (and even tertiary) radiation the latter induces. Consequently, if the radiation effect is mostly due to the effect produced by secondary (or tertiary) emission, the latter can be used instead of the primary radiation. As concerns the structure of tracks, such a simulation will be correct if the spatial distribution of chemically active particles in the irradiated volume remains close to the one produced by the primary source. 

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