Calculations of electron inelastic mean free paths. XIII. Data for 14 organic compounds and water over the 50 eV to 200 keV range with the relativistic full Penn algorithm

Abstract

We have calculated inelastic mean free paths (IMFPs) for 14 organic compounds (26-n-paraffin, adenine, β-carotene, diphenyl-hexatriene, guanine, Kapton, polyacetylene, poly (butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene, poly(2-vinylpyridine), thymine, and uracil) and liquid water for electron energies from 50 eV to 200 keV with the relativistic full Penn algorithm including the correction of the bandgap effect in insulators. These calculations were made with energyloss functions (ELFs) obtained from measured optical constants and from calculated atomic scattering factors for X-ray energies. Our calculated IMFPs could be fitted to a modified form of the relativistic Bethe equation for inelastic scattering of electrons in matter from 50 eV to 200 keV. The average root-mean-square (RMS) deviation in these fits was 0.17%. The IMFPs were also compared with a relativistic version of our predictive Tanuma-Powell-Penn (TPP-2M) equation. The average RMS deviation in these comparisons was 7.2% for energies between 50 eV and 200 keV. This average RMS deviation is smaller than that found in a similar comparison for our group of 41 elemental solids (11.9%) and for our group of 42 inorganic compounds (10.7%) for the same energy range. We found generally satisfactory agreement between our calculated IMFPs and values from other calculations for energies between 200 eV and 10 keV. We also found reasonable agreement between our IMFPs for organic compounds and measured IMFPs for energies between 50 eV and 200 keV. Substantial progress for IMFP measurements for liquid water has been made in recent years through the invention of liquid water microjet photoelectron spectroscopy and droplet photoelectron imaging. We found that the IMFPs from these experiments and the associated analyses were larger than our IMFPs by factors between two and four for energies between about 30 eV and 1000 eV. The energy dependences of the measured IMFPs are, however, similar to that of our IMFPs in the same energy range.Since IMFPs calculated from the same algorithm for a number of inorganic compounds agree reasonably well with measured IMFPs for energies between 100 eV and 200 keV, the large differences between IMFPs for water from recent experiments and our results are surprising and need to be resolved with additional experiments.

Inelastic scattering of electrons in water from first principles: cross sections and inelastic mean free path for use in Monte Carlo track-structure simulations of biological damage

“…Our results quantitatively agree with the RPA model of Emfietzoglou et al [ 39 ] in the whole energy range and with the IMFP obtained by Taioli et al [ 65 ] at intermediate energies (from 100 eV to 10 keV). The data of Shinotsuka et al [ 93 ] are below our IMFP and resemble more the shape of the results of Taioli et al [ 65 ], except for the region around the minimum. The inset of figure 6 shows the comparison of the LR-TDDFT results from this work and from Taioli et al [ 65 ] with the experimental data for amorphous ice below 100 eV.…”

“…The IMFP obtained in this work is shown in figure 6 and compared to the semi-empirical calculations [ 39 , 47 ], to the LR-TDDFT results from Taioli et al [ 65 ], and to three Geant4-DNA constructors (the default, the Ioannina and the CPA100 models, denoted as opt2, opt4 and opt6) [ 23 ]. A more recent semi-empirical result of Shinotsuka et al [ 93 ] obtained using the relativistic full Penn algorithm that includes the correction of the bandgap effect in water is also shown in figure 6 . Our results quantitatively agree with the RPA model of Emfietzoglou et al [ 39 ] in the whole energy range and with the IMFP obtained by Taioli et al [ 65 ] at intermediate energies (from 100 eV to 10 keV).…”

“…Below this energy, the results of this work are closer to the experimental data than the ones from Taioli et al [ 65 ].

Figure 6 Inelastic mean free path as a function of the electron incident kinetic energy compared to calculations by Garcia-Molina et al [ 47 ] (dash-dotted line), Emfietzoglou et al [ 39 ] (dotted lines), Geant4-DNA options 2, 4 and 6 [ 23 ] (dashed lines), Shinotsuka et al [ 93 ] and Taioli et al [ 65 ] (dash-dot-dotted line, calculated as the inverse of the total cross section shown in figure 5 ). The inset shows the comparison of the LR-TDDFT results from this work and from Taioli et al [ 65 ] with experimental data for amorphous ice [ 91 ].

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Electron inelastic mean free path (IMFP) values of Kapton, polyethylene (PE), polymethylmethacrylate (PMMA), polystyrene (PS) and polytetrafluoroethylene (PTFE) measured with elastic peak electron spectroscopy (EPES)

“…IMFP values derived from the present elastic peak measurements (datapoints) for the investigated materials: PS (A), PTFE (B), PMMA (C), Kapton (D) and PE (E). Open datapoints: without correction for surface excitations; filled datapoints: after correction for surface excitations; red datapoints: Ni reference; blue datapoints: Si reference; solid black curve: IMFP values from Shinotsuka et al 12 ; red dashed curve: TPP2M‐formula 11 ; blue dash‐dotted curve: calculation of the IMFP using Equation () and optical constants from Ridzel et al 18 for zero dispersion ( in Equation )…”

“…The work by Shinotsuka, Tanuma, Powell and Penn 5–12 is the most important point of reference in this connection. These authors recently published a comprehensive report on IMFP values for 14 organic compounds (and water) in the energy range between 50 eV and 200 keV 12 . This was done by employing optical constants found in the literature, 13–17 and linear response theory was used to derive IMFP values.…”