Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

Abstract

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy-loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm (FPA) that has been used for previous IMFP and electron stopping-power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single-pole approximation (SPA), the relativistic simplified SPA, and the relativistic extended Mermin method. These calculations were made using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP-2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the FPA. The resulting values were in good agreement with results from first-principles calculations and with inelastic X-ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length (EAL). There were large variations in the measured IMFPs and EALs (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs.

A comparative study on Monte Carlo simulations of electron emission from liquid water

“…(), determines the ELF of a non‐free electron‐like material, such as water, from the experimental optical data. It has been applied to elemental solids and compounds, including liquid water …”

“…): (a) 0.69; (b) 1.18; (c) 1.81; (d) 2.39; (e) 3.59. The solid circles represent measurement with inelastic x‐ray scattering spectroscopy by Watanabe et al; the blue line represents calculation based on the improved Mermin‐Penn algorithm by Nguyen‐Truong; the green line represents calculation based on FPA method by Shinotsuka et al; the red and black lines represent the calculations based on FPA and SPA method, respectively. (f) Evolution of ELF with as calculated by FPA.…”

“…It has been applied to elemental solids 41 and compounds, 42 including liquid water. 38 Once the ELF is determined, the energy loss distribution and the electron IMFP, k in , can be respectively evaluated using the integrations,…”

“…The same ELF has been used to calculate the IMFP of liquid water by FPA. 38 The accuracy of the ELF was assessed by applying the oscillator-strength sum rule (f-sum rule) and perfect screening sum rule (ps-sum rule). 48 The results of fsum rule and ps-sum rule are 10.51 and 1.037, respectively, with relative errors being 5.1% and 3.7%.…”

“…x ð Þ f g , into finite values of momentum transfer q for liquid water, as calculated by FPA and SPA from the optical ELF at q = 0, with other sources: the experimental data obtained using inelastic X-ray scattering spectroscopy by Watanabe et al, 54 calculation based on the improved Mermin-Penn algorithm by Nguyen-Truong 49 and FPA calculation by Shinotsuka et al 38 Except SPA, all these algorithms result in similar loss distributions and agree well with the experiment, particularly, at large q-values. As shown in Fig.…”