Electron Scattering in Liquid Water and Amorphous Ice: A Striking Resemblance

The lack of accurate low-energy electron scattering cross sections for liquid water is a substantial source of uncertainty in the modeling of radiation chemistry and biology. The use of existing amorphous ice scattering cross sections for the lack of liquid data has been discussed controversially for decades. Here, we compare experimental photoemission data of liquid water with corresponding predictions using amorphous ice cross sections, with the aim of resolving the debate regarding the difference of electron scattering in liquid water and amorphous ice. We find very similar scattering properties in the liquid and the ice for electron kinetic energies up to a few hundred electron volts. The scattering cross sections recommended here for liquid water are an extension of the amorphous ice cross sections. Within the framework of currently available experimental data, our work answers one of the most debated questions regarding electron scattering in liquid water.

Figure 1

Effective attenuation length ${\mathrm{EAL}}^{\text{eff}}$. Experimental effective attenuation length ${\mathrm{EAL}}_S^{\text{eff}}$ for liquid water from Ref. [19] (black dots). The black error bars for ${\mathrm{EAL}}_S^{\text{eff}}$ indicate three standard deviations of data resulting from measurements on different days [19], while the blue shaded area represents an estimate of additional systematic uncertainties arising from various sources (Ref. [30], Sec. S1). Both contributions determine the total uncertainty of ${\mathrm{EAL}}_S^{\text{eff}}$. Monte Carlo prediction of the effective attenuation length ${\mathrm{EAL}}_M^{\text{eff}}$ using electron scattering CSs derived from experiments on amorphous ice [25, 26] (full black line). The CSs above 100 eV eKE (dash-dotted line) are obtained by extrapolation with the model from Ref. [10]. The uncertainty for ${\mathrm{EAL}}_M^{\text{eff}}$ (shaded yellow area) corresponds to an uncertainty of the absolute total CSs of 45% [25, 26]. The dashed line is obtained by extrapolation of the CSs with the model from Ref. [11].

Figure 2

Anisotropy parameters $\mathit{\beta }$. (a) Experimental ${\beta }_T$ for ionization from the $O1s$ orbital of liquid water from Ref. [22] (black dots). Monte Carlo prediction ${\beta }_M$ for ionization from $O1s$ using electron scattering cross sections derived from experiments on amorphous ice [25, 26] (full black line). The black error bars for ${\beta }_T$ indicate three standard deviations quoted in Ref. [22]. The uncertainty for ${\beta }_M$ (shaded green area) corresponds to an uncertainty of 20% in the relative cross sections for electronically inelastic and quasielastic scattering [25, 26]. (b) Experimental ${\beta }_N$ for ionization from the three valence orbitals $1b_1$, $3a_1$, and $1b_2$ of liquid water from Ref. [23] (black dots). Monte Carlo prediction ${\beta }_M$ for ionization from the valence orbitals using electron scattering cross sections derived from experiments on amorphous ice [25, 26] and water cluster data [24] (full black line). The black error bars for ${\beta }_N$ indicate the statistical errors quoted in Ref. [23]. The uncertainty for ${\beta }_M$ (shaded green area) is the same as in (a). The dashed lines represent uncertainties arising from the uncertainty of the hexamer water cluster [24].

Figure 3

MFPs for subexcitation electrons. (a) VMI photoelectron spectra of water droplets recorded at a photon energy of 14.9 eV (see also [18, 36]). Left: Experimental spectrum. Right: Spectrum simulated with liquid CSs (Ref. [30], Sec. S5). (b) TMFP of amorphous ice (black dots) with uncertainties (black error bars) from Refs. [25, 26] and of liquid water (black full line) with uncertainties (green shaded area) (Ref. [30], Sec. S3). Total IMFP (black dash-dotted line) and isotropic EMFP (black dashed line) of liquid water. The total IMPF includes all inelastic channels (electronic, vibrational, and phonon). $E$ is the electron’s total energy with respect to the vacuum level [25, 26].