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# Athena charged particle diverter simulations: effects of micro-roughness on
proton scattering using Geant4

Jean-Paul Breuer  Department of Theoretical Physics and Astrophysics, Faculty
of Science, Masaryk University, Brno, Czech Republic  Gábor Galgóczi
Department of Theoretical Physics and Astrophysics, Faculty of Science,
Masaryk University, Brno, Czech Republic  Institute of Physics, Eötvös Loránd
University, Budapest, Hungary  Valentina Fioretti  INAF/Osservatorio di
Astrofisica e Scienza dello Spazio, Bologna, Italy  Jakub Zlámal  CEITEC, Brno
University of Technology, Brno, Czech Republic  Petr Liška  CEITEC, Brno
University of Technology, Brno, Czech Republic  Norbert Werner  Department of
Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University,
Brno, Czech Republic  Giovanni Santin  ESTEC/ESA, Keplerlaan 1, 2201AZ
Noordwijk, The Netherlands  Nathalie Boudin  ESTEC/ESA, Keplerlaan 1, 2201AZ
Noordwijk, The Netherlands  Ivo Ferreira  ESTEC/ESA, Keplerlaan 1, 2201AZ
Noordwijk, The Netherlands  Matteo Guainazzi  ESTEC/ESA, Keplerlaan 1, 2201AZ
Noordwijk, The Netherlands  Andreas von Kienlin  Max Planck Institut für
extraterrestrische Physik, Garching bei München, Germany  Simone Lotti
INAF/Istituto di Astrofisica Spaziale e Fisica cosmica, Milan, Italy  Teresa
Mineo  INAF/Istituto di Astrofisica Spaziale e Fisica Cosmica, Palermo, Italy
Silvano Molendi  INAF/Istituto di Astrofisica Spaziale e Fisica cosmica,
Milan, Italy  Emanuele Perinati  Eberhard Karls University, Tübingen, Germany

###### Abstract

The last generation of X-ray focusing telescopes operating outside the Earth’s
radiation belt discovered that optics were able to focus not only
astrophysical X-ray photons, but also low-energy heliophysical protons
entering the Field of View (FOV). This “soft proton” contamination affects
around 40% of the observation time of XMM-Newton. The ATHENA Charged Particle
Diverter (CPD) was designed to use magnetic fields to move these soft protons
away from the FOV of the detectors, separating the background-contributing
ions in the focused beam from the photons of interest. These magnetically
deflected protons can hit other parts of the payload and scatter back to the
focal plane instruments. Evaluating the impact of this secondary scattering
with accurate simulations is essential for the CPD scientific assessment.
However, while Geant4 simulations of grazing soft proton scattering on X-ray
mirrors have been recently validated, the scattering on the unpolished
surfaces of the payload (e.g. the baffle or the diverter itself) is still to
be verified with experimental results. Moreover, the roughness structure can
affect the energy and angle of the scattered protons, with a scattering
efficiency depending on the specific target volume. Using Atomic Force
Microscopy to take nanometer-scale surface roughness measurements from
different materials and coating samples, we use Geant4 together with the
CADMesh library to shoot protons at these very detailed surface roughness
models to understand the effects of different material surface roughnesses,
coatings, and compositions on proton energy deposition and scattering angles.
We compare and validate the simulation results with laboratory experiments,
and propose a framework for future proton scattering experiments.

###### keywords:

Particle Scattering, Proton simulations, Scanning Probe Microscopy, Geant4,
Surface Roughness

##  1 INTRODUCTION

The last generation of X-ray observatories were extremely successful in
resolving astrophysical objects and answering many questions regarding the
cosmos and our observable universe. Launched in 1999, the NASA Chandra X-ray
Observatory (Chandra) and the European Space Agency (ESA) X-ray Multi-Mirror
Mission (XMM) Newton telescopes are complementary missions, with Chandra
providing better spatial resolution, while XMM-Newton provides a larger
collecting area offering better spectroscopic information. With these modern
observatories, it was discovered that low energy protons ($\leq$300 keV) can
also scatter through the optics at low angles and get funneled towards the
focal plane. These “soft protons” manifest as sudden flares in the detector
background count rates. They populate the interplanetary space, as well as
different parts of the Earth’s magnetosphere, and are collected during the
orbit cycle of the observatory [1, 2, 3, 4].

This soft proton contamination is highly variable over time and can not be
efficiently modeled, as their signal in the detector is registered as events
similar to the ones created by X-ray photons. Current treatment methods
involve looking for anomalous periods of high count rate in the detector light
curves and removing all data during these events [5]. This soft proton
contamination currently affects around 40% of XMM-Newton observations, and can
be a significant contribution to the background for future X-ray missions [3].
Over the last 20 years, many attempts have been made to better understand and
predict soft proton flares [5, 6].

ESA’s second large-class mission is also the next generation X-ray focusing
observatory mission, the Advanced Telescope for High-ENergy Astrophysics
(Athena), which will launch in the 2030’s and will provide unprecedented
spectroscopic and imaging capabilities from the 0.5 keV to 12 keV band [7].
Athena will use Silicon Pore Optics (SPO) technology together with two focal
plane instruments, the Wide Field Imager (WFI) and a calorimeter spectrometer,
the X-ray Integral Field Unit (X-IFU), with the science goal of exploring the
hot and energetic Universe. Athena should be placed in a halo orbit around L1,
the first Lagrange point of the Sun-Earth system, after studies of the plasma
environment in both L1 and L2 [8, 9].

To limit the soft proton contamination, the WFI has a challenging scientific
requirement for the soft proton background to be $<5\times 10^{-4}$
cts/cm2/keV/s, less than 10% of the non-focused background requirement [10].
Athena will directly address this soft proton contamination problem using a
new device, which will be placed between the optics and the detector systems.
This Charged Particle Diverter (CPD) will be close to the instruments in the
Science Instrument Module (SIM), and will create a magnetic field which will
deflect the soft energy protons outside the field of view[11]. However,
simulations also predict a potential secondary scattering of the deflected
protons with the CPD walls and surfaces of the focal plane assembly (e.g. WFI
baffle). To test if the CPD is compliant with the background requirement, it
is first necessary to understand how surface roughness and composition can
affect the proton energy and angles after scattering. To do this, an accurate
simulation of the proton scattering with the surfaces of the focal plane
assembly as well as the wall of the WFI baffle and CPD must be performed to
know the impact of the roughness on the scattering efficiency. Previous
validations of Geant4 simulations of soft proton scattering were performed at
grazing angles and on polished X-ray mirror samples [8]. Since roughness and
composition can affect the proton energy and angles after scattering,
laboratory measurements of proton scattering from representative samples were
taken to verify dedicated Geant4 and SRIM simulations. This work specifically
focuses on the validation of the proton scattering simulations performed in
Geant4 using the experimental results, with the preliminary results already
giving some general implications on the roughness and composition effects on
low-energy proton scattering.

This work fits into the context of a larger scale experiment to characterize
the soft proton background, as part of the scientific assessment of the CPD.
Our working group aims to perform end-to-end simulations of these soft
protons, starting with ray-tracing simulations of the proton interaction with
the mirror assembly, followed by the effect of the CPD induced magnetic field
on the way towards the detector systems, the proton interaction and scattering
against the walls of the focal assembly, and finally the endpoint of these
protons.

Section 2 aims to explain the surface data, the experimental set up, as well
as the experimental set up within Geant4 and SRIM. Section 3 will discuss a
statistical systematic uncertainty introduced as a result of a computational
optimization originating from the binning of the surface roughness model.
Sections 4 and 5 will discuss the results and validity of the simulations, and
end with some concluding remarks and details for the future work.

##  2 DATA EXPLORATION, EXPERIMENTAL SET-UP, AND GEANT4 SET-UP

###  2.1 SURFACE IMAGING

The basis for all of the experiments began with measurements of the WFI baffle
surface, performed via Scanning Probe Microscope (SPM) Bruker Dimension Icon
at Brno CEITEC Nano111https://www.ceitec.eu/scanning-probe-microscope-bruker-
dimension-icon/e1359, which gave ASCII text output of a 5122 pixel matrix of
measured values spanning the 922 $\mu$m2 dimensions of the physical sample.
The atomic composition of the sample was also measured, by EDS X-Max 20 by
Oxford Instruments installed in the Scanning Electron Microsope TESCAN Mira in
BUT CEITEC Nano222https://nano.ceitec.cz/scanning-electron-microscope-e-beam-
writer-tescan-mira3raith-lis-mira/. The WFI baffle sample has an average
surface roughness of 6.5 $\mu$m, a calculated density of 2.15 g/cm3, and also
has an optical coating called “Magic Black”, with the composition in weight of
44% Oxygen and 56% Aluminum.

---
Figure 1: Highly detailed CAD model of the WFI baffle surface sample, where
over a half million triangles represent the 922 $\mu$m2 area. The samples were
imported into Geant4 using the CADMesh library and measured atomic
composition, and were created from measurements using Matlab and Blender.

The first step to prepare this measurement for the simulations is to convert
the measured data from a text file into a Standard Tessellation Language (STL)
file, the Computer Aided Design (CAD) standard file format that describes the
whole geometry of an object in the form of a triangular mesh. Matlab has some
user-defined functions that manage to make this conversion to STL by first
defining the sample as a surface mesh object; however, this object has no
thickness, and can be considered as an empty wireframe. The second step in
creating the model is to import this empty wireframe STL file into Blender, a
free and open-source 3D computer graphics software toolset, often used for 3D
modelling. An example of this high resolution model is shown in Fig. 1, where
over a half million small triangles represent the 922 $\mu$m2 surface. The 922
$\mu$m2 model object is given a equivalent thickness of 300 $\mu$m. We then
close and fill the extruded model, making it a full solid and not an empty
shell, and rotate and flip the model so that it has the correct orientation
after it is loaded into Geant4.

###  2.2 EXPERIMENTAL SET UP

The WFI baffle sample was then placed in an experimental configuration as seen
in Fig. 2, used to characterize the scattering efficiency, performed at the
Tandem laboratory of Uppsala
University333https://www.tandemlab.uu.se/?languageId=1. The WFI baffle surface
sample was shot by a beam of 100 keV protons at an incidence angle of both 20
degrees and 40 degrees, with the energy and scattering angles ($\theta$) of
the deflected protons being measured by a circular detector. The detector
provides a signal from three separate areas, each with a diameter of 4
degrees, and simultaneously covers three different scattering angles per
experiment, specifically, at scattering angles $\theta$ and $theta\pm 5$
degrees. Fig. 2 shows a schematic of the experimental set up. The azimuth of
proton scattering ($\phi$) is not explicitly measured with this experimental
set up.

---
Figure 2: Schematic view of the experimental setup: a particle beam shoots 100
keV protons at incidence angles of 20 degrees and 40 degrees, with the energy
and scattering angles ($\theta$) of the deflected protons being measured by a
detector at various positions, $\theta$ and $\theta\pm 5$.

As the detector covers three scattering angles simultaneously, the detector
was placed at 30 degrees, 50 degrees, and 65 degrees for the 20 degree
incidence angle experiment, measuring all proton scattering angles $\theta$
from 30, 35, 40, etc. up to 70 degrees with respect to the measured surface
plane. For the 40 degree proton incidence angle case, the circular detector
was moved to lower scattering angles, measuring scattered protons from 10, 15,
20, etc. up to 50 degrees. The experiment was performed several times to
normalize the proton beam.

###  2.3 GEANT4 MICRO-ROUGHNESS SIMULATION

The Geant4 simulation framework is a toolkit library for particle transport
codes based on Monte Carlo simulations, initially developed by CERN [12, 13,
14]. All simulations in this work were based on Geant4 version 10.7.1, using
the previously validated single Coulomb scattering (SS) model [8]. To
establish the framework to simulate the particle scattering, we additionally
used version 1.1 of the CADMesh library, which allows us to load triangular
mesh-based CAD files into Geant4[15]. This combination of tools is
particularly powerful, as it opens up many possibilities for future work and
exploring the effects of different materials and treatments on scattering.

The Geant4 set-up is similar to the schematic from the experiment shown in
Fig. 2, where a particle gun shoots the digitized WFI baffle sample with a
parallel beam of 100 keV protons at incidence angles of 20 and 40 degrees. The
WFI baffle sample geometry is imported into Geant4 using the CADMesh library
and is given the same atomic composition obtained from measurements. We
deviate from the experimental set up in that we instead build a half-sphere
around the sample surface to function as the main particle detector and record
all the scattered particle hits. This half-sphere records the same proton
energy and polar scattering angles $\theta$ as from the experiment, as well as
the azimuthal scattering angles $\phi$. Additionally, this sphere provides a
2D angular distribution of $\theta$ vs $\phi$, which can be integrated over
the detector area from the experiment, and provides the basis for validating
the simulation results with the experimental results.

We observed that shooting the 90 degree edges of the surface sample greatly
increased the scattering efficiency of the protons at low scattering angles.
We try to limit the particle interactions with the edges, sides, and corners
of the CAD model, so the surface area of the reference sample which the proton
gun covers is restricted to the central 722 $\mu$m2 of the sample,
corresponding to 80.4% of the total sample.

###  2.4 SRIM SIMULATION

A new algorithm for the calculation of the scattering of protons was
implemented in a FORTRAN tracing code using SRIM [16]. SRIM itself calculates
only ideal surface scattering, and in this case, was first used to pre-
calculate the scattering of protons of various incidence energies and covering
a full range of incidence angles. The total probability of proton scattering
for each energy and incidence angle is then determined as the number of
scattered protons to incident protons.

Similar to the Geant4 and CADMesh implementation, the surface roughness of the
WFI baffle sample is interpreted using 3D triangular meshes, but in this
implementation, the protons do not penetrate or directly interact with the
material. The FORTRAN code instead calculates the proton incidence angle with
respect to the intersecting triangle and samples the derived probability
distribution of scattering for that angle [17]. The scattering direction of
the proton is randomly chosen from the precalculated proton list, and the
previous step is repeated in case of an intersection with another triangle
from the 3D triangular mesh. The collecting of protons is done in FORTRAN,
with detectors in the same positions according to the experiment, shown in
Fig. 2, making it possible to compare results with the experiment and other
simulations.

##  3 RESULTS

###  3.1 COMPARISON OF BINNED SAMPLES WITH FULL SAMPLES

One of these SPM-measured surface roughness samples can have over 1 million
small triangles, meaning that the memory and computational requirements for
simulating protons are non-trivial. As a benchmark, one hundred thousand 100
keV protons at 40 degree incidence angle takes over 70 hours to simulate on
the full resolution sample using 48 threads. To have reasonable statistics for
validating this simulation via comparison with the laboratory measurements, we
require several million proton simulations, equivalent to about a month of
non-interrupted computation time.

The computational time requirements are reduced for both lower incidence
angles and for samples with less surface roughness. This is because the
scattering efficiency at lower incidence angles is higher, so obtaining better
statistics requires less proton simulations; meanwhile, surfaces that are more
smooth reduce the likelihood that a particle enters and exits the surface
material several times before scattering.

With the future objective of creating a proton transfer function and
understanding the proton scattering efficiency at many different incidence
angles and energies, the computational time requirement can go up to several
years, and can easily increase to over a lifetime to further explore different
levels of surface roughness, compositions, and surface treatments.

The memory specific requirements are mainly dependent on the requested binning
of the angle in the 2D angular distribution and the total number of threads.
Besides the basic memory requirements for loading the sample and running
Geant4, the estimated memory requirements can be described by the cumulative
product between the bit-size of double variables, the number of threads used
in a simulation, the specified binning for the output histogram, and the
number of protons simulated. Assuming histogram bin sizes of 1 deg2, memory
requirements are easily met even for the full resolution sample.

---
Figure 3: (left) 2D visualization of the full WFI baffle sample roughness
profile (with height in meters), treated with the “Magic Black” optical
surface coating, same as the 3D version shown in Fig. 1. (middle)
Visualization of the same sample, but binned by 4. (right) Power spectrum
density plot comparing the binned and full resolution samples with regards to
the effective power of each spatial frequency, from small scales up to the
Nyquist frequency. As expected, at large scales the sample looks fairly
identical, but some information is lost on the small scales as it becomes
averaged by the binning. This binning by 4 specifically reduces the effective
power of smaller scale features by around 15%.

Binning the surface roughness samples was one of the optimization paths taken
to reduce computation time. Extensive Geant4 simulations were run on both the
full sample and the binned sample to determine the proton scattering
efficiency of both distributions. Fig. 3 shows the full resolution WFI baffle
sample, the binned version of the same sample, and a comparison of the two
using a normalized power spectrum density plot. As evident in the plot, at
least when binning the sample by four, 25% of the smallest scale information
is encoded in the averaging of the bins, but this binning only reduces the
effective power of smaller scale features by around 15%; in other words, the
majority of the information is conserved.

To test the effect of this binning on the proton scattering efficiency,
millions of protons are simulated for both the full resolution WFI baffle
sample, as well as the binned sample, over several weeks. The respective
probability density distributions are then compared with each other using a
Kolmogorov–Smirnov (KS) test to determine how similar the results are to each
other, as well as to verify whether the binned samples are statistically self-
similar enough to their own full resolution versions to be realistically used
for the remainder of the simulation campaign. As can be seen in the left and
middle of Fig. 4, the binning has a trivial effect in the shape of the
distributions, with 99% self similarity in proton scattering energy and
scattering angle $\theta$. Meanwhile, the KS test determined that the final
proton scattering efficiencies are 98% percent similar to each other when
integrating the results in the 2D angular distribution over the area of the
detector used for the experiment, shown in the right plot of Fig. 4.

---
Figure 4: (left) Comparison of proton scattering efficiency as a function of
the scattering angle $\theta$ between the full resolution sample and the
binned sample. (middle) Comparison of proton scattering efficiency as a
function of the proton energy between the full resolution sample and the
binned sample. (right) Comparison of the integrated proton scattering angles
between the full resolution sample and the binned sample, in the frame of the
laboratory detector. The pvalue result of the KS tests, from left to right,
are 0.9999, 0.9999, and 0.9831, meaning that the difference between the full
resolution and binned samples is less than 2% when integrated to the frame of
the lab experiment.

As mentioned previously, the benchmark of one hundred thousand 100 keV protons
at 40 degree incidence angle took around 68 hours to simulate on the full
resolution sample using 48 threads. The same configuration using the binned
sample takes 6.3 hours for the same number of simulated protons. The
difference in computation time between the full resolution sample and the
binned sample is around 10x, so we can justify using the binned samples, since
the statistical uncertainty introduced as a systematic of the binning is less
than 2% with respect to the integrated result. Millions of protons need to be
simulated to obtain decent statistics, so this small change greatly reduces
the computational overhead for the project at the cost of introducing a rather
negligible systematic error.

###  3.2 VALIDATION OF SIMULATIONS WITH EXPERIMENTAL RESULTS

Fig. 5 and Fig. 6 show the simulated proton scattering efficiencies compared
with the measured results, with initial incidence angles of the proton beam at
20 degrees and 40 degrees, respectively. The left plot of Fig. 5 and Fig. 6
show our high resolution WFI baffle Geant4 simulations as a red line, with
additional comparisons with other simulations, specifically, a simulation
baseline from Geant4, where an ideal surface was used with no roughness, as
well as results obtained from the SRIM simulations. The top and bottom right
plots of Fig. 5 and Fig. 6 show, respectively, a distribution of the proton
scattering angles and proton scattering energies, after interactions with the
WFI baffle surface sample, compared with the ideal surface.

---
Figure 5: From the CPD Scientific Assessment: Results for the WFI baffle
sample with incidence angle of 20 deg, and 100 keV protons fired from the
beam. (left) Comparison between a baseline Geant4 simulation of an ideal
surface, the SRIM simulation, the experimental results, and our Geant4
simulations with roughness and atomic composition. (top) A distribution of the
proton scattering angles after interactions with the WFI baffle surface
sample, compared with the ideal surface. (bottom) A distribution of the proton
scattering energies after interactions with the WFI baffle surface sample,
compared with the ideal surface.

As can be seen in both Fig. 5 and Fig. 6, our simulation results which include
the binned roughness and exact composition of the samples are the closest with
the experimental results. The SRIM simulation shows lower scattering
efficiency than Geant4, but this could be due to an incorrect approximation of
the scattering distribution, since many assumptions were necessary to optimize
for computation time. The 40 degree proton incidence angle case is not a
smoking gun, but is still the closest match to the experimental data out of
all the simulations. Due to the lower scattering efficiency of larger
incidence angles, more proton simulations and more computation time is
required to reduce the size of the error bars and to better converge the
integrated results to the true distribution.

---
Figure 6: From the CPD Scientific Assessment: Results for the WFI baffle
sample with incidence angle of 40 deg, and 100 keV protons fired from the
beam. (left) Comparison between a baseline Geant4 simulation of an ideal
surface, the SRIM simulation, the experimental results, and our Geant4
simulations with roughness and atomic composition. (top) A distribution of the
proton scattering angles after interactions with the WFI baffle surface
sample, compared with the ideal surface. (bottom) A distribution of the proton
scattering energies after interactions with the WFI baffle surface sample,
compared with the ideal surface.

Looking at the top and bottom right plots of Fig. 5 and Fig. 6, which compare
the surface sample with roughness with a smooth ideal surface, we can see that
modeling the roughness structure in Geant4 not only lowers the scattering
angle of the protons, but also shifts the scattering proton energy, with less
protons at higher energies and more protons below 40 keV. The shape of these
two distributions also change a lot between the 20 degree to 40 degree cases,
with the peak of the proton scattering angle shifting to larger scattering
angles, and the same but more pronounced effect on the proton scattering
energy distribution as previously observed.

##  4 Conclusions and Future Activities

It is clear when comparing the simulation on a rough surface to the simulation
on an ideal surface, that the current micro-roughness scale of 6.5 $\mu$m
contributes to increase reflectivity at smaller scattering angles, with proton
energies skewed to lower energies.

We also proved that including a refined modeling of the micro-structure of the
surface where particles scatter improves the precision of the Geant4
simulation, with benefits in various applications where Coulomb scattering is
the dominant interaction. Long computational requirements for simulations
remain a concern, but we have been able to make some optimizations to this
through the binning of surface sample CAD models with the minimal introduction
of systematic uncertainties.

Table 1: Table of all of the available surface roughness samples measured by Scanning Probe Microscope (SPM) Bruker Dimension Icon. Base roughness indicates the arithmetical mean roughness in micrometers. All samples listed were simulated, but the sample investigated with the most computation and laboratory time, and focus of this report, is marked in bold. Material | Base Roughness |  Surface Treatment | Sample No
---|---|---|---
| Ra0.1 - polished |  No (reference of flat surface) | 0
AL7075 T7351 | Ra1.6 - machined |  Surtec 650 (Finitec document ref. 1558830-914_00) | 5
| Ra0.1 - polished |  Solar black by Enbio | 10
Ti6Al4V | Ra1.6 - machined |  No | 19
Kapton sample |  |  Kapton foil on Al | Kapton
WFI Baffle Sample |  |  Magic Black | WFI

The final goal of this research project is to create a proton transfer
function to cut down on simulation time for other proton experiments. Now that
the Geant4 simulation framework has been successfully validated by the
experimental results, we can move on to the next phase of the project, which
is to begin a simulation campaign for a greater range of proton incidence
angles and energies.

Table 2:  Summary of the samples with measured compositions and calculated densities. Atomic composition was measured by EDS X-Max 20 by Oxford Instruments installed in Scanning Electron Microscope TESCAN Mira in BUT CEITEC Nano. The sample investigated with the most computation and laboratory time, and the focus of this report, is marked in bold. Sample No | Composition | Density |
---|---|---|---
0 | 89.05% Al, 2.5% Mg, 2.5% Cr, 5.5% Zn, 1.8% Cu, 0.5% Fe, 0.4% Si | 3.16 g/cm3 |
5 | 36.22% Al, 41.33% C, 16.25% O, 1.23% Zn, 4.96% Zr | 2.55 g/cm3 |
10 | 2.73% Al, 0.37% Mg, 36.59% C, 37.57% O, 8.58% P, 14.15% Ca | 1.81 g/cm3 |
WFI Baffle | 55.64.% Al, 44.36% O | 2.15 g/cm3 |

At lower incidence angles, the incoming proton may enter and exit a rough
surface sample several times before being scattered away, so we know that the
scattering energy distribution is related to the final scattering angle to
some extent; however, it is difficult to speculate on how the surface features
directly contribute to these final distributions. By creating a probability
density cube from all of our simulations, we can create an accurate sampling
distribution function that statistically accounts for the effect of these
unknown surface features, so given some input proton angle and energy we can
quickly output a new scattering angle and energy for these protons.

Besides the WFI baffle sample presented in this report, several other
materials and surfaces were measured and digitized, shown in Tab. 1 and Tab.
2. Given that much infrastructure was developed for these high-performance
computing routines, we hope to further explore these samples in the future and
create various proton transfer functions for different materials and surfaces.

###### Acknowledgements.

JPB and NW are supported by the GACR grant 21-13491X. Part of the funding was
provided by the Internal Grant Agency of Masaryk University, specifically the
Operational Programme Research, Development and Education within the framework
of the implemented project IGA MU reg. No. CZ.02.2.69/0.0/0.0/19_073/0016943
as well as by the MASH3 grant. Computational resources were supplied by the
project “e-Infrastruktura CZ” (e-INFRA CZ LM2018140 ) supported by the
Ministry of Education, Youth and Sports of the Czech Republic. The work was
partly supported by the ESA go/esacloud computing infrastructure. CzechNanoLab
project LM2018110 funded by MEYS CR is gratefully acknowledged for the
financial support of the measurements at CEITEC Nano Research Infrastructure.

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