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Transition metal diboride-based thin films are promising candidates to replace state-of-the-art protective and functional coating materials due to their unique properties. Here, we focus on hexagonal WB2−z , showing that the AlB2 structure is stabilized by B vacancies exhibiting its energetic minima at sub-stoichiometric WB1.5. Nanoindentation reveals super-hardness of 0001 oriented α-WB2−z coatings , linearly decreasing by more than 15 GPa with predominant 1011 orientation. This anisotropy is attributed to differences in the generalized stacking fault energy of basal and pyramidal slip systems, highlighting the feasibility of tuning mechanical properties by crystallographic orientation relations.
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Anisotropic super-hardness of hexagonal WBz
thin films
C. Fuger, R. Hahn, L. Zauner, T. Wojcik, M. Weiss, A. Limbeck, O. Hunold, P.
Polcik & H. Riedl
To cite this article: C. Fuger, R. Hahn, L. Zauner, T. Wojcik, M. Weiss, A. Limbeck, O. Hunold,
P. Polcik & H. Riedl (2022) Anisotropic super-hardness of hexagonal WBz thin films, Materials
Research Letters, 10:2, 70-77, DOI: 10.1080/21663831.2021.2021308
To link to this article: https://doi.org/10.1080/21663831.2021.2021308
© 2022 The Author(s). Published by Informa
UK Limited, trading as Taylor & Francis
Group
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MATER. RES. LETT.
2022, VOL. 10, NO. 2, 70–77
https://doi.org/10.1080/21663831.2021.2021308
ORIGINAL REPORTS
Anisotropic super-hardness of hexagonal WB2±zthin films
C. Fuger a,R.Hahn a,L.Zauner a,T.Wojcik a,M.Weiss b,A.Limbeck b, O. Hunoldc,P.Polcik
dand
H. Riedl a,e
aChristian Doppler Laboratory for Surface Engineering of high-performance Components, TU Wien, Wien, Austria; bInstitute of Chemical
Technologies and Analytics, TU Wien, Wien, Austria; cOerlikon Balzers, Oerlikon Surface Solutions AG, Balzers, Liechtenstein; dPlansee
Composite Materials GmbH, Lechbruck am See, Germany; eInstitute of Materials Science and Technology, TU Wien, Wien, Austria
ABSTRACT
Transition metal diboride-based thin films are promising candidates to replace state-of-the-art pro-
tective and functional coating materials due to their unique properties. Here, we focus on hexagonal
WB2z, showing that the AlB2structure is stabilized by B vacancies exhibiting its energetic minima at
sub-stoichiometric WB1.5. Nanoindentation reveals super-hardness of 0001 oriented α-WB2zcoat-
ings, linearly decreasing by more than 15 GPa with predominant 10¯
11 orientation. This anisotropy is
attributed to differences in the generalized stacking fault energy of basal and pyramidal slip systems,
highlighting the feasibility of tuning mechanical properties by crystallographic orientation relations.
IMPACT STATEMENT
First report of an anisotropic elastoplastic behaviour in super-hard PVD AlB2structured WB2z. Theo-
retical and experimental verification of thermodynamically most stable sub-stoichiometric α-WB2z
coatings by structural and mechanical analysis.
ARTICLE HISTORY
Received 20 September 2021
KEYWORDS
WB2; physical vapour
deposition; DFT; structural
defects; anisotropy;
super-hardness
Introduction
Transition metal diborides (TMB2)exhibitatremen-
dous potential to be applied in various applications
ranging from wear- and corrosion resistant coatings,
superconductive thin lms, up to extremely stable pro-
tective layers [14]. Diborides of group 2–5 prefer to
crystallize in the hexagonal AlB2structure (α,space
group 191—P6/mmm), while TMB2of group 6 and
higher typically reveal the so-called W2B5based struc-
ture (ω, space group 194—P63/mmc) [5,6]– except for
CrB2[7,8].Frotscheretal.alreadypointedout,that
the pretended Mo2B5and W2B5are Mo2B4and W2B4,
whereas only non-stoichiometric compounds TMB2±z
prefer to crystallize in the α-structure [9]. Nevertheless,
due to strongly limited kinetics during physical vapour
deposition (PVD), WB2zis stabilized in its metastable
α-phase rather than in the thermodynamically preferred
CONTACT C. Fuger christoph.fuger@tuwien.ac.at
Supplemental data for this article can be accessed here. https://doi.org/10.1080/21663831.2021.2021308
ωstructure [1012]. Structural defects—being predom-
inant in PVD materials—are presumed to stabilize the
α-phase.ThisisconrmedindetailfortheTiB
2mate-
rial system, where sub-stoichiometric TiB1.9 is stabilized
by the absence of B between Ti-planes locally relaxing the
structure [13].
In general, the enhanced hardness of hexagonal mate-
rial systems is related to limited slip systems (slip plane
and -direction)—compared to cubic systems—impeding
dislocation movement and thus, plastic deformation [14].
Furthermore, in hexagonal SiC and GaN the dislo-
cation motion and activated slip systems have been
described and anisotropic mechanical properties were
shown [1519]. The experimental observations of SiC
single crystal polytypes revealed higher hardness of basal
indentations compared to prismatic indentations [15].
Moreover, Huang et al. indicated specic slip planes being
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor& Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
MATER. RES. LETT. 71
active during plastic deformation of GaN, suggesting
that anisotropic elastoplastic mechanical properties cor-
relate with plastic deformation [17]. In contrast, no dis-
tinct orientation-dependent fracture toughness could be
detected so far [15,18].
Moreover, WB2±zis known for its enhanced material
propertieslikehardness,Youngsmodulusaswellasfrac-
ture toughness, and therefore often consulted as a base
system forming ternary TMITMIIB2±z[10,11,20,21].
In previous studies, we successfully showed the posi-
tive eect of Ta alloying on the mechanical properties
(H, KIC), thermal stability, and oxidation resistance of
WB2±zthin lms [10,21,22].
The focus of this study is to obtain new insights into
the elastoplastic behaviour of WB2±zthin lms concern-
ing their detailed structural constitution using dierent
structural as well as micro-mechanical characterization
techniques. Furthermore, theoretical investigations using
ab initio methods should clarify structural uncertainties
of the AlB2type WB2±z.
Experimental
Computational details
DFT coded VASP [23,24] calculations using the projector
augmented waves method within the generalized gra-
dient approximation (PAW-PBE) [25]wereappliedto
investigate the energy of formation (Ef)andelasticcon-
stants of α-andω-structured WBxcells (x =2±z). The
perfect, as well as the defected structures, were gener-
ated using the SQS special quasirandom structure (SQS)
approach. The elastic constants were calculated using the
stress/strain method [26], further details are described in
the Supplementary Material.
Thin lm synthesis
To oer a broad spectrum of deposition parameters
beyond temperature, pressure, and bias, we used three
dierent deposition systems. An in-house developed
magnetron sputtering system (for details see Supple-
mentary) an AJA International Orion 5 magnetron
sputtering system, and an Oerlikon Balzers Innova depo-
sition system providing diverse sputter congurations
with dierent target-substrate distances and angles. The
coating facilities have been equipped with six-inch and
three-inch powder-metallurgically prepared W2B4tar-
gets—manufactured by Plansee Composite Materials
GmbH—exhibiting the ω- structure. The deposition pro-
cesses were carried out in pure argon with a rotating
substrate holder. For detailed information to the in-
house developed system and on the variated parameter
settings on each deposition system, see Table S1–3 in the
Supplementary.
Characterization methods
For detailed structural characterization of all coat-
ings deposited, a Philips XPERT diractometer in
BraggBrentanoconguration,aswellasthenanofocus
endstation (DESY Petra III), were used (selected
samples).
Hardness (H), and Young’s modulus (E), of all lms,
were investigated by an Ultra Micro-Indentation System
(UMIS), equipped with a Berkovich diamond tip. The
resulted loading and unloading curves were evaluated
afterOliverandPharr[27] to gain H and E, respectively.
The elemental composition of selected lms on Si
substrates was analyzed by liquid inductively coupled
plasmaopticalemissionspectroscopy(ICP-OES).LICP-
OES measurements were carried out on an iCAP 6500
RAD (Thermo Fisher Scientic, USA), with an ASX-
520 autosampler (CETAC Technologies, USA) using an
HF resistant sample introduction kit, consisting of a
Miramist nebulizer (Burger Research, USA), a PTFE
spray chamber and a ceramic injector tube. The WB2z
coatings were acid digested with the method presented
and validated in [2830]–describedindetailintheSup-
plementary Material.
In addition, one selected sample was surveyed by
transmission electron microscopy (TEM FEI TECNAI,
F20, acceleration voltage of 200kV). Detailed struc-
turalinformationwasgainedbyselectedareaelectron
diraction (SAED). The sample preparation was done
by focused ion beam (FIB, Quanta 200 3D DualBeam),
applying a standard lift-out technique [31].
In situ micromechanical bending tests of substrate-
free coating cantilevers are conducted to obtain the frac-
ture toughness of selected coatings. The experiments
were performed within an SEM equipped with a Hysitron
PI-85 SEM pico-indenter whose spherical diamond tip
was pressed onto the top of the pre-notched cantilever (in
the growth direction of the coatings) until fracture [32].
The calculation of the fracture toughness was per-
formed after Matoy et al. [33]—see also Supplementary
Material.
Results and discussion
DFT calculations revealed the energy of formation, Ef,of
perfect and defected α-andω-structuredWB
2±zcells.
In Figure 1(a) the development of Efwith increasing B
vacancies (blue lled squares for α, red lled triangles for
ω), W vacancies (blue half-lled squares for α,redhalf-
lled triangles for ω) and Schottky defects (blue empty
72 C. FUGER ET AL.
Figure 1. (a) Efvalues of fully converged α-WBx(2×2×4) and ω-WBx(2×2×1) supercells (x =1.25–4.0) as a function of chemical
composition represented by the value of x =2±zin WBx.Figure1b gives the evolution of lattice constant a (orange triangles), and c
(blue squares) of α-WBx. Additionally, the elastic constant C44 (c), the theoretical hardness Htheo (d), and the theoretical Young’s modulus
Etheo (e) of all mechanically stable structures are illustrated. The change in valence electron concentration (VEC) of defected WBxcrystals
is depicted in the abscissa on top of Figure 1a–e.
squares for α,redemptytrianglesforω), is indicated,
respectively. The vertical grey line represents stoichio-
metric WB2expressing the value of x =2.0 in WBx.
With increasing B vacancy population x is decreasing,
while an increase of W vacancies leads to an increase of x
(indicated on the bottom abscissa of Figure 1(a)). More-
over, an increasing vacancy concentration is decreasing
the valence electron concentration (VEC) of the material
system, highlighted on the top abscissa of Figure 1(a).
Generally, Efraises by adding vacancies to the ω-
lattice, having its minima around the perfect W2B4/WB2
stoichiometry [9] and lowered with increasing number
of vacancies within the α-lattice. The α-structured cell is
thermodynamically preferred compared to ω—meaning
Efof α-WB2zis below ω-WB2z—at a vacancy con-
centration >6%. Boron defected α-andω-structured
cells energetically intersect at WB1.70 (Ef=−0.23 eV/at)
followed by a thermodynamic minimum at WB1.50
(Ef=−0.28 eV/at) for the α-lattice. The atomic concen-
tration of the α-cell at the Efminima leads to 40 at.%
W and 60 at.% B, hence matching the experimentally
measured compositions obtained by ICP-OES for var-
ious WB2zlms deposited on the dierent routes
(WB2_01: W =40.74 ±0.91 at.%, B =59.26 ±0.91
at.%; WB2_20: W =39.14 ±1.67 at.%, B =60.86 ±
1.67 at.%; WB2_21: W =40.41 ±2.04 at.%, B =59.59
±2.04 at.%). Moreover, investigations on the evolu-
tion of α-WB2±zlattice constants revealed convergence
of α-WB1.5 (a =3.0488 Å, b =3.0483 Å, c =3.0683
Å, V =24.74 Å3) during DFT calculations with our
experimentally obtained values of WB1.47 (a =3.0168 Å,
c=3.0608 Å) using nanobeam diraction on powdered
coating material (stars in Figure 1(b))—for details see
Supplementary. Due to correlating lattice parameters
from our α-WB1.47 with those reported from Woods
et al. (a =b=3.0200 Å, c =3.0500 Å, V =24.09
Å3)[34], we would suggest a sub-stoichiometric compo-
sition also for their structure. In addition, Hayami et al.
theoretically determined lattice constants for WB1.625 of
a=b=3.072 Å, c =3.117 Å [35].
MATER. RES. LETT. 73
All defected lattice congurations (considered in
Figure 1(a)) have been consulted for calculating the
stiness tensor C. To ensure validity of the resulted
elastic constants Cij, the following criteria have to be ful-
lled in hexagonal crystals: C11 >|C12|; 2C2
13 <C33 ·
(C11 +C12);C
44 >0; C66 >0. All data points presented
in Figure 1(b–d) satisfy the above-mentioned stability
conditions, thus revealing mechanically stable structures.
For the quantication of mechanical stability of per-
fect and defected structures, the elastic constant C44 is
highlighted in Figure 1(c). The data points reveal val-
ues of C44 =131 GPa for stochiometric αas well as
C44 =221 GPa for ω, indicating enhanced mechanical
stability for ω. This trend is inverted by introducing B
vacancies to the crystal structures leading to a maxi-
mum C44 =250 GPa at x =1.5 and VEC =10.5 for α
structured WB1.5.Moreover,theC
44 maximum of the
α-lattice is correlating with the Efminima (Figure 1(a)),
revealing highest thermodynamic stability is also lead-
ing to the highest mechanical stability of this crystal.
Furthermore, theoretical hardness values, Htheo,have
been evaluated using a widely established model [36],
H=0.92·(G/B)1.137·G0.708,whereGandBareshear-
and bulk modulus, respectively. Figure 1(d) illustrates
Htheo, showing a maximum value of Htheo =28 GPa
for αstructured WB1.5 and maximum Htheo =31 GPa
for ω-WB1.93. The same trend was experienced for the
theoretical Young’s moduli (E =9·B·G/(3B+G)) with
a maximum Etheo =546 GPa for αstructured WB1.5
and Etheo =565 GPa for ω-WB1.93, as indicated in
Figure 1(e).
Although the used target material is of ω-WB2struc-
ture, the deposition of ω-WB2coatings points out to be
very challenging, since α-structured WB2zis prefer-
entially formed within magnetron sputtering techniques
(see XRD patterns in the Supplementary Material). The
broad parameter variation on 3 dierent deposition sys-
tems revealed always sub-stoichiometric α-WB2zstruc-
tured thin lms but in various crystal orientations. The
reasonforthealphastabilizationisthehighdefectden-
sity especially on the non-metal sublattice (dislocations,
vacancies) due to the extreme cooling rates during con-
densation from the vapour phase to the solid state. Fur-
thermore, the dierence in mass between light (B) and
heavy (W) elements promotes scattering eects dur-
ing sputtering leading to sub-stoichiometric composi-
tions. A highly 0001 oriented α-WB2zcoating (WB1.45)
has been investigated using TEM (see Figure 2). The
coating exhibits a columnar and defected morphology,
see Figure 2(a,b). Section 2a also represents the area
for the recorded SAED pattern, depicted in the inset
a-i. SAED exhibits highly oriented crystals in [11¯
20]
zone axis. Additionally, the inset a-i contains a VESTA
model [37]oftheα-structured WB2unit cell—the W
and B atoms are represented in red and blue, respec-
tively—oriented as obtained from SAED. Figure 2(b)
shows a high-resolution TEM image of the investigated
coating, emphasizing defected zones within the highly-
oriented crystal. However, the FFT image, depicted
in section c, conrms the same crystal orientation as
already revealed from SAED –masking regions for the
InverseFastFourierTransform(IFFT)aremarkedas
white dashed circles. The sections d-f show ltered TEM
images (for technical details see [38]) from the same
region marked in b overlaid with a masked IFFT in
the depicted directions ((1000), (0001), and (10¯
11) for
d, e, and f respectively). Conducting this procedure,
defect/strain-rich domains can be highlighted, conrm-
ing the structural stabilization in the α-phase of the
chemically sub-stoichiometric WB1.45 lm. In corre-
spondence to [13], structural defects (i.e. Boron vacan-
cies) seem to compensate for the sub-stoichiometry of the
coating.
In Figure 3(a) experimentally determined hardness H
(blue open squares) and Young’s modulus E (red open
triangles) are plotted as a function of increasing frac-
tion of 0001 lattice orientation of the various α-WB2z
coatings. H is increasing from 25 GPa for coatings
without any 0001 orientation up to 40 GPa for purely
0001 oriented coatings. Thus, the dataset reveals a lin-
ear dependency of H with an increasing 0001 ratio (see
linear t with 95% condence limit in Figure 3(a)). On
the other hand, the evaluation of the 10¯
11 ratio shows
a contrary picture. Figure 3(b) depicts the experimen-
tally determined H as a function of increasing 10¯
11 ratio
(blue open squares), revealing a decrease of H with an
increasing 10¯
11 orientation (blue dashed line and blue
shadedarea).Theseresultspointouttheanisotropic
mechanical property of α-WB2zcoatings, revealing the
highest hardness when 0001 oriented by simultaneously
showingno10
¯
11 orientation. In comparison, the sto-
chiometric α-structured WB2ispredictedtoobtaina
Htheo =15 GPa, whereas the boron defected α-WB1.5
reveals Htheo =28 GPa coinciding with the experimen-
taldata.Here,weneedtopointoutthatinH
theo neither
anisotropic eects nor hardening due to a Hall-Petch
eect is considered.
The observed anisotropy in hardness can be related
to aggravated dislocation movement due to energeti-
cally less preferred slip systems. Through DFT, Hunter
et al. [39] showed that various slip systems in hexagonal
ZrB2(AlB2prototype, SG191, α) reveal dierent general-
ized stacking fault energies (GSFE). The <a>type basal
slip 0001 is the easiest a-type slip system to activate, ener-
getically followed by pyramidal <1¯
210 >10¯
1¯
1andboth
prismatic <1120 >10 ¯
10 slip systems. Additionally, the
74 C. FUGER ET AL.
Figure 2. TEM analysis of the WB1.45 coating. Section a presents a cross-sectional BF image of the WB1.45 lamella, pointing out the area
for the recorded SAED (white dashed circle) displayed in the inset a–i. An FFT cut out of the HR-TEM in b (region of interest) is depicted
in section c, furthermore marking the masking regions for the IFFT as white dashed circles. Section d-f show defect/strain rich domains
corresponding to the indicated directions (based on IFFT).
Figure 3. Hardness H (blue open squares) and Young’s modulus E (red open triangles) of various α-WB2zthin films deposited. The
dataset presents the mechanical properties as a function of the 0001 (a) and 10¯
11 lattice plane (b) orientation factor, determined from
XRD data (see Supplementary Material). The dashed lines give a linear fit from H (blue dashed line) and E (red dashed line). The blue and
red shaded areas represent a 95% confidence limit.
MATER. RES. LETT. 75
Figure 4. The hexagonal α-WB2structure is illustrated in 0001 (a)
and 10¯
11 (b) orientation. W and B atoms are depicted in green
and grey, respectively. Indentation experiments leading to a nor-
mal force F (grey arrow) which is appearing perpendicular to the
(0001) plane (a) (basal slip plane, orange area) or (10¯
11) plane (b)
(pyramidal slip plane, red area).
calculated GSFE values are correlating with interplanar
spacing, meaning the closer the planes are spaced, the
larger the GSFE value becomes. Due to structural corre-
lations of α-ZrB2and α-WB2z, we can assume a similar
behaviour for both hexagonal material systems. Thus, a
hardness increase for [0001] crystals can be explained by
a larger GSFE value of the pyramidal slip system (10¯
11
slip plane)—compared to the basal slip system—which
experiences the maximum shear stress τmax whenaforce
(during indentation) is applied in [0001] direction (see
Figure 4(a)). However, for a 10¯
11 crystal, the basal slip
system (0001 slip plane) is preferentially activated due
to τmax appearing at a 45° angle to the force vector F
(Schmid’s law), directing in [10¯
11] in this scenario (see
Figure 4(b)).
In contrast to the hardness results, indentation exper-
iments revealed relatively constant Young’s moduli in
the range of 500 GPa, depicted in Figure 3(a,b). The
data set emphasizes that the 0001 and 10¯
11 crystal ori-
entationshaveonlyaminorinuenceonE(depicted
by the linear t; red dashed line). For comparison, the
DFT calculations exhibit a Young’s modulus of 408 GPa
for perfect α-WB2structured cells. Only after intro-
ducing B vacancies, the theoretical Young’s modulus
increases to Etheo =546 GPa for α-WB1.5 approaching
the experimentally observed data. Moreover, by evalu-
ating the spatial dependency of the Young’s modulus of
perfect α-WB2and defected α-WB1.5 acleardecrease
of the anisotropy for the α-WB1.5 could be observed
(see Figure S4 and S5 in the Appendix). The anisotropy
reduces from 1.804 for α-WB2to 1.151 for α-WB1.5
furtherunderliningthepresenceofahighlydefected
structure within our WB2zthin lms.
In addition to the anisotropy of the hardness, we also
evaluated the fracture toughness of selected coatings to
gain a deeper insight into a possible orientation-related
fracture behaviour. Micromechanical cantilever bending
experiments of selected α-WB2zcoatings,revealedK
IC
values ranging from 2.89 ±0.26 MPam(WB
1.45, 0001-
ratio: 0.80), 3.23 ±0.19 MPam(WB
1.87, 0001-ratio:
0.99), to 3.65 ±0.26 MPam(WB
1.55, 0001-ratio: 0.04),
revealing no perceptible inuence of the lm orientation
(for further details see Table S4 in the Supplementary
Material). The results indicate that the fracture tough-
ness of our thin lm materials is not aected by dislo-
cation movement, hence other mechanisms govern the
observed variation in KIC values. Such mechanisms can
be for example: the cohesive grain boundary strength
(inuenced by the growth conditions or the introduc-
tion of column boundary ane elements), introduction
of third order residual stresses by i.e. precipitation tough-
ening or unwanted impurities such as oxygen, or eects
of the microstructure on the fracture behaviour.
Conclusion
In summary, the AlB2structure formation of WB2±zwas
investigated by DFT. The calculations indicate the stabi-
lization of hexagonal α-WB2zby B vacancies, compared
to a thermodynamic minimum of perfect, stoichiometric
ω-WB2. This theoretical result is experimentally under-
lined by: matching lattice parameters, mechanical prop-
erties, and chemical compositions of physical vapour
deposited α-WB2zthin lms. Moreover, nanoindenta-
tion of the synthesized coatings revealed anisotropy in
the elastoplastic behaviour. Super-hardness was deter-
mined for 0001 oriented lms, linearly decreasing by
morethan15GPawithanincreasing10
¯
11 orientation.
VarietiesinGSFEofbasalandpyramidalslipsystemsin
hexagonalcrystalsmayconstituteanisotropyinhardness.
In contrast, no impact of the crystal orientation on KIC
could be detected.
Acknowledgement
We also thank for the nancial support of Plansee SE, Plansee
Composite Materials GmbH, and Oerlikon Balzers, Oerlikon
SurfaceSolutionsAG.Inaddition,wewanttothanktheX-ray
centre (XRC) of TU Wien for beam time as well as the electron
microscopy centre—USTEM TU Wien—for using the SEM
andTEMfacilities.TheauthorsacknowledgeTUWienBib-
liothek for nancial support through its Open Access Funding
Programme. The computational results presented have been
achieved using the Vienna Scientic Cluster (VSC). We fur-
ther acknowledge the granted use of the Nanofocus Endstation
of the Beamline P03 of PETRA III at DESY, a member of the
Helmholtz Association (HGF).
Disclosure statement
No potential conict of interest was reported by the author(s).
76 C. FUGER ET AL.
Funding
The nancial support by the Austrian Federal Ministry for Dig-
ital and Economic Aairs, the 10.13039/100007224 National
Foundation for Research, Technology and Development and
the Christian Doppler Research Association is gratefully
acknowledged (Christian Doppler Laboratory ‘Surface Engi-
neering of high-performance Components’).
ORCID
C. Fuger http://orcid.org/0000-0003-2685-4808
R. Hahn http://orcid.org/0000-0002-7322-8108
L. Zauner http://orcid.org/0000-0002-8373-6552
T. Wojcik http://orcid.org/0000-0001-5091-5215
M. Weiss http://orcid.org/0000-0002-4312-9256
A. Limbeck http://orcid.org/0000-0001-5042-2445
H. Riedl http://orcid.org/0000-0002-8108-1185
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