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Anisotropic super-hardness of hexagonal WB2±z
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 WB2±z 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
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MATER. RES. LETT.
2022, VOL. 10, NO. 2, 70–77
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
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
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
WB2−z, 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-WB2−zcoat-
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.
First report of an anisotropic elastoplastic behaviour in super-hard PVD AlB2structured WB2−z. Theo-
retical and experimental verification of thermodynamically most stable sub-stoichiometric α-WB2−z
coatings by structural and mechanical analysis.
Received 20 September 2021
WB2; physical vapour
deposition; DFT; structural
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 [1–4]. 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
the pretended Mo2B5and W2B5are Mo2B4and W2B4,
whereas only non-stoichiometric compounds TMB2±z
prefer to crystallize in the α-structure . Nevertheless,
due to strongly limited kinetics during physical vapour
deposition (PVD), WB2−zis stabilized in its metastable
α-phase rather than in the thermodynamically preferred
CONTACT C. Fuger email@example.com
Supplemental data for this article can be accessed here. https://doi.org/10.1080/21663831.2021.2021308
ωstructure [10–12]. Structural defects—being predom-
inant in PVD materials—are presumed to stabilize the
rial system, where sub-stoichiometric TiB1.9 is stabilized
by the absence of B between Ti-planes locally relaxing the
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 .
Furthermore, in hexagonal SiC and GaN the dislo-
cation motion and activated slip systems have been
described and anisotropic mechanical properties were
shown [15–19]. The experimental observations of SiC
single crystal polytypes revealed higher hardness of basal
indentations compared to prismatic indentations .
Moreover, Huang et al. indicated specic 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 . In contrast, no dis-
tinct orientation-dependent fracture toughness could be
detected so far [15,18].
Moreover, WB2±zis known for its enhanced material
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 eect 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 dierent
structural as well as micro-mechanical characterization
techniques. Furthermore, theoretical investigations using
ab initio methods should clarify structural uncertainties
of the AlB2type WB2±z.
DFT coded VASP [23,24] calculations using the projector
augmented waves method within the generalized gra-
dient approximation (PAW-PBE) 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 , further details are described in
the Supplementary Material.
Thin lm synthesis
To oer a broad spectrum of deposition parameters
beyond temperature, pressure, and bias, we used three
dierent 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 congurations
with dierent 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
For detailed structural characterization of all coat-
ings deposited, a Philips XPERT diractometer in
endstation (DESY Petra III), were used (selected
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 to gain H and E, respectively.
The elemental composition of selected lms on Si
substrates was analyzed by liquid inductively coupled
OES measurements were carried out on an iCAP 6500
RAD (Thermo Fisher Scientic, 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 WB2−z
coatings were acid digested with the method presented
and validated in [28–30]–describedindetailintheSup-
In addition, one selected sample was surveyed by
transmission electron microscopy (TEM FEI TECNAI,
F20, acceleration voltage of 200kV). Detailed struc-
diraction (SAED). The sample preparation was done
by focused ion beam (FIB, Quanta 200 3D DualBeam),
applying a standard lift-out technique .
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 .
The calculation of the fracture toughness was per-
formed after Matoy et al. —see also Supplementary
Results and discussion
DFT calculations revealed the energy of formation, Ef,of
perfect and defected α-andω-structuredWB
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  and lowered with increasing number
of vacancies within the α-lattice. The α-structured cell is
thermodynamically preferred compared to ω—meaning
Efof α-WB2−zis below ω-WB2−z—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 WB2−zlms deposited on the dierent 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 diraction 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), 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 .
MATER. RES. LETT. 73
All defected lattice congurations (considered in
Figure 1(a)) have been consulted for calculating the
stiness 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 ·
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 quantication 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
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 ,
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
Although the used target material is of ω-WB2struc-
ture, the deposition of ω-WB2coatings points out to be
very challenging, since α-structured WB2−zis prefer-
entially formed within magnetron sputtering techniques
(see XRD patterns in the Supplementary Material). The
broad parameter variation on 3 dierent deposition sys-
tems revealed always sub-stoichiometric α-WB2−zstruc-
tured thin lms but in various crystal orientations. The
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 dierence in mass between light (B) and
heavy (W) elements promotes scattering eects dur-
ing sputtering leading to sub-stoichiometric composi-
tions. A highly 0001 oriented α-WB2−zcoating (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¯
zone axis. Additionally, the inset a-i contains a VESTA
model 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, conrms the same crystal orientation as
already revealed from SAED –masking regions for the
white dashed circles. The sections d-f show ltered TEM
images (for technical details see ) from the same
region marked in b overlaid with a masked IFFT in
the depicted directions ((1000), (0001), and (10¯
d, e, and f respectively). Conducting this procedure,
defect/strain-rich domains can be highlighted, conrm-
ing the structural stabilization in the α-phase of the
chemically sub-stoichiometric WB1.45 lm. In corre-
spondence to , structural defects (i.e. Boron vacan-
cies) seem to compensate for the sub-stoichiometry of the
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-WB2−z
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% condence 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¯
(blue open squares), revealing a decrease of H with an
11 orientation (blue dashed line and blue
mechanical property of α-WB2−zcoatings, revealing the
highest hardness when 0001 oriented by simultaneously
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-
anisotropic eects nor hardening due to a Hall-Petch
eect 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.  showed that various slip systems in hexagonal
ZrB2(AlB2prototype, SG191, α) reveal dierent 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¯
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-WB2−zthin 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)
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-WB2−z, we can assume a similar
behaviour for both hexagonal material systems. Thus, a
hardness increase for  crystals can be explained by
a larger GSFE value of the pyramidal slip system (10¯
slip plane)—compared to the basal slip system—which
experiences the maximum shear stress τmax whenaforce
(during indentation) is applied in  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
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-
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
structure within our WB2−zthin 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-WB2−zcoatings,revealedK
values ranging from 2.89 ±0.26 MPa√m(WB
ratio: 0.80), 3.23 ±0.19 MPa√m(WB
0.99), to 3.65 ±0.26 MPa√m(WB
1.55, 0001-ratio: 0.04),
revealing no perceptible inuence 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 aected 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
(inuenced by the growth conditions or the introduc-
tion of column boundary ane elements), introduction
of third order residual stresses by i.e. precipitation tough-
ening or unwanted impurities such as oxygen, or eects
of the microstructure on the fracture behaviour.
In summary, the AlB2structure formation of WB2±zwas
investigated by DFT. The calculations indicate the stabi-
lization of hexagonal α-WB2−zby 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-WB2−zthin 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
In contrast, no impact of the crystal orientation on KIC
could be detected.
We also thank for the nancial support of Plansee SE, Plansee
Composite Materials GmbH, and Oerlikon Balzers, Oerlikon
centre (XRC) of TU Wien for beam time as well as the electron
microscopy centre—USTEM TU Wien—for using the SEM
liothek for nancial support through its Open Access Funding
Programme. The computational results presented have been
achieved using the Vienna Scientic 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).
No potential conict of interest was reported by the author(s).
76 C. FUGER ET AL.
The nancial support by the Austrian Federal Ministry for Dig-
ital and Economic Aairs, 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’).
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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