Correlation between fracture characteristics and valence electron concentration of sputtered Hf-C-N based thin films

Abstract

Hard protective coating materials based on transition metal nitrides and carbides typically suffer from limited fracture tolerance. To further tune these properties non-metal alloying – substituting C with N – has been proven favorable for magnetron sputtered Hf-C-N based thin films. A theoretically predicted increase in valence electron concentration (from 8.0 to 9.0 e/f.u. from HfC to HfN) through nitrogen alloying lead to an increase in fracture toughness (KIC obtained during in-situ SEM cantilever bending) from 1.89 ± 0.15 to 2.33 ± 0.18 MPa·m1/2 for Hf0.43C0.57 to Hf0.35C0.30N0.35, respectively. The hardness remains close to the super-hard regime with values of 37.8 ± 2.1 to 39.9 ± 2.7 GPa for these specific compositions. Already the addition of small amounts of nitrogen, while sputtering a ceramic HfC target, leads to a drastic increase of nitrogen on the non-metallic sublattice for fcc single phased structured HfC1-xNx films, where x = N/(C + N). The here obtained results also provide experimental proof for the correlation between fracture characteristics and valence electron concentration.

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Surface & Coatings Technology
journal homepage: www.elsevier.com/locate/surfcoat
Correlation between fracture characteristics and valence electron
concentration of sputtered Hf-C-N based thin films
T. Glechner
a,⁎
, S. Lang
a
, R. Hahn
a
, M. Alfreider
b
, V. Moraes
c
, D. Primetzhofer
d
, J. Ramm
e
,
S. Kolozsvári
f
, D. Kiener
b
, H. Riedl
a,c
a
Christian Doppler Laboratory for Surface Engineering of high-performance Components, TU Wien, Austria
b
Department of Materials Science, Montanuniversität Leoben, Austria
c
Institute of Materials Science and Technology, TU Wien, A-1060 Wien, Austria
d
Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden
e
Oerlikon Balzers, Oerlikon Surface Solutions AG, 9496 Balzers, Liechtenstein
f
Plansee Composite Materials GmbH, D-86983 Lechbruck am See, Germany
ARTICLE INFO
Keywords:
Hf-C-N
Fracture resistance
Non-metal alloying
Valence electron concentration
Thermal stability
ABSTRACT
Hard protective coating materials based on transition metal nitrides and carbides typically suffer from limited
fracture tolerance. To further tune these properties non-metal alloying – substituting C with N – has been proven
favorable for magnetron sputtered Hf-C-N based thin films. A theoretically predicted increase in valence electron
concentration (from 8.0 to 9.0 e/f.u. from HfeC to HfeN) through nitrogen alloying lead to an increase in
fracture toughness (K
IC
obtained during in-situ SEM cantilever bending) from 1.89 ± 0.15 to
2.33 ± 0.18 MPa·m
1/2
for Hf
0.43
C
0.57
to Hf
0.35
C
0.30
N
0.35
, respectively. The hardness remains close to the super-
hard regime with values of 37.8 ± 2.1 to 39.9 ± 2.7 GPa for these specific compositions. Already the addition
of small amounts of nitrogen, while sputtering a ceramic HfeC target, leads to a drastic increase of nitrogen on
the non-metallic sublattice for fcc single phased structured HfC
1-x
N
x
films, where x = N/(C + N). The here
obtained results also provide experimental proof for the correlation between fracture characteristics and valence
electron concentration.
1. Introduction
Various challenges in the field of environmental sustainability as
well as emission reduction in general are closely linked to the usage of
ultra-stable materials. Especially, protective coatings of high-perfor-
mance components – such as blades or drive train systems in jet engines
or steam turbines – depict a key role to achieve further milestones
concerning efficiency and operating ranges [1,2]. For these extremely
harsh environments, involving highest temperatures accompanied by
abrasive and corrosive media, transition metal nitrides (TMN), and
carbides (TMC) are highly interesting coating materials due to their
excellent thermomechanical properties and chemical inertness [2].
Nevertheless, these ceramic compounds typically lack ductility com-
pared to common metals and metallic alloys [3–5]. Also, the formation
of continuous and dense oxide scales at the highest temperatures is a
strong limitation for wide usage [7,6].
Among diverse concepts [8], substitutional alloying of the non-
metallic sublattice by exchanging C with N atoms – forming
carbonitrides – depict an interesting approach to intrinsically tune these
coating properties. Through this substitutional exchange, a distinct
adaption of the prevalent bonding character and hence valence electron
concentration (VEC) is accomplished [9]. This fundamental approach
was initially proven for face-centered cubic (fcc) TiC
1-x
N
x
adjusting the
VEC to 8.4 e/f.u. exhibiting a hardness maximum due to the population
of a particular s band, located between the non-metal p and metal d
orbitals, being strongly resistive against shape changes and shearing
[10]. While for the hardness a distinct correlation with an ideal VEC for
various systems can be made, more or less positive behavior is sug-
gested for the toughness by increasing VEC up to 10 [11–15]. In our
previous studies, we could show, that the exchange of about 36% C
with N atoms in fcc-structured TaC
y
(VEC increasing from 8.24 to 9.36
e/f.u. compared to the binary TaC
0.81
) lead to a fracture toughness
increase from 1.8 to 2.9 MPa·m
-1/2
(while keeping the thin film mor-
phology similar, especially regarding their columnar growth), respec-
tively [4,16]. As already shown in previous studies [17–19], these
transition metal carbides and nitrides are strongly effected by structural
https://doi.org/10.1016/j.surfcoat.2020.126212
Received 11 March 2020; Received in revised form 2 July 2020; Accepted 16 July 2020
⁎
Corresponding author.
E-mail address: thomas.glechner@tuwien.ac.at (T. Glechner).
Surface & Coatings Technology 399 (2020) 126212
Available online 19 July 2020
0257-8972/ © 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/BY/4.0/).
T

defects, such as vacancies, influencing similarly the bonding states.
However, a distinct population of structural defects is for sure more
challenging compared to non-metal alloying, especially with respect to
the deposition process [17]. Furthermore, different theoretical studies
using ab initio molecular dynamics [20,21] also predict an increase of
the melting temperature of about 200 K for Hf
0.53
C
0.27
N
0.20
compared
to pure to HfeC – suggesting a new highest melting material. Next to
these fundamental aspects while exchanging C with N in transition
metal carbides, the selection of a proper transition metal is also highly
important. Based on their extremely high phase stability and the above-
mentioned facts, TaC
y
and HfC
y
are promising candidates [22]. Espe-
cially, the Hafnium based system is encouraging as one oxide is highly
stable – in its high-temperature modification (HfO
2
, fcc, #SG 225) even
up to 3083 K [23,24]. It can be synthesized by reactive cathodic arc
evaporation in an Al-Hf-O material system, but it is difficult to stabilize.
Studies on Hf-containing thin films [25] and bulk materials [26] sug-
gested high oxidation resistance and hence great potential (even above
1600 °C). However, only a few studies are available for Hf-C-N coatings
in general, but also for sputtered deposited coatings. These papers
mainly concentrate on the impact of deposition parameters (tempera-
ture, bias) on structure, chemical composition as well as tribological
performance [27,28].
Therefore, within this study, we combine theoretical Density
Functional Theory (DFT) calculations with an experimental validation
by magnetron sputtered HfeC and Hf-C-N thin films. Thereby, we
wanted to gain an in-depth understanding of the impact of the non-
metallic sublattice occupation (varying nitrogen content) on the ther-
momechanical properties, especially for fracture tolerance.
2. Experimental procedures
We used two laboratory-scaled magnetron sputtering systems
(modified Leybold Heraeus Z400 and AJA Orion 5) having different
target to substrate arrangements – a parallel face to face configuration
obtaining a target to substrate distance of 50 mm as well as a tilted set-
up with a normalized distance of 70 mm – to deposit HfeC and Hf-C-N
thin films. Both deposition systems were equipped with a 3-in. HfeC
compound target (99.6% purity, Plansee Composite Materials GmbH)
operated in DC-pulsed mode (pulse frequency 150 kHz, pulse width
2576 ns). The HfeC coatings were deposited in pure Argon atmosphere
(99.999% purity), while Hf-C-N thin films were sputtered reactively in
an Argon/Nitrogen gas mixture. All depositions were carried out at a
total pressure of 0.4 Pa, as well as a bias potential of −10 V. A base
pressure below 10
−4
Pa was ensured for all deposition runs. We want to
emphasize that all coatings were deposited using the same target.
In the tilted setup, a total gas flow of 20 sccm has been used. To
obtain different nitrogen concentrations within the Hf-C-N coatings, we
varied the amount of nitrogen in the total gas flow (f
[N2]norm
=
+
f
f f
N
N Ar
2
2
)
from 0.0 to 0.15, respectively. The heater temperature was fixed at
600 °C, which corresponds to T
sub
= 415 ± 15 °C at the substrate
surface. The confocally arranged cathode (tilted by 25° to the rotating
substrate holder) was powered by an MKS RPG-50 Pulsed DC plasma
generator.
For the parallel configuration (bottom to top set-up), all depositions
were carried out at a total gas flow of 34.1 sccm. The non-metal sub-
lattice occupation was again varied through the nitrogen to the total gas
flow rate from 0.0 to 0.50, respectively. In contrast to the tilted setup,
the working gas pressure was not fixed through a pressure valve but
adjusted by the gas flow and pumping speed. Therefore, it decreased
from 0.393 Pa in pure Argon to 0.376 Pa for f
[N2]norm
= 0.5. The heater
temperature was varied between 300 °C and 500 °C, which corresponds
to 250 ± 15 °C and 380 ± 15 °C at the substrate surface, respectively.
Based on the physical limits of the flow controller, our lowest ni-
trogen to total gas flow ratio (f
[N2]norm
) was 0.05 for both systems. All
thin films were deposited on single-crystalline Al
2
O
3
platelets (0001-
oriented, 10x10x0.53 mm
3
), single-crystalline Si stripes (100-oriented,
20x7x0.38 mm
3
), and polished austenitic stainless-steel platelets
(20x7x0.8 mm
3
). Selected coatings were also grown on 0.05 mm thick
steel foils, which were dissolved afterward in 20% hydrochloric acid
[22]. The residual Hf
1-y
C
y
and Hf
1-y-z
C
y
N
z
coating flakes were grounded
mechanically to fine-grained powders, which was used for substrate-
interference free X-Ray Diffraction (XRD) analysis. Preliminary, to the
coating process, the target, and all substrates were sputter-cleaned in a
pure Argon atmosphere at a total pressure of 7.0 Pa in the tilted and
1.3 Pa in the face-to-face set up, respectively.
Time-of-flight Elastic Recoil Detection Analysis (ERDA) using a
36 MeV I8+ primary ion beam and detecting recoils at an detection
angle of 45° by a segmented gas ionization chamber [29] was per-
formed at the tandem laboratory at Uppsala University to determine the
chemical composition of the coatings. Data evaluation is described in
more detail in [22]. The structure of all coatings has been analyzed by
XRD in Bragg Brentano configuration using a Panalytical Empyrean
diffractometer – equipped with a Cu-K
α
radiation source operating at
45 kV and 40 mA (wavelength λ = 1.54 Å). Scanning Electron Mi-
croscopy (SEM, FEI Quanta 250 FEGSEM operated at 15 kV) was used
to scale the coating thicknesses and survey the coating quality in gernal.
More detailed analysis on the film morphology was done by Trans-
mission Electron Microscopy (TEM FEI TECNAI G20, an acceleration
voltage of 200 kV) – only for selected coatings.
Thermal treatments on sapphire substrates were done in a high-
temperature vacuum furnace (Centorr Vacuum Industries Series
LF22–2000) up to 1200 °C. The heating rate was 20 K·min
−1
followed
by an isothermal annealing time of 10 min and subsequent passively
cooling.
Mechanical properties such as Young's modulus and hardness were
examined on sapphire substrates by nanoindentation using an Ultra-
Micro-Indentation System (UMIS) equipped with a Berkovich diamond
tip. For every sample measurement, at least 25 indents with different
loads, 3 to 45 mN, were performed and their load-displacement curves
were analyzed after Oliver and Pharr [30]. The load range was chosen
to identify the ideal range where we have no influence of the substrate
and the surface roughness on our obtained values. It should be noted
that the indentation depths were below 10% of the film thickness,
which is reported to be sufficient to extinguish substrate interference
[31]. The Young's modulus was calculated using the Poisson's ratio for
HfC
1-x
N
x
obtained by the DFT calculations. In addition, we did not see
any clear dependency of the hardness and moduli on the load. All the
results presented in this study are averages of hardness and modulus
data obtained using loads from 3 to 45 mN (step size varied gradullay
from 2 to 0.5 to smaller loads). Residual stresses within the HfeC and
Hf-C-N coatings were investigated by using the modified Stoney Eq.
[32]. The curvature of the coated silicon substrates was analyzed by an
optical profilometer (Nanovea PS50).
All micro-mechanical tests were done on free-standing cantilevers,
which have been prepared by FIB machining. Before FIB-milling (using
an FEI Quanta 200 3D DualBeam-FIB), the silicon substrates were
etched using an aqueous 40 wt% KOH solution at 70 °C to obtain free-
standing film material. After that, the geometry was machined using a
beam current of 1.0 nA for coarse milling and 0.5 nA for fine milling at
an acceleration voltage of 30 keV. The initial notch was milled with 50
pA. The micromechanical experiments were conducted inside an LEO-
1540 FE-SEM/FIB dual-beam workstation with a PI 85 SEM pi-
coindenter mounted. The indenter was equipped with a diamond wedge
tip. All experiments were performed in displacement-controlled mode
(5 nm∙s
−1
). The calculation of the fracture toughness was then per-
formed following guidelines given by [33–35]. A load-deflection curve
and an image of the fractured cantilever can be found in the supple-
mentary material.
T. Glechner, et al. Surface & Coatings Technology 399 (2020) 126212
2

3. Calculational methodology
Density Functional Theory (DFT) calculations were performed with
the VASP code (Vienna Ab Initio Simulation Package) [36], using the
projector-augmented plane-wave (PAW) pseudopotentials [37]. To gain
a deeper insight into the effect of a chosen exchange-correlation (xc)
potential, we compared two different standard approximations namely,
Local Density Approximation (LDA) [38] and Perdew-Burke-Ernzerhof
Generalized Gradient Approximation (GGA-PBE) [39]. We used the fcc,
Fm
3
m, #SG 225 crystal structure creating a 2 × 2 × 2 supercell with
64 atoms from the conventional 8-a.u. cell. Various HfC
1−x
N
x
compo-
sitions were obtained by substituting carbon atoms with nitrogen uti-
lizing the Special Quasi-random Structure (SQS) method [40]. The in-
fluence of structural defects was investigated by the systematic removal
of either metallic or non-metallic species, also applying the SQS code.
The Brillouin zone of the cubic supercell was sampled with
6 × 6 × 6 k-points, and a plane wave cut-off energy of 500 eV was
chosen based on convergence tests guaranteeing a total energy accuracy
of at least 1 meV/at. Equilibrium lattice parameters and ground-state
energies were obtained by relaxing the supercell volumes, shapes, and
atomic positions (ISIF = 3 tag in VASP). Elastic constants of the
HfC
1−x
N
x
supercells were calculated using the Universal Linear-In-
dependent Coupling Strain (ULICS) method [41].
Polycrystalline bulk and shear modulus (B and G), Poisson ratio (ν),
and Young's modulus, E, were calculated applying Hill's average [42] of
the Reuss and Voigt bulk moduli (B
R
and B
V
) and shear moduli (G
R
and
G
V
), respectively.
4. Results and discussion
The angular distribution of metal and non-metal species (due to
their diverging atomic masses of Hf = 178.49 u compared to C = 12.01
u) during sputter deposition (e.g. HfeC) was the main driving force for
comparing two different target to substrate alignments [43]. Based on
the geometrically differences for these two setups, distinct target cur-
rents (0.5 and 0.8 A, respectively), as well as substrate heater tem-
peratures were used to gain similar coating morphologies. The chemical
compositions of all coatings (Hf
1-y
C
y
and Hf
1-y-z
C
y
N
z
) were analyzed by
TOF-ERDA. During these measurements, Hafnium (Hf) Carbon (C), and
Nitrogen (N), as well as Argon (Ar) and Oxygen (O) were detected.
Expected systematic uncertainties in the Hf-C-N system are typically
found to be at most 5 to 10% of the detected concentrations for absolute
measurements free from standards. Nevertheless, much higher preci-
sion is obtained for inter-sample comparison, as performed within this
study [43]. For the binary coatings deposited with the parallel and
tilted configuration, we obtained Hf
0.6
C
0.4
and Hf
0.43
C
0.57
, respectively.
The difference in stoichiometry is related to the angular distribution
during sputtering. In Fig. 1, an isothermal section of the ternary Hf-C-N
system is presented including the δ-Hf(C, N)
1-x
(light blue) as well as the
α-Hf phase-field as suggested by S. Binder [44] for an experimentally
validated isothermal section at 1150 °C (the temperature has no direct
relation to the synthesis or growth process and is only based on the
limited data set for isothermal sections within the ternary Hf-C-N
system). All coatings deposited are plotted in half-filled cubes and open
diamonds for the parallel and tilted set-up, respectively. In agreement
with a previous study [22], are binary HfeC compounds most likely off-
stoichiometric phases (Hf
0.43
C
0.57
and Hf
0.6
C
0.4
), which is typically
observed when using TMC compound targets in Ar atmospheres (in
relation to the angular distribution) [45]. Furthermore, already rela-
tively low f
[N2]norm
results in high nitrogen contents on the non-metallic
sublattice, x (x = N/(C + N)). This behavior is also highlighted in
Fig. 2, where the non-metallic sublattice occupation is plotted against
the nitrogen flow rate and underlines that we were unable to obtain
compositions below x = 0.50. The trends are similar for both target
configurations and show a big increase in, x, from f
[N2]norm
= 0 to 0.05,
followed by a slight rise for higher nitrogen flow rates (from 0.05 to
0.20). The occupation of nitrogen on the non-metallic sublattice is ac-
companied not only by a decrease in Carbon but also by a decrease in
Hafnium, resulting in Hafnium sub-stoichiometric thin films, deviating
from a hypothetical HfC-HfN tie line – see the right border of the δ-Hf
(C, N)
1-x
phase-field indicated in Fig. 1. This behavior is similar to the
Ta-C-N system [16], where it is less pronounced. The reduction of the
deposition temperature (hence surface mobility of incoming species)
enhances this effect further, see open cube (T
sub
= 250 °C) in Fig. 1,
whereby the nitrogen content increases on the cost of the Hf content.
The substrate surface temperature also influences the residual stress
state within the coatings, increasing the compressive character for de-
creased surface temperatures from −2.2 GPa to −2.8 GPa for 380 °C
and 250 °C, respectively. As the net stress state is influenced by several
factors, e.g. temperature and thickness (after R. Abermann [46]), a
higher growth rate for T
sub
= 380 °C (30 nm/min compared to 22 nm/
min) most likely dominates the compressive influence. The difference in
growth rate is mostly related to the varied nitrogen flow rate ratio for
these specific coatings, respectively. Nevertheless, lower surface tem-
peratures, as well as target currents accompanied by higher f
[N2]norm
might promote the introduction of reactive working gas nitrogen onto
the non-metallic sublattice.
Fig. 1. Isothermal section (1150 °C [44]) of the ternary Hf-C-N system with
indicated compositions of the parallel and tilted target configuration obtained
by ERDA. Open diamonds refer to the tilted set up (T
sub
= 415 °C), whereas
half-filled cubes indicate coatings obtained from the parallel configuration
(T
sub
= 380 °C). The open cube refers to the composition at a lower substrate
temperature (T
sub
= 250 °C) in the parallel set up with f
[N2]norm
=0.05.
Fig. 2. Influence of the nitrogen to total gas flow ratio f
[N2]norm
on the nitrogen
sublattice occupation x = N/(C + N). The tilted set up is indicated by open
diamonds, whereas half-filled squares refer to the parallel configuration.
T. Glechner, et al. Surface & Coatings Technology 399 (2020) 126212
3

Furthermore, the effect of slightly different angular sputter dis-
tributions was also obvious in the colors of the coatings. In general,
HfeC coatings appear dark grey up to black, whereas Hf-C-N coatings
have a coppery color. Hf-C-N coatings deposited with the face to face
arrangement, obtain a color-gradient, from coppery to black to coppery
over a distance of 20 mm (substrate size) being centered with respect to
the race track. This gradient is contributed to the angular sputter dis-
tribution of Hf and C as well as the relatively short substrate to target
distance (50 mm). The black regions exhibit about 7 at.% more carbon
on the extend of Hf, whereas the nitrogen content remains the same
throughout the substrate width. However, no gradient is observed in
the coatings deposited using the tilted arrangement. Due to this fact, all
further mechanical characterizations and annealing experiments are
done on coatings deposited in the tilted setup.
Fig. 3 a and b show the structural evolution with increasing nitrogen
content for both experimental set-ups. All coatings, Hf
1-y
C
y
as well as
Hf
1-y-z
C
y
N
z
, exhibit face-centered cubic (fcc) structures. Furthermore,
we observe a broadening of the peaks with increasing f
[N
2
]norm
in-
dicating a decrease in crystallite size as well as being a hint for higher
defect densities within the columns. The incorporation of nitrogen in
the thin films leads to a shift of the 2Θ values to higher angles towards
HfeN, which indicates a smaller lattice parameter [47,48] – visible for
pure Hf
1-y
C
y
compared to nitrogen alloyed coatings.
To further evaluate the obtained structural results, we performed
TEM investigations shown in Fig. 4 for Hf
0.43
C
0.57
(a to c) and
Hf
0.35
C
0.24
N
0.41
(d to f), respectively. Films on Si substrate have been
prepared for these TEM anlysis. Here a focus is to prove the presence of
amorphous phases, as a clear picture about the over stoichiometric
HfeC and Hf-C-N (especially on the non-metal sublattice) compositions
is not obvious. Both coatings show a dense columnar growth mor-
phology, while the addition of nitrogen leads to a decreasing column
size for the Hf
0.35
C
0.24
N
0.41
coatings – as also seen in the XRD spectra.
For Hf
0.43
C
0.57
the SAED analysis reavealed distinct spots on a ring-
pattern clearly corresponding to fcc structures – see Fig. 4b. These spots
get more blurred around the diffraction spots for Hf
0.35
C
0.24
N
0.41
due to
smaller diffracting domains (e.g. grains and/or crystallites) – see
Fig. 4e. As the dark-field image in Fig. 4e consist out of nice shaped
columns, also a highly crystalline state is assumed for the
Hf
0.35
C
0.24
N
0.41
coating. The high-resolution image of Hf
0.43
C
0.57
(see
Fig. 4c) give a detailed insight on the crystal structure and the mor-
phology at the column boundaries, which are marked with white da-
shed lines. In addition FFT analysis of the marked areas have been
conducted to prove the high crystallinity of these areas. The FFT clearly
revealed dot-like patterns, suggesting also the crystalline character on
this small length scale. For the Hf
0.35
C
0.24
N
0.41
coating, also no obvious
amorphous grain boundary phases are visible at a higher resolution (see
Fig. 4f). This is an indication, that carbon and nitrogen are sharing the
octohetral sites on the non-metal sublattice, and may minor amorphous
CNx regions are formed as suggested by further studies [45] on TMC
based caotings (reporting access carbon accumalated on grain bound-
aries in nano-composite morphologies). However, with respect to the
access non-metal species in the observed chemistry – and limited ex-
perimental proof – we have to admit, that detailed analysis, e.g. using
XPS, could draw a more clear picture about the grain boundary mor-
phology (e.g. very thin CN
x
interface phases) at this nano-scale level.
The obtained experimental findings on the structural evolution of
Hf-C-N were also verified by DFT calculations applying VASP. Fig. 5a
shows that the Energy of formation (E
f
) lowers with increasing nitrogen
content on the non-metallic sublattice, x (HfC
1-x
N
x
), suggesting stabi-
lization of HfeN based structures (using PBE potentials). Compared to
calculations for the TaC
1-x
N
x
system [16] the decrease in E
f
and hence
the driving force to form nitrogen-rich compounds is much stronger for
HfC
1-x
N
x
. This might be the reason why we observed such a high affi-
nity of incorporating nitrogen during the reactive sputter process. Va-
cancies (vacancy concentration of 6% on the corresponding sublattice)
only slightly influence the phase formation of HfC
1-x
N
x
structures as the
defect-free cells are preferred over the full compositional range – please
compare open with half-filled and full squares in Fig. 4a, respectively.
Nevertheless, Carbon-rich compositions are more prone to non-metal
vacancies, whereas HfN prefers metal vacancies. Fig. 5b presents the
lattice parameter with respect to the sublattice occupation, x, applying
LDA and PBE exchange-correlation potential (xc). The lattice parameter
decreases with increasing nitrogen content as it was also observed in
the XRD analysis of the thin films. Both potentials result in the same
trend but with different absolute values. The calculated lattice para-
meters are compared with lattice parameters determined by XRD (open
diamonds, green) using a LaB
6
standard powder as a reference. Based
on simplifications, we used the sublattice occupation x = N/(C + N)
for the experimental compositions to compare the calculated with the
experimental lattice constants. Nevertheless, the experimental trend
matches the PBE lattice parameter quite well. The lattice constants of
the XRD references, 4.63 Å [48] and 4.51 Å [47] for HfC and HfN,
respectively, are exactly in-between the values obtained by LDA (HfC
a
c
= 4.58 Å, HfN a
c
= 4.46 Å) and PBE (HfC a
c
= 4.65 Å, HfN
a
c
= 4.54 Å).
As already mentioned above, the mechanical properties, especially
hardness and elastic modulus, of transition metal carbides and nitrides
are strongly influenced by their VEC – obtaining a maximum at VEC of
8.4 e/f.u. This correlation was proven for TiC
1-x
N
x
, but still, some
Fig. 3. Structure evolution with increasing nitrogen content for tilted (a) and
parallel (b) target to substrate configuration. Spectra are obtained from pow-
dered coatings. The reference fcc-structured HfeC and HfeN pattern are taken
from [47,48].
T. Glechner, et al. Surface & Coatings Technology 399 (2020) 126212
4

questions arise for specific systems with respect to the way how the VEC
(e.g. through vacancies) is achieved [13,10,17]. However, a correlation
between the fracture tolerance and VEC, and specifically the nitrogen
sublattice occupation in transition metal carbide-based materials, is
rare. Therefore, this work gives additional information on how the
sublattice occupation, hence the VEC, affects the ductility in HfC
1-x
N
x
.
To develop this correlation, we compared the semi-empirical criteria B/
G ratio (Pugh-ratio) [49] as well as Pettifor's Cauchy pressure (C
12
-C
44
)
[50] with experimentally evaluated fracture characteristics. In addi-
tion, Niu et al. proposed recently a universal ductile to brittle criterion
((C
12
-C
44
)/E) [51]. Fig. 6a gives the Bulk, B (open squares), and Shear
modulus, G (half-filled squares) – on which base the Pugh-ratio is cal-
culated – in comparison to literature data (open stars) [13]. The bulk
modulus is in good agreement with the endpoints provided by the lit-
erature. Furthermore, the increase in B accompanied by a decrease in G
suggests higher Pugh-ratios. In Fig. 6b C
12
-C
44
and (C
12
-C
44
)/E are
plotted over the VEC, whereby more positive values (above the Pettifor
criterion) indicate a more ductile character. The criteria result in the
same trend with a small decrease in ductility for VEC = 8.25 e/f.u.
(x = 0.25), followed by a subsequent increase with increasing nitrogen
content (VEC). However, for all compositions, we are below the Pettifor
criterion and hence in the so-called brittle regime.
Comparing the Pugh-ratio of the group IV TM‑carbonitride, HfC
1-
x
N
x
, with the group V TM‑carbonitride, TaC
1-x
N
x
[16], with experi-
mentally obtained K
IC
values emphasizes an almost continuous increase
in ductility with increasing VEC, see Fig. 7. Here the fracture toughness,
K
IC
, is plotted on the left y-axis in relation to the VEC and compared
with the B/G ratio plotted on the right y-axis for HfC
1-x
N
x
(open
squares) and TaC
1-x
N
x
(open circles), respectively. This is in excellent
agreement with calculations from Ref. [13] indicating a positive effect
on the fracture characteristics for VEC up to 10. All indicated toughness
Fig. 4. Cross sectional bright images of Hf
0.43
C
0.57
(a) as well as a dark field micrograph of Hf
0.35
C
0.24
N
0.41
(d), respectively (films depsoted on Si substrates). The
corresponding SAED analysis to Hf
0.43
C
0.57
and Hf
0.35
C
0.24
N
0.41
are given in (b) and (e), respectively. Bright field images with higher resolution (c) and (f) provide a
closer look at the column boundaries of the respective coatings. In (c) column boundaries are marked with dashed lines and the insets show the FFTs of the
corresponding columns.
Fig. 5. (a) Trend of the calculated E
f
over the nitrogen sublattice occupation, x,
for perfect and defected supercells. Defect-free cells possess the lowest E
f
and
are therefore most preferred. (b) Comparison of the two used xc potentials LDA
(open cubes) and PBE (open circles) based on the lattice parameter, a
c
. The
calculated values are furthermore compared with the experimentally de-
termined ones (open diamonds) from XRD and references (star symbols)
[47,48].
T. Glechner, et al. Surface & Coatings Technology 399 (2020) 126212
5

values, K
IC
, have been obtained by equal single cantilever beam
bending tests (values obtained for at least 5 or more beams). Values for
the Ta-C-N system are taken from a previous study [4]. Here the authors
want to highlight, that the VEC of all compounds denotes the valence
electrons per unit cell as commonly reported in the literature for these
compounds [10] only taking into account the carbon substitution with
nitrogen in the metal-normalized notation (HfC
1-x
N
x
and TaC
1-x
N
x
).
Therefore, sub-stoichiometries are more or less neglected within this
depiction. For both systems, the introduction of nitrogen increases the
fracture toughness following the theoretical predictions. The fracture
toughness of the HfC
1-x
N
x
increases from 1.89 ± 0.15 to
2.33 ± 0.18 MPa·m
1/2
for Hf
0.43
C
0.57
and Hf
0.35
C
0.30
N
0.35
respectively.
The experimentally observed slight increase for HfC
1-x
N
x
also fits the B/
G prediction, as the ratio is growing slower with VEC compared to TaC
1-
x
N
x
. However, the effect of grain size and sub-stoichiometry is neglected
here and therefore an absolute comparison is difficult.
To further validate the quality of the theoretically evaluated elastic
constants (e.g. B or G), we compare the calculated Young's Modulus
with the experimentally determined mechanical properties, especially
Indentation Modulus, of the deposited thin films in Fig. 8a. Hardness
and indentation modulus were measured on sapphire substrates
whereas residual stresses were evaluated on silicon substrates. The
predicted Young's Modulus is in good agreement with the measured
Indentation Modulus values – see Fig. 8a. For Carbon-rich composition,
the slight deviation – also compared to literature data [13,22,52,53] –
may be related to the deviations in sub-stoichiometry for the binary Hf
1-
y
C
y
system. Nevertheless, the trend follows the already observed results,
suggesting moderately reduced Young's modulus with increasing ni-
trogen contents. In contrast to that, the hardness, see Fig. 8b, starts with
a slight increase from 37.8 ± 2.1 to 39.9 ± 2.7 GPa for Hf
0.43
C
0.57
to
Hf
0.35
C
0.30
N
0.35
, respectively. When the nitrogen content is further in-
creased the hardness drops to 33.6 ± 1.9 GPa for Hf
0.32
C
0.20
N
0.48
. The
residual stress – as plotted in Fig. 8b right y-axis – decreases from
−3.2 GPa to −2.1 GPa for x = 0 to x = 0.70, respectively. It follows a
different trend than the hardness, which we suggest is due to the
bonding nature and not the residual stress, assuming that the residual
stress state follows the same trend for the films grown on both sapphire
and on silicon substrates. However, we have to mention that: (i) the
residual stress states may follow a different trend in the samples grown
on sapphire (from which hardness data is extracted) from those grown
on silicon substrates and (ii) even if the stress states were to follow the
same trend for the films on both sapphire and silicon, differences in
grain sizes and film textures on sapphire and silicon can lead to dif-
ferent trends in hardness of films on sapphire and silicon substrates.
Neverthelss, the higher compressive stresses are also in good agreement
to the increased deposition rates for Nitrogen poor gas mixture.
As already mentioned, Nitrogen alloying in the HfeC system is
predicted to increase the melting temperature [20]. To investigate the
potential change in the mechanical properties of the HfeC and Hf-C-N
coatings due to thermal loading, we performed different annealing tests
Fig. 7. Empirical criterion for ductility, Pugh ratio (B/G), for Group IV (Hf) and
Group V (Ta) TM-Carbonitrides with respect to the VEC [4]. These calculations
are compared with experimentally determined K
IC
values – open square denotes
to Hf and open circles to the Ta based systems, respectively. All experimental
data analysis were done on Si substrates, with growth temperatures of 415 °C
for the Hf-based and 450 °C for the Ta-based films, respectively.
Fig. 8. (a) Experimentally determined Indentation Modulus in relation to the
sublattice occupation in comparison to DFT based Young's Modulus values and
literature data for HfC and HfN [13,22,51,52] (star symbols). (b) Hardness
(open squares) and residual stress (open diamonds) as a function of x (N/
(C + N)) in comparison with hardness values from literature [22,51,52] (star
symbols). The indentation analysis was performed on Si substrates deposited in
the tilted set-up at 415 °C.
Fig. 6. (a) Bulk modulus (B) and shear modulus (G) as a function of the ni-
trogen sublattice occupation, x, and hence VEC. (b) Cauchy pressure (C
12
-C
44
)
and (C
12
-C
44
)/E in relation to the sublattice occupation with indicated Pettifor
criterion – (C
12
-C
44
) > 0 is expected to be ductile. Star symbols represent
literature [13] values for B and C
12
-C
44
.
T. Glechner, et al. Surface & Coatings Technology 399 (2020) 126212
6

and subsequent mechanical characterization, see Fig. 9a and b. We
annealed the thin films deposited on sapphire in a vacuum furnace at
600 °C, 800 °C, 1000 °C, and 1200 °C. We observed no visible change in
the color of the thin films after annealing up to 800 °C. Beyond this
temperature, we observed a change in color towards more greenish or
blueish. Furthermore, delamination occurred for the Hf
0.43
C
0.57
coating
at 1200 °C. However, we assume that in this case, the delamination took
place because of the reduced adhesion to the substrate, assumed to be
due to high compressive stresses. For all composition tested, the hard-
ness remains almost constant until 800 °C followed by a decrease at
higher temperatures. With increasing nitrogen content, the slope for
decreasing hardness levels out, and HfC
1-x
N
x
exhibits a higher hardness
after annealing. For example, the initial hardness value for Hf
0.43
C
0.57
is
37.8 ± 2.1 GPa and after annealing at 1000 °C, it reduces to
25.2 ± 1.3 GPa, whereas for Hf
0.35
C
0.24
N
0.41
the hardness is
37.9 ± 2.4 GPa and after annealing to 1000 °C it settles at
33.0 ± 1.7 GPa, respectively. For all Hf-C-N coatings, the Young's
modulus stays approximately constant over the annealing temperature.
5. Conclusion
We investigated the influence of nitrogen alloying on the synthesis,
structure, and thermomechanical properties of magnetron sputtered
HfeC thin films. The influence of the non-metallic sublattice occupation
x = N/(C + N) – hence the variation of the valance electron con-
centration – on structural and mechanical properties, was studied both
theoretically as well as experimentally. The thin films were deposited
by non-reactive and reactive magnetron sputtering from a ceramic
HfeC target. Already at low nitrogen partial pressures, we obtained a
high nitrogen content within the coatings, which was even intensified
by a lower substrate temperature as well as power density. Therefore,
only compositions with x above 0.50 could be deposited. All HfeC and
Hf-C-N coatings exhibit a single-phase fcc structure with dense co-
lumnar morphologies. DFT based calculations on the lattice constants –
decrease from a
c
= 4.65 Å for HfC to a
c
= 4.54 Å for HfN – are in
excellent agreement with experimental values a
c
= 4.67 Å for
Hf
0.43
C
0.57
and a
c
= 4.61 Å for Hf
0.35
C
0.30
N
0.35
(x = 0.54,
HfC
0.46
N
0.54
), respectively. In addition, the predicted elastic constants –
B/G ratio as well as Cauchy pressure – also suggest a more ductile
character with increasing nitrogen content, implying an increased VEC.
This prediction could be also validated experimentally with an increase
in fracture toughness from 1.89 ± 0.15 to 2.33 ± 0.18 MPa·m
1/2
for
Hf
0.43
C
0.57
to Hf
0.35
C
0.30
N
0.35
, respectively. As the VEC ranges between
8.0 e/f.u. to 9.0 e/f.u. for HfC
1-x
N
x
based composition the increase is
moderate, as an optimum VEC is suggested slightly below 10. The
measured hardness exhibits a maximum of 39.9 ± 2.7 GPa for
Hf
0.35
C
0.30
N
0.35
. The Young's modulus ranges from 532 to 426 GPa for
Hf
0.43
C
0.57
and Hf
0.32
C
0.20
N
0.48
, respectively. The compressive stress
state decreases (−3.2 to −2.1 GPa for x = 0 up to 0.70) with in-
creasing nitrogen content. Nevertheless, we want to mention, that these
mechanical enhancements need to be seen in correlation also with
morphological changes – which were not clearly observable within this
study – and therefore related to the VEC. Furthermore, the non-metal
alloying of nitrogen increases the hardness of Hf-C-N coatings after
annealing to a maximum of 25.4 ± 1.7 GPa for Hf
0.35
C
0.24
N
0.41
at
1200 °C. In summary, the obtained results indicate the correlation of
fracture characteristics and valence electron concentration for transi-
tion metal ceramics – such as HfeC or Hf-C-N. Furthermore, the great
potential of Hf-C-N coatings – for well-defined deposition conditions to
reach the desired C to N ratios could be validated for its thermo-
mechanical properties.
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.surfcoat.2020.126212.
CRediT authorship contribution statement
T. Glechner:Conceptualization, Software, Investigation, Writing -
original draft.S. Lang:Investigation.R. Hahn:Investigation, Writing -
review & editing.M. Alfreider:Investigation.V. Moraes:Investigation.D.
Primetzhofer:Investigation.J. Ramm:Writing - review & editing.S.
Kolozsvári:Resources.D. Kiener:Investigation.H. Riedl:Supervision,
Conceptualization, Writing - review & editing, Project administration.
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influ-
ence the work reported in this paper.
Acknowledgments
The financial support by the Austrian Federal Ministry for Digital
and Economic Affairs and the National Foundation for Research,
Technology, and Development is gratefully acknowledged (Christian
Doppler Laboratory “Surface Engineering of high-performance
Components”). We also thank for the financial support of Plansee SE,
Plansee Composite Materials GmbH, and Oerlikon Balzers, Oerlikon
Surface Solutions AG. In addition, we want to thank the X-ray center
(XRC) of TU Wien for beam time as well as the electron microscopy
center - USTEM TU Wien - for using the SEM and TEM facilities. The
computational results presented have been achieved using the Vienna
Scientific Cluster (VSC). The authors acknowledge the TU Wien
Bibliothek for financial support through its Open Access Funding
Program.
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