Powder Metallurgy Progress, Vol.13 (2013), No 3-4
132
THE EFFECT OF RESIDUAL STRESSES ON NANOINDENTATION
BEHAVIOR OF THIN W-C BASED COATINGS
M. Novák, F. Lofaj, P. Hviščová
Abstract
The work investigates the effect of compressive residual stresses
generated in thin W-C based coatings during DC magnetron deposition
process on nanohardness (HIT) and indentation modulus (EIT). It was
discovered that the hardness values increase approximately linearly from
16.5 to 19.5 GPa with an increase of the compressive residual stresses
from 1.5 to 4.5 GPa. This hardness increase results from the presence of
mostly intrinsic compressive residual stresses induced into the coating
during the deposition process while the influence of thermal stresses is
negligible. Simultaneously, an inverse effect of coating thickness on
residual stresses was observed. The indentation modulus exhibits no
dependence on residual stresses and coating thickness however.
Apparently, the coatings studied have a standard microstructure because
no hardness increase due to nanocomposite structure was obtained.
Keywords: residual stresses, nanohardness, indentation modulus, thin
coatings
INTRODUCTION
In many bulk materials, tensile or compressive stresses may be presented. Thin
films or coatings on different substrates are often also in a stressed state. The stresses
present in thin films and/or in coatings may be tensile or compressive and within the range
of several GPa. One of the principal reasons for a coating to be in a stressed state is a
deposition at a higher temperature than the temperature at which the stress is measured. The
stress arises due to the difference in thermal expansion coefficients between the coating and
substrate. In addition to this, thermal residual stress, intrinsic residual stresses may be also
present [1-3]. Intrinsic stresses are induced by external factors during the deposition process
and they vary during the film growth. Compressive intrinsic stresses in thin coatings can be
generated by the ions or atoms that arrive at the growing film with energies above the
lattice displacement energy (10 – 30 eV) [1,2,4,5] due to the atomic peening mechanisms. It
is an important source of the stress in sputter – deposited films growing under low –
mobility conditions [1,3,5,6]. The contribution of the peening mechanisms depends
strongly on the sputtering pressure. It dominates at low sputtering pressures, where the high
energetic particles hit the coating surface directly. At larger sputtering pressures, multiple
collisions with gas atoms and molecules during their flight cause gradual loss of their
kinetic energy. When the particles arrive at the surface, they are already thermalized, thus
hardly generating defects leading to compressive stress.
Michal Novák, František Lofaj, Slovak University of Technology in Bratislava, Faculty of Materials Science and
Technology in Trnava, Bottova 25, 917 02 Trnava, Slovak Republic
Michal Novák, František Lofaj, Petra Hviščová, Slovak Academy of Sciences, Institute of Materials Research,
Watsonova 47, 04001 Košice, Slovak Republic
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Powder Metallurgy Progress, Vol.13 (2013), No 3-4
The works of Abermann and others [5-9] demonstrated strong correlation between
the stress evolution and mobility of the deposited species and dependence on the growth
mechanisms of polycrystalline metal films: [5,6,10] low-mobility Frank – van der Merve
[5] or high-mobility Volmer - Weber mechanism [5,6], each characterized by specific
morphology and stress behavior. In the coatings with high – mobility atoms at room
temperature, such as Cu or Ag, the average stresses become compressive. The asymptotic
value is on the order of ~ 100 MPa. Since the biaxial modulus is on the order of ~ 100 GPa,
a stress of this magnitude is achieved by the incorporation of one atom among 1000 atoms
[4, 11-13]. These stresses are around 2 orders of magnitude smaller than the stresses in the
range of several GPa measured in thin coatings. Thus, intrinsic stresses are controlled by
peening rather than by high – or low – mobility growth mechanisms.
One of the techniques suitable for fast measurement of residual stresses in thin
coatings is the substrate curvature change method [14]. The principle is to measure the
radius of curvature of the substrate prior to and after the deposition. Residual stress is
determined from the Stoney equation (1).
2
1
E
 ts 
r 
1   6t f R
(1)
where E is the elastic modulus of the substrate,  is the Poisson ratio of the substrate, ts is
the thickness of the substrate, tf is the thickness of the film and R is the radius of substrate
curvature.
It is well known that the residual stresses presented in thin coatings may seriously
affect the nanoindentation data [1, 11-13, 15]. A linear increase of nanohardness as the
function of residual stresses was usually reported. Some authors [11,13,15] also
investigated the correlation between the residual stresses and the thickness of the coatings.
They found out that the residual stresses decrease with the increase of the coating thickness,
i.e., stress relaxation occurs in thicker films. However, these studies were done on TiN,
CrN and ZrN coatings and the effects of thermal and intrinsic residual stresses on
nanohardness were not separated. Hence, the aim of this paper is to find the correlation
between the coating thickness, residual stress and nanohardness (HIT) and indentation
modulus (EIT) in thin W-C based coatings with possible nanocomposite structure, which
may have a hardness significantly increased by their nanosized W-C grains. The separation
of the contributions of residual stresses and nanostructure is therefore crucial for
understanding the contributions of nanocomposite structure and residual stresses.
EXPERIMENTAL PROCEDURE
Ten samples of thin nanocomposite coatings were deposited by DC magnetron
sputtering from 75 mm WC target on microslide glasses using the identical deposition
parameters. Based on the previous optimization results [16,17], the power on a target was
kept at 150W, working pressure was 0.25 Pa and the duration of the deposition process was
20 minutes. Acetylene was used as a reactive gas and an additional source of carbon. The
thickness of the coatings was measured using an optical profilometer (Sensofar Plu Neox)
in an interferometric regime. The thickness of the coating is evaluated across the sharp edge
between the coating and the substrate surface. The edge was obtained after the removal of
the Capton foil glued on the substrate surface prior to deposition. The thicknesses of the
coatings were in the range from 500 to 600 nm. Residual stresses were determined from the
change of substrate curvature using an optical bench, Fig.1 [14].
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Powder Metallurgy Progress, Vol.13 (2013), No 3-4
Fig.1. Principle of the substrate curvature measurement using optical bench.
The principle of the substrate curvature change method is based on the
measurement of the focal distance of the reflected beam. The change of the curvature of the
substrate is determined from the difference between the focal positions prior to and after the
deposition. The radius of curvature is determined from the following equation:
f
2
(2)
 f a

where R – radius of the curvature, f – focal distance of the objective, Δ – focal position
change, a – distance of the sample from the focal lens. The obtained radius is introduced to
eq. (1) to calculate the residual stress.
Nanoindentation measurements were performed using nanohardness tester G200
(Agilent Technologies) and the continuous stiffness measurement (CSM) method with a
sinusoidal loading cycle. The measurements were performed using the constant strain rate
(CSR) loading regime with a frequency of 45 Hz and depth modulated sinus amplitude of 2
nm. For a better statistics, 25 indentations were performed on each coating.
R
RESULTS
The measured residual stresses were compressive in all cases and they were in the
range from 1.5 GPa to 4.5 GPa. As the film becomes thicker, the compressive stresses
decreased linearly within the studied range of thicknesses (520 – 610 nm). Figure 2
describes the dependence of residual stress decrease with the increase of the coating
thickness.
Linear regression equation:
Y = 649.894 - 32.005*X
Residual stress (GPa)
4.5
4.0
3.5
3.0
95% upper confidence limit
2.5
2.0
95% lower confidence limit
1.5
480
500
520
540
560
580
600
620
640
Thickness (nm)
Fig.2. The influence of thickness on residual stress in thin based W-C coatings.
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Powder Metallurgy Progress, Vol.13 (2013), No 3-4
The corresponding nanohardness values varied from 16.5 up to 19.5 GPa. As
indicated in Fig.3a, nanohardness increases approximately linearly as a function of the
corresponding compressive residual stresses.
a)
b)
Fig.3. The influence of residual stresses on nanoindentation behavior in thin W-C coatings
(a – nanohardness, b – indentation modulus).
The slope of the linear regression is close to unity. It means that practically all
increase of residual stresses is transferred into an increase of HIT. In contrast, the
indentation modulus remained the same at a value of about 185 GPa with the scatter 10 –
15 GPa (Fig.3b).
a)
b)
Fig.4. a) The indentation hardness and b) the indentation modulus as a function of coating
thickness.
Since residual stresses depend on the coating thickness, an inverse correlation
between hardness and coating thickness via residual stresses can be expected. Indeed, the
linear decrease of the nanohardness with a thickness increase was obtained (Fig.4a).
Because the indentation modulus is not sensitive to the stresses, it remains approximately
the same in the range of study thicknesses (Fig.4b).
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136
DISCUSSION
Figures 3 and 4 suggest that the presence of compressive residual stresses in the
studied coatings strongly influence nanohardness, which is in agreement with the literature
data [10,14,15]. A linear increase of hardness with residual stresses and inverse dependence
on coating thickness was observed earlier by several authors in different systems. For
example, Hernandez et al. [14,15,21] found out that nanohardness in a thin TiN
nanocomposite coating linearly increases with the increase of compressive stress. They
used substrate bias to control the level of residual stresses. The measured residual stresses
were in the range from 300 MPa at floating bias up to 11 GPa at -300 V bias. Nanohardness
varied from 19 GPa up to 30 GPa, respectively.
Such high compressive stresses were not achieved in the studied W-C coatings
because the full delamination occurred already at the stresses >5 GPa and also because only
a floating bias was used during our deposition. The extrapolation of linear fit in Fig.3a to
zero stress suggests that the hardness of stress influence free W-C coating is 14 - 15 GPa.
This is a value range typical for conventional WC coatings and its increase is only due to
residual stresses. No hardness increase due to the possible nanocomposite structure is
observed. This implies, that the structure of the coatings is not nanocomposite and the
residual stresses are the only factors increasing the resulting hardness of the coating.
However, other contributions are theoretically also possible. Meng et al. [15]
investigated the effect of the residual stress on nanohardness in thin magnetron deposited
ZrN coatings and included the pile – up effects into consideration. Depending on the gas
pressure in the chamber, Ar/N2 ratio and substrate bias, they found that the compressive
residual stresses increased from 300 MPa at floating bias up to 3.5 GPa at -100 V bias. The
corresponding nanohardness increased from 27 GPa up to 30.5 GPa linearly with the slope
of 1.2. However, when the contact area under the indenter was recalculated based on AFM
images of the indent to eliminate the contribution of pile – up, the slope was reduced to
approximately 1. It is close to our results and suggests that the pile – up may not be
important in the studied W - C coatings. However, the investigation of the contribution of
pile – up and/or sink – in effects will be the subject of our further study.
The residual stresses in the current W-C coatings on microslide glasses may
consist of thermal and intrinsic residual stresses. The thermal stresses due to different
thermal expansion of the substrate and coating were estimated for ΔT ≈ 100C according to
Eq. (3).
E
(3)
 th  WC   glass  T WC
1  WC
The corresponding thermal expansion coefficients were αglass = 8.10-6 K-1 and αWC
-6
= 5.8.10 K-1, the elastic modulus in these coatings measured by instrumented indentation
was EWC ~ 185 GPa and Poisson ratio was υWC = 0.24 [17,18,20]. Calculated thermal stress
is ~60 MPa. Because the measured residual stresses ranged from 1.5 up to 4.5 GPa, the
value of thermal stresses is negligible. Subsequently, the intrinsic residual stresses have to
be in the range from 1.4 GPa up to 4.4 GPa, which is the dominant contribution similarly,
as it was observed in Cr – N coatings [18,21]. The intrinsic stresses seem to result mainly
from peening, because growth mechanisms generate stresses comparable to low thermal
stresses.
Figure 2 describes the progress of residual stresses presented in thin W-C coating
as a function of coating thickness. Extrapolation to the stress free hardness value of 14.5
GPa implies that the effect of residual stresses is fully eliminated in the coatings thicker
than 650 nm. Such a finding is supported by the observations in other systems. Hernandez


Powder Metallurgy Progress, Vol.13 (2013), No 3-4
137
et al. [21] found out that the stresses presented in TiN thin coating decrease from 11 GPa
down to approximately 300 MPa with the thickness increase from 2600 nm up to 3300 nm.
The decrease in the compressive stress could be due to the formation of the layered
structure or enhancement of the atom mobility [5,10,21]. The explanation of these effects is
supported by bombardment influences of energetic particles on the temperature of the
growing film. It enhances the surface mobility of the condensed species, promoting the
displacement of surface atoms towards more stable positions in terms of surface energy. It
results not only in the elimination of voids, cavities, and vacancies in the coatings but also
in the ability of stress relaxation [5,15,19]. This seems to be applicable also to our case.
When the temperature reaches a limit when stress fully relaxes, no dependence on coating
thickness is expected. Because the range of coating thicknesses studied was very narrow
(500 – 600 nm), only the linear dependence of stresses was observed. A thickness of at least
650 nm is necessary to accumulate enough energy from impigning particles for stress
relaxation. It can be expected, that the increase of the particle energy will shift this
“relaxation” thickness to lower values.
CONCLUSIONS
It was discovered that the residual stresses in thin W-C coatings decrease with the
increase of the coating thickness, and they simultaneously cause an approximately linear
increase of nanohardness. This increase seems to result only from the presence of the
intrinsic compressive residual stresses induced into the coating surface during the
deposition by peening mechanism while the contribution of thermal stresses is negligible.
The minimum thickness to obtain stress – free W – C coatings is around 650 nm while the
corresponding stress – free nanohardness in the range ~ 14.5 GPa is excepted. Thus, the
hardness of the studied W – C coatings does not exhibit hardness increase typical for
nanocomposite coatings.
Acknowledgements
The authors are grateful for financial support within the framework of APVV 0520
– 10 and VEGA 2/0098/14 projects.
REFERENCES
[1] Fischer–Cripps, A. In: Nanoindentation. 2nd ed. Springer, 2004, p. 89
[2] Chaudri, MM., Philips, MA.: Phil. Mag. A, vol. 62, 1990, no. 1, p. 1
[3] Chandrasekar, S., Chaudri, MM.: Phil. Mag. A, vol. 67, 1993, no. 6, p. 1187
[4] Koch, R.: Surf. and Coat. Technology, vol. 204, 2010, p. 1973
[5] Janssen, GCAM.: Thin solid films, vol. 515, 2007, p. 6654
[6] Lee, YH., Kwong, D.: J. Mater. Res., vol. 17, 2002, no. 4, p. 901
[7] Carasco, CA., Vergara, V., Benavente, R., Mingolo, N., Rios, JC., Hernandez, LC.:
Mater. Charact., vol. 48, 2002, p. 81
[8] Abermann, R., Kramer, R., Mäser, J.: Thin Solid Films, vol. 52, 1978, p. 215
[9] Spaepen, F.: Acta Materialia, vol. 48, 2000, p. 31
[10] Quaeyhaegens, C. Knuyt, G., Stals, LM.: J. Vac. Sci. Technol. A, vol. 14, 1996, p.
2462
[11] Dean, J., Aldrich–Smith, G., Clyne, TW.: Acta Materialia, vol. 59, 2011, p. 2749
[12] Lepienski, CM., Pharr, GM., Park, YJ. et al.: Thin Solid Films, vol. 447–448, 2004, p.
251
[13] Kese, K., Tehler, M., Bergman, B.: J. Eur. Cer. Soc., vol. 26, 2006, p. 1003
[14] Lalinský, T., Držík, M., Chlpík, J., Krnáč, M., Haščík, Š., Mozolová, Ž., Kostič, I.:
Powder Metallurgy Progress, Vol.13 (2013), No 3-4
138
Sensors and Actuators A, vol. 123-124, 2005, p. 99
[15] Meng, QN., Wen, M., Hu, CQ., Wang, SM. et al.: Surf. and Coat. Technology, vol.
206, 2012, p. 3250
[16] Hviščová, P., Lofaj, F., Novák, M.: Powder metallurgy progress, vol. 3, 2013, In press
[17] Hviščová, P., Lofaj, F., Novák, M.: Key Engineering Materials, 2014, In press
[18] Abadiasa, G., Guerin, P.: Appl. Phys. Lett., vol. 93, 2008, 111908:1
[19] Benegra, M., Lamas, DG., Fernandez, R., Mingolo, N., Kunrath, AO., Souza, RM.:
Thin Solid Films, vol. 494, 2006, p. 146
[20] Harper, CA. In: Handbook of ceramics, glasses, and diamonds. Chapter 1. New York :
McGraw Hill Editorial, 2001, p. 42
[21] Hernandéz, LC., Ponce, L., Fundora, A., López, E., Pérez, E.: Materials, vol. 4, 2011,
p. 929