The effects of hydrogenated carbon films with different film thickness and nitrogen content on specimen mechanical properties, scratch critical load, adhesion work and tribological behavior

Diamond & Related Materials 13 (2004) 1895 – 1906 www.elsevier.com/locate/diamond

The effects of hydrogenated carbon films with different film thickness and nitrogen content on specimen mechanical properties, scratch critical load, adhesion work and tribological behavior Jen-Fin Lin a,*, Chin-Chung Wei a, Yuan-Kei Yung a, Chi-Fong Ai b a

Department of Mechanical Engineering, National Cheng Kung University, No. 1, Ta-Hsueh Road, Tainan 701, Taiwan b Physics Division, Institute of Nuclear Energy Research. P.O. Box 3 – 4, Lung Tan 325, Taiwan Received 14 November 2003; received in revised form 14 June 2004; accepted 14 June 2004 Available online

Abstract The contact mechanics developed for a sphere in contact with a flat plane is employed in this study to obtain the stress functions distributing in the elastic and plastic-deformation regions formed in a specimen with a hydrogenated carbon film. These stress functions are then used in the evaluation of the adhesion work of the specimen. All coating films using a silicon wafer as the substrate were prepared by differing the film thickness and the volume fraction of nitrogen in the gas mixture of (N2 + C2H2) during the deposition process. The critical load of a specimen with a coating film can be determined from a scratch test on a nanotester. The proportional relationship of the adhesion work and the critical load is found to be valid only for the specimens having the same film thickness and the same nitrogen content in the coating film. Nanoindentation tests have been carried out on a nanotester to obtain the Young’s modulus of all specimens. The wear volumes of all specimens were also obtained from the nanoscratch tests under various operating conditions. The wear volume results are then tried to establish their connection with the parameters including adhesion work, Young’s modulus and operating conditions. The behavior analysis indicates that the adhesion work of a specimen is not the unique factor to the wear volume; the mechanical properties of a specimen and the operating conditions are also involved as dominant factors. The elevation in either the adhesion work or the Young’s modulus is helpful for the reduction of the wear volume. D 2004 Elsevier B.V. All rights reserved. Keywords: Hydrogenated carbon films; Film thickness and nitrogen content; Young’s modulus; Adhesion work; Critical load; Wear volume

1. Introduction The scratch-test method is being increasingly used to evaluate coating adhesion. The test consists of a stylus, which is drawn over the sample surface under a normal force, which is increased either stepwise or continuously until the coating becomes detached. The normal force at the moment of coating detachment is called the critical load and gives a comparative value of coating adhesion. Modern coating techniques now offer the possibility of detecting the degree of adhesion between the coating and its substrate. In Rickerby’s study [1], several methods, which can be used to assess the critical property of the coating – substrate system, have been discussed; the advantages and disadvantages of each technique were reviewed. The devel* Corresponding author. Tel.: +886-6-2757575; fax: +886-6-2352973. E-mail address: [email protected] (J.-F. Lin). 0925-9635/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.diamond.2004.06.011

opment of the scratch-test method of adhesion assessment was reported in the study of Valli et al. [2]. The aim of their work was to investigate further the practical basis of the scratch test by considering a number of coating/substrate materials, and particularly, to ascertain the relevance of friction in the generation and detection of coating failure. Jacobson et al. [3] use friction measurement in connection with the scratch test to measure the differences in coating adhesion. They noticed that the friction force was unstable when the coating adhesion was poor. Laugier [4] had calculated some adhesion values and confirmed that friction should have an important role in the scratch tests. The work of Richard et al. [5] proposed a combination of the scratchtest technique and the acoustic microscopy image for the study of adhesion of thick ductile coatings. It is the technique capable of imaging the interface defects. In the study of Hedenqvist et al. [6], scratch tests were performed on TiN-coated steel substrates with various

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coating thicknesses and substrate hardnesses; four groups of coating damage and detachment mechanisms were identified. The maximum normal force that the coating – substrate composite could sustain is increased with increasing coating thickness and substrate hardness. It is well known that a range of possible failure modes can occur in the search tests, and only some of these are dependent upon adhesion; other failure modes which depend on plastic deformation and fracture within the coating film may be just as useful in the assessment of coating quality for tribological applications [7]. Chemically vapordeposited and physically vapor-deposited coatings of hard and wear-resistant materials were prepared in the study of Hintermann [8]. The life of the coated tools or machine elements as well as their performance are considerably increased, provided that the adhesive strength of the coating of the substrate and the intrinsic cohesion of the coating are sufficient. Bed adhesion loads to flaking, while poor cohesion causes chipping. The effect of the interface topography, coating thickness and elastic mismatch on the interfacial stresses was investigated in the study of Wiklund et al. [9]. Generally, thin coatings, compared to the interface topography, are less sensitive to residual stress-induced failure. At a critical coating thickness, normal stress across the interface of a magnitude comparable to that of the residual stress level is induced, which may initiate coating delamination. In the study of Lhermitte-Sebire et al. [10], the results of the scratch tests show that the adhesive bond of much higher strength is the mixed adhesive –cohesive type. The effect of coating film thickness on adhesion strength has been investigated by Hedenqvist et al. [6] and Perry [11]. The adhesion strength was elevated by increasing the film thickness. The critical load of a coating– substrate interface determined by the scratch test depends not only on the adhesion, but also on the substrate hardness and coating thickness [12]. The critical load determined by the scratching test is widely regarded as representative of coating adhesion. However, it remains difficult to express quantitatively the adherence because the critical load depends on several parameters related to the testing and to the coating – substrate system [13]. Both intrinsic parameters, such as scratching speed, loading rate, diamond tip radius and diamond wear, and extrinsic parameters, such as substrate hardness, coating thickness, substrate and coating roughness and friction coefficient, are considered in order to improve the interpretation of the critical load results. Amorphous carbon coatings prepared by four deposition processes and with thicknesses ranging from 20 to 400 nm were studied in the use of nanoscratch to investigate the critical load varying with the film thickness [14]. The thinner thickness exhibited instant damage when the normal load exceeded the critical load, whereas thicker coatings exhibited gradual damage through the formation of tensile cracks.

In the results of Laidani et al. [15], the adhesion properties and scratch hardness were studied using the scratch test for carbon and zirconia’s films with a comparable stored elastic strain energy. The residual internal stress and Young’s modulus were investigated. Different adhesion failure mechanisms appeared of either a cohesive nature or a high internal stress relief. Observations with respect to the cracking of hybrid organic– inorganic coatings were reported in the study of Malzbender and de With [16]. The films showed cracks above a critical thickness and delaminated largely from the substrate. Thicker films had a higher initial stress associated with a larger number of cracks. An energy criterion has recently been proposed for the onset of coating removal, which is applicable to both ductile and brittle coating materials [17]. Debonding requires the application of an interfacial shear stress of a critical value, representative of the coating adhesion. However, coating removal will not occur unless the associated strain-energy release rate is at least equal to the work of adhesion. A model in the study of Venkataraman et al. [18] has been developed to determine the work of adhesion of the Pt/NiO system. This model used an elastic contact mechanics to approach the strain energy released during film delaminating. Relationships used to evaluate the shear stress required for film-substrate failure and the ‘‘work of adhesion’’ concept were reviewed by Coghill and Stjohn [19]. In general, the critical load of a specimen with a coating film is not a constant; rather it varies with the operating conditions applied in the scratch tests. However, the experimental data indicate that adhesive strength determined by this method is varying with mechanical properties and is independent of operating conditions. The purpose of this study is to evaluate the adhesion work of a specimen with a coating film first; then, it will investigate the correlation of the adhesion work with the critical load obtained from the scratch test. The second purpose is to establish the correlation of the wear volumes of a specimen produced in the tribological test with either the adhesion work or the critical load. All specimens in the present study were prepared using the silicon wafer as the substrate and depositing an amorphous hydrogenated carbon film as the coating layer. These coating films were formed by differing the coating film thickness and the nitrogen content in the coating film. The mechanical properties such as the hardnesses and the Young’s modulus of these specimens could be obtained from the nanoindentation tests. Then the Young’s modulus of the coating film was used in the evaluation of the adhesion work of a specimen. The critical load results attained from the nanoscratch tests are tried to establish their correlation with the adhesion work results. The wear volumes of all specimens produced in the tribological tests under different operating conditions could be determined. The combined effect of the mechanical properties and the adhesion work of a specimen are used in the interpretation of the wear behavior exhibited in the specimens with

J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

different film thickness or the nitrogen content in the coating film.

2. Theories and experimental details for different tests 2.1. Specimen preparations In the present study, the silicon wafer (p type/orientation: 100) is chosen as the substrate material of the coating films differing in film thickness and nitrogen content. Before depositing the coating film, the 6-in. silicon wafers were cut out to be chips with dimensions of 1
1 cm. The mean surface roughness of the wafer is 0.009 Am Ra. A variety of hydrogenated amorphous carbon films were prepared in a chamber by varying the nitrogen volume fraction in the gas mixture of (N2 + C2H2) during the coating process. Before depositing the coating film, the silicon substrate surface was cleaned by feeding the argon gas into the chamber and sputtering the surface by a nitrogen ion beam. The nitrogen content of the coating film can be varied by changing the volume fractions of nitrogen in the gas mixture of (N2 + C2H2). In the present study, the volume fractions of 0, 25, 40 and 66 vol.% were prepared for each kind of coating film thickness. The coating film thickness can be controlled by varying the deposition time. Five film thicknesses, 70, 100, 150, 200 and 300 nm were prepared for each kind of nitrogen content in the film. The coating processes of these specimens were carried out in the Institute of Nuclear Energy Research using a linear ion beam source (Advanced Energy, USA) in the anode layer type. The advantages of this deposition system include: (1) simple interior structure; (2) high deposition rate; (3) large deposition area; and (4) deposition at low temperature. This deposition system consists of three components: the cathode, the anode and a magnet. The cathode provides two functions: (1) 90 –95% electrons collide with the influent gas to create plasma; (2) the rest of the electrons are used in the neutralization of the ions with a positive charge. The electron sources can be a hot filament or a hollow cathode. The anode voltage was applied to govern the energy of the ion beam. The optimum choice of the anode voltage is made such that the energy of the ion beam is about 60% of the anode voltage. In order to increase the free path and thus the frequency of an ion traveling in the chamber, a magnet is provided such that the electrons are in a spiral motion as subjected to the Lorentz force. The vacuum pressure at the chamber was lowered by two kinds of vacuum pumps such that it finally reached 1
10 6 Torr. When the coating process was started, the substrate was first cleaned by the ion beam with the energy of 250 eV. Then, the film deposition began when the reactive gases combining C2H2 and N2 at different volume ratio were fed into the chamber.

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The atomic concentrations of C, N, O and Si in specimens along the lateral surface measured from the top surface of the coating film have been obtained by Auger electron spectrometer (AES). Fig. 1(a) and (b) shows the two examples with the volume fractions of nitrogen of 25 and 40 vol.%, respectively. The coating film thicknesses of these two specimens are investigated to be near 300 nm. The depth values at which the atomic concentration of Si rises near to 100% are 310 nm in Fig. 1(a) and 290 nm in Fig. 1(b), whereas the depth values at which the atomic concentration of Si drops to 0% are 260 nm in Fig. 1(a) and 270 nm in Fig. 1(b). In the thin region of having the atomic concentration of Si higher than 0% but lower than 100%, the nitrogen concentration in either case is shown to be nonzero. In this case, the surface of the silicon substrate may arise thin hard Si3N4 film that can change mechanical properties of the coating film. For the depths in the region with 0% Si, these two figures show that the atomic con-

Fig. 1. Atomic concentrations of C, N, O and Si from the top surface and along the depth of the specimen. The AES analyses for (a) N25-300 and (b) N40-300 specimens are shown.

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Table 1 Operating conditions for scratch tests Scratch velocity

5, 10 and 15 Am/s

Loading rate

4.19, 1.87, 0.93, 0.52, 0.27 and 0.08 mN/s

centration of carbon is generally higher than that of nitrogen. The small concentration of oxygen observed in our films is attributable to the voids which generally occur in a thin film for oxygen adsorption during post-deposition exposure to atmospheric air. 2.2. Theoretical models and experimental details for scratch tests A qualitative adhesion of a thin hard coating film to its substrate generally can be achieved by scratch tests with the use of a nanotester (Micro Materials, UK) with the scratching function. Two stages of scratching tests were arranged in the present study. In the first stage, the scratching velocities and the loading rates as shown in Table 1 were arranged to meet the requirement in the use of the response surface method to determine the optimum conditions of having the largest critical load. In the second stage, the optimum conditions of the scratching velocity and the loading rate are then used in the scratching tests of the specimens prepared by differing the film thickness and the volume fraction of the nitrogen in the gas mixture of (N2 + C2H2). In the scratch tests, the indenter of the Rockwell C type was used in the indentation tests. The indenter has a conical shape with a spherical tip; the radius of curvature at the tip is 25 Am. The indenter is made of diamond material. The load, at which the onset of coating failure occurs, as demonstrated in the form of cracking, palliation, buckling,

chipping, or the loss of the coating, is defined as the critical load. The onset of failure is thus determined by linking the variations of indentation load and indentation depth and the frictional force. Fig. 2 shows an example to indicate the behavior arising at the critical load. The plot shows that a sharp rise in the frictional force is identified to be the incipient point of the critical load. The operating conditions of the loading rate and the scratching velocity applied in the scratch tests are fixed in the present study. The surface response method [20] was applied here to determine a curved surface to fit the experimental results of critical load, which were obtained from 18 sets of operating conditions as shown in Table 2. The normalized X parameter is here defined as X=(scratch velocity  (15 + 5)/2)/(15  5), whereas the normalized Y parameter is defined as Y=(loading rate  (4.19 + 0.08)/2)/ (4.19  0.08). Then the curved surface (Z) which can fit these 18 critical load results is expressed as Z(critical load) = 110.8291 + 119.1569Y + 13.6905X  159.0244Y2 + 43.3437XY  20.0300X2. Then, the operating conditions corresponding to the largest critical load can thus be obtained in the use of this Z expression. The operating conditions of having a scratch velocity of 18.75 Am/s and a loading rate of 4.1648 mN/s are predicted theoretically by this method to have the largest critical load for the coating films with the film thickness of 100 nm. These specimens were all prepared by using 25 vol.% nitrogen in the gas mixture of (C2H2 + N2). A scratch test was then arranged using the above operating conditions (18.75 Am/s, 4.1648 mN/s); the critical load was 150.92 mN. This critical load is indeed larger than all the critical loads shown in Table 2. Therefore, these two operating conditions were then adopted as the fixed scratch operating conditions in the succeeding studies.

Fig. 2. Schematic diagram shown for a scratch test.

J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

In the scratch tests, the stress distributions in the coating film and the substrate can be obtained in principle to be the combination of the stresses formed in these two specimen regions due to an indentation load applied to create the elastic and plastic deformations and the frictional force formed at the interface of the indenter and the specimen. For the purpose of simplifying the complex contact mechanics arising at an indenter having a shape not symmetrical w.r.t to the axis of the indenter, a spherical indenter shape is assumed in the present study, and the strain and shearing analyses are thus developed on the base of this indenter shape. In this simplified model for an elastic – plastic indentation, we think of the contact surface of the indenter as being encased in a hemi-spherical ‘core’ of radius a. Within the core, there is assumed to be a hydrostatic component of stress P¯. Outside the core, it is assumed that the stresses and displacements are radically symmetric and are the same as arising in an infinite elastic, perfectly plastic body, which contains a spherical cavity under a pressure P¯. The elastic –plastic boundary lies at a radius c, where c>a. At the interface between core and the plastic zone, the hydrostatic stress in the core is just equal to the radial component of the stress in the external zone. The radius c in the elastic – plastic boundary can be determined by the analyses of contact mechanics to be a function of the Young’s modulus (E) and the Poisson’s ratio (m) of the substrate material (the silicon wafer in this study), the yielding strength ( Y) of the substrate and the angle b of the indenter at the edge of contact. With a spherical indenter, we put tan bisin b = a/R, where R denotes the indenter radius of curvature at the tip. For an incompressible mate-

Table 2 Arrangements of the operating conditions and the critical loads for the predictions of the operating conditions with the largest critical load through the use of the surface response method Loading rate (mN/s)

Scratch velocity (Am/s)

X

Y

Critical load (mN)

4.19 1.87 0.93 0.52 0.27 0.08 4.19 1.87 0.93 0.52 0.27 0.08 4.19 1.87 0.93 0.52 0.27 0.08

5 5 5 5 5 5 10 10 10 10 10 10 15 15 15 15 15 15

 0.5  0.5  0.5  0.5  0.5  0.5 0 0 0 0 0 0 0.5 0.5 0.5 0.5 0.5 0.5

0.5  0.0645  0.2932  0.3929  0.4538  0.5 0.5  0.0645  0.2932  0.3929  0.4538  0.5 0.5  0.0645  0.2932  0.3929  0.4538  0.5

112.11 90.01 50.99 39.23 19.95 12.97 123.99 99 79.81 41 17.64 8.88 145.92 107.45 46.44 35.89 10.64 8.86

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rial, the radius c of the elastic – plastic boundary corresponding to the critical load L in the scratch test is expressed as [21,22] 2

E 6 YR 6 c¼6 4




L pHs






L þ4 pHs 6ð1  mÞ

31=3

3=2

ð1  2mÞ 7 7 7 5

ð1Þ

where Hs denotes the substrate hardness. The stress distributions formed in the coating film and the substrate due to the frictional force created in the sliding motion are added to the stresses formed in the indentation tests. In the scratch test, compression stresses are developed at the tip of the indenter. Therefore, the stresses in the x direction (the scratching direction) are much larger than that formed in the y and z directions. Here, the y-axis is located on the contact surface and in the direction normal to the x-axis; therefore, the z-axis points to the semi-infinite body. The largest stress is formed at the surface of y = z = 0. For a round tip in contact with the specimen, three deformation regions, as previously mentioned, are formed in the substrate material. The friction coefficient l can be attained if the frictional force during the scratching process can be measured by the nanotester. In the substrate region arising the elastic deformation (c V x), the x-directional compression stress rxf formed in the coating film is expressed as [23]: Y Ef ð1 þ mÞð2  mf Þ c 3 lY ð1 þ mÞ 3 E x 1  m2f 

c 2 1
ln þ 2
a 3 x 1 a

ðrxf Þe ¼ 

ð2Þ

where Ef denotes the Young’s modulus of the coating film and mf is the Poisson’s ratio of the coating film. Similarly, the compression stress in the y direction is expressed as [23]: ðryf Þe ¼

Y Ef ð1 þ mÞð1  mf Þ c 3 3 E x 1  m2f

ð3Þ

In the substrate region arising the plastic deformation (a V x V c), the x-directional compression stress (rxf)p formed in the coating film is written as [23]: c

Ef Y h 6ð1  2mÞln ðrxf Þp ¼  x E 1  m2f

1 c 3 þ ð1 þ mÞð2  mf Þ 3 x 

c 2 1 lY ð1 þ mÞ ln ð4Þ þ 2
a 3 x 1 a

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whereas the y-directional compression stress (ryf)p formed in the coating film is written as [23]:  c

Ef Y ðryf Þp ¼ ð1  2mÞln  6m f x E 1  m2f c 3 1 þ ð1 þ mÞð2  mf Þ ð5Þ 3 x With the existences of the above stresses in the coating film, the elastically stored energy (U) in per unit volume of coating film is expressed as [24]: U¼

1 r2 2 Ef

ð6Þ

where r denotes the local stress of the coating film. Then, the elastically stored energy (V) in the entire film with the film thickness of t is given as [24]:
 pr2 t r2 pr2 tr2 V ¼ ð7Þ ¼ 2 2Ef 4Ef where r denotes the radius of the semicircle, which is formed in front of the indenter under the critical load; the coating film is detached from the substrate under this normal load. This r value is equal to one-half of the scratching width created under the critical load. Eq. (7) is theoretically valid for the substrate region occurring either in the elastic (c V x) or the plastic deformation (a V x V c). When the normal load applied in the indentation test reaches the critical load, the elastically stored energy V in the entire film is equal to the total energy of adhesion (Wfs). Theoretically, this adhesion energy (Wfs) is composed of the energy occurring the elastic and plastic deformations. Therefore, 2 2 pr2 Wfs pr2 tr2e pr trp ¼ þ 2 4Ef 4Ef

ð8Þ

where these two terms on the right-hand side of Eq. (8) represent the elastically stored energy arising in the two substrate regions (c V x and a V x V c), respectively [24]. In Eq. (8), the local stress with the elastic deformation (re) is expressed as re ¼ ½ðrxf Þ2e þ ðryf Þ2e 1=2

The work W1 is denoted by the shadow area in the schematic diagram of the load-displacement profile shown in Fig. 3. In the load-displacement profile, even a constant load is needed to produce a sharp increase in the indentation depth if the load is up to the point able to initiate the delamination of the coating film. This delamination or palling-off of the coating film can be interpreted to be the process of AO shown in Fig. 3. The dash line CF is determined to be perpendicular to the displacement axis. The extensions of AO and FC will intersect at point B. The area of the triangle, DABC, thus represents the W1 work. It can be noted that the real work of adhesion (Wr) is lowered by increasing the W1 work. Nevertheless, the specimen’s work of adhesion is still dominated by the Wfs value. 2.3. Theoretical models and experimental details for indentation and tribological tests The film hardness generally decreases with the increase in the indentation load if a hard material is deposited on the soft substrate as the coating film; this phenomenon is the indentation size effect (ISE). In order to overcome the indentation size effect of a coating film with a small film thickness, a nanotester (Micro Materials) was applied with the maximum indentation load (the peak load of an indentation test) set on the load-depth curve to be in the range of 0.1– 50 mN. The maximum indentation depth thus varies in the range of 20 nm to several hundred nanometers. The experimental results corresponding to the indentation depth equal to or less than 20% of the coating film thickness can be widely accepted as the coating film hardness without the influence of the substrate hardness. A Berkovick indenter which has a radius of curvature at the tip in the range of 100– 150 nm is made of the diamond material. The indenter loading rate or unloading rate was 4.19 Am/s during the indentation test. The indentation tests were carried out at room temperature of 25 jC as well as at a relative humidity of 50%.

ð9aÞ

whereas the local stress with the plastic deformation (rp) is expressed as rp ¼ ½ðrxf Þ2p þ ðryf Þ2p 1=2

ð9bÞ

Define W1 as the work that is needed for a coating film delaminating from the substrate. Then, the real adhesion work (Wr) is obtained by the subtraction of the work (W1), from the total energy of adhesion (Wtotal = mWfsdx). Then, the real adhesion work is written as [25] Wr ¼ Wtotal  W1

ð10Þ

Fig. 3. Schematic diagram of indentation load-depth profile for the indentation occurring depth shift.

J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

In the present study, the models developed by Oliver and Pharr [26] for the composite hardness and Young’s modulus are adapted. The composite hardness (H) of a specimen undergoing the sink-in phenomenon during the indentation processes is determined by the definition H¼

Pmax Aðhc Þ

ð11Þ

where Pmax, as Fig. 4 shows, is the maximum indentation load, which is always set prior to the start of the indentation test. For a perfect pyramid indenter (one-half of the indenter angle w = 65.3j) considering the size effect arising in the real indentation test, the projection area A(hc) of an indentation cavity with an indentation depth of hc can be expressed as [26] 1=4 1=128 Aðhc Þ ¼ 24:5h2c þ C1 hc þ C2 h1=2 c þ C3 hc þ . . . þ C8 hc

ð12Þ Here, C1 – C8 are eight constant coefficients. The indentation depth, hc, can be calculated by the following expression [26] Pmax ð13Þ hc ¼ hmax  x¯ S where S denotes the unloading stiffness and it represents the slope of the initial 20% unloading curve; hmax denotes the indentation depth corresponding to Pmax. S is thus expressed as
 dP S¼ ð14Þ dh P¼Pmax The geometric constant x¯ for a perfect triangular-based pyramid indenter is about 0.75. The reduced Young’s modulus (Er) of a specimen with a coating film is obtained

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by the model developed by Oliver and Pharr [26]. It is given as


dP dh



2 pffiffiffi ¼ b pffiffiffi AEr p

ð15Þ

The indentation load gradient, dP/dh, in Eqs. (9a) and (9b) is obtained to be the slope of the straight line tangential to the initial 20% unloading curve of the load-displacement profile. b, which denotes the correction factor related to the indenter geometry different from a sphere, is 1.034 for a perfect pyramid indenter. The reduced Young’s modulus Er is defined as
Er ¼

1  c2 1  c2i þ E Ei

 ð16Þ

where c and ci represent the Poisson’s ratios of the specimen and the indenter, respectively, and E and Ei represent the Young’s modulus of the specimen and the indenter, respectively. The Young’s modulus (E) of a specimen can be obtained if c, ci and Ei are available. The Young’s modulus (Ei) of the diamond indenter is 1140 GPa and the Poisson ratio (ci) is 0.07 [27]. In the present study, ci = 0.07 is given for the specimen with a hydrogenated carbon film. The micro-/nanotribological tests for wear volume were also carried out on this nanotester. A conical indenter with a spherical tip (Rockwell C type) having a radius of curvature of 25 Am was employed. The load was always remained to be constant over the entire tribological process. The scratch length for each wear test was set to be 100 Am. In the present study, three sliding velocities (5, 25 and 75 Am/s) and three scratch normal loads (10, 25 and 50 mN) make up nine operating conditions of the tribological tests. The experimental results of wear volume are the average of four readings under the same operating conditions. The wear loss was calculated by employing a high-precision surface roughness-measuring instrument (Kosaka ET-4000) to measure the topography of the wear scar first, and then a software to evaluate the wear volume.

3. Results and discussion

Fig. 4. Schematic diagrams of an indenter in contact with a specimen with an indentation depth of hc and the load-displacement profile arising in the indentation process.

In general, the critical load of a specimen with a coating film is factored by several parameters, including the loading rate and scratch velocity of a scratch test, the coating film thickness and the volume fraction of nitrogen in the gas mixture of (N2 + C2H2) during the deposition process. These results are obtained from the changes of five loading rates and three scratch velocities. When the scratch velocity during scratch test is fixed as Fig. 5(a) shows, the critical load of a coating film can be elevated by increasing the loading rate. The differences in the critical load due to a different scratch velocity become significant only when the loading rate is sufficiently high.

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Fig. 5. Results of the critical load varying with (a) the loading rate and (b) the scratch velocity.

The variations of the critical load with the scratch velocity are shown in Fig. 5(b). The behavior, which is exhibited in the critical load, becomes more complex; it is also dependent upon the loading rate. At small loading rates, the critical load of the specimen is slightly reduced by increasing the scratch velocity. However, at large loading rates, the critical load is conversely raised by increasing the scratch velocity. The reason why these two operating parameters can affect the critical load of a specimen is still unclear. According to the results shown in Fig. 5(a) and (b), the critical load of a specimen with a coating film is determined as a function of both the loading rate and the scratch velocity. The influence of the loading rate parameter on the specimen’s critical load is obviously greater than that of the scratch velocity. Apart from the operating conditions applied to the scratch tests, the film properties, including the film thickness and the nitrogen content in the coating film, also

govern the critical load of a specimen. The critical load results varying with the volume fraction of nitrogen in the gas mixture of (N2 + C2H2) and the film thickness are shown in Fig. 6. For all these five film thicknesses, the highest critical load always occurs in the film prepared by the nitrogen volume fraction of 40 vol.%, whereas the lowest critical load always occurs in the film prepared by the volume fraction of 66 vol.%. This behavior implies that an excessive increase in the nitrogen content of the coating film may cause a significant drop in the critical load. The critical load results affected by the coating film thickness are also shown in Fig. 6. The behavior demonstrated in the critical load due to the change in the film thickness is also affected by the nitrogen content in the film. As to the specimens prepared by the volume fraction of nitrogen equal to or less than 40 vol.%, the critical load is first lifted by increasing the coating film thickness until the maximum critical load is reached at the film thickness of 200 nm. The further increase in the film thickness tends to lower the critical load. As to the specimen prepared by the volume fraction of nitrogen up to 66 vol.%, the experimental data also show the maximum critical load arising at the film thickness of 200 nm, although the regression curve shows that an increase in the film thickness can elevate the critical load. The results of the adhesion work (Wr) evaluated by differing the volume fraction of nitrogen in the gas mixture and the coating film thickness are shown in Fig. 7. The results of the adhesion work for all five film thicknesses show different lowering rate as the volume fraction of nitrogen is raised. The lowering rate of the adhesion work is obviously enhanced by increasing the volume fraction of nitrogen (thus the nitrogen content in the coating film). The differences in the adhesion work among the specimens with five different film thicknesses are narrowed to be quite small as the volume fraction of nitrogen is up to 66 vol.%. This

Fig. 6. Critical load results varying with the volume fraction of nitrogen in the gas mixture of (N2 + C2H2) and the coating film thickness.

J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

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Table 3 Evaluations of the total energy of adhesion of all the presently used specimens

Fig. 7. Adhesion work results varying with the volume fraction of nitrogen in the gas mixture of (N2 + C2H2) and the coating film thickness.

implies that the effect of the coating film thickness on the adhesion work becomes considerably small as the nitrogen content in the coating film is sufficiently high. Fig. 7 also shows the effect of the coating film thickness on the adhesion work. The adhesion work of a coating film, irrespective of the volume fraction of nitrogen, is always raised by increasing the film thickness. The largest adhesion work is formed by a coating film without the nitrogen content as well as with the largest film thickness. As Eq. (10) shows, the adhesion work of a specimen with a coating film is determined by factors such as the film thickness (t), the local stresses formed in the film (re and rP), the film’s elastic modulus (Ef) and the work needed for the film delamination from the substrate (W1). The total adhesion energy in per unit width of a specimen (with a coating film) can be obtained from the integration of Wfs w.r.t. x if the elastic modulus Ef is available from the indentation test of a specimen. The results of the total adhesion energy for all these specimens prepared in the present study are shown in Table 3. Except for the two cases arising in the specimens with the film thickness of 100 nm, which were prepared by the volume fractions of 40 and 66 vol.%, the total adhesion energy of a specimen is lifted by increasing the film thickness. The rising rate is remarkably enhanced by the specimen with a large film thickness. The effect of the nitrogen content in the film displays the behavior that the total energy of adhesion is in general (but not always) lowered by increasing the volume fraction of nitrogen in the gas mixture (N2 + C2H2) and thus the nitrogen contact in the film. As to the work (W1) consumed in the film delimitation from the substrate, the quantity becomes substantial only for the films having a small film thickness; it becomes negligibly small as the film thickness becomes large. The combined effect of Wtotal and W1 causes the real adhesion work varying with the volume fraction of nitrogen and the film

Specimen code

Volume fraction of N2 (vol.%)

Film thickness (nm)

Total adhesion energy
(10 8 J)

N00-070 N00-100 N00-150 N00-200 N00-300 N25-070 N25-100 N25-150 N25-200 N25-300 N40-070 N40-100 N40-150 N40-200 N40-300 N66-070 N66-100 N66-150 N66-200 N66-300

0 0 0 0 0 25 25 25 25 25 40 40 40 40 40 66 66 66 66 66

70 100 150 200 300 70 100 150 200 300 70 100 150 200 300 70 100 150 200 300

2.3392 2.9526 3.5617 4.9237 8.9701 2.3142 2.4817 3.5449 3.7435 6.1598 2.2688 2.2389 2.7908 3.8049 4.6350 0.87827 0.84976 0.97251 0.99629 1.6028

thickness; it behaves as shown in Fig. 7. The real adhesion work is elevated by either increasing the film thickness or decreasing the volume fraction of nitrogen. The highest increasing rate of the real adhesion work occurs in a specimen with the largest film thickness as well as without nitrogen content. A significant gap in the real adhesion work is shown in curve 4 (66 vol.%) compared with the other three curves (0, 25 and 40 vol.%). The experimental results of the elastic modulus, which were obtained from the indentation tests of the coating films by differing the film thickness and the nitrogen content, are shown in Fig. 8. As Fig. 8 shows, the elastic modulus of a specimen, irrespective of its film thickness, is always

Fig. 8. Young’s modulus results varying with the volume fraction of nitrogen and the coating film thickness.

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J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

Fig. 9. Variations of the Young’s modulus with the indentation depth for the volume ratio of nitrogen at 40 vol.%. Four kinds of film thickness are prepared for each nitrogen contents [29].

lowered by increasing the volume fraction of nitrogen in the gas mixture of (N2 + C2H2). The results also reveal that the elastic modulus of the specimen with a film thickness of 200 nm is always the lowest of these five film thicknesses, whereas the elastic modulus of the specimen with the smallest film thickness (70 nm) is the highest one, irrespective of the nitrogen content (thus the volume fraction of nitrogen) in the coating film. The Young’s modulus of a specimen with a coating film in the present study was obtained from the indentation test. The Young’s moduli were evaluated at an indentation depth about 20% of the coating film thickness; they were considered to be rarely affected by the mechanical properties of the substrate. According to the experimental results, the Young’s modulus of a specimen is still dependent upon the coating film thickness even though the volume fraction of nitrogen in the coating film is fixed. This characteristic may be attributable to the variations of the coating film microstructure and thus the mechanical properties caused by different film thickness growth rate during the deposition process. Apart from the Young’s modulus, other mechanical properties are also confirmed to be varied by differing the film thickness [28,29]. In the present study, the depth sensing indentation tests were carried out in a wide range of indentation depth (0– 300 nm). Fig. 9 shows the Young’s moduli of the specimens prepared with a nitrogen volume fraction of 40 vol.% [29]. It is exampled to illustrate the variations of Young’s modulus with the indentation depth. The results indicate that the Young’s modulus is varied by the indentation depth, rather than a constant value. In the present study, the Young’s moduli shown in Fig. 8 were all obtained at the indentation depth 20% of the film thickness, rather than a constant indentation depth. Therefore, the Young’s modulus of a specimen is elevated significantly by decreasing the inden-

tation depth, especially for the case of having a small film thickness. According to the study of Li et al. [30], the Young’s moduli of the hydrogenated carbon films for an indentation depth of 40 nm (without the data of film thickness) are varied in the range of 70 –120 GPa. The ones reported in the study of Schultrich et al. [31] show the Young’s moduli of the hydrogenated DLC films lying in the range between 100 and 200 GPa; however, the details of the indentation depth and the film thickness were not provided. If the Young’s moduli of the specimens with different film thickness are obtained at the same indentation depth of 40 nm in the present study, they are approximately varied in the range of 200– 380 GPa as to the specimens with a nitrogen volume fraction of 40 vol.% and the film thickness in the range of 50– 300 nm. This range is quite consistent with that reported in the literatures [30 –32]. An attempt has been made to establish the relationship between the adhesion work of a specimen and the critical load. However, this effort seems not successful if their connection is not based on the specimens with the same film thickness as well as the same nitrogen content in the coating film (the same volume fraction in the coating process). The critical loads produced in the specimens with different film thickness or nitrogen content in the coating film are also different, although the same operating conditions were applied. A proportional relationship exists between these two parameters only in the specimens having the same film thickness as well as the same nitrogen content in the coating film. The curves in Fig. 10 show the relationship between these two parameters. They look like a straight line because the coating film thickness in the present study is varied only in the range of 50– 300 nm. Four curves shown in Fig. 11 for four volume fractions are obtained following this rule. The results of this figure also reveal that a specimen with a larger critical load does not

Fig. 10. Relationships between the adhesion work and the critical load. They are valid only for the specimens with the same film thickness as well as the same nitrogen content in the film.

J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

Fig. 11. Wear volume results varying with the coating film thickness. The operating conditions are (a) load: 10 mN, sliding velocity: 5 Am/s; (b) load: 10 mN, sliding velocity: 75 Am/s; (c) load: 50 mN, sliding velocity: 5 Am/s. The sliding distance is 1 mm.

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imply having a higher adhesion work if different types of specimens are considered. Fig. 11(a) –(c) is exampled to investigate the effect of differing the operating conditions on the wear volume of a specimen. Despite the operating conditions (the normal loads and the sliding velocities) applied in the tribological tests and the film thickness, the experimental results show that the wear volume is always increased in the specimen prepared by increasing the volume fraction of nitrogen in the gas mixture. All these curves show that the wear volume of a specimen is increased by increasing the coating film thickness, and the growth rate of the wear volume is governed by the coating film thickness and the nitrogen content in the coating film. A high wear growth rate is, in general, generated in a specimen with a thick coating film. Apart from the nitrogen content in the film, the differences in the wear volume due to the use of different film thicknesses are also factored by the operating conditions applied in the tribological test. These differences in the wear volume are significantly narrowed by increasing the normal load. Obviously, the load applied to the tribological test gradually becomes the dominant factor in the wear volume as the load is elevated to be sufficiently high. Either increasing the load or decreasing the scratch velocity may elevate the wear volume quantity; this feature is valid for all specimens in the present study. The maximum wear scar depth of all these wear tests was generated by the maximum wear volume (about 200 Am3) shown in curve 4 of Fig. 11(c). The very small wear depth is not uniform but is slightly varying along the scratch track. However, it is roughly estimated to be about 0.080 Am because the scratch length, the diameter of the spherical indenter and the wear volume are now available. This maximum wear depth is much smaller than the film thickness; therefore, the wear behavior actually takes place in the coating film layer. However, the wear volume of this coating film is characteristically affected by the substrate material. Investigation and comparison can be made for the results of adhesion work shown in Fig. 7 and the results of wear volume shown in Fig. 11(a) – (c). In Fig. 7, curve 4 for the volume fraction of 66 vol.% shows a large deviation from the other three curves (curves 1, 2 and 3), and the deviation is enlarged by increasing the film thickness. The experimental results of wear volume also exhibit similar characteristics as shown in Fig. 11(a) –(c). The coincidence in the behavior between the work of adhesion and the nitrogen content due to the change in the nitrogen content implies that a connection exists between the wear volume and the work of adhesion. An increase in the work of adhesion is helpful for the reduction of wear volume, although the work of adhesion is not the sole factor as to the wear volume of a specimen. Detailed investigation made in the experimental results reveals that the behavior exhibited in the wear volume results seems also somewhat related to that exhibited in the Young’s modulus results shown in Fig. 8. In Fig. 11(a) – (c), curve 4 for

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J.-F. Lin et al. / Diamond & Related Materials 13 (2004) 1895–1906

the volume fraction of 66 vol.% shows noticeable separations from the other three curves (curves 1, 2, 3), irrespective of the operating conditions of these tribological tests. Analogous behavior is also present at the curves of the Young’s modulus shown in Fig. 8. However, due to the complex behavior exhibited in the Young’s modulus varying with the coating film thickness, the attempt to establish a single relationship between the Young’s modulus and the wear volume of a specimen seems not so easy. The comparisons of the results shown in adhesion work (see Fig. 7), Young’s modulus (see Fig. 8) and wear volumes [see Fig. 11(a) –(c)] reveal the fact that the wear volumes of a specimen is actually factored by many parameters including the adhesion work, the Young’s modulus and the operating conditions applied in the tribological tests. It seems difficult to clarify the individual relationship of each of the above parameters with the wear volume results. However, the following conclusions can still be drawn from these results. (1) Either a large adhesion work or a high Young’s modulus is, in general, advantageous to reduce the wear volume of a specimen, irrespective of the film thickness and the nitrogen content in the film. (2) Apart from the combined effect of the adhesion work and the mechanical properties (such as Young’s modulus and hardness), the operation conditions become the governing factor as to the wear volume of a specimen.

4. Conclusions 1. The critical load of a specimen with a coating film generally varies with the loading rate and the scratch velocity, rather than a constant value independent of the scratch operating conditions. As the operating conditions in the scratch test are fixed, the critical load of a specimen is still dependent upon the combined effect of the film thickness and the nitrogen content in the coating film. 2. The adhesion work of a specimen is varying as a function of the coating film thickness and the nitrogen content in the coating film. For a specimen with a constant film thickness, the increase in the nitrogen content in the coating film may cause the lowering of the adhesion work. Increasing the film thickness but fixing the nitrogen content in the coating film can elevate the specimen’s adhesion work. 3. A clear correlation between the results of adhesion work and critical load can be established only when the specimens have the close film thickness and nitrogen content in the coating films. The critical load is elevated by increasing the adhesion work of the specimen if the above two prerequisite conditions are satisfied. 4. The elevation in either the adhesion work or the Young’s modulus of a specimen with a coating film is helpful for the reduction of the wear volume of this specimen. In

general, the combined effect of the adhesion work, the mechanical properties (including the Young’s modulus) and the operating conditions becomes the controlling factor as to the wear volume of the specimen.

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