A Simple Technique for Measuring the Adhesion of Brittle Films to Ductile

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A simple technique for measuring the adhesion of brittle ﬁlms to ductile substrates with application to diamond-coated titanium Joost J. Vlassak Department of Materials Science and Engineering, Stanford University, Stanford, California 94305 M. D. Drory Crystallume, Santa Clara, California 95054 W. D. Nix Department of Materials Science and Engineering, Stanford University, Stanford, California 94305

https://doi.org/10.1557/JMR.1997.0260 (Received 18 November 1996; accepted 6 March 1997) . . We have developed a new technique for measuring the adhesion of brittle ﬁlms to ductile substrates. In this technique, a wedge indenter is driven through the brittle coating and into the underlying substrate. Plastic deformation of the substrate causes the coating to delaminate from the substrate. The width of the delaminated area can be directly related to the interface toughness. We present a simple analysis of this technique and apply it to diamond-coated titanium. The toughness of the diamond-titanium interface as measured with this wedge delamination technique is approximately 51 6 11 J͞m2. XPS measurements reveal that a reaction layer of titanium carbide forms between the

diamond coating and the titanium substrate. Delamination of the coating occurs by crack https://www.cambridge.org/core/terms propagation in this reaction layer and in the diamond ﬁlm itself. These observations agree well with nanoindentation measurements performed in the delaminated area of the substrate.

I. INTRODUCTION indentation.7–9 In this technique, the coating is deformed The reliability of many thin-film coatings in engi- by means of a microindenter, avoiding penetration of the neering applications depends critically on the adhesion substrate. The residual stresses thus introduced into the of the coating to its substrate. If adhesion is poor, coating cause it to delaminate or spall from the substrate the coating may fail even if the coating itself satisfies during unloading of the microindenter. The extent of the design criteria. Despite this fact, relatively few the delaminated area can be related directly to the , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , measurement techniques are available to quantify the critical crack extension force for coating delamination. energy required to separate a coating from the substrate, The indentation load is typically applied by means of a particularly for brittle substrates. Here we introduce a microhardness tester with loads smaller than 20 N. This new technique for measuring the adhesion of strongly indentation technique works well for relatively ductile adhering brittle films to ductile substrates and we use it coatings that are easily deformed with an indenter. As

20 Jul 2020 at 19:43:31 at 2020 Jul 20 to measure the adhesion of diamond to titanium. the hardness of the coating increases, it becomes more

, on on , By far the most popular technique is the scratch and more difﬁcult to deform the coating without also test, in which a stylus is drawn over the coating with plastically deforming the substrate, greatly complicating an ever increasing load until the coating spalls. This the analysis. technique allows one to compare the adhesion of various A variation on the indentation technique, for brittle

coatings qualitatively, but does not provide an absolute coatings on ductile substrates, was recently developed Harvard University Harvard . . measure for the critical crack extension force for the by Drory and Hutchinson.10,11 In this technique, an in- substrate-coating interface. More quantitative techniques denter (e.g., a Rockwell “C” indenter) is forced through have also been developed such as the blister test,1–3 the the brittle coating and into the underlying substrate. In- residual stress driven delamination test,4 and the edge dentation loads are much larger than in the previous test delamination test.5,6 These techniques usually require and are typically in the range of 0.6 to 1.5 kN. Plastic complicated sample preparation and are often limited to deformation of the substrate forces the coating to be dis- coatings with poor adhesion. placed radially, inducing a compressive radial stress in Delamination of ductile coatings on brittle sub- the coating that decreases with increasing distance from https://www.cambridge.org/core strates has been studied successfully by means of micro- the indentation. This radial stress provides the driving

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force for delamination of the coating. Measurement of the size of the delaminated area allows one to determine the critical crack extension force of the coating-substrate interface. However, as the coating is displaced radially, tensile hoop stresses also develop in the coating. These hoop stresses may cause radial cracks to form in the brittle coating, which may complicate the interpretation of the results. We have developed a new version of this technique, called the wedge delamination technique. In this method a wedge is forced through the coating and into the ductile substrate. This causes delamination of

the coating to occur along with substrate deformation. https://doi.org/10.1557/JMR.1997.0260 . . The main advantage of the wedge delamination test FIG. 1. Schematic of the wedge delamination test. over the cone delamination technique is the plane-strain condition imposed by wedge indentation: Rather than placement field around the wedge indentation. This tensile hoop stresses, compressive stresses develop in model is based on the experimental observations by the direction parallel to the wedge, minimizing cracking Samuels and Mulhearn13 and by Hirst and Howse14 that of the coating. the displacement field produced by any blunt wedge is In this study, we first present an analysis of the approximately radial from the line of first contact. We wedge delamination test relating the extent of the de- assume the material follows the Tresca yield criterion laminated zone to the critical crack extension force and does not strain-harden. We also assume that the https://www.cambridge.org/core/terms of the interface. We then present results from wedge material does not pile up around the indenter. The delamination experiments we have performed to measure influence of strain hardening and pileup will be discussed the delamination energy of CVD diamond films on later. As a first approximation, we neglect the elastic titanium substrates. The titanium-diamond interface was deformation in the plastic zone around the indentation. further characterized by means of x-ray photoelectron The stresses and displacements in the elastic zone spectroscopy (XPS) and nanoindentation. XPS was used are given by Lamé’s formulae for a pressurized cylindri- to determine the composition profile near the titanium- cal cavity in an infinite medium.15,16 The radial displace- diamond interface and nanoindentation was used to ment, i.e., the displacement in the direction perpendicular measure the hardness and stiffness of the interface as to the wedge, is found to be a function of indentation depth. 2 1 1n sy c II. ANALYSIS OF THE WEDGE u͑x͒ ෇ , (1) E s 2 x DELAMINATION TEST µ ∂ where E and n are Young’s modulus and Poisson’s ratio, When a wedge is driven through a thin-film coating respectively, the subscript s refers to the substrate, s , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , y and into a ductile substrate, plastic deformation of the is the yield stress of the substrate, x is the distance substrate forces the coating to be displaced away from to the center of the indentation, and c is the radius of the wedge. This increases the stress in the coating the plastic zone. Note that under the assumptions stated and hence the driving force for delamination of the above, the plastic zone has a cylindrical shape centered coating (see Fig. 1). In order to calculate the energy around the line of first contact. Assuming the material 20 Jul 2020 at 19:43:31 at 2020 Jul 20 release rate when a crack propagates along the interface is incompressible inside the plastic zone, the size of , on on , between coating and substrate, i.e., during delamination, the plastic zone and the displacements within it can be the initial residual stress is needed along with the level of readily calculated. When the indenter is driven into the film stress after delamination. This provides insight into sample, conservation of displaced volume requires that the delamination process of the film-substrate interface.

Finally, detailed knowledge of the displacement field a2 tan b ෇ pcu͑c͒ , (2) Harvard University Harvard . . caused by the wedge indentation is required as elaborated below. It is assumed that the wedge indentation is where a is half the width of the indentation and b is much deeper than the coating thickness, so that the the inclination of the face of the wedge to the surface coating does not affect significantly the substrate dis- of the sample (see Fig. 1). Combining Eqs. (1) and (2) placement field. results in the following expression for the radius of the plastic zone: A. A simple model for wedge indentation 2 tan bE Following Johnson,12 we use a cylindrical cavity c ෇ a , (3) https://www.cambridge.org/core expanding in an infinite medium to model the dis- s p͑1 1n͒sy

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where the elastic properties are those of the substrate. energy change in the coating, where ts is the substrate The radial displacement in the plastic zone can be found thickness. Any contribution to the strain energy of the in a similar fashion and is given by the same expression substrate can therefore be safely neglected. Equation (7) as the displacement in the elastic zone, i.e., Eq. (1). combined with Eq. (6) allows one to calculate the strain Taking into account Eq. (3), the displacement at the energy release rate for delamination. The curves in Fig. 2 surface of the sample is show G as a function of delaminated distance for various values of E ͞s . The residual stress in the coating a2 tan b film res u͑x͒ ෇ . (4) is assumed to be compressive. The strain energy release px rate is normalized by the strain energy release rate due The displacement ﬁeld is completely determined by the to just the residual stress in the coating, given by geometry of the indenter and is independent of the prop- 2 2

erties of substrate. Equation (4) also describes the dis- ͑1 2nfilm͒srest https://doi.org/10.1557/JMR.1997.0260

. . G0 ෇ . (8) placement of the thin-film coating on the substrate. The 2Efilm indentation induced strains in the coating are then given by: Note that the strain energy release rate in this simple model is independent of the substrate properties. Ac- du a2 tan b Dexx ෇ ෇ 2 , cording to Fig. 2, the strain energy release rate rises dx px 2 dramatically close to the indentation. Wedge indentation Deyy ෇ 0, (5) will therefore induce coating delamination in the region where y is the coordinate parallel to the wedge indenter. where the strain energy release rate exceeds the critical Using Hooke’s law, the stresses in the coating can be crack extension force for the interface. The width of the https://www.cambridge.org/core/terms readily computed: delaminated zone caused by wedge indentation can be readily measured; if the elastic properties of the film E a2 tan b and the residual stress in it are known, the interface sxx ෇ sres 2 , 2 2 toughness can be determined graphically from a figure µ1 2n ∂film px similar to Fig. 2. If the residual stress in the coating E a2 tan b s s 2n , (6) is tensile (Fig. 3), the energy release rate decreases yy ෇ res film 2 2 µ1 2n ∂film px with decreasing distance from the indentation before where sres is the residual stress present in the coating. increasing rapidly near the indentation. The extent of If the stresses in the coating are large enough, the the delaminated zone will therefore be smaller than coating will delaminate. On delamination, the stress in for compressive coatings, making it more difficult to the x-direction, sxx, relaxes to zero and the stress in the apply the test. The results presented in Figs. 2 and 3 y-direction takes the value syy 2nfilmsxx. For a plane- are qualitatively similar to results found by Drory and strain fracture mechanics problem like the one presented Hutchinson for the axisymmetric delamination test.11 here, the energy release rate, G, or the driving force , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , for film delamination may be calculated as the coating thickness, t, times the difference in strain energy density in the coating ahead of the crack tip and that behind the crack tip10:

2 2 20 Jul 2020 at 19:43:31 at 2020 Jul 20 ͑1 2nfilm͒sxxt G ෇ t͑W1 2 W2͒ ෇ , (7) , on on , 2Efilm where 2 2 sxx syy nfilmsxxsyy W1 ෇ 1 2 ,

Harvard University Harvard 2Efilm 2Efilm Efilm . . 2 ͑syy 2nfilmsxx͒ W2 ෇ . 2Efilm The implicit assumption here is that the coating thickness is much smaller than the characteristic size of the indentation displacement ﬁeld. This ensures that there FIG. 2. Normalized energy release rates as a function of distance from is locally a steady state at the crack front. One can the indentation for coatings with a compressive stress. The solid lines show that the strain energy change in the substrate, as a

https://www.cambridge.org/core are for ﬁlms with Poisson’s ratio of 0.3 and the dashed lines for ﬁlms ± result of the delamination, is on the order t͞ts times the with Poisson’s ratio of 0.07. The dihedral angle of the indenter is 90 .

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where we have neglected a term on the order of sy͞Es. The radius of the expanding cavity can be related to the size of the indentation by equating the volume of the cavity to the volume displaced by the indenter:

1 pb2 ෇ a2 tan b . (11) 2

Combining Eqs. (10) and (11) leads to a new expression for c

4 tan bE https://doi.org/10.1557/JMR.1997.0260 s . . c ෇ a . (12) s ͑5 2 4ns ͒psy

Equation (12) predicts a radius approximately 20% FIG. 3. Normalized energy release rates as a function of distance from smaller than Eq. (3). This is a direct consequence of the indentation for coatings with a tensile stress and Poisson’s ratio of 0.3. The dihedral angle of the indenter is 90±. the elastic compressibility of the material in the plastic zone. In order to find the displacement at a point in The wedge delamination test, however, provides a sub- the plastic zone, Eq. (9) needs to be integrated with stantially larger driving force for film delamination than respect to c, taking into account that the position of the point changes during the deformation process. The https://www.cambridge.org/core/terms the axisymmetric test. displacement is also subject to the boundary condition B. The influence of elastic compressibility that it be continuous across the elastic-plastic boundary. in the plastic zone Equation (9) can be integrated analytically to yield the following expression for the displacement: In the previous section, we have assumed that the material is incompressible in the plastic zone. This assumption allows one to obtain an analytical expression u͑x͒ ෇ 2͑A11͒ 2͑A11͒ 2 2A for the crack extension force and is acceptable as long B͑c 2 x ͒ 1 ͑x 1 uel͒ ͑A 1 1͒x 2 x , as the plastic strains are large compared to the elastic s ͑A 1 1͒c2A strains. In an indentation, however, the material is highly (13) constrained and one would expect the elastic dilatation to influence results significantly. Again, the indentation process is modeled as the expansion of a cylindrical where cavity in an infinite medium. The displacements in

, subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , 3͑1 2 2ns͒sy the elastic zone are still given by Eq. (1). In order to A ෇ , determine the displacement ﬁeld in the plastic zone, the 2Es full plasticity problem using the Prandtl–Reuss equa- ͑5 2 4ns͒sy tions need to be solved. This was ﬁrst done by Hill,16 B ෇ , who derived the following differential equation for the 2Es

20 Jul 2020 at 19:43:31 at 2020 Jul 20 displacements in the plastic zone:

, on on , ͑1 1ns͒syx du 3͑1 2 2ns͒sy x ͑5 2 4ns͒syc uel ෇ . ෇ 2 1 , 2Es dc 2Esc 2Esx where b < x < c , (9) Equation (13) allows one to calculate the stresses induced in the coating by the wedge indentation. The

Harvard University Harvard and where b and c are the radii of the cylindrical cavity . . and the plastic zone, respectively. On the surface of procedure to calculate the crack extension force is the the cavity, the left-hand side of Eq. (9) is equal to same as in the previous section with Eqs. (13) and db͞dc. The geometrical similarity of the displacement (12) replacing Eqs. (1) and (3), respectively. Figure 4 field requires that b͞c be constant. Equation (9) can then shows the influence of the elastic compressibility on the be rewritten to yield an expression for the radius of the energy release rate. The parameters used are for a 1 mm plastic zone diamond film on a titanium substrate. Not surprisingly, the energy release rate at a given distance from the 2Es indentation is smaller if the elastic compressibility of https://www.cambridge.org/core c ෇ b , (10) s͑5 2 4ns͒sy the material is taken into account.

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III. EXPERIMENTS We have used the wedge delamination test to measure the interface toughness of the diamond-titanium interface. To this effect, a diamond coating was grown on two substrates of pure titanium (nominally 99.6% Ti from Goodfellow Corp. Cambridge, U.K.). The 25 mm diameter substrates were ﬁrst cleaned in solvents and scratched with a ﬁne diamond powder to enhance diamond nucleation. The diamond was deposited in a chemical vapor deposition (CVD) reactor using microwave

excitation at 2.45 GHz. The deposition was performed https://doi.org/10.1557/JMR.1997.0260

. . at a pressure of 50–80 Torr in a mixture of 1% methane in hydrogen with a total gas flow rate of 200 std. cm3 min21. The presence of diamond was verified by means of Raman spectroscopy. In addition, a shift in the FIG. 4. Comparison of the energy release rate with and without elastic characteristic peak allowed the residual stress in the film compressibility in the plastic zone. The parameters used are for a to be measured as 25 GPa.19 1 mm diamond film on a titanium substrate. Wedge indentations were made in the diamond- coated titanium substrates using a wedge indenter with a dihedral angle of 90±. The indenter was made of a tool steel bit, 9.53 mm in length. Tool steel was found https://www.cambridge.org/core/terms C. The influence of pileup and strain hardening to be sufficiently hard to indent the substrates without In the present analysis, we have neglected the occur- noticeable wear of the indenter. Indentation loads varied rence of pileup during the indentation process. For sharp from 7 to 9 kN and were applied by means of an indenters or for materials with large stiffness-to-yield- Instron tensile tester at a constant displacement rate of 17 stress ratios, pileup around the indenter may occur. 0.254 mm͞min. A minimum of four measurements were The resultant displacement field is very complicated and made in each of the two samples. The width of the differs significantly from Eq. (13). The displacments in indentations and the size of the delaminated area were the substrate can then be determined only by means measured using an optical microscope. The width of the of the finite element technique. Once the displacements delaminated zone was determined by dividing the area are known, however, the stress in the coating and the of delamination by the length of the indentation. Two energy release rate, Eq. (7), can be readily calculated. If indentations were scanned with a surface profilometer the extent of pileup can be measured, e.g., by surface to determine the extent of pileup that occurred during profilometry, it is still possible to obtain an estimate the indentation. Following the indentation experiments,

, subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , for the energy release rate by subtracting the pileup delaminated ﬁlms were examined by scanning elec- volume from the volume displaced by the indenter. If tron microscopy (SEM), where the ﬁlm thickness was this corrected volume is used in Eq. (11), the size of measured as 0.75 6 0.14 mm and 0.52 6 0.09 mm for the plastic zone and the energy release rate are reduced samples 1 and 2, respectively. accordingly. All equations remain unchanged, except X-ray photoelectron spectroscopy was used to de- that the indentation width is replaced by an effective

20 Jul 2020 at 19:43:31 at 2020 Jul 20 termine the composition proﬁle of the titanium-diamond width aeff:

, on on , interface. The XPS experiments were made in the delaminated area immediately adjacent to the wedge indenta- V0 2 Vpileup tions. The analysis was performed using an S-PROBE aeff ෇ a , (14) s V0 Surface Spectrometer. All spectra presented here were 2

collected from a 250 3 1000 mm area using Al Ka

Harvard University Harvard . . where V0 is the volume displaced by the indentation and radiation. Carbon 1s, oxygen 1s, and titanium 2p spectra Vpileup is the volume of the pileup. were taken from the exposed substrate. A scan from 0 to If the substrate strain hardens, pileup is reduced 1100 eV confirmed that these were the only elements significantly.18 Equation (12), on the other hand, is valid present. A composition profile of the substrate was for elastic, perfectly plastic materials only. If the yield determined by sputtering it with 10 keV argon atoms for stress in Eq. (12) is replaced by the substrate flow stress 40 min and measuring the carbon, oxygen, and titanium at a strain that represents the average strain in the plastic spectra at 480 s intervals. Film spalling accompanies zone, a good approximation to the displacement field delamination, which produces sample areas too small https://www.cambridge.org/core should be obtained. for subsequent analysis by XPS. As a result, it was not

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possible to determine the composition on the coating side of the interface in the present study. Nanoindentation experiments were performed in the delaminated areas of the substrate through use of a Nanoindenter. The Nanoindenter is a high-resolution, depth-sensing hardness tester described elsewhere in the literature.20 In a typical nanoindentation experiment, both applied load and indenter displacement are contin- uously recorded. Two sets of 36 indentations were made to six different depths ranging from 40 to 1000 nm. This range was selected in order to measure the variation of

the mechanical properties with indentation depth. The https://doi.org/10.1557/JMR.1997.0260 . . ﬁrst set of indentations was made in an area of the substrate where the diamond ﬁlm had delaminated, and the second set was made in a similar area after the surface region of the substrate had been removed by 40 min of argon sputtering. Additionally, indentation experiments were also performed on the back side of one of the diamond-coated substrates and on a blank titanium substrate. These experiments allowed us to investigate the effect of the diamond deposition environment on

https://www.cambridge.org/core/terms the mechanical properties of the titanium substrates. The surfaces of these samples were polished according to standard metallographic methods before the indentation measurements. The indenter tip used in this study was a Berkovich diamond tip, i.e., a three-sided pyramid with the same depth-to-area ratio as the standard Vickers FIG. 5. SEM micrograph of a wedge indentation in one of the indenter tip. As a result of the very small displacements samples. in this technique, a detailed calibration procedure is used 21 to account for the precise diamond tip geometry. The Figure 7 shows a typical profilometer scan of one velocity of the indenter upon loading was held constant of the indentations. The difficulty in determining the between 10 and 15 nm͞s. When the desired indentation amount of pileup from such a scan lies in determining depth was reached, the load was held constant until the the position of the sample surface before pileup. A small indenter velocity dropped below the noise level (, 0.1 shift in surface height can change the measured pileup nm͞s). The load was cycled twice before finally unload-

, subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , volume signiﬁcantly. This problem was resolved by ing the sample to ensure that the unloading segment using an iterative procedure in which the position of the in the indentation curve would be completely elastic. surface was allowed to shift until the size of the plastic The indentation results were analyzed using the method zone as given by Eq. (12) coincided with the width of proposed by Oliver and Pharr.22

20 Jul 2020 at 19:43:31 at 2020 Jul 20 TABLE I. Summary of wedge delamination results; w is the width

IV. RESULTS AND DISCUSSION of the delaminated area; a is the indentation width. , on on , A. Wedge delamination 2 a ͑mm͒ w ͑mm͒ aeff ͑mm͒ w͞aeff G ͑J͞m ͒ Figure 5 shows an SEM micrograph of a wedge indentation in one of the samples. The area in which the Sample 1 164 866 129 6.71

diamond film has delaminated may be easily discerned. 153 706 121 5.85 Harvard University Harvard . . The widths of the delaminated zones are listed in Table I. 242 1167 191 6.12 239 1166 189 6.18 Cracks emanate from the corners of the indentations, 6 6 but are absent elsewhere. The micrograph in Fig. 6 is a Average 6.22 0.36 53 9 close-up of an area near the corner of the indentation. Sample 2 218 1024 172 5.97 The fine-grained microstructure of the diamond film and 235 1163 185 6.30 250 970 198 4.91 the cracks are clearly visible. These cracks occur not only 246 1060 194 5.47 in the diamond film, but also extend into the substrate. 230 1109 181 6.12 This observation indicates that the diamond-titanium https://www.cambridge.org/core Average 5.75 6 0.56 48 6 13 interface is somewhat brittle.

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Given the widths of the delaminated areas and the effective widths of the indentations, the critical crack extension force for delamination of the diamond ﬁlm can be read from the plot in Fig. 4. The substrate yield stress (732 MPa) used to calculate the curves in Fig. 4 was taken to be one third of the hardness of the titanium substrate as measured with wedge indentation. The elastic properties of both titanium and diamond were taken from the literature.10,23 A summary of the experimental results is given in Table I. According to Fig. 4 and taking into account the thickness of each sample, the crack extension

force at which the interface crack ceases to propagate https://doi.org/10.1557/JMR.1997.0260 . . is approximately 51 6 11 J͞m2. This value, then, corresponds to the diamond-titanium interface toughness. It is many times the atomistic fracture energy of the interface and far exceeds the fracture toughness of the diamond film itself.11 A large portion of the energy required for delamination of the diamond film is spent in plastic deformation of the substrate. A small amount of energy is also dissipated as the diamond film is fractured into small fragments after delamination. This energy,

https://www.cambridge.org/core/terms however, is negligible as long as the fragments are substantially larger than the film thickness. The interface toughness found in our experiments is in very good agreement with the value of 48 J͞m2 reported by Drory and Hutchinson11 for a diamond-coated titanium alloy FIG. 6. SEM micrograph of an area near one of the corners of the (Ti–6Al–4V). They used the axisymmetric indentation wedge indentation. The cracks in the substrate are clearly visible. technique combined with a finite element analysis of the substrate displacement field. the piled-up area in Fig. 7. In order to calculate the size of the plastic zone, the effective indentation width B. XPS results defined in Eq. (14) was used in Eq. (12). Implicit in this We have made XPS measurements to determine the procedure is the assumption that pileup occurs over the composition profile of the titanium-diamond interface in entire extent of the plastic zone. This procedure showed the delaminated area immediately adjacent to the wedge , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , that the pileup constituted 38 6 2% of the displaced indentations. A scan of the photo-electron binding ener- volume, resulting in aeff ෇ 0.79a. gies from 0 to 1100 eV showed that the only chemical species present on the surface of the substrate are carbon, titanium, and oxygen. The spectra collected for these elements are shown in Figs. 8 to 10, respectively. The

20 Jul 2020 at 19:43:31 at 2020 Jul 20 carbon 1s spectrum (Fig. 8) shows two peaks, a large

, on on , peak at a binding energy of 284.5 eV and a smaller one at 282.0 eV. The large peak is the 1s peak of elemental carbon. It is caused by residual diamond or some amorphous carbon phase on the surface. The small

peak agrees well with the 281.6 eV value for TiC.24 Harvard University Harvard . . The spectrum shown in Fig. 9 contains two broad peaks centered around 455.6 eV and 461.6 eV, corresponding to the 2p3/2 and 2p1/2 binding energies of titanium, respectively. The titanium 2p peaks are off-set from the normal values by 1.6 eV. This indicates that the titanium on the surface of the sample is present as 3/2 3/2 titanium oxide (TiO 2p : 455 eV; TiO2 2p : 459 eV) or carbide (TiC 2p3/2: 455 eV).25,26 There is no evidence

https://www.cambridge.org/core FIG. 7. A typical proﬁlometer scan across one of the indentations. The arrow shows the extent of the plastic zone. for metallic titanium (Ti 2p3/2: 454 eV)27 on the surface

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J. J. Vlassak et al.: A simple technique for measuring the adhesion of brittle ﬁlms

https://doi.org/10.1557/JMR.1997.0260 . .

FIG. 8. Photoelectron spectrum for carbon in delaminated area. FIG. 11. Composition proﬁle as a function of sputter time for the various chemical species found in the diamond-titanium interface.

Figure 11 shows the composition proﬁle as a function of sputter time for the various chemical species

https://www.cambridge.org/core/terms found in the sample. It is clear from Fig. 11 that the titanium oxides are present on the surface of the sample only. The oxides may have formed while the interface was exposed to the ambient after delamination of the diamond ﬁlm or may be a remnant of the native oxide on the titanium substrate before diamond deposition. The carbide concentration drops off relatively quickly, indicating that titanium carbide is found only in a small region near the surface of the sample. As the carbide concentration decreases and the titanium concentration increases, the titanium 2p peaks increase in intensity FIG. 9. Photoelectron spectrum for titanium in delaminated area. The and shift toward lower binding energies. This energy arrow indicates the position of the 2p3/2 peak for pure titanium. shift is due to the presence of metallic titanium deeper in the sample. The diamond concentration increases , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , slightly with depth and then remains constant. This is caused by diamond still embedded in the substrate after delamination. After long sputtering times, the diamond is completely removed and the underlying titanium carbide is exposed to the x-rays. This explains the sudden

20 Jul 2020 at 19:43:31 at 2020 Jul 20 increase in titanium carbide concentration at long sput-

, on on , tering times. Since there is no evidence for the presence of oxides under these diamond particles, we can safely assume that the oxides on the fracture surface were formed after diamond delamination, rather than during

the deposition process. Figure 12 summarizes the XPS Harvard University Harvard . . results in the form of a schematic of the diamond- titanium interface after delamination. The delamination crack apparently propagates along the interface between the diamond film and the titanium carbide, exposing FIG. 10. Photoelectron spectrum for oxygen in delaminated area. titanium carbide, but also leaving diamond behind in some areas. Our observations agree with a study by of the sample. The oxygen 1s peak is shown in Fig. 10. Perry et al.,24 who find that film delamination occurs It is a broad peak centered around 532 eV, indicating near the nucleation plane of the diamond film within a https://www.cambridge.org/core that the oxygen is present on the surface as an oxide. reaction layer containing oxides and carbides and that

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FIG. 12. Schematic of diamond-titanium interface after delamination.

https://doi.org/10.1557/JMR.1997.0260 . . small regions of diamond remain at the interface. The crack does not propagate entirely within the diamond film, despite the fact that the interface is much tougher than the diamond film. This can be attributed to the com- FIG. 14. Hardness of the diamond-titanium interface as a function of pressive stress in the diamond film, which closes flaws in plastic depth. the diamond film that may act as crack nucleation sites. For shallow indentations, the hardness of this diamond- C. Nanoindentation results titanium carbide layer dominates, whereas the hardness https://www.cambridge.org/core/terms Figure 13 shows a typical load-displacement plot for measured in large indentations is mostly determined an indentation in the titanium substrate in an area where by the underlying titanium. After argon sputtering, the the diamond film has delaminated. Indentation plots hardness decreases to approximately 4 GPa. It does not such as this one yield information on the mechanical vary significantly with indentation depth except for very properties of the diamond-titanium interface. The hard- shallow indentations, where an increased hardness is ness of the interface as determined by the Oliver–Pharr found. This increase is probably due to damage induced technique22 is plotted as a function of plastic indentation in the titanium surface by impinging argon ions. depth in Fig. 14. The hardness after 40 min of argon Figure 15 shows the hardness of a blank titanium sputtering is also shown. Each data point in Fig. 14 substrate and that of the back side of one of the diamond- corresponds to the average hardness for all indentations coated samples as a function of indentation depth. The with the same depths. The hardness before sputtering hardness of the titanium substrate before diamond depo- increases rapidly for indentation depths below 400 nm sition is approximately 1.3 GPa for indentations deeper and reaches a value as high as 14 6 4 GPa. This is than 700 nm. The increased hardness for shallow inden-

consistent with the presence of a thin hard layer con- tations is probably due to work-hardening of the titanium , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject ,

sisting of diamond and titanium carbide at the interface.

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FIG. 15. Hardness of the titanium substrate as a function of plastic

https://www.cambridge.org/core FIG. 13. Typical load-displacement plot for an indentation in an area depth. Open circles are for a substrate exposed to the diamond of the substrate where the diamond ﬁlm has delaminated. deposition environment; squares are for an unexposed substrate.

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surface that may have occurred during sample prepara- sputtering. This indicates that the indentation modulus tion. Exposing the substrate to the diamond deposition of the interface is dominated by that of the underlying environment increases the hardness of the titanium to titanium. The experimental moduli are indeed close to, 2.6–3.0 GPa. This observation is conﬁrmed by Rockwell but slightly higher than the indentation modulus of pure “B” hardness measurements of the same samples: The titanium. This discrepancy between the experimental and blank titanium substrate has a hardness of 85 6 1 HRB, the literature values may be due to some extent to while the diamond-coated substrate has a hardness of the titanium carbide remaining at the interface, even 97 6 1 HRB. The increased hardness of the diamond- after 40 min of sputtering (see Fig. 11). Pileup of the coated substrate can be explained by the diffusion of titanium around the indenter also causes the experimental small amounts of impurity atoms such as carbon and indentation modulus to be higher than the actual mod- hydrogen into the substrate during the diamond depo- ulus and is thought to be the main reason for a high

sition process. Since the hardness enhancement is much modulus. https://doi.org/10.1557/JMR.1997.0260 . . larger for the nanoindentation measurements than for the macroscopic Rockwell measurements, one can conclude that the affected area is limited mostly to the surface V. CONCLUSIONS of the substrate. The presence of these impurities in The wedge delamination test can be used to esti- the substrate could cause embrittlement of the titanium mate the adhesion of brittle ﬁlms to ductile substrates. substrate, which may be a concern in practical applica- The technique has the advantage over the axisymmetric tions of diamond-coated pure titanium. Additional work indentation test that no tensile hoop stresses develop in is needed on diamond-coated titanium alloys designed the coating. Radial cracking of the coating is therefore for resistance to hydrogen embrittlement. Embrittlement not a problem. Using the wedge delamination test, it is

https://www.cambridge.org/core/terms of the substrate also explains why the cracks observed in also possible to apply much larger energy release rates Fig. 6 are not just limited to the diamond film, but also to the interface between film and substrate. This makes extend into the substrate. However, in many applications the technique suitable for the study of brittle coatings titanium may be used as an interlayer between diamond that exhibit very good adhesion to their substrates. and the substrate, such as in the case of steel.28 It The critical crack extension force for the diamond- is unclear whether embrittlement of the interlayer is titanium interface is estimated at 51 6 11 J͞m2. This of concern for the mechanical reliability of diamond value is much larger than what one would expect for coatings in such applications. the atomistic work of fracture for the titanium-diamond The indentation modulus of the diamond-titanium interface because a large portion of the energy required interface, E͑͞1 2n2͒, can be determined by analyz- for delamination of the diamond film is spent in plastic ing the unloading portions of indentation curves similar deformation of the substrate. Photoelectron spectroscopy to that in Fig. 13.20,22 Figure 16 shows the indentation (XPS) shows that the interface consists of a thin reac- modulus as a function of plastic depth. There is no tion layer of titanium carbide. When the diamond film significant difference in modulus before and after argon delaminates, failure occurs partly in the titanium carbide , subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject , layer, partly in the diamond film, and a substantial amount of diamond is left behind on the substrate. After delamination, a thin layer containing titanium oxides forms on top of the titanium carbide due to exposure of the interface to the ambient.

20 Jul 2020 at 19:43:31 at 2020 Jul 20 These observations agree well with Nanoindentation

, on on , experiments performed on the diamond-titanium interface after delamination. The hardness of the interface is as high as 14 GPa for shallow indentations, but drops off quickly with increasing depth. This observation is

consistent with the presence of a thin, hard layer at Harvard University Harvard . . the interface. The diamond deposition ambient greatly enhances the hardness of the (99.6%) titanium substrate. This may be the result of impurities diffusing into the titanium at the diamond deposition temperature. These impurities may also cause embrittlement of the pure titanium substrate, which may limit the practical applications of this system. Further examination is needed of diamond-coated titanium alloys that are more resistant

https://www.cambridge.org/core FIG. 16. Indentation modulus of the diamond-titanium interface as a function of plastic depth. to embrittlement.

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ACKNOWLEDGMENTS 12. K. L. Johnson, J. Mech. Phys. Solids 18, 115 (1970). 13. T. O. Mulhearn, J. Mech. Phys. Solids 7, 85 (1959). Support for this study was provided by the Air 14. W. Hirst and M. G. J. W. Howse, Proc. Roy. Soc. A 311, 429–444 Force Materiel Command through Crystallume, subcon- (1968). tract No. CRY93-C-0199. The authors would like to 15. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity acknowledge the help of K. W. McElhaney for some of (McGraw-Hill, Inc., New York, 1987). the SEM work. 16. R. Hill, The Mathematical Theory of Plasticity, Oxford Engineer- ing Science (Oxford University Press, Oxford, 1950). REFERENCES 17. K. L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985). 1. M. G. Allen and S. D. Senturia, J. Adhesion 25, 303 (1988). 18. D. Tabor, Hardness of Solids (Oxford University Press, Oxford, 2. M. G. Allen and S. D. Senturia, J. Adhesion 29, 219 (1989). 1951). 3. Y. Z. Chu and C. J. Durning, J. Appl. Polym. Sci. 47, 1151–1164 19. J. W. Ager, G. Conti, and M. D. Drory, unpublished research. (1992).

https://doi.org/10.1557/JMR.1997.0260 20. M. F. Doerner and W. D. Nix, J. Mater. Res. 1, 601–609 (1986). . . 4. A. Bagchi, G. E. Lucas, Z. Suo, and A. G. Evans, J. Mater. Res. 21. M. F. Doerner, Mechanical properties of metallic thin ﬁlms on 9, 1734–1741 (1994). substrates using sub-micron indentation methods and thin ﬁlm 5. E. O. Shaffer II, F. J. McGarry, and F. Trusell, in Thin Films: stress measurements techniques, Ph.D. Thesis, Stanford Univer- Stresses and Mechanical Properties IV, edited by P. H. Townsend, sity (1987). T. P. Weihs, J. E. Sanchez, Jr., and P. Børgesen (Mater. Res. Soc. 22. W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564–1583 Symp. Proc. 308, Pittsburgh, PA, 1993), pp. 535–539. (1992). 6. E. O. Shaffer II, S. A. Sikorski, and F. J. McGarry, in Materials 23. G. E. Dieter, Mechanical Metallurgy (McGraw-Hill, New York, Reliability in Microelectronics IV, edited by P. Børgesen, J. C. 1986). Coburn, J. E. Sanchez, Jr., K. P. Rodbell, and W. F. Filter (Mater. Res. Soc. Symp. Proc. 338, Pittsburgh, PA, 1994), pp. 541–551. 24. S. S. Perry, J. W. Ager, G. A. Somorjai, R. J. McClelland, and 7. A. G. Evans and J. W. Hutchinson, Int. J. Solids Structures 20, M. D. Drory, J. Appl. Phys. 74, 7542 (1993). https://www.cambridge.org/core/terms 455–466 (1984). 25. L. Ramqvist, K. Hamrin, G. Johansson, A. Fahlman, and 8. D. B. Marshall and A. G. Evans, J. Appl. Phys. 56, 2632–2638 C. Nordiling, J. Phys. Chem. Solids 30, 1835 (1969). (1984). 26. H. Ihara, Y. Kumashiro, A. Itoh, and K. Maeda, Jpn. J. Appl. 9. C. Rossington, A. G. Evans, D. B. Marshall, and B. T. Khuri- Phys. 12, 1462 (1973). Yakub, J. Appl. Phys. 56, 2639–2644 (1984). 27. Handbook of X-ray Photoelectron Spectroscopy, edited by J. F. 10. M. D. Drory and J. W. Hutchinson, Science 263, 1753 (1994). Moulder, W. F. Stickle, P. E. Sobol, and K. D. Bomben (Perkin- 11. M. D. Drory and J. W. Hutchinson, Proc. Roy. Soc. 452, 2319 Elmer, Eden Prairie, MN, 1992).

(1996). 28. M. D. Drory, NIST Spec. Publ. 885, pp. 313–320 (1995).

, subject to the Cambridge Core terms of use, available at at available use, of terms Core Cambridge the to subject ,

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. . https://www.cambridge.org/core

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