XRD Stress Analysis of Nano-diamond Coatings on WC-Co Substrates

Y. K. Choua*, R. Schadb, P. Lua aDepartment of Mechanical Engineering, University of Alabama, Tuscaloosa, Alabama, United States bDepartment of Physics and Astronomy, University of Alabama Tuscaloosa, Alabama, United States *Corresponding author. E-mail address: kchou@eng.ua.edu (Y.K. Chou).

Abstract

Residual stresses in diamond coatings grown on WC-Co substrate have been investigated by

X-ray diffraction (XRD) method. Nano-diamond coatings were deposited by microwave plasma-enhanced chemical vapor deposition technique (MP-CVD). To measure residual stress, we tried different peak selection and instrument setting mode (χ mode and ω mode). For getting reliable residual stress value, sin2ψ-method with omega-tilting mode (χ=0) was employed. The (311) plane of CVD diamond was used with tilting angle (ψ) from -40 to 40 degrees. A compressive stress of 1.65GPa was obtained by linear fitting the mean d-spacing values of positive and negative tilting. The occurrence of “ψ-splitting” demonstrates the existence of non-zero shear stress normal to the surface. Keywords: Diamond coating, Residual stress, X-ray diffraction, ω mode, ψ-splitting

Introduction

Diamond is considered as an ideal material for cutting tool applications because of its unique characteristics such as wear resistance and high hardness, low friction, good thermal conductivity, and low coefficient of thermal expansion (CTE). Diamond tools, polycrystalline diamond (PCD) or chemical vapor deposition (CVD) coating based, have be successfully used in machining of nonferrous alloys (such as aluminum, cooper, magnesium), composite materials (such as fiber reinforced polymers), wood, semi-sintered ceramics, hard rubbers, graphite, etc. [1]. Compared to uncoated cemented tungsten carbide (WC) tool, CVD diamond coated tools, show a much greater abrasive wear resistance, also less tendency for build-up edge formations and lower cutting forces, leading to over ten times longer tool life and better surface finish of the machined workpieces [2].

However, insufficient adhesion between diamond coatings and substrates results in coating delamination and is the main obstacle for widespread adoption of CVD diamond-coated tools. One of the important causes of poor interface adhesion is the high deposition-induced residual stresses in the diamond-coated tools, which greatly degrade the adhesion strength of diamond coating [3-7]. Generally, the residual stresses in the coating are generated by two mechanisms.

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One is the thermal stress, which results from the difference in thermal expansion coefficients between the diamond coating and WC substrate and the high diamond deposition temperature, ~700 to 900 °C. Another is the intrinsic stress, which is built up during the coating crystal growth and it is associated with the non-diamond material at the grain boundaries and structural defects [8]. In the diamond-WC coating system, the thermal stress in the coating is compressive, but the intrinsic stress tends to be tensile.

Residual stresses in coatings are typically measured by the curvature method [9], Raman spectroscopy [10-11] and X-ray diffraction [12-14]. Particularly, Raman spectroscopy is a simple method that evaluates the stress through the diamond Raman peak shift. However, it may present difficulty in quantitative evaluations associated with the domain size effect [15]. In addition, multiple peaks may appear attributed to peak splitting due to a degeneracy of the optical phonons and the presence of inhomogeneous micro stresses [15]. Compared to Raman spectroscopy, X-ray diffraction allows evaluating an average stress at a larger sample area. In addition, the high penetration depth (about 600 μm) of the x-ray beam in diamond allows probing the coating throughout its whole depth [16]. The principle of residual stress measurement by XRD is simple; the crystalline lattice is used like an atomic-level stain gauge. Increases or decreases in the lattice spacing are recorded as angular shifts in the diffraction peak position [17]. Among many of XRD methods for residual stress measurements (such as the two-tilt method, single exposure method, etc.), sin2ψ method is commonly used, which consists of measuring the lattice spacing, d, of a specific plane at different tilting angles, ψ.

Many researchers have conducted residual stress measurements of diamond coatings deposited on various substrate materials like silicon [18, 19], aluminum [20], titanium [21-23]. However, very few studies were made on the analysis of residual stress in diamond coatings grown on cemented tungsten carbide tools. Evaluations of residual stresses of diamond coated cutting tools will help develop better cutting tools with stronger adhesion and, thus, a longer tool life. In this paper, a methodology of using sin2ψ-method with omega-tilting mode (χ=0) to measure residual stresses of diamond coated carbide tools. Results attained and problems encountered during the measurement of residual stress were discussed.

Experimental Details NCD Coating Preparation

The substrates were 6% Co fine grain WC of square-shape inserts (SPG422), 12.7 mm wide and 3.2 mm thick. The inserts were chemically etched for surface cobalt removal to facilitate diamond coating. The NCD coating was produced by a high-power microwave plasma-assisted CVD process using an in-house built reactor. The deposition conditions were an average H2 flow rate of 1650 standard cubic centimeters per minute (sccm), about 50 sccm CH4 flow rate, and 5 sccm N2 flow rate. The chamber pressure was less than 90 Torr and the substrate temperature was about 800 °C. The coating thickness at the bulk area is about 30 μm, comparable to commercial CVD diamond coating tools. The coating is uniform over the insert rake surface and

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the coating thickness at the flank surface decreases linearly to zero at about 0.9 mm from the substrate bottom. Scanning electron microscopic (SEM) characterization of NCD coating surface was shown in a previously published paper [25].

Selection of the Diffraction Peaks and χ Mode Trial

XRD measurements were performed using a Philips Analytical X-Ray Diffractometer PW 3040 with a Cu X-ray tube. In order to select diamond peaks for residual stress measurement, a conventional θ-2θ X-ray diffraction scan was carried out with the result shown in Fig1. Both WC and diamond peaks were detected. Generally, diamond has five diffraction peaks; whose positions shown in Table 1. As for the samples tested, only three diamond peaks were detectable which are the peaks associated with the lattice planes of (111), (220) and (311). Because the diamond peak from (220) diffraction overlaps with the WC peak from (200), it cannot be readily used for residual stress measurements. Thus, a choice must be made between from the (111) and (311) diffraction peaks. Compare to (111), the (311) peak is expected to be more responsive to the measurement as the lattice plane with a higher Miller index (hkl) is normally more sensitive to strain/stress [15,19]. However, its low intensity may be a potential trouble for accurate measurements. Therefore, a set of experiments was conducted to determine the peak selection.

Figure 1 X-ray diffraction pattern of nano-crystalline diamond coating on WC-Co substrate (2θ range: 30-80°)

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Table 1 Diffraction peak for diamond (Radiation: CuKα1) d-spacing(Å) Relative intensity Miler indices (hkl) Position(2θ)

2.06 100 111 43.915° 1.261 25 220 75.302°

1.0754 16 311 91.495° 0.8916 8 400 119.521° 0.8182 16 331 140.587°

To ensure peaks are detectable at all tilting angles, the (111) peak was attempted for stress

measurements first. For the instrument setting, the socalled “χ mode” (ω=θ) was used as it is more widely used among the sin2ψ-methods for residual stress measurements. The results, however, show an increase of the peak widths with the increasing of sin2ψ, which greatly affects the accuracy of the diffraction angle of the peak. Moreover, the asymmetric peak broadening phenomenon makes it literally impossible to obtain accurate values of peak shifting caused only by residual stresses. Literature reported such a similar phenomenon. The increasing of the peak widths with increasing sin2ψ may originate from an increased deviation from an ideal sample height adjustment at higher tilt angles [26]. Also, as the Kα radiation technique was employed, variable blending of Kα doublet caused by defocusing when ψ is changing [27] might also contribute toward the peak broadening. Given the aforementioned results and reasons, it seems impractical to employ the (111) lattice plane when using χ mode for residual stress measurements. On the other hand, the intensity of peak from (311) is too low when using the χ mode to accurately measure, Thus, a different mode, namely, the ω mode of conventional x-ray diffraction, was applied for residual stress measurements. Although both peaks from (111) and (311) diffraction can be measured in ω mode, we chose (311) for measurement as a higher angle peak will display a larger shift in 2θ [28]. It turned out that this method can be effectively applied to our samples. Details about the method are discussed below. Conventional X-ray Diffraction—ω Mode vs. χ Mode

For better understanding, we will describe detailed information about the ω mode and χ mode about conventional XRD residual stress measurements. The χ mode, also called ψ mode or side-inclination methods, occurred later than the ω mode. Differences between them lie in the configuration of the ψ angle. Fig.2 [29] shows tilting differences and various angle definitions for the χ mode and ω mode. In Fig.2, the specimen Cartesian reference frame was denoted S, in which S3 axis is oriented perpendicular to the specimen surface. Laboratory Cartesian reference frame was denoted L, in which L3 axis coincides with the diffraction vector. The normal of the {hkl} planes is parallel to the diffraction vector L3. The angles φ and ψ describe the orientation of the normal of {hkl} planes with respect to the specimen system S. Φ, ω, χ represents the rotation angle of the instrument.

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Figure 2 Definition of the various angles required to describe the diffraction geometries and variation of the angle ψ using (a) the ω mode (shown for ψ<0) or (b) the χ mode. L3 is the diffraction vector; S3 is the surface normal [29]

Residual Stress Measurements — sin2ψ-method with ω Mode

For residual stress measurements, the sin2ψ-method with omega-tilting mode (χ=0) was employed. Specimen was finely mounted on the stage of diffractometer. (311) lattice plane was used to determine the residual stress. θ/2θ scans were performed around a (311) Bragg diffraction peak (2θ~91.5°) at tilting angles ψ between -40° and 40°. Both positive and negative ψ tilts were employed. Points were counted with a step increment of 0.02°. The measurement time for each ψ was 6h or 12h. Peak locations were determined by fitting the diffraction peaks with Lorentizian

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function performed after background removal. Repeated measurements were carried out on the same specimen for 3 to 5 times so that by averaging measured results, instrumental errors caused by non-ideal alignment and specimen displacement [30, 31] could be minimized.

The residual stress can then be obtained from the following equation:

ψσνψ 2

0

0 sin1⋅⋅

+=

−totalEd

dd (1)

Where dψ is the lattice spacing at each ψ, and d0 is the spacing when ψ is 0°. For diamond coatings, we use 1250 GPa as the Young’s modulus, E, and 0.07 for Poisson’s ratio, υ. The value of dψ for each ψ was calculated and then plotted as a function of sin2ψ. If the behavior of plotted curve is linear, it indicates a bixial and homogeneous stress existing in diamond coating. The value of d0 is determined as the intercept of linear fitting curve base on dψ versus sin2ψ. Stress estimation was carried out by using the slope of the curve.

The diffraction spectrum for different ψ angles (0~-40°) from one round measurement was shown in Fig. 3. The peak intensity for high ψ angles (ψ=30, 40°) is slightly higher because X-ray diffracts shallower on the coating surface. Fig. 4 shows the plot of the lattice spacing dψ versus sin2ψ, evidencing the negative and positive ψ values. The mean value of dψ from positive and negative ψ was calculated and plotted versus sin2ψ as shown in Fig. 5. Linear fitting of the mean value shows a negative slope which suggests a compressive residual stress in the diamond coating. The calculated total residual stress based on the fitted slope (-0.00152) is 1.65 GPa.

Figure 3 The diffraction spectrum for different ψ angle of diamond coating (only negative ψ angle was shown)

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Figure 4 Plot of lattice spacing dψ versus sin2ψ for (311) reflection from CVD diamond coating.

Figure 5 Plot of mean lattice spacing dψ versus sin2ψ for (311) reflection from CVD diamond coating. The negative

slope indicates a compressive residual stress.

1.0744

1.0746

1.0748

1.075

1.0752

1.0754

1.0756

-0.1 0 0.1 0.2 0.3 0.4 0.5

sin2ψ

d(Å

)

ψ>0ψ<0

sin2ψ

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Discussion

As shown in Fig.4, lattice spacing measured at a negative ψ differs from those measured at a positive angle. It is a non-linear behavior and this phenomenon is termed as “ψ-splitting” [17, 28]. In this study, “ψ-splitting” is very obvious when ψ = 10° and 20°. However, the mean d-spacing of positive and negative ψ as shown in Fig.5 is linear. This indicates an existence of shear stresses (σ13 or σ23≠0) in the diamond coatings [17].

The X-ray method for determination of residual stresses in crystalline materials is based on the measurement of inter-planar spacing d at various tilts, φ and ψ, to the X-ray beam (Fig.6). The fundamental equation of x-ray strain determination is

sin2ψsinεsin2ψcosεψcosεψsinsinεψsinsin2εψsincosεdψ),Δd(

23132

3322

222

1222

11 ϕϕϕϕϕϕ+++++= (2)

Generally, a linear sin2ψ plots is based on the assumption of biaxial stress states. For a biaxial stress state, εij with j=3 can be neglected, for a constant φ, ∆d(φ,ψ)/d and sin2ψ are linearly related. However, if either of the shear ε13 or ε23 is non-zero, according to the above equation, strains measured at negative ψ tilts will differ from those measured at positive angles, which is known as “ψ-spliting”. The existence of shear stresses (σ13, σ23≠0) will cause curvature in the d vs. sin2ψ plots.

Based on the results of “ψ-spliting”, it can be concluded that the stress state in diamond coating is triaxial not biaxial, and the shear stress normal to the surface cannot be neglected. The penetration of X-ray tends to be in the tens of micrometers range increasing sharply with deceasing atomic numbers. In this study, C has a very small atomic number, thus the penetration of X-ray on diamond coatings should be comparatively deep. This might also render the biaxial assumption being not valid in our study.

Figure 6 Definition of the coordinate system for the specimen Si and the laboratory system Li

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Conclusions

In summary, residual stresses in nano-diamond coatings on WC substrates have been measured by XRD methods. (311) lattice plane was selected. The sin2ψ-method with omega-tilting mode was employed during the measurements. Lattice spacing measured at negative ψ differs from those measured at a positive angle. This occurrence of “ψ-splitting” demonstrates the existence of non-zero shear stress in the normal direction of sample surface. By linear fitting of the mean d-spacing values from the positive and negative tilting, a compressive stress of 1.65 GPa was measured in nano-diamond coatings.

Acknowledgements

This research was supported by NSF, CMMI-0728228. The authors would like to thank X.

Liu for conducting and analyzing some experiments.

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