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Triaxial stress distribution in a textured titanium nitride coating
Surface and Coatings Technology, 68/69 (1994) 259—265
259
Triaxial stress distribution in a textured titanium nitride coating J. A. Sue Praxair Surface Technologies, Inc., 1500 Polco Street, Indianapolis, IN 46224, USA
Abstract The elastic constants and residual stresses of a physical vapor deposition, highly (111) textured TiN coating were measured using X-ray diffraction Cu Ka and Cr K~radiation. No significant difference in elastic constants was found on the (222) and (333 )—( 511) planes which were determined from sampling depths of 1.8 jIm and 5.3 .tm respectively. The depth profiles oftriaxial residual stresses in the coating were characterized using Cr Ka radiation. Within the coating, the principal stresses in the coating plane exhibit a symmetric biaxial state, varying with the coating depth from 2400 to 3000 MPa in compression, whereas the principal stress normal to the coating surface is between 107 and 650 MPa in tension. A steep stress gradient is observed at the near-surface region in the coating.
1. Introduction The residual stresses of coatings obtained by physical vapor deposition (PVD) have a strong influence on their mechanical and physical properties. The X-ray diffraction method is most commonly used to determine the state and magnitude of residual stress in the coating. To obtain an accurate stress measurement, however, known values of X-ray elastic constants (XEC5) in the measured crystallographic plane are needed. XECs on various reflections in a variety of TiN coatings have been determined by several researchers [1—4], and then reliable values of residual stress were obtained. Since the X-ray penetration depth is generally very small, the measurement of surface stress represents an average over an irradiated volume. Surface residual stress in a coating is critical to coating process development, and the depth profile of the stress field which characterizes the stress gradient in the coating has a direct influence on its wear behavior. Hirsch and Mayr [1] studied the in-plane residual stress depth profiles in TiN and Ti(C, N) coatings using a low energy ion sputtering technique to remove coating layers incrementally, but the stress variation normal to the coating surface was not determined. Rickerby et a!. [5] observed that the magnitude of the normal tensile stress was 2%—15% of the in-plane compressive stresses in TiN coatings. Nonetheless, little is known on the distribution of triaxial stress within TiN coatings. A recently developed electrolytic stripping process [6] is capable of removing TiN coating layers without introducing any additional stress in the coating. A study incorporating this coating stripping technique was undertaken to determine the tnaxial stress distnbution
0257—8972/94/$7.00 SSDI 0257-8972(94)08069-B
as a function of coating thickness. The study is an extension of the work published in [4]. XECs for the (222) reflection were determined using Cr K~cradiation. A comparison in XECs was then made between (222) and (333)—(511). Triaxial stress analysis using Cu Kcc and Cr K~tradiation was applied to TiN coatings on various substrates. The in-plane and normal stress distributions as functions of coating depth from the coating surface were determined. The stress distribution is discussed in terms of variations in crystallite size, crystallographic orientation, microstrain and nitrogen gradient in the coating.
2. Theory and measurement techniques 2.1. X-ray diffraction method Stress measurement using the X-ray diffraction method is based on the change in the lattice spacing (strain) at the near-surface of the material at various tilts to X-ray beam. The details of the theory and interpretation of residual stress measurement have been well described elsewhere [7—9]. For an isotropic material with d0 as the strain-free lattice spacing in the sample plane normal, the measured strains in the azimuth angle 4 and the tilting angle ~Jiat a given orientation of the diffracting plane (hkl) with respect to the sample coordinate system are related to stress tensor components a~ (j, I x, y, z) by d — d0 d =
~‘
=
=
S2 2
[a
cos
2
4
+
2
a~sin(24) + a sin çb
—
aj sin
2
© 1994 — Elsevier Science S.A. All rights reserved
J. A. Sue
260
/
Triaxial stress distribution in TiN coating
S2 M~90=d0-~-(a5—a) +~
cos ~ + ay, sin ~)sin(2~)
(1)
2.1.1. Biaxial stress state For stress measurements, one usually assumes a biaxial stress state in the coating with a~,= a~,= = a, = 0: — d0 =
d~
=
-~-(a~ cos
2 q$ + ay sin2 q5) sin2 ~fr + Si(a~+ a~)
(2)
coating parallel to2 its q5 +a, surface a~ q5 aisangle the macrostress 4 to the principal in the axis Forofathe biaxial sample. state = sin2 a~=at where a4 = a~cos 4, at t1/i = 0. d44 d0 = 2S~ a4 —
d0
From Eqs. (2) and (3) d44 = d4~0+ a4d0 2 ~,& (4) sin In the linear plot of d 2 i4’, the slope M = 44 vs. sin a 4d0(S2/2) and the intercept I = ~ The stress can then be determined from a4
=
M d0(S2/2)
(5)
2.1.2. Triaxial stress state without shear stress For a material in the three-dimensional stress state without i.e. no ‘~i splitting’ a plota offinite d44 2 ~i,shear but stress, the stress component a, inhaving vs. sin value within the X-ray penetration volume, the Eq. (1) is given by
S2
I = d0
(7)
a, + Si(a~+ a~+ ar))
From the sum of the slopes and the intercepts in Eq. (7), a~,ay and a, can be easily determined. 2.2. Determination ofstrain-free lattice spacing For a triaxial stress state, a strain-free lattice spacing can be determined in the strain-free directions at ~ = 0 and
~ ~fr* which =
is given [10] by
dsin2~Ji’~’= —2Sf 52 (i+a~~z+(3+S 2 ~1i’~’ a, a, a, a, 0 = d4~0+ M sin 2/2Si)az) 3. Experimental details —
—
(8)
3.1. Materials A TiN coating was deposited on disk substrates (diameter, 23 mm; thickness, mm) bymaterials a PYD cathodic arc (d.c.) process. The 4.8 substrate were Ti—6 wt.%Al—4 wt.%V, 17—4 PH, AM-355, Inconel 718 and AISI 304 stainless steel. The coated samples had already been previously investigated for XECs on (422) and (333)—(511) of the coating by X-ray diffraction [4]. The coating thicknesses were 10—12 p.m. The deposition parameters were as follows: chamber pressure, 3.7 Pa; arc current, 125 A; d.c. bias voltage, —150 V; substrate temperature, 733 K. The details of substrate preparation, coating apparatus and deposition process have been described elsewhere [4,11,12]. 3.2. Deflection measurement The deflection of the disk was measured from the change in its curvature during coating deposition by
d 44
—
d0
d~
=
52 =
2 q~+ ay sin2
4~
—
a,) sin2 ~4
(a~cos
+
a, + Si(a, + a~+ a,)
(6)
Two data sets, ~ = 0°and q~= 90°,are needed to obtain a,, a~and a,. The slopes and intercepts of the linear function of d 2 li at ~ = 00 and q5 = 90°are given 44 vs. sin by
profilometry. The measurements were performed at the same position across the diameter of the disk before and after coating. Based on the measured deflection, the internal stress of the coating was then calculated [4,13]. 3.3. Removal of TiN coating TiN coating on a Ti—6 wt.%Al—4 wt.%V substrate was electrolytically stripped in successive layers in a hydrogen-peroxide-containing solution with 10 V d.c. and 0.6 A for 30—80 mm [6]. A control sample with a known coating thickness accompanied the test sample during each removal of a thin coating layer. Subsequently, the stripped coating thickness was measured
M 40
=
d0
(a~— a,)
metallographically on the control sample after each removal of a coating layer, and the stripping rate was
J. A. Sue
/
Triaxial stress distribution in TiN coating
then computed. A typical coating stripping rate was 0.04 p.m min’.
261
6
5~
3.4. X-ray diffraction analysis X-ray diffraction analysis was carried out on a Scintag PTS four-circle goniometer and a computer-controlled and fully automated X-ray diffractometer with a Ge solid state detector, using Cu Kc~and Cr Kct radiations. The diffractometer is arranged in the parafocusing configuration. The measured data were reduced using a Micro Vax 3100 computer and Scintag diffraction management system (DMS) software. The system is capable of measuring the diffraction peak position to within ±0.01°. For crystallographic orientation, microstrain and crystallite size analysis, the divergent beam from the X-ray tube was limited by the 4 mm/Soller/2mm slits to the sample and the diffraction beam was converged at 0.5°/Soller/0.3°receiving slits. The crystallographic onentation of the coating was quantitatively analyzed using the full width at half-maximum (FWHM) from the rocking-curve measurement on (111) reflection. The microstrain and crystallite size of the coating were determined on double orders of the { 111 } reflection by the Warren—Averbach method [14]. An LaB 6 powder (NIST SRM 660) was used as a reference standard to correct the instrumental effect. For residual stress measurements, the irradiated area was positioned at the center of the disk sample using an incident beam collimator of 2 mm diameter. The divergent and receiving slit2 widths were was 4mm applied and 2mm i4 method to respectively. The sin (333)—(511) and (222) reflections which had 20 values of approximately 139° and 137° using Cu Kci~ (A = 0.154 060 nm) and Cr Kx (A = 0.228 970 nm) radiations respectively. The penetration depths tm in (333)—(511) and (222) in TiN from these two sources as a function of sin2 ~‘ were calculated and are shown in Fig. 1. For both radiations, the irradiated volume clearly decreased with increasing tilt angle ti’. Because of the highly (111) preferred orientation of the coating, the (511) contribution to the diffraction 2 ~ distribution intensity was negligible. d44 in vs.both sin directions ±ii’. was measured up to sin2 ~(iThe = 0.95 The peak position of diffraction lines at various angles was determined by profile fitting using the Pearson VII function. XECs for (333)—(511) and (222) reflections 2 i/i distributions of TiN were obtained from substrates. d44 vs. sin In tniaxial stress analycoating on various sis, d 2 i~ distributions at çb = 0° and q5 = 90° vs. sin on (222) of the TiN coating on were 4~, obtained Ti—6 wt.%Al—4 wt.%V substrate. The measurements of crystallographic orientation, microstrain, crystallite size and triaxial stress were performed at different coating
(333)/(511),
~--~
Cu
Ka
.~
.3
4
~ 3
~
2 (222), Cr Ka 1
0 0.0 .
0.2
0.4
.
sin2w
0.6
0.8
1.0
.
Fig. 1. ~, Penetration depth of X-rays in a TiN coating as a function of sin2
depths by successive removal of a thin layer of TiN coating.
4. Results and discussion 4.1.Figs. X-ray constants 2(a)elastic and 2(b) show typical least-squares fits of d 2 i~Le for (333)—(511) and (222) in TiN coating 4,1, vs. sin (sample 1 in Table 1) with linear correlation coefficient
of —0.97 and —0.99 respectively. No ,/, splitting was observed; shear stresses were then taken to be zero. Since the coating was highly (111) textured, the diffraction intensities at sin2 i~!i = 0.06—0.17 for (333)—(511) and 0.13—0.17 for (222) were so low that the peak positions could not be determined precisely. The data in these regions were then excluded from the analysis. The XECs S S~for the (333)—(511) (222) reflections of 2/2 TiNand were obtained from theand plot of ~d 2 iji) vs. a~+ ash and d 44/~ (sin 4~0 vs. a1 + ash, as shown in Figs. 3(a) and 3(b) respectively. a~represent the intrinsic sress of the coating resulting from the deposition process, and ash is the thermal arising from thermal expansion mismatch betweenstress the coating and the substrate. Table 2 gives a comparison of XECs for (333)—(511) and (222) in TiN determined using Cu K~ and Cr Kcx radiations respectively. Both (333)—(511) and (222) have the same crystallographic orientation parameter 3F= 1 (F= (h2k2 + k212 + 12h2)/ (h2 + k2 + 12)2) and their XEC values are expected to be
J. A. Sue
262
/
Triaxial stress distribution in TiN coating
0.0820
-0.0012 TIN COATING
~
TIN COATING
3T~N
~
____________________
0.1232 TIN COATING
__
E
KaRADITION
0.1232
0.1222
-5000
0.1220
-4000
RESIDUAL STRESS, aj
-3000 +
Fig.3. Measurement of X-ray elastic constants for (222) ofTiN using
0.1218
.
0.0
0.2
(b)
0.4
2w
0.6
0.8
1.0
sin
Fig. 2. d~ vs. sin2 1 distributions of TiN from (a) (333)—(511) and (b) (222) reflections,
identical as well. Although there was a marked difference between the irradiated volumes, good agreement between the XECs of (222) and (333)—(511) was observed. However, greater standard deviation in XECs for (222) was evident. This can probably be attributed to the statistical average over a relatively small sampling volume during diffraction measurements.
4.2. Biaxial stress Biaxial residual stresses in (222) and (333)—(511) planes of the TiN coatings were calculated from the slope of linear distribution of d 2 i~li and the 44 vs. sin measured XECs (Table 2). These stresses were considered as surface stresses. Table 1 gives a comparison in residual stresses measured via deflection and X-ray diffraction for a set of samples. The magnitude of residual stresses determined using Cr Kct radiation were consistently higher than those measured using Cu Kc radiation. This behavior was also observed in Ti(C, N) [1]. Stresses in (333)—(511) were comparable with those
Table 1 Residual stresses determined by X-ray diffraction and deflection Sample
I II III IV V
-2000
~ ~th (Mpa)
Substrate
Ti—6 wt.%Al—4 wt.%V 17—4 PH AM-355 Inconel 718 AISI 304
Residual stress (MPa) X-ray diffraction ________________________________________ (222) (333)—(511)
Deflection, overall average
—3014 ±59 —3219 ±47 —3397±64 —3751 ±56 —4628±58
—2688 ±285 —2746 ±247 —2844±279 —3431 ±343 —4167±408
—2630 ±67 —2946 ±39 —3165±63 —3571 ±62 —4345±40
J. A. Sue
/
Triaxial stress distribution in TiN coating
Table 2 X-ray elastic constants of TiN from (222) and (333)—(511) reflections
(222) (333)—(511) [4]
(xlO~GPa
—0.63 ±0.11 —0.67 ±0.07
average within the penetration depth. The data were not corrected for the removal of the surface layers. The location irradiated of each depth measurement within t +ofT~, where t volume is the coating removedwas by
1)
10~GPa~i)
Reflection
263
3.31 ±0.48 3.42 ±0.29
measured by the deflection technique within experimental uncertainty, whereas stresses in (222) deviated significantly from those measured by the deflection. The discrepancy between them may arise from the surface effect and the disregard of the normal stress, 4.3. Triaxial stress
Triaxial stress analysis with the assumption of no shear stresses was performed on TiN coatings on various substrates (samples I—V) at 4~= 0° and 4’ = 90° using Cu K~and Cr Kit radiation. Table 3 summarizes the in-plane stresses a~and ay and normal stress a, in the coating. Relatively large scatter in a, on (333)—(511) was observed. With considerations of a,, the in-plane stresses measured from both radiations were in remarkable agreement, within 6%. In contrast, stresses obtained from biaxial sin2 i~i method varied from 6.5 to 14.6% (Table 1). Implicitly, a biaxial stress approach is adequate to obtain an accurate result if the sampling depth is sufficient; a triaxial stress analysis is highly recommended because it accounts for the influence of the normal stress on the in-plane stress measurement if a, ~ 0. 4.4. Triaxial stress distribution 4.4.1. Triaxial stress depth profiles The in-plane and normal stresses at various depths from the coating surface were calculated and given in Table 4 together with other parameters. Fig. 4 shows the depth profiles of residual stresses a~,a~and a,. Each data point represents the diffracting volume-weighted
stripping from the coating surface and Tm is the penetration depth of X-rays. The stress normal to the coating surface was tensile, whereas the in-plane stresses were highly compressive and exhibited rotational symmetry throughout the coating thickness. Both stresses exhibited a steep gradient in the near-surface region. The former decreased from 193 MPa at a depth of 8.4—10.2 p.m to a minimum of 107 MPa at 1.3—3.1 p.m and increased to a maximum of 650 MPa toward the surface. The latter increased from —2728 MPa at a depth of 8.4—10.2 p.m to a maximum of —3015 MPa at 1.3—3.1 p.m and then decreased to —2369 MPa toward the surface. The in-plane stress relaxation at the near-surface of the coating was clearly evident. To avoid diffraction interferences from the substrate, the analysis was carried out only to a coating depth of 8.4 p.m. The residual stress in substrate after complete removal of the coating was equal biaxially and slightly in compression, about —70 MPa, which was within experimental uncertainty. 4.4.2. Crystallographic orientation, crystallite size and microstrain Figure 5 shows the crystallite size, microstrain and FWHM from the (111) rocking-curve measurement as a function of the coating depth from the surface. The FWHM indicated that the (111) plane of crystallites throughout the coating thickness was parallel to the coating surface within 4—5.5°. The crystallite size was found to be smaller near the coating—substrate interface, about 12.4 nm, and slightly larger near the surface, about 15.3 nm. The microstrain was found to increase gradually with increasing coating depth and a marked increase toward the coating—substrate interface. No apparent correlation was observed between FWHM, microstrain, crystallite size and triaxial stress distribution.
Table 3 Triaxial stresses of TiN coating determined from (222) and (333)—(511) reflections Sample
Residual stress (MPa) (222) 0’,
I II III IV V
—2364±183 —2677±128 —2846±156 —3224±156 —4024±236
(333)—(511) O’y
0,
0
O’y
0’,
—2370±190 —2649±128 —2833±150 —3034±172 —4099±259
651±173 543±119 551±142 527±157 605±228
—2536±183 —2464±119 —2534±180 —3150±142 —4078±95
—2430±195 —2449±122 —2568±183 —3214±144 —4009±98
93±170 482±111 630±169 246±129 266±87
J. A. Sue
264
/
Triaxial stress distribution in TiN coating
Table 4 Triaxial stresses, lattice spacings of (222) and lattice constants as functions of coating depth Coating depth
Sampling depth + Tm
Residual stress (MPa)
Strain-free direction
(222) lattice spacing
(jim)
(iim)
a,
sin(2~)
d0 (nm)
0 1.3 3.0 5.0 8.4
0—1.8 1.3—3.1 3.0—4.8 5.0—7.8 8.4—10.2
—2369 —3015 —2858 —2754 —2728
0.469752 0.395124 0.402617 0.394299 0.414419
0.1223689 0.1224267 0.1224181 0.1224303 0.1224046
—2317 —3011 —2854 —2812 —2811
651 107 156 164 193
__________________________________________
Lattice constant a 0 (nm)
0.4238982 0.4241177 0.4240689 0.4241110 0.4240220
4.4.3. Strain-free lattice constant and nitrogen gradi-
2000 TiN COATING
ent effect Table 4 also gives the strain-free direction, strain-free lattice spacing and lattice constant at various depths in the coating. A significant gradient in strain-free lattice spacing and lattice constant occurred at the near-surface
i
1000
SUBSTRATE ~©~©
\0
ci)
W
z
I
region. profile of concentration Figure in TiN,6 shows which the wasdepth determined by Nsputtered neutral mass spectrometry [15]. In the near-surface
I.I 0 ii)
region, the N concentration decreased from 52.5 at.% at the to approximately 50 at.% at the depth greater thansurface 0.4 p.m. A similar increase in N concentration at
1000
_1
0y 2000
w
the near-surface region of TiN coating was also reported elsewhere [1]. The decrease in lattice constant resulting from increase in N content by Sundgren et a!. an [16]. A marked decreasewas in reported lattice constant in the
-3000 COATING/SUBSTRATE—~.1
INTERFACE -4000
‘
0
i
‘‘‘
2
4
6
8
10
DISTANCE FROM COATING SURFACE
12
(jim)
Fig. 4. Triaxial stresses vs. the depth of TiN coating. 20
‘‘‘‘‘‘
18
CRYSTALLITE SIZE
~
FWHM
_________________________________
U
2
X16
0.20
‘
—0-—
near-surface region can probably be attributed to a composition gradient and surface relaxation. The overall variation in lattice constant, in a physical sense, coincided with the behavior of in-plane compressive stresses and normal tensile stress.
I
70 0.18
TIN COATING
I
MICROSTRAIN
I
0.16
I u14~
._
a0.14~
I~ Ia: IC,)
Ui
~
0.12~ 1 Cl) I 1
60
~. Z
~
50
~
0.10
Z Ui
0 z
I
40
0.08
C) COATING/SUBSTRATE INTERFACE
‘—~~
....,
6 0
2
I 4
6
8
10
0.06 12
DISTANCE FROM COATING SURFACE (jim)
Fig. 5. Variations in crystallite size, microstrain and FWHM of (111) reflection from the rocking-curve measurement with coating thickness of TiN,
I 30! 0
1
2
3
4
DISTANCE FROM COATING SURFACE (jim)
Fig. 6. Neutral sputter mass spectrometry nitrogen concentration depth profile in TiN coating.
J. A. Sue
/
Triaxial stress distribution in TiN coating
5. Conclusions
265
References
(i) The XECs for (222) of TiN are S~= —0.63 x iO~GPa~ and S2/2 = 3.31 x iO~GPa’. The XEC va!ues appear to be independent of irradiated volume during the measurement. 2 i~’biaxial approach is adequate to (ii) The X-rayin-plane sin obtain accurate stress measurement if the penetration depth of the X-ray is sufficient, whereas a triaxia! stress analysis without consideration of shear stresses is recommended to obtain precise in-plane stresses and the normal stress as well. (iii) The in-plane stresses in TiN coating are in cornpression and have rotational symmetry throughout the coating thickness. The compressive stress increases to a maximum of —3000 MPa at approximately 2 p.m from the coating surface and then decreases to 2400 MPa toward the surface. The normal stress of the coating is in tension. The tensile stress decreases gradually from 193 MPa at 8.4—10.2 p.m to a minimum of 107 MPa at 1.3—3.1 p.m from the coating surface and then increases to a maximum of 650 MPa toward the surface. Both the steep gradients in the in-plane stress and the norma! stress in the near-surface region of the coating are probably due to surface relaxation and nitrogen concentration gradient. —
[1] T. Hirsch and P. Mayr, Surf. Coat. Technol., 36 (1988) 729. [2] A. J. Perry, Thin Solid Films, 193—194 (1990) 463. [3] A. J. Perry, V. Valvoda and D. Rafaja, Thin Solid Films, 214 (1992) 169. [4] D. J. A.S. Sue, Surf. Coat. Technol., 154. [5] Rickerby, A. M. Jones 54—55 and B.(1992) A. Bellamy, Surf Coat. Technol., 36 (1988) 661. [6] J. A. Sue, US Pat. 5,062,941, 1991. [7] V. M. Hauk, Adv. X-ray Anal., 27 (1984) 81. [8] Soc. Auto. Engrs., Residual Stress Measurement by X-ray D(ffraction, SAE Handbook J784a, Society of Automotive Engineers, Warrendale, PA, 2nd edn., 1971. [9] I. C. Noyan and J. B. Cohen, in B. Ilschner and N. J. Grant (eds.), Residual Stress Measurement by Djffraction and Interpretation, Springer, New York, 1987. [10] V. Hauk and E. Macherauch, in E. Macherauch and V. Hauk (eds.), Residual Stress in Science and Technology, Deutsche Gesellschaft fur Metallkunde Informationsgesellschaft, Oberursel, 1987, p. 246. [11] J. A. Sue and H. H. Troue, US Pat. 4,929,322, 1990. [12]J. A. Sue and H. H. Troue, US Pat. 4,895,765, 1990. [13] D. S. Campbell, in L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology, McGraw-Hill, New York, 1970, p. 12. [14] H. P. Klug and L. E. Alexander, X-ray D)[fraction Procedure for Polycrystalline and Amorphous Materials, Wiley, New York, 1974, p. 643. [15] J. A. Sue, Surf. Coat. Technol., 61(1993)115. [16] J.-E. Sundgren, B.-O. Johansson, S.-E.
Karlsson
H. T. G. Hentzell, Thin Solid Films, 105 (1983) 367.
Acknowledgment The author is grateful to Mr R. E. Newman for preparation of the coating and carrying out the deflection experiment and measurements.
and
259
Triaxial stress distribution in a textured titanium nitride coating J. A. Sue Praxair Surface Technologies, Inc., 1500 Polco Street, Indianapolis, IN 46224, USA
Abstract The elastic constants and residual stresses of a physical vapor deposition, highly (111) textured TiN coating were measured using X-ray diffraction Cu Ka and Cr K~radiation. No significant difference in elastic constants was found on the (222) and (333 )—( 511) planes which were determined from sampling depths of 1.8 jIm and 5.3 .tm respectively. The depth profiles oftriaxial residual stresses in the coating were characterized using Cr Ka radiation. Within the coating, the principal stresses in the coating plane exhibit a symmetric biaxial state, varying with the coating depth from 2400 to 3000 MPa in compression, whereas the principal stress normal to the coating surface is between 107 and 650 MPa in tension. A steep stress gradient is observed at the near-surface region in the coating.
1. Introduction The residual stresses of coatings obtained by physical vapor deposition (PVD) have a strong influence on their mechanical and physical properties. The X-ray diffraction method is most commonly used to determine the state and magnitude of residual stress in the coating. To obtain an accurate stress measurement, however, known values of X-ray elastic constants (XEC5) in the measured crystallographic plane are needed. XECs on various reflections in a variety of TiN coatings have been determined by several researchers [1—4], and then reliable values of residual stress were obtained. Since the X-ray penetration depth is generally very small, the measurement of surface stress represents an average over an irradiated volume. Surface residual stress in a coating is critical to coating process development, and the depth profile of the stress field which characterizes the stress gradient in the coating has a direct influence on its wear behavior. Hirsch and Mayr [1] studied the in-plane residual stress depth profiles in TiN and Ti(C, N) coatings using a low energy ion sputtering technique to remove coating layers incrementally, but the stress variation normal to the coating surface was not determined. Rickerby et a!. [5] observed that the magnitude of the normal tensile stress was 2%—15% of the in-plane compressive stresses in TiN coatings. Nonetheless, little is known on the distribution of triaxial stress within TiN coatings. A recently developed electrolytic stripping process [6] is capable of removing TiN coating layers without introducing any additional stress in the coating. A study incorporating this coating stripping technique was undertaken to determine the tnaxial stress distnbution
0257—8972/94/$7.00 SSDI 0257-8972(94)08069-B
as a function of coating thickness. The study is an extension of the work published in [4]. XECs for the (222) reflection were determined using Cr K~cradiation. A comparison in XECs was then made between (222) and (333)—(511). Triaxial stress analysis using Cu Kcc and Cr K~tradiation was applied to TiN coatings on various substrates. The in-plane and normal stress distributions as functions of coating depth from the coating surface were determined. The stress distribution is discussed in terms of variations in crystallite size, crystallographic orientation, microstrain and nitrogen gradient in the coating.
2. Theory and measurement techniques 2.1. X-ray diffraction method Stress measurement using the X-ray diffraction method is based on the change in the lattice spacing (strain) at the near-surface of the material at various tilts to X-ray beam. The details of the theory and interpretation of residual stress measurement have been well described elsewhere [7—9]. For an isotropic material with d0 as the strain-free lattice spacing in the sample plane normal, the measured strains in the azimuth angle 4 and the tilting angle ~Jiat a given orientation of the diffracting plane (hkl) with respect to the sample coordinate system are related to stress tensor components a~ (j, I x, y, z) by d — d0 d =
~‘
=
=
S2 2
[a
cos
2
4
+
2
a~sin(24) + a sin çb
—
aj sin
2
© 1994 — Elsevier Science S.A. All rights reserved
J. A. Sue
260
/
Triaxial stress distribution in TiN coating
S2 M~90=d0-~-(a5—a) +~
cos ~ + ay, sin ~)sin(2~)
(1)
2.1.1. Biaxial stress state For stress measurements, one usually assumes a biaxial stress state in the coating with a~,= a~,= = a, = 0: — d0 =
d~
=
-~-(a~ cos
2 q$ + ay sin2 q5) sin2 ~fr + Si(a~+ a~)
(2)
coating parallel to2 its q5 +a, surface a~ q5 aisangle the macrostress 4 to the principal in the axis Forofathe biaxial sample. state = sin2 a~=at where a4 = a~cos 4, at t1/i = 0. d44 d0 = 2S~ a4 —
d0
From Eqs. (2) and (3) d44 = d4~0+ a4d0 2 ~,& (4) sin In the linear plot of d 2 i4’, the slope M = 44 vs. sin a 4d0(S2/2) and the intercept I = ~ The stress can then be determined from a4
=
M d0(S2/2)
(5)
2.1.2. Triaxial stress state without shear stress For a material in the three-dimensional stress state without i.e. no ‘~i splitting’ a plota offinite d44 2 ~i,shear but stress, the stress component a, inhaving vs. sin value within the X-ray penetration volume, the Eq. (1) is given by
S2
I = d0
(7)
a, + Si(a~+ a~+ ar))
From the sum of the slopes and the intercepts in Eq. (7), a~,ay and a, can be easily determined. 2.2. Determination ofstrain-free lattice spacing For a triaxial stress state, a strain-free lattice spacing can be determined in the strain-free directions at ~ = 0 and
~ ~fr* which =
is given [10] by
dsin2~Ji’~’= —2Sf 52 (i+a~~z+(3+S 2 ~1i’~’ a, a, a, a, 0 = d4~0+ M sin 2/2Si)az) 3. Experimental details —
—
(8)
3.1. Materials A TiN coating was deposited on disk substrates (diameter, 23 mm; thickness, mm) bymaterials a PYD cathodic arc (d.c.) process. The 4.8 substrate were Ti—6 wt.%Al—4 wt.%V, 17—4 PH, AM-355, Inconel 718 and AISI 304 stainless steel. The coated samples had already been previously investigated for XECs on (422) and (333)—(511) of the coating by X-ray diffraction [4]. The coating thicknesses were 10—12 p.m. The deposition parameters were as follows: chamber pressure, 3.7 Pa; arc current, 125 A; d.c. bias voltage, —150 V; substrate temperature, 733 K. The details of substrate preparation, coating apparatus and deposition process have been described elsewhere [4,11,12]. 3.2. Deflection measurement The deflection of the disk was measured from the change in its curvature during coating deposition by
d 44
—
d0
d~
=
52 =
2 q~+ ay sin2
4~
—
a,) sin2 ~4
(a~cos
+
a, + Si(a, + a~+ a,)
(6)
Two data sets, ~ = 0°and q~= 90°,are needed to obtain a,, a~and a,. The slopes and intercepts of the linear function of d 2 li at ~ = 00 and q5 = 90°are given 44 vs. sin by
profilometry. The measurements were performed at the same position across the diameter of the disk before and after coating. Based on the measured deflection, the internal stress of the coating was then calculated [4,13]. 3.3. Removal of TiN coating TiN coating on a Ti—6 wt.%Al—4 wt.%V substrate was electrolytically stripped in successive layers in a hydrogen-peroxide-containing solution with 10 V d.c. and 0.6 A for 30—80 mm [6]. A control sample with a known coating thickness accompanied the test sample during each removal of a thin coating layer. Subsequently, the stripped coating thickness was measured
M 40
=
d0
(a~— a,)
metallographically on the control sample after each removal of a coating layer, and the stripping rate was
J. A. Sue
/
Triaxial stress distribution in TiN coating
then computed. A typical coating stripping rate was 0.04 p.m min’.
261
6
5~
3.4. X-ray diffraction analysis X-ray diffraction analysis was carried out on a Scintag PTS four-circle goniometer and a computer-controlled and fully automated X-ray diffractometer with a Ge solid state detector, using Cu Kc~and Cr Kct radiations. The diffractometer is arranged in the parafocusing configuration. The measured data were reduced using a Micro Vax 3100 computer and Scintag diffraction management system (DMS) software. The system is capable of measuring the diffraction peak position to within ±0.01°. For crystallographic orientation, microstrain and crystallite size analysis, the divergent beam from the X-ray tube was limited by the 4 mm/Soller/2mm slits to the sample and the diffraction beam was converged at 0.5°/Soller/0.3°receiving slits. The crystallographic onentation of the coating was quantitatively analyzed using the full width at half-maximum (FWHM) from the rocking-curve measurement on (111) reflection. The microstrain and crystallite size of the coating were determined on double orders of the { 111 } reflection by the Warren—Averbach method [14]. An LaB 6 powder (NIST SRM 660) was used as a reference standard to correct the instrumental effect. For residual stress measurements, the irradiated area was positioned at the center of the disk sample using an incident beam collimator of 2 mm diameter. The divergent and receiving slit2 widths were was 4mm applied and 2mm i4 method to respectively. The sin (333)—(511) and (222) reflections which had 20 values of approximately 139° and 137° using Cu Kci~ (A = 0.154 060 nm) and Cr Kx (A = 0.228 970 nm) radiations respectively. The penetration depths tm in (333)—(511) and (222) in TiN from these two sources as a function of sin2 ~‘ were calculated and are shown in Fig. 1. For both radiations, the irradiated volume clearly decreased with increasing tilt angle ti’. Because of the highly (111) preferred orientation of the coating, the (511) contribution to the diffraction 2 ~ distribution intensity was negligible. d44 in vs.both sin directions ±ii’. was measured up to sin2 ~(iThe = 0.95 The peak position of diffraction lines at various angles was determined by profile fitting using the Pearson VII function. XECs for (333)—(511) and (222) reflections 2 i/i distributions of TiN were obtained from substrates. d44 vs. sin In tniaxial stress analycoating on various sis, d 2 i~ distributions at çb = 0° and q5 = 90° vs. sin on (222) of the TiN coating on were 4~, obtained Ti—6 wt.%Al—4 wt.%V substrate. The measurements of crystallographic orientation, microstrain, crystallite size and triaxial stress were performed at different coating
(333)/(511),
~--~
Cu
Ka
.~
.3
4
~ 3
~
2 (222), Cr Ka 1
0 0.0 .
0.2
0.4
.
sin2w
0.6
0.8
1.0
.
Fig. 1. ~, Penetration depth of X-rays in a TiN coating as a function of sin2
depths by successive removal of a thin layer of TiN coating.
4. Results and discussion 4.1.Figs. X-ray constants 2(a)elastic and 2(b) show typical least-squares fits of d 2 i~Le for (333)—(511) and (222) in TiN coating 4,1, vs. sin (sample 1 in Table 1) with linear correlation coefficient
of —0.97 and —0.99 respectively. No ,/, splitting was observed; shear stresses were then taken to be zero. Since the coating was highly (111) textured, the diffraction intensities at sin2 i~!i = 0.06—0.17 for (333)—(511) and 0.13—0.17 for (222) were so low that the peak positions could not be determined precisely. The data in these regions were then excluded from the analysis. The XECs S S~for the (333)—(511) (222) reflections of 2/2 TiNand were obtained from theand plot of ~d 2 iji) vs. a~+ ash and d 44/~ (sin 4~0 vs. a1 + ash, as shown in Figs. 3(a) and 3(b) respectively. a~represent the intrinsic sress of the coating resulting from the deposition process, and ash is the thermal arising from thermal expansion mismatch betweenstress the coating and the substrate. Table 2 gives a comparison of XECs for (333)—(511) and (222) in TiN determined using Cu K~ and Cr Kcx radiations respectively. Both (333)—(511) and (222) have the same crystallographic orientation parameter 3F= 1 (F= (h2k2 + k212 + 12h2)/ (h2 + k2 + 12)2) and their XEC values are expected to be
J. A. Sue
262
/
Triaxial stress distribution in TiN coating
0.0820
-0.0012 TIN COATING
~
TIN COATING
3T~N
~
____________________
0.1232 TIN COATING
__
E
KaRADITION
0.1232
0.1222
-5000
0.1220
-4000
RESIDUAL STRESS, aj
-3000 +
Fig.3. Measurement of X-ray elastic constants for (222) ofTiN using
0.1218
.
0.0
0.2
(b)
0.4
2w
0.6
0.8
1.0
sin
Fig. 2. d~ vs. sin2 1 distributions of TiN from (a) (333)—(511) and (b) (222) reflections,
identical as well. Although there was a marked difference between the irradiated volumes, good agreement between the XECs of (222) and (333)—(511) was observed. However, greater standard deviation in XECs for (222) was evident. This can probably be attributed to the statistical average over a relatively small sampling volume during diffraction measurements.
4.2. Biaxial stress Biaxial residual stresses in (222) and (333)—(511) planes of the TiN coatings were calculated from the slope of linear distribution of d 2 i~li and the 44 vs. sin measured XECs (Table 2). These stresses were considered as surface stresses. Table 1 gives a comparison in residual stresses measured via deflection and X-ray diffraction for a set of samples. The magnitude of residual stresses determined using Cr Kct radiation were consistently higher than those measured using Cu Kc radiation. This behavior was also observed in Ti(C, N) [1]. Stresses in (333)—(511) were comparable with those
Table 1 Residual stresses determined by X-ray diffraction and deflection Sample
I II III IV V
-2000
~ ~th (Mpa)
Substrate
Ti—6 wt.%Al—4 wt.%V 17—4 PH AM-355 Inconel 718 AISI 304
Residual stress (MPa) X-ray diffraction ________________________________________ (222) (333)—(511)
Deflection, overall average
—3014 ±59 —3219 ±47 —3397±64 —3751 ±56 —4628±58
—2688 ±285 —2746 ±247 —2844±279 —3431 ±343 —4167±408
—2630 ±67 —2946 ±39 —3165±63 —3571 ±62 —4345±40
J. A. Sue
/
Triaxial stress distribution in TiN coating
Table 2 X-ray elastic constants of TiN from (222) and (333)—(511) reflections
(222) (333)—(511) [4]
(xlO~GPa
—0.63 ±0.11 —0.67 ±0.07
average within the penetration depth. The data were not corrected for the removal of the surface layers. The location irradiated of each depth measurement within t +ofT~, where t volume is the coating removedwas by
1)
10~GPa~i)
Reflection
263
3.31 ±0.48 3.42 ±0.29
measured by the deflection technique within experimental uncertainty, whereas stresses in (222) deviated significantly from those measured by the deflection. The discrepancy between them may arise from the surface effect and the disregard of the normal stress, 4.3. Triaxial stress
Triaxial stress analysis with the assumption of no shear stresses was performed on TiN coatings on various substrates (samples I—V) at 4~= 0° and 4’ = 90° using Cu K~and Cr Kit radiation. Table 3 summarizes the in-plane stresses a~and ay and normal stress a, in the coating. Relatively large scatter in a, on (333)—(511) was observed. With considerations of a,, the in-plane stresses measured from both radiations were in remarkable agreement, within 6%. In contrast, stresses obtained from biaxial sin2 i~i method varied from 6.5 to 14.6% (Table 1). Implicitly, a biaxial stress approach is adequate to obtain an accurate result if the sampling depth is sufficient; a triaxial stress analysis is highly recommended because it accounts for the influence of the normal stress on the in-plane stress measurement if a, ~ 0. 4.4. Triaxial stress distribution 4.4.1. Triaxial stress depth profiles The in-plane and normal stresses at various depths from the coating surface were calculated and given in Table 4 together with other parameters. Fig. 4 shows the depth profiles of residual stresses a~,a~and a,. Each data point represents the diffracting volume-weighted
stripping from the coating surface and Tm is the penetration depth of X-rays. The stress normal to the coating surface was tensile, whereas the in-plane stresses were highly compressive and exhibited rotational symmetry throughout the coating thickness. Both stresses exhibited a steep gradient in the near-surface region. The former decreased from 193 MPa at a depth of 8.4—10.2 p.m to a minimum of 107 MPa at 1.3—3.1 p.m and increased to a maximum of 650 MPa toward the surface. The latter increased from —2728 MPa at a depth of 8.4—10.2 p.m to a maximum of —3015 MPa at 1.3—3.1 p.m and then decreased to —2369 MPa toward the surface. The in-plane stress relaxation at the near-surface of the coating was clearly evident. To avoid diffraction interferences from the substrate, the analysis was carried out only to a coating depth of 8.4 p.m. The residual stress in substrate after complete removal of the coating was equal biaxially and slightly in compression, about —70 MPa, which was within experimental uncertainty. 4.4.2. Crystallographic orientation, crystallite size and microstrain Figure 5 shows the crystallite size, microstrain and FWHM from the (111) rocking-curve measurement as a function of the coating depth from the surface. The FWHM indicated that the (111) plane of crystallites throughout the coating thickness was parallel to the coating surface within 4—5.5°. The crystallite size was found to be smaller near the coating—substrate interface, about 12.4 nm, and slightly larger near the surface, about 15.3 nm. The microstrain was found to increase gradually with increasing coating depth and a marked increase toward the coating—substrate interface. No apparent correlation was observed between FWHM, microstrain, crystallite size and triaxial stress distribution.
Table 3 Triaxial stresses of TiN coating determined from (222) and (333)—(511) reflections Sample
Residual stress (MPa) (222) 0’,
I II III IV V
—2364±183 —2677±128 —2846±156 —3224±156 —4024±236
(333)—(511) O’y
0,
0
O’y
0’,
—2370±190 —2649±128 —2833±150 —3034±172 —4099±259
651±173 543±119 551±142 527±157 605±228
—2536±183 —2464±119 —2534±180 —3150±142 —4078±95
—2430±195 —2449±122 —2568±183 —3214±144 —4009±98
93±170 482±111 630±169 246±129 266±87
J. A. Sue
264
/
Triaxial stress distribution in TiN coating
Table 4 Triaxial stresses, lattice spacings of (222) and lattice constants as functions of coating depth Coating depth
Sampling depth + Tm
Residual stress (MPa)
Strain-free direction
(222) lattice spacing
(jim)
(iim)
a,
sin(2~)
d0 (nm)
0 1.3 3.0 5.0 8.4
0—1.8 1.3—3.1 3.0—4.8 5.0—7.8 8.4—10.2
—2369 —3015 —2858 —2754 —2728
0.469752 0.395124 0.402617 0.394299 0.414419
0.1223689 0.1224267 0.1224181 0.1224303 0.1224046
—2317 —3011 —2854 —2812 —2811
651 107 156 164 193
__________________________________________
Lattice constant a 0 (nm)
0.4238982 0.4241177 0.4240689 0.4241110 0.4240220
4.4.3. Strain-free lattice constant and nitrogen gradi-
2000 TiN COATING
ent effect Table 4 also gives the strain-free direction, strain-free lattice spacing and lattice constant at various depths in the coating. A significant gradient in strain-free lattice spacing and lattice constant occurred at the near-surface
i
1000
SUBSTRATE ~©~©
\0
ci)
W
z
I
region. profile of concentration Figure in TiN,6 shows which the wasdepth determined by Nsputtered neutral mass spectrometry [15]. In the near-surface
I.I 0 ii)
region, the N concentration decreased from 52.5 at.% at the to approximately 50 at.% at the depth greater thansurface 0.4 p.m. A similar increase in N concentration at
1000
_1
0y 2000
w
the near-surface region of TiN coating was also reported elsewhere [1]. The decrease in lattice constant resulting from increase in N content by Sundgren et a!. an [16]. A marked decreasewas in reported lattice constant in the
-3000 COATING/SUBSTRATE—~.1
INTERFACE -4000
‘
0
i
‘‘‘
2
4
6
8
10
DISTANCE FROM COATING SURFACE
12
(jim)
Fig. 4. Triaxial stresses vs. the depth of TiN coating. 20
‘‘‘‘‘‘
18
CRYSTALLITE SIZE
~
FWHM
_________________________________
U
2
X16
0.20
‘
—0-—
near-surface region can probably be attributed to a composition gradient and surface relaxation. The overall variation in lattice constant, in a physical sense, coincided with the behavior of in-plane compressive stresses and normal tensile stress.
I
70 0.18
TIN COATING
I
MICROSTRAIN
I
0.16
I u14~
._
a0.14~
I~ Ia: IC,)
Ui
~
0.12~ 1 Cl) I 1
60
~. Z
~
50
~
0.10
Z Ui
0 z
I
40
0.08
C) COATING/SUBSTRATE INTERFACE
‘—~~
....,
6 0
2
I 4
6
8
10
0.06 12
DISTANCE FROM COATING SURFACE (jim)
Fig. 5. Variations in crystallite size, microstrain and FWHM of (111) reflection from the rocking-curve measurement with coating thickness of TiN,
I 30! 0
1
2
3
4
DISTANCE FROM COATING SURFACE (jim)
Fig. 6. Neutral sputter mass spectrometry nitrogen concentration depth profile in TiN coating.
J. A. Sue
/
Triaxial stress distribution in TiN coating
5. Conclusions
265
References
(i) The XECs for (222) of TiN are S~= —0.63 x iO~GPa~ and S2/2 = 3.31 x iO~GPa’. The XEC va!ues appear to be independent of irradiated volume during the measurement. 2 i~’biaxial approach is adequate to (ii) The X-rayin-plane sin obtain accurate stress measurement if the penetration depth of the X-ray is sufficient, whereas a triaxia! stress analysis without consideration of shear stresses is recommended to obtain precise in-plane stresses and the normal stress as well. (iii) The in-plane stresses in TiN coating are in cornpression and have rotational symmetry throughout the coating thickness. The compressive stress increases to a maximum of —3000 MPa at approximately 2 p.m from the coating surface and then decreases to 2400 MPa toward the surface. The normal stress of the coating is in tension. The tensile stress decreases gradually from 193 MPa at 8.4—10.2 p.m to a minimum of 107 MPa at 1.3—3.1 p.m from the coating surface and then increases to a maximum of 650 MPa toward the surface. Both the steep gradients in the in-plane stress and the norma! stress in the near-surface region of the coating are probably due to surface relaxation and nitrogen concentration gradient. —
[1] T. Hirsch and P. Mayr, Surf. Coat. Technol., 36 (1988) 729. [2] A. J. Perry, Thin Solid Films, 193—194 (1990) 463. [3] A. J. Perry, V. Valvoda and D. Rafaja, Thin Solid Films, 214 (1992) 169. [4] D. J. A.S. Sue, Surf. Coat. Technol., 154. [5] Rickerby, A. M. Jones 54—55 and B.(1992) A. Bellamy, Surf Coat. Technol., 36 (1988) 661. [6] J. A. Sue, US Pat. 5,062,941, 1991. [7] V. M. Hauk, Adv. X-ray Anal., 27 (1984) 81. [8] Soc. Auto. Engrs., Residual Stress Measurement by X-ray D(ffraction, SAE Handbook J784a, Society of Automotive Engineers, Warrendale, PA, 2nd edn., 1971. [9] I. C. Noyan and J. B. Cohen, in B. Ilschner and N. J. Grant (eds.), Residual Stress Measurement by Djffraction and Interpretation, Springer, New York, 1987. [10] V. Hauk and E. Macherauch, in E. Macherauch and V. Hauk (eds.), Residual Stress in Science and Technology, Deutsche Gesellschaft fur Metallkunde Informationsgesellschaft, Oberursel, 1987, p. 246. [11] J. A. Sue and H. H. Troue, US Pat. 4,929,322, 1990. [12]J. A. Sue and H. H. Troue, US Pat. 4,895,765, 1990. [13] D. S. Campbell, in L. I. Maissel and R. Glang (eds.), Handbook of Thin Film Technology, McGraw-Hill, New York, 1970, p. 12. [14] H. P. Klug and L. E. Alexander, X-ray D)[fraction Procedure for Polycrystalline and Amorphous Materials, Wiley, New York, 1974, p. 643. [15] J. A. Sue, Surf. Coat. Technol., 61(1993)115. [16] J.-E. Sundgren, B.-O. Johansson, S.-E.
Karlsson
H. T. G. Hentzell, Thin Solid Films, 105 (1983) 367.
Acknowledgment The author is grateful to Mr R. E. Newman for preparation of the coating and carrying out the deflection experiment and measurements.
and