Hardening mechanisms of nanocrystalline Ti–Al–N solid solution films

Thin Solid Films 468 (2004) 161 – 166 www.elsevier.com/locate/tsf

Hardening mechanisms of nanocrystalline Ti–Al–N solid solution films Z.-J. Liu, P.W. Shum, Y.G. Shen * Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong, China Received 22 December 2003; received in revised form 14 April 2004; accepted 17 May 2004 Available online 26 June 2004

Abstract Nanocrystalline Ti1
xAlxN (0 V x V 0.41) solid solution films were produced by reactive unbalanced close-field magnetron sputtering. Nanoindentation measurements showed that the hardness of Ti1
xAlxN films increased monotonously with the content of Al. A calculation based on a semiempirical method revealed that the effect of intrinsic hardening, which arises from the change of the nature of atomic bonding due to the incorporation of Al atoms into TiN lattice, played a negligible role in the observed hardening phenomena. Further analysis revealed that the grain boundary hardening was also very weak and the improvement of hardness of Ti1
xAlxN films with relatively low content of Al (x V 0.33) could be well explained by the Fleischer model of solid solution hardening. However, for Ti1
xAlxN films with x>0.33, an obvious deviation from the solid solution hardening was observed, probably due to the grain boundary segregation of solutes that might lead to an enhanced effect of grain boundary hardening when the amount of Al is high. D 2004 Elsevier B.V. All rights reserved. Keywords: Hardening mechanisms; Sputtering; Titanium aluminum nitride

1. Introduction Multicomponent hard coatings, e.g., TiN-based ternary or quaternary nitrides, benefit from the combined attributes of individual components and thus exhibit much better mechanical performance. For the best known example, namely, Ti– Al –N, the incorporation of Al atoms into TiN lattice not only improves the oxidation resistance by forming a stable compact aluminum oxide layer on the surface, but also leads to a significant enhancement of hardness in comparison with simple binary nitride TiN films [1 –9]. For example, Zhou et al. [4] reported that, before the formation of hexagonal wurtzite structure of AlN, the hardness of Ti1
xAlxN films prepared by r.f. plasma-assisted magnetron sputtering increased monotonously with the Al content up to a critical value ( f x = 0.6) with an initial oxidation temperature up to 950 jC. Similar results of hardness improvement of Ti1
xAlxN films were also reported in a number of experiments based on other deposition techniques such as ion plating [5] and plasma-enhanced chemical vapor deposition (CVD) [6]. Despite considerable experimental efforts devoted to ameliorating the mechanical properties of Ti– Al– N * Corresponding author. Tel.: +852-2784-4658; fax: +852-2788-8423. E-mail address: [email protected] (Y.G. Shen). 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.05.087

films, no consensus has yet been reached on the hardening mechanisms of Ti –Al – N films. Up to date, three main hardening origins have been proposed. (i) The improved hardness of Ti –Al – N films is a result of solid solution hardening due to the substitution of small-sized Al atoms for Ti atoms in the crystal lattice [2,8]. (ii) The hardness enhancement of Ti–Al – N films is attributed to the change of bonding structure of TiN caused by the incorporation of Al atoms [4]. (iii) Ti– Al –N films exhibit a nanocomposite structure like nanocomposite Ti– Si –N films [7], and thus the effect of gain boundary hardening plays a crucial role in the improved hardness. In this work, we present a study on the hardening mechanisms of nanocrystalline Ti – Al – N solid solution films prepared by reactive unbalanced closefield magnetron sputtering. An approach based on a semiempirical relationship is given for analyzing the crucial hardening origins of Ti– Al– N films. Hardness is a measurement of the resistance against localized plastic deformation, microscopically related to the motion of dislocations. The resistance against the dislocation motion may come from the chemical bonding among their constituent atoms and other obstacles, e.g., solution atoms, precipitates, grain boundaries, and other dislocations. Our analysis of the hardening mechanisms of Ti– Al –N films is based on the idea that hardness of a

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material can be divided into intrinsic and extrinsic parts, with each, respectively, originating from the nature of atomic bonding and the above-mentioned obstacles. Thus, the value of intrinsic hardness gives an indication of bonding structure of a material, while the extrinsic part, which includes solid solution hardening, precipitation hardening, grain boundary hardening, work hardening, and so on, depends strongly on the material microstructure. To determine which hardening mechanism dominates in Ti– Al – N solid solution films, the contributions of various hardening effects, e.g., intrinsic hardening, grain boundary hardening, and solid solution hardening, are investigated by using semiempirical methods.

2. Experimental details Ti1
xAlxN films (0 V x V 0.41) were deposited onto Si(100) substrates using reactive unbalanced close-field magnetron sputter deposition system (UDP650, Teer Coating Limited). The substrates were ultrasonically cleaned in acetone and methanol bath sequentially and then dried in N2 before placed into the vacuum chamber. Sputtering was performed with four high-purity targets (three Ti and one Al) in an Ar and N2 gas mixture. The base pressure in the chamber was V 2.7  10
4 Pa, and the working pressure, consisting of Ar and N2 with a constant gas-flow rate of F(N2) + F(Ar) = 40 sccm, was set at 0.26 Pa during all depositions. The substrate bias was
60 V and the deposition time was 60 min ( f 700– 800 nm in thickness). The Ti target current was typically 5 A with the Al target current ranging from 0 to 5 A to obtain Ti1
xAlxN films with different Al concentrations. The targets, which were sputtercleaned for 20 min before deposition, were water-cooled and the substrate holder was neither cooled nor initially heated. During deposition, the substrate was rotated with typically 10 rpm to ensure a homogenous film composition and thickness. The crystal structure of the films was characterized by X-ray diffraction (XRD) h– 2h scan using X-ray diffractometer (Siemens D500). The atomic concentration of elements was analyzed by X-ray photoelectron spectroscopy (XPS) using a PHI Quantum 2000 hemispherical energy analyzer equipped with an unmonochromatized Al Ka X-ray source (hr = 1486.6 eV). In order to evaluate the mechanical response of the films, nanoindentation experiments were carried out using a Nano-Indenter II instrument. Indentations were made by a trigonal (Berkovich) diamond tip with a tip roundness of f 300 nm using a single loading – unloading cycle. The indenter tip shape (area function) was calibrated using the method described in Ref. [10]. The calibration of the hardness value was frequently checked by measuring on a fused silica sample. In order to minimize the substrate effect, all the indentations were measured by an indentation load of 3 mN such that the indentation depth was limited to around 60 – 80 nm ( f 10% of the film thickness) which depends on the hardness of the

films. Ten separated measurements were taken for each sample in order to get a mean value.

3. Results and discussion The XRD h– 2h measurements indicate a linear decrease in the lattice parameter of the films from 0.4247 to 0.4209 nm [calculated from the (111) diffraction peak position], while the Al content (x) increases from 0 to 0.41 as shown in Table 1. Typical XRD patterns collected from the films deposited at six different Al contents are shown in Fig. 1. The observation that the XRD 2h peaks shift toward higher Bragg angles as the Al content increases indicates the contraction of lattice by the incorporated Al atoms, resulting in the formation of a ternary solid solution. This is clarified by the fact that the covalent radius of aluminum (0.143 nm) is smaller than that of titanium (0.146 nm). Table 1 also shows the average grain sizes of the crystallites in different solid solutions, calculated from the full width at half maximum (FWHM) value of the XRD peaks using the Scherrer equation [11]. As can be seen from Table 1, the average grain size substantially decreases with increasing Al content in the range of x = 0 –0.41. The average grain size ranges from about 15 –30 nm, indicating that Ti– Al –N solid solutions exhibit a nanocrystalline structure. The improvement in mechanical properties by the formation of such nanocrystalline solid solutions is evident. For the TiN film, the mean values of hardness and elastic modulus obtained from 10 independent measurements were f 23.0 and f 245.3 GPa, respectively. The hardness and elastic modulus of the films increase with increasing Al content and reach a maximum for a film at x = 0.41 (hardness = 31.4 GPa and elastic modulus = 312.2 GPa). These results are close to values reported by other groups [4,5]. In order to analyze the hardening mechanisms of the above nanocrystalline Ti– Al– N solid solution films, we first determine the contribution of the intrinsic hardening. Similar to the covalent crystals, the intrinsic hardness of transition metal nitrides also depends on the atomic bonding or electronic structure [12]. Unfortunately, up to now, no theoretical calculation on the electronic structure of Ti –Al – N is available. Thus, despite some authors mentioning this intrinsic

Table 1 Summary of the structural and mechanical properties of as-prepared Ti1
xAlxN films Al content (x)

Phase structure

Lattice constant (nm)

Grain size (nm)

Elastic modulus (GPa)

Hardness (GPa)

0 0.09 0.17 0.25 0.33 0.41

rocksalt rocksalt rocksalt rocksalt rocksalt rocksalt

0.4247 0.4238 0.4235 0.4233 0.4224 0.4209

28.9 25.4 19.8 18.6 17.7 16.8

245.3 262.9 276.7 288.3 295.6 312.2

23.0 25.4 26.1 27.3 27.4 31.4

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163

Fig. 1. XRD h – 2h scan patterns obtained from six different Ti1
xAlxN (0 V x V 0.41) films: (a) x = 0, (b) x = 0.09, (c) x = 0.17, (d) x = 0.25, (e) x = 0.33, and (f) x = 0.41.

hardening effect [4], how the incorporation of small-sized Al atoms into TiN lattice changes the intrinsic hardness is not clear. To estimate this effect, we use a semiempirical method recently developed by Gao et al. [13] at which the intrinsic hardness Hin depends on bond density or electronic density, bond length, and degree of covalent bonding, Hin ¼ c1 qb e
c2 fi =d 2:5

ð1Þ

where c1 and c2 are constants, qb is the number of covalent bond per unit area, d is the bond length, and fi is the bond ionicity with fi = 1
Eh2/Eg2. Here, the average band gap Eg has the form of Eg2 = Eh2 + C2 with Eh and C being, respectively, the covalent gap and ionic gap. Thus, for TiN, we can calculate its intrinsic hardness by 2:5 Hin;TiN ¼ c1 qb;TiN ec2 fi;TiN =dTiN

ð2Þ

Similarly, the intrinsic hardness of solid solution Ti– Al –N is estimated by 2:5 Hin;Ti
Al
N ¼ c1 qb;Ti
Al
N ec2 fi;Ti
Al
N =dTi
Al
N

ð3Þ

Here, qb,Ti – Al – N is approximately related to qb,TiN by qb,Ti – Al – N c (aTiN/aTi – Al – N)2  qb,TiN and dTi – Al – N is related to dTiN by dTi – Al – N c (aTi – Al – N/aTiN)  dTiN where aTiN and aTi – Al – N are the lattice constants of pure TiN and metastable phase Ti –Al – N, respectively. Because of the bond ionicity fi denoting the charge transfer between two bonding atoms, XPS measurements can provide a clue to change of the ionicity due to the Al incorporation. Our XPS results reveal that the N 1s electron-level spectra obtained from six different Ti1
xAlxN (0 V x V 0.41) films showed the same binding energies around 397.0 eV within experimental uncertainty of 0.2 eV, indicating that the ionicity fi,Ti – Al – N can be approximated as fi,TiN. Thus, combining Eqs. (2) and (3), we can obtain Hin;Ti
Al
N ¼ Hin;TiN  ðaTiN =aTi
Al
N Þ4:5

ð4Þ

To estimate the intrinsic hardening effect through Eq. (4), we first need to determine the intrinsic hardness of a TiN film. Since our TiN film shows a nanocrystalline structure, the measured hardness of TiN film (namely, 23 GPa) apparently

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Burgers vector. Obviously, k should be a constant for a given material. However, for Ti –Al – N films, k may change with the amount of Al. The value of k for a pure TiN film can be calculated by kTiN ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1=2 sc;TiN GTiN bTiN ¼ ðHTiN
Hin;TiN Þ=dTiN

ð6Þ

Using HTiN = 23 GPa, Hin,TiN = 20 GPa, and dTiN = 28.9 nm, we can obtain kTiN c 16.13 GPa nm1/2 ffi . For Ti– Al –N films, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kTi
Al
N ¼ sc;Ti
Al
N GTiN bTi
Al
N . Thus, we have pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sc;Ti
Al
N GTi
Al
N bTi
Al
N pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sc;TiN GTiN bTiN       bTi
Al
N 1=2 GTi
Al
N 1=2 sc;Ti
Al
N 1=2 ¼ bTiN GTiN sc;TiN

kTi
Al
N ¼ kTiN Fig. 2. The calculated results of intrinsic hardening and grain boundary hardening in Ti1
xAlxN (0 V x V 0.41). Both two hardening effects are very weak and negligible.

ð7Þ contains the extrinsic hardening effects (e.g., grain boundary hardening) and should be larger than the value of TiN intrinsic hardness. Thus, to estimate the intrinsic hardness of a TiN film, we use the hardness of a stoichiometric singlecrystal TiN film ( f 20 GPa) [14] at which the extrinsic hardening effects can be minimized. Fig. 2 shows the calculated values of Ti1
xAlxN hardness (open dots) including the intrinsic hardening effect. It can be seen from the figure that the intrinsic hardening effect is very small and cannot account for the much higher improvement of hardness due to the incorporation of Al atoms observed in experiments. Thus, the extrinsic hardening effects must be taken into account to explain the hardening mechanisms in Ti1
xAlxN solid solution films. Two obvious extrinsic hardening mechanisms in nanocrystalline Ti – Al – N solid solution are grain boundary hardening and solid solution hardening. The incorporation of Al atoms into TiN lattice leads to a decrease in grain size (see Table 1), indicating a high density of grain boundaries. The increasing density of grain boundaries can diminish dislocation activity, thus resulting in a grain boundary hardening. This is because even in materials with weak grain boundaries, the deformation begins with the motion of dislocations that can interact with each other and impinge on the grain boundary [15,16], and the grain boundary can accommodate many dislocations before it responds. The decrease in dislocation activity caused by the grain boundary is supported by the fact that the hardness at the grain boundary is higher than that at the grain interior. Normally, this grain boundary effect can be described by the classic Hall –Petch relation [17 – 19]: H ¼ Hin þ kd
1=2

ð5Þ

where H is the hardness, Hin is the intrinsic hardness, d is the pffiffiffiffiffiffiffiffiffiffi grain size, and k ¼ sc Gb with sc being the critical yield stress of the grain boundary, G the shear modulus, and b the

To calculate the value of kTi – Al – N, we need to know the ratios of bTi – Al – N to bTiN, GTi – Al – N to GTiN, and sc,Ti – Al – N to sc,TiN. Since both TiN and Ti– Al –N have a rocksalt-type phase structure, the ratio of bTi – Al – N to bTiN can be approximated by the ratio of aTi – Al – N to aTiN where a denotes lattice constant. To calculate the ratio of GTi – Al – N to GTiN, a mixing rule is used, namely, by linear interpolations, GTi
Al
N ¼ ð1
xÞGTiN þ xGAlN

ð8Þ

where x is the content of Al, GAlN is shear modulus of metastable rocksalt-AlN, rather than wurtzite-AlN. However, due to no theoretical or experimental data of sc,AlN (rocksalt type) available, the value of sc,Ti – Al – N cannot be estimated by the similar mixing rule. For this reason, we assume that the replacement of Ti atoms with Al atoms will not significantly change the value of sc, namely, sc,Ti – Al – N c sc,TiN. Thus, using the calculated parameters shown in Table 2, we can estimate the grain boundary hardening effect caused by the addition of Al atoms into TiN. The calculated results (solid squares) are also shown in Fig. 2. Similar to the intrinsic hardening, the grain boundary hardening effect is also very weak and contribTable 2 Parameters used for calculating the effect of grain boundary hardening     Ti1
xAlxN Shear GTi
Al
N 1=2 bTi
Al
N 1=2 kTi – Al – N films modulus (GPa nm1/2) GTiN bTiN (GPa) TiN Ti0.91Al0.09N Ti0.83Al0.17N Ti0.75Al0.25N Ti0.67Al0.33N Ti0.59Al0.41N Rocksalt-AlN a b

Ref. [20]. Ref. [21].

192a 199.7 206.5 213.2 220.0 226.9 277b

1 1.020 1.037 1.054 1.070 1.087

1 0.9989 0.9985 0.9984 0.9973 0.9955

16.13 16.43 16.70 16.97 17.21 17.45

Z.-J. Liu et al. / Thin Solid Films 468 (2004) 161–166

30

H' (GPa)

28 26 24 22 20

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

c1/2 Fig. 3. Plot of the calculated hardness value H V of Ti1
xAlxN (0 V x V 0.41) films vs. square root of Al concentration c1/2.

utes much less to the improved hardness of Ti– Al– N films. The replacement of Ti atoms with smaller-sized Al atoms in TiN not only affects the grain size of crystals, but also can cause lattice distortion. The incorporated Al atoms can serve as centers of contraction and the resulting compressive stress field can react with the elastic stress field of a dislocation, thus leading to a mechanism of solid solution hardening. In order to investigate the solid solution hardening effect in Ti– Al –N films, we use the Fleischer model based on the atomic size misfit and elastic modulus mismatch [22]. In this model, the increase in shear strength shows a c1/2 dependence of solution concentration c, Ds~AeG
bea A3=2 c1=2

ð9Þ

where eG and ea are, respectively, the modulus misfit parameter and the size misfit parameter, and b is a constant which equals 3 for screw dislocations or 16 for edge dislocations. To test whether the Fleischer model can account for the improved hardness in nanocrystalline solid solution Ti– Al –N films, for each Ti1
xAlxN (0 V x V 0.41) film, we subtract the enhanced parts of hardness caused by both intrinsic hardening and grain boundary hardening from the measured hardness to obtain a hardness pffiffiffi value H V, and then plot this value H Vas a function of c where c is taken as the atomic function of Al in TiN, namely, c = x. As can be seen from Fig. 3, despite the existence of deviation for the Ti0.59Al0.41N film, the increasing hardness for small values of Al content x (x V 0.33) can be well explained by this classic solid solution hardening model, indicating that solid solution hardening is the crucial origin of the hardness enhancement of Ti1
xAlxN films. However, the obvious deviation from solid solution hardening observed in Fig. 3 for Ti0.59Al0.41N films suggests that other factors may also affect the hardness of Ti1
xAlxN solid solution when the amount of incorporated Al atoms is high. According to the XRD measurements (Fig. 1), no

165

second-phase particles are detected, which indicates that the effect of precipitation hardening can be excluded in Ti1
xAlxN films. Another possible factor is vacancy hardening [23]. When the Al amount is high, the atom substitution might lead to the formation of N vacancies probably due to that Al atoms have a tendency to form a wurtzite structure of AlN at which Al atoms have a lower coordination number of 4. In fact, the formation of vacancies due to the atom substitution has been observed in both B2 intermetallics [24,25] and ionic crystals [26], resulting in anomalous substitutional hardening. However, based on our XPS analysis (not shown here), the N concentration maintains almost constant (47 F 2 at.%) for all the deposited Ti1
xAlxN films. This indicates that N vacancy hardening might not exist in Ti1
xAlxN films. Thus, a most possible factor is the grain boundary segregation of solutes. From a thermodynamic view of point, Al atoms in metastable Ti –Al – N have a tendency of segregation on the grain boundary when the amount of Al is high. Previous experiments have shown that the segregation of solutes on the grain boundary may either increase or decrease the effect of grain boundary hardening [27,28]. The much higher hardness of Ti0.59Al0.41N films observed here indicates that the segregation of solutes seems to enhance the grain boundary hardening of Ti –Al – N and thus play an important role in the rapid rise in hardness.

4. Conclusion We have presented a detailed analysis of hardening mechanisms of nanocrystalline Ti1
xAlxN (0 V x V 0.41) solid solution films using an approach based on the semiempirical relationship. It is found that the improved hardness in Ti1
xAlxN films primarily originates from the effect of solid solution hardening, with both intrinsic hardening and grain boundary hardening having a very weak contribution for films with relatively low Al amount. However, our analysis also shows that for Ti1
xAlxN films with relatively high Al amount, e.g., x = 0.41, the enhanced effect of grain boundary hardening caused by the segregation of solutes on the grain boundary might also have an important impact on the change of hardness. Acknowledgements The work described in this article was supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1097/02E). References [1] W.D. Mu¨nz, J. Vac. Sci. Technol. A 4 (1986) 2717. [2] O. Knotek, M. Bo¨hmer, T. Leyendecker, J. Vac. Sci. Technol. A 4 (1986) 2695.

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