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The inverse Hall–Petch effect in nanocrystalline ZrN coatings
Surface & Coatings Technology 205 (2011) 3692–3697
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Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
The inverse Hall–Petch effect in nanocrystalline ZrN coatings Z.B. Qi a, P. Sun a, F.P. Zhu a, Z.C. Wang a,⁎, D.L. Peng b, C.H. Wu c a b c
College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China College of Materials, Xiamen University, Xiamen, China China National R&D Center for Tungsten Technology, Xiamen, China
a r t i c l e
i n f o
Article history: Received 7 October 2010 Accepted in revised form 11 January 2011 Available online 15 January 2011 Keywords: Nanocrystalline Coating Microstructure Hardness Inverse Hall–Petch effect
a b s t r a c t For the purpose of studying the inverse Hall–Petch effect in nanocrystalline hard coatings, nanocrystalline ZrN coatings have been fabricated using magnetron sputtering with grain sizes ranging from 45 nm to 10 nm by varying negative biases from 0 V to 150 V. The transition from the classical Hall–Petch effect to an inverse Hall–Petch effect in nanocrystalline ZrN coatings is observed at a grain size between 19.0 nm and 14.2 nm. The reality of the inverse Hall–Petch effect in the present study is validated by exclusion of other possible effects on hardness of nanocrystalline ZrN coatings, such as porosity, multiphase, chemical composition, texture, and residual stress. Furthermore, a concise model based on lattice dislocations piling up mechanism is proposed to illustrate the breakdown of the Hall–Petch effect and calculate the critical grain size. The predictions of the model fit well with experimental data in some nitride and carbide nanocrystalline coatings. Both experimental and theoretical results indicate that the inverse Hall–Petch effect is an essential property of nanocrystalline hard coatings as similar to nanocrystalline metals and alloys. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The effect of grain size on the hardness (e.g. yield strength) of solids ranging from millimeters to nanometers is both of scientific and of technologic interest. For conventional materials, the classical Hall–Petch equation predicts that: H = H0 + kd−1/2, where H is hardness, Ho is grain-body hardness, k is positive constant, and d is the grain size. If such an empirical plot is extrapolated to the grain size of about 10 nm, extremely high hardness is expected. However, to data, as the grain size is down to only tens of nanometers (defined as critical grain size), a novel behavior is observed with an actual negative k (the slope of Hall–Petch plot) in nanocrystalline metals and alloys, namely the inverse Hall–Petch effect [1–5]. It is worthy to note that previous research aimed at understanding the inverse Hall–Petch effect has constituted a main focus on the nanocrystalline metals for bulk materials and coatings. Challenging experimental and theoretical studies concerning this effect in nanocrystalline PVD coatings have not received much attention, in particular nitride and carbide hard coatings, of which high hardness and mechanical strength are considered as the primary requirements. To work on the inverse Hall–Petch effect in nanocrystalline hard coatings with clarity and in detail, the two problems need to be resolved. First, is the inverse Hall–Petch effect also an intrinsic property in nanocrystalline hard coatings and what is the critical grain size in such coatings? In case the inverse Hall–Petch effect is observed, it is also necessary to determine whether this effect is fact or artifact. Secondly,
what is novel deformation mechanism responsible for this grain size softening in nanocrystalline coatings? Previously, Wang et al. [6] used laser physical vapor deposition to fabricate nanocrystalline TiN coatings with grain sizes ranging from 55 nm to 8 nm by varying substrate temperature from 25 °C to 600 °C and reported that the coating hardness decreased with decreasing grain size, namely an inverse Hall–Petch effect. However, no transition between Hall–Petch effect and inverse Hall–Petch effect was observed in this grain size range. Thus there were still some questions as to whether the inverse Hall–Petch effect is a true grain size softening effect. In the above study, only dependence of grain size on hardness was investigated, other factors contributing to the observed softening behavior were ignored. Conrad et al. [7] have pointed out that texture and imperfections may possibly account for the observed inverse Hall–Petch effect of nanocrystalline TiN coatings, rather than grain size. In this work, in order to explore the inverse Hall–Petch effect in nanocrystalline hard coatings, typical ZrN hard coatings were deposited using magnetron sputtering with grain sizes ranging from 45 nm to 10 nm by adjusting the substrate negative bias. A transition between the Hall–Petch effect and the inverse Hall–Petch effect is observed in this study. For the purpose of establishing whether the inverse Hall–Petch effect is a reality, other factors that may possibly influence hardness are analyzed in detail. 2. Experimental details 2.1. Preparation of nanocrystalline ZrN coatings
⁎ Corresponding author. Tel./fax: + 86 592 2180738. E-mail address: [email protected] (Z.C. Wang). 0257-8972/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2011.01.021
A series of nanocrystalline ZrN coatings were deposited on mirror-like polished cemented carbide and silicon (111) wafers using a DC
Z.B. Qi et al. / Surface & Coatings Technology 205 (2011) 3692–3697
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magnetron sputtering technique. Before the coating process, all substrates were ultrasonically cleaned for 10 min, each successively in baths of acetone and alcohol, and blown dried. For cleaning the target surface, 30 min of pre-sputtering in pure argon (99.999% in purity) atmosphere was carried out with sputtering power 200 W and gas pressure 1.0 Pa. The deposition was carried out in an Ar and N2 atmosphere of 99.999% purity. The base pressure was 8.0 ×10−4 Pa and deposition gas pressure was kept constant at 0.5 Pa. The DC power was adjusted to 250 W applied at the zirconium target (99.99% in purity) during deposition. ZrN coatings were deposited with temperature and nitrogen flow ratio N2/(N2 +Ar) fixed at 300 °C and 20% respectively. Substrate negative bias was chosen as the controlling parameter varying from 0 V to 150 V to generate nanocrystalline ZrN coatings with different grain sizes. 2.2. Characterization The coating thickness was measured by a Dektak3 profilometer (VEECO, U.S.) and the thickness of ZrN coatings was kept constant at 1.1 ± 0.1 μm with a deposition time of 90 min. All samples were analyzed by electron probe microanalysis (EPMA, JXA-8100, Japan) for determining their composition. The crystal structure of ZrN coatings was investigated by Panalytical X'pert PRO MPD X-ray diffraction (XRD, Philips, Netherlands) using Cu Kα radiation as X-ray source and θ–2θ diffraction mode. The texture coefficient of (111) plane was calculated using the following equation: Texture coefficient of ð111Þ =
Ið111Þ Ið111Þ + Ið200Þ + Ið220Þ + Ið311Þ
ð1Þ
where I(111), I(200), I(220), I(311) are integrated intensities of the corresponding peaks (111), (200), (220) and (311). The texture coefficient of (111) of the ZrN powder sample from JCPDS 35-0753 is 0.427 according to Eq. (1). The biaxial residual stress was determined by the conventional sin2ψ method [8] and Co radiation as X-ray source was used to obtain a higher angle of diffraction angle 2θ to improve the accuracy in stress measurement. The shifts of the (111) and/or (200) peaks positions as a function of the tilt angle together with the elastic modulus, measured by nanoindentation, were used to calculate the residual stress. Field emission scanning electron microscopy (FESEM, LEO-1530, Germany) was used to observe cross-sectional morphologies. A nanoindentation tester (CSM Instrument, Switzerland) was used to determine the coating hardness using Oliver–Pharr techniques [9], which could be executed from the software supplied with the CSM Instrument. Before testing, an area function of Berkovich indenter was calibrated by performing 110 indentations on a standard fused silicon specimen. In order to eliminate the influence of the substrate, the penetration depth was controlled to less than 10% of the film thickness. The average values of the twenty indentations as well as standard deviations for the measurement were obtained. 3. Results and discussion 3.1. Microstructure and residual stress The XRD patterns of nanocrystalline ZrN coatings deposited under different negative biases are shown in Fig. 1. The position and height of dotted lines represent the position and relative intensity of diffraction peaks of ZrN powder sample from JCPDS 35-0753. It is seen that all the crystalline structures of the coatings are cubic NaCl structure and (111) and (200) peaks coexist combined with substrate peaks, (220) and (311) peaks are not obvious. Apparently, the relative intensity of (111) increases with increasing negative bias while the (200) intensity exhibits a reverse trend to the (111) peak. The calculated texture coefficient of (111) slightly decreases with negative bias increasing from
Fig. 1. XRD patterns of nanocrystalline ZrN coatings deposited under different negative biases.
0 V to 50 V and followed by an increase with further increasing in negative bias shown in Table 1, which is a summary of experimental results. Compared with the ZrN powder sample, the XRD patterns reveal that the growth orientation parallel to substrate normal of ZrN coatings changes from (200) to random, and finally (111) orientations, as the negative bias increasing from 0 V to 150 V. This orientation transition can be attributed to the re-nucleation mechanism given by Abadias et al. [10], in which preferred growth direction of (111) is considered to be favored by the high defect density produced by bombardment of the energetic ions. The largely concentrated defects serve as preferable sites for re-nucleation and grain boundary migration. The kinetic energy of bombarding ions increases with improved negative bias, producing more re-nucleation sites and thus more grains grown on the (111) plane. From Fig. 1, it also can be seen that the width of the (111) peak increases with increasing negative bias which may possibly be attributed to two physical effects: finer grain size and increased microstrain. To estimate the grain size, the well-known Scherrer's equation [11] was used by measuring the full width at half maximum (FWHM) of XRD peaks. However, determination of the grain size does not deal with microstrain that can also cause broadening of the diffraction peaks. Therefore, there is a tendency to underestimate the effect of grain size because of ignorance of the microstrain effect, particularly for bombarding deposition that contains higher internal strain. In order to deconvolute these two contributions, the Williamson– Hall method [12] is generally applied, involving measurement of several (hkl) reflections. Unfortunately, for the thin ZrN coatings in present study only (111) and (200) reflections were observed in XRD patterns. Therefore, an alternative single line method [13] was applied to determine grain size and microstrain, using the Voigt function for analysis of the integral breadths of each XRD peak. In such analysis, it is assumed that the Cauchy component of integral breadth is due solely to grain size and the Gaussian contribution arises from microstrain. Table 1 shows the grain size obtained from such single line method, as well as the grain size obtained using the Scherrer's equation for comparison. It can be seen that the grain size obtained with the single line method is consistent with that from FESEM cross-sectional observation under high magnification, as shown in Table 1 and Fig. 2a, b, and c (here the column diameter is defined as apparent grain size of ZrN coatings), while the grain size from Scherrer's analysis is underestimated, especially for those coatings deposited under high energy bombardment. The estimated grain size using this method fits well with transmission electron microscope (TEM) investigation in the case of a nanocrystalline TiN coating [14]. Grain size decreases with increasing negative bias which can also be explained by the above-mentioned re-nucleation mechanism [10]. The elevated generation of defects with increasing
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Table 1 Summary of experimental results of nanocrystalline ZrN coatings. Negative bias [V]
Texture coefficient of (111)
0 50 75 100 125 150
0.096 0.091 0.540 0.852 0.863 0.981
Grain size [nm] Scherrer's equation
Single line method
FESEM observation
43.4 ± 2.7 33.3 ± 4.6 15.0 ± 0.5 11.6 ± 0.6 8.6 ± 0.3 7.4 ± 0.4
45.0 ± 5.0 31.5 ± 3.2 23.3 ± 1.7 19.0 ± 1.3 14.2 ± 1.1 10.0 ± 0.8
42–52 31–38 23–30 19–24 14–17 Equiaxed
Compressive stress [GPa]
Hardness [GPa]
0.50 0.90 3.71 4.24 7.95 13.28
19.74 ± 1.25 22.60 ± 0.22 25.48 ± 0.55 34.11 ± 0.66 31.47 ± 0.50 30.51 ± 0.71
bombarding particle energy proportional to the applied negative bias will lead to an increased number of preferential nucleation sites resulting in finer grains. Similar decrease in grain size with increasing negative bias has been reported in the case of magnetron sputtered TiC coatings [15]. According to Thornton's structure-zone model (SZM) [16], the ZrN coating deposited without negative bias exhibits columnar and very porous structure with open boundaries, corresponding to Zone 1 (cf. Fig. 2a), while that deposited at a negative bias of 75 V displays denser and finer columns with boundaries being sufficiently dense and difficult to resolve, corresponding to Zone T (cf. Fig. 3a). As the negative bias is increased to 125 V, the cross-sectional structure transforms from a columnar structure to a dense, almost equiaxed structure, corresponding to Zone 3 (cf. Fig. 3b). This structural transition follows the revised SZM by Messier et al. [17] taking into account ion bombardment induced structure evolution. Those effects
Fig. 2. FESEM cross-sectional morphologies of nanocrystalline ZrN coatings: (a) deposited without negative bias; (b) deposited at negative bias of 100 V; and (c) deposited at negative bias of 125 V.
Fig. 3. Low magnification of FESEM cross-sectional morphologies of nanocrystalline ZrN coatings: (a) deposited at negative bias of 75 V and (b) deposited at negative bias of 125 V.
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caused by increasing ion bombardment with raised negative bias, namely (1) increasing the nucleation density by forming nucleation sites (defects), (2) increasing the surface mobility of adatoms, and (3) decreasing the formation of interfacial voids, are responsible for structure development and formation of finer and denser columnar structures and finally equiaxed grains [18]. From the XRD patterns, a shift of the diffraction peak to lower angle can be observed in both of the two growth orientations, and correspondingly the residual stress is expected to rise. In present study, residual stress was determined using the sin2ψ method. The lattice spacing with different tilt angle dψ vs. sin2ψ plot of ZrN coatings deposited at 100 V, 125 V and 150 V is shown in Fig. 4. The slopes of linear fitting curve are negative and the absolute values increase with increasing negative bias, which implies that all coatings are in a state of compressive stress and the values are improved with increasing bias. The detailed compressive stress as a function of the substrate negative bias for ZrN coatings is shown in Table 1 where it can be seen that the compressive stress monotonously increases with increasing negative bias from 0.50 GPa at a negative bias of 0 V to a maximum value of 13.28 GPa at 150 V without stress relaxation. The residual stress in PVD coatings can be generated by both intrinsic and thermal sources. Given that all the coatings were obtained under the same preparation temperature of 300 °C, the thermal stress due to the difference in thermal expansion coefficient between coating and substrate can be estimated to be almost the same and negligible in comparison with the intrinsic residual stress, which just varies with the increased bias. Similar results have been reported in the case of magnetron sputtered NbN coatings with substrate bias from 0 V to 200 V [19]. As negative bias increases, the elevated energy of bombardment ions, which is proportional to the negative bias, causes more defects in the as-deposited coatings and equivalently higher degree of lattice distortion, and thus higher compressive stress. 3.2. Hardness and inverse Hall–Petch effect Typical load–displacement data of nanoindentation tests conducted at four different negative biases from 0 V to 150 V are shown in Fig. 5. The curves shift to smaller indentation depths and larger loads with increasing negative bias up to 100 V reflecting a rise in hardness. As the negative bias is raised above 100 V, the curve shifts to smaller load, indicating a drop in hardness. The detailed results of hardness and deviation are shown in Table 1 and it can be found that the hardness of nanocrystalline ZrN coating rapidly increases from 19.74 GPa to 34.11 GPa with increasing substrate negative bias up to 100 V. Beyond this range, the hardness decreases to 30.51 GPa at negative bias of 150 V. In nanoindentation test, the maximum deviation of hardness is 1.25 GPa for ZrN coating deposited without
Fig. 4. The lattice spacing with different tilt angle dψ vs. sin2ψ plot of ZrN coatings deposited at negative biases of 100 V, 125 V and 150 V.
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Fig. 5. Typical load–displacement data of nanoindentation tests conducted at negative biases of 0 V, 50 V, 100 V, and 150 V.
bias, almost 6% of the average value. In practice, there are several factors affecting the accuracy of the results that nanoindentation provides, such as instrument compliance, tip wear or defects, indentation size effect, piling-up and surface roughness [20]. The former two factors are considered to result from the design and manufacture of the instrument. Thus, the area function of indenter has been calibrated before testing. The later three factors are related to material tested itself. For hard coatings coated on hard substrate, piling-up and indentation size effect are negligible [20]. The last factor (surface roughness) is very important in nanoindentation test, since the roughness causes errors in determination of the area of contact between indenter and surface. As penetration depth is made at 20 times the surface roughness, almost 5% deviation of penetration depth is obtained [20]. The average roughness of ZrN coating's surface deposited without bias is ~ 10 nm determined from atomic force microscopy (AFM) while the penetration depth is ~ 110 nm in present study. As a result, the deviation of hardness in this study is probably due to surface roughness. The lower value of hardness in present study is approximately 20 GPa in accordance with that of cathodic vacuum arc deposited ZrN coatings [21], while the peak hardness is much higher. A possible explanation for this discrepancy is finer grains in present sputtered ZrN coatings as compared with cathodic vacuum arc deposited ZrN coatings. The variation of hardness with respect to negative bias could be separated into two distinct regions, region 1 (negative biases ranging from 0 V to 100 V) and region 2 (negative biases from 100 V to 150 V). As is well known, grain size plays a significant role in hardness and other mechanical properties in both bulk materials and coatings following the classical Hall–Petch effect. The hardness of nanocrystalline ZrN is summarized as a function of the inverse square root of grain size from XRD by the single line method in a Hall–Petch plot (Fig. 6). Moreover, as can be seen in region 1, the small grain size causing hardening of the ZrN coatings is in accordance with Hall–Petch effect. The deviation from linearity of the Hall–Petch plot may be attributed to two effects, the measurement deviations of hardness and grain size, and other factors such as density, texture, and compressive stress affecting the hardness of ZrN coatings. These will be discussed in the following sections. In region 2, as the grain size decreases from 19.0 nm to 10.0 nm, the data show a significant decrease in hardness and the Hall–Petch plot becomes negative (i.e. an inverse Hall–Petch effect). Although the inverse Hall–Petch effect is observed in nanocrystalline ZrN coatings, the reality of present inverse Hall–Petch effect needs to be validated, since in several instances an observed inverse Hall–Petch effect may have been due to artifacts in the nanocrystalline bulk materials such as porosity, multiphase, and changes in chemical composition [1]. Thus, the influences of aforementioned factors on hardness need to be considered. First, the atomic ratio of Zr/N slightly
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Fig. 6. Hall–Petch plot of hardness of nanocrystalline ZrN coatings against the inverse square-root of grain size.
increases from 1.0 without bias to 1.1 at negative bias of 150 V, nearly under stiochiometry. Whatever the experimental conditions may be, the atomic content of oxygen is less than 3% due to the oxidation of ZrN coating. The atomic ratio of Zr/N has been calculated by excluding oxygen content. Next, the ZrN coatings exhibit single NaCl structure and no other phase is observed, as shown in Fig. 1. Lastly, for the nanocrystalline bulk materials, porosity is the major explanation of the artifact of the inverse Hall–Petch effect [1]. However, previous studies reported that with increasing negative bias, the density of TiN coatings increased from 4.3 g/cm3 up to 5.6 g/cm3 (the density of TiN bulk materials is 5.3 g/cm3) [22]. In present ZrN nanocrystalline coatings, denser structures with increasing negative bias and equiaxed grains are also observed, as discussed in Section 3.1. This is expected to improve the hardness of the ZrN coating deposited at higher negative bias. It can be concluded that the inverse Hall–Petch effect in this study is unlikely to have been caused by aforesaid three factors. Compared with bulk materials, PVD coatings often have completely different microstructures, e.g. textured structures, much smaller grain size, and a higher compressive stress due to non-equilibrium deposition process. Such typical features will affect the plastic deformation process and thus the coating hardness. Therefore, for PVD coatings, both compressive stress and texture need to be determined and their roles on hardness should be analyzed before conclusions can be drawn for the inverse Hall–Petch effect. For NaCl structure nitride coatings, Schmid factors are 0, 0.25, 0.5 for applied loading on (111), (220), and (200) planes, respectively [23]. As a result, (111) plane is supposed to be harder than other planes owing to its lowest Schmid factor. Based upon the above geometrical strengthening, the hardness of NaCl structure hard coating is expected to increase with increasing texture coefficient of (111). Another major factor influencing hardness is residual stress. This hardening effect is attributed to the high concentration of defects due to ion bombardment effect that are not only responsible for the high compressive stress but also act as an obstacle for dislocations movement and thus improves the hardness [14]. Such a compressive hardening effect was confirmed by previous studies in sputtered NbN and TiC coatings [15,19]. Comparing the trends of texture coefficient of (111), compressive stress, and hardness with negative bias in Fig. 7, it can be seen that these three physical quantities vary in a similar fashion as a function of negative bias up to 100 V in region 1. This behavior implies that, in addition to grain size refinement, structure densification, increasing texture coefficient, and compressive stress may also contribute to the increased hardness at higher negative bias up to 100 V. In present study, ion bombardment induced microstructure evolutions simultaneously containing grain size refinement, structure densification, preferred orientation evolution, and compressive stress state. As a result, it can be difficult to separate the respective influence of these four factors on hardness of the prepared ZrN coatings. However, our
Fig. 7. The variation of hardness, texture coefficient of (111) and compressive stress of nanocrystalline ZrN coatings with respect to negative bias.
research mainly focuses on is not the hardening effect but the softening behavior in nanocrystalline ZrN coatings. According to the above-mentioned geometrical strengthening and compressive stress hardening, both increased texture coefficient of (111) and compressive stress are predicted to result in increasing hardness. However, in region 2 in Fig. 7, it can be seen that the hardness of nanocrystalline ZrN coatings decreases while the texture coefficient of (111) and compressive stress still increase. This indicates that texture coefficient and compressive stress may not be major factors that affect hardness in region 2. Thus, after the foregoing rigorous analysis, it can be concluded that the decreased hardness in nanocrystalline ZrN coatings is merely attributed to grain size softening, and no obvious artifacts (i.e. porosity, multiphase, chemical composition, texture, and compressive stress) are present to induce the inverse Hall–Petch effect. Two popular dislocation models have been proposed to account for the empirical Hall–Petch effect: (a) the stress concentration due to the piling up of dislocations at grain boundaries [24,25] and (b) the increase in internal stress due to the additional dislocation density which results from the presence of grain boundaries [26–28]. Nevertheless, piling up is still widely recognized as the dominating effect [29,30]. Thus, piling up of dislocations at grain boundaries is envisioned as a key physical explanation of Hall–Petch effect here. This type of dislocation mechanism would be valid in case of a large array of dislocations piling up at grain boundaries. However, at still smaller grain sizes (only tens of nanometers), this dislocation mechanism should cease since the dislocation image forces are sufficient to eliminate dislocations by moving them into the grain boundaries and thus few dislocations are observed within grains to support these dislocations piling up [1]. This induces breakdown of Hall–Petch effect. Additionally, we note that geometrical strengthening and compressive stress hardening are both based on a dislocation mechanism. As the grain size reduces to 19.0 nm, the breakdown of geometrical strengthening and compressive stress hardening may confirm a cessation of the dislocation mechanism in ultra-small grains. Further decrease of grain size from 19.0 nm to 10.0 nm results in a decrease of hardness, see Fig. 6. It has been proposed by Weng et al. [31,32] that the volume fraction of grain boundaries increases noticeably as the grain size decreases to tens of nanometers. Consequently, for these ultra small grains the deformation is dominated by elevated grain boundary phase (via grain boundary sliding), while the dislocation mechanism becomes invalid [32]. This would leads to a decrease of hardness and strength, since grain boundary phase is softer than grain due to increased atomic spacing [31]. In the future, the experimental evidence of such inverse Hall–Petch effect for nanocrystalline ZrN coating is required to further extend this investigation using in situ transmission electron microscopy (TEM) observations during nanoindentation test.
Z.B. Qi et al. / Surface & Coatings Technology 205 (2011) 3692–3697 Table 2 The theoretical and experimental results of critical grain sizes in nanocrystalline hard coatings. Coatings
E [GPa]
H [GPa]
b [nm]
ν
Theoretical D [nm]
Experimental D [nm]
ZrN
404 421 367 367 216 325
34.1 31.5 38.3 35.0 30.2 23.2
0.323 0.323 0.292 0.292 0.332 0.332
0.186
15.2 17.1 11.4 12.5 9.4 18.4
14.2–19.0
CrN [14,23] ZrC [27]
0.25 0.19
10.0–16.0 3.5–12.1
3.3. Theoretical calculation of critical grain size In present study, the critical grain size at which the transition between Hall–Petch effect and inverse Hall–Petch effect is observed is between 19.0 nm and 14.2 nm and this is similar to the value of nanocrystalline CrN coatings (between 16 nm and 10 nm) observed by Mayrhofer et al. [14,33]. For the sake of further illustration of the breakdown of Hall–Petch effect and related critical grain size, we propose a concise model quantitatively to compute the critical grain size. A previous study [34] has pointed out that, for ultra small grains, the dislocation mechanism should cease when there were only two dislocations in the piling up, which results in the breakdown of Hall– Petch effect. Based on above assumption, the critical grain size D can be calculated theoretically using a modified Eshelby's equation for the number of dislocations in a piling up [24]: 2nGb D= Kπτ
ð2Þ
where G is shear modulus, for isotropic materials G = E/2(1 + pffiffiν), where E is elastic modulus, b is magnitude of Burgers vector (b = 22 a, a is lattice parameter), K is a constant factor equal to (1 − ν) for an edge dislocation, ν is Poisson's ratio, n is the number of dislocations in a pile-up (here assumed to be 2), τ is critical shear stress. Invoking the Tresca shear stress criterion, plastic deformation occurs at τ = 0. 5Yand Y is yield stress equal to one third of the hardness H under plastic constraint [35]. For comparison, the critical grain sizes of our ZrN, Mayrhofer's CrN [14,33] and Chen's ZrC [36] nanocrystalline coatings are all calculated and their details are shown in Table 2. As discussed above, the critical grain size obtained from the Hall– Petch plot is not an accurate value but a value range. Correspondingly, the theoretical calculation also gives this value range to the critical grain size. From Table 2, it can be seen that the theoretical critical grain sizes of ZrN and CrN are in good agreement with experimental values using the dislocation piling-up model whereas the theoretical value for ZrC is a little higher than the experimental one. A possible explanation is that in Chen's study [36], grain size was calculated using Scherrer's equation [11] neglecting the contribution of microstrain and thus the values were underestimated, as discussed in Section 3.1. Although the theoretical model does not deal with any detailed deformation mechanism without the presence of dislocations, it seems to be applicable in roughly estimating the critical grain size of nitride and carbide hard coatings. After determination of critical grain size, from the standpoint of material design, a possible strategy for hard coatings to reach maximum hardness is to deposit coatings with a grain size close to the critical value. 4. Conclusion Nanocrystalline ZrN coatings with different microstructures have been deposited using magnetron sputtering by varying the negative bias.
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Nanoindentation tests reveal that the hardness of nanocrystalline ZrN coating increases with increasing negative bias up to 100 V, while further increase in negative bias results in softening behavior. The increased hardness with increasing negative bias from 0 V to 100 V is attributed to the comprehensive effects of grain size refinement, structure densification, preferred orientation evolution, and compressive stress state. As the negative bias increases from 100 V to 150 V, an inverse Hall–Petch effect is observed. The reality of the inverse Hall–Petch effect is validated by serially excluding other possible effects on hardness of nanocrystalline ZrN coatings, such as porosity, multiphase, chemical composition, texture, and residual stress. Additionally, a theoretical model based on the piling up of dislocations is proposed as a basis for calculating the critical grain size. The accuracy of this model is validated by comparing the theoretical values with experimental ones for nanocrystalline ZrN coatings and other nitride and carbide hard coatings.
Acknowledgements The authors thank for the financial support from the National Key Technology R&D Program of China (2007BAE05B04). The authors also thank Prof. G. M. Blackburn from the University of Sheffield, UK for reading the manuscript.
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Surface & Coatings Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / s u r f c o a t
The inverse Hall–Petch effect in nanocrystalline ZrN coatings Z.B. Qi a, P. Sun a, F.P. Zhu a, Z.C. Wang a,⁎, D.L. Peng b, C.H. Wu c a b c
College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, China College of Materials, Xiamen University, Xiamen, China China National R&D Center for Tungsten Technology, Xiamen, China
a r t i c l e
i n f o
Article history: Received 7 October 2010 Accepted in revised form 11 January 2011 Available online 15 January 2011 Keywords: Nanocrystalline Coating Microstructure Hardness Inverse Hall–Petch effect
a b s t r a c t For the purpose of studying the inverse Hall–Petch effect in nanocrystalline hard coatings, nanocrystalline ZrN coatings have been fabricated using magnetron sputtering with grain sizes ranging from 45 nm to 10 nm by varying negative biases from 0 V to 150 V. The transition from the classical Hall–Petch effect to an inverse Hall–Petch effect in nanocrystalline ZrN coatings is observed at a grain size between 19.0 nm and 14.2 nm. The reality of the inverse Hall–Petch effect in the present study is validated by exclusion of other possible effects on hardness of nanocrystalline ZrN coatings, such as porosity, multiphase, chemical composition, texture, and residual stress. Furthermore, a concise model based on lattice dislocations piling up mechanism is proposed to illustrate the breakdown of the Hall–Petch effect and calculate the critical grain size. The predictions of the model fit well with experimental data in some nitride and carbide nanocrystalline coatings. Both experimental and theoretical results indicate that the inverse Hall–Petch effect is an essential property of nanocrystalline hard coatings as similar to nanocrystalline metals and alloys. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The effect of grain size on the hardness (e.g. yield strength) of solids ranging from millimeters to nanometers is both of scientific and of technologic interest. For conventional materials, the classical Hall–Petch equation predicts that: H = H0 + kd−1/2, where H is hardness, Ho is grain-body hardness, k is positive constant, and d is the grain size. If such an empirical plot is extrapolated to the grain size of about 10 nm, extremely high hardness is expected. However, to data, as the grain size is down to only tens of nanometers (defined as critical grain size), a novel behavior is observed with an actual negative k (the slope of Hall–Petch plot) in nanocrystalline metals and alloys, namely the inverse Hall–Petch effect [1–5]. It is worthy to note that previous research aimed at understanding the inverse Hall–Petch effect has constituted a main focus on the nanocrystalline metals for bulk materials and coatings. Challenging experimental and theoretical studies concerning this effect in nanocrystalline PVD coatings have not received much attention, in particular nitride and carbide hard coatings, of which high hardness and mechanical strength are considered as the primary requirements. To work on the inverse Hall–Petch effect in nanocrystalline hard coatings with clarity and in detail, the two problems need to be resolved. First, is the inverse Hall–Petch effect also an intrinsic property in nanocrystalline hard coatings and what is the critical grain size in such coatings? In case the inverse Hall–Petch effect is observed, it is also necessary to determine whether this effect is fact or artifact. Secondly,
what is novel deformation mechanism responsible for this grain size softening in nanocrystalline coatings? Previously, Wang et al. [6] used laser physical vapor deposition to fabricate nanocrystalline TiN coatings with grain sizes ranging from 55 nm to 8 nm by varying substrate temperature from 25 °C to 600 °C and reported that the coating hardness decreased with decreasing grain size, namely an inverse Hall–Petch effect. However, no transition between Hall–Petch effect and inverse Hall–Petch effect was observed in this grain size range. Thus there were still some questions as to whether the inverse Hall–Petch effect is a true grain size softening effect. In the above study, only dependence of grain size on hardness was investigated, other factors contributing to the observed softening behavior were ignored. Conrad et al. [7] have pointed out that texture and imperfections may possibly account for the observed inverse Hall–Petch effect of nanocrystalline TiN coatings, rather than grain size. In this work, in order to explore the inverse Hall–Petch effect in nanocrystalline hard coatings, typical ZrN hard coatings were deposited using magnetron sputtering with grain sizes ranging from 45 nm to 10 nm by adjusting the substrate negative bias. A transition between the Hall–Petch effect and the inverse Hall–Petch effect is observed in this study. For the purpose of establishing whether the inverse Hall–Petch effect is a reality, other factors that may possibly influence hardness are analyzed in detail. 2. Experimental details 2.1. Preparation of nanocrystalline ZrN coatings
⁎ Corresponding author. Tel./fax: + 86 592 2180738. E-mail address: [email protected] (Z.C. Wang). 0257-8972/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2011.01.021
A series of nanocrystalline ZrN coatings were deposited on mirror-like polished cemented carbide and silicon (111) wafers using a DC
Z.B. Qi et al. / Surface & Coatings Technology 205 (2011) 3692–3697
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magnetron sputtering technique. Before the coating process, all substrates were ultrasonically cleaned for 10 min, each successively in baths of acetone and alcohol, and blown dried. For cleaning the target surface, 30 min of pre-sputtering in pure argon (99.999% in purity) atmosphere was carried out with sputtering power 200 W and gas pressure 1.0 Pa. The deposition was carried out in an Ar and N2 atmosphere of 99.999% purity. The base pressure was 8.0 ×10−4 Pa and deposition gas pressure was kept constant at 0.5 Pa. The DC power was adjusted to 250 W applied at the zirconium target (99.99% in purity) during deposition. ZrN coatings were deposited with temperature and nitrogen flow ratio N2/(N2 +Ar) fixed at 300 °C and 20% respectively. Substrate negative bias was chosen as the controlling parameter varying from 0 V to 150 V to generate nanocrystalline ZrN coatings with different grain sizes. 2.2. Characterization The coating thickness was measured by a Dektak3 profilometer (VEECO, U.S.) and the thickness of ZrN coatings was kept constant at 1.1 ± 0.1 μm with a deposition time of 90 min. All samples were analyzed by electron probe microanalysis (EPMA, JXA-8100, Japan) for determining their composition. The crystal structure of ZrN coatings was investigated by Panalytical X'pert PRO MPD X-ray diffraction (XRD, Philips, Netherlands) using Cu Kα radiation as X-ray source and θ–2θ diffraction mode. The texture coefficient of (111) plane was calculated using the following equation: Texture coefficient of ð111Þ =
Ið111Þ Ið111Þ + Ið200Þ + Ið220Þ + Ið311Þ
ð1Þ
where I(111), I(200), I(220), I(311) are integrated intensities of the corresponding peaks (111), (200), (220) and (311). The texture coefficient of (111) of the ZrN powder sample from JCPDS 35-0753 is 0.427 according to Eq. (1). The biaxial residual stress was determined by the conventional sin2ψ method [8] and Co radiation as X-ray source was used to obtain a higher angle of diffraction angle 2θ to improve the accuracy in stress measurement. The shifts of the (111) and/or (200) peaks positions as a function of the tilt angle together with the elastic modulus, measured by nanoindentation, were used to calculate the residual stress. Field emission scanning electron microscopy (FESEM, LEO-1530, Germany) was used to observe cross-sectional morphologies. A nanoindentation tester (CSM Instrument, Switzerland) was used to determine the coating hardness using Oliver–Pharr techniques [9], which could be executed from the software supplied with the CSM Instrument. Before testing, an area function of Berkovich indenter was calibrated by performing 110 indentations on a standard fused silicon specimen. In order to eliminate the influence of the substrate, the penetration depth was controlled to less than 10% of the film thickness. The average values of the twenty indentations as well as standard deviations for the measurement were obtained. 3. Results and discussion 3.1. Microstructure and residual stress The XRD patterns of nanocrystalline ZrN coatings deposited under different negative biases are shown in Fig. 1. The position and height of dotted lines represent the position and relative intensity of diffraction peaks of ZrN powder sample from JCPDS 35-0753. It is seen that all the crystalline structures of the coatings are cubic NaCl structure and (111) and (200) peaks coexist combined with substrate peaks, (220) and (311) peaks are not obvious. Apparently, the relative intensity of (111) increases with increasing negative bias while the (200) intensity exhibits a reverse trend to the (111) peak. The calculated texture coefficient of (111) slightly decreases with negative bias increasing from
Fig. 1. XRD patterns of nanocrystalline ZrN coatings deposited under different negative biases.
0 V to 50 V and followed by an increase with further increasing in negative bias shown in Table 1, which is a summary of experimental results. Compared with the ZrN powder sample, the XRD patterns reveal that the growth orientation parallel to substrate normal of ZrN coatings changes from (200) to random, and finally (111) orientations, as the negative bias increasing from 0 V to 150 V. This orientation transition can be attributed to the re-nucleation mechanism given by Abadias et al. [10], in which preferred growth direction of (111) is considered to be favored by the high defect density produced by bombardment of the energetic ions. The largely concentrated defects serve as preferable sites for re-nucleation and grain boundary migration. The kinetic energy of bombarding ions increases with improved negative bias, producing more re-nucleation sites and thus more grains grown on the (111) plane. From Fig. 1, it also can be seen that the width of the (111) peak increases with increasing negative bias which may possibly be attributed to two physical effects: finer grain size and increased microstrain. To estimate the grain size, the well-known Scherrer's equation [11] was used by measuring the full width at half maximum (FWHM) of XRD peaks. However, determination of the grain size does not deal with microstrain that can also cause broadening of the diffraction peaks. Therefore, there is a tendency to underestimate the effect of grain size because of ignorance of the microstrain effect, particularly for bombarding deposition that contains higher internal strain. In order to deconvolute these two contributions, the Williamson– Hall method [12] is generally applied, involving measurement of several (hkl) reflections. Unfortunately, for the thin ZrN coatings in present study only (111) and (200) reflections were observed in XRD patterns. Therefore, an alternative single line method [13] was applied to determine grain size and microstrain, using the Voigt function for analysis of the integral breadths of each XRD peak. In such analysis, it is assumed that the Cauchy component of integral breadth is due solely to grain size and the Gaussian contribution arises from microstrain. Table 1 shows the grain size obtained from such single line method, as well as the grain size obtained using the Scherrer's equation for comparison. It can be seen that the grain size obtained with the single line method is consistent with that from FESEM cross-sectional observation under high magnification, as shown in Table 1 and Fig. 2a, b, and c (here the column diameter is defined as apparent grain size of ZrN coatings), while the grain size from Scherrer's analysis is underestimated, especially for those coatings deposited under high energy bombardment. The estimated grain size using this method fits well with transmission electron microscope (TEM) investigation in the case of a nanocrystalline TiN coating [14]. Grain size decreases with increasing negative bias which can also be explained by the above-mentioned re-nucleation mechanism [10]. The elevated generation of defects with increasing
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Table 1 Summary of experimental results of nanocrystalline ZrN coatings. Negative bias [V]
Texture coefficient of (111)
0 50 75 100 125 150
0.096 0.091 0.540 0.852 0.863 0.981
Grain size [nm] Scherrer's equation
Single line method
FESEM observation
43.4 ± 2.7 33.3 ± 4.6 15.0 ± 0.5 11.6 ± 0.6 8.6 ± 0.3 7.4 ± 0.4
45.0 ± 5.0 31.5 ± 3.2 23.3 ± 1.7 19.0 ± 1.3 14.2 ± 1.1 10.0 ± 0.8
42–52 31–38 23–30 19–24 14–17 Equiaxed
Compressive stress [GPa]
Hardness [GPa]
0.50 0.90 3.71 4.24 7.95 13.28
19.74 ± 1.25 22.60 ± 0.22 25.48 ± 0.55 34.11 ± 0.66 31.47 ± 0.50 30.51 ± 0.71
bombarding particle energy proportional to the applied negative bias will lead to an increased number of preferential nucleation sites resulting in finer grains. Similar decrease in grain size with increasing negative bias has been reported in the case of magnetron sputtered TiC coatings [15]. According to Thornton's structure-zone model (SZM) [16], the ZrN coating deposited without negative bias exhibits columnar and very porous structure with open boundaries, corresponding to Zone 1 (cf. Fig. 2a), while that deposited at a negative bias of 75 V displays denser and finer columns with boundaries being sufficiently dense and difficult to resolve, corresponding to Zone T (cf. Fig. 3a). As the negative bias is increased to 125 V, the cross-sectional structure transforms from a columnar structure to a dense, almost equiaxed structure, corresponding to Zone 3 (cf. Fig. 3b). This structural transition follows the revised SZM by Messier et al. [17] taking into account ion bombardment induced structure evolution. Those effects
Fig. 2. FESEM cross-sectional morphologies of nanocrystalline ZrN coatings: (a) deposited without negative bias; (b) deposited at negative bias of 100 V; and (c) deposited at negative bias of 125 V.
Fig. 3. Low magnification of FESEM cross-sectional morphologies of nanocrystalline ZrN coatings: (a) deposited at negative bias of 75 V and (b) deposited at negative bias of 125 V.
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caused by increasing ion bombardment with raised negative bias, namely (1) increasing the nucleation density by forming nucleation sites (defects), (2) increasing the surface mobility of adatoms, and (3) decreasing the formation of interfacial voids, are responsible for structure development and formation of finer and denser columnar structures and finally equiaxed grains [18]. From the XRD patterns, a shift of the diffraction peak to lower angle can be observed in both of the two growth orientations, and correspondingly the residual stress is expected to rise. In present study, residual stress was determined using the sin2ψ method. The lattice spacing with different tilt angle dψ vs. sin2ψ plot of ZrN coatings deposited at 100 V, 125 V and 150 V is shown in Fig. 4. The slopes of linear fitting curve are negative and the absolute values increase with increasing negative bias, which implies that all coatings are in a state of compressive stress and the values are improved with increasing bias. The detailed compressive stress as a function of the substrate negative bias for ZrN coatings is shown in Table 1 where it can be seen that the compressive stress monotonously increases with increasing negative bias from 0.50 GPa at a negative bias of 0 V to a maximum value of 13.28 GPa at 150 V without stress relaxation. The residual stress in PVD coatings can be generated by both intrinsic and thermal sources. Given that all the coatings were obtained under the same preparation temperature of 300 °C, the thermal stress due to the difference in thermal expansion coefficient between coating and substrate can be estimated to be almost the same and negligible in comparison with the intrinsic residual stress, which just varies with the increased bias. Similar results have been reported in the case of magnetron sputtered NbN coatings with substrate bias from 0 V to 200 V [19]. As negative bias increases, the elevated energy of bombardment ions, which is proportional to the negative bias, causes more defects in the as-deposited coatings and equivalently higher degree of lattice distortion, and thus higher compressive stress. 3.2. Hardness and inverse Hall–Petch effect Typical load–displacement data of nanoindentation tests conducted at four different negative biases from 0 V to 150 V are shown in Fig. 5. The curves shift to smaller indentation depths and larger loads with increasing negative bias up to 100 V reflecting a rise in hardness. As the negative bias is raised above 100 V, the curve shifts to smaller load, indicating a drop in hardness. The detailed results of hardness and deviation are shown in Table 1 and it can be found that the hardness of nanocrystalline ZrN coating rapidly increases from 19.74 GPa to 34.11 GPa with increasing substrate negative bias up to 100 V. Beyond this range, the hardness decreases to 30.51 GPa at negative bias of 150 V. In nanoindentation test, the maximum deviation of hardness is 1.25 GPa for ZrN coating deposited without
Fig. 4. The lattice spacing with different tilt angle dψ vs. sin2ψ plot of ZrN coatings deposited at negative biases of 100 V, 125 V and 150 V.
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Fig. 5. Typical load–displacement data of nanoindentation tests conducted at negative biases of 0 V, 50 V, 100 V, and 150 V.
bias, almost 6% of the average value. In practice, there are several factors affecting the accuracy of the results that nanoindentation provides, such as instrument compliance, tip wear or defects, indentation size effect, piling-up and surface roughness [20]. The former two factors are considered to result from the design and manufacture of the instrument. Thus, the area function of indenter has been calibrated before testing. The later three factors are related to material tested itself. For hard coatings coated on hard substrate, piling-up and indentation size effect are negligible [20]. The last factor (surface roughness) is very important in nanoindentation test, since the roughness causes errors in determination of the area of contact between indenter and surface. As penetration depth is made at 20 times the surface roughness, almost 5% deviation of penetration depth is obtained [20]. The average roughness of ZrN coating's surface deposited without bias is ~ 10 nm determined from atomic force microscopy (AFM) while the penetration depth is ~ 110 nm in present study. As a result, the deviation of hardness in this study is probably due to surface roughness. The lower value of hardness in present study is approximately 20 GPa in accordance with that of cathodic vacuum arc deposited ZrN coatings [21], while the peak hardness is much higher. A possible explanation for this discrepancy is finer grains in present sputtered ZrN coatings as compared with cathodic vacuum arc deposited ZrN coatings. The variation of hardness with respect to negative bias could be separated into two distinct regions, region 1 (negative biases ranging from 0 V to 100 V) and region 2 (negative biases from 100 V to 150 V). As is well known, grain size plays a significant role in hardness and other mechanical properties in both bulk materials and coatings following the classical Hall–Petch effect. The hardness of nanocrystalline ZrN is summarized as a function of the inverse square root of grain size from XRD by the single line method in a Hall–Petch plot (Fig. 6). Moreover, as can be seen in region 1, the small grain size causing hardening of the ZrN coatings is in accordance with Hall–Petch effect. The deviation from linearity of the Hall–Petch plot may be attributed to two effects, the measurement deviations of hardness and grain size, and other factors such as density, texture, and compressive stress affecting the hardness of ZrN coatings. These will be discussed in the following sections. In region 2, as the grain size decreases from 19.0 nm to 10.0 nm, the data show a significant decrease in hardness and the Hall–Petch plot becomes negative (i.e. an inverse Hall–Petch effect). Although the inverse Hall–Petch effect is observed in nanocrystalline ZrN coatings, the reality of present inverse Hall–Petch effect needs to be validated, since in several instances an observed inverse Hall–Petch effect may have been due to artifacts in the nanocrystalline bulk materials such as porosity, multiphase, and changes in chemical composition [1]. Thus, the influences of aforementioned factors on hardness need to be considered. First, the atomic ratio of Zr/N slightly
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Fig. 6. Hall–Petch plot of hardness of nanocrystalline ZrN coatings against the inverse square-root of grain size.
increases from 1.0 without bias to 1.1 at negative bias of 150 V, nearly under stiochiometry. Whatever the experimental conditions may be, the atomic content of oxygen is less than 3% due to the oxidation of ZrN coating. The atomic ratio of Zr/N has been calculated by excluding oxygen content. Next, the ZrN coatings exhibit single NaCl structure and no other phase is observed, as shown in Fig. 1. Lastly, for the nanocrystalline bulk materials, porosity is the major explanation of the artifact of the inverse Hall–Petch effect [1]. However, previous studies reported that with increasing negative bias, the density of TiN coatings increased from 4.3 g/cm3 up to 5.6 g/cm3 (the density of TiN bulk materials is 5.3 g/cm3) [22]. In present ZrN nanocrystalline coatings, denser structures with increasing negative bias and equiaxed grains are also observed, as discussed in Section 3.1. This is expected to improve the hardness of the ZrN coating deposited at higher negative bias. It can be concluded that the inverse Hall–Petch effect in this study is unlikely to have been caused by aforesaid three factors. Compared with bulk materials, PVD coatings often have completely different microstructures, e.g. textured structures, much smaller grain size, and a higher compressive stress due to non-equilibrium deposition process. Such typical features will affect the plastic deformation process and thus the coating hardness. Therefore, for PVD coatings, both compressive stress and texture need to be determined and their roles on hardness should be analyzed before conclusions can be drawn for the inverse Hall–Petch effect. For NaCl structure nitride coatings, Schmid factors are 0, 0.25, 0.5 for applied loading on (111), (220), and (200) planes, respectively [23]. As a result, (111) plane is supposed to be harder than other planes owing to its lowest Schmid factor. Based upon the above geometrical strengthening, the hardness of NaCl structure hard coating is expected to increase with increasing texture coefficient of (111). Another major factor influencing hardness is residual stress. This hardening effect is attributed to the high concentration of defects due to ion bombardment effect that are not only responsible for the high compressive stress but also act as an obstacle for dislocations movement and thus improves the hardness [14]. Such a compressive hardening effect was confirmed by previous studies in sputtered NbN and TiC coatings [15,19]. Comparing the trends of texture coefficient of (111), compressive stress, and hardness with negative bias in Fig. 7, it can be seen that these three physical quantities vary in a similar fashion as a function of negative bias up to 100 V in region 1. This behavior implies that, in addition to grain size refinement, structure densification, increasing texture coefficient, and compressive stress may also contribute to the increased hardness at higher negative bias up to 100 V. In present study, ion bombardment induced microstructure evolutions simultaneously containing grain size refinement, structure densification, preferred orientation evolution, and compressive stress state. As a result, it can be difficult to separate the respective influence of these four factors on hardness of the prepared ZrN coatings. However, our
Fig. 7. The variation of hardness, texture coefficient of (111) and compressive stress of nanocrystalline ZrN coatings with respect to negative bias.
research mainly focuses on is not the hardening effect but the softening behavior in nanocrystalline ZrN coatings. According to the above-mentioned geometrical strengthening and compressive stress hardening, both increased texture coefficient of (111) and compressive stress are predicted to result in increasing hardness. However, in region 2 in Fig. 7, it can be seen that the hardness of nanocrystalline ZrN coatings decreases while the texture coefficient of (111) and compressive stress still increase. This indicates that texture coefficient and compressive stress may not be major factors that affect hardness in region 2. Thus, after the foregoing rigorous analysis, it can be concluded that the decreased hardness in nanocrystalline ZrN coatings is merely attributed to grain size softening, and no obvious artifacts (i.e. porosity, multiphase, chemical composition, texture, and compressive stress) are present to induce the inverse Hall–Petch effect. Two popular dislocation models have been proposed to account for the empirical Hall–Petch effect: (a) the stress concentration due to the piling up of dislocations at grain boundaries [24,25] and (b) the increase in internal stress due to the additional dislocation density which results from the presence of grain boundaries [26–28]. Nevertheless, piling up is still widely recognized as the dominating effect [29,30]. Thus, piling up of dislocations at grain boundaries is envisioned as a key physical explanation of Hall–Petch effect here. This type of dislocation mechanism would be valid in case of a large array of dislocations piling up at grain boundaries. However, at still smaller grain sizes (only tens of nanometers), this dislocation mechanism should cease since the dislocation image forces are sufficient to eliminate dislocations by moving them into the grain boundaries and thus few dislocations are observed within grains to support these dislocations piling up [1]. This induces breakdown of Hall–Petch effect. Additionally, we note that geometrical strengthening and compressive stress hardening are both based on a dislocation mechanism. As the grain size reduces to 19.0 nm, the breakdown of geometrical strengthening and compressive stress hardening may confirm a cessation of the dislocation mechanism in ultra-small grains. Further decrease of grain size from 19.0 nm to 10.0 nm results in a decrease of hardness, see Fig. 6. It has been proposed by Weng et al. [31,32] that the volume fraction of grain boundaries increases noticeably as the grain size decreases to tens of nanometers. Consequently, for these ultra small grains the deformation is dominated by elevated grain boundary phase (via grain boundary sliding), while the dislocation mechanism becomes invalid [32]. This would leads to a decrease of hardness and strength, since grain boundary phase is softer than grain due to increased atomic spacing [31]. In the future, the experimental evidence of such inverse Hall–Petch effect for nanocrystalline ZrN coating is required to further extend this investigation using in situ transmission electron microscopy (TEM) observations during nanoindentation test.
Z.B. Qi et al. / Surface & Coatings Technology 205 (2011) 3692–3697 Table 2 The theoretical and experimental results of critical grain sizes in nanocrystalline hard coatings. Coatings
E [GPa]
H [GPa]
b [nm]
ν
Theoretical D [nm]
Experimental D [nm]
ZrN
404 421 367 367 216 325
34.1 31.5 38.3 35.0 30.2 23.2
0.323 0.323 0.292 0.292 0.332 0.332
0.186
15.2 17.1 11.4 12.5 9.4 18.4
14.2–19.0
CrN [14,23] ZrC [27]
0.25 0.19
10.0–16.0 3.5–12.1
3.3. Theoretical calculation of critical grain size In present study, the critical grain size at which the transition between Hall–Petch effect and inverse Hall–Petch effect is observed is between 19.0 nm and 14.2 nm and this is similar to the value of nanocrystalline CrN coatings (between 16 nm and 10 nm) observed by Mayrhofer et al. [14,33]. For the sake of further illustration of the breakdown of Hall–Petch effect and related critical grain size, we propose a concise model quantitatively to compute the critical grain size. A previous study [34] has pointed out that, for ultra small grains, the dislocation mechanism should cease when there were only two dislocations in the piling up, which results in the breakdown of Hall– Petch effect. Based on above assumption, the critical grain size D can be calculated theoretically using a modified Eshelby's equation for the number of dislocations in a piling up [24]: 2nGb D= Kπτ
ð2Þ
where G is shear modulus, for isotropic materials G = E/2(1 + pffiffiν), where E is elastic modulus, b is magnitude of Burgers vector (b = 22 a, a is lattice parameter), K is a constant factor equal to (1 − ν) for an edge dislocation, ν is Poisson's ratio, n is the number of dislocations in a pile-up (here assumed to be 2), τ is critical shear stress. Invoking the Tresca shear stress criterion, plastic deformation occurs at τ = 0. 5Yand Y is yield stress equal to one third of the hardness H under plastic constraint [35]. For comparison, the critical grain sizes of our ZrN, Mayrhofer's CrN [14,33] and Chen's ZrC [36] nanocrystalline coatings are all calculated and their details are shown in Table 2. As discussed above, the critical grain size obtained from the Hall– Petch plot is not an accurate value but a value range. Correspondingly, the theoretical calculation also gives this value range to the critical grain size. From Table 2, it can be seen that the theoretical critical grain sizes of ZrN and CrN are in good agreement with experimental values using the dislocation piling-up model whereas the theoretical value for ZrC is a little higher than the experimental one. A possible explanation is that in Chen's study [36], grain size was calculated using Scherrer's equation [11] neglecting the contribution of microstrain and thus the values were underestimated, as discussed in Section 3.1. Although the theoretical model does not deal with any detailed deformation mechanism without the presence of dislocations, it seems to be applicable in roughly estimating the critical grain size of nitride and carbide hard coatings. After determination of critical grain size, from the standpoint of material design, a possible strategy for hard coatings to reach maximum hardness is to deposit coatings with a grain size close to the critical value. 4. Conclusion Nanocrystalline ZrN coatings with different microstructures have been deposited using magnetron sputtering by varying the negative bias.
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Nanoindentation tests reveal that the hardness of nanocrystalline ZrN coating increases with increasing negative bias up to 100 V, while further increase in negative bias results in softening behavior. The increased hardness with increasing negative bias from 0 V to 100 V is attributed to the comprehensive effects of grain size refinement, structure densification, preferred orientation evolution, and compressive stress state. As the negative bias increases from 100 V to 150 V, an inverse Hall–Petch effect is observed. The reality of the inverse Hall–Petch effect is validated by serially excluding other possible effects on hardness of nanocrystalline ZrN coatings, such as porosity, multiphase, chemical composition, texture, and residual stress. Additionally, a theoretical model based on the piling up of dislocations is proposed as a basis for calculating the critical grain size. The accuracy of this model is validated by comparing the theoretical values with experimental ones for nanocrystalline ZrN coatings and other nitride and carbide hard coatings.
Acknowledgements The authors thank for the financial support from the National Key Technology R&D Program of China (2007BAE05B04). The authors also thank Prof. G. M. Blackburn from the University of Sheffield, UK for reading the manuscript.
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